simplify the following. (x²+2x)-(x²-7x)​

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.

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Answer:

Step-by-step explanation:

(3,9)

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:

The complete question can be found online.

The missing information is:

Carson drove a total distance of 120km, he initially has 30L of fuel on his tank, and his car efficiency is 100 cm^3/km

Remember that 1000cm^3 = 1 L

then:

100cm^3 = 0.1L

This means that he uses 0.1 L per kilometer.

The equation that shows how many liters of fuel he will have is:

initial fuel - consumed fuel.

We know that the initial fuel is 30 liters.

And the consumed fuel will be the amount of fuel he used to drive the 120 km

Remember that for each km, he consumes 0.1 L of fuel.

Then for the 120km he used 120 times 0.1 L of fuel, so he used a total of:

120*0.1 = 12 L of fuel

Then the remaining fuel in the tank is:

30 L - 12 L = 18L

There are 18 L of fuel in the tank.

Answer:

Should be 30-100/1000*120

Step-by-step explanation:

Answer:

I am in 5 classso i did not known answer

The equivalent equation solved for h is [tex]\frac{P}{mg} = h[/tex]

From the question, we are to determine the equivalent equation solved for h

From the given information,

The amount of potential energy, P, is modeled by the equation

P = mgh

To determine the equivalent equation solved for h, we will make h the subject of the equation,

From,

P = mgh

Divide both sides of the equation by mg

That is,

[tex]\frac{P}{mg} = \frac{mgh}{mg}[/tex]

∴ [tex]\frac{P}{mg} = h[/tex]

Hence, the equivalent equation solved for h is [tex]\frac{P}{mg} = h[/tex]

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Answer

B

Step-by-step explanation:

Edge 2022

Answer:

x- intercept = - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - [tex]\frac{1}{2}[/tex] and c = - 2 , then

y = - [tex]\frac{1}{2}[/tex] x - 2 ← equation of line

To find the x- intercept let y = 0

0 = - [tex]\frac{1}{2}[/tex] x - 2 ( add 2 to both sides )

2 = - [tex]\frac{1}{2}[/tex] x ( multiply both sides by - 2 to clear the fraction )

- 4 = x

The x- intercept is - 4

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:

,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

Answer:

see explanation

Step-by-step explanation:

Using the Pythagorean identity

sin²θ + cos²θ = 1 ( divide terms by sin²θ )

[tex]\frac{sin^20}{sin^20}[/tex] + [tex]\frac{cos^20}{sin^20}[/tex] = [tex]\frac{1}{sin^20}[/tex] , that is

1 + cot²θ = cosec²θ ← as required

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

Explanation:

If the diagonals are congruent, then we'd have a rectangle. Any rectangle is a parallelogram, but not the other way around.

If we had a non-rectangular parallelogram, with none of the angles 90 degrees, then the diagonals will not be the same length.

Choices A, C and D are true for any parallelogram (rectangle or not).

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:

$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!

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-Chetan K

Hello!

7(x + 8) = 84 <=>

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

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

<=> 7x = 28 <=>

<=> x = 28 : 7 <=>

<=> x = 4

Good luck! :)

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:

25m + 10b = 400

Step-by-step explanation:

Total amount that can be earned = $ 400

Amount earned on mowing a lawn = $ 25

Amount earned per hour on babysitting = $10

Amount earned for mowing one lawn is $ 25, so amount earned for mowing m lawns will be $ 25m

Amount earned for one hour of babysitting is $ 10, so amount earned for babysitting for b hours will be $ 10b

Using the values from above, we can set up the equation as:

400 = 25m + 10b

or

25m + 10b = 400

This equation represents the number of lawns they can mow, m, and hours they can babysit, b, to earn $400.

Hope this helps have a good day

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.

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:

Step-by-step explanation:

what is it that you don't understand about how to get this?  

2(4-3x) + 5(2x-3) = 20-5x

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

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Answer: random events

Step-by-step explanation:

Based on the information given in the question, the scenario can be best explained by a random event.

Random event refers to the event that cannot be made exact and one whose outcome can't be predicted. An example is the sum of numbers that are gotten when two rolled dice are rolled.

From the experiment, one student had five heads in a row, while the other student's coin toss had no pattern depicts a random event.

Answer:

512

Step-by-step explanation:

8^3 = 512

.................

Answer:

512

Step-by-step explanation:

Given

[tex]m^{n}[/tex] ( substitute m = 8, n = 3 into the expression

= 8³

= 8 × 8 × 8

= 64 × 8 = 512

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:

5 years

Step-by-step explanation:

(x+15)=4x

15=4x-x

15=3x

5=x

Answer:

Sale price = $45.75

Step-by-step explanation:

Original price = $48.41

Percentage Discount = 5.5%

Amount of discount = Percentage Discount × Original price

= 5.5% × $48.41

= 5.5/100 × $48.41

= 0.055 × $48.41

= $2.66255

Sale price = Original price - Amount of discount

= $48.41 - $2.66255

= $45.74745

Approximately,

Sale price = $45.75

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

Step-by-step explanation:

hi friend I can help you in this geometry work via Wazapp

Given:

The graph of h(x) is the greed dashed line segment.

To find:

The endpoints of the function [tex]h^{-1}(x)[/tex].

Solution:

If (a,b) is the point on the graph of the function f(x), then (b,a) must be the point on the inverse function [tex]f^{-1}(x)[/tex]

From the given graph, it is clear that the endpoint of the line segment h(x) are (-8,1) and (3,-4).

So, the endpoints of the inverse function [tex]h^{-1}(x)[/tex] are (1,-8) and (-4,3).

Therefore, the endpoints of [tex]y=h^{-1}(x)[/tex] are (1,-8) and (-4,3), and the graph is shown below.