Find the value of x.

m∠FGH = 148°
m∠FGL = (x + 12)°
m∠LGH = (16x)°

A) 3
B) 5
C) 6
D) 8

Answer:

  6

Step-by-step explanation:

The center of the circle is the midpoint of the diameter. The midpoint can be found by averaging the coordinates of the end points:

  ((-4, 2) +(12, 10))/2 = ((-4+12)/2, (2+10)/2) = (4, 6)

The y-coordinate of the center is 6.

The center of the circle has a y-coordinate of 6, determined by averaging the y-coordinates (2+10)/2 of the diameter's endpoints (-4,2) and (12,10).

The y-coordinate for the center of a circle can be determined by finding the midpoint of the y-coordinates of the diameter's endpoints. Given the endpoints (-4,2) and (12,10), the midpoint can be found by averaging the y-coordinates: (2 + 10) / 2 = 12 / 2 = 6. Therefore, the y-coordinate of the center of the circle is 6.

Answer:

Step-by-step explanation:

We need to analyze the surface

Look at the L shape, it has a mirror image at the back, which is symmetrical to the front side

Then,

area of rectangle = length × breadth

The L shape can be divided into two plane shape

1. A rectangle of length 10in and breadth 6in,

Then, A=l×b=10×6 = 60in²

2. To a square of side a=4in

Then, A=s²=4²=16in²

Then, the total area of one side of the L shape is

A=60+16=76in²

Also, the total area of the two L shape is =2×76

A=152in²

Then, let look at the back side of the solid and the front side, they are also symmetrical.

It forms a rectangle of length 10in and breadth 6in

Then, A= l×b=10×6=60in²

Area of the two sides is =60×2

A=120in²

The total are of the front and back side is 120in²

A=120in²

Let take a look at the top and bottom, they are also symmetrical and has a dimension of length 10in and breadth 6in

Then, A=l×b=10×6=60in²

So, total area =2×60 =120in²

The total area of the shape is the total area of top+ total are of the sides + total area of the L shape

Total area=152+120+120=392in²

A(total)=392in²

Then, the total area of the solid shape is 392in²

The first option is correct

Answer:

The distance between (-4, 3) and (4, 3) is 8

Step-by-step explanation:

Distance formula:  [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2)}[/tex]

Distance:  [tex]\sqrt{(4 - (-4)^2 + (3 - 3)^2}[/tex]

Distance:  [tex]\sqrt{(4 + 4)^2 + (0)^2}[/tex]

Distance:  [tex]\sqrt{8^2} \\[/tex]

Distance:  8

Answer:  The distance between (-4, 3) and (4, 3) is 8

Answer:

1,607  volume

Step-by-step explanation:

Answer:

I believe it would be true

Answer: D

Step-by-step explanation: yes, because with each simulation, as the number of trials increase, the experimental probability gets closer and closer to the theoretical probability of

1/4.

The answer is D

Step-by-step explanation:

because with each simulation, as the number of trials increase, the experimental probability gets closer and closer to the theoretical probability of

1

4

. The law of large numbers indicates that if an event of probability p is observed repeatedly during independent repetitions, the ratio of the observed frequency of that event to the total number of repetitions approaches p as the number of repetitions becomes arbitrarily large.

Answer:

40

Step-by-step explanation:

add 21 + 20

hope this helps :)

The volume of the lid is approximately 113.8 cubic inches.

The volume of the lid can be found by multiplying the area of the triangular base by the height of the lid. The area of a triangle can be found by using the formula: Area = (base x height) / 2. In this case, the base is 6 1/2 inches and the height is 3 1/2 inches. Plugging these values into the formula, we get: Area = (6.5 x 3.5) / 2 = 11.375 square inches. Now, to find the volume of the lid, we multiply the area by the height: Volume = 11.375 x 10 = 113.75 cubic inches. Rounding to the nearest tenth, the volume of the lid is 113.8 cubic inches.

The volume of the lid is 113.8 cubic inches.

To determine the volume of the lid of the jewelry box, we need to use the formula for the volume of a triangular prism, which is V = (1/2 * base * height of triangular base) * height of the prism.

First, calculate the area of the triangular base:

Next, multiply the area of the triangular base by the height of the prism:

Therefore, the volume of the lid to the nearest tenth is 113.8 cubic inches.

Answer:

x = 10

Step-by-step explanation:

3x + 55 = 9x - 5  (add 5 to both sides)

3x + 55 + 5 = 9x - 5 + 5

3x + 60 = 9x  (subtract 3x from both sides)

60 = 9x - 3x

60 = 6x (rearrange)

6x = 60   (divide both sides by 6)

x = 60/6

x = 10

Answer:

x=10

Step-by-step explanation:

[tex]\mathrm{Subtract\:}55\mathrm{\:from\:both\:sides}\\3x+55-55=9x-5-55[/tex]

[tex]\mathrm{Simplify}\\3x=9x-60[/tex]

[tex]\mathrm{Subtract\:}9x\mathrm{\:from\:both\:sides}\\3x-9x=9x-60-9x[/tex]

[tex]\mathrm{Simplify\:}again\\-6x=-60[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-6\\\frac{-6x}{-6}=\frac{-60}{-6}[/tex]

[tex]\mathrm{\:Simplify\:one\:more\:time}\\x=10[/tex]

I hope this helps you out!

Have a wonderful afternoon!

Answer:

-12

Step-by-step explanation:

we know that

(fºg)(x)=f(g(x))

To find out the composite function f(g(x)) substitute the variable x in the function f(x) by the function g(x)

we have

[tex]f(x)=-3x-9[/tex]

[tex]g(x)=x+7[/tex]

so

[tex]f(g(x))=-3(x+7)-9[/tex]

For x=-6

substitute

[tex]f(g(-6))=-3(-6+7)-9[/tex]

[tex]f(g(-6))=-3(1)-9[/tex]

[tex]f(g(-6))=-12[/tex]

Answer:

2/3

Step-by-step explanation:

Rewrite the equation into the form of y=mx+c

m is the gradient of the line.

2x-3y=6

3y= 2x-6 (bring y terms to one side, the rest to the other)

y= 2/3x -2 (÷3 throughout)

Thus the gradient is 2/3.

Answer:

-0.125

Step-by-step explanation:

To find the decimal version of the fraction, divide using a calculator or long division.

-1 / 8 = -0.125

Best of Luck!

The value of x that satisfies the equation 41 - x = 157 is x = -116.

To solve for x in the equation 41 - x = 157, we need to isolate x on one side of the equation.

Let's go step by step:

Step 1: Start with the given equation.

41 - x = 157

Step 2: Get rid of the constant term on the left side (41) by subtracting it from both sides of the equation.

(41 - x) - 41 = 157 - 41

Simplifying the left side:

41 - 41 - x = 157 - 41

0 - x = 116

Step 3: We have -x on the left side, and we want to solve for x, so we need to get rid of the negative sign in front of x.

To do that, we can multiply both sides of the equation by -1.

When we multiply a number by -1, the sign changes.

(-1) * (-x) = (-1) * 116

Simplifying the left side:

x = -116

Step 4: Now we have found the value of x, which is x = -116.

To verify our solution, we can substitute the value of x back into the original equation and see if it holds true:

41 - (-116) = 157

Simplifying:

41 + 116 = 157

157 = 157

Since both sides of the equation are equal after simplification, our solution x = -116 is correct.

Therefore, the value of x that satisfies the equation 41 - x = 157 is x = -116.

To learn more on equation click:

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Answer:13.9

Step-by-step explanation:

Using the compound interest formula, it will take approximately 14.9 years for an account with a $3,200 initial deposit and an 8.25% annual interest rate to grow to $9,600.

To find out how long it will take for an account with an initial value of $3,200 and an annual interest rate of 8.25% to grow to $9,600, we can use the future value formula for compound interest:

The formula is FV = PV (1 + r)^n, where:

To find n when FV is $9,600, we rearrange our formula to solve for n:

n = log(FV / PV) / log(1 + r)

Now, plug in the values:

n = log(9600 / 3200) / log(1 + 0.0825)
n = log(3) / log(1.0825)
n ≈ 14.9 years

So, it will take approximately 14.9 years for the account value to reach $9,600.

Answer:

5.14

Step-by-step explanation

6/x = 42/36

42x= 216

x= 5.14

A.12 grapes, 23 plums

Step-by-step explanation:

1. solve all the equations by multiplying each number by how much each item is worth

2. A: 290 =(12× 5)+(10×23)

B: 100 =(10×5)+(5×10)

C:125 =(5×5)+(10×10)

D:235 =(23×5)+(12×10)

Answer: $1090.80

Step-by-step explanation:

Answer:

$1,090.80

Step-by-step explanation:

Bodily injury; 25/50=$220

Property; 100=$375

Collision deductibles;$250=$185

Comprehensive deductibles;$100=$129

220+375+185+129 = 909

909*1.2=1,090.8

Took the test

Answer:

55m

Step-by-step explanation:

a²+b²=c²

19 x 19 = 361

52 x 52 = 2704

2704 + 361= 3065

the square root of 3065 is 55.4 so round that to 55.

IS THERE AN OPTION TO SAY THEY ARE EQUAL IF THERE IS THEN THAT IS THE ANSWER :}

Answer:

18

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Answer:

The right answer is, -420

Step-by-step explanation:

Because we use common factor:

60 (x - 15)

We multiply for each term:

60 (x) - 60 (15)

60 (8) - 60 (15)

We solve:

480 - 900 = -420

Answer:

Option A, V = π(7)^2h

Step-by-step explanation:

The formula for the volume of a cylinder:  V = πr^2h

Step 1:  Since the give us diameter we need to find radius

radius = diameter/2

radius = 14/2

radius = 7

Answer:  Option A, V = π(7)^2h

Answer:

A

Step-by-step explanation:

Volume of a cylinder = pi r2 h

Where pi = 3.14

Radius r = diameter/2

Diameter given is 14,

So radius = 24/2 = 7

Height h

Volume = pi(7)^2 h

The app uses 2^28 bytes.

Step-by-step explanation:

⇒ 4^4 × 2^20 = (2²)^4 × 2^20 = 2^8 × 2^20

                       = 2^8+20

                       = 2^28 bytes (using the law of exponents a^m × a^n = a^m+n)

Step-by-step explanation:

[tex]y = 6x[/tex]

[tex]2x + 3y = -20[/tex]

To solve this system of equations, let's multiply the first equation by [tex]-3[/tex] to get a [tex]3y[/tex] term in each equation:

[tex]-3y = -18x[/tex]

Now, let's add the two equations together:

[tex](2x + 3y) + (-3y) = -20 + (-18x)[/tex]

[tex]2x = -20 - 18x[/tex]

[tex]20x = -20[/tex]

[tex]x = -1[/tex]

Now, we can plug in this value of [tex]x[/tex] into either equation to solve for [tex]y[/tex]:

[tex]y = 6x[/tex]

[tex]y = 6(-1)[/tex]

[tex]y = -6[/tex]

or

[tex]2x + 3y = -20[/tex]

[tex]2(-1) + 3y = -20[/tex]

[tex]-2 + 3y = -20[/tex]

[tex]3y = -18[/tex]

[tex]y = -6[/tex]

Therefore, the solution to this system of equations is [tex](-1, -6)[/tex].

Answer:

x = -1

y = -6

Step-by-step explanation:

y = 6x

2x + 3y = -20

Substitute the first expression into the second one

We have

2x + 3y = -20

2x + 3(6x) = -20

2x + 18x = -20

20x = -20

Divide both sides by 20 to isolate x

20x/20 = -20/20

x = -1

Remember the first expression

y = 6x

Therefore

y = 6(-1)

y = 6 x -1

y = -6

Check

2(-1) + 3(-6) = -20

-2 + -18 = -20

-2 - 18 = -20

-20 = -20

So our answer is correct

Answer:

26 gallons of juice

Step-by-step explanation:

156/12 = 13

13x2=26

Answer: 26 gallons

Step-by-step explanation:

2 gallons for every 12 people so you want to do 156 divided by 12 which would be 13. That shows that there are 13 times more people than there were before. You would then multiply 2 by 13 which would give you 26 gallons of juice.

Answer:

B :)

Step-by-step explanation:

Answer:  8^3,  Eight to the third power,  Eight times eight times eight.

To calculate the volume of a cube with a side length of 8 inches, you write the calculation in exponential form as V = 8^3, which is read as '8 cubed' or '8 to the third power', resulting in a volume of 512 cubic inches.

To calculate the volume of a cube using a side length of 8 inches, you can write the calculation in exponential form as V = 8^3. This represents the volume (V) as the length of a side of the cube (8 inches) raised to the power of 3. In exponential form, 8^3 is 8 cubed or 8 to the third power, both of which mean 8 multiplied by itself twice more (8 x 8 x 8).

Therefore, the volume of the cube would be 512 cubic inches because 8 x 8 x 8 equals 512.

Answer:

y = 6x − 11

Step-by-step explanation:

x = t + (1/t), y = t² + (1/t²)

If we square x:

x² = t² + 2 + (1/t²)

x² = y + 2

When x = 3, y = 7.

Taking derivative with respect to time:

2x = dy/dx

dy/dx = 6

So the equation of the tangent line is:

y − 7 = 6 (x − 3)

y − 7 = 6x − 18

y = 6x − 11

Answer:

Eli has to run for 2.25 minutes at this pace to win the bet.

Step-by-step explanation:

At his last track meet, Eli ran the 400-meter dash in 54 seconds.

So, the speed of Eli's run is [tex]\frac{400}{54} \times 60 = 444.44[/tex] meters per minute.

Now, if Eli is determined to run a whole kilometer with the same speed, then it will take Eli to run 1 kilometer within [tex]\frac{1000}{444.44} = 2.25[/tex] minutes.

Hence, Eli has to run for 2.25 minutes at this pace to win the bet. (Answer)

Question 1: Option B: [tex]\frac{10}{14}=\frac{5}{7}[/tex]

Question 2: Option C: [tex]\frac{12}{18}=\frac{4}{6}[/tex]

Solution:

Question 1:

Given ratio is [tex]\frac{10}{14}[/tex].

To find the equivalent ratio of [tex]\frac{10}{14}[/tex].

10 and 14 have the common factor 2.

So divide both numerator and denominator by the common factor 2.

[tex]$\frac{10}{14}=\frac{10\div2}{14\div 2}[/tex]

    [tex]$=\frac{5}{7}[/tex]

[tex]$\frac{10}{14}=\frac{5}{7}[/tex]

Hence option B is the correct answer.

Question 2:

Given ratio is [tex]\frac{10}{14}[/tex].

To find the equivalent ratio of [tex]\frac{12}{18}[/tex].

12 and 18 have the common factor 3.

So divide both numerator and denominator by the common factor 3.

[tex]$\frac{12}{18}=\frac{12\div3}{18\div 3}[/tex]

    [tex]$=\frac{4}{6}[/tex]

[tex]$\frac{12}{18}=\frac{4}{6}[/tex]

Hence option C is the correct answer.