The average value of a certain type of automobile was 14,220 in 1993 and depreciated to 9,780 in 1997.
Let y be the average value of the automobile in the year x, where x=0 represents 1993. Write and graph a linear equation that models the value of the automobile in terms of the year x.

Answer:

∠ C < ∠ B < ∠ A.

Step-by-step explanation:

The length of the sides of a triangle are proportional to the measurement of its opposite side and vice-versa.

Now, in a triangle Δ ABC the opposite angle of side AB is ∠ C, the opposite angle of the side BC is ∠ A and the opposite angle of the side CA is ∠ B.

So, if it is given that AB < AC < BC, then we can say that ∠ C < ∠ B < ∠ A. (Answer)

To find (g * f)(x), compute f(x) and substitute it into g(x), resulting in g(f(x)) = (√{x}+3)² + 2/√(x+3). Expand and simplify as needed.

To find (g * f)(x) for the given functions f(x)=√{x}+3 and g(x)=x²+2/x, we first need to compute f(x) and then substitute the result into function g.

First, we compute f(x):
f(x)=√x+3

Now, we substitute f(x) into g(x):
g(f(x)) = (√x+3)² + 2/√(x+3)

Step-by-step calculation:

Answer: 68%

Step-by-step explanation: Since Tim made 85 free throws out of 125 free throws in total, we have the fraction 85/125 where 85 represents the number of free throws Tim made out of all of the free throws he shot last season.

To write the fraction 85/125 as a percent, remember that a percent is a ratio that compares a number to 100. So we need to find a fraction equivalent to 85/125 that has a 100 in the denominator. We can do this by setting up a proportion.

So we have [tex]\frac{85}{125} = \frac{n}{100}[/tex] where n is our variable.

Now using cross products to find the missing value in the proportion, we have 85 x 100 which is 8,500 = 125 x n or 125n

Now just divide both sides by 125 and we find that 68 = n.

This means that Tim made 68% of his free throws.

Answer:

Step-by-step explanation:

Let the total cost for renting a car a day be X

: X = $22 + 20m cent

ANSWER: y= 3x - 6

STEP-BY-STEP EXPLANATION:

(1,-3) and (3,3)

X1=1           X2=3

Y1= - 3       Y2=3

1) Find the slope of the line.

To find the slope of the line passing through these two points we need to use the slope  formula:

m = [tex]\frac{Y2-Y1}{X2-X1}[/tex]

m= [tex]\frac{3-(-3)}{3-1}[/tex]   m=[tex]\frac{6}{2}[/tex] = 3

2)Use the slope to find the y-intercept.

Now that we know the slope of the line is 3 we can plug the slope into the equation and  we get:

y= 3x+b

Next choose one of the two point to plug in for the values of x and y. It does not matter  which one of the two points you choose because you should get the same answer in either  case. I generally just choose the first point listed so I don’t have to worry about which  one I should choose.

y= 3x+b       point (1,-3)

-3= 3(1) + b

-3-3=b

-6=b

3)Write the answer.

Using the slope of 3 and the y-intercept of -6 the answer is:

y = 3x - 6

For this case we must propose a rule of three:

20 people ----------------> 24 days

32 people ----------------> x

Where the variable "x" represents the number of days it takes 32 people to build the barn.

[tex]x = \frac {32 * 24} {20}\\x = \frac {768} {20}\\x = 38.4[/tex]

Thus, it takes 32 people approximately 39 days to build the barn.

Answer:

It takes 32 people about 39 days to build the barn.

To find how many days it will take 32 people to build the barn, calculate the total man-hours (20 × 24 = 480 man-hours) and divide that by the number of workers (480 \/ 32 = 15). Thus, it takes 32 people 15 days to build the barn.

The student's question involves solving a problem by understanding the concept of work rate and man-hours. To find out how many days it would take for 32 people to build a barn if it takes 20 people 24 days, we first need to calculate the total man-hours required to build the barn. The total man-hours is the product of the number of workers and the number of days they work, which in this case is 20 people × 24 days = 480 man-hours.

Once we have the total number of man-hours, we can then calculate how many days it will take for 32 people to complete the same amount of work. This is done by dividing the total man-hours by the number of workers, resulting in 480 man-hours / 32 people = 15 days.

Therefore, it will take 32 people 15 days to build the barn.

Answer:

[tex]A=x^2+12x+27\ units^2[/tex]

Step-by-step explanation:

we know that

The area of the model is equal to the area of a rectangle

The area of a rectangle is equal to

[tex]A=LW[/tex]

we have

[tex]L=x+9\ units[/tex]

[tex]W=x+3\ units[/tex]

substitute

[tex]A=(x+9)(x+3)[/tex]

Apply distributive property

[tex]A=x^2+3x+9x+27[/tex]

Combine like terms

[tex]A=x^2+12x+27\ units^2[/tex]

Answer:

The range and mid-range are equal

Step-by-step explanation:

the range is 75-25=50

the mid-range is (75+25)/2 = 100/2 = 50

50 = 50

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.

30, 25, 50, 75, 75, 60

The range is the difference between the highest value and the lowest values in the given set of numbers.

Midrange = Range ÷ 2

Option A is the correct answer.

The range of the set of numbers is 50

The midrange of the set of numbers is 25

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,

30, 25, 50, 75, 75, 60

The range is the difference between the highest value and the lowest values in the given set of numbers.

Now,

The lowest value is 25

The highest value is 75

Range = 75 - 25 = 50

Midrange = 50/2 = 25

Thus,

The range of the set of numbers is 50

The midrange of the set of numbers is 25

Learn more about expressions here:

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Answer:

x = 61

Step-by-step explanation:

Angles A and D are consecutive interior angles of a parallelogram.

Consecutive interior angles of a parallelogram are supplementary.

m<A + m<D = 180

x + 2x - 3 = 180

3x - 3 = 180

3x = 183

x = 61

Number of days Elizabeth spend making jam if she jarred 9 liters of jam is 4 days

Solution:

Given that, Elizabeth has already jarred 1 liter of jam

She will jar an additional 2 liters of jam every day

To find: Number of days Elizabeth spend making jam if she jarred 9 liters of jam

Let "x" be the number of days Elizabeth spend making jam

Then, by given information, we frame a equation as,

9 liters of jam = 1 liter of jam + 2 liters of jam( "x" days )

[tex]9 = 1 + 2x\\\\9 - 1 = 2x\\\\2x = 8\\\\x = 4[/tex]

Thus she spend 4 days in making jam

Missing term = –2xy

Solution:

Let us first find the quotient of [tex]-8x^2y^3 \div xy[/tex].

[tex]-8x^2y^3 \div xy=\frac{-8x^2y^3 }{xy}[/tex]

                    [tex]=\frac{-8\times x\times x\times y\times y\times y}{xy}[/tex]

Taking common term xy outside in the numerator.

                    [tex]=\frac{xy(-8\times x\times y\times y)}{xy}[/tex]

Both xy in the numerator and denominator are cancelled.

                    [tex]=-8xy^2[/tex]

Thus, the quotient of [tex]-8x^2y^3 \div xy[/tex] is [tex]-8xy^2[/tex].

Given the quotient of [tex]-8x^2y^3 \div xy[/tex] is same as the product  of 4xy and ____.

[tex]-8xy^2=4xy[/tex] × missing term

Divide both sides by 4xy, we get

⇒ missing term = [tex]\frac{-8xy^2}{4xy}[/tex]

Cancel the common terms in both numerator and denominator.

⇒ missing term = –2xy

Hence the missing term of the product is –2xy.

Answer:

A

Step-by-step explanation:

If your on e2020 Then A is your answer

Answer:

A

Step-by-step explanation:

TOOK QUIZ MADE 100

Answer:

Yes opposite sides are parallel

Step-by-step explanation:

The 2 pairs of opposite triangles are congruent by (SAS).

Therefore alternate angles are congruent, so opposite sides are parallel.

Answer:

Solving Systems of Equations (Simultaneous Equations) If you have two different equations with the same two unknowns in each, you can solve for both unknowns. There are three common methods for solving: addition/subtraction, substitution, and graphing.

Step-by-step explanation:

Answer:

x=2 and y=−5

Step-by-step explanation:

Alisia and Luis are both at the gym every 12 days. After the 12th day, the next day they will both be at the gym is the 24th day.

In this math problem, we figure out when Alisia and Luis will both be at the gym at the same time again. Alisia goes every 3 days, and Luis goes every 4 days. The days when they're both at the gym are multiples of the least common multiple (LCM) of 3 and 4. The LCM of 3 and 4 is 12, so they're both at the gym every 12 days.

They both are at the gym on the 12th day. To find out when they'll be there together next, we simply add 12 to the current day: 12 + 12 = 24. So, the next day they will both be at the gym is the 24th day.

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Answer:

Part A) Circumference

Part B) [tex]C=\pi D[/tex]

Part C) The distance traveled in one rotation is 628.32 feet

Step-by-step explanation:

Part A) we know that

The distance around the circle is equal to the circumference.

The Ferris Wheel have a circular shape

so

To find out the distance around the Ferris Wheel you should use the circumference

Part B) What is the formula needed to solve this problem?

we know that

The circumference is equal to multiply the number π by the diameter of the circle

so

[tex]C=\pi D[/tex]

Part C) What is the distance traveled in one rotation?

we know that

One rotation subtends a central angle of 360 degrees

The distance traveled in one rotation is the same that the circumference of the Ferris wheel

we have

[tex]D=200\ ft[/tex] ----> diameter of the Ferris wheel

substitute in the formula of circumference

[tex]C=\pi (200)\\C=200\pi\ ft[/tex]

assume

[tex]\pi=3.1416[/tex]

[tex]C=200(3.1416)=628.32\ ft[/tex]

therefore

The distance traveled in one rotation is 628.32 feet

Answer:               m<1 is 62°

Step-by-step explanation:

Alright, lets get started.

The two angles are given as 56° and 62°.

We know the sum of the angles of a triangle is 180°

So,

[tex]x+56+62=180[/tex]

[tex]x+118=180[/tex]

Subtracting 118 in both sides

[tex]x+118-118=180-118[/tex]

[tex]x=62[/tex]

Hence the desired angle 1 is 62°  ...........   Answer

Hope it will help :)

Answer:

B. 62°

Step-by-step explanation:

Hope this helps

Answer:

We just add numerators and rewrite denominator.

Adding unlike dominators:

We need to find the same denominators. You need to find the least common multiple (LCM) of the two denominators.

Step-by-step explanation:

You mean unlike denominators and like denominators.

Adding like dominators: We just add numerators and rewrite denominator :

Example : [tex]\frac{1}{4} +\frac{2}{4}=\frac{1+2}{4} =\frac{3}{4}[/tex]

Adding unlike dominators:

We need to find the same denominators. You need to find the least common multiple (LCM) of the two denominators.

For example :

[tex]\frac{1}{5}+\frac{3}{4}[/tex]

LCM for 5 and 4 is 20 : Now, divide by 5 and multiply by 1 for first fraction. 20 divide by 4 and multiply by 3 :

[tex]\frac{1*4}{20} +\frac{3*5}{20}=\frac{4}{20} +\frac{15}{20}=\frac{19}{20}[/tex]

Step-by-step explanation:

If you have a problem like 1 5/21 + 3 42/56 = ?

You have to find a common denominator. So you should of got 1 280/1176 and 3 882/1176. Then you add 1 280/1176 + 3 882/1176 = 4 1162/1176. Then you need to simplify the fraction. When you simplify the fraction you get 83/84. So your answer is 4 83/84.

If you have a common denominator you save your denominator and the numerator change. If you can then simplify it.

The domain of g(x) contains the domain of f(x) as a subset.

The given functions are f(x) = -log(x-2)-3 and g(x) = log(x-2). To determine which function has its domain contained within the domain of the other, we need to compare the two domains. The domain of f(x) consists of all real numbers greater than 2, while the domain of g(x) also consists of all real numbers greater than 2. Therefore, the domain of g(x) contains the domain of f(x) as a subset.

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Answer:

5.43×10^14 or

[tex]5 .43 \times 10^{14} [/tex]

Step-by-step explanation:

Scientific notation, the number must always be less than 10, in this case 5.43. The exponent represents how much times I moved the decimal point to the left.

Answer:

The original length was 41 inches and the original width was 16 inches

Step-by-step explanation:

Let

x ----> the original length of the piece of​ metal

y ----> the original width of the piece of​ metal

we know that

When squares with sides 5 in long are cut from the four corners and the flaps are folded upward to form an open box

The dimensions of the box are

[tex]L=(x-10)\ in\\W=(y-10)\ in\\H=5\ in[/tex]

The volume of the box is equal to

[tex]V=(x-10)(y-10)5[/tex]

[tex]V=930\ in^3[/tex]

so

[tex]930=(x-10)(y-10)5[/tex]

simplify

[tex]186=(x-10)(y-10)[/tex] -----> equation A

Remember that

The piece of metal is 25 in longer than it is wide

so

[tex]x=y+25[/tex] ----> equation B

substitute equation B in equation A

[tex]186=(y+25-10)(y-10)[/tex]

solve for y

[tex]186=(y+15)(y-10)\\186=y^2-10y+15y-150\\y^2+5y-336=0[/tex]

Solve the quadratic equation by graphing

using a graphing tool

The solution is y=16

see the attached figure

Find the value of x

[tex]x=16+25=41[/tex]

therefore

The original length was 41 inches and the original width was 16 inches

Final answer:

calculate the length as x + 25, and solve the volume equation to find the dimensions as 30 inches by 55 inches.

Explanation:

The original dimensions of the piece of metal can be calculated as follows:

Let x be the width of the metal.

Then, the length would be x + 25.

After cutting out the squares and folding, the volume of the box would be (x-10)(x-10)(30) = 930.

Solving this equation, we get x = 30, so the original dimensions were 30 inches by 55 inches.

Answer:

they are equal

Step-by-step explanation:

Both -4 4/25 and -4.16 are the same number. Neither is 'bigger' because they hold an equal value.

To determine which number is bigger between -4 4/25 and -4.16, we should understand that a larger negative number is the one closer to zero on the number line. First, let's convert -4 4/25 into a decimal format. This number is the same as -4.16 (as 4/25 is equal to 0.16).

Therefore, both -4 4/25 and -4.16 are exactly the same. In the context of negative numbers, 'bigger' means being closer to zero. Thus, neither is 'bigger' because they are equal.

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Answer:

9x + 5y = 29 ........... (1) and

3x + y = 7 ........... (2)

Each game of ping pong requires 1 number of token and each game of pinball requires 4 number of tokens.

Step-by-step explanation:

Let, each game of ping pong requires x number of tokens and each game of pinball requires y number of tokens.

So, from the given conditions we can write

9x + 5y = 29 ........... (1) and

3x + y = 7 ........... (2)

Now, solving equations (1) and (2) we get,

9x + 5(7 - 3x) = 29

⇒ 35 - 6x = 29

⇒ 6x = 6

⇒ x = 1 token.

Now, putting x = 1 in equation (2) we get,

3 + y = 7

⇒ y = 4 tokens.

So, each game of ping pong requires 1 number of token and each game of pinball requires 4 number of tokens. (Answer)

Answer:

5

Step-by-step explanation:

Answer:

The perimeter of ABCD will be 14 units.

Step-by-step explanation:

Points A(-5,-1) and B(-1,-1) lies on the same line which is parallel to the x-axis.

So, length of line segment AB will be |- 5 - (- 1)| = 4 units.

Points B(-1,-1) and C(-1,-4) lies on the line which is parallel to the y-axis.

So, length of line segment BC will be |- 4 - (- 1)| = 3 units.

Points C(-1,-4) and D(-5,-4) lies on the same line which is parallel to the x-axis.

So, length of line segment CD will be |- 5 - (- 1)| = 4 units.

Points D(-5,-4) and A(-5,-1) lies on the line which is parallel to the y-axis.

So, length of line segment DA will be |- 4 - (- 1)| = 3 units.

Therefore, the perimeter of ABCD will be (4 + 3 + 4 + 3) = 14 units. (Answer)

The value of given expression is 341

Solution:

Given that we have to find the value of given expression

Given expression is:

[tex]4x^2 + 2x - 1[/tex]

Given value is x = 9

Substitute x = 9 in given expression

[tex]\rightarrow 4(9)^2+2(9) - 1[/tex]

Solve the above expression

[tex]\rightarrow 4 \times (9 \times 9) + 18 -1\\\\\rightarrow 4 \times 81 + 17\\\\\text{Multiply the terms 4 and 81 }\\\\\rightarrow 324 + 17\\\\\text{Add the numbers }\\\\\rightarrow 341[/tex]

Thus the value of given expression is 341