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2. In ATVW if VW is three meters longer than TV, TW
is 19 meters shorter than the sum of VW and TV,
and the perimeter of ATVW is 62 meters, find the length of VW.
20.75 m
15.75 m
25.5 m
21.75 m
None of the above

Answer:

x = 1

y = 5

z = 2

Step-by-step explanation:

System of equations:

6x - 2y + z = -2

2x + 3y - 3z = 11

x + 6y = 31

Isolate one variable in any of the equations:

x + 6y = 31

x = 31 - 6y

Plug in this value for x in another equation:

6(31 - 6y) - 2y + z = -2

186 - 36y - 2y + z = -2

186 - 38y + z = -2

-38y + z = -188

z = -188 + 38y

Plug in these values in the remaining equation:

2(31 - 6y) + 3y - 3(-188 + 38y) = 11

62 - 12y + 3y + 564 - 114y = 11

626 - 12y + 3y - 114y = 11

626 - 9y - 114y = 11

626 - 123y = 11

-123y = -615

y = 5

Plug in value of y into our other answers to solve for x and z:

x = 31 - 6(5)

x = 31 - 30

x = 1

z = -188 + 38(5)

z = -188 + 190

z = 2

Check your work:

6x - 2y + z = -2

6(1) - 2(5) + 2 = -2

6 - 10 + 2 = -2

-4 + 2 = -2

-2 = -2

Correct!

*Note there are several ways to solve for these types of problems. I used substitution*

Answer:

33.33%

Step-by-step explanation:

Prime numbers from 1 to 30 are 2,3,5,7,11,13,17,19,23,29.

So There are 10 prime numbers

Therefore,

P(of randomly selecting a prime number from the first 30 natural numbers)=10/30= 1/3 = 33.33%

9514 1404 393

Answer:

  -15

Step-by-step explanation:

If 'a' and 'b' are zeros of the quadratic f(x), its factored form is ...

  f(x) = (x -a)(x -b)

and its standard form is ...

  f(x) = x^2 -(a+b)x +ab

This tells us that ...

  a+b = -7

  ab = 7

for the given quadratic.

Then the expression of interest is ...

  [tex]a^{-1}+b^{-1}-2ab=\dfrac{1}{a}+\dfrac{1}{b}-2ab=\dfrac{a+b}{ab}-2ab\\\\=\dfrac{-7}{7}-2\cdot7=-1-14=\boxed{-15}[/tex]

Answer:

no...you can just use a clip on

Answer:

it's absolutely worth it. The pain of getting one isn't that bad, at least for me. It's just a quick pinch. It'll look so good. Just make sure you are also cleaning it.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

9514 1404 393

Answer:

  d, b, c, a, e

Step-by-step explanation:

The order of the letters in the congruence statement tells you ...

  ΔQOP ≅ ΔABC

  ∠Q ≅ ∠A

  ∠O ≅ ∠B ≅ 115°

  ∠P ≅ ∠C

  QO ≅ AB = 5 m

  OP ≅ BC = 8 m

  PQ ≅ CA

Answer:

[tex]{ \tt{ w = 2hx - 11x}} \\ \\ { \bf{w = x(2h - 11)}} \\ \\ { \bf{x = \frac{w}{2h - 11} }}[/tex]

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = \frac{w}{(2h - 11)} }}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]w = 2hx - 11x[/tex]

[tex]✒ \: w = x \: (2h - 11)[/tex]

[tex]✒ \: x = \frac{w}{(2h - 11)} [/tex]

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

Answer:

Graph 4

Step-by-step explanation:

Answer:

b bc it is i got it right

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

I believe it is this answer bur don't hold me to. If it is wrong I'm sorry in advance

Answer:

The two angles are 31° and 149°

Step-by-step explanation:

Let the two supplementary angles be , x and y.

         Then, x + y = 180° ----- ( 1 )

Given :  one is 25° more than 4 times other

           Let y = 25° + 4x ------ ( 2 )

Substitute ( 2 ) in  ( 1 ) :

     x + y = 180°

     x + 25° +4x = 180°

     x + 4x = 180° - 25°

           5x = 155°

             x = 31°

Substitute x in ( 2 ) :

            y = 25° + 4x

               = 25 + 4 ( 31 )

               = 25 + 124

               = 149°

Answer:

B) Coefficient.

Step-by-step explanation:

The coefficient is the numerical constant in the given term.

For example, the given term is 4x, in which:

4 is the coefficient.

x is the variable.

5 is the constant.

20 is another constant.

~

Answer:

Hi im not got with graphs

Step-by-step explanation:

Answer:

m=2, n=-1 or (2,-1)

Step-by-step explanation:

Hi there!

We're given this system of equations:

3n+5m=7

m-4n=6

we want to solve by substitution; in one equation, we'll set one variable to equal an expression containing the other variable, substitute that expression as the variable into the other equation, solve for the variable substituted, and use the value of that variable to find the other variable

First, let's get the expression we'll substitute into the other

let's use m-4n=6 as it has 1m (m by itself)

add 4n to both sides

m=4n+6

now substitute 4n+6 as m into 3n+5m=7 to solve for n

3n+5(4n+6)=7

do the distributive property

3n+20n+30=7

combine like terms

23n+30=7

subtract 30 from both sides

23n=-23

divide both sides by 23

n=-1

we found the value of n

now let's substitute -1 as n in m=4n+6 to find the value of m

m=4(-1)+6

multiply

m=-4+6

add

m=2

so the answer is m=2, n=-1. As a point, it's (2,-1)

Hope this helps! :)

Answer:

x = 4 (ONE solution)

Step-by-step explanation:

This is a first order linear equation, so we can expect 1 solution.

Multiplying out the left side, we get:

8x - 24 = 7x - 20, which simplifies to:

x = 4 (ONE solution)

Answer:

Step-by-step explanation:

y=5px+5x2+p2

y=10p2x2p

Answer:

(0,6)

Step-by-step explanation:

Answer:

(0,6)

Step-by-step explanation:

We need to find the midpoint of the line segment having end points (-4,5) and (4,7). So, here we can use the Midpoint Formula :-

Points :- (-4,5) and (4,7).

Using Midpoint Formula ,

[tex]\rm\implies Midpoint =\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)[/tex]

Substitute the respective values ,

[tex]\rm\implies Midpoint =\bigg(\dfrac{-4+4}{2},\dfrac{7+5}{2}\bigg)[/tex]

Simplify the numbers ,

[tex]\rm\implies Midpoint =\bigg(\dfrac{0}{2},\dfrac{12}{2}\bigg)[/tex]

This equals to ,

[tex]\rm\implies \boxed{\blue{\rm Midpoint =\bigg( 0,6\bigg)}}[/tex]

Hence the midpoint is (0,6) .

Answer:

I think the answer is 1^2 - 10

Answer:

C, "She could have found the sum of 15 and 20 and then squared the sum."

Step-by-step explanation:

I just took the test on Edge :)

The answer is C, I got it right on edge.

Have a nice day everyone <3.

Answer:

The value of the z-test statistic is [tex]z = 0.68[/tex]

Step-by-step explanation:

An article claims that 12% of trees are infested by a bark beetle.

At the null hypothesis, we test if the proportion is of 12%, that is:

[tex]H_0: p = 0.12[/tex]

At the alternative hypothesis, we test if the proportion is different of 12%, that is:

[tex]H_1: p \neq 0.12[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.12 is tested at the null hypothesis:

This means that [tex]\mu = 0.12, \sigma = \sqrt{0.12*0.88}[/tex]

A random sample of 1,000 trees were tested for traces of the infestation and found that 127 trees were affected.

This means that [tex]n = 1000, X = \frac{127}{1000} = 0.127[/tex]

What is the value of the z-test statistic?

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.127 - 0.12}{\frac{\sqrt{0.12*0.88}}{\sqrt{1000}}}[/tex]

[tex]z = 0.68[/tex]

The value of the z-test statistic is [tex]z = 0.68[/tex]

Answer:

50 books were sold

Step-by-step explanation:

there are 5 books in the Red Crow row, and each book is worth 10 sold.

Answer:

No, 6 hours would cost $335, 35 over her limit of $300.

Step-by-step explanation:

she has to pay $200 plus 22.50 for every hour she rents. So, if she rents for 6 hours, she has to pay $200 + 6(22.50) or $200 + 135=335. She only has $300 so she can’t afford the event.

Answer:

31.3

Step-by-step explanation:

Reference angle given = 56.1°

Hypotenuse = 56.1

Adjacent side = x = ?

We would apply CAH, which is:

Cos 56.1° = Adj/Hyp

Cos 56.1° = x/56.1

56.1 × Cos 56.1° = x

31.2895006 = x

x = 31.3 (approximated to the nearest tenth)

Answer: c

Step-by-step explanation: edge 2021

Answer:

7 hours

Just divide 880/120 = 7.3333333

So if 7*120 = 840

An hour more would be more expensive.

Answer:

m∠A = 32°

Step-by-step explanation:

8^2 = 12^2 + 15^2 - 2*12*15*cosA

Answer:

B

Step-by-step explanation:

did it on edge

Answer:

x2+y2-12x24y+36=36.

2

+

y

2

−

12

x

+

18

y

=

−

36

Step-by-step explanation:

Answer:

Step-by-step explanation:

(x^2-12x+36) + (y^2-24y+144-144) = 0

(X-6)^2 + (y-12)^2=144