Using the Pythagoras Theorem

Answer:

b = -9

Step-by-step explanation:

-7b - 4(b + 7) = -3b - 4(b -2)

First we want to distribute the coefficients across the parentheses. To do so, we multiply the coefficient by every term within the parentheses.

-7b - 4(b + 7) = -3b - 4(b - 2)

-4 • b = -4b

-4 • 7 = -28

-4 • b = -4b

-4  • -2 = 8

Simplify the expression with these new values.

-7b - 4b - 28 = -3b - 4b + 8

Now we want to combine the like terms. First combine the variables.

-7b - 4b - 28 = -3b - 4b + 8

-11b - 28 = -7b + 8

Combine further by adding 7b to both sides.

-4b - 28 = 8

Combine the constants by adding 28 to both sides.

-4b = 36

Isolate b by dividing both sides by -4.

b = -9

This is your answer.

Check your answer by plugging b = -9 back into the original equation.

-7b - 4(b + 7) = -3b - 4(b - 2)

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

63 - 4(-2) = 27 - 4(-11)

63 + 8 = 27 + 44

71 = 71

Your answer is correct.

Hope this helps!

Answer:

-9 is the required answer of b

Step-by-step explanation:

-7b - 4(b + 7) = -3b - 4(b-2)

open bracket

-7b-4b-28=-3b-4b+8

-11b-28=-7b+8

-11b+7b=28+8

-4b=36

b=36/-4=-9

Answer:

d = 711 miles

Step-by-step explanation:

The speed s of the car is given by :

[tex]s=3\sqrt{d}[/tex] ...(1)

Where

d is the stopping distance

We need to find the stopping distance of a car travelling at 80 mph.

Rearranging equation (1) for d.

[tex]s^2=9d\\\\d=\dfrac{s^2}{9}\\\\d=\dfrac{80^2}{9}\\\\d=711.1\ miles[/tex]

or

d = 711 miles

So, the required stopping distance is 711 miles.

Answer:

Put a pretend dot at number 2 and number -4, then since the line is undefined, it will simply be vertical and look like this:

Answer:

536.17 cubic yards

Step-by-step explanation:

Answer:

its 50.27

Step-by-step explanation:

its asking what the base is equal to, so u find basically the area of the base

Answer:

58

Step-by-step explanation:

you need to order all the numbers together:

28​, 54, 56, 60, 62, 64

since the middle 2 are 56 and 60 you need to find the average of those.

(56 + 60)/2 = 58

Answer:

The two triangles are congruent, or equal to each other.

Step-by-step explanation:

In order to solve this question, you first need to compare the measurements. Since AB and PQ both equal 4 cm, you know that they are congruent. Since BC and QR are also congruent, you know that the last two have to be congruent as well. Therefore, the triangles ABC and PQR are congruent, or equal, to each other.

Answer:

x=60 y=50

Step-by-step explanation:

60+y=110

y=50

Answer: 1225

Step-by-step explanation:

Just plug in 350 for 'm':

3.5m

3.5m (350)

^^^^^^^^^^

times these two together, to get your final answer!

Multiply:

1225

Answer:

V = 226.08 m³

Step-by-step explanation:

The formula for the volume of a cone of base radius r and height h is

V = (1/3)(πr²)(h).

In this case, r = 6 m and h = 6 m.  Thus, the volume of this conical pile is

V = (1/3)(3.14)(6 m)²(6 m), or

V = 226.08 m³

Answer:

c

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan64° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{11}{c}[/tex] ( multiply both sides by c )

c × tan64° = 11 ( divide both sides by tan64° )

c = [tex]\frac{11}{tan64}[/tex] ≈ 5.4 ( to the nearest tenth )

Answer:

6

Step-by-step explanation:

The function is of the form

y =a f(bx) where |a| is the amplitude and b is the frequency

y = 6 sin (3x)

The amplitude is |6| = 6

Answer:

A. 61 degrees

Step-by-step explanation:

tan x = 9/5

[tex]tan^{-1} x=1.8[/tex]

x≈60.9

Answer:

y - 9 = -3/2 (x - 6)

Step-by-step explanation:

Equation of line: 4x - 6y - 15 = 0

Equation of perpendicular line: bx - ay + k = 0

                                                 = -6x - 4y + k = 0 → (equation 1)

Since the equation passes through (6,9)

-6(6) - 4(9) + k = 0

-36 -36 + k = 0

-72 + k = 0

k = 72

Substituting the value of in equation 1,

∴ Equation of perpendicular line = -6x -4y + 72 = 0

dividing by -2,

3x + 2y - 36 = 0

This equation is the simplified version of Option 1.

y - 9 = -3/2 (x - 6)

y - 9 = (-3x + 18)/2

2y - 18 = -3x + 18

3x + 2y - 36 = 0

Answer:

2

Step-by-step explanation:

Answer:

2.

Step-by-step explanation:

So you take your numbers, 1 and 1.

You add them together 1+1.

You have your answer, 2.

Answer:

[tex] - (x - 1) {}^{2} + 5[/tex]

Step-by-step explanation:

F(x) is a transformation from h(x).

So our starting equation is

[tex] - (x - 1) {}^{2} - 1[/tex]

F(x) is also facing the same direction h(x) is so we dont have to reflect nothing across the x or y axis.

There isn't a vertical or horizontal stretch, compressions.

There isn't a horizontal shift as the x values stay in the same place.

There is a vertical shift. We can simply move h(x) up 6 units to get to f(x).

So our equation looks like.

[tex] - (x - 1) {}^{2} + 5[/tex]

Answer:

Angle 1: 95 degrees

Angle 2: 85 degrees

Angle 3: 95 degrees

Step-by-step explanation:

Vertical angles are opposite and equal so in this case angle 1 and 3 are vertical and so are 2 and 85°

So that means angle 2 also equals 85 degrees and because of supplementary angles the other angle must add up to equal 180 degrees

85 + ? = 180

?=95

So both angle 1 and 3 equal 95 degrees

Answer:

(p - 8) / 2 = Maddie's pretzels

Answer:

Congruent Step-by-step explanation:

          b

Step-by-step explanation:

Answer:

volume of prism = lbh

Step-by-step explanation:

Volume of a cuboid = (length × breadth × height) cubic units. = (l × b × h)

lbh

Don't know for sure whether this is what the question wanted but oh well

Answer:

area of whole pizza = 200.96 in²

area of slice of pizza = 25.12 in²

Step-by-step explanation:

16"/2 = 8" radius

area = πr² = (3.14)(8²) = 200.96 in²

200.96 in²/8 = 25.12 in²

Answer:

100

Step-by-step explanation:

Given:

The points are A(3, -3), B(-3, -2), C(-5, 1), D(-5, 4), E(-4 ,6), F(-2, 6), G(3, 2).

To find:

The length of EF and plot each point on a coordinate plane and connect them.

Solution:

Plot the given point A(3, -3), B(-3, -2), C(-5, 1), D(-5, 4), E(-4 ,6), F(-2, 6), G(3, 2) on coordinate plane and connect them as shown in the below figure.

From the below graph it is clear that the length of EF is 2 units. We can verify this solution by using the distance formula.

Distance formula:

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using the distance formula, the distance between E(-4 ,6) and F(-2, 6) is

[tex]D=\sqrt{(-2-(-4))^2+(6-6)^2}[/tex]

[tex]D=\sqrt{(-2+4)^2+(0)^2}[/tex]

[tex]D=\sqrt{(2)^2+0}[/tex]

[tex]D=2[/tex]

Therefore, the length of EF is 2 units.

Answer:

24÷3+12 would be 20

Step-by-step explanation:

You do 24÷3 which is 8 and then you add 12. I hope this helps!

Answer:

Amber ran 8,333 kilometers during each hour, and the equation to determine that amount is 25/3 = X.

Step-by-step explanation:

Given that Amber ran a 25 kilometer road race in 3 hours, and she ran at the same speed and covered the same distance each hour, to draw a visual model to find the distance Amber ran each hour the following calculation must be performed:

25/3 = X

8.333 = X

So Amber ran 8,333 kilometers during each hour, and the equation to determine that amount is 25/3 = X.

Answer:

5 minutes

Step-by-step explanation:

2 minutes per lap

2 minutes for 2/5 km = 1 minute for 1/5 lap

1 x 5/5 = 5 minutes

y = (2x + 1)/(3x + 4)

y(3x + 4) = (2x + 1)

3xy + 4y = 2x + 1

4y - 1 = 2x - 3xy

4y - 1 = x(2 - 3y)

x = (4y - 1)/(2 - 3y) , answer = E

9514 1404 393

Answer:

  65 miles

Step-by-step explanation:

The Pythagorean theorem applies.

  d^2 = 33^2 +56^2

  d^2 = 1089 +3136 = 4225

  d = √4225 = 65

The diagonal road is 65 miles long.

Answer: B and E

Step-by-step explanation:

Answer:

B C and E

Step-by-step explanation:

have a great day :D

Answer:

1 cone

Step-by-step explanation:

2. rectangular prism

Answer:

the first one is a cone

Step-by-step explanation:

the second one is a rectangular prism

Answer:

Answer:

m∠2= 86

Step-by-step explanation:

since they are vertical angles, that means they are both equal to eachother.

so lets set them equal!

17x+1=20x-14

17x+15=20x

15=3x

x=5

now input x into m∠2

m∠2 = 20(5) – 14 = 86

Step-by-step explanation: