The distance a race car travels is given by the equation, [tex]d=v_{0} t+\frac{1}{2} at^{2}[/tex], where [tex]v_{0}[/tex] is the initial speed of the race car, a is the acceleration and t is the time traveled. Near the beginning of a race, the driver accelerates for 9 seconds at a rate of [tex]4m/s^{2}[/tex]. The driver's initial speed was 75 m/s.

Find the driver's average speed during the acceleration.

Answer:

y = - [tex]\frac{2}{3}[/tex] x - 3

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 )

Calculate m using the slope formula

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

with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (- 4.5, 0 ) ← coordinates of intercepts

m = [tex]\frac{0-(-3)}{-4.5-0}[/tex] = [tex]\frac{0+3}{-4.5-0}[/tex] = [tex]\frac{3}{-4.5}[/tex] = - [tex]\frac{2}{3}[/tex]

The line crosses the y- axis at (0, - 3 ) ⇒ c = - 3

y = - [tex]\frac{2}{3}[/tex] x - 3 ← equation of line

9514 1404 393

Answer:

  525 km

Step-by-step explanation:

Let d represent the distance to the town. Let s represent the nominal speed of the car. The relation between time, speed, and distance is d = st.

  t1 = d/s

  t2 = d/(s+15)

  t1 : t2 = 6 : 5 . . . increasing the speed reduces the time

Substituting for t1 and t2, we have ...

  (d/s)/(d/(s+15)) = 6/5

  (s +15)/s = 6/5

  1 +15/s = 1 +1/5

  s = 5·15 = 75 . . . . nominal speed in km/h

__

Decreasing the speed increases the time.

  d/75 +(105/60) = d/(75-15)

  d(60/75) +105 = d . . . . . . multiply by 60

  105 = d/5 . . . . . . . . . . . subtract 4/5d

  525 = d . . . . . . . . . . multiply by 5

The distance traveled by the car is 525 km.  

A solution to a system

Is the point two lines cross each other.

3. The lines cross at y = 0 and x = 2, so the solution is x = 2

4. The lines do not cross so there are no solutions.

5. It looks like there is one line which means the two lines are identical so there are infinite solutions

Answer:

Step-by-step explanation:

3)  y = x - 2

y = -x +2

Both lines are intersecting at (2 , 0).So, (2, 0) is the solution of the equations.

(2,0)

4) Both lines are parallel to each other and they will never intersect. So, it has no solution.

5) Both lines are coincide. So all points in the line are solutions of the equations.

Infinity solutions

Answer:

x=10

Step-by-step explanation:

The whole figure is symmetric hence x=10

Answer:

C

Step-by-step explanation:

You are looking at the domain which is on the K axis. It starts at 6 and ends at 11. The range J is 80 to 120

Answer:

Step-by-step explanation:

Answer:

The p-value of the test is 0.0023 < 0.02, which means that there is sufficient evidence at the 0.02 level to dispute the company's claim.

Step-by-step explanation:

The company's promotional literature claimed that 28% do not fail in the first 1000 hours of their use.

At the null hypothesis, we test that at least 28% do not fail, that is:

[tex]H_0: p \geq 0.28[/tex]

At the alternative hypothesis, we test if the proportion is of less than 28%, that is:

[tex]H_1: p < 0.28[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.28 is tested at the null hypothesis:

This means that [tex]\mu = 0.28, \sigma = \sqrt{0.28*0.72}[/tex]

Sample of 1800 computer chips revealed that 25% of the chips do not fail in the first 1000 hours of their use.

This means that [tex]n = 1800, X = 0.25[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.25 - 0.28}{\frac{\sqrt{0.28*0.72}}{\sqrt{1800}}}[/tex]

[tex]z = -2.83[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion below 0.25, which is the p-value of Z = -2.83.

Looking at the z-table, z = -2.83 has a p-value of 0.0023.

The p-value of the test is 0.0023 < 0.02, which means that there is sufficient evidence at the 0.02 level to dispute the company's claim.

Answer:

1/3

Step-by-step explanation:

Next term ÷ Previous term = common ratio

Answer:

Hello,

Answer: q=1/3

Step-by-step explanation:

[tex]u_1=1\\u_2=\dfrac{1}{3} =1*\dfrac{1}{3}\\u_3=\dfrac{1}{9}=u_2*\dfrac{1}{3}=u_1*(\dfrac{1}{3})^2\\u_4=\dfrac{1}{27}=u_3*\dfrac{1}{3}=u_1*(\dfrac{1}{3})^3\\\\Common\ ratio\ q=\dfrac{1}{3}[/tex]

Step-by-step explanation:

= 45÷3(90÷2(6+3(19-16))))

= 45÷3(90÷2(6+3×3)))

= 45÷3(90÷2(6+9)))

= 45÷3(90÷2×15))

= 45÷3(45×15)

= 45÷3×675

= 15×675

= 10125

hope it will help u

Answer:

Step-by-step explanation:

Answer:

D. -8x-4

E. 8x+6y-28

Step-by-step explanation:

D. 8(-x-1/2) = -8x-4

E. -8(-x-3/4y+7/2 = 8x+6y-28

Step-by-step explanation:

mark me brainlist

please mark mep

Answer:

70%

Step-by-step explanation:

First find the ones that still need to be installed

270-81

189

Percent to be done = number to be installed / total

                                   =189/270 =.7

Change to percent form = .7 *100% = 70%

Answer:

the answer for y=4 and x=4✔3

Answer:

0.235 = 0.24

13.467 = 13.47

0.24+13.47=13.71

Answer:

[6x] + [-7y] + [-4]

Step-by-step explanation:

There are only two like terms in this expression "4x" and "2x." Since they are like terms we can combine them by adding the coefficients and keeping the variable attached. Therefore we can combine 4x and 2x into 6x. Since there are no more like terms, this expression can be simplified to 6x - 7y - 4.

Answer:

The central angle is 5/3 radians or approximately 95.4930°.

Step-by-step explanation:

Recall that arc-length is given by the formula:

[tex]\displaystyle s = r\theta[/tex]

Where s is the arc-length, r is the radius of the circle, and θ is the measure of the central angle, in radians.

Since the intercepted arc-length is 10 meters and the radius is 6 meters:

[tex]\displaystyle (10) = (6)\theta[/tex]

Solve for θ:

[tex]\displaystyle \theta = \frac{5}{3}\text{ rad}[/tex]

The central angle measures 5/3 radians.

Recall that to convert from radians to degrees, we can multiply by 180°/π. Hence:

[tex]\displaystyle \frac{5\text{ rad}}{3} \cdot \frac{180^\circ}{\pi \text{ rad}} = \frac{300}{\pi}^\circ\approx 95.4930^\circ[/tex]

So, the central angle is approximately 95.4930°

9514 1404 393

Answer:

  105.0°, 255.0°

Step-by-step explanation:

Many calculators do not have a secant function, so the cosine relation must be used.

  sec(θ) = -3.8637

  1/cos(θ) = -3.8637

  cos(θ) = -1/3.8637

  θ = arccos(-1/3.8637) ≈ 105.000013°

The secant and cosine functions are symmetrical about the line θ = 180°, so the other solution in the desired range is ...

  θ = 360° -105.0° = 255.0°

The angles of interest are θ = 105.0° and θ = 255.0°.

Answer:

348 frogs

Step-by-step explanation:

ratio = 3:7

total of ratio = 10

frogs = 3/10 × 1280 = 348 frogs

Answer:

let the ratio be 3x and 7x.

3x+7x=1280

10x=1280

x=128

Now

frogs =3x=3*128=384

toads =7x=7*128=896

Answer:

1/(x^3 + 6x^2 + 12x + 8)

Step-by-step explanation:

The first thing we do is rationalize this expression. (2+x)^-3 is written as

1/(2+x)^3

Then from there we can foil out the denominator. It is easiest to foil (2+x)(2+x) first and then multiply that product by (2+x).

(2+x)(2+x) = 4 + 4x + x^2

(4+4x+x^2)(2+x) = 8+8x+2x^2+4x+4x^2+x^3.

Then we combine like terms and put them in order to get:

x^3 + 6x^2 + 12x + 8

And of course we can't forget that this was raised to the negative third power, so our answer is 1/(x^3 + 6x^2 + 12x + 8)

Answer:

Hello,

Step-by-step explanation:

[tex](a+x)^n=a^n+\left(\begin{array}{c}n\\ 1\end{array}\right)*a^{n-1}*x+\left(\begin{array}{c}n\\ 2\end{array}\right)*a^{n-2}*x^2+\left(\begin{array}{c}n\\ 3\end{array}\right)*a^{n-3}*x^3+\left(\begin{array}{c}n\\ 4\end{array}\right)*a^{n-4}*x^4+...+\left(\begin{array}{c}n\\ n\end{array}\right)*a^{n-n}*x^n[/tex]

[tex]with \\\\\left(\begin{array}{c}n\\ 1\end{array}\right)=n\\\\\left(\begin{array}{c}n\\ 2\end{array}\right)=\dfrac{n(n-1)}{2!} \\\\\left(\begin{array}{c}n\\3 \end{array}\right)=\dfrac{n(n-1)(n-2)}{3!} \\\\...\\[/tex]

[tex]\dfrac{1}{(2+x)^3} =\dfrac{1}{8} +3*\dfrac{x}{4}+3\dfrac{x^2}{2}+x^3\\\\[/tex]

The final amount is $7,615.27

A = P(1 + r/n)^t

Where,

A = Final amount

P = principal = $7, 200

r = interest rate = 2.5% = 0.025

n = number of periods = 4

t = time = 9 years

A = P(1 + r/n)^t

= 7,200(1 + 0.025/4)^9

= 7,200(1 + 0.00625)^9

= 7,200(1.00625)^9

= 7,200(1.0576769512798)

= 7,615.2740492152

Approximately,

A = $7,615.27

https://brainly.com/question/14003110

Answer:

In mathematics, an area model is a rectangular diagram or model used for multiplication and division problems, in which the or the and define the length and width of the rectangle.

We can break one large of the rectangle into several smaller boxes, using number bonds, to make the calculation easier. Then we add to get the area of the whole, which is the or quotient.

To multiply two 2-digit numbers, using the area model, follow the given steps:

Write the multiplicands in expanded form as tens and ones.

For example, 27 as 20 and 7, and 35 as 30 and 5.

Draw a 2 × 2 grid, that is, a box with 2 rows and 2 columns.

Write the terms of one of the multiplicands on the top of the grid (box). One on the top of each cell.

On the left of the grid, write the terms of the other multiplicand. One on the side of each cell.

Write the product of the number on the tens in the first cell. Then write the product of the tens and ones in the second and third cell. Write the product of the ones in the fourth cell.

write the product in the cell

Finally, add all the partial products to get the final product.

Here, for example, the area model has been used to multiply 27 and 35.

area model multiplication

Let us see how to find the product of 3-digit number by a 2-digit number using the area model.

Find the Product using Area Model

Let us now use the area model for the division. Here, we divide 825 by 5.

Area Model Division 1

Area Model Division 2

Fun Facts

The area model is also known as the box model.

The area model of solving multiplication and division problems is derived from the concept of finding the area of a rectangle. Area of a rectangle = Length × Width.

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Answer:

100

Step-by-step explanation:

100/ 10

= 10

Answer:

true

Step-by-step explanation:

what else would it be. that is exactly the reason why we have constants.

Answer:

is it like this

64653=65000

Answer:

là 64652/64654

Answer:

x< - 8

Step-by-step explanation:

3x <-24

x < - 24

3

x< - 8

x < - 8

Step-by-step explanation:

3x < - 24

Divide 3 on both sides,

3x / 3 < - 24 / 3

x < - 8

9514 1404 393

Answer:

  30 gallons

Step-by-step explanation:

Let c represent the capacity of the container. Then we have ...

  2/5c + 8 = 2/3c

Multiplying by 15 clears the fractions:

  6c +120 = 10c

  120 = 4c . . . . . . . . subtract 6c

  30 = c . . . . . . . . . . divide by 4

The container can hold 30 gallons.

_____

Additional comment

Often, you are told to "clear fractions" first when solving equations that involve them. Here, you can work directly with the fractions, if you like.

  8 = (2/3c) -(2/5c) = 4/15c . . . . . find the difference of the fractions

  8(15/4) = c = 30 . . . . . . . . . . . . . multiply by its inverse

Answer:

144 = c - 379

Step-by-step explanation:

"144 is the same as 379 less than c"

144 = c - 379

Answer and Step-by-step explanation:

This can be written in an equation like this:

144 = c - 379

The question is saying that 144 is the same answer as the result of 379 less than c (or c minus 379). This is why we equal 144 to the result of c minus 379.

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