The measure of two supplementary angles are (6x+28)° and (7x+87)°. Find the value of x.

Answer:

a. 18 percent

b. $90 billion

Step-by-step explanation:

a. Calculation to use Okun's law to determine the size of the GDP gap in percentage-point terms.

First step is to find the difference between ACTUAL RATE of unemployment and NATURAL RATE of unemployment

Difference=13%-4%

Difference= 9%

Based on the information above calculation we can see that the ACTUAL RATE of unemployment EXCEEDS the NATURAL RATE of unemployment by 9%, which indicates a CYCLICAL UNEMPLOYMENT.

Thus, According to Okun's law, this translates into an 18 % GDP gap in percentage-point terms (= 2 × 9%).

Therefore the the size of the GDP gap in percentage-point terms is 18 percent

b. Calculation to determine how much output is forgone because of cyclical unemployment

Forgone Output :

By applying Okun’s law we known that the GDP gap is 18%, which means that we are 18% below the GDP amount which is given as $500 billion,

Hence,

Output forgone = (18/100) ×$500 billion

Output forgone=0.18×$500 billion

Output forgone=$90 billion

Therefore the Forgone Output is $90 billion

Answer:

The fraction of cup filled with water is 3/4.

Step-by-step explanation:

Antonia has a mug with a capacity of 2/3L of water. What fraction of that mug will she fill with 1/2L of water?

Capacity =  2/3 L

Amount of water = 1/2 L

Fraction of amount of water to the capacity of mug is

[tex]\frac{1}{2}\div \frac{2}{3}\\\\\frac{3}{4}[/tex]

Answer:

d

Step-by-step explanation:

ive had this exac problem before

Answer:

B. 1

Step-by-step explanation:

Since the sides are equal to each other, the equations will be equal.

4x + 7 = x + 10

      -7          -7

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

4x= x + 3

-x    -x

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

3x = 3

----   ---

3      3

x = 1

The answer is 1.

Answer:

800 M &Ms

Step-by-step explanation:

First, we can operate on the estimate that the proportion of M&Ms of the sample is equal to the proportion of M&Ms in the giant bag.

Therefore,

number of orange M&Ms in sample / sample size = number of orange M&Ms in bag / bag size

3/50 = 48 / bag size

multiply both sides by 50 to remove a denominator

3  = 48 * 50 / bag size

multiply both sides by bag size to remove the other denominator

3 * bag size = 48 * 50

divide both sides by 3 to isolate bag size

bag size = 48 * 50 / 3

bag size  = 800 M &Ms

Answer:

I am in 5 classso i did not known answer

Answer:

See Below.

Step-by-step explanation:

We want to prove that:

[tex]\displaystyle \sin\theta\sec\theta+\cos\theta\csc\theta = 2\csc2\theta[/tex]

Let secθ = 1 / cosθ and cscθ = 1 / sinθ:

[tex]\displaystyle \frac{\sin\theta}{\cos\theta}+\frac{\cos\theta}{\sin\theta}=2\csc2\theta[/tex]

Creat a common denominator. Multiply the first fraction by sinθ and the second by cosθ. Hence:

[tex]\displaystyle \frac{\sin^2\theta}{\sin\theta\cos\theta}+\frac{\cos^2\theta}{\sin\theta\cos\theta}=2\csc2\theta[/tex]

Combine fractions:

[tex]\displaystyle \frac{\sin^2\theta + \cos^2\theta}{\sin\theta\cos\theta}=2\csc2\theta[/tex]

Simplify. Recall that sin²θ + cos²θ = 1:

[tex]\displaystyle \frac{1}{\sin\theta\cos\theta}=2\csc2\theta[/tex]

Multiply the fraction by two:

[tex]\displaystyle \frac{2}{2\sin\theta\cos\theta}=2\csc2\theta[/tex]

Recall that sin2θ = 2sinθcosθ. Hence:

[tex]\displaystyle \frac{2}{\sin2\theta}=2\csc2\theta[/tex]

By definition:

[tex]\displaystyle 2\csc2\theta = 2\csc2\theta[/tex]

Hence proven.

Answer:

m∠60

Step-by-step explanation:

30 + 90 = 120

180-120=60

Answer:

x = 60°

Step-by-step explanation:

A triangle is equal to 180°

Make an equation and solve:

30° + 90° + x = 180°

120° + x = 180°

x = 180° - 120°

x = 60°

Answer:

Its 48

Step-by-step explanation:

subtract 69 and 56 from 173, what you have left is your answer

48

Step-by-step explanation:

total 176 subtract 69 and 58 since they are given.

176 - 69 -56 = 48

the answer is in the picture

The congruent arcs are P Q and S R

In geometry, congruent refers to equality, agreement in form.

Given:

< P T Q = < S T R

since they are congruent they are equal therefore arcs formed from them are congruent .

Arcs formed from them

Read more on congruent here: https://brainly.com/question/2938476

Answer:

5 years

Step-by-step explanation:

(x+15)=4x

15=4x-x

15=3x

5=x

Answer:

2c+b-w   It is a trinomial.

Step-by-step explanation:

Making the equation is pretty easy. Since you get 2 points for corrent answers, we can write down 2c. You get one point for blank, so you can write down 1b, or just b. And, since you get -1 point for each incorrect answer, you can write down -1w, or just -w.

So, if you put the equation together, you will get 2c+b-w for the equation.

Since this equation have 3 terms (2c, b, and w) seperated by the + and -, we know that it is a trinomial.

Answer:

The terminal velocity is 8.00ft/s

Step-by-step explanation:

Given

[tex]v(t) = 1000t^2 - 5t + 8[/tex]

Required

The terminal velocity

This implies that we calculate the maximum velocity.

First, we calculate the maximum value of t using:

[tex]t_{max} = -\frac{b}{2a}[/tex]

Where:

[tex]v(t) = at^2 + bt + c[/tex]

So, we have:

[tex]t_{max} = -\frac{-5}{2*1000}[/tex]

[tex]t_{max} = \frac{5}{2000}[/tex]

[tex]t_{max} = 0.0025[/tex]

Substitute this value of t in [tex]v(t) = 1000t^2 - 5t + 8[/tex] to get the maximum velocity

[tex]v(t) = 1000t^2 - 5t + 8[/tex]

[tex]v(t) = 1000 * 0.0025^2 - 5 * 0.0025 + 8[/tex]

Using a calculator, we have:

[tex]v(t) = 7.99375[/tex]

Approximate

[tex]v_{max} = 8.00ft/s[/tex]

Velocity is the rate of change of its position with respect to time. The terminal velocity of the skydiver is 200 ft/sec.

Velocity is the rate of change of its position with respect to time.

[tex]V = \dfrac{dy}{dt}[/tex]

Given the velocity of the skydiver by the function v(t)=1000t/(5t+8), after some time, the velocity will become terminal velocity and then it can not be increased further, therefore, the terminal velocity can be written as,

[tex]\lim_{t \to \infty} V(t) = \lim_{t \to \infty} \dfrac{1000t}{5t+8}\\\\[/tex]

                    [tex]= \lim_{t \to \infty} \dfrac{\frac{1000t}{t}}{\frac{5t}{t}+\frac{8}{t}}\\\\[/tex]

                    [tex]= \dfrac{1000}{5+\frac{8}{t}}\\\\= \dfrac{1000}{5}\\\\=200[/tex]

Hence, the terminal velocity of the skydiver is 200 ft/sec. It can be confirmed by plotting the function on the graph.

Learn more about the Terminal Velocity:

https://brainly.com/question/18084516

#SPJ5

Answer:

,29.25m

Step-by-step explanation:

maybe answer is correct

Answer: B. 29.25 cm

Step-by-step explanation:

Given

The prefix nona- came from Latin meaning "nineth"

Thus, nonagon has 9 sides

Solve

1 side = 3.25 cm

9 sides = 3.25 × 9 = 29.25 cm

Hope this helps!! :)

Please let me know if you have any question

Hello!

7(x + 8) = 84 <=>

<=> 7x + 56 = 84 <=>

<=> 7x = 84 - 56 <=>

<=> 7x = 28 <=>

<=> x = 28 : 7 <=>

<=> x = 4

Good luck! :)

Given:

Slope of line F = [tex]-\dfrac{6}{3}[/tex]

Slope of line G = [tex]-\dfrac{8}{4}[/tex]

To find:

The conclusion about distinct lines F and G.

Solution:

We have,

Slope of line F = [tex]-\dfrac{6}{3}[/tex]

                        = [tex]-2[/tex]

Slope of line G = [tex]-\dfrac{8}{4}[/tex]

                        = [tex]-2[/tex]

The slopes of lines F and G are equal and we know that the slopes of two parallel lines are always equal.

Therefore, the line F and line G are parallel to each other.

Answer:

Step-by-step explanation:

(3,9)

Answer:

1) Please find the attached drawing of the archway created with MS Excel

2) The y-intercept is (0, 24)

The x-intercepts are (-3, 0), and (8, 0)

3) The width of the archway at its base is 11

The height of the archway at its highest point = 30.25

Step-by-step explanation:

The given function representing the archway is y = -x² + 5·x + 24

1) Please find attached the required drawing of the archway created with MS Excel

2) The y-intercept is given by the point where x = 0

Therefore, we have, the y-value at the y-intercept = -0² + 5×0 + 24 = 24

The y-intercept = (0, 24)

The x-intercept is given by the point where y = 0

Therefore, the x-values at the x-intercept are found using the following equation;

0 = -x² + 5·x + 24

x² - 5·x - 24 = 0

By inspection, we have;

x² - 8·x + 3·x - 24 = 0

x·(x - 8) + 3·(x - 8) = 0

∴ (x + 3) × (x - 8) = 0

Either (x + 3) = 0, and x = -3, or (x - 8) = 0, and x = 8

Therefore, the x-intercepts are (-3, 0), and (8, 0)

3) The width of the archway at its base = The distance between the x-values at the two x-intercepts

∴ The width of the archway at its base = 8 - (-3) = 11

The highest point of the arch is given by the vertex of the parabola, y = a·x² + b·x + c, which has the x-value of the vertex = -b/(2·a)

∴ The x-value of the vertex of the given parabola, y = -x² + 5·x + 24, is x = -5/(2×(-1)) = 2.5

Therefore;

The y-value of the vertex, is y = -(2.5)² + 5×2.5 + 24 = 30.25 = The height of the archway at its highest point

∴ The height of the archway at its highest point = 30.25.

Answer:

$110

Step-by-step explanation:

We are looking for the decrease in money per desk purchased. Because the x-axis is the number of desks purchased, what we have to find is the (opposite) of the slope. The formula to represent slope can be written as:

[tex]\frac{y_{2} -y_{1} }{x_{2}- x_{1} }[/tex]

We can substitute the points given, (2, 480) and (5, 150) and simplify:

[tex]\frac{150-480}{5-2} =\frac{-330}{3} = -110[/tex]

We would multiply by -1 because we are asking for the decrease, and negative increase is decrease. -1 * -110, gives us $110

Given:

A figure of a circle.

To find:

The value of x.

Solution:

First label the given figure as shown below.

In triangle ABO,

[tex]OA=OB[/tex]                                          (Radii of same circle)

[tex]\Delta ABO[/tex] is an isosceles triangle.      (By the definition of isosceles triangle)

[tex]\angle OAB\cong \angle OBA[/tex]                               (Base angles of an isosceles triangle)

[tex]m\angle OAB=m\angle OBA[/tex]

[tex]42^\circ=m\angle OBA[/tex]

In triangle ABO,

[tex]m\angle AOB+m\angle OAB+m\angle OBA=180^\circ[/tex]      (Angle sum property)

[tex]m\angle AOB+42^\circ+42^\circ=180^\circ[/tex]

[tex]m\angle AOB=180^\circ-42^\circ-42^\circ[/tex]

[tex]m\angle AOB=96^\circ[/tex]

Now,

[tex]m\angle AOB+m\angle BOC=180^\circ[/tex]         (Linear pair)

[tex]96^\circ+x=180^\circ[/tex]

[tex]x=180^\circ-96^\circ[/tex]

[tex]x=84^\circ[/tex]

Therefore, the value of x is 84 degrees.

Answer:

B.

Step-by-step explanation:

If you put the second triangle upright then turn it over (as if you were flipping a pancake). That would make B equal to R.

C would equal S

A would equal T

and

B would equal R

Answer:

b = R,  mark me brainiest cause we besties

Step-by-step explanation:

Answer:

Step-by-step explanation:

i think A

Hope this helps!

Answer:

$0.72 per pound

Step-by-step explanation:

1 ton = 2000

5 tons = 10000

10000 lb = $7200

7200/10000 = 0.72

0.72 dollars a pound

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

C y=x^2+2x+1

Step-by-step explanation:

Answer:

2.4cm

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

that means two lengths of the triangle have to be multiplied.

and to have 2 similar triangles means that all lengths inside one triangle are the corresponding lengths inside the other triangle multiplied by the scaling factor f.

multiplying 2 if these lengths with each other means also including the square of the scaling factor (multiplying with the scaling factor twice).

so, if the area of triangle 1 is

"baseline 1" × "height 1" / 2 = 45 cm²

then the area of triangle 2 is

"baseline 2" × "height 2" / 2 =

= "baseline 1"×f × "height 1"×f /2 =

= "baseline 1" × "height 1" × f² / 2 =

= ("baseline 1" × "height 1" / 2) × f² =

= 45 × f² = 20 cm²

f² = 20/45 = 4/9

f = 2/3

so, for a side of ABC being 3.6cm long, that means the corresponding side in DEF is

3.6 × f = 3.6 × 2/3 = 7.2/3 = 2.4cm

Answer:

Answer D is TRUE because on the graph if you were to keep going left even after the picture of the graph ends, the graph will still keep going up infinitely.

Step-by-step explanation:

Answer:

89 minutes

Step-by-step explanation:

let he talked for x minutes.

$12.79=1279 cents

1279=300+11x

11x=1279-300=979

x=89

Answer:

Equal to 1,204-299

Step-by-step explanation:

Anything divided by 1 is equal to itself.

Answer:

19

Step-by-step explanation:

(3-2)(3^2+3x2+2^2)

(1)(9+6+4)

(1)(19)

[tex]\displaystyle\bf \underbrace{ (x-y)(x^2+xy+y^2)}}_{x^3-y^3}=3^3-2^3=19\\\\Answer: b)19[/tex]