Suppose that y varies directly with x, and y = 10 when x = 25.
(a) Write a direct variation equation that relates x and y.

Equation:

(b) Find y when x = 6.

y =

Answer:

A. 8

Step-by-step explanation:

BE = ½(CD) (midsegment theorem)

BE = 2x - 10

CD = 12

Plug in the values

2x - 10 = ½(12)

2x - 10 = 6

Add 10 to both sides

2x - 10 + 10 = 6 + 10 (addition property of equality)

2x = 16 (addition property of equality)

Divide both sides by 2

2x/2 = 16/2

x = 8 (division property of equality)

Answer:

2.5 hours

Step-by-step explanation:

They are 22.5 miles apart. Chase is going 6 mph and Jada is going 3 mph.

6 × 2 = 12

6 × 0.5 = 3

12 + 3 = 15 miles

3 × 2 = 6

3 × 0.5 = 1.5

6 + 1.5 = 7.5 miles

15 + 7.5 = 22.5 miles

It would take them 2.5 hours to reach each other.

Hope that helps.

Answer:

$168

Step-by-step explanation:

Answer:

20% = 0.20

0.20 x 210 = $42

$42 discount

210 - 42 = 168

Your total amount you would pay would be $168. The discount is $48.

Answer:

D

Step-by-step explanation:

10(4 - 7)/-(4 - 1)

40-70/-4+1

-30/-3

=10

Answer:

1/8

Step-by-step explanation:

1/8 + 1/2 + 1/4 = 1/8 + 4/8 + 2/8 = 7/8

so 1/8 remains

Answer:

D is your answer

hopefully this helps

kill meStep-by-step explanation:

Answer:

8,667.14

Step-by-step explanation:

1. Multiply 29.1 by 20.4 = 593.64

2. Multiply 593.64 by 14.6 =  8,667.14

Answer:

Step-by-step explanation:

Nose

Answer:

2.25 F

Step-by-step explanation:

I subtracted 3/4 from 3.

Hope this helped.

-Pepsi

Answer:

14.

[tex]x = 11[/tex]  [tex]m<B = 108[/tex]   [tex]m<C= 36[/tex]   [tex]m<D = 36[/tex]

15.

[tex]x = 4[/tex]     [tex]WX = 25[/tex]     [tex]XY = 17[/tex]     [tex]WY = 25[/tex]

Step-by-step explanation:

Solving (14):

[tex]BC = BD[/tex]

[tex]m<B = 13x - 35[/tex]

[tex]m<C = 5x - 19[/tex]

[tex]m<D = 2x + 14[/tex]

First, we solve for x.

Since sides [tex]BC = BD[/tex], then

[tex]m<C = m<D[/tex]

This is so because the theorem of ASA (Angle-Side-Angle)

So, we have:

[tex]5x - 19 = 2x + 14[/tex]

Collect Like Terms

[tex]5x - 2x = 19 + 14[/tex]

[tex]3x = 33[/tex]

Divide both sides by 3

[tex]x = 11[/tex]

Solving for m<B, m<C and m<D.

We simply substitute 11 for x in their respective expressions.

[tex]m<B = 13x - 35[/tex]

[tex]m<B = 13*11 - 35[/tex]

[tex]m<B = 143 - 35[/tex]

[tex]m<B = 108[/tex]

[tex]m<C = 5x - 19[/tex]

[tex]m<C= 5*11 - 19[/tex]

[tex]m<C= 55 - 19[/tex]

[tex]m<C= 36[/tex]

[tex]m<D = 2x + 14[/tex]

[tex]m<D = 2*11 + 14[/tex]

[tex]m<D = 22 + 14[/tex]

[tex]m<D = 36[/tex]

Solving (15):

[tex]<X = <Y[/tex]

[tex]WX = 9x - 11[/tex]

[tex]XY = 4x + 1[/tex]

[tex]WY = 7x - 3[/tex]

First, we solve for x.

Since [tex]<X = <Y[/tex], then

[tex]WX = WY[/tex]

This is so because the theorem of SAS (Side-Angle-Side)

So, we have:

[tex]9x - 11 = 7x - 3[/tex]

Collect Like Terms

[tex]9x - 7x = 11-3[/tex]

[tex]2x = 8[/tex]

Divide both sides by 2

[tex]x = 4[/tex]

Solving for WX, WY and XY

We simply substitute 4 for x in their respective expressions.

[tex]WX = 9x - 11[/tex]

[tex]WX = 9 * 4 - 11[/tex]

[tex]WX = 36 - 11[/tex]

[tex]WX = 25[/tex]

[tex]XY = 4x + 1[/tex]

[tex]XY = 4 * 4 + 1[/tex]

[tex]XY = 16 + 1[/tex]

[tex]XY = 17[/tex]

[tex]WY = 7x - 3[/tex]

[tex]WY = 7 * 4 - 3[/tex]

[tex]WY = 28 - 3[/tex]

[tex]WY = 25[/tex]

Answer:

1 3/4

Step-by-step explanation:

Answer:

B. rational

Explanation:

Every integer is a rational number since each integer n can be written in the form n/1. For example 5 = 5/1 and thus 5 is a rational number.

Answer:

41

Step-by-step explanation:

101+38=139

180-139 = 41

Answer:

22-9t

Step-by-step explanation:

(7 - 3t) + 3(-2t + 5)

=

7+−3t+(3)(−2t)+(3)(5)=

7+−3t+−6t+15

=

Now you need to combine like terms.

7+−3t+−6t+15

=

(−3t+−6t)+(7+15)=

-9t+22=

22-9t

There you go.

Answer:

22 - 9t

Step-by-step explanation:

(7 - 3t) + 3(-2t + 5)

7 - 3t + -6t + 15

7 - 9t + 15

22 - 9t

Answer:

14

Step-by-step explanation:

If AC = 24, you just have to subtract AB = 10 from AC to find BC.

24 - 10 = 14

Answer:

B

Step-by-step explanation:

For your question: A dolphin jumps from the water with an initial velocity of 44 feet per second at an elevation angle of 60°. Which parametric equations model the dolphin’s path through the air?

After doing the math in my notebook, I got the answer D.

Please let me know if you have any other questions down below.

Answer:

D

Step-by-step explanation:

2 sin²x=sin x

2 sin² x-sin x=0

sin x(2 sin x-1)=0

sin x=0

x=0,π

2 sin x-1=0

2 sin x=1

sin x=1/2= sin π/6,sin (π-π/6)

x=π/6,5π/6

Greetings.

The answer is y = 2x + 7.

Explanation:

If you are an expert in graph then you are able to find the slope without calculating. (Rise over Run by looking at the graph.)

We can also find the slope by calculating m-value.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]   ---> Rise Over Run

But how are we gonna calculate if we don't have any two given ordered pairs?

The answer is, we can just pick two ordered pairs that are part of the graph, or rather say that the graph passes through.

The graph passes through (-3,1) and (-2,3).

Then we can calculate the slope by using rise/run.

[tex]m=\frac{3-1}{-2-(-3)}\\m=\frac{2}{-2+3}\\m=\frac{2}{1}\\m=2[/tex]

Thus, the slope is m = 2.

However, we are not done yet. We just only found out the slope. We need to find the y-intercept too.

From Linear Function - [tex]y=mx+b[/tex]

Where m = slope and b = y-intercept.

Since b = y-intercept, we don't need to calculate/substitute x = 0. We simply find which number the graph has y-intercept at.

Which is (0,7), the y-intercept.

Then we substitute b = 7 as y-intercept.

Thus the answer is [tex]y=2x+7[/tex]

Answer:

you need more than one point to find the slope of a line?

Step-by-step explanation:

Answer:

x = -14, 0

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

(x + 7)² - 49 = 0

Step 2: Solve for x

Step 3: Check

Plug in x values into original equation to verify they are a solution.

x = -14

Here we see that 0 does indeed equal 0.

∴ x = -14 is a solution of the equation

x = 0

Here we see that 0 does indeed equal 0.

∴ x = 0 is also a solution of the equation.

Answer:

Lesser x=-14 Greater x=0

Step-by-step explanation:

x+7)  

2

−49

(x+7)  

2

(x+7)  

2

​  

​  

=0

=49

=  

49

​  

​  

Hint #22 / 3

\begin{aligned} x+7&=\pm7 \\\\ x&=\pm7-7 \\ \phantom{(x + 7)^2 - 49}& \\ x=-14&\text{ or }x=0 \end{aligned}  

x+7

x

(x+7)  

2

−49

x=−14

​  

=±7

=±7−7

or x=0

​  

Answer:

Yes

Step-by-step explanation:

$24 divided by 6 equals 4

$52 divided by 13 equals 4

Answer: 41.3m

Step-by-step explanation: Hope this helps

Answer:

using distance formula you can solve it

Answer:

28.57%

Step-by-step explanation

I added all the animals together and got the precentage of rabbits

Hopefully its right :)

Answer:

The roots are real.

Step-by-step explanation:

Given quadratic equation to us is 4x² -4x -19 = 0.

With respect to Standard form ax² +bx +c = 0 , Discriminant of the quadratic equation is given by b² - 4ac . Here's a table for Nature of Roots .

[tex]\boxed{\begin{array}{|r|r|r|} \underline{\red{\bf S.no.}} & \underline{\red{\bf Condition }} & \underline{\red{\bf Nature \ of \ Roots }} \\\\ \sf 1 & \sf Discriminant > 0 & \sf Real \:Roots \\\\ \sf 2 &\sf Discriminant = 0 &\sf Equal \:Roots \\\\ \sf 3 & \sf Discriminant < 0 &\sf Complex \: Roots \end{array} }[/tex]

Hence here , wrt Standard form ,

• a = 4 , • b = -4 & •c = -19 .

[tex]\implies Discriminant = b^2-4ac \\\\\implies Discriminant = (-4)^2-4(4)(-19) \\\\\implies Discriminant = 16+304 \\\\\boxed{\red{\bf \implies Discriminant = 320 }}[/tex]

Hence since Discriminant is Greater than 0 , hence the nature of roots of the quadratic equation is real.

Answer:

b, c, e

Step-by-step explanation: