Solve the equation. Select the correct answer below, and, if necessary, fill in the answer box to complete your choice.

A cosine function has the form.

Where A refers to the changes of the y-coordinate along the curve, that is, the amplitude. And B refers to the period, that is, the repetition period of the curve.

According to the graph, the amplitude is 1, so A = 1.

Notice that from 0 to 2(pi) the function completes two cycles, which means B = 3.

Answer:

32m

Step-by-step explanation:

The distance he would've covered is 32m if he ran through a straight line.

What is Pythagoras's Theorem?

In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

We can proceed to use this to find the distance from point a to point b assuming he ran through a straight line.

Mathematically, the theorem can be expressed as

Let's substitute the values into the equation and solve.

Jimmy would've jogged 32m if he ran through a straight line.

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Answer:

5

Step-by-step explanation:

put it in order

6056605570546055

and the one that appears the most is the mode

only answer ;( c.

Step-by-step explanation:

so hope it help

Solution

We have the following function given:

y =-8x+7

If we compare this with the general formula for a slope given by:

y= mx+b

We can see that the slope m is:

m =-8

And the y-intercept would be: (0,7)

x=-4, y=1 and z=-5 are solutions of x+y+2z=-5" 5x+4y-4z=4 x-3y-2z=3

Two or more expressions with an Equal sign is called as Equation.

The given three equations are

-x+y+2z=-5.....(1)

5x+4y-4z=4....(2)

x-3y-2z=3....(3)

Add equations (1) and (3)

-x+y+2z+x-3y-2z=-5+3

Add the like terms

-2y=-2

y=1

Now put value of y in equations (1) and (2)

-x+2z=-6..(4)

5x-4z=0...(5)

Multiply with 5 on equation 4 and add with equation 5

-5x+10z+5x-4z=-30

6z=-30

z=-5

Now put y and z values in equation (1)

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

-x+1-10=-5

-x-9=-5

-x=4

x=-4

Hence x=-4, y=1 and z=-5 are solutions of x+y+2z=-5" 5x+4y-4z=4 x-3y-2z=3

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Okay, here we have this:

Considering that the scale is of 1 to 60, we obtain the following:

2.75 inches * 60 =165.

Given:

The radius , r=20 ft.

The height , h=23 ft.

The volume of the cylinder can be calculated as,

Therefore, the volume of the cylinder is 28902.65 sq.ft.

The volume of the cone can be calculated as,

Therefore, the volume of the cone is 9634.22 sq.ft.

In this problem we have to calculate the total spences so we add all the costs so:

So 1500 is the 100% so now we can calculate which percentage correspount to 250 so:

so the equation is:

So she spend 16.66% in fun

Compound interest - The amount in the account at the end of 1st year is $9720 and The amount in the account at the end of 2nd years is $10497.6

What is compound interest?
The interest earned on savings that is calculated using both the initial principal and the interest accrued over time is known as compound interest. It is thought that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a sum more quickly than simple interest, which is only calculated on the principal sum. Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.

We are given that the principal amount is $9000

An the interest is 8%

Hence after 1 year the amount will be

[tex]A=9000(1+0.08)\\A=9000(1.08)\\A=9720\\[/tex]

After 1 year the amount becomes $9720

Now After 2 years we will get interest on $9720

Hence the amount after 2 years will be

[tex]B=9720(1+0.08)\\B=9720(1.08)\\B=10497.6[/tex]

Therefore the amount after 2 years is $10497.6
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First, we count the number of boxes.

We have: 4,8,12,16

(a)Now:

• 8-4=4

• 12-8=4

• 16-12=4

Since the difference is the same, the sequence is an arithmetic sequence.

(b)In the sequence

First term, a =4

Common difference, d=4

The nth term of an arithmetic sequence is:

The explicit formula for the above sequence, f(n)= 4n.

(c)18th term

f(18)= 4 x 18

=72

The 18th term is 72.

In this case, we can write out the parameters

Thus, substitute the coordinates in the mid-point formula and simplify

Hence, the coordinate of the mid-point is (50, 70)

The velocity is v= 30.6 ft/ sec.

Velocity defines the direction of the movement of the body or the object. Speed is primarily a scalar quantity. Velocity is essentially a vector quantity. It is the rate of change of distance. It is the rate of change of displacement.

Given that,

We have given the height

s(t) = 0.2[tex]t^{3}[/tex] + 21t, where 0 ≤ [tex]x[/tex] ≤ 17.

To find the velocity we have to differentiate s(t) wrt to t.

s(t) = 0.2[tex]t^{3}[/tex] + 21t

    = 0.6[tex]t^{2}[/tex]+21

velocity of the particle at t = 4

s(4) = 0.6*[tex]4^{2}[/tex]+21

     = 9.6+21

     = 30.6

v= 30.6 ft/ sec

Hence, The velocity is v= 30.6 ft/ sec.

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In Part (b) of this problem, we want to determine which function is the bes representation for the graph and table.

We are given:

To determine which function matches best, we can look at the parent function of a linear, logarithmic, and exponential function.

(see comparisons below):

Notice that our graph most closely resembles that of the exponential function. Therefore, the best model for the data would be an exponential function.

The most appropriate choice for area of rectangle will be given by -

Area of classroom = [tex]4\frac{27}{40}[/tex] [tex]m^2[/tex]

What is area of rectangle?

Rectangle is a four sided figure whose parallel sides are equal and whose every angle is 90°

The total space taken by the rectangle is called area of the rectangle.

If the length of the rectangle be l and the breadth of the rectangle be b, then area of the rectangle is given by

Area = [tex]l \times b[/tex]

Here,

Length of classroom = [tex]6\frac{4}{5}[/tex] m = [tex]\frac{34}{5}[/tex] m

Width of classroom = [tex]1\frac{3}{8}[/tex] m = [tex]\frac{11}{8}[/tex] m

Area of classroom = [tex]\frac{34}{5} \times \frac{11}{8}[/tex]

                               = [tex]\frac{187}{40}[/tex]

                               = [tex]4\frac{27}{40}[/tex] [tex]m^2[/tex]

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Given

Principal = $8,000

Rate = 3%

Time = 48 years

Find

Amount at the end of the 48 years

Explanation

Amount = Simple interest + Principal

Simple Interest is given by

now substitute the values ,

amount = 11,520 + 8000 = $19,520.00

Final Answer

Therefore , the amount at the end of the 48 years will be $19,520.00

So we need to solve the following equation for x:

The first step would be substracting 8 from each side of the equation:

The next step is to square

Given the following function

We want to find its roots. Since we already know that (x + 1) and (x - 2) are factors of this polynomial, we can divide our polynomial by those factors and factorize the result to get the other roots.

Let's start by dividing by the first factor

To divide a polynomial by other, we start by dividing the leading term of the dividend by the leading term of the divisor(this will be the first term of our result)

Then, we ultiply it by the divisor

Subtracting this result from the dividend, we have

This means that our division is

Repeating the whole process of division with the second term, we have

From this result, we can rewrite our function as

Repeating this same process with the other know factor, the other division we have to solve is

Then, our function is

Then, to find the roots we need to solve the following equation

Since we have a product of 3 terms, the result will be zero if and only if one of the terms is zero. This means that the roots can be found by assuming each one is zero. The solutions for this equation are the same solutions for the following system

And those are the roots for our function. x = -1, 2, +-3i.

From least to greatest, we have:

2 to 3, 3:4, and 7/8

Given the following:

7/8, 2 to 3, and 3:4

The least is 2 to 3, followed by 3:4, then 7/8

2/2 = 1

The answer would be 1

Answer:64.528 is the decimal

Step-by-step explanation:

A dilation means an elongation of the sides of a figure

So in a dilation the sides are bigger than at the original figure

A key formula for found dilation is Pithagoras theorem

For calculate T'R'

T'R' is the exact diagonal of OT' and OR', that means

OT' + OR' = T'R' in vectorial sum

OT'^ 2 + OR'^ 2 = T'R'^2. In numerical sum

So then T'R'^2 = 5^2 + 5^2 = 50.

and T'R'= √50

Now find TR to find the factor of dilation that is

T'R'/TR

Given:

The zeros of degree 3 polynomial are -2, 3 , 6.

The coefficient of x² is -14.

Let the degree 3 polynomial be,

But given that, coefficient of x² is -14 so, multiply the above polynomial by 2.

Answer: The polynomial is,

Answer:

1728 cm ^ 3.

Step-by-step explanation:

we are given 12 cm

As we know formula of volume of cube = s ^3 ( side * side * side ) So = 12 * 12* 12 = 1728 cm ^ 3.

Find the Volume cylinder (8cm) (12cm) h = 8cm r = 12cm h = 8 cm r = 12 cm. The volume of a cylinder is equal to the area of the base πr2 π r 2 times the height. π⋅(radius)2 ⋅(height) π ⋅ ( r a d i u s) 2 ⋅ ( h e i g h t) Substitute the values of the radius r = 12 r = 12 and height h = 8 h = 8 into the formula to find the volume of the cylinder

P.s hopes this helps

Given: A piece of paper is folded into half repeatedly. The thickness of the paper in inches is modeled by the function y = 2x/1000, where x is the number of folds.

Required: To determine the thickness of the paper if the paper is folded 10 times.

Explanation: The thickness of the paper is given by the function

Here, x is the number of folds=10

Hence,

Final Answer: After 10 folds, the thickness of the paper is 0.02 inches.

By formula,

Midpoint between two points PQ =

So, (-1,-4) (option 3)

Area of a rectangle is given by the expression:

Then:

The area that will need to be covered is 287 square feet.

ANSWER:

19 m

STEP-BY-STEP EXPLANATION:

We have that the formula for the area of a trapezoid is the following:

We substitute each value and calculate the length of the other base, like so:

The dimension of the other base of the trapezoid is 19 m

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given equations

STEP 2: Define the point that is the solution for the given functions on the graph

The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.

STEP 3: Determine the solution for the system of equations

It can be seen from the image below that the two lines intersect at the origin and hence they are given as the solutions to the given system of equations.

Hence, the solutions are:

First, find the equation of the line, given that the points (3,2) and (-3,-6) belong to that line. To do so, use the slope formula and then substitute the value of the slope and the coordinates of a point on the slope-point formula of a line:

The slope of the line, is:

Therefore, the equation of a line (using the point (3,2)) is:

Since the colored region on the coordinate plane is placed above the line

y=(4/3)x-2, then the equation of the inequality is:}