The ratio of boys to girls in the ninth grade is 6:5. If there are 185 girls in the class, how many boys are there?

Answer:

S = 2πr + 326/r

Step-by-step explanation:

Given

Volume = 163cm³

Required

Explain why S = 2πr² + 163r is not correct

The volume (V) of a cylinder is:

V = πr²h ----- (1)

And the surface area (S) is:

S = 2πr² + 2πrh ----- (2)

Make h the subject in (1)

h = V/πr²

Substitute V/πr² for h in (2)

S = 2πr² + 2πr(V/πr²)

Simplify the express in bracket

S = 2πr² + (2πrV)/(πr²)

S = 2πr² + 2V/r

Substitute 163 for V

S = 2πr + 2 * 163/r

S = 2πr + 326/r

The above shows the correct equation that solves the surface area and also shows how it was fixed by substituting proper values and following due process.

Answer:

Prime factors of 84 = 4 . 3 . 7

Prime factors of 126 = 2 . 9 . 7

Prime factors of 245 = 5 . 49

Step-by-step explanation:

Answer:

g = 10

Step-by-step explanation:

Distribute 7 to the parentheses:

7(g + 5) = 105

7g + 35 = 105

Solve for g:

7g + 35 = 105

7g = 170

g = 10

So, the answer is g = 10

Answer:

g = 10

7g + 35 = 105

.       -35    -35

7g = 70

g = 10

Answer:

c+9

Step-by-step explanation:

Key word SUM means addition

Answer:

He used the distributive property

Answer:

Robert used the distributive property.

Step-by-step explanation:

3(x + 2) = 21 <------- is the original equation.

3x + 6 = 21   <------- is Robert's first step.

Distributive property is a property that states that multiplying the constant by the numerical values/variables in the parentheses will equal the same as multiplying the consonant by the values added together.

Robert multiplied 3 times "x" and "2." This is the distributive property.

I hope this helps! :)

Answer:

they are corresponding angles. hope that helps!

Step-by-step explanation:

Answer:

From the photo we can see that a pair of parallel lines are intersecting one line. BEcause those lines are parallel they form the same angles . Therefore the <1 is equal to the m<5.

A. The relationship between <1 and <5 is that they are congruent meaning they share the same angle measure.

If the m<1 and m<5 are equal then that means the equations of those anlges must also be equal:

3x+7=5x-3

Now we can solve for x

3x+7=5x-3

7=2x+3

10=2x

5=x

x=5

Therefore for question b, x=5

B. X=5

Step-by-step explanation:

Answer:

(-2)4=-8

Step-by-step explanation:

Answer:

endpoints (4,5)

Step-by-step explanation:

endpoints = (2+6/2,7+3/2)

= (8/2,10/2)

= (4,5)

Answer:

Step-by-step explanation:

3). Definition of midpoint

4). Midpoint theorem ( ≅ parts are = )

7). Division Property of Equality.

8).  QR = 5 + 2 = 7     Substitution x by equal value

9). PQ = 4(2)  - 1 = 7    Substitution x by equal value

10). Segment addition postulate

11). Substitution

Answer:

[tex] y' = -\dfrac{\cot x \csc x}{2 \sqrt{x}} [/tex]

Step-by-step explanation:

y = csc x

y' = -cot x csc x

[tex] y = \csc \sqrt{x} [/tex]

[tex] y' = \dfrac{d}{dx} [\csc \sqrt{x}] [/tex]

[tex]y' = (-\cot x \csc x) \dfrac{d}{dx} \sqrt{x}[/tex]

[tex]y' = (-\cot x \csc x) \dfrac{d}{dx} x^{\frac{1}{2}}[/tex]

[tex]y' = (-\cot x \csc x) \dfrac{1}{2} x^{-\frac{1}{2}}[/tex]

[tex] y' = -\dfrac{\cot x \csc x}{2 \sqrt{x}} [/tex]

Answer:

3 is the question mark my friend u just have to simply

Answer:

-3

Step-by-step explanation:

2^x = 2^-3

x= -3

i hope this helps !!

Answer:

a

Step-by-step explanation:

it has to  have to same slope as the first equation so you have y=5x+b then what you do is plug in the points and solve for b. which gives you 2. so your final equation is y=5x+2

7=5+b

-5  -5

2=b

Answer:

The equation that represents the line that passes through (1,7) and is parallel to y = 5x + 4 will be:

Step-by-step explanation:

Given the equation

[tex]y = 5x + 4[/tex]

Here the slope is:

[tex]m=5[/tex]

as comparing with the [tex]y=mx+b[/tex], which is the slop-intercept form where m is the slope and b is the y-intercept.

As we know the point-slope form is

[tex]y-y_1=m\:\left(x-x_1\right)[/tex]

[tex]y-7=5\left(x-1\right)[/tex]

Add 7 to both sides

[tex]y-7+7=5\left(x-1\right)+7[/tex]

[tex]y=5x+2[/tex]

Therefore, the equation that represents the line that passes through (1,7) and is parallel to y = 5x + 4 will be:

Answer:

given us,

(x1y1) = (4,6)

(x2y2)= (1,10)

here

slope= (y2-y1)/ (x2-x1)

= (10-6)/ (1-4)

= 4/ (-3)

Step-by-step explanation:

4/ (-3)

Answer:

25%

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

Bc you are adding 1/4 of 120 which equals 150

Answer:

Im dumb but cant you just be like, I subtracted 146° and 62°?

Answer: 1. ( 9r - 8 ) x ( r - 2 )

2. ( 5b - 3 ) x ( 5b + 3 )

Step-by-step explanation:

Answer:

Negative 3 plus:) hope this helps!

Answer:

Part A)

[tex]390=(15+x)(13+x)[/tex]

Part B)

Approximately 18.77 feet long by 20.77 feet wide.

Step-by-step explanation:

Currently, the patio is 13 feet long by 15 feet wide. Therefore, the area right now is:

[tex]A=13(15)=195\text{ feet}^2[/tex]

We will increase the length and width of the patio by the same amount such that the new area is double the previous amount.

Part 1)

The previous area is 195. Therefore, we would like to the new area to be twice of that. Hence, the new area is:

[tex]A=2(195)=390[/tex]

We will increase the length and the width by the same amount. Let’s call this amount x. Then by the area formula (A=bh), we can write:

[tex]390=(15+x)(13+x)[/tex]

390 represents the doubled area. (15+x) is the width after the increase x, and (13+x) is the length after the same x increment.

Part 2)

So, we will solve for x. First, expand:

[tex]390=195+15x+13x+x^2[/tex]

Simplify:

[tex]x^2+28x+195=390[/tex]

Subtract 390 from both sides:

[tex]x^2+28x-195=0[/tex]

This is a quadratic. Hence, we can use the quadratic formula:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Our a=1, b=28, and c=-195. Hence:

[tex]x=\frac{-28\pm\sqrt{(28)^2-4(1)(-195)}}{2(1)}[/tex]

Evaluate:

[tex]x=\frac{-28\pm\sqrt{1564}}{2}[/tex]

Simplify the square root:

[tex]\sqrt{1564}=\sqrt{4}\cdot\sqrt{391}=2\sqrt{391}[/tex]

Hence:

[tex]x=\frac{-28\pm2\sqrt{391}}{2}\\[/tex]

Simplify:

[tex]x=-14+\sqrt{391} \text{ or } -14-\sqrt{391}[/tex]

Approximate:

[tex]x\approx5.77\text{ or } x\approx-33.77[/tex]

In this case, we can reject the negative solution.

Hence, the value of x is 5.77.

This means that we should increase the our length and width by 5.77.

Hence, the new length will be 13+5.77 or about 18.77.

And our new width will be 15+5.77 or about 20.77.

So, the new dimensions is approximately 18.77 by 20.77

Answer:

105°

Step-by-step explanation:

Since 4 and 5 are equal, 210/2=105°

Answer:

the ansewr is 5

Step-by-step explanation:

1 plus 1 equal 5555555

Answer:

listen when in doubt go with c

Step-by-step explanation:

Answer:

15625 is 5 to the power of 6.

You didn't give your answer choices, so I will assume you are referring to the answer.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

pent means 5

a pentagon looks like this

count the sides

Answer:

Step-by-step explanation:

sin(x+y) = sin(x)cos(y) + sin(y)cos(x)

sin(x-y) = sin(x)cos(y) - sin(y)cos(x)

Sin(x+y)sin(x-y) = (sin(x)cos(y) + sin(y)cos(x))(sin(x)cos(y) - sin(y)cos(x))

= sin^2(x)cos^2(y) - sin^2(y)cos^2(x)

= sin^2(x)(1-sin^2(y)) - sin^2(y)(1-sin^2(x))

= sin^2(x) - sin^2(x)sin^2(y) - sin^2(y) + sin^2(x)sin^2(y)

= sin^2(x) - sin^2(y)

So L.H.S=R.H.S

Hence proved

Answer:

A. 32.08

Step-by-step explanation:

The figure given is a right triangle. We would apply trigonometric ratios formula to find x.

Reference angle = 58°

Hypotenuse = x

Adjacent length = 17

Thus, we would apply the following:

[tex] Cos(\theta) = \frac{Adjacent}{Hypotenuse} [/tex]

Plug in the values

[tex] Cos(58) = \frac{17}{x} [/tex]

Multiply both sides by x

[tex] Cos(58) \times x = \frac{17}{x} \times x [/tex]

[tex] Cos(58) \times x = 17 [/tex]

Divide both sides by Cos(58)

[tex] \frac{Cos(58) \times x}{Cos(58)} = \frac{17}{Cos(58)} [/tex]

[tex] x = \frac{17}{Cos(58)} [/tex]

[tex] x = 32.08 [/tex] (2 d.p)

Answer:

Step-by-step explanation:

As per table

So

Correct option is D) 1