Mathematics College

The length of the hypotenuse of a right triangle is 157 units. The length of one leg of the triangle is 132. Lara wrote the following step to find the length of the unknown leg: Length of the unknown leg = 1572 – 1322 = 24,649 – 17,424 = 7,225 units Which statement best explains whether Lara's step is correct or incorrect? It is correct because the length of the unknown side is the difference of the lengths of the sides. It is correct because the length of the unknown side is the difference of the squares of the sides. It is incorrect because the length of the unknown side is the square root of 42,073. It is incorrect because the length of the unknown side is the square root of 7,225.

Answers

Answer 1

the correct answer for this is the last choice:

It is incorrect because the length of the unknown side is the square root of 7,225.

Answer 2

Answer:

It is incorrect because the length of the unknown side is the square root of 7,225.

Step-by-step explanation:

Related Questions

A movie rental gives a free popcorn to every 15th customer and a free movie rental to every 4th customer. Which customer was the first to win both prizes?

Answers

The 60th customer will win both prizes.

In both cases, start with 0.

Every 15th customer includes #15, #30, #45, #60, etc.

Every 4th customer includes #4, #8, #12, #16, #20, #24, #28, #32, #36, #40, #44, #48, #52, #56, #60

#60 is the first customer to win both prizes.

What is the value of log5 125

Answers

Answer:

[tex]log_5125=3[/tex]

Step-by-step explanation:

Given : [tex]log_5125[/tex]

We have to find the value of [tex]log_5125[/tex]

Consider the given expression [tex]log_5125[/tex]

Rewrite 125 in power- base form, [tex]125=5^3[/tex]

[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)[/tex]

[tex]\log _5\left(5^3\right)=3\log _5\left(5\right)[/tex]

[tex]=3\log _5\left(5\right)[/tex]

[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(a\right)=1[/tex]

[tex]\log _5\left(5\right)=1[/tex]

[tex]3\log _5\left(5\right)=3[/tex]

Thus, [tex]log_5125=3[/tex]

The value of log_5 125 is 3.

We have,

To find the value of log base 5 of 125, we need to determine the exponent to which we need to raise 5 to obtain 125.

In other words,

What power do we need to raise 5 to in order to get 125.

So,

By evaluating 5³ (5 raised to the power of 3), we find that 5³ = 125.

So, log base 5 of 125 is equal to 3, as log base 5 of 125 = 3.

So,

log base 5 of 125 equals 3 because 5 raised to the power of 3 gives us 125.

Thus,

The value of log_5 125 is 3.

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Trevor had 4 small boxes of raisins to share equally among himself and 2 friends.

How many boxes of raisins would each person receive?

A.

B.

C.

D.

Answers

Divide: 4 boxes / 3 persons = (4/3) box per person.

thirty-eight and ninety-seven hundredths kilograms in standard form

Answers

Standard form - Regular typing and writing with numbers

so it's 38.97 kg

Answer:

The answer is 38.97 kilograms.

Step-by-step explanation:

Thirty-eight and ninety-seven hundredths kilograms in standard form is 38.97 kilograms.

Thirty eight is simply 38.

And ninety-seven hundredths means that 97 is written after decimal. This is because when there exists an 'and' in a mathematical number, this means there is a decimal.

So, the answer is 38.97 kilograms.

which equation is not true for the solution x = -8

Answers

-3 1/4 ≠ 1/3x-2 3/4

Explanation: I tried all the other answers and the results match the expression, however, when I plug in -8 into this equation, the results are not equivalent.

HELP ME

On a Saturday, Tyler earned $97.20 waiting tables at a restaurant. He earned $9.25 an hour, and an additional $60.20 in tips. How many hours did he work that day? (Write and solve an equation to solve this problem.)

sorry my writing is messy

Answers

$97.20 divided by $9.25 is 10 hours

Gwen, Tristan, and Keith like to work out at the gym. They each have an app on their phone that estimates the calories they burn. By the time Tristan and Keith started exercising, Gwen had already burned 100 calories. Gwen burns 10 calories every minute, Tristan burns 125 every 10 minutes, and Keith burns 300 calories every 30 minutes. Let x represent the number of minutes since Tristan and Keith started exercising and y represent the number of app-estimated calories burned. Part A

Answers

For part A)
Let's make a function for each person, and then combine them to find total calories
Gwen burns 10 cal/min, and had already burned 100 calories when Tristan and Keith started (Yg=100 when x=0)
Yg= 10x + 100
Tristan burns 125 cal every 10 minutes, or 12.5 cal every minute.
Yt= 12.5x
Keith burns 300 calories every 30 min, or 10 calories every minute.
Yk= 10x
Add Yg, Yt, and Yk to find the general function y:
y=10x +100 + 12.5x + 10x
y = 32.5x + 100

Answer:

For part A)

Let's make a function for each person, and then combine them to find total calories

Gwen burns 10 cal/min, and had already burned 100 calories when Tristan and Keith started (Yg=100 when x=0)

Yg= 10x + 100

Step-by-step explanation:

I got a 100% on it.

If 5+6i is a root of the polynomial function f(x),which of the following must also be a root of f(x)

Answers

The complex conjugate root theorem states that if a+bi (with a and b being numbers) is a root, then a-bi is also a root. Plugging that in here, this means that 5-6i is also a root

Answer:

5 - 6i must also be a root of f(x)

Step-by-step explanation:

Complex conjugates states that the two complex numbers are conjugates of each other if they have the same real part and their imaginary parts are negatives of each other i.e, the complex conjugate of a + bi is a - bi where i is imaginary.

Conjugate root theorem states that if the complex number a + bi is a root of a polynomial P(x) in one variable with real coefficients, then the complex conjugate a-bi is also a root of that polynomial.

Given: if 5+ 6i is a root of the polynomial function f(x).

then,

by the conjugate root theorem;

5 - 6i is also be a root of the polynomial f(x).

Roger can run one mile in 8 minutes. jeff can run one mile in 6 minutes. if jeff gives roger a 1 minute head start, how long will it take before jeff catches up

Answers

recall your d = rt, distance = rate * time.

now, if Roger can do 1 mile in 8 minutes, so in 1 minute, he has done then 1/8 of a mile, so his rate is 1/8 miles per minute.

if Jeff can do 1 mile in 6 minutes, he's faster, in 1 minute he has done 1/6 of a mile, so his rate is 1/6 miles per minute.

now, when Jeff catches up with Roger, the distance covered by both will be the same, say "d" miles, because, at that millisecond, Jeff will be neck and neck with Roger, and their covered distance will be the same.

now, Jeff is generous and let Roger roll on for 1 minute before him, so, by the time time Roger has covered "d" miles, he has been running for say "t" minutes.

however, since Jeff started later by 1 minute, he hasn't been running for "t" minutes, but for "t - 1" minutes.

[tex]\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mpm}{rate}&\stackrel{minutes}{time}\\ &------&------&------\\ Roger&d&\frac{1}{8}&t\\\\ Jeff&d&\frac{1}{6}&t-1 \end{array} \\\\\\ \begin{cases} \boxed{d}=\frac{1}{8}t\\\\ d=\frac{1}{6}(t-1)\\ ------\\ \boxed{\frac{1}{8}t}=\cfrac{t-1}{6} \end{cases} \\\\\\ \cfrac{t}{8}=\cfrac{t-1}{6}\implies 6t=8t-8\implies 8=2t\implies \cfrac{8}{2}=t\implies \boxed{\stackrel{mins}{4}=t}[/tex]

Find the first partial derivatives of the function. f(x, y) = ax + by/ cx + dy

Answers

Final answer:

The partial derivatives of the given function f(x, y) = ax + by / cx + dy with respect to x and y have been calculated, showing how the function changes with each variable while holding the other constant.

Explanation:

For the function f(x, y) = ax + by / cx + dy, the first partial derivatives with respect to x and y are:

∂f/∂x = a(cy - by') / (cx + dy)²∂f/∂y = (ax - ay) / (cx + dy)²

These partial derivatives measure the rate of change of the function f(x, y) with respect to x and y while treating the other variable as constant.

explain how you could convert a rate of 18000 miles per hour to miles per second

Answers

You could multiply that fraction by (1 hour / 3,600 seconds) .

   (18,000 mile / 1 hour) x (1 hour / 3,600 second) =

   (18,000 x 1) / (1 x 3,600) (mile-hour) / (hour-second) =

   (18,000 / 3,600) (mile / second) =  5 mile/second

18000 miles / 1 hour)(1 hour / 60 minutes)(1 minute / 60 seconds) =

18000 miles / 3600 seconds =

5 miles / 1 second

5 miles per second

Divide (8.6 x 108) by (3.2 x 103). Express your answer in scientific notation.

Answers

In doing this division, we will first divide the 8.6 by the 3.2 to get 2.6875. Thankfully, that number is already in scientific notation so we don't have to worry about changing it. Now for the rest of the problem. When the bases are the same, and they are both 10's, you subtract the exponents. [tex]10^{8-3}[/tex] gives us 10^5. The answer then in scientific notation is [tex]2.6875*10^5[/tex].

For the expression below, write an equivalent expression that involves x only. assume x is positive.

Answers

Could you please elaborate on this question, which expression below. I will gladly help answer your inquires.

(b) how many measurements must be averaged to get a margin of error of ±0.0001 with 98% confidence? (round your answer up to the nearest whole number.)

Answers

Given that the scale readings of the laboratory scale is normally distributed with an unknown mean and a standard deviation of 0.0002 grams.

Part A:

If the weight is weighted 5 times and the mean weight is 10.0023 grams, the 98% confidence interval for μ, the true mean of the scale readings is given by:

[tex]98\% \ C. \ I.=\bar{x}\pm z_{\alpha/2}\left(\frac{\sigma}{\sqrt{n}}\right) \\ \\ =10.0023\pm2.33\left(\frac{0.0002}{\sqrt{5}}\right) \\ \\ =10.0023\pm2.33(0.000089) \\ \\ =10.0023\pm0.00021 \\ \\ =(10.0023-0.00021, \ 10.0023+0.00021) \\ \\ =(10.0021, \ 10.0025)[/tex]

Thus, we are 98% confidence that the true mean of the scale readings is between 10.0021 and 10.0025.

Part B:

To get a margin of error of +/- 0.0001 with a 98% confidence, then

[tex]\pm z_{\alpha/2}\left(\frac{\sigma}{\sqrt{n}}\right)=\pm0.0001 \\ \\ \Rightarrow2.33\left(\frac{0.0002}{\sqrt{n}}\right)=0.0001 \\ \\ \Rightarrow\left(\frac{0.0002}{\sqrt{n}}\right)= \frac{0.0001}{2.33} =0.0000429 \\ \\ \Rightarrow\sqrt{n}= \frac{0.0002}{0.0000429} =4.66 \\ \\ \Rightarrow n=4.66^2=21.7156\approx22[/tex]

Therefore, the number of measurements that must be averaged to get a margin of error of ±0.0001 with 98% confidence is 22.

Final answer:

To find the number of measurements that must be averaged to get a margin of error of ±0.0001 with 98% confidence, you can use the formula for the margin of error.

Explanation:

To find the number of measurements that must be averaged to get a margin of error of ±0.0001 with 98% confidence, we can use the formula for the margin of error:

Margin of Error = Z * (Standard Deviation / √(Sample Size))

Given that we want a margin of error of ±0.0001 and a confidence level of 98%, we can find the corresponding Z-value using a standard normal distribution table.

Once we have the Z-value, we can rearrange the formula to solve for the sample size, which represents the number of measurements that must be averaged.

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Which of the following sets of points is a direct variation?

(0, 0); (2, 4); (5, 15)
(0, 0); (-1, -2); (1, 2)
(3, 6); (-2, 4); (-1, 2)
(0, 5); (1, 6); (2, 7)

Answers

I got the second one. Good Luck. Hope it helped.

Answer:

(0, 0); (-1, -2); (1, 2) and (0, 5); (1, 6); (2, 7).

Step-by-step explanation:

The set will have a direct variation if each pair is added or subtracted by a common number in each component. You also can see it graphically, if the points form a straight growing line then the set is a direct variation. Then,

In the first set we have

(0,0), (0+2,0+4), (0+2+3, 0+4+11). The behavior is not uniform, then it is not a direct variation.

Second set: (-1, -2); (0,0); (1, 2)

(-1,-2)(-1+1,-2+2), (-1+1+1, -2+2+2). The behavior is uniform and it is increasing, then it is a direct variaton.

Third set:

(-2, 4), (-2+1,4-2), (-2+1+4, 4-2+4). The behavior is not uniform, then it is not a direct variation.

Fourth set:

(0,5), (0+1, 5+1), (0+1+1, 5+1+1). The behavior is uniform and it is increasing, then it is a direct variaton.

Use substitution to determine which of the following points is a solution to the standard form equation below. 2y = 5

Answers

2.5=y is the answer to the problem and if its wrong you didn't show me the answers

263,148 what is the value of the digit 6 in this number?

Answers

the ten thousands place

sixty thousand

hope this helps :)

sixth thousand hope it helps

How do you represent any number in an equation?

Answers

any unknown number in an equation you represent with a variable

You can represent it as a variable.

Which number is a prime number??

111
121
131
141

Answers

The prime number you are looking for is 141

Final answer:

Among the given options, the number 131 is a prime number, as it only has two divisors: 1 and itself.

Explanation:

The student has asked to identify which number among the given options is a prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Analyzing the given options:

111 is divisible by 3.

121 is divisible by 11 (11 x 11).

131 is a prime number because it has no divisors other than 1 and itself.

141 is divisible by 3.

Therefore, the correct answer is 131, which is a prime number.

Carol ate 2/5 of the cake, Dima ate 3/8 of the REMAINING cake, mom ate the rest.
If it was a POUND cake, how many OZ did MOM eat? PLEASE HELP ASAP, GIVING BRAINLIEST.

Answers

she would've eaten half of the cake, or 8 oz.

Her mum ate 31/40 of the cake

Given the weight of the cake to 1 pound

If Carol ate 2/5 of the cake, the remaining fraction of the cake will be 1 - 2/5 = 3/5

If Dima ate 3/8 of the REMAINING cake, then the fraction of cake Dima ate will be:

Dima = 3/8 * 3/5

Dima = 9/40

Fraction of the cake that her mum ate = 1 - 9/40 = 31/40

Hence her mum ate 31/40 of the cake

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If one side of a square notebook measures 20 cm, what is the area of the front cover of the notebook?

Answers

Salutations!

We know tat square has equal sides, so we will just multiply 20 twice as in [tex]S*S[/tex] or [tex]S^2[/tex]. Both of them are equal.

Area of the front cover of the notebook = [tex]s^2[/tex]

= [tex]20*20[/tex]

= [tex]400cm^2[/tex]

Hope I helped (:

have a great day!

Theoretically, what would happen if a nation had an unlimited supply of a certain resource?

Answers

There are several ways this could go, this is my theory. This would be very dangerous because if one Nation had an unlimited supply of a certain resource, other Nations would possibly go to war. Also, the Nation would have trouble controlling its citizens, immigration, and power.

Suppose that a person with a push mower can mow a large lawn in 2 hours, whereas the lawn can be mowed with a riding lawn mower in 1 hours. working together, how long will it take to mow the lawn

Answers

Working together, the job takes x hours to do.

If a lawn can be mowed with a push mower is 2 hours, then in 1 hour, you do 1/2 of the job.

If the same lawn can be mowed with a riding mower in 1 hour, then in 1 hour you do 1 job.

If the same lawn can be mowed by the two mowers together in x hours, then in 1 hour you get 1/x done.

1/2 + 1 = 1/x

3/2 = 1/x

x = 2/3

They take 2/3 of an hour. 2/3 * 60 min = 40 minutes.

2/3 hours take to mow the lawn.

what is Fraction?

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.

Given:

Time taken to mow by push mower= 2 hours

Time taken to mow by riding mower= 1 hours

So, if working together the time taken

= 1 / (1/2 + 1/1)

=1/ (3/2)

= 2/3

Hence, it will take 2/3 hours.

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show the zero property of multiplication using the number 25

Answers

Anything divided by 0 is 0 for example 25x0=0 12020202020x0=0

What is 1/7^9 × 1/7^-6

Answers

[tex]\bf \cfrac{1}{7^9}\cdot \cfrac{1}{7^{-6}}\implies \cfrac{1\cdot 1}{7^9\cdot 7^{-6}}\implies \cfrac{1}{7^{9-6}}\implies \cfrac{1}{7^3}\implies \cfrac{1}{343}[/tex]

what is 79.4÷8 what is the answer in decimal form

Answers

79.4 / 8 is;

9.925. Hope this helps you.

Divide 8 into 79.4, either by hand or with a calculator:

9.925 (this is in decimal fraction form)

Write three decimals that have a sum of 27.905. Parts of the needed decimals are listed below! thanks!

14. + 8. + 4. = 27.905

Answers

we have to add three decimals that have a sum of 27.905
parts that are given is 14. + 8. + 4.
if we add these we get the sum of 26, so we need 1.905 more, if we add 0.95 + 0.5 + 0.5 we get 1.905
So, if the numbers are 14.905, 8.50 + 4.50 and we add these numbers we get the answer 27.905
14.905 + 8.50 + 4.50 = 27.905
Thus, the three decimals that have sum of 27.905 are 14.905, 8.50 and 4.50.

jillian bought 1/2 pound of turkey and 1 1/3 pound of cheddar cheese at the deli. both items are on sale for $6 per pound. how much does each turkey cost>

Answers

To calculate the cost of the turkey, multiply the weight of the turkey (1/2 pound) by the cost per pound ($6). The total cost for the turkey is $3.

Jillian bought 1/2 pound of turkey and 1 1/3 pounds of cheddar cheese at the deli, with both items on sale for $6 per pound. To find out how much the turkey costs, you need to multiply the weight of the turkey by the cost per pound. Here's how you do it:

Determine the weight of the turkey: 1/2 pound.Multiply the weight of the turkey by the cost per pound: (1/2 pound) x ($6/pound).Calculate the cost: 1/2 x 6 = $3.

Therefore, the cost of the turkey is $3.

Mary is making some shirts for her school's drama department. The fabric store has 3 1/6 yards of the fabric she wants in stock. But this quantity of fabric can make only 1 1/3 shirts. What length of fabric does Mary need to buy if she wants to sew 2 shirts?

A)1 1/6
B)2 3/8
c)3 5/6
D)4 3/4

Answers

Solve this problem using an equation of ratios.

3 1/6 yards of the fabric she wants in stock. But this quantity of fabric can make only 1 1/3 shirts

Write the ratio

3 1/6 yards to 1 1/3 shirts:

19
---
6
---------------
4
---
3

We need to reduce this. The first (upper) ratio is 19/6; the second (lower() ratio is 4/3. We can mult. numerator and denom. of 4/3 both by 2 to obtain the equivalent ratio 8/6.

Then we have the ratio

19/6
-------- which can be reduced to 19/8. That's (19/8) yard/shirt. We can use
8/6 this as a conversion factor.

To make 2 shirts, Mary will need (19/8 yards per shirt)(2 shirts) of material, or 38/8 yards, or 19/4 yards (answer).

One card is drawn at random from the deck of cards shown. Which of the following probabilities is equal to one?

P(even or odd)P(even and odd)P(not yellow)

Answers

P(even or add).
I hope i helped!
If so, Please mark as brainliest!

Answer:

P(Even or ODD) ( .Y .)

Step-by-step explanation:

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