A car's velocity is modeled by v(t) = 0.5t^2 -14t+ 80 for 0 less than or equal to t less than or equal 14, where the velocity is in feet per second and time is in seconds. Where does the car come to a complete stop?

Answer:

(1; 8)

Step-by-step explanation:

x = (5 + (-3))/2 = 1

y = (10 + 6) = 8

1) The x-intercept lies at (1, 14), and the y-intercept lies at (3, 42).

2) This means that after 3 cuts, the length of the string is 33 inches.

3) Therefore, the 42-inch string can be cut into 14 pieces of 3 inches each.

The x-intercept is the point on the graph where a line crosses the x-axis.

The y-intercept is the point on the graph where a line crosses the y-axis.

The x- and y-intercepts are the coordinate points for graphing data.

Thus, the x- and y-intercepts are coordinate points where the graph of a function or an equation touches the two axes.

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The length in feet of the pole is 13 ft.

The right-angled triangle's relationship between its three sides is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The square of a triangle's hypotenuse is equal to the sum of its other two sides' squares, according to the Pythagoras theorem. Let's learn more about the Pythagoras theorem, its proofs, and its equations before moving on to cases that have been solved using the triangle and square Pythagoras theorem. The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this.

Use the Pythagorean relationship:

c²= a² + b²

= 5²  +  12²

= 25 + 144

= 169

c = 13

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lets remember what it means compound continuously,

the interest never stopped, the balance is earning interest at all time

Joseph is 22 and he wants to know how much money he will have at 55

55-22=33

his balance will gain interest for 33 years, this is our time

there is a 7% rate

the formula is

P(t)= P(0) e ^rt

our t is 33

rate=7%

Joseph will have a balance at age 55, 45,334.99 dollars

The width of the rectangular garden is 40feet. The equation that represents the garden's perimeter is 2(60 + w) = 200.

A rectangular garden has a length of 60 feet (ft)

a width of w ft

and a perimeter of 200 ft.

The formula of perimeter of a rectangle is 2(lenght + width)

The equation that represents the garden's perimeter is 2(60 + w) = 200

2(60 + w) = 200

120 + 2w = 200

2w = 200 - 120

2w = 80

w = 40

Therefore, width of the rectangular garden is 40feet. The equation that represents the garden's perimeter is 2(60 + w) = 200

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The correct option regarding the ratio is given as follows:

For a ratio of 3:2, divide AB into 5 equal parts. Each equal part is 2 units, so the point that divides AB into a 3:2 ratio is 2.

A ratio of an amount a over a total amount a + b is given as follows:

r = a/(a + b) = a:b.

In the context of this problem, the ratio is given as follows:

r = 3:2.

Hence the number of equal parts is given by:

equal parts = 3 + 2 = 5.

The length of the segment is:

B - A = 6 - (-4) = 10 units.

Hence the length of each equal part is:

length equal part = 10/5 = 2.

The point that is 3/5 of the way from point -4 to point 6 is found as follows:

x - (-4) = 3/5(6 - (-4))

x + 4 = 30/5

x + 4 = 6

x = 2.

Meaning that the correct option is given by the last one.

The coordinates of A and B are missing, and they are given as follows:

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Answer:373248

Step-by-step explanation:

Answer:

Step-by-step explanation:

12*6=72

72^3=373248

The new coordinates when we rotate the triangle counterclockwise is  (3, -1), (-2, -4),  (-5, 3).

Given,

The triangle with vertices;

(-3, 1) (2, 4) and (5, -3).

We have to find the new coordinates, when the triangle rotated 180 degrees counter clockwise;

Here,

The vertices;

(-3, 1) (2, 4) and (5, -3).

When we rotate 180 degree counter clockwise, the plane changes not the point.

That is,

(-3, 1) becomes (3, -1)

(2, 4) becomes (-2, -4)

(5, -3) becomes (-5, 3)

That is,

The new coordinates when we rotate the triangle counterclockwise is  (3, -1), (-2, -4),  (-5, 3).

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The new coordinates when we rotate the triangle counterclockwise is  (3, -1), (-2, -4),  (-5, 3).

Given,

The triangle with vertices;

(-3, 1) (2, 4) and (5, -3).

We have to find the new coordinates, when the triangle rotated 180 degrees counter clockwise;

Here,

The vertices;

(-3, 1) (2, 4) and (5, -3).

When we rotate 180 degree counter clockwise, the plane changes not the point.

That is,

(-3, 1) becomes (3, -1)

(2, 4) becomes (-2, -4)

(5, -3) becomes (-5, 3)

That is,

The new coordinates when we rotate the triangle counterclockwise is  (3, -1), (-2, -4),  (-5, 3).

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Answer:

Step-by-step explanation:

2x+4y=32

Get Y on one side of equation by itself

(subtract 2x on both sides)

leaves           4y = 32 - 2x

Divide by 4 to get Y alone (without coefficient)

4y = 32 - 2x

         4

y = 8 - 1/2x

$3

the amount paid after adding tip is $21

the amount for the meal is $18

$21-$18=$3

The factors of the given quadratic equations are [tex]\frac{-13+\sqrt{409} }{8}[/tex] and [tex]\frac{-13-\sqrt{409} }{8}[/tex]

What is factorization?

When we try to write the given equation in terms of linear values from which we calculate the roots of the given equation then we say that we have factorized them. Root of a equation means a value which satisfies a equation.

We are given a quadratic equation

[tex]4x^2+13x-15[/tex]

We use quadratic formula to compute the factor of the equation

[tex]x=\frac{-b}{2a}[/tex]±[tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]

[tex]x=\frac{-13}{8}[/tex]±[tex]\frac{\sqrt{169+240} }{8}[/tex]

[tex]x=\frac{-13}{8}[/tex]±[tex]\frac{\sqrt{409} }{8}[/tex]

Therefore the factors are [tex]\frac{-13+\sqrt{409} }{8}[/tex] and [tex]\frac{-13-\sqrt{409} }{8}[/tex]

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Answer:

50

Step-by-step explanation:

Solution for 700 is what percent of 1400:

700:1400*100 =

(700*100):1400 =

70000:1400 = 50

Now we have: 700 is what percent of 1400 = 50

The following is not a step in a hypothesis test; d. if the sample data is located in the critical region, we reject the null hypothesis.

There are two hypotheses. The first one is called the null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test.

The hypothesis which substitutes the null hypothesis is an alternate hypothesis.

We know that the Null hypothesis is the one that researchers try to disprove.

The null hypothesis must be rejected if we choose the 99.7 percent of  confidence level.

The following is not a step in a hypothesis test; d. if the sample data is located in the critical region, we reject the null hypothesis.

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Answer:

C)

Step-by-step explanation:

elimination is not substitution.

therefore, A and B are out.

D does not work, because in the described way the x terms don't get different signs, and the addition does not eliminate any variable.

C brings both y terms to the same absolute value, and their signs are different, so the addition will eliminate the y terms leaving us with one equation in x that we can solve :

15x + 12y = 21

8x - 12y = 12

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

23x 0 = 33

23x = 33

x = 33/23

Answer:

a is the right answer for you

Answer:

2

Step-by-step explanation:

convert 1 + the other one is 2

Answer:

2

Step-by-step explanation:

You add both numbers that have been given which are 1+1

Answer: Midpoint = 0

Explanation:

The midpoint of segment ED can be calculated as:

Where E and D are the coordinates of E and D respectively.

So, replacing E by 2 and D by -2, we get:

Therefore the midpoint of segment ED is equal to 0.

The value of the expression (-3.69)0 is zero as any number multiplied zero times is zero.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

The value of the expression (-3.69)0 is zero itself.

Anything multiplied by nothing is nothing right.

A numerical value is given which is  -3.69 it is multiplied with zero, so a number multiplied zero times is obviously zero.

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Answer:

9x^2-1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Multiply (3x - 1) * (3x + 1)

= 9(x)^2 + 3x - 3x -1

= 9(x)^2 - 1

Answer:

y = - 2x + 2

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 )

given

2x + y = 2 ( subtract 2x from both sides )

y = - 2x + 2 ← in slope- intercept form

The table represent a direct proportional relation.

In this question we find a table with four pairs of elements that have to be tested with respect to the direct proportional formula, which is defined below:

y = k · x

Where:

The table represents a direct proportional relation if and only if there is only one constant of proportionality:

k₁ = 12 / 3

k₁ = 4

k₂ = 20 / 5

k₂ = 4

k₃ = 8 / 2

k₃ = 4

k₄ = 32 / 8

k₄ = 4

As k₁ = k₂ = k₃ = k₄, the table represent a proportional relationship.

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Answer:

10 : 0.02 (20m)

If in Central city, there are 29791 registered voters and 93 voting centers, then each voting centers serves about 320 of the city population.

Total number of registered voters in Central city = 29791 voters

Total number of voting centers = 93 voting centers

The number of population serves by each center = Total number of registered voters in Central city ÷ Total number of voting centers

Substitute the values in the equation

The number of population serves by each center = 29791/93

= 320.33

≈ 320

Hence, If in Central city, there are 29791 registered voters and 93 voting centers, then each voting centers serves about 320 of the city population.

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The approximate air distance from La Sarre to Lebel-sur-Quevillon is 167.71 km.

To determine the air distance from La Sarre to Lebel-sur-Quevillon, analyze the path she has traveled.

When she drove east and drove another north, the total path she ave traveled is similar to the sides of a right triangle, where the distance from the start and end point is the hypotenuse. (see photo attached)

Using Pythagorean theorem, solve the distance from La Sarre to Lebel-sur-Quevillon.

c² = a² + b²

where a = 150 km and b = 75 km

distance² = 150² + 75²

distance² = 22500 + 5625

distance² = 28125

distance = 167.71 km

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Answer:

1 week

Step-by-step explanation:

After 1 week

Saving account: $25 + $5 = $30

Checking amount: $50 + $10 = $60

30 x 2 = 60

So it's 1 week

Here the graph shows reflection across x - axis by 2 units.

f(x) = |x| => g(x) = -2|x|.

Here given the parent function, f(x)=|x|

The translation is , g(x)= -2|x|

Which is an absolute function.

Here the transformation is .

f(x)=|x|  => g(x)= -2|x|

The value of f(x) is reflecting over x- axis and value of y changes by 2 units.

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4 algebra books, 5 geometry and 2 chemistry books can be arranged in 5760 ways.

Given ,

4 algebra books , 5 geometry , 2 chemistry books,

The number of permutations =

2! x 5! x 4!

= (1 x 2) x (5 x 4 x 3 x 2) x (4 x 3 x 2)

= 2 x (120) x (24)

= 5760 ways.

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The lines aren't parallel since they intersect at point B.

Parallel lines never intersect.

The probability that the mean diameter of the sample shafts would vary from the population mean by less than 0.3 inches exists 0.0757.

Let X the random variable that represent the diameters of interest for this case, and for this case we know the following info

Where [tex]$\mu=205$[/tex] and [tex]$\sigma=1.5$[/tex]

Let the probability be

[tex]$P(205-0.3=204.7 < \bar{X} < 205+0.3=205.3)$$[/tex]

For this case they select a sample of n = 79 > 30, so then we have enough evidence to utilize the central limit theorem and the distribution for the sample mean can be approximated with:

[tex]$\bar{X} \sim N\left(\mu, \frac{\sigma}{\sqrt{n}}\right)$$[/tex]

To simplify this problem is utilizing the normal standard distribution and the z score given by:

[tex]$z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$$[/tex]

To find the z scores for each limit and we got:

[tex]$z=\frac{204.7-205}{\frac{1.5}{\sqrt{79}}}=-1.778$$[/tex]

[tex]$z=\frac{205.3-205}{\frac{1.5}{\sqrt{79}}}=1.778$$[/tex]

To find this probability:

P(-1.778 < Z < 1.778) = P(Z < 1.778) - P(Z < -1.778)

simplifying the above equation, we get

= 0.962 - 0.0377

= 0.9243

The interest exists the probability that the mean diameter of the sample shafts would vary from the population mean by more than 0.3 inches utilizing the complement rule we got:

P = 1 - 0.9243 = 0.0757

The probability that the mean diameter of the sample shafts would vary from the population mean by less than 0.3 inches exists 0.0757.

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