A recipe for cornbread calls for 3 cups of flour for every 1/4 cup of water. Using the same recipe, how much water will you need for 8 cups of flour?
The 1/4 is supposed to be like 1 on top and then 4 at bottom
Answer: 2/3
Step-by-step explanation:
3/8 * .25/X
3X = 2
X = 2/3
Determine the equation of the hyperbola with foci (3, 11) and (3, -9), and co-
vertices (11, 1) and (-5,1).
The equation of the hyperbola with the given foci and vertices is (x - 3)² - (y - 1)² = 64
What is hyperbola?Hyperbola is a type of conic section, which is a curve formed by the intersection of a cone with a plane. It is similar to a circle, but with two separate halves that are mirror images of each other. These two halves are called branches, and the point where they intersect is the vertex. The hyperbola is characterized by its two foci, which are points that lie on the inside of the structure.
The equation of a hyperbola with foci (h, k) and (h, l) and vertices (m, n) and (p, n) is given by:
((x - h)² / (m - h)²) - ((y - n)² / (k - n)²) = 1
In this case, h = 3, k = 11, l = -9, m = 11, and n = 1. Plugging these values into the equation, we get:
((x - 3)² / (11 - 3)²) - ((y - 1)² / (11 - 1)²) = 1
Simplifying, we get:
(x - 3)² - (y - 1)² = 8²
Therefore, the equation of the hyperbola with the given foci and vertices is: (x - 3)² - (y - 1)² = 64.
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10.8 angle relationships & triangles
∠M and ∠N are supplementary and m∠M = 37°
. If m∠N = (13x)°
, what is the value of x and the m∠N?
Answer: x = 50, m∠N = 50°
Step-by-step explanation:
x = 50, m∠N = 50°
Since ∠M and ∠N are supplementary, the two angles add up to 180°. Therefore, m∠N = 180° - 37° = 143°. Because m∠N = 13x, we can solve for x by dividing both sides by 13, which gives x = 50. Therefore, m∠N = 13x = 13(50) = 50°.
In the figure angle article equal to angle pqs and QS equal to PR. Prove that angle PQR equal and PQS
Hence, in answering the stated question, we may say that As a result, we angles have demonstrated that angle PQR equals angle PQS, assuming that angle article equals angle pqs and QS = PR.
what are angles?An angle is a shape in Euclidean geometry that is comprised of two rays, known as such angle's flanks, that meet at a central location known as the angle's set of vertices. Two rays might combine to generate an angle there in plane in which they are located. An angle is formed when two planes collide. They are known as dihedral angles. In plane geometry, an angle is a potential configuration between two rays and lines that meet a termination. The English name "angle" is derived from the Latin phrase "angulus," which means "horn." The apex is the point at where the two rays, also known also as angle's sides, converge.
It is difficult to propose a specific solution without a diagram or a comprehensive description of the figure. But, based on the facts provided, we can apply the following argument to demonstrate that angle PQR equals angle PQS.
Assuming that angle article equals angle pqs and QS = PR.
To demonstrate: angle PQR = PQS angle.
We know that angle pqs = angle article. This signifies that the two angles are parallel.
We also understand that QS Equals PR. That is, these two line segments are congruent.
As a result, angle PQR equals angle PQS.
As a result, we have demonstrated that angle PQR equals angle PQS, assuming that angle article equals angle pqs and QS = PR.
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A function is shown in the table. which equation represents this function?
X: 0,5,10,15
Y: 8,-7,-22,-37
The equation that represents this function is y = -3x + 8
How to determine which equation represents this function?From the question, we have the following parameters that can be used in our computation:
X: 0,5,10,15
Y: 8,-7,-22,-37
A linear relation is represented as
y = mx + c
Where
c = y when x = 0
Using the above as a guide, we have the following:
c = 8
So, we have
y = mx + 8
Using the points on the table, we have
5m + 8 = -7
This gives
5m = -15
m = -3
So, the function is
y = -3x + 8
Hence, the function is y = -3x + 8
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3x-y=2, Y=2x-1 substitude for y
Answer:
x = 3
y = 7
Step-by-step explanation:
3x - y = 2 Y = 2x - 1
3x - 2x - 1 = 2
x - 1 = 2
x = 3
Now put 3 in for x and solve for y
3(3) - y = 2
9 - y = 2
- y = -7
y = 7
Let's check
3(3) - 7 = 2
9 - 7 = 2
2 =2
So, x = 3 and y = 7 is the correct answer.
Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard deviation σ=20. Find the probability that a randomly selected adult has an IQ between 93 and 117.
The probability that a randomly selected adult has an IQ between 93 and 117 is approximately 0.6827 or 68.27%.
What is probability?
Probability is a branch of mathematics that deals with the study of random events and their outcomes. It is the measure of the likelihood of an event occurring, expressed as a number between 0 and 1.
To find the probability that a randomly selected adult has an IQ between 93 and 117, we need to standardize the distribution using the z-score formula, and then find the area under the normal distribution curve between those two z-scores.
The z-score formula is:
z = (x - μ) / σ
where x is the IQ score we are interested in, μ is the mean IQ score, and σ is the standard deviation of IQ scores.
For the lower bound of 93, the z-score is:
z = (93 - 105) / 20 = -0.6
For the upper bound of 117, the z-score is:
z = (117 - 105) / 20 = 0.6
Now, we need to find the area under the normal distribution curve between these two z-scores. We can use a standard normal distribution table or a calculator to find this probability. Using a calculator, we can use the normalcdf function:
normalcdf(-0.6, 0.6, 0, 1)
This gives us a probability of 0.6827.
Therefore, the probability that a randomly selected adult has an IQ between 93 and 117 is approximately 0.6827 or 68.27%.
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Review the graph of function f(x). On a coordinate plane, a curve starts at open circle (negative 3, negative 2), increases through (negative 1, 0) to (1, 2), and then curves down to closed circle (3, 0). Which statement describes whether the extreme value theorem applies? The extreme value theorem applies, and f(x) has both a minimum and a maximum. The extreme value theorem applies, and f(x) has a maximum but not a minimum. The extreme value theorem does not apply, and f(x) does not have a minimum or a maximum. The extreme value theorem does not apply, and f(x) has a maximum but not a minimum.
The correct answer is "The extreme value theorem applies, and f(x) has both a minimum and a maximum."
What is the extreme value theorem?
The extreme value theorem states that if a function is continuous on a closed interval, then it must have both a maximum and a minimum value on that interval. To determine whether the extreme value theorem applies to the graph of f(x), we need to check if the function is continuous on a closed interval and whether it has a highest and lowest point within that interval.
Looking at the graph of f(x), we can see that the function is continuous on the closed interval [-3, 3] since it has no breaks or jumps. Additionally, the graph has the highest point at (1, 2) and the lowest point at (-3,-2). Therefore, we can conclude that the extreme value theorem applies and that f(x) has both a minimum and a maximum value on the interval [-3, 3].
Therefore, the correct answer is (a) "The extreme value theorem applies, and f(x) has both a minimum and a maximum."
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simplify sqrt (196y^8)
this is basically saying the square root of 196y to the power of 8.
btw i can do this. i just feel rlly lazy today :[
Hence, in response to the provided question, we can say that As a result, exponents [tex]/sqrt(196y^8)[/tex] simplifies to [tex]14y^4[/tex].
what are exponents?Exponentiation, sometimes known as "raising b to the nth power," is a substitution cipher that includes two numbers: a base quantity, b, and an argument, meaning power, n. Exponents represent the number of times a value has been increased by itself. As an example, 2-3 (represented as 23) represents: 2 x 2 x 2 = 8. 2 + 3 = 6 does not equal 23. Remember that an integer multiplied by one equals itself. Exponents are a method for expressing large numbers as powers. The amount that represents however many times a statistic has already been amplified by itself is called the exponent. As an example, multiplying 6 by 4 yields 6 x 6 x 6.
Using exponent principles and the square root of perfect squares, we may simplify sqrt(196y8) as follows:
[tex]\sqrt(196y8) = \sqrt((142*(y4)2) [since 196 = 142 and (y4)2 = y8]\\\sqrt(142) * \sqrt((y4)2) [using the \sqrt(ab) = \sqrt(a) * \sqrt(b) rule]\\= 14y^4[/tex]
As a result, [tex]/sqrt(196y^8)[/tex] simplifies to [tex]14y^4[/tex].
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Solve the following system of equations:
y = 3x + 1
y = 3x + 7
(3,1)
(3,7)
No Solutions
Infinite Solutions
Answer:
No solutions
Step-by-step explanation:
i have a feeling it's "no solutions". looking at the equations, the only thing that's different is the y intercepts (one being +1 and the other +7). that tells me they are parallel, so they'll never touch each other
Which expression does not belong with the other three? explain
The only expression that does not belong to the other 3 is the one that is a binomial.
How to identify the type of algebraic expression?A monomial is defined as an algebraic expression that has only one non- zero term. Examples of a monomial expression are x, 7xy²
A binomial is defined as an algebraic expression that has two non-zero terms. Examples of a binomial expression: x² + 2y
A trinomial is defined as an algebraic expression that possesses three non-zero terms. Examples of a trinomial expression: a + b + c
A polynomial is defined as an algebraic expression that has one, two or more terms.
The only expression that does not belong to the other 3 is (b - 2⁻¹) because it is the only binomial.
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The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 10 to 14.5 on the number line. A line in the box is at 12.5. The lines outside the box end at 5 and 20. The graph is titled Fast Chicken.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
Which drive-thru is able to estimate their wait time more consistently, and why?
Fast Chicken, because it has a smaller IQR
Fast Chicken, because it has a smaller range
Super Fast Food, because it has a smaller IQR
Super Fast Food, because it has a smaller range
The range, which is the distance between the smallest and greatest linear equation values in the data, does not take into account the distribution of the data within that range.
What is a linear equation?In algebra, a linear equation refers to one with its form y=mx+b. B is the gradient, and m is the esta. The preceding clause is commonly referred to as a "linear function with two variables" so even though y and x are variables. Bivariate linear equations are linear equations with two variables. There are several linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation seems to have the structure y=mx+b, where m is the slope and b is the y-intercept, it is said to be linear. When a measurement seems to have the formula y=mx+b, both with m identifying its slope and b denoting the y-intercept, it is said to be linear.
Because it has a lower IQR, Fast Chicken can more consistently estimate their wait time (Interquartile Range). In this case, the IQR is the range of the middle 50% of the data, which is the distance between the first and third quartiles.
Super Fast Food, on the other hand, has a higher IQR, indicating that the data is more dispersed. This means that customers report a wider range of wait times, making it more difficult to estimate a consistent wait time. The range, which is the distance between the smallest and greatest values in the data, is not as useful for measuring consistency in this case because it does not take into account the distribution of the data within that range.
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two are supplementary. the measure of one of these angles is 12 degrees less than one-third the measure of the other.what is the measure of each angle
Answer:
two are supplementary. the measure of one of these angles is 12 degrees less than one-third the measure of the other.what is the measure of each angle
Let's call the measures of the two angles x and y, where x is the larger angle. We know that the two angles are supplementary, which means they add up to 180 degrees:
x + y = 180
We also know that one of the angles (let's say y) is 12 degrees less than one-third the measure of the other angle (x):
y = (1/3)x - 12
Now we can substitute the second equation into the first equation to solve for x:
x + (1/3)x - 12 = 180
Multiplying both sides by 3 to get rid of the fraction, we have:
3x + x - 36 = 540
Combining like terms, we get:
4x - 36 = 540
Adding 36 to both sides, we get:
4x = 576
Dividing both sides by 4, we get:
x = 144
Now we can use the first equation to solve for y:
144 + y = 180
Subtracting 144 from both sides, we get:
y = 36
Therefore, the measures of the two angles are 144 degrees and 36 degrees.
Find the probability of exactly 5 successes in 7 trials of a binomial experiment in which the probability of success is 70%
Answer:
0.3176523
Step-by-step explanation:
You want the probability of exactly 5 successes in 7 trials of a binomial experiment in which the probability of success is 70%.
ProbabilityThe desired probability is the product of the probability of 5 success and 2 failures, multiplied by the number of ways that result might occur.
P(x=5) = 7C5·(0.7^5)(1 -0.7)^2 = 0.3176523
The probability of exactly 5 successes is 0.3176523.
__
Additional comment
Any of a number of probability calculators can tell you this probability. Spreadsheets have appropriate functions built in as well.
[tex]\blue{\huge {\mathrm{PROBABILITY}}}[/tex]
[tex]\\[/tex]
[tex]{===========================================}[/tex]
[tex]{\underline{\huge \mathbb{Q}{\large \mathrm {UESTION : }}}}[/tex]
Find the probability of exactly 5 successes in 7 trials of a binomial experiment in which the probability of success is 70%.[tex]{===========================================}[/tex]
[tex] {\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} [/tex]
The probability of exactly 5 successes in 7 trials of a binomial experiment in which the probability of success is 70% is 0.3176523.[tex]{===========================================}[/tex]
[tex] {\underline{\huge \mathbb{S} {\large \mathrm {OLUTION : }}}} [/tex]
We can use the binomial probability formula to find the probability of exactly 5 successes in 7 trials:
[tex]\sf P(5\: successes\: in\: 7\: trials) = (7\: choose\: 5) (0.7)^5 (0.3)^2[/tex]
where:
n = 7 (number of trials),p = 0.7 (probability of success),q = 0.3 (probability of failure), and(7 choose 5) = 7!/(5!2!) = 21 (the number of ways to choose 5 successes in 7 trials).Plugging in these values, we get:
[tex]\begin{aligned}\sf P(5\: successes\: in\: 7\: trials)& =\sf 21 (0.7)^5 (0.3)^2\\& =\bold{ 0.3176523}\end{aligned}[/tex]
Therefore, the probability of exactly 5 successes in 7 trials of a binomial experiment in which the probability of success is 70% is 0.3176523.
[tex]{===========================================}[/tex]
[tex]- \large\sf\copyright \: \large\tt{AriesLaveau}\large\qquad\qquad\qquad\tt 04/01/2023[/tex]
What is the correct numerical expression for "subtract the
sum of 2 and 9 from the product of 4 and 3?"
2+9-4x3
(2+9) - 4 x 3
(4 x 3) (2 + 9)
4x (3-2) +9
Answer:
[tex](4 \times 3) - (2 + 9)[/tex]
For the numbers 683 and 2329, round each number to the nearest hundred. Then find the product of the rounded numbers
683 rounded to the nearest hundred is 700
2329 rounded to the nearest hundred is 2300
The product of the rounded numbers is 1,610,000.
Rounding to the nearest hundred and Product of numbersFrom the question, we are to round the given numbers to the nearest hundred and determine the product of the rounded numbers.
The given numbers are 683 and 2329.
Rounding 683 and 2329 to the nearest hundred gives:
683 rounded to the nearest hundred is 700
2329 rounded to the nearest hundred is 2300
Now, we will determine the product of these rounded numbers.
That is,
The product of 700 and 2300
700 × 2300 = 1610000
Hence, the product of the rounded numbers is 1,610,000.
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Coach Walker has a cooler that can hold 5 1/2 gallons of a sports drink. He fills 3/4 of
the cooler with the sports drink to bring to football practice.
B. How many players can fill their water bottles with the sports drink before the cooler is empty? (1 Gallon = 8 pints)
The answer of the question based on the players can fill their water bottles with the sports drink before the cooler is empty is 15 players.
What is Amount?An amount may refer to quantity of something that can be measured, such as amount of substance or amount of the time.
The cooler can hold 5 1/2 gallons of sports drink, and Coach Walker fills 3/4 of it, which means he fills:
5 1/2 gallons * 3/4 = (5 * 2/2 + 1/2) * 3/4 = 15/4 gallons
We know that 1 gallon equals 8 pints, so we can convert the 15/4 gallons to pints:
15/4 gallons * 8 pints/gallon = 30 pints
Therefore, there are 30 pints of sports drink in the cooler. Assuming each player's water bottle can hold 2 pints of sports drink, we can find how many players can fill their bottles before the cooler is empty by dividing the total amount of sports drink by the amount used by each player:
30 pints / 2 pints/player = 15 players
Therefore, 15 players can fill their water bottles with the sports drink before the cooler is empty.
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There are 12 bronze stars, 12 silver stars, and 12 gold. If 3 were removed from the bag and none of them were bronze. What is the probability of drawing a bronze star the second time?
In response to the stated question, we can state that The odds of equation drawing a bronze star the second time are 9/32.
What is equation?An equation is a mathematical assertion that establishes the equality of two expressions that are joined together by the equals sign ('='). For example, 2x – 5 = 13. 2x-5 and 13 are examples of expressions. The letter '=' connects the two expressions. A mathematical formula is called an equation if it contains two algebraic expressions on either side of the equal sign (=). It shows how the right and left formulas are equivalent to one another. Any formula will result in L.H.S. = R.H.S. (left side = right side).
There are 12-3=9 bronze stars remaining in the bag if none of the three stars that were removed were bronze.
12 + 12 + 12 + 3 = 33 stars are still in the bag.
There are now 33-1=32 stars in the bag after drawing one star out of it without replacing it.
The following formula can be used to determine the likelihood of drawing a bronze star a second time:
Bronze stars remaining in the bag divided by the total number of stars in the bag is 9/32 for P(drawing a bronze star).
The odds of drawing a bronze star the second time are 9/32.
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9 + 6g + 1 = 100 please I need help these are difficult
Answer:
So g would be 15.
What is the bill of a house that consumed 1000 units of electricity,if the first 100 units are charged $10.00 per unit and the remaining units at $5.00 per unit?
Answer:
$14500
Step-by-step explanation:
$10 per unit means 1 unit is equivalent to 10 dollars.
∴Unit multiplier = [tex]\frac{10 dollars}{unit}[/tex]
$5 per unit means 1 unit is equivalent to 5 dollars
∴Unit multiplier = [tex]\frac{5 dollars}{unit}[/tex]
Remaining units = 1000 - 100 = 900 units
The unit multipliers are arranged in such a way that the "units” in the numerator and denominator will cancel each other out leaving us with “dollars” in the numerator. Our answer should be expressed in dollars
since the question requires us to calculate the bill
Bill of the House = Charge of first 100 units + Charge of remaining units
= (1000 units)([tex]\frac{10dollars}{unit}[/tex]) + [(900)units][[tex]\frac{5dollars}{unit}[/tex]]
= $10000 + $4500
= $14500
In ΔQRS, q = 3.9 cm, � m∠S=10° and � m∠Q=74°. Find the length of s, to the nearest 10th of a centimeter.
S thus measures around 2.77 centimetres in length.
What is the purpose of law of sines?The law of sines is frequently used to find the elusive side or angle of a triangle. This law can be used if precise triangle measurement combinations are given. ASA The objective is to identify the unknown side given two angles and an included side.
The Law of Sines can be used to determine the length of side s: s/sin(mS) = q/sin(mQ).
replacing the specified values:
s/sin(10°) = 3.9/sin(74°)
s ≈ sin(10°) × 3.9 ÷ sin(74°)
s ≈ 0.684 × 3.9 ÷ 0.961
s ≈ 2.77 cm (rounded to the nearest 10th)
S thus measures around 2.77 centimetres in length.
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Based on a poll, 50% of adults believe in reincarnation. Assume that 6 adults are randomly selected, and find the indicated probability. What is the probability that all of the selected adults believe in reincarnation?
Answer:
a)0.25
b)0.063
c)0.313
d)Yes, because the probability that 3 or more of the selected adults believe in reincarnation is greater than 0.05.
Step-by-step explanation:
Probability nation is that adult believe in reincarnation
Therefore,
Using binomial distribution
Where
a) When r=3
The probability that exactly 3 of the 4 adults believe in reincarnation is
0.25
b) Now,
The probability that all of the selected adults believe in reincarnation is
. 0.063
c) In this case atleast 3 will believe therefore
The probability that at least 3 of the selected adults believe in reincarnation is 0.313
d)Yes, because the probability that 3 or more of the selected adults believe in reincarnation is greater than 0.05 i.e 0.313.
Colin's mom had a long day at work. "I feel like I drank 3 gallons of coffee today!" she joked. If she really drank that much coffee, how many times would she have filled her 12-fluid-ounce mug?
Answer:
32
Step-by-step explanation:
given that there are 128 fluid ounces in a gallon and she would have drank 3 gallons which is 384 ounces then divide
384 divided by 12 = 32
Suppose a sample of O-rings was obtained and the wall thickness (in inches) of each was recorded. Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed. Click here to view the table of critical values.LOADING... Click here to view page 1 of the standard normal distribution table.LOADING... Click here to view page 2 of the standard normal distribution table.LOADING...
The normal probability plot is a useful tool for assessing the normality of a sample of data. By plotting the sample values against the quantiles of a normal distribution, one can quickly determine whether the data could have come from a population that is normally distributed.
What is sample?Sample data is a subset of data taken from a larger population. It is used to estimate the characteristics of the larger population. Sample data is usually collected using a variety of methods such as surveys, experiments, and simulations. It is important to select a sample that accurately represents the population in order to draw reliable conclusions.
A normal probability plot is a graphical tool used to assess whether or not a sample of data could have come from a population that is normally distributed. The data is plotted on a graph, with the x-axis representing the sample values and the y-axis representing the quantiles of a normal distribution. If the points form a straight line, then the population is normally distributed.
In this situation, the sample data being studied is the wall thickness of O-rings. To create the normal probability plot, each sample value should first be converted to a standard normal deviate, which can be found using the standard normal distribution table. The standard normal deviate is then plotted against the sample values, and the points are connected to form a line. If the line is straight, then it can be concluded that the sample data could have come from a population that is normally distributed. If the line is curved, then the data does not fit the normal distribution.
The normal probability plot is a useful tool for assessing the normality of a sample of data. By plotting the sample values against the quantiles of a normal distribution, one can quickly determine whether the data could have come from a population that is normally distributed.
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At Cheng's Bike Rentals, it costs $22 to rent a bike for 4 hours. How many dollars does it cost per hour of bike use?
Answer:
Step-by-step explanation:
To find the cost per hour of bike use at Cheng's Bike Rentals, we need to divide the total cost of renting the bike by the number of hours it was rented for.
If it costs $22 to rent a bike for 4 hours, then the cost per hour is:
$22 / 4 hours = $5.50/hour
Therefore, it costs $5.50 per hour of bike use at Cheng's Bike Rentals.
Find the ordered pair solutions for the system of equations. ([?], f(x) = x² + 1 f(x) = -x + 3 ) and ( Enter the smallest x first.
The ordered pair solutions for the system of equations are (-2, 5) and (1, 2).
How to determine ordered pair?To determine if an ordered pair is a solution to two systems of equations, substitute the values of the variables into each equation. If an ordered pair makes both equations true, it is the solution of the system.
To find the ordered pair solutions for the system of equations, we need to solve the two equations simultaneously.
f(x) = x² + 1 ...(1)
f(x) = -x + 3 ...(2)
Setting the two equations equal to each other, we get:
x² + 1 = -x + 3
Rearranging this equation, we get:
x² + x - 2 = 0
Factoring this quadratic equation, we get:
(x + 2)(x - 1) = 0
Therefore, the solutions for x are x = -2 and x = 1.
Substituting these values of x into either equation (1) or (2), we get:
For x = -2: f(-2) = (-2)² + 1 = 5, and f(-2) = -(-2) + 3 = 5.
For x = 1: f(1) = 1² + 1 = 2, and f(1) = -1 + 3 = 2.
Therefore, the ordered pair solutions for the system of equations are (-2, 5) and (1, 2).
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The scatter plot shows prize money, in thousands of dollars, for a contest over eight consecutive years.
Predict the amount of prize money in year 10 of the contest.
A) $11,790
B) $20,340
C) $35,200
D) $45,900
Based on the information in the graph, it can be inferred that the amount of prize money in year 10 of the contest would be $11,790 (option A).
How to predict the amount of prize money in year 10 of the contest?To predict the amount of prize money in year 10 of the contest we must take into account the information of the image. As can be seen from year 1 to year 8, the amount of prize money has not had a very radical variation, but has remained in a range between 6,000 and 12,000.
Based on the foregoing, it could be inferred that for year 10 the amount of prize money does not fall outside these ranges. Then we could affirm that in year 10 the amount of prize money will be $11,790 because it is within the range in which this value has fluctuated.
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Given: QS/TV=RS/UV=3, QR=3TU
Prove: Triangle QRS ~ triangle TUV
A triangle is a geometrical shape that is formed by three straight lines connecting three non-collinear points. The three points are called the vertices of the triangle, and the lines connecting them are called sides or edges.
How to prove that the Triangle QRS ~ triangle TUV?To prove that triangle QRS is similar to triangle TUV, we need to show that their corresponding angles are equal and their corresponding sides are proportional.
Let's start by identifying the corresponding angles:
Angle QRS corresponds to angle TUV (they are both right angles)Angle QSR corresponds to angle TVU (they are opposite angles formed by intersecting lines)Angle RQS corresponds to angle UTV (they are opposite angles formed by intersecting lines)Now, let's look at the corresponding sides:
QS corresponds to TVRS corresponds to UVQR corresponds to TU (given)To prove that the triangles are similar, we need to show that the ratios of the corresponding sides are equal:
QS/TV = RS/UV (given)
QS/TV = 3/3 (since QR=3TU)
QS/TV = 1
RS/UV = 3/3 (since QR=3TU)
RS/UV = 1
Since the ratios of the corresponding sides are equal, the triangles are similar. Therefore, we can conclude that triangle QRS ~ triangle TUV.
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find the following angles
The result are Blank #1: 65°, Blank #2: 115°, Blank #3: 65°, Blank #4: 115°
What is Vertical angles?Vertical angles are pairs of angles that are formed by two intersecting lines or two intersecting line segments. These angles are opposite each other and are located at the opposite corners of the intersection.
Vertical angles, ∠BAD = ∠CAE
it means (x+75)° = (3x-5)°
so, x = 40°
1. ∠BAC = 180° - (x+75)° = 180 - (40 + 75) = 65°
2. ∠CAE = (3x-5)° = 3×40 - 5 = 115°
3. ∠DAE = ∠BAC = 65°
4. ∠BAD = (x+75)° = 40+75 = 115°
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Select the correct answer. Which number line represents the solution to |x − 21| < 3? A. B. C. D.
Number line that represents the solution to |x − 21| < 3 is C.
Tο sοlve the inequality |x - 21| < 3, we need tο find all the values οf x that are less than 3 units away frοm 21 οn the number line.
Starting frοm 21, we can cοunt 3 units tο the left and 3 units tο the right tο find the interval οf values that satisfy the inequality:
| x - 21 | < 3 can be written as -3 < x - 21 < 3
Adding 21 tο all parts οf the inequality gives:
18 < x < 24
Therefοre, the sοlutiοn tο the inequality is the interval οf values between 18 and 24, excluding the endpοints.
Lοοking at the answer chοices, we can see that οptiοn C represents this interval οf values:
A:
B:
C: |----|----|----|----|----|----|
18 19 20 21 22 23 24
D:
Therefore, the correct answer is C.
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