The numbers in order from smallest to in largest are 65.6, 66.6. and 67.6 respectively
What are algebraic expression?Algebraic expression are expressions comprising of terms, variables, coefficients, constants and factors.
These algebraic expressions are also composed of arithmetic operation, such as;
DivisionSubtractionAdditionMultiplicationFloor divisionBracketParenthesesFrom the information given as;
x+1 + 2x + 4 + 2x + 6 = 334
collect like terms
x + 2x + 2x = 334 - 11
add or subtract like terms
5x = 323
Make 'x' the subject of formula
x = 64. 6
The numbers are;
x + 1 = 65.6
x+ 2 = 66. 6
x + 3 = 67. 6
Hence, the numbers are 65.6, 66.6. and 67.6
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Question 6
Find the area of triangle ABC:
AD is 1cm and BC is 1cm and D is 90
The area of triangle ABC is 0.5cm² where base and height are given.
Describe Area.Triangle area is used to measure the size of a region on a surface. The area of a form or planar lamina is referred to as the plane region or plane area, as opposed to surface area, which denotes the area of an open surface or the boundary of a three-dimensional object.
The area of a triangle can be compared to the volume of material at a specific thickness needed to make a model of the form or the amount of paint needed to cover a surface in a single coat. It is equivalent to a solid's volume or a curve's length in two dimensions (a three-dimensional concept).
From the given figure, we can say that
Height = AD = 1cm
Base = BC = 1cm
Area of Triangle = Base × Height/2
Area = 1 × 1 /2
Area = 0.5 cm²
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Suppose your MP3 player contains 100 songs. 10 of those songs ae by your favorite group (say U2). Suppose the shuffle feature is used to play the songs in random order: What is the probability that the first U2 song heard is the Sth song played? What is the probability that one of the first five songs played is U2 song?
The probability that the first MP3 song heard is the fifth song played is:
[tex]\frac{C^9^0_4.C^1^0_1}{C^1^0^0_5}[/tex] = [tex]\frac{2,555,190. 10}{75,287,520}[/tex] ≈ 0.3394
The probability that there are exactly two MP3 songs in the first five songs played is:
[tex]\frac{C^1^0_2.C^9^0_3}{C^1^0^0_5}[/tex] [tex]= \frac{45.117,480}{75,287,520}[/tex] ≈ 0.0702
Now, According to the question:
The 1st MP3 player songs heard is the 5th song played means that first 4 songs are not MP3 songs (there are 100 - 10 = 90 such songs) and the 5th song is MP3 song (there are 10 such songs). Hence, the probability that the first MP3 song heard is the fifth song played is:
[tex]\frac{C^9^0_4.C^1^0_1}{C^1^0^0_5}[/tex] = [tex]\frac{2,555,190. 10}{75,287,520}[/tex] ≈ 0.3394
There are exactly two MP3 songs in the first five songs played means there are 2 MP3 songs and 3 not MP3 songs (the number when these songs are played do not matter). Hence, the probability that there are exactly two MP3 songs in the first five songs played is:
[tex]\frac{C^1^0_2.C^9^0_3}{C^1^0^0_5}[/tex] [tex]= \frac{45.117,480}{75,287,520}[/tex] ≈ 0.0702
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Which of the following statements is true about the first quartile (Q1) value of a box and whisker plot?
Group of answer choices
One-quarter of the data lies below Q1 and three-quarters of the data lies above Q1.
Q1 means the same as Q3.
Half of the data lies below Q1 and half of the data lies above Q1.
Three-quarters of the data lies below Q1 and one-quarter of the data lies above Q1.
The correct option regarding the first quartile of a data-set is given as follows:
One-quarter of the data lies below Q1 and three-quarters of the data lies above Q1.
What is the first quartile of a data-set?The first quartile Q1 of a data-set is the 25th percentile, meaning that:
25% of the data lies below Q1.100 - 25 = 75% of the data lies above Q1.This means that the correct option is given by the first option.
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In how may years ₹ 4,000 will amount to ₹ 14,400 at 10% p.a. Compounded interest payable quarterly ?
Answer:
P = ₹4,000
F = ₹14,400
r = 10% = 0.10
m = 4 (because interest is compounded quarterly)
So, we can plug in these values into the formula:
n = (log(14400 / 4000)) / (log(1 + 0.10 / 4))
n = (log(3.6)) / (log(1.025))
n = 2.59
Therefore, it will take approximately 2.59 years for the investment of ₹4,000 to grow to ₹14,400 at a 10% annual interest rate compounded quarterly.
FILL IN THE BLANK when calculating the confidence interval for the mean using a sample size of 30 or greater with a known population standard deviation, the ____ is used
The standard normal distribution is used when calculating the confidence interval for the mean using a sample size of 30 or greater with a known population standard deviation.
The Z-distribution (also known as the standard normal distribution) is a normal distribution with a mean of 0 and a standard deviation of 1. When the population standard deviation is known, the sample mean follows a normal distribution and the standard error is given by the population standard deviation divided by the square root of the sample size. So, the Z-score is given by (x - μ) / (σ / √(n)) where x is the sample mean, μ is the population mean and σ is the population standard deviation and n is the sample size.
With a sample size of 30 or greater, the central limit theorem states that the sample mean will be approximately normally distributed, regardless of the shape of the population distribution. So, a Z-score can be used to find the probability that a sample mean falls within a certain range of the population mean, which is commonly used to construct a confidence interval.
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Please, very important for me, I’ll give brainliest if you want
The quartic function y = 0.5 · x⁴ - x³ - 15.5 · x² + 30 · x + 21 contains roots 4 - √2 and - 3 + √6 and intercept - 21.
How to derive a quartic function
Quartic functions are polynomials of grade 4, whose factor form is introduced below:
y = a · (x - r₁) · (x - r₂) · (x - r₃) · (x - r₄)
Where:
a - Lead coefficientr₁, r₂, r₃, r₄ - RootsAccording to statement, the quartic equation has an intercept of - 21 and two real roots: 4 - √2, - 3 + √6. The two remaining roots can be found based on features exhibited by quadratic formula and that quartic functions are the product of two quadratic functions: 4 + √2, - 3 - √6
Now we proceed to expand the quartic function:
y = a · (x - 4 + √2) · (x - 4 - √2) · (x + 3 - √6) · (x + 3 + √6)
y = a · (x² - 8 · x + 14) · (x² + 6 · x + 3)
y = a · [x² · (x² - 8 · x + 14) + 6 · x · (x² - 8 · x + 14) + 3 · (x² - 8 · x + 14)]
y = a · (x⁴ - 8 · x³ + 14 · x² + 6 · x³ - 48 · x² + 84 · x + 3 · x² - 24 · x + 42)
y = a · (x⁴ - 2 · x³ - 31 · x² + 60 · x + 42)
And we find the lead coefficient:
- 21 = 42 · a
a = - 0.5
And we obtain the quartic function in standard form:
y = 0.5 · x⁴ - x³ - 15.5 · x² + 30 · x + 21
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Nancy has to mark 1 1/2 and-1 1/2 on this number line. How many parts does she need between the integers 1 and 2, and between -1 and -2, to show1 1/2 and-1 1/2 on the number line?
Answer:
1
Step-by-step explanation:
according to hooke's law and Pythagorean theorem your answer is should be most definitely will be or is it honestly I don't know. but the answer should be too is in the number not the figure of speech.
32.- The high costs of the California real estate market have caused families who cannot afford to buy larger houses to consider backyard sheds as an expansion option. Many are using their patio structures to build their studios, art rooms, and hobby areas, as well as for additional storage. The median price for a custom-built backyard clapboard frame is $3,100 (Newsweek, September 29, 2003). Assume that the standard deviation is $1,200.
The z-score for a backyard structure costing $2300 is -0.67.
How to calculate the z score?The standard score in statistics is the amount of standard deviations that a raw score deviates from or exceeds the mean of the phenomenon being observed or measured. Standard scores are positive for raw scores above the mean and negative for raw scores below the mean.
The Z-score quantifies the deviation between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a given data point deviates from the mean. In essence, standard deviation represents the degree of variability present in a given data set.
The z score will be:
= (2300 - 3100) / 1200
= -0.67.
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The high costs in the California real estate market have caused families who cannot afford to buy bigger homes to consider backyard sheds as an alternative form of housing expansion. Many are using the backyard structures for home offices, art studios, and hobby areas as well as for additional storage. The mean price of a customized wooden, shingled backyard structure is $3100 (Newsweek, September 29, 2003). Assume that the standard deviation is $1200.
a. What is the z-score for a backyard structure costing $2300?
In order to determine whether this horizontal position of the pumpkin trajectory represents a minimum or maximum, evaluate at Im. View Available Hint(s) dy a = -8.0 x 10-3m (negative, so this is a minimum) d=2a = –16 x 10-3 (negative, so this is a minimum) ay=2a = -16 x 10-4 (negative, so this is a maximum) = -8.0 x 10m (negative, so this is a maximum)
A projectile have a minimum speed at the highest point of its trajectory. This is because horizontal speed of the projectile remains constant.
Since the only force exerted on the projectile is gravity, which is
9.8 ms ^2 acting downwards and has no effects on the horizontal velocity.The maximum height the pumpkin reaches occurs at 62.5 horizontal meters from its launching spot.
The calculation is as follows;
The equation is y = -0.008x^2 +x
that corresponds to a curve presented by a parabola.
Now we can determine the maximum of this parabola with arms pointing down requesting the derivative slope of the tangent line to
the curve to be zero
So,= 62.5m
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-86
8
6 8
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
008
Clear all
Enter the correct answer.
+00
+?
DONE
The equation of the linear function in this problem is given as follows:
y = 0.5x + 4.
How to define the linear function?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.When x = 0, y = 4, hence the intercept b is given as follows:
b = 4.
When x increases by 8, y increases by 4, hence the slope m is given as follows:
m = 4/8 = 0.5.
Missing InformationThe linear function goes through the points (-8,0) and (0,4).
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what is the correct ordering, from smallest to largest, of the following: $\dfrac{7}{6},$ $\dfrac{17}{15},$ $\dfrac{28}{25}\,?$
So, the correct ordering from smallest to largest is 17/15, 7/6, 28/25.
When comparing fractions, one way to determine which fraction is larger or smaller is by finding a common denominator and then comparing the numerators. A common denominator is a multiple of both denominators. The least common denominator (LCD) is the smallest common denominator.
In this case, the least common denominator for the fractions 7/6, 17/15, 28/25 is 30.
This is because 30 is the smallest multiple of 6 and 15 that is also a multiple of 25
So, 7/6 = 35/30, 17/15 = 17/15 and 28/25 = 84/75
The numerators of the fractions are 35, 17, and 84 respectively. Since 17 is the smallest numerator and 84 is the largest numerator, we can conclude that 17/15 is the smallest fraction and 84/75 is the largest fraction.
Therefore, the correct ordering from smallest to largest is 17/15, 7/6, 28/25.
In summary, to compare fractions, we can find a common denominator, then compare the numerators. In this case, we used the least common denominator 30, and then compared the numerators 35, 17, 84, which allowed us to order the fractions in an increasing order.
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A card is drawn at random from a standard pack of playing cards.
Then a fair coin is flipped.
What is the probability of selecting a 9 and the coin landing on tails?
The probability of selecting a 9 and the coin landing on tails is 1/26.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Here,
The probability of selecting a card 9 is
Total number of outcomes =52
Number of favourable outcomes =4
Now, probability = 4/52
= 1/13
The probability of coin landing on tails is
1/2
Probability of an event = 1/13 × 1/2
= 1/26
Therefore, the probability of selecting a 9 and the coin landing on tails is 1/26.
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If nm, find the value of x and the value of z.
In the triangles value of x is 10.39 and z is 2.6.
What are the sides of right angle triangle?We can see from the diagram that both triangles are right triangles. As a result, we can use Pythagorean theorems. The longest side of a right triangle is the hypotenuse. In the diagram, those are sides with lengths of 4 and 12. The formula for this is:
c² = (a²+ b²), where c is the hypotenuse and the other shorter sides are a and b.
c = [tex]\sqrt{(a^{2} + b^{2} )}[/tex]
To calculate z,
By substituting the values,
4² = (z² + 3²)
16 = (z² + 9)
z² = 16 - 9
z² = 7
z = √7
z = 2.6
To find x,
use the following formula: 12² = (x² + 6²)
144 = x² + 36
x² = 144 - 36 = 10.39
x = 10.39
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The ratio of the measures of the angles of a triangle is 5:7:9. How many degrees is the largest angle? Round answer to the nearest whole number.
50 POINTS FOR WHOEVER HELPS
Based on the ratio of the largest angle of the triangle with 180°, the degrees of the largest angle is 77°.
What is the ratio?The ratio is the proportion of one value to the whole.
Ratios compare the relative sizes of components.
Ratios are computed as the quotients resulting from division operations.
The ratio of the measures of the angels of a triangle = 5:7:9
The sum of ratios = 21
The ratio of the largest angle = 9/21
We know that the total angles of a triangle = 180°
The angle (degrees) of the largest angle = 77° (180° x 9/21)
Thus, the degree of the largest angle is 77°.
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7) The perimeter of a triangle is 10z² +42-3. The sum of two of the sides is 82² +6x-7. What is the length of the missing side?
8/9
Length of missing side is 8/9x² - 5/9
What is the length of the missing side?The steps for this process are as follows
Step 1: Add the two equations together to form a new equation.
10z² + 42 - 3 + 82² + 6x - 7 = 8/9x² - 5/9
Step 2: Simplify the expression on the left side of the equation.
92² + 48x - 10 = 8/9x² - 5/9
Step 3: Subtract 8/9x² from both sides of the equation.
92² + 48x - 10 - 8/9x² = - 5/9
Step 4: Simplify the left side of the equation.
92² + 40x - 10 = -5/9
Step 5: Add 10 to both sides of the equation.
92² + 40x = 5/9
Step 6: Divide both sides of the equation by 40.
92²/40 + x = 5/9
Step 7: Simplify the left side of the equation.
x = 5/9 - 92²/40
Step 8: The length of the missing side is 8/9x² - 5/9 = 8/9 (5/9 - 92²/40) - 5/9.
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Using the given equation, Length of missing side is 8/9x² - 5/9
What is the length of the missing side of an equation?The steps for this process are as follows
Step 1: Add the two equations together to form a new equation.
10z² + 42 - 3 + 82² + 6x - 7 = 8/9x² - 5/9
Step 2: Simplify the expression on the left side of the equation.
92² + 48x - 10 = 8/9x² - 5/9
Step 3: Subtract 8/9x² from both sides of the equation.
92² + 48x - 10 - 8/9x² = - 5/9
Step 4: Simplify the left side of the equation.
92² + 40x - 10 = -5/9
Step 5: Add 10 to both sides of the equation.
92² + 40x = 5/9
Step 6: Divide both sides of the equation by 40.
92²/40 + x = 5/9
Step 7: Simplify the left side of the equation.
x = 5/9 - 92²/40
Step 8: The length of the missing side is 8/9x² - 5/9 = 8/9 (5/9 - 92²/40) - 5/9.
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What way does f(x) shift for log (DWX) ?
Left, right, down, up?
The function f(x) can shift for log (w ± dx) in any of the four directions
How to determine the direction of shiftFrom the question, we have the following parameters that can be used in our computation:
log(DWX)
Express properly
log(w ± dx)
Where w and d are constants and x is the variable
The above function is a logarithmic function, and the parent function is
log(x)
The direction the function shifts is dependent on the values of w and d i.e.
w ± dx > 1 will shift the function right0 < w ± dx < 1 will shift the function leftAlso, the vertical shift depends on the w ± dxRead more about transformation at
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Aiden asked a group of students to choose their favorite type of music from the choices of rock, hip-hop, and country. The results of the survey are shown in the graph.
Based on the graph, how many students in a class of 360 students would be expected to choose hip-hop or rock as their favorite type of music?
Number of students who are expected to choose hip hop or rock as their favorite type of music is 240.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
So the percentage actually means a part per 100.
Percentage is usually denoted by the symbol '%'.
From the graph,
Number of students who choose rock music = 20
Number of students who choose hip hop music = 40
Number of students who choose country music = 30
Total number of students = 20 + 40 + 30 = 90
Percentage of students who choose rock or hip hop = (20+ 40) / 90
= (60 / 90)
= 66.67%
Out of 360 students, 66.67% of students will chose hip hop or rock.
360 × (60/90) = 240
Hence 240 students choose either hip hop or rock as their favorite music.
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9x-20=3x+32 solve for x
Answer:
[tex]x=\frac{26}{3}[/tex]
Step-by-step explanation:
Lets solve for [tex]x[/tex].
Subtract [tex]3x[/tex] from both sides of the equation.
[tex]9x-20-3x=32[/tex]
Add 20 to both sides of the equation.
[tex]9x-3x=32+20[/tex]
Simplify both sides.
[tex]6x=52[/tex]
Divide both sides of the equation by 6.
[tex]x=\frac{52}{6}[/tex]
Write the fraction in simplest form.
[tex]52 \div 2 = 26\\6 \div 2 = 3[/tex]
[tex]x=\frac{26}{3}[/tex]
Answer:
x=26/3Step-by-step explanation:
9x-20=3x+32
9x-20+20=3x+32+20
9x=3x+52
9x-3x=3x+52-3x
6x=52
6x/6=52/6
x=26/3
(PLEASE HELP IM GIVING OUT BRAINLIST PLEASE help help).
The number of papers ms. Motley grades increases exponentially as
time goes on. On the first day she grades 9 papers , on the second day she grades 27 papers and on the third day she grades 31 papers
How many will she grade in five days?
After many days will it take her to grade 6,000 papers?
The papers graded exponentially at the end of 5 days are 134, and it will take approximately around 12 days to complete 6000 papers.
What is exponential function?A function is considered to be exponentially growing if its value rises faster than any polynomial. The function e^x, serves as a good illustration.
The exponential growth is given by the following formula:
[tex]A = Pe^{rt}[/tex]
where, A is the final amount, P is the initial amount, r is the rate and t is the time.
For t = 0, the number of papers graded are, 9, hence the value of P = 9.
To calculate the rate at which the work is done, substitute the value of P = 9, A = 27 and t = 2 in the equation:
[tex]27 = 9 e^{2r}\\3 = e^{2r}[/tex]
Taking ln on both sides of the equation:
[tex]ln (3) = ln(e^{2r})\\\\ln(3) = 2r[/tex]
1.09 = 2r
r = 0.54
To calculate the number of papers graded in five days, substitute the value of P = 9, t = 5 and r = 0.54.
[tex]A = 9 e^{(0.54)(5)}[/tex]
A = 134
Hence, the papers graded at the end of 5 days are 134.
To complete grading 6000 papers, the time taken will be:
6000 = 9e^(0.54)(t)
666.66 = e^(0.54)(t)
Taking ln on both sides of the equation:
ln (666.66) = ln(e^(0.54)(t))
6.50 = (0.54)(t)
t = 12.04
Hence, it will take approximately around 12 days to complete 6000 papers.
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based on the histogram shown, of the following, which is closest to the average (arithmetic mean) number of seeds per apple?
The closest to the average(arithmetic mean) number of seeds per apple is 6.
What is average ?
An average, also known as a mean, is a measure of central tendency that represents the typical value of a set of data. To calculate the average of a set of numbers, you add them up and then divide by the number of items in the set. For example, the average of the numbers 2, 4, 6, and 8 is (2 + 4 + 6).
Average = Total number of seeds/12
⇒ Average = 2×3+4×5+1×6+2×7+3×9/12
⇒ Average = 73/12
⇒ Average ≈6
The closest to the average(arithmetic mean) number of seeds per apple is 6.
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P(A)=0.60, p(b)=0..25 and p(A and B)=.15 what is p(A or B)?
Answer:
0.70
Step-by-step explanation:
You want p(A+B) given that p(A) = 0.60, p(B) = 0.25, and p(A·B) = 0.15.
ProbabilityThe relevant formula is ...
p(A+B) = p(A) +p(B) -p(A·B)
p(A+B) = 0.60 +0.25 -0.15
p(A+B) = 0.70
__
Additional comment
In the attached Venn diagram, the sum of the numbers inside the circle labeled A is p(A) = 0.45 +0.15 = 0.60. Likewise, the sum of the numbers inside circle B is p(B) = 0.15 +0.10 = 0.25.
As the attachment shows, the event A includes the event 'A and B'. Likewise, event B includes the event 'A and B'. Simply adding the probabilities of A and B will cause p(A and B) to be counted twice.
Use the following equation to derive a demand schedule and a demand curve. What types of products might exhibit this type of nonlinear demand curve?
The equation is as follows: Q = a - bP^2.Nonlinear demand curve like this can be found in luxury goods and Veblen goods. Where the luxury goods are the goods whose demand increases as the price increases and Veblen goods are the goods whose demand increases with an increase in the consumer's income.
The equation is as follows: Q = a - bP^2.
To derive a demand schedule, we can plug in different values of P (price) and solve for Q (quantity demanded). For example:
Q = a - bP^2
Q = a - (b * 10^2)
Q = a - 1000b
Q = a - (b * 9^2)
Q = a - 810b
Q = a - (b * 8^2)
Q = a - 640b
and so on.
To derive a demand curve, we can plot the different points from the demand schedule on a graph, with P on the x-axis and Q on the y-axis. The demand curve will be a downward-sloping parabola.
Nonlinear demand curve like this can be found in luxury goods and Veblen goods. Where the luxury goods are the goods whose demand increases as the price increases and Veblen goods are the goods whose demand increases with an increase in the consumer's income.
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determine elements of set A
The items in A or the elements included in set A are A = 1, 2, 3, 4.
What is an element in a set?
In mathematics, any one of the unique things that make up a set is referred to as an element (or member). A distinct object belonging to a set is referred to as an element (or member) of a set.
The items in A and B, or the elements included in both sets, make up its constituent parts.
Example The elements of the set A B should be listed if A = 1, 2, 3, 4 and B = 2, 4, 6, 8.
A little letter, like x, y, or z, is typically used to represent a set element.
By listing all of a set's components inside braces, a set can be explained.
A = 2, 4, 6, 8 for instance, if Set A is composed of the integers 2, 4, 6, and 8.
Hence, The items in A, or the elements included in set A are A = 1, 2, 3, 4.
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The sum of ages of akua and yeboa is 23years akua is 3years older than yeboah fine , the age of yaboah, the product of their ages
Answer:
yaboah: 10product: 130Step-by-step explanation:
Given that akua is 3 years older than yaboah and the sum of their ages is 23, you want the age of yaboah and the product of their ages.
Sum and differenceLet 'a' and 'y' represent the ages of akua and yaboah, respectively. The given relations are ...
a + y = 23
a - y = 3
Adding these equations gives ...
2a = 26
a = 13
Using this in the second equation, we find ...
y = a -3 = 13 -3 = 10
ProductThe product of their ages is ...
a·y = 13·10 = 130
Yaboah is 10 and the product of their ages is 130.
a person weighs 156 pounds, convert their weight to kilograms
Answer:
70.824
Step-by-step explanation:
to solve, multiply the amount of pounds by 0.454.
EX:
156 * 0.454 = 70.824
what it actually equals:
70.7604 (answ on web)
vs
70.824 (answ with formula)
not bad eh?
hope this helps :)
Which of the following describes dependent events?
✔
a.) Rufus spins a spinner and it randomly lands on the number
7. Rufus spins the spinner again, and it lands on the
number 7 again.
32°F
b.) Rudolph randomly picks names out of a hat. He chooses
"Mark" first. He puts Mark's name back in the hat and
chooses again. This time he chooses "Indira."
c.) Renata randomly chooses a chocolate chip cookie from a
cookie jar. She eats the cookie and chooses again. This
time she gets a sugar cookie.
d.) Rocky tosses a six-sided die that lands on the number 1.
Next, he picks a card from a standard deck of playing
The situation that can be described as dependent events is c.) Renata randomly chooses a chocolate chip cookie from a cookie jar. She eats the cookie and chooses again. This time she gets a sugar cookie.
What are dependent events ?Events that are dependent upon prior events are called dependent events. The results of earlier events have an impact on these current ones. For example, two or more occurrences that are interdependent are referred to as dependent events. An event generally qualifies as being reliant if it offers details about another event. If an event provides no information about other events, it is considered independent.
The dependent event would be Renata picking a sugar cookie the second time she chooses another cookie because she ate from the first cookie and so was able to avoid it the second time.
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how to Solve the following Systems of Linear Equations 4X + 3Y= 7
Answer:
4x−3y+4=0
⟹x=
4
−4+3y
Let, y=4, then x=
4
−4+3(4)
=2
Similarly, when y=0,x=−1
4x+3y−20=0
⟹x=
4
20−3y
Let, y=4, then x=
4
20−3(4)
=2
Similarly, when y=0,x=5
NO LINKS!! NOT MULTIPLE CHOICE!!
For each of the functions below, find the following information. Then sketch a graph.
a. x- int and y-int.
b. vertical asymptote(s) or any holes
c. end behavior asymptotes
d. domain and range
33. g(x) = (x - 2)/(x^2 - 2x - 3)
34. k(x)= (x^2 - x - 2)/(x - 3)
35. f(x)= -x/(x^3 - 4x)
Answer:
Question 33
a) x-int (2, 0). y-int (0, 2/3)
b) Vertical asymptotes: x = -1 and x = 3
Horizontal asymptote: y = 0
c) f(x) → -∞, as x → -1⁻
f(x) → +∞, as x → -1⁺
f(x) → -∞, as x → 3⁻
f(x) → +∞, as x → 3⁺
d) Domain: (-∞, -1) ∪ (-1, 3) ∪ (3, ∞)
Range: (-∞, ∞)
Question 34
a) x-int (-1, 0) and (2,0). y-int (0, 2/3)
b) Vertical asymptote: x = 3
c) f(x) → -∞, as x → 3⁻
f(x) → +∞, as x → 3⁺
d) Domain: (-∞, 3) ∪ (3, ∞)
Range: (-∞, 1] ∪ [9, ∞)
Question 35
a) No axis intercepts
b) Vertical asymptotes: x = -2 and x = 2. Hole at (0, ¹/₄).
c) f(x) → -∞, as x → -2⁻
f(x) → +∞, as x → -2⁺
f(x) → +∞, as x → 2⁻
f(x) → -∞, as x → 2⁺
d) Domain: (-∞, -2) ∪ (-2, 0) ∪ (0, 2) ∪ (2, ∞)
Range: (-∞, 0) ∪ (¹/₄, ∞)
Step-by-step explanation:
Definitions
The x-intercepts are the points at which the curve crosses the x-axis, so when y = 0.The y-intercept is the points at which the curve crosses the y-axis, so when x = 0.The domain of a function is the set of all possible input values (x-values).The range of a function is the set of all possible output values (y-values).A vertical asymptote occurs at the x-value(s) that make the denominator of a rational function zero.A horizontal asymptote occurs at y = 0 if the degree of the numerator is less than the degree of the denominator.A hole occurs when a rational function has a factor with an x that is in both the numerator and the denominator.Question 33Given rational function:
[tex]g(x) =\dfrac{x - 2}{x^2 - 2x - 3}[/tex]
x-intercept
[tex]\begin{aligned}y=0 \implies \dfrac{x - 2}{x^2 - 2x - 3}&=0\\x - 2&=0\\x&=2\end{aligned}[/tex]
y-intercept
[tex]x=0 \implies \dfrac{0 - 2}{0^2 - 2(0) - 3}=\dfrac{2}{3}[/tex]
Vertical asymptotes
Set the denominator to zero and solve for x:
[tex]\implies x^2-2x-3=0[/tex]
[tex]\implies x^2-3x+x-3=0[/tex]
[tex]\implies x(x-3)+1(x-3)=0[/tex]
[tex]\implies (x+1)(x-3)=0[/tex]
[tex]\implies x+1=0 \implies x=-1[/tex]
[tex]\implies x-3=0 \implies x=3[/tex]
Horizontal asymptote
As the degree of the numerator is less than the degree of the denominator, there is a horizontal asymptote at y = 0.
Holes
Factor the denominator:
[tex]g(x) =\dfrac{x - 2}{(x+1)(x-3)}[/tex]
There are no holes as there is no common factor in the numerator and the denominator.
End behaviour near the vertical asymptotes
f(x) → -∞, as x → -1⁻
f(x) → +∞, as x → -1⁺
f(x) → -∞, as x → 3⁻
f(x) → +∞, as x → 3⁺
Domain
As there are vertical asymptotes at x = -1 and x = 3, the domain is restricted:
Interval notation: (-∞, -1) ∪ (-1, 3) ∪ (3, ∞)Range
The range is unrestricted:
Interval notation: (-∞, ∞)Question 34Given rational function:
[tex]k(x)= \dfrac{x^2 - x - 2}{x - 3}[/tex]
x-intercepts
[tex]\begin{aligned}y=0 \implies \dfrac{x^2 - x - 2}{x - 3}&=0\\x^2 - x - 2&=0\\x^2-2x+x-2&=0\\x(x-2)+1(x-2)&=0\\(x+1)(x-2)&=0\\\\x+1&=0 \implies x=-1\\x-2&=0 \implies x=2\end{aligned}[/tex]
y-intercept
[tex]x=0 \implies \dfrac{(0)^2 - 0 - 2}{0 - 3}=\dfrac{2}{3}[/tex]
Vertical asymptotes
Set the denominator to zero and solve for x:
[tex]\implies x-3=0[/tex]
[tex]\implies x=3[/tex]
Holes
Factor the numerator:
[tex]k(x)= \dfrac{(x+1)(x-2)}{x - 3}[/tex]
There are no holes as there is no common factor in the numerator and the denominator.
End behaviour near the vertical asymptote
f(x) → -∞, as x → 3⁻
f(x) → +∞, as x → 3⁺
Domain
As there is vertical asymptote at x = 3, the domain is rest:
Interval notation: (-∞, 3) ∪ (3, ∞)Range
The extreme points are (1, 1) and (5, 9). Therefore, the range is restricted:
Interval notation: (-∞, 1] ∪ [9, ∞)Question 35Given rational function:
[tex]f(x)= -\dfrac{x}{x^3 - 4x}[/tex]
x-intercepts
As the degree of the numerator is less than the degree of the denominator, there is a horizontal asymptote at y = 0. Therefore, there are no x-intercepts.
y-intercept
Substitute x = 0 and solve for y:
[tex]x=0 \implies -\dfrac{0}{0(x+2)(x-2)}=\dfrac{0}{0}=\textsf{unde\:\!fined}[/tex]
Therefore, there is no y-intercept.
Factor the denominator:
[tex]f(x)= -\dfrac{x}{x(x+2)(x-2)}[/tex]
Cancel the common factor x:
[tex]f(x)= -\dfrac{1}{(x+2)(x-2)}[/tex]
Vertical asymptotes
Set the denominator to zero and solve for x:
[tex]\implies (x+2)(x-2)=0[/tex]
[tex]\implies x+2=0 \implies x=-2[/tex]
[tex]\implies x-2=0 \implies x=2[/tex]
Holes
Factor the denominator:
[tex]f(x)= -\dfrac{x}{x(x+2)(x-2)}[/tex]
As the numerator and denominator have a common factor of x, the function is not defined when x = 0. Therefore, there is a hole when x = 0.
To find the y-value of the hole, cancel the common factor x and input x = 0 into the resulting function:
[tex]x=0 \implies -\dfrac{1}{(0+2)(0-2)}=\dfrac{1}{4}[/tex]
Therefore, there is a hole at (0, ¹/₄).
End behaviour near the vertical asymptotes
f(x) → -∞, as x → -2⁻
f(x) → +∞, as x → -2⁺
f(x) → +∞, as x → 2⁻
f(x) → -∞, as x → 2⁺
Domain
As there are vertical asymptotes at x = -2 and x = 2, and a hole at (0, ¹/₄), the domain is restricted:
Interval notation: (-∞, -2) ∪ (-2, 0) ∪ (0, 2) ∪ (2, ∞)Range
As there is a hole at (0, ¹/₄) and a horizontal asymptote at y = 0, the range is restricted:
Interval notation: (-∞, 0) ∪ (¹/₄, ∞)At a given point 67.7ft at ground level of a covered court, the angle of elevation of a roof worker from the bottom is 38.6⁰ and the angle of elevation of the roof from the top is 42.4 degrees find the height of the roof worker and the distance of the ø if someone is observing below.
The height is 114.83 ft and the distance of the ø if someone is observing below is 84.8.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that at a given point of 67.7ft at the ground level of a covered court, the angle of elevation of a roof worker from the bottom is 38.6⁰ and the angle of elevation of the roof from the top is 42.4 degrees.
The base will be calculated as:-
tan(38.6) = P / B
tan(38.6) = 67.7 / B
B = 67.7 / tan(38.6)
B = 54.8 ft
The height will be calculated as:-
Cos(42.4) = B / H
H = 84.8 / Cos(42.4)
H = 114.83 ft
Therefore, If someone were to look down from above, they would be 114.83 feet from the object and 84.8 feet away.
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If you divide a whole number greater than 10 by a fraction, the result is always larger than the original number.
Answer:
Yes
Step-by-step explanation:
This only works for positive integers. For example, 11/0.5 equals 22, but if you were to negate the 11 then the answer would be -22 which is less than negative 11 so the answer is yes it is true for whole positive integers.