Mathematics College

If the vertices of three squares are connected to form a right triangle, the sum of the areas of the two smaller squares is the same as the area of the largest square. Based on this statement and the model below, what is the area of square B? (Figure is not drawn to scale.) B 8 m 2 289 m

Answers

Answer 1

One square has area 289 square meters, and the other has area

[tex]8m\times8m=64m^2[/tex]

Then, since the sum of the two areas of the smaller squares is equal to the area of the big square, we have

[tex]\begin{gathered} B+64m^2=289m^2 \\ B=289m^2-64m^2 \\ B=225m^2 \end{gathered}[/tex]

Related Questions

Walnuts make up half of the nuts in this nut bread:
It has exactly 2 pecans

The number of walnuts is double the number of pecans.
Write an equation to show how many of each nut this nut bread contains.

Answers

The equation to show how many of each nut this nut bread contains is w = 2p and there are 4 walnuts.

What is an equation?

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The number of walnuts is double the number of pecans. This can be illustrated as:

w = 2p

Therefore, the number of buts will be:

w = 2p

w = 2(2)

w = 4

Therefore, ther are 4 walnuts

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Can you help me solve my homework question I will follow along the steps

Answers

Notice that both fractions have the same denominator, therefore, we can simply add the numerators:

[tex]\frac{-5a-3x-2a+9x}{6a}.[/tex]

Adding like terms, we get:

[tex]\frac{-7a+6x}{6a}.[/tex]Answer: [tex]\begin{gathered} \frac{-7a+6x}{6a},\text{ or equivalently} \\ -\frac{7}{6}+\frac{x}{a}. \end{gathered}[/tex]

y−10=2(x−8)Write in Standard Form

Answers

The standard form of a linear equation in two variables is given by the expresssion:

[tex]Ax+By=C[/tex]

So, rewriting the equation:

y-10=2x-16

y-2x=-16+10

y-2x=-6

2x-y=6

In which graph does the height difference between Winter Hill and Frozen Field equal the height of BlizzardRun?Choose 1 answer:605040Height (in meters)30.©20100Blizzard RunSnow SlopeWinter HillFrozen FieldSledding hill

Answers

In graph A, you can see that:

• The height of Frozen Field is 50 meters

• The height of Winter Hill is 15 meters

• The height of Blizzard Run is 35 meters

Now, we can write the equation that describes the height difference between Winter Hill and Frozen Field.

[tex]\text{ Height of Frozen Field }-\text{ Height of Winter Hill }=50m-15m=35m_{}=\text{ Height of Blizzard Run }[/tex]

In graph B, you can see that:

• The height of Frozen Field is 45 meters

• The height of Winter Hill is 10 meters

• The height of Blizzard Run is 55 meters

Now, we can write the equation that describes the height difference between Winter Hill and Frozen Field.

[tex]\text{ Height of Frozen Field }-\text{ Height of Winter Hill }=45m-10m=35m\ne55m_{}=\text{ Height of Blizzard Run }[/tex]

Therefore, the graph where the height difference between Winter Hill and Frozen Field is equal to the height of Blizzard Run is graph A.

i need immediate help.The exercise consists of finding the axis of symmetry for the equation below.

Answers

Explanation

Our equation

[tex]y=\frac{1}{3}(x+2)^2-1,[/tex]

is a quadratic equation. In simple words, it's a parabola, whose graph (red curve) is the following:

The axis of symmetry of a parabola is just the line dividing the parabola into its two arms. In the graph, the axis of symmetry is the blue vertical line. It's usually represented algebraically by

[tex]x=\text{ The first component of the vertex}[/tex]

Answer

The axis of symmetry of our quadratic equation is

[tex]x=-2[/tex]

(4,0) and (0,2) write an equation in standard form for the line that passes through the given points

Answers

We have the following:

The first thing is to find the slope of the line, like this:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

replacing:

[tex]m=\frac{2-0}{0-4}=\frac{2}{-4}=-\frac{1}{2}[/tex]

now, the equation has the following form:

[tex]y=mx+b[/tex]

for b,

m = -1/2

y = 2

x = 0

replacing:

[tex]\begin{gathered} 2=-\frac{1}{2}\cdot0+b \\ b=2 \end{gathered}[/tex]

Therefore, the equation in standard form is:

[tex]\begin{gathered} y=-\frac{1}{2}x+2 \\ y+\frac{1}{2}x=2 \\ 2y+x=4 \end{gathered}[/tex]

Select the three expressions that are equivalent to 410

Answers

Answer:

A, C, E

Step-by-step explanation:

4^10 = 1048576

A: (4^5)^2 = 1048576

C: 4^20 / 4^10 = 1048576

E: (4^2 x 4^3)^2 = 1048576

How does a graph of quadratic function (f(x) = ax2 + bx + c) vary when the a,b, c changes from -1 to +1?

Answers

When a, b, c changes from -1 to +1, the parabolas opens and widens.

Given,

The quadratic function, f(x) = ax² + bx + c

We have to find the change in graph when a, b, c changes from -1 to 1.

First lets consider:

a and b as constants and c is varying.

That is,

x² + x + c

Then, the parabola will move up and down.

Now, lets consider:

a and c as constants and b is varying.

That is,

x² + bx + 1

Then, the vertex will move but all parabolas passes through the points (0, c)

Now, we can move to the question.

What happens to graph when +1 changes to -1.

So,

b and c should keep constant and a is varying.

Then,

ax² + x + 1

Here, the parabolas opens and widens.

That is,

When a, b, c changes from -1 to +1, the parabolas opens and widens.

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Calculate each percent increase or percent decreases Round to the nearest whole percent if necessary 1. original amount: 30, new amount: 45 2. original amount: 12, new amount: 16 3. original amount: 17 new amount: 21 4. original amount: 85, new amount: 56 5. original amount: 48, new amount: 37 6. original amount: 124, new amount: PLS HELP ME!!!

Answers

The percentage increase is 50%

Here, we want to calculate the percentage increase or decrease

To know if it is a decrease or an increase, we use the following simple logic.

If new amount is greater than original amount, then it is an increase.

If new amout is less than original amount, then it is a decrease

For the first question, we can see that the new amount is greater than the old amount

This indicates an increase

Mathematically;

[tex]\text{percentage increase = }\frac{(new\text{ amount - original amount)}}{\text{old amount}}\text{ }\times\text{ 100 percent}[/tex]

According to the first question, new amount = 45 while old amount = 30

so;

percentage increase = (45-30)/30 * 100%

= 15/30 * 100% = 100%/2 = 50%

Prove that every differentiable function is continuous

Answers

To prove :

every differentiable function is continuous.

thus, every differentiable function is continuous.

Write a quadratic function in intercept form whose graph passes through the points (-5,0)(-1,0) and (-7,-24)

Answers

EXPLANATION

The intercept-form of a quadratic function is as follows:

y = a(x - p)(x - q)

Now, as the roots are (-5,0)

Since the parabola passes through the point (−5,0), then 0=25a−5b+c

Since the parabola passes through the point (−1,0), then 0=a−b+c.

Since the parabola passes through the point (−7,−24), then −24=49a−7b+c.

Thus, we have obtained the following system:

Solving it we get that a=−2, b=−12, c=−10.

Thus, the equation of the parabola is y=(−2x−10)(x+1)

How to put 7^3/4 in radical form

Answers

Given:

[tex]7^{\frac{3}{4}}[/tex]

Resolving it to its radical form can be gotten based on the general laws of indices.

We have:

[tex]A^{\frac{x}{y}}=\sqrt[y]{A^x}[/tex]

I.e. the number is raised to the power of the numerator and then we get the denominator's root of the number obtained.

Thus:

[tex]\begin{gathered} 7^{\frac{3}{4}}=\sqrt[4]{7^3}=\sqrt[4]{343} \\ \sqrt[4]{343}=343^{\frac{1}{4}}=343^{(\frac{1}{2}\times\frac{1}{2})} \\ =343^{(\frac{1}{2}\times\frac{1}{2})}=\sqrt[]{343^{\frac{1}{2}}} \end{gathered}[/tex]

Now, we have our value in the square root form as:

[tex]\sqrt[]{343^{\frac{1}{2}}}=\sqrt[]{7^{\frac{3}{2}}}[/tex]

Match each function on the left with the ordered pairs on the right.

Answers

We have to match the functions with the corresponding ordered pair.

The easiest way is to pick an ordered pair and replace (x,y) in the function to verify if the equality stands or not. If it does stand, then the ordered pair is part of the function.

Then, we start with (-8,9) and function y = 6x+9. Replacing x and y, we get:

[tex]\begin{gathered} (x,y)=(-8,9) \\ y=6x+9 \\ 9=6\cdot(-8)+9 \\ 9=-48+9 \\ 0=-48\longrightarrow\text{False} \end{gathered}[/tex]

As this equation does not verify for (-8,9), this ordered pair does not belong to the function.

We repeat the same process with the next function, y = -9x-1:

[tex]\begin{gathered} (x,y)=(-8,9) \\ y=-9x-1 \\ 9=-9(-8)-1 \\ 9=72-1 \\ 9=71\longrightarrow\text{False} \end{gathered}[/tex]

As with the previous function, the equation does not verify.

The next function is y = -1x+1:

[tex]undefined[/tex]

Sketch the graph of each line.

24)

y=3/5x-4

Answers

The graph of the given line is attached below.

We are given the line:-

y = (3/5)x - 4

We will find the x and y intercepts of the line to plot in the graph.

As the equation is already in the slope intercept form, we can write,

The y-intercept of the line is -4.

Hence, the coordinates of the point will be (0,-4).

To find the x - intercept of the line we will put y = 0 in the given line.

0 = (3/5)x - 4

4 = 3x/5

x = 20/3

The coordinates of the point will be (20/3,0).

We can plot these points to get the desired graph.

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Put the following equation of a line into slope-intercept form, simplifying all fractions.
3y-3x=15

Answers

Answer:

[tex]y=x+5[/tex]

Step-by-step explanation:

[tex]3y-3x=15 \\ \\ y-x=5 \\ \\ y=x+5[/tex]

What is the area of the blue shape?

Pls help :(

Answers

Answer:

38.5 sq units

Step-by-step explanation:

Hello!

We can split the shape into two rectangles.

The small rectangle at the top has an area of 14 sq units (2 * 7).

The middle rectangle has an area of 49 sq units ( 7*7).

Since the blue part in the middle rectangle is half of the whole rectangle, the area of the blue part there is 24.5 sq units.

Adding that to 14 sq units will give us 38.5 sq units.

Alision has an interest in entomology, the study of insects. Her collection of insects from around the world includes the four specimens shown in the table below.

Answers

we know that

the mass of Alison's Emperor Scorpio is

[tex]2^{-5}=(\frac{1}{2})^5=\frac{1}{2^5}=\frac{1}{32}\text{ kg}[/tex]The answer is the second option

Solve for u.u + 8 = 16

Answers

In this case the answer is very simple. .

We must apply algebraic rules to find the solution.

u + 8 = 16

u = 16 - 8

u = 8

The answer is:

u = 8

REDUCE 48/96 TO THE LOWEST TERMS

Answers

48/96 simplified to lowest terms is 1/2.

In triangle ABC, angle A is 44 degrees and angle B is 76 degrees. What is the measure of the third angle?

Answers

Answer:

60 degrees

Step-by-step explanation:

Total of angles of a triangle is 180

180-76-44= 60

Maria is planting a row of flowers in a bed 77 feet long. The instructions say to space the plants 1 foot apart, allowing room for 77 flowers. The flowers come in flats containing 6 plants per flat.

Answers

She will need 12 flats and there will be 5 leftovers

The number of flats she will need

From the question, we have

Length = 77 feetDistance apart = 1 footNumber of flowers = 77Rate = 6 plants per flat

The number of flats is calculated as

So, we have the following equation

Number of flats = (Length)/Rate

So, we have

Number of flats = (77)/6

Evaluate

Number of flats = 12

The number of plants leftover

This is calculated as

Leftover = Length - Number of flats * Rate

So, we have

Leftover = 77 - 12 * 6

Evaluate

Leftover = 5

Hence, the left over is 5

Answers

Answer:

3.34

Step-by-step explanation:

625 is 5^4

Using the log rule [tex]log_b(x^a)=alog_b(x)[/tex],

log_b(5^4) = 4*log_b(5)

4*0.835 = 3.34

Find the equation of the line passing through point (3,5) and with a slope ⅓

Answers

hello

we are given 1 point with x and y co-ordinate and a slope, we can easily write down the equation of the line

standard equation of a straight line is

[tex]\begin{gathered} y=mx+c \\ m=\text{slope} \\ c=\text{intercept} \end{gathered}[/tex]

to solve this problem, we need to find the intercept first

substitute the x and y co-ordinates in the equation

[tex]\begin{gathered} y=mx+c \\ m=\frac{1}{3} \\ y=5 \\ x=3 \\ 5=\frac{1}{3}(3)+c \\ 5=1+c \\ c=4 \end{gathered}[/tex]

we know our intercept is equal to 4 and we can proceed to write out our equation

[tex]y=\frac{1}{3}x+4[/tex]

we can leave it this way or multiply through by 3

[tex]3y=x+12[/tex]

use matrices D, E, and F to find each sum or product

Answers

Problem

Solution

5. E-D

Procedure

-3-2 =-5

-4-1=-5

0-7=-7

1-5=-4

2-3=-1

6- (-4)=10

And the answer would be:

-5 -5

-7 -4

-1 10

6. 3F

Procedure

3* -2=-6

3 *5 = 15

3* 1= 3

3*3 = 9

3*14=12

3 * -6= -18

And the answer would be:

-6 15 3

9 12 -18

May I please help with this. I have tried to find the correct answers but still couldn’t get them right

Answers

Solution

[tex]1cm\text{ to 7in}[/tex]

We can use ratio to solve the problem

Part A

5cm to x in

[tex]\begin{gathered} 1cm\colon7in \\ 5cm\colon x\text{ in} \end{gathered}[/tex]

Now

[tex]\begin{gathered} 1\colon7 \\ 5\colon x \\ \therefore\frac{1}{7}=\frac{5}{x} \\ \\ \text{cross multiply} \\ 1\times x=5\times7 \\ x=35 \end{gathered}[/tex]

The final answer

[tex]5cm\text{ to 35inches}[/tex]

Part B

Similar step as part a

[tex]\begin{gathered} 1\colon7 \\ y\colon63 \\ \frac{1}{7}=\frac{y}{63} \\ \\ \text{cross multiply} \\ 7y=63 \\ \text{divide both sides by 7} \\ \frac{7y}{7}=\frac{63}{7} \\ y=9 \end{gathered}[/tex]

The final answer

[tex]9cm\text{ to 63inches}[/tex]

Summary

13) An airline weighed the carry-on luggage of all its 1,106 passengers in a single day. How many of these passengers had carry-on luggage that weighed less than 20 lb? *

Answers

we know that

4 lb or less ------> is less than 20 lb ------> 120

5-9 lb------------> is less than 20 lb -------> 222

10-14 lb -------> is less than 20 lb ------->378

15-19 lb ------> is less than 20 lb-------> 256

Adds the number of passenger

120+222+378+256=976

thereforethe answer is 976

In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If 4 boys and 5 girls are competing, how many different ways could the six medals possibly be given out?

Answers

ANSWER

1,440

EXPLANATION

We have that 4 boys are competing and also 5 girls are competing. 3 medals are given to the boys and 3 medals are given to the girls.

For the boys, the gold medal can be awarded to one of 4 boys, then the silver medal can be awarded to 3 boys because 1 of them already got the gold medal. Finally, the bronze medal can be awarded to one of 2 boys, since the gold and silver medals are already taken. The number of ways the medals can be given to the boys is,

[tex]permutations_{boys}=4\cdot3\cdot2=24[/tex]

This situation is similar for the girls, but in this case, there are 5 girls in total,

[tex]permutations_{girls}=5\times4\times3=60[/tex]

The total ways the six medals can be given is,

[tex]permutations_{boys}\times permutations_{girls}=24\times60=1,440[/tex]

Hence, there are 1,440 ways to give the six medals to the 4 boys and 5 girls.

WILL GIVE BRIANLYEST 100 POINTS ACULLY 200 BC IM GIVING EXTRA POINTS

Answers

Answer:

the mean would increase to a value to about 24.6

Q2: median is 7.

Step-by-step explanation:

Answer:

Q1) the mean would increase in value to about 24.6

Q2) 7

1 x(x-2) how I do this

Answers

x(x-2)

Apply the distributive property:

x(x)+x(-2)

x^2-2x

If licorice costs $6.59 a pound, how much would it cost to buy a quarter-pound of licorice?

If a 10-foot piece of electrical tape has 0.037 feet cut from it. What is the new length of tape?

A director replayed 231 of the 1000 scenes filmed for a movie. Write a decimal to represent the part of the movie the director replayed.

If you had half a dollar, three quarters, eight dimes, six nickels, and nine pennies, how much money would you have altogether?

What is the combined thickness of these shims: 0.008, 0.125, 0.15, 0.185, and 0.005 cm?

All the people of a neighborhood pooled together and won the lottery. They won $10,000,000 and each person got a 0.02 share. How much money did each person receive?

Answers

Answer:

1. 1.6475.

2. 9.963.

3. 0.231

4. $1.69

5. 0.473 cm.

6. x = $200,000

Step-by-step explanation:

1.$6.59 ÷ 4 = 1.6475.

2. 10-0.037 = 9.963

3. 231 divided by 1000.

4. $0.50 + $0.80 + $0.30 + $0.09 = $1.69

5. 0.008 + 0.125 + 0.15 + 0.185 + 0.005

6. x =$10,000,000(0.02) where x is the amount of money each person will receive. x=$200,000 (multiply)

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