19. Roof trusses often use right triangles to make a flimsy 2 x 4 more rigid to hold up the weight of the roof. If a
house is 40 feet wide and the roof is an isosceles triangle with base angles of 30, how far is it from the
bottom edge of the roof to the peak?
(Answer is radical form please!!!)

Answer:

Step-by-step explanation:

[tex]\frac{3}{2} + \frac{2m}{9} = \frac{37}{18}[/tex]

Multiply through by 18 to eliminate the fraction

That's

[tex]18 \times \frac{3}{2} + 18 \times \frac{2m}{9} = 18 \times \frac{37}{18} \\ 27 + 4m = 37[/tex]

Subtract 27 from both sides

That's

[tex]27 - 27 + 4m = 37 - 27 \\ 4m = 10[/tex]

Divide both sides by 4

That's

[tex] \frac{4m}{4} = \frac{10}{4} [/tex]

We have the final answer as

[tex]m = \frac{5}{2} [/tex]

Hope this helps you

[tex]\Huge{\boxed{\sf{\red{m = \frac{5}{2}}}}}[/tex]

[tex]\displaystyle{\sf{ \frac{3}{2} + \frac{2m}{9} = \frac{37}{18}}} [/tex]

| ∵ Transposing 3/2 to R.H.S

[tex]\implies[/tex] [tex]\displaystyle{\sf{ \frac{2m}{9} = \frac{37}{18} - \frac{3}{2}}} [/tex]

[tex]\implies[/tex] [tex]\displaystyle{\sf{ \frac{2m}{9} = \frac{37-27}{18}}} [/tex]

[tex]\implies[/tex] [tex]\displaystyle{\sf{ \frac{2m}{9} = \frac{10}{18} = \frac{5}{9}}} [/tex]

[tex]\implies[/tex] [tex]\displaystyle{\sf{ 2m = \frac{5}{9} \times 9}} [/tex]

[tex]\implies[/tex] [tex]\displaystyle{\sf{ 2m = 5}} [/tex]

[tex]\longrightarrow[/tex] [tex]\large{\boxed{\sf{\red{ m = \frac{5}{2}}}}}[/tex]

you calculate for the LCM of the denominator

9

7

6

5

which Thier Lcm is 630

Answer:

9,000,000

Step-by-step explanation:

Since the 5 next to the 8 is a number with a value of 5 or higher, you can round the 8 up to a 9 thus rounding to the nearest million.

Answer:

[tex]\huge\boxed{x=12}[/tex]

Step-by-step explanation:

If B is the midpoint of line AC, we know that lines AB and BC will be equivalent to each other.

Since we know the measures of AB and BC, we can just set these expressions equal to each other and find the value of [tex]x[/tex].

[tex]6x - 27 = 3(x+3)[/tex]

Let's simplify this equation until we have [tex]x[/tex] on one side of it.

[tex]6x-27=3x+9\\\\6x=3x+36\\\\3x=36\\\\x=12[/tex]

Hope this helped!

Answer:

r = 7

Step-by-step explanation:

Step 1: Write out equation

4r + 7 = 35

Step 2: Subtract 7 on both sides

4r + 7 - 7 = 35 - 7

4r = 28

Step 3: Divide both sides by 4

4r/4 = 28/4

r = 7

Solve 4r+7=35

4r=35-7

4r=28

r=7

:)

Answer: 5x + 2y = 10, 15x = -6y - 9

Step-by-step explanation: good luck on your algebra Nation test

The dimensions of this rectangle are 4 units by 3 units

4 units * 3 units = 12 sq units

Answer:

mode = maximum repeated item

here mode = 4.2

Answer:

1/2b=-4+16

1/2b= 12

b=12×2

b=24

Answer:

constants = -16 and -4

coefficients are 1/2

Step-by-step explanation:

a constant is a number not attached to a variable. a coefficient is a number attached to a variable

Answer:

Susie rounded to the nearest thousandth.

Step-by-step explanation:

since the 100th place is 0 it would round down to 39,000 when you are rounding to the nearest thousand.

Answer:

y=-2

Step-by-step explanation:

9(y−4)−7y=5(3y−2)

(9)(y)+(9)(−4)+−7y=(5)(3y)+(5)(−2)

9y+−36+−7y=15y+−10

(9y+−7y)+(−36)=15y−10

2y+−36=15y−10

2y−36=15y−10

Step 2:

2y−36−15y=15y−10−15y

−13y−36=−10

Step 3:

−13y−36+36=−10+36

−13y=26

divide

/13     /13

y=-2

Answer:

y=-2

Step-by-step explanation:

Simplifying

9(y + -4) + -7y = 5(3y + -2)

Reorder the terms:

9(-4 + y) + -7y = 5(3y + -2)

(-4 * 9 + y * 9) + -7y = 5(3y + -2)

(-36 + 9y) + -7y = 5(3y + -2)

Combine like terms: 9y + -7y = 2y

-36 + 2y = 5(3y + -2)

Reorder the terms:

-36 + 2y = 5(-2 + 3y)

-36 + 2y = (-2 * 5 + 3y * 5)

-36 + 2y = (-10 + 15y)

Solving

-36 + 2y = -10 + 15y

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-15y' to each side of the equation.

-36 + 2y + -15y = -10 + 15y + -15y

Combine like terms: 2y + -15y = -13y

-36 + -13y = -10 + 15y + -15y

Combine like terms: 15y + -15y = 0

-36 + -13y = -10 + 0

-36 + -13y = -10

Add '36' to each side of the equation.

-36 + 36 + -13y = -10 + 36

Combine like terms: -36 + 36 = 0

0 + -13y = -10 + 36

-13y = -10 + 36

Combine like terms: -10 + 36 = 26

-13y = 26

Divide each side by '-13'.

y = -2

Simplifying

y = -2

Answer:

slope is undefined

Step-by-step explanation:

x = - 5 is the equation of a vertical line, parallel to the y- axis.

The slope of a vertical line is undefined.

Answer:

Two rays that share the same endpoint form an angle. The point where the rays intersect is called the vertex of the angle. The two rays are called the sides of the angle. An angle is also the space between the sides.

Step-by-step explanation:

Answer:

3

1

4

-2

Step-by-step explanation:

imma math mannnnn

Answer:

Step-by-step explanation:

(5x + 4)(x^2 - 7x + 12)

5x^3 - 35x^2 + 60x + 4x^2 - 28x + 48

5x^3 - 31x^2 + 32x + 48

Answer:

[tex]MP= (-6,3)[/tex]

Step-by-step explanation:

[tex]MP= (\frac{x_1+x_2}{2} )(\frac{y_1+y_2}{2} )\\MP= (\frac{6+-6}{2} )(\frac{12+-6}{2} )\\MP= (\frac{-12}{2} )(\frac{6}{2} )\\MP= (-6,3)[/tex]

Answer:

Rational

Step-by-step explanation:

The square root of 16 is 4, and 4 + 1.5 is = to 5.5. An irrational number is defined as infinite and never-ending. Since 5.5 is not infinite, we can conclude that it isn't irrational.

Answer:

7/8

Step-by-step explanation:

Given the length of the actual movie time and the length of the total movie time, the actual movie is 7/8 of the total movie time.

Given the data in the question;

Total time of the movie is 2 hours and 40 minutes = 160 minutes

Preview time is 20 minutes

Now time of the actual movie will be;

Total time of the movie - Preview time

2 hours and 40 minutes - 20 minutes

160 minutes - 20 minutes

Time of the actual movie is 140 minutes

Now we get the fraction

Time of the actual movie / Total time of the movie

= 140 minutes / 160 minutes

= 14/16

= 7/8

Therefore, given the length of the actual movie time and the length of the total movie time, the actual movie is 7/8 of the total movie time.

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Answer:

1) 21

2) -10

3)10

4)50

5) 3,700

Answer:

3m=18+12

3m=30

divide both sides by 3

m=10

Answer:

m = 10

Step-by-step explanation:

3m - 12 =18

Add 12 to each side

3m - 12+12 =18+12

3m = 30

Divide by 3

3m/3 = 30/3

m = 10

Answer:

substitute value of x and y as 2 and 4

y=5x-6

4= 5*2-6

4=4 so yes

Step-by-step explanation:

The point (2, 4) lie on the line y = 5x-6

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

For example, 3x + 5 = 15.

Given that, we need to check whether the point 2,4 lie on the line y=5x-6 or not,

So, the verification of the same, we will simply put the value of x (2) in the equation and see whether we are getting 4 or not, if not then points do not lie on the line, if yes, the point lies on the line.

So, the equation is

y = 5x-6

Put x = 2,

y = 5(2) - 6

y = 10-6

y = 4

Since, we get the value of y = 4, therefore, the point lies on the line.

Hence, the point (2, 4) lie on the line y = 5x-6

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The number 4.5x10⁻⁶ can be expressed in standard notation as decimal 0.0000045.

In scientific notation, numbers are expressed as a decimal number between 1 and 10 multiplied by a power of 10. In this case, 4.5 is the decimal number and 10⁻⁶ represents the power of 10.

To convert this to standard notation, we move the decimal point six places to the left to match the negative exponent of 10⁻⁶. This gives us:

0.0000045

In standard notation, this number is written as 0.0000045, where the zeros after the decimal point indicate the value of the number in the place of each digit. The last non-zero digit in this case is 5, which is in the sixth decimal place.

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The complete question:

What is 4.5x10⁻⁶ in standard notation?

Answer:

5/4

Step-by-step explanation:

(y₂ - y₁) / (x₂ - x₁)

(4,9) (-8, -6)

plug in

(-6 - 9) / (-8 - 4)

solve within parentheses

-15/-12

simplify

5/4

what is the slope of points (4,9) (-8,-6)

Answer:

5/4