Use the APR table in the Business Math Handbook to estimate the APR for the following installment purchase. You received a $2,000 rebate that brought the price of your car down to $20,000; the financing was for 48 months, and your total interest was $3,279.

The correct classification for each function is as follows:

1. [tex]\( y = 5x + 1 \)[/tex] - Linear

2. [tex]\( y = 23 \)[/tex] - Linear

3. [tex]\( y = 1 - 2x^2 \)[/tex]- Nonlinear

A linear function is one that can be written in the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] and [tex]\( b \)[/tex] are constants, and [tex]\( x \)[/tex] is the independent variable. The graph of a linear function is a straight line.

1. For the function [tex]\( y = 5x + 1 \)[/tex], we can see that it is already in the form of a linear equation with [tex]\( m = 5 \)[/tex] and [tex]\( b = 1 \)[/tex]. Therefore, this function is linear.

2. The function [tex]\( y = 23 \)[/tex] is a constant function. Although it does not have an [tex]\( x \)[/tex] term, it can still be considered linear because it can be written as [tex]\( y = 0x + 23 \)[/tex], where the slope [tex]\( m = 0 \)[/tex] and the y-intercept [tex]\( b = 23 \)[/tex]. The graph of this function is a horizontal line, which is a special case of a linear function.

3. The function [tex]\( y = 1 - 2x^2 \)[/tex] contains an [tex]\( x^2 \)[/tex] term, which makes it a quadratic function. Quadratic functions are nonlinear because their graphs are parabolas, not straight lines. The presence of the [tex]\( x^2 \)[/tex] term means that the rate of change of [tex]\( y \)[/tex] with respect to [tex]\( x \)[/tex] is not constant, which is a key characteristic of nonlinear functions. Therefore, this function is nonlinear.

Answer:

1728

Step-by-step explanation:

You could write it like this

5.4 * 10^5 * 3.2 * 10^-3  

You could do this by multiplying the numbers first

5.4 * 3.2 = 17.28

Now work with the powers of 10

10^5 * 10^-3 = 10^(5 - 3) = 10^2

10^2 = 100

So the answer is 17.28 * 100 = 1728

Answer: The volume is 603.19, so whichever answer doesn't equal that.

Step-by-step explanation:

V= πr^2h

V= π(8)^2(3)

V= 603.19

Volume = 192πunits³

Work is provided in the image attached.

a. x ∈ {-1.2, 0.2}

b. x ∈ {-4 2/3, -1 2/3}

c. x ∈ {2 2/3, 4}

For this sort of exercise, I find a graphing calculator to be very handy. While the one shown in the attachment (Desmos) can solve the equation as written, I find it convenient to recast the equation to the form f(x) = 0. The calculator finds the values of zero crossings very nicely. Some, like my TI-84, will show the value to 8 or 10 significant digits. Here, 4 digits is sufficient to determine the exact solution.

_____

If you want to work these by hand, you rewrite them to standard form, then use factoring, completing the square, or the quadratic formula to solve them.

a. 25x² +30x +9 -5x -15 = 0 . . . . subtract the right side

... 25x² +25x -6 = 0 . . . . . . . . . . . collect terms

... (5x+6)(5x-1) = 0 . . . . . . . . . . . . . factor (the graphing calc helps here)

... x = -6/5, 1/5

b. 9x² +60x +100 -3x -30 = 0 . . . . subtract the right side

... 9x² +57x +70 = 0 . . . . . . . . . . . . collect terms

... (3x +14)(3x +5) = 0 . . . . . . . . . . . factor

... x = -14/3, -5/3

c. 9x² -48x +64 -3x² +8x = 0 . . . . . subtract the right side

... 6x² -40x +64 = 0 . . . . . . . . . . . . collect terms

... 3x² -20x +32 = 0 . . . . . . . . . . . . factor out 2

... (3x -8)(x -4) = 0 . . . . . . . . . . . . . . factor

... x = 8/3, 4

Answer:

C

Step-by-step explanation:

Triangle CGF and triangle CED are similar. Hence, the ratio of their corresponding sides are equal. Thus we can write:

[tex]\frac{5x+4}{2x+3}=\frac{CD}{3x+0.8}[/tex]

We can now cross multiply and solve for CD:

[tex]\frac{5x+4}{2x+3}=\frac{CD}{3x+0.8}\\(5x+4)(3x+0.8)=(2x+3)(CD)\\15x^2+4x+12x+3.2=(2x+3)(CD)\\15x^2+16x+3.2=(2x+3)(CD)\\CD=\frac{15x^2+16x+3.2}{2x+3}[/tex]

Since GF is a midsegment of CDE, CD is double of CF. So we can write:

[tex]CD=2CF\\\frac{15x^2+16x+3.2}{2x+3}=2(3x+0.8)\\\frac{15x^2+16x+3.2}{2x+3}=6x+1.6\\15x^2+16x+3.2=(6x+1.6)(2x+3)\\15x^2+16x+3.2=12x^2+18x+3.2x+4.8\\15x^2+16x+3.2=12x^2+21.2x+4.8\\3x^2-5.2x-1.6=0[/tex]

By using quadratic formula [tex]\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex] and with a=3, b= -5.2, and c= -1.6, we find the value of x to be:

[tex]\frac{5.2+-\sqrt{(-5.2)^2-4(3)(-1.6)} }{2(3)}=2[/tex]

Since the expression for CD is [tex]\frac{15x^2+16x+3.2}{2x+3}[/tex] , we plug in [tex]x=2[/tex] into this expression to find value of CD:

[tex]\frac{15(2)^2+16(2)+3.2}{2(2)+3}=13.6[/tex]

The correct answer is C

Answer:

C. 13.6

Step-by-step explanation:

We have been given that GF is a mid-segment of CDE.

Since we know that mid-segment of a triangle is half the length of its parallel side.

We can see that ED is parallel to GF , so measure of GF will be half the measure of ED. We can represent this information as:

[tex]GF=\frac{1}{2}ED[/tex]

Let us substitute given value of GF and ED to find our x.

[tex]2x+3=\frac{1}{2}(5x+4)[/tex]

Multiply both sides of equation by 2.

[tex]2*(2x+3)=2*\frac{1}{2}(5x+4)[/tex]

[tex]2*(2x+3)=5x+4[/tex]

[tex]4x+6=5x+4[/tex]

[tex]6=5x+4-4x[/tex]

[tex]6=x+4[/tex]

[tex]6-4=x[/tex]

[tex]2=x[/tex]

We can see that triangle CFG is similar to triangle CDE, so we will use proportions to find length of CD.

[tex]\frac{CF}{GF}=\frac{CD}{ED}[/tex]

Substitute given values.

[tex]\frac{3x+0.8}{2x+3}=\frac{CD}{5x+4}[/tex]

Upon substituting x=2 in our equation we will get,

[tex]\frac{3*2+0.8}{2*2+3}=\frac{CD}{5*2+4}[/tex]

Let us simplify our equation.

[tex]\frac{6+0.8}{4+3}=\frac{CD}{10+4}[/tex]

[tex]\frac{6.8}{7}=\frac{CD}{14}[/tex]

[tex]14*\frac{6.8}{7}=CD[/tex]

[tex]2*6.8=CD[/tex]

[tex]13.6=CD[/tex]

Therefore, CD equals 13.6 and option C is the correct choice.

Answer:

37.5 g

Step-by-step explanation:

The final solution will contain 3% × 100 g = 3 g of solute. This amount of solute will be found in w grams of 8% solution, where ...

... 3 = 0.08 × w

... 3/0.08 = w = 37.5 . . . . . grams of 8% solution

Answer:

37.5 grams

Step-by-step explanation:

;)

A. {(5,  5), (6,  −6), (8,  7), (−9,  9)}

Compare the table contents to the ordered pairs in each relation. The first pair of table values, (5, 5) matches relations A and B, but not C or D.

The second pair of table values (8, 7), matches relation A, but not B. Since all pairs of table values show up in relation A, and we have rejected relations B, C, and D as inappropriate choices, the answer is A.

The given formula is f(x) = 20(1.2)^x

The formula is the starting amount multiplied by 1 + the percentage raised to the number of weeks.

A) the percent increase is 20% ( 1.2 in the formula is 1 +20% as a decimal)

B) the original amount is $20

C) for 2 weeks, replace x with 2 and solve:

20(1.2)^2

20(1.44) = $28.80

After 2 weeks the coupon is $28.80

D)  To solve for the number of weeks (x) set the equation equal to $100:

100 = 20(1.2)^x

Divide both sides by 20:

5 = 1.2^x

Take the natural logarithm of both sides:

ln(5) = ln(1.2^x)

Use the logarithm rule to remove the exponent:

ln(5) = x ln(1.2)

Divide both sides by ln(1.2)

x = ln(5) / ln(1.2)

Divide:

X = 8.83

At 8.83 weeks the coupon would be $100, so after 9 weeks the coupon would be greater than $100

The answer is 9 weeks.

Answer:

Parker is 6 years old

Step-by-step explanation:

Parker is 6 years old

Let q, p, k represent the ages of Quinn, Parker, and Karl, respectively.

... q = 2k . . . . . . Quinn is twice as old as Karl

... q = p+4 . . . . . Quinn is 4 years older than parker

... q + p + k = 21 . . . . the sum of their ages is 21

_____

We can use the first two equations to find Karl's age in terms of Parker's.

... p+4 = q = 2k

... (p+4)/2 = k

Now, we can substitute for q and k in the last equation.

... (p+4) +p +(p+4)/2 = 21

... 5/2p +6 = 21 . . . . . . collect terms

... p = (2/5)(21 -6) . . . . subtract 6, multiply by 2/5

... p = 6 . . . . . . Parker is 6 years old

The solution of the expression 3a+2b/2 is -13 when a = -3 and b = -4

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operation is called the arithmetic operator.

Operators which let do a basic mathematical calculation

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

Given the expression as :

⇒ 3a + 2b/2

when a = -3 and b = -4

Substitute the values of a and b

⇒ 3 × (-3) + 2 × (-4/2)

⇒ -9 - 4

⇒ -13

Hence, the solution of the expression 3a+2b/2 is -13 when a = -3 and b = -4

Learn more about Expressions here:

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Answer:

2968.30 cm cube.

Step-by-step explanation:

Given is a cone and top of it is a hemisphere of radius 9 cm.

Cone has height as 17 and radius same 9 cm.

We have to find the volume of the compound shape

We find that the volume would be the sum of that of hemisphere of radius 9 cm and cone of height 17, and radius 9 cm.

Volume of compound shape = volume of cone+Volume of hemisphere

= [tex]\frac{1}{3} \pi r^{2} h+\frac{2}{3} \pi r^{3}[/tex]

substitute for h and r in the equation

Required volume =

[tex][tex]\frac{1}{3}\pi  r^{2} (h+2r) = \frac{1}{3}\pi  9^{2} (17+2(9))\\= 1441.99+1526.31\\=2968.30[/tex][/tex]

So answer is 2968.30 cm cube.

=

Answer:

4 years

Step-by-step explanation:

The exponent of 0.5 is 1 when t=4. So, half the original amount will be remaining when t=4.

feb

When the number of cars needed to be sold to meet fixed plus variable expenses is subtracted from the number of cars projected to be sold, the result is negative for all months listed except February. In that month, Barney covers is expenses.

We have computed ...

... (expected car sales) - (needed car sales)

where ...

... (needed car sales) = (variable expenses + fixed expenses)/(income per car sold)

For January, this calculation gives ...

... 32 - (2600 +3100)/175 = 32 -32.571 = -0.571

That is, Barney does not project he will sell enough cars to pay his January expenses.

In February, the result is 0, which means he will sell enough cars in February to pay all his monthly expenses.

Answer:

1.4 × 10^-8

Step-by-step explanation:

The chip is 14  nanometers

14 * .000000001

.000000014

Move the decimal 8 places to the right, because we need 1 number in front of the decimal for scientific notation.  The exponent will be -8 because  we moved it 8 places to the right

1.4 × 10^-8

The thickness of the silicon chip in scientific notation is 1.4 x 10^-8 m.

To express the thickness of the silicon chip in scientific notation, we need to convert the given thickness of 14 nanometers to meters.

Since 1 nanometer (nm) is equal to 0.000000001 meters, we can convert 14 nanometers to meters by multiplying it by the conversion factor:

14 nm x 0.000000001 m/nm = 0.000000014 m

Now, we can express the thickness of the chip in scientific notation:

0.000000014 m = 1.4 x 10-8 m

Another equation that shares the same solutions as x²-16x+12=0 is 2x² - 32x + 24 = 0. This equation is the initial equation multiplied by 2 and thus would produce the same solutions when the quadratic formula is applied.

The equation given is a quadratic equation, which is in the form ax²+bx+c = 0. The solutions of a quadratic equation are given by the formula: -b ± √b² - 4ac / 2a. This formula can be used to find the solutions of any other quadratic equation. For the given equation, x²-16x+12=0, the values of a, b, and c are 1, -16, and 12 respectively. So, another equation with the same solutions could be 2x² - 32x + 24 = 0. This equation has the same solutions because it's simply the initial equation multiplied by 2, so this doesn't change the results of the quadratic formula.

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Answer:

B. 5/12 feet

Step-by-step explanation:

We know that Eric is [tex]6\frac{1}{6}[/tex] feet tall while his brother is [tex]5\frac{3}{4}[/tex] feet tall. We are supposed to find out how many feet is Eric taller than his brother.

So basically we have to find the difference between the height of the two brothers.

First, let's just change the mixed numbers to improper fractions:

[tex]6\frac{1}{6}[/tex] = [tex]\frac{37}{6}[/tex]

[tex]5\frac{3}{4}[/tex]=  [tex]\frac{23}{4}[/tex]

Now taking their difference:

[tex]=\frac{37}{6} -\frac{23}{4}\\\\=\frac{148-138}{24}\\\\=\frac{10}{24}\\\\=\frac{5}{12}[/tex]

Therefore, Eric is 5/12 feet taller than his brother.

The mean age decreased.

I find it convenient to look at the additions with respect to the current mean age.

The current total age is 14×34. We have added members with ages (34 -10) and (34 +2), so the new total age is ...

... (34×14) + (34 -10) + (34 +2) = (16×34) - 8

Dividing this total by 16 will give the new mean age. (We already know it is less than 34.)

... ((16×34) -8)/16 = 34 - 1/2 = 33 1/2 . . . new mean age; a decrease

Answer:

6 2/3 hours

Step-by-step explanation:

We assume the time of interest is the total time spent on the main road and side road.

In each case, ...

... time = distance/speed

On the main road, ...

... tmain = s/v

On the side road, ...

... tside = (2s)/(v -2)

Then the total time spent is ...

... ttotal = tmain + tside

... = s/v + (2s)/(v -2)

For s=10 and v=6, this is ...

... ttotal = 10/6 + 2·10/(6 -2) = 5/3 + 20/4 = 5/3 + 5 . . . . hours

... ttotal = 6 2/3 hours

Answer:

6 hr 40 min

Step-by-step explanation:

Step-by-step explanation:

f(x) = 15(b)x

f(4) = 1215

15(b)4 = 1215

(15)(4)b = 1215

60b = 1215

60b / 60 =  1215 / 60

b = 20.25

Check the answer

15 * 20.25 * 4 = 1215

Answer:

3

Step-by-step explanation:

if you did this on prepworks its 3.

1215=15(b)4  

121515=(b)4

81=b4

92=b4

(32)2=b4

34=b4

b = ±3

Answer:

2 is a factor 5 times

Step-by-step explanation:

2 x 2 x 2 x 2 x 2 =32

Answer:

8 gallons have to be evaporated to have a 20% salt solution.

hope this helped :)

Step-by-step explanation:

.10*20=2 gallons of salt.

That leaves 18 gallons of water.

.2x=2

x=2/.2

x=10 gallons after evaporation.

18-10=8

To obtain a 20% salt solution from a 10% salt solution, 20 gallons of water must be evaporated.

To obtain a 20% salt solution from a 10% salt solution, the amount of water that needs to be evaporated can be calculated using a proportion. First, convert the percentages to decimals by dividing them by 100. Let x be the amount of water to be evaporated. The amount of salt in the initial solution is 10% of 20 gallons, or 0.10 * 20 = 2 gallons. The resulting solution will have 20% salt in a total volume of 20 - x gallons. Set up a proportion:

(2 gallons)/(20 gallons) = (0.20 * (20 - x) gallons)/(20 - x gallons)

Cross multiply and solve for x:

2(20 - x) = 0.20(20 - x)

Now solve the equation:

40 - 2x = 4 - 0.20x

2x - 0.20x = 40 - 4

1.8x = 36

x = 36/1.8

x = 20

Therefore, 20 gallons of water must be evaporated from the initial 20-gallon solution to obtain a 20% salt solution.

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[tex]\theta=\dfrac{3\pi}{4}=\pi-\dfrac{\pi}{4}\\\\y=\tan\theta x\\\\y=\left(\tan\dfrac{3\pi}{4}\right)x\\\\y=\left(\tan\left(\pi-\dfrac{\pi}{4}\right)\right)x\\\\y=\left(\tan\left(-\dfrac{\pi}{4}\right)\right)x\\\\y=\left(-\tan\dfrac{\pi}{4}\right)x\\\\y=-1x\\\\\boxed{y=-x}\to\boxed{D.}[/tex]

Answer:

If you are doing it on edge it is x+y=0

Step-by-step explanation:

x+y=0 when you solve for y it equals -x( y=-x)

half-turn

There is a point of rotational symmetry at the center of the pattern. Thus, turning it 180° (a half-turn) will map it to itself.

_____

Comment on other choices

Any sort of reflection will change it to bqbqbqbqbq. Translation puts its somewhere else, not on top of itself.

Answer:

A half turn reversal of direction (as in a staircase) either by one 180-degree turn or two right-angle turns

Step-by-step explanation:

Hope this helps :) -Mark Brainiest Please :)

[tex]2a+b=\dfrac{2ab}{b}+\dfrac{bb}{b}=\dfrac{2ab}{b}+\dfrac{b^2}{b}=\boxed{\dfrac{2ab+b^2}{b}}[/tex]

Answer:

d. $425.65

Step-by-step explanation:

The total value of Ralph's stuff is ...

... 150 + 60 + 100 + 80 + 200 + 100 + 40 + 20 + 850 + 200 + 600 + 175 = 2575

The premium is 16.53% of that, so is ...

... 0.1653 × 2575 = 425.65

Answer:

The insurance company charges an annual premium of $425.65 .

Option (d) is correct .

Step-by-step explanation:

As given

Ralph wants to purchase a renters insurance policy for his new apartment.

His insurance company charges an annual premium of 16.53% of the approximate value of the items he owns and is keeping in his apartment.

Total amount of the items he owns and is keeping in his apartment = TV cost + VCR cost + DVD Player cost + Stereo cost + Sofa cost + Entertainment centre cost  +  Microwave cost + Coffee Maker cost +  Computer cost + Bicycle cost  +  Coin Collection cost  + Pictures/Posters cost

Putting all the values in the above

Total amount of the items he owns and is keeping in his apartment = $150 + $60 +$100 + $ 80 + $200 + $100 + $40 + $20 + $850 + $ 200 + $ 600 + $ 175

Total amount of the items he owns and is keeping in his apartment = $ 2575

16.53 % is written in the decimal form .

[tex]= \frac{16.53}{100}[/tex]

= 0.1653

Insurance company charges an annual premium = 0.1653 × Total amount of the items he owns and is keeping in his apartment .

                                                                                   = 0.1653 × 2575

                                                                                   = $ 425.65 (Approx)

Therefore the insurance company charges an annual premium of $425.65 .

Option (d) is correct .

Answer:

I believe it would still be considered 1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Multiply the total number of questions by the percent:

50 questions x 90% =

50 x 0.90 = 45

She answered 45 questions correctly.

Answer:

See picture

Step-by-step explanation:

The rule is ...

[tex]x^{m/n}=\sqrt[n]{x^m}[/tex]

The index of the surd becomes the denominator of the exponents inside.

Answer:

x^(5/3)*y^(1/3)

Step-by-step explanation:

note (a*b)^c = a^c*b^c

the given expression can be rewritten as (x^5*y)^1/3

=x^(5/3)*y^(1/3)

ans is the 2nd choice