please help with math

c^2 = a^2+b^2       now subtract a^2 from both sides

c^2 - a^2 = b^2       Now take the square root of both sides

b = +- sqrt(c^2-a^2)

Final answer:

To solve for B in the equation C = sqrt(A^2 + B^2), you square both sides of the equation, subtract A^2 from both sides, and then take the square root of the result to find B = sqrt(C^2 - A^2).

Explanation:

The equation C = sqrt(A^2 + B^2) is representative of the Pythagorean theorem, which is used in mathematics to relate the sides of a right triangle. To solve for B, we must isolate B on one side of the equation. Here's how you can do it:

This gives us the magnitude of B in terms of A and C.

16

Okay, so Jack started with 50 chocolates and ended with 2. 
The simple way to calculate it would be by realizing that Jack only distributed 48 chocolates. We can find how many times 3 fits into 48 by dividing 48÷3=16.

Using algebra, we substitute the value we want to find with x. Here what we want to find is the number of friends that were at Jack's party.

We know that he started with 50 chocolates, then distributed 3× the number of friends present (which is x). 
We write that down as 50−3x 
(It's minus because when chocolates are distributed, Jack is taking away from what he has.)

We know that after this, there were only 2 chocolates left, so it's 
50−3x=2

Then we proceed by moving all the numbers to the right until only x is left:

−3x=2−50
−3x=−48

x=−48−3

x=16

Conclusion: The number of people that attended the party was 16.

Answer:

The equation is 3x+2=50

There were 16 friends at Jack's party.

Step-by-step explanation:

I JUST TOOK THE TEST

For the first image, the median range would be 88. In order to find the median, you'll place all your numbers in numerical order (smallest to largest). If there are an odd amount of numbers, find the one directly in the middle. If there is an even amount, you'll take the two most central ones and find the mean, that will tell you the median. Therefore, B (88)  would be the answer to your first one.

The second one would be C (20.4). It's asking for the mean. In order to find the mean of a set of numbers, you'll simply add up all of the numbers and divide by how many numbers are in your number set. That gives you the mean.

The required missing term of the given sequence is given as 485 and 1457.

The sequence is a pattern of placing the values in a specified manner.

here,

5 = 1 + 4
Since, [tex]b_0 = 4[/tex] and [tex]a_0 = 1[/tex]

17 = 5 + 12

So, the general term is given as

[tex]a_n = a_{n-1} + b_{n}[/tex]

Where, [tex]b_n = 3b_{n-1}[/tex]

For 6 th term

6 the term = 161 + 3(108)

6 the term   = 485

For the 7th term
7th term = 485 + 3(324)
7th term =  1457

Thus, the required missing term of the given sequence is given as 485 and 1457.

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Answer:

C

Step-by-step explanation:

Because The Equation Represents how many of those thingy's were stuffed

I can tell you for sure that the answer to the first one is

C) 63,475

and the second is

A) 22,149

The attendance at the movie theater in seven years will be 63,476. Then option C is correct. And the number of customers that visit the business in 10 years will be 22,149. Then option A is correct.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

The yearly participation at a neighborhood movie theater is 42,000 and develops ceaselessly at a pace of 5.9% every year. Then the attendance at the movie theater in seven years will be given as,

[tex]\rm y = 42,000 \times (e)^{0.059\times 7}\\\\y = 42,000 \times (e)^{0.413}[/tex]

Simplify the equation further, then we have

y = 42,000 × 1.5113

y = 63,476

The quantity of clients that visit a neighborhood private venture is 29,600 and has been persistently declining at a pace of 2.9% every year.

Then the number of customers that visit the business in 10 years will be given as,

[tex]\rm y = 29,600\times (e)^{-0.029\times 10}\\\\y = 29,600 \times (e)^{-0.29}\\[/tex]

Simplify the equation further, then we have

y = 29,600 × 0.748

y = 22,149

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1/12 is the probability that a 5 is rolled on at least one of the two dice

It is a branch of mathematics that deals with the occurrence of a random event.

Given that  two standard six-sided dice are tossed,

We need to find the probability that a 5 is rolled on at least one of the two dice.

When we roll two  dice there is a possibiltiy of 36 outcomes.

In these 36 outcomes atleast one of the dice should show 5.

There are 36 possible rolls

(5, x), (x, 5) and (5, 5) are the possible outcomes with 5 on any of the dice.

x represents any number from one to five.

So  the probability that a 5 is rolled on at least one of the two dice is 3/36

which is equal to 1/12.

Hence, 1/12 is the probability that a 5 is rolled on at least one of the two dice

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Answer:

[tex]2\frac{7}{40}[/tex] pounds

Step-by-step explanation:

Given information:

Weight on the left side = [tex]3\frac{3}{8}[/tex] pounds

Weight on the right side = [tex]1\frac{1}{5}[/tex] pounds

We need to balance both sides.

Let x be the weight which is added to the right side to balance the scale.

[tex]3\frac{3}{8}=1\frac{1}{5}+x[/tex]

[tex]\frac{24+3}{8}=\frac{5+1}{5}+x[/tex]

[tex]\frac{27}{8}=\frac{6}{5}+x[/tex]

Subtract 6/5 from both sides.

[tex]\frac{27}{8}-\frac{6}{5}=x[/tex]

[tex]\frac{135-48}{40}=x[/tex]

[tex]\frac{87}{40}=x[/tex]

[tex]2\frac{7}{40}=x[/tex]

Therefore, [tex]2\frac{7}{40}[/tex] pounds weight is added to the right side to balance the scale.

Ethan paid $31.99 for the video game on sale.

To calculate the discount that Ethan obtained in the price of his video game, we do the following operations:

We divide the total price by one hundred and multiply the result by the discount, in this case 20.

Subsequently, we subtract the result of the previous operation (value of the discount) from the total value of the video game.

$39,99 - $7,998 = $31,992

According to the above, the value that Ethan paid for the video game was $31,992

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Answer: $31.99

Step-by-step explanation:

$39,99 ÷ 100 = $0,3999

$0,3999 × 20 = $7,998

$39,99 - $7,998 = $31,992

Final answer:

Belinda's total expenses for the week are the sum of her bus fare, lunch out, hair cut, and movie rental, which adds up to d. $38.00.

Explanation:

To calculate the total of Belinda's expenses for the week, we should add up each of the expenses mentioned. This includes the bus fare, lunch out, hair cut, and movie rental. Here's how we do it step-by-step:

Now, let's add them up:

$8.70 (Bus fare) + $7.35 (Lunch out) + $16.00 (Hair cut) + $5.95 (Movie rental)

When we sum these amounts, we get $8.70 + $7.35 + $16.00 + $5.95 = $38.00.

Therefore, the total of Belinda's expenses for the week is $38.00, which corresponds to option D.

The formula for volume of cylinder is:

V = π r^2 h

since volume is 100 cubic inches, so:

100 = π r^2 h

Rewriting in terms of h:

h = 100 / π r^2

The least amount of metal means least amount of surface area needed. The surface area of cylinder is:

A = 2 π r h + 2 π r^2

insert the value of h in terms of r:

A = 2 π r (100 / π r^2) + 2 π r^2

A = 200 r-1 + 2 π r^2

Take the 1st derivate and set to 0, dA/dr = 0:

dA/dr = - 200 r-2 + 4 π r

0 = - 200 r-2 + 4 π r

200 / r^2 = 4 π r

r^3 = 50 / π

r = 2.52 inches

So height h is:

h = 100 / π r^2

h = 100 / π (2.52)^2

h = 5.01 inches

Answers:

r = 2.52 inches

h = 5.01 inches

First let’s find the mean and standard deviation for both test and then we can calculate the probability of getting that score in his respective test and compare. 

First test

P(x < 56)

P(z < 56-47.80/16.38)

P(z<0.50) = 1 – 0.3085 = 0.6915 or 69 percentile

Second test

P(x < 74)

P(z < 74 – 73.45 / 8.37)

P(z<0.07) = 1 – 0.4721= 0.5279 or 53 percentile

The probability for this normal distribution also means the percentile, so we can say that in the first test she was in the 69 percentile while in the second test she was in the 53 percentile. Therefore, she did worse in the second test

Julia did better on the first test compared to the second test.

To determine whether Julia did better or worse on the second test, we need to compare her score on the first test with her score on the second test. For the first test, Julia received a score of 56 and for the second test, she received a score of 74. To determine which score is better, we can compare their positions in the distribution of scores.

First, we can calculate the mean and standard deviation of the scores for each test. For the first test, the mean is 49.9 and the standard deviation is 12.8. For the second test, the mean is 73.6 and the standard deviation is 7.3.

Next, we can calculate the z-scores of Julia's scores on each test. A z-score represents the number of standard deviations a data point is from the mean. For the first test, Julia's z-score is 0.16, and for the second test, her z-score is -0.2538.

Since a higher z-score indicates a better performance relative to the mean, Julia did better on the first test than the second test.

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By using the formula for the perimeter of a rectangle and substitution, it is determined that the dimensions of the rectangle are 6 inches for the length and 2 inches for the width.

This is a traditional problem in algebra that we can solve using known formulas and principles.

The perimeter of a rectangle is calculated using the formula 2(l+w), where 'l' stands for length and 'w' stands for width. In this problem, we know the perimeter (P) is 24 inches, and we know the length (l) is the width (w) + 4 inches.

We can set up and solve an equation using these facts. Replace 'l' in the equation with '(w + 4)' and solve for 'w': 2[(w + 4) + w] = 24, which simplifies to 2w + 8 = 12, and finally, w = 2.

Having found 'w', we can find 'l' by substituting 'w' in our equation of 'l', l = w + 4 = 2 + 4 = 6.

Therefore, the length is 6 inches and the width is 2 inches.

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Answer:

Triangle 4

Step-by-step explanation:

Congruent triangles are identical in all aspects. They have identical sides and angles.

The ASA the Angle Side Angle criterion.

Congruent triangles should be able to "close up" on each other if one triangle is placed on top of the other. Let's look at the triangle in question.

The triangle ABC is made distinct by the lines on it.

The lines mark the different angles on the triangle.

By looking at the triangle and comparing, Triangle satisfies the ASA criterion

We want to create a system of equations that allows us to find the values of two supplementary angles.

We will find that the larger angle measures 140° and the smaller one measures 40°.

------------------------

Two angles A and B are supplementary if their measures add up to 180°, so we have:

A + B = 180°.

Let's assume that B is the larger one, we also do know that:

"The larger is 20° less than 4 times the smaller"

Then we can write:

B = 4*A - 20°.

Then our system of equations is:

A + B = 180°.

B = 4*A - 20°.

To solve it we need to isolate one variable in one of the equations and replace it on the other equation. Here we can see that B is already isolated on the second equation, so we can replace it in the first one to get:

A + B = 180°.

A + (4*A - 20°) = 180°

Now we can solve this for A:

A + (4*A - 20°) = 180°

5*A - 20° = 180°

5*A = 180° + 20° = 200°

A = 200°/5 = 40°

Now that we know the value of A we can get the value of B:

B = 4*A - 20° = 4*40° - 20° = 140°

Then the larger angle measures 140° and the smaller measures 40°

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