The velocity function of a car is given by v(t) = -3t2 + 18t + 9 m/s. Find the acceleration of the car three seconds before it comes to a stop.

A.
a = -6.46 m/s²
B.
a = -2.76 m/s²
C.
a = -0.46 m/s²
D.
a = 2.76 m/s²

Answer: In photo below

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(3.201 x 10^9) * (4.85 x 10^3) =

15524850000000

in scientifc notation

1.552485 x 10^13

Answer:

$9.25

Step-by-step explanation:

$397.75÷43=$9.25

Weekly salary divided by hours of work = hourly pay

Answer:

1,344

Step-by-step explanation:

First, find how many steps he climbs every day

32*6=192

Now, multiply that by 7 to see how many he climbs in a week

192*7=1,344

Answer:

b

Step-by-step explanation:

The correct option is (b) The data does not contain an outlier. This means that the people at the center were all seniors around the same age.

Outlier in a data set is simply the extremely low data point or an extremely high data point compared to other points in the dataset.

It will stand out from the other values in the dataset.

The line plot shows the ages of people visiting a senior center one afternoon.

The data points are,

70, 70, 70, 75, 75, 80, 80, 85, 90, 90, 95, 95, 95, 100.

If there is an outlier in the set, it would be extremely low or high compared to other points.

But there are no such points.

So there are no outliers.

This means that people visited at the center were all seniors around the same age.

Hence the correct option is (b).

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Answer:

5.33 inches

Step-by-step explanation:

Mean is another term for average. Therefore, we add up all precipitation items from Column B and divide by the total number of items (9):

[tex]5.98+6.05+7.59+5.27+3.11+7.18+2.95+7.22+2.61=47.96[/tex]

[tex]47.96\div{9}\approx{5.33}[/tex]

Answer:

a^-6 or 1/a^6

Step-by-step explanation:

(a³)-²

=a^-6

=1/a^6

Answer:

See below

Step-by-step explanation:

You can pull  one y   and 6 n's out to start

then   4/5 = 24/30     and 5 / 6 = 25/30

and you can factor out a   -1

- y n^6 /30  ( 24  + 25 y^3n^2 )

The expression that represents the age of randy's brother is

2x.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Randy age = 8 years old

Randy's brother age = 2 x 8 = 16

Randy's sister age = 8 - 3 = 5

The expression that represents the age of randy's brother.

Let the age of Randy = x.

=  2x

= 2x

= 2 x 8

= 16 years old.

Thus,

The expression that represents the age of randy's brother is

2x.

Where x is the age of Randy.

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Answer:

D: 3x9/5

Step-by-step explanation:

the formula for dividing fractions is skip flip multiply where we keep the first term the same and then flip the second to multiply

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Answer:

I = (2350)(0.0277)(6)

Step-by-step explanation:

We're told the principal, rate, and time so we just plug in.

We must convert the 2.77% to a decimal by moving the period two places to the left to get the rate 0.0277

The equations of both trees are Tree A = 38 + 6t and Tree B = 20 + 9t and the growth interval of tree A is t < 6

From the question, we have the following parameters that can be used in our computation:

Tree A

Tree B

The height after t years is

Tree = Initial height + rate * t

So, we have

Tree A = 38 + 6t

Tree B = 20 + 9t

Recall that

Tree A = 38 + 6t

Tree B = 20 + 9t

When Tree A is taller than Tree B, we have

38 + 6t > 20 + 9t

Evaluate the like terms

-3t > -18

Divide

t < 6

Hence, the interval is t < 6

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Answer: 2.5>9.5

Step-by-step explanation: maybe we should both pay attention to math

The zeroes of the parabola is -1, -5.

What is parabola and zeroes of parabola?

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.

The equation of parabola can be expressed in two different ways, such as the standard form and the vertex form. The standard form of parabola equation is expressed as follows:

f(x) = y= ax2 + bx + c

To find zeroes of parabola

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

Given equation is

f(x) = [tex]x^{2} +6x+5[/tex]

a = 1, b = 6, c = 5

x = -6 ±[tex]\sqrt{36-4(5)}[/tex]/2

x = -6 ±[tex]\sqrt{16} /2[/tex]

x = -6 ± 4 /2

hence,

x = -6-4/2 and x = -6 +4/2

x = -5 or x = -1

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The value of the larger number and the smaller number are 25 and 8 respectively.

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y.

They are called simultaneous equations because the equations are solved at the same time.

If the bigger value is represented by x and the smaller value is represented by then

x+y= 33 equation 1

3x+ 4y= 107 equation 2

using Elimination method,

we multiply the coefficients of x by opposite equation

3x+3y=99 equation 3

3x+4y= 107 equation4

subtracting equation 3 from 4

y=107- 99

y= 8

substituting 8 for y in equation 1

x+8= 33

x= 33-8=25

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standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ 3}(x-\stackrel{x_1}{(-4)}) \implies y -1= 3 (x +4) \\\\\\ y-1=3x+12\implies y=3x+13\implies -3x+y=13\implies \boxed{3x-y=-13}[/tex]

After solving the equation of vector, the value obtained is equal to one, which shows that vectors are orthogonal.

A vector is a quantity with both magnitude and bin physics. It is often depicted by an arrow with the same direction as the amount and a length proportionate to the size of the quantity. A vector has magnitude and the direction, but no position. As soon as a vector's length remains unchanged, it is consequently untouched by movement perpendicular to itself.

In contrast to vectors, scalars are normal variables having a magnitude but no direction. Displacement, velocity, and acceleration are all vector quantities, unlike speed, time, or weight, which are scalar variables.

uw = -6 + 10- 3

uw = 1.

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Answer:

The Y intercept of this line is -3.

Step-by-step explanation:

The X intercept of the crossing line is about -1.4.
On finding the Y intercept:
Step 1: look at the vertical black line (Y Axis)

Step 2: Locate where the blue line crosses on this line.
Step 3: graph Y function of the point as your answer.

Hope this helped a bunch!
Have a great day!
- Kit-Kat~

Answer:

-1,-2,0

Step-by-step explanation:

n(2-3)

1st term=n(2-3)

substitute value

1(2-3)=-1

2nd term=2(2-3)=-2

3rd term=3(3-3)=0

The measure of ∠5 is 62 degrees if the value of ∠2 is 48 degrees and ∠3 is 62 degrees. Option B is correct.

First, let us understand the types of angles formed by parallel and transversal lines:

Corresponding Angles — Corresponding angles are angles on the same side of a transversal that are either above or below the lines.

Alternate Interior Angles - Alternate interior angles are the pairs of interior angles on opposing sides of the transversal.

Alternate Exterior Angles - Alternate exterior angles are the pairs of exterior angles on opposing sides of the transversal.

Consecutive interior angles - Internal angles on the same side of a transversal are also known as consecutive interior angles, related angles, or co-interior angles.

We are given:

∠2 is 48 degrees and ∠3 is 62 degrees.

We need to find the ∠5.

From the given figure we can see that;

∠3 and ∠5 are alternate interior angles.

So, ∠3 = ∠5 = 62 degrees.

So, the measure of ∠5 is 62 degrees.

Thus, the measure of ∠5 is 62 degrees if the value of ∠2 is 48 degrees and ∠3 is 62 degrees. Option B is correct.

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Answer:

8.25

Step-by-step explanation:

Answer:

the change is in %age of decrease of 10%

Step-by-step explanation:

original value = 20

new value = 18

decrease = 2

%age decrease = decrease/original value * 100

                         =  2/20 * 100

                         =  10%

The new temperature is given as -15°F.

A measurement unit is a unit to measure certain quantities.

For example, the mass can be measured in kilograms, length can be measured in meter and time can be measured in seconds.

To find the measurement of a new quantity known units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.

Given that,

The present temperature is 0°F.

And, the drop in the temperature is 15°.

The new temperature after the drop can be found by subtracting the amount of drop from the initial temperature as follows,

0 - 15°F

=  -15°F

Hence, the new temperature after the drop is  -15°F.

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The solution of 5√3 × 3√12 = 30√3.

Square root of a number is defined as the number in which the multiplication by itself gives the original number. That is the square root of 9 would be = 3 in which when multiplied by itself gives the original number being 9.

Other examples include √ 4 = 2, √ 25 = 5, √100 = 10.

To simplify the give expression;

5√3 × 3√12= 5√3 × 3√4×3

= 5√3 × 3×2√3

= 5√3 × 6 √3

= 30√3.

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The exact solutions of the given equation in the interval are;

A: x = 0, π/2, π, ³/₂π

We are given the equation as;

sin 4x = –2sin 2x

Writing the equation in standard form gives;

sin 4x + 2sin 2x = 0

Using trigonometric Identity, substitute (sin 4x) with (2sin 2x.cos 2x) to get;

2sin 2x cos 2x + 2sin 2x = 0

Factorize to get;

2sin 2x(cos 2x + 1) = 0

A. sin 2x = 0

The unit circle will give us 3 solutions for 2x as follows;

2x = 0

Thus; x = 0

2x = π

Thus; x = π/2

2x = 2π

Thus; x = π

B. cos 2x = - 1

The unit circle gives 2 solutions for 2x as;

2x = π

Thus; x = π/2

2x = 3π

Thus; x = ³/₂π

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Complete question is;

How do you find the exact solutions of the equation sin4x = −2sin2x in the interval [0, 2π)?

Answer:
3/2

Step-by-step explanation:

the answer is 3/2 because you take the slope by using the equation y/x. I did this problem by starting prop the point (0,-6). I then counted for how many points I went up, how many did I go to the right or left. If it went to the right it’s positive, to the left it is negative. In this case it went to the right 2 times every time it went up 3. Meaning 3/2

The inequality to find the value of x for the rectangle is 2(2x+4) < 122 and the value of x should be less than 28.5.

According to the question,

We have the following information:

The perimeter of the rectangle is less than 122.

A rectangle has a width of x and a length of x plus 4.

Now, the expressions for the width and length of the rectangle are given below:

Width = x units

Length = (x+4) units

We know that the following formula is used to find the perimeter of rectangle:

2(length+width) < 122

2(x+4+x) < 122

2(2x+4) < 122

Dividing by 2 on both sides:

2x+4 < 122/2

2x+4 < 61

Subtracting 4 from both sides:

2x < 61-4

2x < 57

Dividing by 2 on both sides:

x < 57/2

x < 28.6

Hence, the inequality to find the value of x for the rectangle is 2(2x+4) < 122 and the value of x should be less than 28.5.

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Answer:

i think, x equal 12 and y equal 20

The rational zeros for f(x) = 3x^4 - 4x^3 + x^2 + 6x - 2 are x = -1 and x = 1/3 whereas the linear factors of f(x) are (x + 1) and (3x - 1).

We will use the synthetic division method to determine the rational zeros and linear factors of given polynomials.

Polynomials are divided via synthetic division.

The procedure entails of synthetic division:

Step 1: Create a synthetic divide.

Step 2: Bring the leading coefficient down to the bottom row.

Step 3: Divide this by the value stated in the bottom row.

Step 4: Finally, add the column you defined in step 3.

This can proceed as:

Given: f(x) = 3x⁴- 4x³ + x² + 6x - 2

3x⁴ - 4x³ + x² + 6x - 2 = 0

We will put x = -1 in f(x). In this case, replace x with -1. This will be:

f(-1) = 3 * 1⁴ - 4 * 1³ + 1² + 6 * 1 - 2 = 0

Since f(-1) = 0, so (x + 1) is a factor of f(x).

Using synthetic division:

-1)....3....-4....1....6....-2

.........3.....-7...8....-2..|..0

Remainder = 0

Quotient = 3x³ - 7x² + 8x - 2

For 3x³ - 7x² + 8x - 2,  f(1/3) = 0, so (x - 1/3) is a factor.

1/3)....3....-7....8....-2

..........3.....-6...6...|..0

Remainder = 0

Quotient = 3x² - 6x + 6 = 3(x² - 2x + 2)

Because x² - 2x + 2 has no more rational zeros or linear components. The rational zeros are hence x = -1 and x = 1/3.

Thus, the rational zeros for f(x) = 3x^4 - 4x^3 + x^2 + 6x - 2 are x = -1 and x = 1/3 whereas the linear factors of f(x) are (x + 1) and (3x - 1).

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Answer: 42.86%

Step-by-step explanation: 120/280*100 = 42.86%