Expression of logarithms is log₅a³b = 3log₅a + log₅b.
Given expression is log₅a³b.
We have to express given expression as a sum or difference of logarithms.
We know the logarithmic formulas which is,
logₐ(PQ) = logₐP + logₐQ
logₐ([tex]P^{Q}[/tex]) = QlogₐP
we will use above formulas and solve the given equation.
log₅a³b = log₅a³ + log₅b
log₅a³b = 3log₅a + log₅b
Logarithms, like exponents, have many helpful properties that can be used to simplify logarithmic expressions ans solve logarithmic equation.
The product property states that to miltiply two powers that have the same base, add the exponents.
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Solve this equation by undoing
AKA solve for x
2x + 8 = 26
Step-by-step explanation:
[tex]2x + 8 = 26 \\ [/tex]
[tex]2x + 8 - 8 = 26 - 8[/tex]
[tex]2x = 18[/tex]
[tex]x = \frac{18}{2} \\ [/tex]
[tex]x = 9[/tex]
Answer:
[tex]\boxed{\tt x=9}[/tex]Step-by-step explanation:
[tex]\tt 2x + 8 = 26[/tex]
Subtract 8 from both sides:-
[tex]\tt 2x+8 \bf{-8}= \tt 26 \bf{-8}[/tex]
[tex]\tt 2x=18[/tex]
Divide both sides by 2:-
[tex]\tt \cfrac{2x}{\bf2}=\cfrac{18}{\bf2}[/tex]
[tex]\tt x=9[/tex]
___________________
Hope this helps!
Have a great day!
Find the missing side length.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit.in your answer.
7 yd
9 yd
L
13 yd
15 yd
4 yd
Answer: 8 yards
Step-by-step explanation:
15-7=8
Which one blue, light blue , yellow or red
Step-by-step explanation:
I just answered this. how often did you post this question ?
the answer is light blue.
A ball is thrown into the air vertically with a velocity of 112 feet per second.
Answer: It will reach the ground after 15 seconds. The force is 50.5%
Step-by-step explanation:
Plot the points (2, -1) and (7,-1) and find the slope.
Answer:
slope = 0Step-by-step explanation:
Slope =
[tex] \frac{change \: in \: y}{change \: in \: x} [/tex]
X1=2 X2=7
Y1=-1 Y2=-1
hence
[tex] \frac{ - 1 - ( - 1)}{7 - 2} [/tex]
[tex] \frac{ - 1 + 1}{7 - 2} [/tex]
[tex] \frac{0}{5} [/tex]
[tex]slope = 0[/tex]
evaluate the summation for the indicated value of the variable. 1(1!) 2(2!) 3(3!) 4(4!) m(m!); m
The summation for the indicated value of the variable is 23.
What is factorial?
The product of all positive integers less than or equal to n in mathematics is known as the factorial of a non-negative integer, indicated by the symbol n!. Additionally, the factorial of n is equal to the sum of n and the subsequent smaller factorial: For instance, According to the convention for an empty product, the value of 0! is 1.
Here, we have
Given
1(1!) +2(2!) +3(3!) + 4(4!)+......... m(m!)
By applying summation,
For m = 3, it will become,
= 1(1!) +2(2!) +3(3!)
Now we open factorization and we get
= 1(1) +2(2×1) +3(3×2×1)
= 1 + 4 + 18
= 23
Hence, the summation for the indicated value of the variable is 23.
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two events are mutually exclusive if . a. the probability of their intersection is .5 b. the probability of their intersection is 1 and they have no sample points in common c. the probability of their intersection is 1 d. they have no sample points in common
Two events are mutually exclusive if the probability of their intersection is 0 and they have no sample points in common. Hence, option D is the correct answer.
The two events are called mutually exclusive when they have no sample points in common. Thus, the probability of event A and event B happening is zero. this means that their intersection set is the empty set.
let us take an example-
Let A be a set of odd numbers and B be a set of even numbers.
A = {1,3,5,7,9}
B = {0,2,4,6,8}
A ∩ B = { }
Hence, the two sets - A and B are mutually exclusive of each other.
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One year, the population of a city was 312,000. Several years later it was 274,560. Find the percent decrease.
The percent decrease will be;
⇒ 12%
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
One year, the population of a city was 312,000.
Several years later it was 274,560.
Now,
Since, One year, the population of a city was 312,000.
Several years later it was 274,560.
Hence, The percent decrease is find as;
⇒ Percent = (312,000 - 274,560) x 100 / 312,000
= 12 %
Thus, The percent decrease will be;
⇒ 12%
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Using Pythagoras' theorem, calculate the length of YZ.
Give your answer in centimetres (cm) to 1 d.p.
17 cm
5 cm
The length of two sides is given as 17 cm and 5 cm, then the length of side YZ by Pythagoras' theorem will be equal to 16.25 cm.
What is a Pythagoras' Theorem?According to the Pythagoras theorem, the square on the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of squares of the remaining two sides.
As per the given values in the question,
The length of two sides is given as 17 cm and 5 cm.
As per Pythagoras' theorem,
h² = p² + b²
17² = 5² + b²
b² = 289 - 25
b = √264
b = 16.25 cm.
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a high school senior uses the internet to get in- formation on february temperatures in the town where he’ll be going to college. he finds a web site with some sta- tistics, but they are given in degrees celsius. the conver- sion formula is °f
It reaches a high of 51.8 degrees Fahrenheit. There is a 59.4 degree F range. 12.6 degrees Fahrenheit is the standard deviation. The average temperature is 33.8°F. The median temperature is 35.6 °F. IQR is 60.8 degrees Fahrenheit.
What is statistics?The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem. The study of gathering, analyzing, interpreting, presenting, and organizing data in a particular way is the focus of the mathematic branch known as statistics. The process of gathering data, classifying it, presenting it in a way that makes it understandable, and then conducting additional analyses of the data is known as statistics.
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a research engineer for a tire manufacturer is investigating tire life for a new rubber compound and has built 16 tires and tested them to end-of-life in a road test. the sample mean and standard deviation are 60,139.7 and 3505.42 kilometers. can you conclude, using ????
There is no sufficient evidence to indicate the true standard deviation is less than 4000.
What is the standard deviation?
The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.
given that n = 16
x = 60139.7
s = 3718.06
∝ = 0.05
To test the hypothesis
H0 : = 4000
H1 : < 4000 (claim)
test statistics
x² = ((n-1)s²) / H0²
= (15 * 13823970.16) / (16000000)
= 12.96
P- value = P [x² < 12.96] DF = n-1 = 15
= 0.3946
0.1 < P-value <0.5
Hence, there is no sufficient evidence to indicate the true standard deviation is less than 4000.
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when given two figures or their coordinates, how do you determine which is the preimage (the original) and which is the image (the transformed one)?
A preimage (the original) is the two-dimensional shape before any transformation. The image (the transferred one) is the figure after transformation.
A transformation is a process that manipulates a polygon or other two-dimensional object an a plane or coordinate system. Mathematical transformations describe how two-dimensional figures move around a plane or coordinate system.
Following are the types of transformations:-
Dilation, Reflection, Rotation, Shear, Translation.
Preimage is the set of all elements of the domain that are mapped into a given subset of the co-domain.
A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
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Classify each number according to its value. 2.1 × 10-4 9.2 × 10-4 3.4 × 10-5 2.1 × 10-3 2.8 × 10-7 8.3 × 10-5 7.2 × 10-5
According to the information, the numbers are classified as follows: Greater than 8.2 x 104 = None; between 8.2 x 10⁴ and 8.2 x 10⁻⁶ : 2.1 x 10⁻⁴, 9.2 x 10⁻⁴, 3.4 x 10⁻⁵, 2.1 x 10⁻³, 8.3 x 10⁻⁵, 7.2 x 10⁻⁵; and less than 8.2 x 10⁻⁵: 2.8 x 10⁻⁷.
How to find the classification of numbers?To find the classification of numbers we must know how scientific notation works and know how to classify these numbers. According to its scientific notation, if we want to classify numbers greater than 8.2 x 10⁴ we must take the following into account:
All numbers with a power greater than 10⁴ would be greater than 8.2. Therefore, none of the options would be greater than this number.
In the second case, to find the numbers that are between 8.2 x 10⁴ and 8.2 x 10⁻⁶ we must look at the same element, that is, the numbers that have a power less than 10⁴ and greater than 10⁶ would be in the range of this exercise. So the numbers in this range would be:
2.1 x 10⁻⁴9.2 x 10⁻⁴3.4 x 10⁻⁵2.1 x 10⁻³8.3 x 10⁻⁵7.2 x 10⁻⁵In the third case, to identify the numbers that are less than 8.2 x 10⁻⁵ we must take into account the same element. If power is less than 10⁻⁵, they would classify in this interval. So the values that classify are:
8.2 x 10⁻⁷Note: This question is incomplete because there is some information missing. Here is the complete information:
Greater than 8.2 x 104
Between 8.2 x 104
and 8.2 x 10-6
Less than 8.2 x 10-5
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The bottom of a swimming pool is 12 feet below the surface of the water.
What is the pool's depth in feet?
Enter your answer as an integer.
If it is negative, enter it like this: -42
Answer:12 feet
Step-by-step explanation:
a particular football team is known to run 30% of its plays to the left and 70% to the right. a line backer on an opposing team note that the right guard shifts his stance most of the time (80%) when plays go to the right and he uses a balanced stance the remainder of the time. when plays go to the left, the guard takes a balanced stance 90% of the time and the shift stance the remaining 10%. on a particular play, the line backer notes that the guard takes a balanced stance. i) find the probability that the play will go the left ii) find the probability that the play will go the right iii) if you were the line backer, which direction would you prepare to defend if you saw the balanced stance.
i)The probability that the play will go to the left is 0.659
ii)the probability that the play will go the right is 0.341
iii) The direction I would prepare to defend if I saw the balanced stance if I were the line breaker is It's better to be ready to protect the left side since the likelihood of a play coming via that side so when the right tackle has a balancing stance is nearly double that of a play going it through right because when right guard maintains a neutral position.
Taking the left first
When play travels via the left 30% of the time, the right guard assumes a balanced stance 90% of the time, for a total of 0.9 0.3 = 27%.
- He adopts a new posture. 10% of the time, play goes through the left = 0.1 0.3 = 3% of the time.
70% of the time, play goes through the right.
- He takes a balanced posture 20% of the time that play travels through the right, for a total of 0.7 0.2 = 14%.
- He assumes a shift stance 80% of the time that play travels via the right, for a total of 0.7 0.8 = 56%.
The right guard then assumes a balanced posture 27% of the time + 14% of the time = 41% of the time.
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what is the probability of getting either a spade or an ace when drawing a single card from a deck of 52 cards?
When drawing one card from a deck of 52 cards, the probability of obtaining either a spade or an ace are 4/13.
Given,
Number of cards in a deck = 52
Number of spades = 13
Number of aces = 4
Number of ace of spade = 1
We have to find the probability of getting either a spade or an ace when drawing a single card from the deck;
Here,
Probability of either a spade or an ace :
P(spade or ace) = P(spade U ace)
P(spade U ace) = p(spade) + p(ace) - p(spade n ace)
Now,
Probability = required outcome / Total possible outcomes
P(spade) = 13 / 52
P(ace) = 4 / 52
P(spade n ace) = 1 / 52
Then,
P(spade U ace) = p(spade) + p(ace) - p(spade n ace)
= 13/52 + 4/52 - 1/52
= 16 / 52 = 4 /13
That is,
The probability of getting either a spade or an ace when drawing a single card from a deck of 52 cards is 4/13
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the sum of ellies's age and genya's age is 60. in six years, genya will be eigth times as old as ellie will be. how old is ellie now
The sum of ellies's age and genya's age is 60. in six years, genya will be eigth times as old as ellie now ellie old is 2 years.
Given:
the sum of ellies's age and genya's age is 60. in six years, genya will be eigth times as old as ellie will be.
Let x and y be the ellie's and genya's ages.
x + y = 60
After 6 years x+6 and y +6.
8(x + 6) = y + 6
8x + 48 = y + 6
8x + 42 = y
8x - y = -42
sum of two equations
x + y + 8x - y = 60 + (-42)
x + 8x = 60 - 42
9x = 18
divide by 9 on both sides
9x/9 = 18 / 9
x = 2
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a rectangle has a length of 1 inches and a width of 6 inches whose sides are changing. the length is increasing by 4 in/sec and the width is shrinking at 2 in/sec. what is the rate of change of the perimeter?
The rate of change of the perimeter of a rectangle is 4 in/sec.
What is the perimeter of a rectangle?
The whole length of the outline is referred to as the perimeter of a two-dimensional shape. We add the lengths of all four corners of a rectangle to find its perimeter. Since the opposite sides of a rectangle are always equal, we must determine the length and width of the rectangle in order to determine its perimeter. The rectangle's perimeter can be expressed as twice the sum of its length and width.
Given, the length of a rectangle, L = 1 inches
width of a rectangle, W = 6 inches
rate of increasing length, dL/dt = +4 in/sec
rate of decreasing width, dW/dt = -2 in/sec
Now, the perimeter of a rectangle is given by
P = 2L + 2W
Then, the rate of change of the perimeter is
dP/dt = 2 * ( dL/dt) + 2*(dW/dt )
= 2*(+4) + 2*(-2)
= 8-4
= 4 in/sec
Hence, the rate of change of the perimeter is 4 in/sec.
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Which of the following types of radiation has charge? Select all that apply; this Is.a multiple = cholce question: gamma alpha beta positron
Alpha, Beta and Positron carries charges.
What are Nuclear Reactions?
When a more stable element is to be formed, nuclear reactions frequently produce or capture particles or radiation. The names of several nuclear reactions are given using these particles since they play a significant role in the reaction.
Alpha carries high energy helium nuclei consisting of two protons and two neutrons which makes it a positive particle.
Beta is a high energy electron which is a Negative particle.
Positrons are particles with the same mass as an electron but with 1 unit of positive charge which makes it a Negative particle.
Gamma rays are not particles but carries a very high-energy electromagnetic radiation.
Hence, Alpha is a positive charged particle, Beta is a negative charged particle and Positron is a negative charged particle.
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use the normal distribution to approximate the following binomial distribution: a convenience store owner claims that 55% of the people buying from her store, on a certain day of the week, buy coffee during their visit. a random sample of 35 customers is made. if the store owner's claim is correct, what is the probability that fewer than 20 customers in the sample buy coffee during their visit on that certain day of the week? a) exam image b) exam image c) exam image d) exam image e) exam image f) none of the above.
The probability that fewer than 20 customers in the sample buy coffee during their visit on that certain day of the week is 59.87%
What is the normal distribution?
A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.
The formula for z-score is z = (x -μ)/σ
Where,
Z is standard score.
X is observed value.
μ is mean of the sample.
σ is standard deviation of the sample
Given that 55% of the customers buy coffee, hence p = 55% = 0.55
Sample of 35 customers, hence n = 35.
For the normal distribution μ = np, σ = √[np(1-p)]
The mean and the standard deviation of the approximation are:
μ = 35 ˣ 0.55 = 19.25
σ = √[35 ˣ 0.55(1-0.55)] =2.943
Using continuity correction, the probability that fewer than 20 customers in the sample buy coffee during their visit on that certain day of the week is P(X < 20 - 0.5) = P(X < 19.5), which is the p-value of Z when X = 19.5, hence:
z = (20 -19.25)/2.943
z = 0.25 has a p-value of 0.5987.
0.5987 =59.87%
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g how many ways are there to choose the exec board so that there is at least one masters student and one phd student? (for any of the 4 positions)
The board has a total of 78960006 options from which to select at least one master's and one PhD candidate.
Given,
Total number of students = 8000
Number of Phd students = 5000
Number of masters students = 3000
Number of members in Student Government Executive Board = 4
We have to find the number of ways to choose the exec board so that there is at least one masters student and one Phd student;
Here,
There are 3,000 different ways to have one Master student on the board.
After choosing a masters student, there are 5,000 different methods to have a PhD student on the board.
The number of possible ways to choose the final two members = 7998!/(7998 - 2)!
That is,
5,000 3,000 + 7998!/(7998 - 2) = 78960006
Therefore,
78960006 is the total number of ways the board can choose at least one masters and one PhD.
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in a marketing survey, 60 people were asked to rank three flavors of ice cream, chocolate, vanilla, and strawberry, in order of their preference. all 60 people responded, and no two flavors were ranked equally by any of the people surveyed. if three fifths of the people ranked vanilla last, one tenth of them ranked vanilla before chocolate, and one third of them ranked vanilla before strawberry, how many people ranked vanilla first?
The number of people who ranked vanilla first out of total 60 people is 2.
Define the term linear equation?First order equations include linear equations. In the coordinate system, the linear equations is defined for lines. When a homogeneous factor of degree 1 is present in the equationFor the stated question-
Total number of people = 60.
vanilla last: 3/5×60 = 36
vanilla before chocolate: 1/10×60 = 6
vanilla before strawberry: 1/3×60 = 20
Rank of 3 flavours are-
1st place | 2nd place | 3rd place
Vanilla | Chocolate | StrawberryVanilla | Strawberry | Chocolate Chocolate | Strawberry | Vanilla Chocolate | Vanilla | Strawberry Strawberry | Chocolate | Vanilla Strawberry | Vanilla | ChocolateThus,
vanilla last : 3/5 = 36
C + E = 36 ...eq 1
Vanilla ahead of Chocolate -1/10
A + B + F = 6 ...eq 2
Vanilla ahead of Strawberry- 1/3
A + B + D = 20 ...eq 3
Add all three equations-
A + B + F + A + B + D + C + E = 36 + 6 + 20
A + B + A + B + C + D + E + F = 62
60 people with no ties;
A + B + C + D + E + F = 60
A + B + A + B + C + D + E + F = 62
A + B + 60 = 62
A + B = 62 - 60
A + B = 2
Thus, the number of people who ranked vanilla first is 2.
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11.30 fcat scores and poverty. in the state of florida, elemen- tary school performance is based on the average score obtained by students on a standardized exam called the florida comprehensive assessment test (fcat). an analysis of the link between fcat scores and sociodemo- graphic factors was published in the journal of educational and behavioral statistics (spring 2004). data on average math and reading fcat scores of third graders, as well as the percentage of students below the poverty level, for a sample of 22 florida elementary schools are listed in the table on p. 629.
Math: s=11.2996s=11.2996, Reading: s=14.4128s=14.4128 for the performance in the elementary school of Florida.
What is meant by statistics?The study of data collection, analysis, presentation, and interpretation is known as statistics. Much of the early push for the subject of statistics came from government needs on census in addition to data on a range of economic operations. The current requirement to convert vast volumes of data accessible in many applied disciplines into valuable information has driven both theoretical and practical breakthroughs in statistics.
The facts and statistics that are gathered, standardized, and condensed for presentation and interpretation are known as data. The two types of data are quantitative and qualitative, respectively. Quantitative data quantify how much or how many of something exists, whereas qualitative data offer labels or names for groups of similar objects.
How to solve?
We need to determine whether the math core or the reading score better predicts the percentage of students below the poverty level.
The standard error s=11.2996s=11.2996 for the math scores is less than the standard error s=14.4128s=14.4128 for the reading scores, thus the math scores will result in better prediction.
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What is 504.08 rounded to the nearest whole number?
Answer:
Step-by-step explanation:
So let’s look at the hundredths place. You round .08 to the tenth. So that would be 504.1 then you round the tenths place (the one) to the nearest whole number. But you can’t do that so the answer will be 504. No decimal needed. Or you could’ve just looked at the original number, 504.08 and understood that since there is no number in the tenths place then the answer would be 504.
Answer: 504
Step-by-step explanation:
using the histogram with the normal curve displayed, please determine each of the following values. remember that z
A Z-score is a metric that quantifies the connection between a value and the mean of a set of values.
z-scores are calculated by (observed value - mean)/standard deviation
Mean = 40
Standard Deviation = 8
Observed Value = 52
z-score = (52 - 40)/8 = 2
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pls answer pls brainly
Answer: its 500
Step-by-step explanation:
Answer: mark one point after the half mark between 1 and 2, and then the half point between 2 and 3.
Step-by-step explanation: hope this helps!
a popular soft drink is sold in 2-liter (2,000-milliliter) bottles. because of variation in the filling process, bottles have a mean of 2,000 milliliters and a standard deviation of 18, normally distributed. if the manufacturer samples 100 bottles, what is the probability that the mean is less than 1,998 milliliters?
The probability that the mean is less than 1,998 milliliters is 0.11%
To solve this problem, it is important to understand the normal probability distribution and the central limit theorem
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean μ and standard deviation σ , the z-score of a measure X is given by:
Z = (X -μ) / σ
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p value, we get the probability that the value of the measure is greater than X.
Central Limit theorem
The Central Limit Theorem establishes that, for a random variable X, with mean and standard deviation σ, a large sample size can be approximated to a normal distribution with mean μ and standard deviation δ = σ /√n
In this problem, we have that:
μ = 2000, σ = 18
If the manufacturer samples 100 bottles, what is the probability that the mean is less than 1998 milliliters
So n =100,
δ=18/√100 = 1.8
This probability is the p value of Z when X = 1998. So
Z = (X -μ) / σ
By the Central Limit Theorem
Z = (X -μ) /δ
Z = (1998 -2000) / 1.8
Z = -1.11 has a p-value of 0.0011
So, 0.11% probability that the mean is less than 1998 milliliters.
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Mark is solving an equation where one side is a quadratic expression and the other side is a linear expression. He
sets the expressions equal to y and graphs the equations. What is the greatest possible number of intersections for
these graphs?
Onone
Oone
Otwo
O infinitely many
The maximum number of intersections for the graphs is two.
What is meant by Quadratic expression?A quadratic equation is any equation in algebra that may be rearranged in standard form as:
When x denotes an unknown value while a, b, and c denote known numbers In general, one assumes that a = 0; equations with a = 0 are considered degenerate since the equation becomes linear or even simpler. The numbers a, b, and c are the equation's coefficients, which can be separated by referring to them as the quadratic coefficient, linear coefficient, and constant or free term, respectively.
The task material indicates that the two graphs involved are linear and quadratic graphs.
A quadratic graph produces a parabola, while a linear graph produces a straight line. As a result, the best instance of intersection is when the straight line crosses over the parabola, resulting in two points of intersection.
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You round jumpys time to the nearest tenth of a second, that jumpys time is 19.6 seconds
Answer:
20 seconds
Step-by-step explanation:
Solve.
7 2/5=2/3x−4 1/2
Enter your answer as a mixed number in simplest form in the box.
x =
Answer:
Step-by-step
pp
Answer:
7 2/5=2/3x-4 1/2
37/5=2/3x-9/2 /×30
30×37/5=30×2/3x+30×(-9/2)
222=20x-135
-20x=-135-222
-20x=-357
20x=357
x=357/20
x=17 17/20