4.) Answer the following problems based on the triangle below:



Find X

Find the measure of angle b

Find the measure of angle c

The equation of the line having slope 0 and passing through (-3,-2) is f(x) = -2.

Any horizontal line has the same y-value for every point on the line. We are given that the line passes through the point (-3,-2). This means that f(-3) = -2, since the y-value of the point (-3,-2) corresponds to the value of the function at x = -3.

This is because no matter what x-value we plug into the function, the output (y-value) will always be -2. Therefore, the equation of the line in function notation is f(x) = -2.

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Answer: 81.25mm or 8.125cm

Step-by-step explanation:

Numerator is actual size, denominator is the size in picture

Answer:

This problem wants you to substitute the answers from the table into the equation to find the solution, which is when the input gives the same output basically.

f(x) = 2.5x -10.5                          g(x) = 64(0.5)^x

when x= 2...                                when x= 2...

f(2) = 2.5(2) - 10.5                        g(2) = 64(0.5)^2

f(2) = 5 - 10.5 = -5.5                     g(2) = 64(.25)= 16

when x= 3...                                 when x= 3...

f(3) = 2.5(3) - 10.5                         g(3) = 64(0.5)^3

f(3) = 7.5 - 10.5 = -3                      g(3) = 64(0.125) =8

when x= 4...                               when x = 4...

f(4) = 2.5(4) - 10.5                       g(4) = 64(0.5)^4

f(4) = 10 - 10.5 = -0.5                  g(4) = 64(0.0625) = 4

when x= 5...                               when x= 5...

f(5) = 2.5(5) - 10.5                      g(5) = 64(0.5)^5

f(5) = 12.5 - 10.5 = 2                   g(5) = 64(0.03125) = 2

when x= 6...                               when x = 6...

f(6) = 2.5(6) - 10.5                       g(6) = 64(0.5)^6

f(6) = 15 - 10.5 = 4.5                   g(6) = 64(0.015625) = 1

Answer:

\( \frac{3}{5} \times \frac{4}{3} \times 3 = \frac{3}{5} \times 4 = \frac{12}{5} = 2 \frac{2}{5} \)

The volume of this rectangular prism is

2 2/5 cm^3.

Answer:

-6

Step-by-step explanation:

2 - [6 ÷ 2 + {6 × 1/2 + (7/2 - 3/2)}] =

Follow the correct order of operations.

Do one step at a time and copy everything else each time, so you don't lose track of any operation.

= ​2 - [6 ÷ 2 + {6 × 1/2 + 4/2}]

= 2 - [6 ÷ 2 + {6 × 1/2 + 2}]

= 2 - [6 ÷ 2 + {3 + 2}]

= 2 - [6 ÷ 2 + 5]

= 2 - [3 + 5]

= 2 - 8

= -6

Answer:

-6

hope this helps

Step-by-step explanation:

2_(6÷2+(6*1/2+(7/2-3/2))) solve the ones in bracket first

(7/2-3/2)=2

2-(6÷2+(6×1/2+2))

6×1/2+2

6×1/2=3

3+2=5

2-(6÷2+5)

6÷2=3

3+5=8

2-8

=-6

Answer: A is your answer

Step-by-step explanation:

The transformation that occurs from f(x) to g(x) is that the graph of f(x) is shifted upward to create g(x).

Option A is the correct answer.

We have,

Parent function f(x) = |x|

Transformed function g(x) = |x| + 4

In the transformation from f(x) = |x| to g(x) = |x| + 4, a vertical shift occurs.

Adding a positive value (4 in this case) to the absolute value function f(x) results in the entire graph being shifted upward by 4 units.

A vertical shift on a graph refers to the transformation of a function in which the entire graph is moved up or down without changing its shape or orientation.

This vertical displacement occurs by adding or subtracting a constant value to the function's output (y-coordinate) for all input (x) values.

Thus,

a. The graph of f(x) is shifted upward to create g(x).

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Answer:  I belive it is 360 inches cubed. I could be wrong

Step-by-step explanation:

Using Pythagorean theorem, the height of Oscar's dog house, at its tallest point, is approximately 7.81 feet.

What is Pythagorean Theorem?

The Pythagorean Theorem is a fundamental concept in mathematics that relates to the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. The theorem is expressed mathematically as:

a² + b² = c²

Now,

Let's height of the house = "h":

Using Pythagoras

a² + b² = c²

Where "a" and "b" are the lengths of the slanted sides and "c" is the height of the house. We know that "a" and "b" are both 5 feet long, and the bottom of the house is 6 feet across. Let's use this information to find "c":

a = b = 5 feet

b = 6 feet

c² = a² + b²

c² = 5² + 6²

c² = 25 + 36

c² = 61

c = √(61)

c ≈ 7.81 feet

So the height of Oscar's dog house, at its tallest point, is approximately 7.81 feet.

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Answer:

(a) The odds for and against E are (8:1) and (1:8) respectively.

(b) The odds for and against E are (7:2) and (2:7) respectively.

(c) The odds for and against E are (59:41) and (41:59) respectively.

(d) The odds for and against E are (71:29) and (29:71) respectively.

Step-by-step explanation:

The formula for the odds for an events E and against and event E are:

\(\text{Odds For}=\frac{P(E)}{1-P(E)}\\\\\text{Odds Against}=\frac{1-P(E)}{P(E)}\)

(a)

The probability of the event E is:

\(P(E)=\frac{8}{9}\)

Compute the odds for and against E as follows:

\(\text{Odds For}=\frac{P(E)}{1-P(E)}=\frac{8/9}{1-(8/9)}=\frac{8/9}{1/9}=\frac{8}{1}\\\\\text{Odds Against}=\frac{1-P(E)}{P(E)}=\frac{1-(8/9)}{8/9}=\frac{1/9}{8/9}=\frac{1}{8}\)

Thus, the odds for and against E are (8:1) and (1:8) respectively.

(b)

The probability of the event E is:

\(P(E)=\frac{7}{9}\)

Compute the odds for and against E as follows:

\(\text{Odds For}=\frac{P(E)}{1-P(E)}=\frac{7/9}{1-(7/9)}=\frac{7/9}{2/9}=\frac{7}{2}\\\\\text{Odds Against}=\frac{1-P(E)}{P(E)}=\frac{1-(7/9)}{7/9}=\frac{2/9}{7/9}=\frac{2}{7}\)

Thus, the odds for and against E are (7:2) and (2:7) respectively.

(c)

The probability of the event E is:

\(P(E)=0.59\)

Compute the odds for and against E as follows:

\(\text{Odds For}=\frac{P(E)}{1-P(E)}=\frac{0.59}{1-0.59}=\frac{0.59}{0.41}=\frac{59}{41}\\\\\text{Odds Against}=\frac{1-P(E)}{P(E)}=\frac{1-0.59}{0.59}=\frac{0.41}{0.59}=\frac{41}{59}\)

Thus, the odds for and against E are (59:41) and (41:59) respectively.

(d)

The probability of the event E is:

\(P(E)=0.71\)

Compute the odds for and against E as follows:

\(\text{Odds For}=\frac{P(E)}{1-P(E)}=\frac{0.71}{1-0.71}=\frac{0.71}{0.29}=\frac{71}{29}\\\\\text{Odds Against}=\frac{1-P(E)}{P(E)}=\frac{1-0.71}{0.71}=\frac{0.29}{0.71}=\frac{29}{71}\)

Thus, the odds for and against E are (71:29) and (29:71) respectively.

Answer:

for what

Step-by-step explanation:

Answer:

Step-by-step explanation:

This number line says that  we can take all values of x that are less than or equal to 2. That is, the solution is

                                  \(x\leq 2\)

NOTE: if the circle at 2 were not filled in then that would mean x<2 (2 would not be an accepted value of x)

Answer:

18.36

Step-by-step explanation:

g00gle says so

Answer:

18.9

I hope this helps!

The photographer should set the tripod at an angle of approximately 75.96 degrees to get a picture of the rocket at its maximum altitude.

We have,

We can use trigonometry to solve this problem.

          C

        /   \

       /     \

      /θ     \

     /         \

    /           \

   A-------------B

          50 ft

In this diagram, A represents the launch pad, B represents the maximum altitude of the rocket, C represents the position of the photographer, and θ represents the angle at which the tripod should be set.

We want to find θ.

First, we can find the height of the triangle ABC using the Pythagorean theorem:

AB² = AC² + BC²

200² = AC² + 50²

AC² = 200² - 50²

AC = √(200² - 50²)

AC = 190.526 ft

Next, we can use the tangent function to find θ:

tan(θ) = opposite/adjacent = AB/BC = 200/50 = 4

Taking the arctangent of both sides, we get:

θ = \(tan^{-1}(4)\)

θ = 75.96 degrees

Therefore,

The photographer should set the tripod at an angle of approximately 75.96 degrees to get a picture of the rocket at its maximum altitude.

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Answer:

Step-by-step explanation:

Given:

Conversion: 1 yard = 3 feet = 36 inches

Use the unitary method and solve:

Thus, Dwayne bought 432 inches of wrapping paper.

Answer:

the square root of 3 is 1.73

Step-by-step explanation:

The square root of 3 lies between 1 and 2

The slope of a horizontal line is always zero.

What is slope?

The slope of a line is a measure of how steep the line is. It represents the rate at which the y-coordinate of the line changes with respect to the x-coordinate. Symbolically, it is represented by the letter m, and can be calculated using the following formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are any two points on the line.

The slope of a horizontal line is always zero. This is because a horizontal line has the same y-coordinate at every point, and therefore, there is no change in the y-coordinate for any change in the x-coordinate.

By definition, the slope of a line is the change in y divided by the change in x. In the case of a horizontal line, the change in y is always zero, since the y-coordinate does not change. So, no matter what value of x you choose, the slope of a horizontal line will always be:

slope = change in y / change in x = 0 / (any non-zero value of x) = 0

So, the slope of a horizontal line is always zero.

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Answer:d=4

Step-by-step explanation:

Answer:

I am sure the answer is 300

Answer:

1 Shirt and 185cm remaining cloth

Step-by-step explanation:

2m and 15cm = 215cm

40m = 400cm

400/215=1.860465116

A shirt cant be in decimal so we remove the decimals, and take the as the answer. For the decimals, they are the remaining cloth.. to calculate the amount of remaining cloth we do:

1.860465116-1

=860465116

215*860465116=185cm

The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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The interest rate on the mortgage is 5 %

Let's begin by using the formula for simple interest:

I = P * r * t

where I is the interest, P is the principal (the amount borrowed), r is the interest rate, and t is the time (in years).

For Mr. G's mortgage, we know that the principal is $155,000 and the time is 30 years. We can use this information to solve for the interest rate, r.

First, we need to calculate the total amount that Mr. G will pay over the life of the loan (the principal plus the interest):

A = P + I

where A is the total amount, P is the principal, and I is the interest.

We know that Mr. G will pay $232,500 in interest, so we can solve for A:

Let's begin by using the formula for simple interest:

I = P * r * t

where I is the interest, P is the principal (the amount borrowed), r is the interest rate, and t is the time (in years).

For Mr. G's mortgage, we know that the principal is $155,000 and the time is 30 years. We can use this information to solve for the interest rate, r.

First, we need to calculate the total amount that Mr. G will pay over the life of the loan (the principal plus the interest):

A = P + I

where A is the total amount, P is the principal, and I is the interest.

We know that Mr. G will pay $232,500 in interest, so we can solve for A:

A = P + I

A = $155,000 + $232,500

A = $387,500

Now we can use the formula for simple interest to solve for the interest rate, r:

I = P * r * t

$232,500 = $155,000 * r * 30

r = $232,500 / ($155,000 * 30)

r = 0.05 or 5%

Therefore, Mr. G's interest rate is 5%.

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Answer:

4/9 or 44%

Step-by-step explanation:

4 + 5 = 9

Probability: 4/9 or 44%

The volume of the given figure is 1176 cubic cm.

The value of the figure is calculated by multiplying all three side areas. Volume is a measure of the amount of space that an object or a substance occupies. It is typically expressed in cubic units such as cubic meters (m³), cubic centimetres (cm³), or cubic feet (ft³).

The volume of the figure is calculated as,

Volume = 2 ( 15 x 6 + 20 x 6 + 20 x 18 )

Volume = 1176 Cubic cm

Hence, the volume of the figure will be equal to 1176 Cubic cm.

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Answer:

12/20

Step-by-step explanation:

\(\displaystyle \frac{3}{5}=\frac{3}{5}\cdot\frac{4}{4}=\frac{12}{20}\)

The answer is:

In-depth-explanation:

The denominator of 3/5 is 5. To get from 5 to 20, we multiply it by 4.

We need to multiply both the numerator and the denominator by 4, so we do this:

\(\sf{\dfrac{3\times4}{5\times4}}\)

\(\sf{\dfrac{12}{20}}\)

The solution is:

⇒ 6b = 95.94   (equation to determine cost of one box)

cost of one box 'b' = $`15.99

⇒ 12t = 95.94   (equation to determine cost of per tile)

cost of one tile t = $0.7995.

Given :

Jorge bought a crate of floor tiles for $95.94.

The crate had 6 boxes of floor tiles.

Each box contained 20 floor tiles .

To Find :

Write and solve equation to determine the cost per box'b'.

Write and solve a second equation to determine the cost per tile't'

Solution :

Cost of one box = b

There are 6 boxes

So, cost of 6 boxes = $  6b

Since Jorge bought 1 crate( = 6 boxes) of cost $95.94

⇒     (equation to determine cost of one box)

⇒6b = 95.94

⇒b =15.99

Thus cost of one box = $`15.99

Since 1 box 20 floor tiles

So, 6 boxes (=1 crate) contain tiles = 6*20 = 120 tiles

We are given that cost of 1 crate( = 6 boxes = 120 tiles) is $95.94

Cost of one tile = t

Cost of 120 tiles = $120t

⇒ (equation to determine cost of per tile)

⇒12t = 95.94

⇒t = 0.7995.

Thus cost of one tile t = $0.7995.

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We must calculate the length of an arc of angle 115°.

We know that the length of an arc of angle 360° is equal to: 2 pi * r.

So we can write the following formula for the lenght of an arc of angle A:

In our problem we have:

A = 115

r = 4 cm

So applying the formula of above the answer is:

(rounded to the nearest tenth)