2. What is the slope of the line 2x + y = 8?

Answer:

a. 7.2

Step-by-step explanation:

CAH (cos = adj/hyp)

cos53 = b/12; cross multiply

cos53*12 = 7.2

15. 70° because a right angle is 90° and we have the angle of ADB which is 20°. So 90°-20°=70°.

16. 70° because angle PSQ is 60° and angle QSR is 10°. So 60°+10°=70°.

17. 55° because it says it in the explanation. I assume this is a typo and they meant to ask the measurement of ADC and in that case it would be 130° because angle ADB is 75° and angle BDC is 55°. 75°+55°=130°.

18. 40° because angle PSQ is a right angle which means it's 90°. So 130°-90°=40°.

19. 140° because angle ADB is 120° and angle BDC is 20° so 120°+20°=140°.

20. 125° because again it's in the explanation. But if it's a typo and they meant what is the measurement of PSQ then it is 50° because PSR is 125° and QSR is 75° so 125°-75°=50°.

Hope this helps! :)

Answer:

Step-by-step explanation:

(x+4)^2.(x+4)^2

= x^4 +16x^3+96x^2+256x+256

Answer:

72

Step-by-step explanation:

all you had to do was divide by 2

Answer:

367.5

Step-by-step explanation:

5x7x10.5

Answer:

367.5

Step-by-step explanation:

5 x 7 = 35

35 x 10.5 = 367.5

Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.

Answer:

-3 3/4

Step-by-step explanation:

So we have:

-1 1/4 + (-2 1/2)

Before solving this, lets just clean it up.

First off, since we know that a + and - sign equals a - sign, we can rewrite it as:

-1 1/4 - (2 1/2)

We need to also get a common denominator, which would be 4. The first fraction already has a denominator of 4, so it doesnt change. However, the second fraction is 1/2, and we need to multiply both sides by 2 to change the denominator from 2 to 4:

-1 1/4 - (2 2/4)

Now lets solve:

I will do the fraction seperate from the whole number to make it simpler:

-1 - 2

A negative subtracted makes it a larger negative so:

-3

-1/4 - 2/4

Again, a negative subtracted makes it a larger negative:

-3/4

Now recombine the numbers:

-3 3/4

So this is your answer.

Hope this helps!

Answer:

(a-3)(a+3) is the answer

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {55}}}}}}[/tex]

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

[tex] {a}^{2} - 9[/tex]

Substituting the value "[tex]a = 8[/tex]" in the above expression, we have

➺ [tex] \: {8}^{2} - 9[/tex]

➺ [tex] \: (8 \times 8) - 9[/tex]

➺ [tex] \: 64 - 9[/tex]

➺ [tex] \: 55[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

Answer:

x = -28

Step-by-step explanation:

−1/4x=7

Multiply each side by -4 to isolate the variable

-4 *  −1/4x= -4*7

−1/4x=7

Answer:

 [tex]x_{n} =[/tex] -10 - 3(n-1)

Step-by-step explanation:

The answer is

xn =  -10 - 3(n-1)

The equation of red graph is [tex]F(x) = 2 -x^{2}[/tex].

The general equation of parabola is [tex]y = a(x-h)^{2} + k[/tex].

Where,

(h, k) are the vertices of the parabola.

According to the given question.

We have two graph.

The blue and red graph both represents the equation of downward parabola.

Since, blue graph represents the equation of downward parabola.

Whose equation is given

[tex]G(x) = 5 - x^{2}..(i)[/tex]

The general equation of a parabola is [tex]y = a(x-h)^{2} + k..(ii)[/tex]

Where, (h, k) are the vertices of the parabola.

Compare the equation (i) with (ii)

We get

(h, k) = (0, 5) and a = -1.

Now, the red graph which also represents the downward parabola whose vertices are (0, 2)

Therefore, the equation red graph is given by

[tex]F(x) = a(x-0)^{2} + 2[/tex]

⇒ [tex]F(x) = -1(x-0)^{2} + 2[/tex]

⇒ [tex]F(x) = 2 - x^{2}[/tex]

Hence, the equation of red graph is [tex]F(x) = 2 -x^{2}[/tex].

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Answer:

Step-by-step explanation:

By using the property of similar triangles,

"Corresponding sides of two similar triangles are proportional"

If ΔSMA ~ ΔPOD

[tex]\frac{SM}{PO}=\frac{MA}{OD}=\frac{SA}{PD}[/tex]

[tex]\frac{6}{10}=\frac{5}{10}=\frac{5}{12}[/tex]

[tex]\frac{3}{5}=\frac{1}{2}=\frac{5}{12}[/tex]

Since, ratios of corresponding sides are not equal,

Therefore, the given triangles are not similar.

Answer:

[tex]10\frac{7}{18}[/tex]

Step-by-step explanation:

First revert it to improper fraction.

[tex]\frac{13}{2} +\frac{35}{9} \\\\[/tex]

Now put them to a common denominator.

[tex]\frac{187}{18}[/tex]

=> [tex]10\frac{7}{18}[/tex]

Answer:

b. 113.04 ft³

Step-by-step explanation:

To find the volume of this composite figure, we must find the volumes of the shapes it is composed of. After finding the volumes, add the volumes.

This figure is composed of a circular cone and a cylinder.

To find the volume of a cylinder, multiply the radius by itself twice, then multiply the product pi, lastly multiply the product by its height.

[tex]v=\pi *r^2*h[/tex]

To find the volume of a circular cone, multiply the radius by itself twice, then multiply the product by the height, then multiply the product by pi, lastly multiply the product by 1/3.

[tex]v=1/3*h*\pi* r^2[/tex]

Now that we know the formulas, we can find the volume of this figure.

----------------------------------------------------------------------

The height of the cylinder is 3 feet. The radius is 3 feet as well.

Remember: 3.14 will be used for pi (π).

[tex]v=\pi *3^2*3=84.78[/tex]

The volume of the cylinder is 84.78 feet.

----------------------------------------------------------------------

Further more, we find the volume of the circular cone.

The height of the cone is 3 feet. The radius is 3 feet as well.

[tex]v=1/3*3*\pi *3^2=28.26[/tex]

Lastly, we add the volumes of both shapes.

[tex](84.78+28.26)[/tex]

[tex]=113.04.[/tex]

113.04 does not need to be rounded to the nearest hundredth.

----------------------------------------------------------------------

Therefore, the volume of this composite figure is 113.04 ft.

Answer:

Step-by-step explanation:

100 sq cm

Answer:

The value of sin theta is 5/13

Step-by-step explanation:

In the second quadrant, sin is positive and cos is negative

Cos theta = -12/13 = adjacent/hypotenuse

Sin theta = opposite/hypotenuse

opposite = sqrt(hyp² - adj²) = sqrt (13² - 12²) = sqrt (169 - 144) = sqrt (25) = 5

Sin theta = opposite/hypotenuse = 5/13

Answer:

y = - 3

Step-by-step explanation:

x = 4 is a vertical line parallel to the y- axis

A line perpendicular to it will be a horizontal line parallel to the x- axis with equation

y = c

where c is the value of the y- coordinates of the points the line passes through.

The line passes through (- 3, - 3) with y- coordinate - 3 , then

y = - 3 ← equation of perpendicular line

Answer:

x = 9

Step-by-step explanation:

square each side first to get:

8x - 8 = 64

8x = 72

x = 9

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {x\:=\:33}}}}}}[/tex]

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

[tex]x = 42 - 9[/tex]

➼[tex]\:x = 33[/tex]

Therefore, the value of [tex]x[/tex] is 33.

[tex]\sf\pink{Thank\:you. \:ヅ}[/tex]

Answer:

x =33

Step-by-step explanation:

x = 42-9

We are solving for x, which is already isolated

42-9 = 33

x = 33

Check 33+9 = 42

Answer:

c = -10

Step-by-step explanation:

For this we can use basic algebra. Add 15 on both sides. This gives us 3c = -30. Divide by 3 on both sides. The final answer is c = -10.

The value of c is -10 in the equation 3c - 15 = -45.

Two or more expressions with an Equal sign is called as Equation.

The given equation is 3c-15=-45

Three times of c minus fifteen equal to minus forty five.

In the given equation minus is the operator and c is the variable.

We need to solve for variable c

3c-15=-45

Add 15 on both sides

3c-15+15=-45+15

3c=-30

Divide both sides by 3

c=-10

Hence, the value of c is -10 in the equation 3c - 15 = -45.

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Answer:

y=3    x=1

Step-by-step explanation:

Answer:

above one is correct. I think so

the answers are in the picture

Answer:

2ab

Step-by-step explanation:

6ba + 2ab = 2ab(3+1)

= 2ab (4)

so, the common factor = 2ab

Answer:

2ab

Step-by-step explanation:

Answer:

Step-by-step explanation:

d

Answer:

5.348

Step-by-step explanation:

5 + 0.3 + 0.04 + 0.008

If you find this difficult to calculate put zeroes in Hundredths place and thousandths place

=> 5.000 + 0.300 + 0.040 + 0.008

=>5.348

Answer:

36

Step-by-step explanation:

1/2bh

1/2 (6*4) =12

Considering there are three triangles we will multiply by 3

12*3=36

Answer:

f(x)=x+5

Step-by-step explanation:

x=-1 therefore -1+5=4

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the function is

[tex]y=x^2-4x[/tex], then its derivative is

y' = 2x - 4. This is equal to 0 where

2x - 4 = 0 and

2x = 4 so

x = 2. When x = 2 in the original equation:

[tex]y =2^2-4(2)[/tex] so

y = -4. So the coordinate is (2, -4). On to the next one:

If the function is

[tex]y=25x +\frac{1}{x}[/tex] then its derivative is

[tex]y'=25-\frac{1}{x^2}[/tex]. This is equal to 0 where

[tex]25-\frac{1}{x^2}=0[/tex] and

[tex]-\frac{1}{x^2}=-25[/tex] or, in simpler terms:

[tex]\frac{1}{x^2}=\frac{25}{1}[/tex] so

[tex]25x^2=1[/tex] and

[tex]x^2=\frac{1}{25}[/tex] so

x = ±[tex]\sqrt{\frac{1}{25} }[/tex] so

x = [tex]\frac{1}{5},- \frac{1}{5}[/tex]. When you plug those into the original equation, you get the coordinates

[tex](\frac{1}{5},10)[/tex] and [tex](-\frac{1}{5},-10)[/tex]