ExpenseYearly costor rateGasInsuranceWhat is the cost permile over the course ofa year for a $20,000 carthat depreciates 20%,with costs shown in thetable, and that hasbeen driven for 10,000miles?$425.00$400.00$110,00$100.0020%OilRegistrationDepreciationB. $4.10 per mileA. $1.10 per mileC. $0.25 per mileD. $0.50 per mile

Answer:

(f + g)(x) = 2x³ + 3x² + x + 2

Explanation:

If f(x) = 2x³ - 5x² + x - 3 and g(x) = 8x² + 5, we can calculate (f + g)(x) as follows

(f + g)(x) = f(x) + g(x)

(f + g)(x) = (2x³ - 5x² + x - 3) + (8x² + 5)

Then, we can simplify the expression adding the like terms, so

(f + g)(x) = 2x³ - 5x² + x - 3 + 8x² + 5

(f + g)(x) = 2x³ + (-5x² + 8x²) + x + (-3 + 5)

(f + g)(x) = 2x³ + 3x² + x + 2

Therefore, the answer is:

(f + g)(x) = 2x³ + 3x² + x + 2

Answer:

oop

Step-by-step explanation:

oh

The set of points that represents a dilation from the origin of triangle RST are: D. R'(0 , 8), S'(8 , 36), T'(16, 8).

In Mathematics, dilation is a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

For the given coordinates of triangle RST, the dilation with a scale factor of 4 from the origin (0, 0) or center of dilation should be calculated as follows:

Point R (0, 2) → Point R' (0 × 4, 2 × 4) = Point R' (0, 8).

Point S (2, 9) → Point S' (2 × 4, 9 × 4) = Point S' (8, 36).

Point T (4, 2) → Point T' (4 × 4, 2 × 4) = Point T' (16, 8).

In conclusion, the other sets of points do not represents a dilation from the origin of triangle RST.

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As of the given condition ordered pair in the option D  R'(0 , 8), S'(8 , 36), T'(16, 8), represents the dilated coordinates of the former triangle.

Given that,
Coordinates of the triangle, R(0 , 2), S(2 , 9), and T(4 , 2).
The scale factor for the dilation = 4

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
According to the question,
The dilated coordinate is given as,
R' = (0×4 , 2×4) = (0, 8)
S' = (2×4, 9×4) = (8, 36)
T' = (4×4, 2×2) = (16, 8)

Thus, As of the given condition ordered pair in the option D  R'(0 , 8), S'(8 , 36), T'(16, 8), represents the dilated coordinates of the former triangle.

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We have

and

From these,

The largest measurement is 200 degrees. Thus, option B is correct.

Answer:

translated 8 units down and then reflected across the y-axis

A) 9 cups of berries to 12 cups of juice

Explanation

to figure out this, we need to find the original ratio and then compare

Step 1

find the ratio:

ratio cups of berries to cups of juices

hence, the rario is 3/4

Step 2

now, check the ratio of every option

a)9 cups of berries to 12 cups of juice

b) 12 cups of berries to 9 cups of juice

c) 6 cups of berries to 15 cups of juice

d) 15 cups of berries to 10 cups of juice

therefore, the option that haas the same ratio is a) 3/4

I hope this helps you

Length: L

Width: W

The area of a rectangle is:

The perimeter of a rectangle is:

Given information:

Solve L in the second equation (Perimeter):

Answer:

The measure of the given arcs are;

Given the figure in the attached image.

we want to find the measure of the given arcs.

For arc ED.

The measure of arc ED is equal to the measure of arc AB;

To get the measure of BC, we can see that AB, BC, and CD will sum up to 180 degrees.

To get arc BED;

In the table says that every letter that weighs less that 1 oz. have a price of 42, in the graphic we represented that in this part:

Following the data in the table as above we got the final graphic.

And for the question:

If you have a letter that weighs 1.7 oz. it will be more than 1 oz. but less than 2 oz. so you will pay 66, as we can see in the following graphic:

Answer:

2 x [tex]10^{35}[/tex]

Step-by-step explanation:

7 ÷ 3 is about 2

[tex]\frac{10^{25} }{10^{-10} }[/tex] = [tex]10^{35}[/tex]  When you are dividing powers with the same bases, you subtract the exponents

25 - -10 = 25 + 10 = 35

Solution

In 2011 The temperature in Darrtown is

The temperature increased by 3% in 2012

The temperature will be

The temperature decreased by 4.5% in 2013

The temperature will be

Therefore, the temperature in 2013 is 64 degrees Fareheint

Option B

we use the formula

Where Cn is the final amount= co the initial amount, n the number of months and i the rate dividing between 100

transform the mixed number

now, replace

the solution is 12,862

The probability of NOT choosing the 6 is 7/8.

Probability is used to calculate the likelihood that a random event would happen. The chances that the random event happens is a probability value that lies between 0 and 1. The more likely it is that the event occurs, the closer the probability value would be to 1. If it is equally likely for the event to occur or not to occur, the probability value would be 0.50.

The probability of NOT choosing the 6 = number of cards that are not 6 / total number of card

Cards that do not have a value of 6 = 1, 2, 3, 4, 5, 7, 8

Total is 7

The probability of NOT choosing the 6 = 7 / 8

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F(n) = -11 + 22(n-1)

Hence F(1) = -11

let An = F(n) -F(n-1)

Hence F(n)= f(n-1) +22

To calculate the length between A and B you have to draw them in the cartesian system and link them with a line, then using that line as hypothenuse, draw a right triangle, whose base will be paralel to the x-axis and its height will be paralel to the y-axis.

Using the coordinates calculate the length of the base and height of the triangle:

Base= XA-XB= (-1)-(-8)=7

Height= YB-YA=7-(-7)=14

Now you have to apply pythagoras theorem you can calculate the length of the hypotenuse:

The distance between poins A and B is 15.65

To calculate the probability of event A, divide the number of outcomes favorable to A by the total number of possible outcomes.

so

Step 1

a)let

b) now, replace in the formula and simplify

.

therefore, the answer is

I hope this helps you

we know that

the area of triangle ABC is equal to the area of two right triangles

so

triangle ABD and triangle BDC

D is a point between point A and point C

step 1

Find the length of segment AD

Applying Pythagorean Theorem in the right triangle ABD

10^2=AD^2+8^2

100=AD^2+64

AD^2=100-64

AD^2=36

AD=6

Find teh area of triangle ABD

A=AD*BD/2

A=6*8/2

A=24 units^2

step 2

Find the area of triangle BDC

A=DC*DB/2

DC=21-6=15 units

A=15*8/2

A=60 units^2

step 3

Find teh area of triangle ABC

Adds the areas

A=24+60=84 units^2

therefore

We will assume the next table to answer this question (a linear function) (since the data in the question is not clear):

Having this information, we can find the slope using the formula for it:

If we pick up from the table the next points:

x1 = 1, y1 =6

x2 = 2, y2 = 8

Then

We can use the slope-point formula to find the y-intercept. We can use the point (3, 10). Then, we have:

We end up with the slope-intercept formula for the line. Then the y-intercept is 4. In other words, if we have x = 0, then y = 4.

Then the slope for the values represented in the proposed table is m = 2, and the y-intercept is y = 4.

The Midline of a Sinusoid

A sinusoid is a periodic function which parent expression is:

f(x) = A. sin (wt)

Where A is the amplitude and w is the angular frequency

The sine function has a maximum value of A and a minimum value of -A.

The midline can be found as the average value of the maximum and the minimum value.

For the parent function explained above, the midline is:

Since Mx and Mn are, respectively A and -A, the midline is zero.

The graph shown in the image has a maximum of Mx=1 and a minimum of Mn=-5.

Thus, the midline is:

The midline of the graph is y=-2

We need to give the steps for proving the corresponding angles theorem for parallel lines crossed by a transverse line.

Westart with the

p || q as Given info

Next we use that

< 1 = <7 due to internal alternate angles among parallel lines

< 7 = <5 due to angles opposed by vertex

<1 = <5 due to transitive property <1 = <7 = <5

Given the situation to model the arithmetic and the geometric sequences.

Imagine you are four years old. A rich aunt wants to provide for your future. She has offered to do one of two things.

Option 1: She would give you $1000.50 a year until you are twenty-one.

This option represents the arithmetic sequence

The first term = a = 1000.50

The common difference = d = 1000.50

The general formula will be as follows:

Simplify the expression:

Option 2: She would give you $1 this year, $2 next year, and so on, doubling the amount each year until you were 21.

This option represents the geometric sequence

The first term = a = 1

The common ratio = r = 2/1 = 2

The general formula will be as follows:

Now, we will compare the options:

The first term of both options is when you are four years old that n = 1

you only received money for ten years so, n = 10

So, substitute with n = 10 into both formulas:

So, the answer will be:

For ten years, the option that gives the most money = Option 1

Notice that the relationship between the number of pounds of gummy candy and the number of dollars that that number of pounds costs is a function because there cannot be two prices for the same number of pounds.

Now, notice that the graph that Tommy creates does not represent a function because it fails the vertical line test at x=3.

Also, from the given table we get that (4,11) is a point of the graph.

Then the graph that Tommy creates is not correct.

Answer: No, because the graph does not represent a function and the point (4,11) is not part of the graph.

The numerical length of the line segment RT is 6.

Length:

Length is the measuring unit used to identifying the size of an object or distance from one point to the other.

Given,

There is a point on the line segment RT.

And the values of the pots are,

RT = 3x, RS = 3x - 5 and ST = 3x - 1.

Now we need to find the length of the line segment RT.

To find the line of the line segment RT,

We have to add the length of the segments,

That can be written as,

=> RT = RS + ST

Now, we have to apply the values of the point to the equation, then we get,

=> 3x = 3x - 5 + 3x - 1

=> 3x = 6x - 6

=> 6x - 3x - 6

=> 3x - 6

=> 3x = 6

=> x = 2

If the value of x is 2, then the length of the line segment RT is,

RT = 3x => 3 x 2 = 6

Therefore, the length of the line segment RT is 6.

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Answer:

$160

Step-by-step explanation:

A shop, had a sale. In the sale, normal prices were reduced by 15%. The normal price of a chair was reduced in the sale by $24. Work out the normal price of the chair.

if 15% of normal price equals $24 then:

24/15% or 24/0.15 = $160 normal price

CHECK:

$160 * 0.15 = $24

Answer:

$160

Step-by-step explanation:

We want to know the price of the chair

So:

24 / 0.15 = 160$

or

24 / 15% = 160

• We will determine the domain, range and x ;y intercept then plot the graph

1. The domain is given by :

2. Range is given by :

3. x - and y -intercept :

4. asymptote :

The linear equation that gives the values of P in terms of x which is Madeline's total pay on a given day is; P + 20·x + 80

An equation consists of two expressions that are joined by an equal to sign to complete a mathematical statement.

The given parameters are:

Madeline's daily base pay = $80

Madeline's commission for each computer sold = $20

The given table of values is presented as follows:

Daily pay, in Dollars, P;                     [tex]{}[/tex]        80, 100,  120, 140

Number of computers sold, x; [tex]{}[/tex]                 0,    1,       2,    3

From the above table of values, given that the independent variable, x, is increasing at a constant rate, and that the first difference is constant, we have that the relationship is a linear relationship, that has an equation of the form; P = m·x + c

Where:

m = The slope

c = The y-intercept

The slope which gives the ratio of the rise to the run of the graph is given by the equation; [tex]m = \dfrac{100-80}{1-0} =20[/tex]

The equation in point and slope form is therefore: P - 80 = 20·(x - 0) = 20·x

P - 80 = 20·x

P = 20·x + 80

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To transform a function 1 unit up, we add 1 outside of the function

h(x) = |x| +1

shifting it 4 units to the left, we will add 4 units from x inside

h(x) = |x+4| +1

The transformed function is

h(x) = |x+4| +1

Answer:

I am assuming you are looking for the x-intercepts and y-intercepts...here they are.

x-intercepts: (-7/2,0) , (-1,0) , (4,0)

y-intercepts: (0,-5)

Hope this helps...if not, please expound your question more.

The rule of the length of an arc is

Where L is the length of the arc

x is the central angle subtended by the arc

r is the radius of the circle

∵ BC = r

∵ BC = 16 ft

∴ r = 16

∵ < ABC is a central angle subtended by the arc AC

∴ ∵ < ABC = 51 degrees

∴ x = 51

→ Substitute the values of x and r in the rule above to find The length of arc AC

→ Round it to 2 decimal places

∴ AC arc = 14.23 ft

The volume of a sphere is given as

Where r = 2.94 cm

π = 3.14

Substituting values,

The volume to the nearest tenth is 106.1 cubic centimeters.