2. What is the greatestcommon factor of12. 18, and 36?

Answer

Explanation

Given:

A bug is moving along a straight path with velocity

What to find:

The total distance traveled by the bug over interval [0, 6].

Solution:

To find the total distance traveled by the bug over interval [0, 6], you first integrate v(t)= t² - 6t + 8

y = 2 (option D)

y = -x + 12

4x - 2y = 36

rewriting the equations:

y + x = 12 ....equation 1

-2y + 4x = 36 ....equation 2

Using elimination method:

we will be eliminating y. So we need to make the coefficient of y to be the same in both equation. We will be multiplying the first equation by 2.

2y + 2x = 24 ....equation 1

-2y + 4x = 36 ....equation 2

Add both equations:

2y + (-2y) + 2x + 4x = 24 + 36

2y-2y + 6x = 60

6x = 60

x = 60/6 = 10

Insert the value of x in any of the equation. Using equation 2:

4(10) - 2y = 36

40 -2y = 36

-2y = 36 - 40

-2y = -4

y = -4/-2

y = 2 (option D)

Given

Solution

Standard from of a parabola

In order to find the rate of discount, calculate what is the associated percentage of 5.50 related to 12.99, just as follow:

(5.50/12.99)(100) = 42.34

5.50 is the 42.34% of 12.99.

Hence, the discount was 100% - 42.34% = 57.65%

The Solution.

By formula, the volume of the planet (sphere) is given as below:

In this case,

Substitting these given values into the formula above, we can solve for r, the radius of the planet.

Dividing both sides by

We get

Taking the cube root of both sides, we have

Thus, the correct answer is 1060784.418km.

We are given the number in scientific notation:

To convert it to decimal format, we need to move the decimal point two spaces to the left.

Since we don't have enough digits before the decimal point, we add two zeros before the 4:

Now we move the point as required:

The required number is 0.0458

The function f is given by:

If a quadratic function is written in the form:

Then the function has a minimum point at (h,k)

And the minimum is k

In this case,

Therefore, the minimum of the function f is at (0.25, 5.875)

The minimum of the function given by the table is at (-1, -6).

Therefore, the required horizontal distance is given by:

Therefore, the horizontal distance is 1.25

I) 2y = x - 4

II) 4x + 3y = 5

First, we put all the variables on the same side subtracting x from both sides of equation I:

I) 2y - x = -4

II) 3y + 4x = 5

Now, we multiply equation I by 4:

I) 8y - 4x = -16

II) 3y + 4x = 5

Then, we add equation I to equation II:

I) 8y - 4x = -16

II) 11y = -11

Therefore, we got from equation II:

y = -11/11 = -1

Applying this result on equation I, we got:

-8 - 4x = -16

4x = 8

x = 8/4 = 2

Final answer: (x,y) = (2,-1)

Answer:

(-2,-5)

Step-by-step explanation:

(-5+1÷2, -9+(-1)÷2)

=(-4÷2, -10÷2)

=(-2,-5)

The range of the following function is

We can also call the range of a function an image, the range or image of a function is a set, we can see this set looking at the graph and see which values of y the function have, remember that we can have the same y value for different x value, looking at our graph we can see that this function comes from high y values, have a vertex on (3,1), in other words, it stops at y = 1 and then start growing again, and go on repeated values of y, then we can say that the image (values of y that the function assumes) is all values bigger than 1, therefore {y > 1}.

Start by finding (f+g)(x)

simplify the equation

then, replace x by -2

Answer

a. Vertical shrink by a factor of 1/3

Step-by-step explanation

Function transformation

• a,f(x) vertically compresses f(x) when 0 < a < 1

Given the function:

Multiplying f(x) by a = 1/3, we get:

Then, f(x) is vertically shrunk by a factor of 1/3

Answer:

• Slope perpendicular to the line: 8/5

• Slope parallel to the line: –5/8

Explanation

Given

To know the result, it is better if we work with the slope-intercept form:

Then, to get this kind of form we have to isolate y from the given equation:

Thus, in this case, m = –5/8 and b = 7/8.

Perpendicular lines have negative reciprocal lines:

where m₁ is the slope of line 1 and m₂ is the line perpendicular to line 1.

Then, replacing the values:

Finally, the slopes of parallel lines are the same, meaning:

where m₁ is the slope of line 1 and m₂ is the line parallel to line 1.

Explanation:

The expression is given below as

We have:

L = 5 L's

I = 2 I's

P = 1 P

Y = 2 Y's

so:

We have the following: system of equations:

A: 3c=d-8

B: c=4d+8

To eliminate variable d first, if we want to use elimination method, we need to have variable d in both equations with the same coefficient but with different signs.

As in equation B, the coefficient of d is 4, then we need to have in equation A a coefficient of -4 for variable d.

Then the answer is we need to multiply equation A by -4.

Given:

Solve as:

Hence, the required answer is 6.

Answer:

4.5 pounds

Step-by-step explanation:

21.5 - 3.5 = 18

We divide that by 4 (Aug., Sept, Oct. Nov.)

18/4 = 4.5

Answer:

6.144

Step-by-step explanation:

We are going to use the formula for the compound interest, which is

A = the future value of the investment

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = the time the money is invested or borrowed for

Replacing the values in the first question we have:

Answer for the first question is : $7140

Then, replacing the values in the second question we have:

Answer for the second question is : $8497

2) y = 8x² +2x -15

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

S={-3/2, 5/4}

3) y= 4x² +20x +24

(4x +8)(x +3)

S={-2,3}

1) Factoring these quadratic functions we have:

2) y = 8x² +2x -15

Let's call u, and v two factors.

Multiplying 8 by -15 = we have u*v = -120 Adding u + v= 2, so u = 12 and v =-10

12 x -10 = -120

12 +(-10) = 2

So, now we can rewrite it following this formula:

(ax² + ux) +(vx +c)

(8x² +12x) +(-10x-15) Rewriting each binomial in a factored form

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

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

Equating each factor to zero to find out the roots:

(4x -5) =0

4x =5

x=5/4

(2x +3) = 0

2x = -3

x= -3/2

Hence, the solution set is S={-3/2, 5/4}

3) y= 4x² +20x +24

Proceeding similarly we have:

u * v = 96

u + v = 20

So u = 12, and v =8 12x 8 = 96 12 +8= 20

Rewriting into (ax²+ux)+(vx +c)

(4x²+12x) +(8x+24) Factoring out each binomial

4x(x+3) +8(x+3) As we have a repetition we can write:

(4x +8)(x +3)

3.2) Now to find out the roots equate each factor to zero, and solve it for x:

4x +8 = 0

4x = -8

x =-2

x+3 =0

x=-3

4) Hence, the answers are:

2) y = 8x² +2x -15

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

S={-3/2, 5/4}

3) y= 4x² +20x +24

(4x +8)(x +3)

S={-2,3}

Volume is area * height

area of pentagon is 1/4 * root(5(5 + 2root(5))) a^2

a being length of 1 side

if a =2, area is 6.88

6.88 * 4 = 27.52 yards^3

skill issue hahahahahhaahahhahaha

The average rate of change is:

then computing the first formula, the average rate of change of f(x) is

Question: the line that passes through the point (-1,4) and point (6,y) has a slope of 5/7. find y.

Solution:

By definition, the slope of a line is given by the formula:

where m is the slope of the line and (X1,Y1), (X2,Y2) are any two points on the line. In this case, we have that:

(X1,Y1) = (-1,4)

(X2,Y2) = (6,y)

m = 5/7

thus, replacing the above data into the slope equation, we get:

this is equivalent to:

By cross-multiplication, this is equivalent to:

solving for y, we get:

then, we can conclude that the correct answer is:

The Solution:

Given:

Required:

To find the discriminant of f.

By formula, the discriminant (D) is:

Where:

Substitute:

Therefore, the correct answers are:

Discriminant = -92

No distinct real root.

Answer:

slope = 5/3

y-intercept = -4

Step-by-step explanation:

First, move the x to the other side of the equation:
-3y=-5x+12
Then, divide BOTH sides by -3, so that there is no coefficient next to y:
y=5/3x-4

Then, just look at the constant and coefficient next to x (m). The slope is 5/3 and the y-intercept is -4.

Hope this helps!

Answer:

[tex]y = \frac{5}{3}x - 4[/tex]

Step-by-step explanation:

move the 5x to a -5x

-3y= -5x+12

-3/-3= -5x÷ -3 12÷ -3

When the price of bananas goes from $0.39 per pound to $1.06 per pound, the likely effect of quantity demanded is that it will reduce.

The quantity of a commodity or service that consumers are willing and able to acquire at a particular price within a specific time period is referred to as demand. The quantity required is the amount of an item or service that customers will purchase at a certain price and period.

Quantity desired in economics refers to the total amount of an item or service that consumers demand over a given time period. It is decided by the market price of an item or service, regardless of whether or not the market is in equilibrium.

A price increase nearly invariably leads to an increase in the quantity supplied of that commodity or service, whereas a price decrease leads to a decrease in the quantity supplied. When the price of good rises, so does the quantity requested for that good. When the price of a thing declines, the demand for that good rises.

Learn more about demand on:

https://brainly.com/question/1245771

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Okay, here we have this:

Considering the provided expression, we are going to prove the identity, so we obtain the following: