Which graph represents a linear function?

Answer:

A) car 1: exponential

   car 2: linear

B) car 1: [tex]f(x)=18500(0.94)^{x-1}[/tex]

    car 2: [tex]f(x)=-1000x+19500[/tex]

C) Yes, there will be a significant difference of $1,100.40 which is approx 10% of the value of the cars after 10 years.

Step-by-step explanation:

Part A

Car 1: exponential as the projected value is not decreasing by the same amount each year

Car 2: linear as the projected value decreases by the same amount each year ($1000)

Part B

Car 1

General form of exponential function: [tex]y=ab^x[/tex]

a = initial value = 18500

b = growth factor = [tex]\dfrac{17390}{18500}=0.94[/tex]

[tex]\implies f(x)=18500(0.94)^{x-1}[/tex]

NB We have to change x to "x-1" since we are told in the table that after 1 year the car's value is 18500.

Car 2

General form of linear function:  [tex]y=mx+b[/tex]

[tex]m=\dfrac{\textsf{change in} \ y}{\textsf{change in} \ x}=\dfrac{17500-18500}{2-1}=-1000[/tex]

[tex]y-y_1=m(x-x_1)[/tex]

[tex]\implies y-17500=-1000(x-2)[/tex]

[tex]\implies f(x)=-1000x+19500[/tex]

Part C

Car 1 after 10 years: [tex]\implies f(10)=18500(0.94)^{10-1}=\$10,600.40[/tex]

Car 2 after 10 years: [tex]\implies f(10)=-1000(10)+19500=\$9,500[/tex]

Difference = 10600.40 - 9500 = 1100.40

Yes, there will be a significant difference of $1,100.40 which is approx 10% of the value of the cars after 10 years.

Answer:

80 units²

Step-by-step explanation:

To find the area, we will need to use the formula A = b * h.

We know the height is 8 and the base is 10. We ignore the length of 11 since it is not relevant.

So what the equation would look like, when plugging in the 8 for height and 10 for base is:

A = 10 * 8 = 80 units²

So the area of the parallelogram is 80 units²

The area of a parallelogram is the product of the length of the parallel side and the distance between the parallel sides. Then the area of the parallelogram is 80 square units.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a parallelogram, opposite sides are parallel.

The area of the parallelogram will be given as

Area = bh

Where b is the length of the parallel side and h is the distance between the parallel sides.

Area = 10 × 8

Area = 80

The area of the parallelogram is 80 square units.

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Answer:

1

Step-by-step explanation:

add then together

-2 + 4 = 2

then divide by the amount of numbers added up (in this case 2)

2/2 = 1

Answer:

I'm gonna say positive 2.

Step-by-step explanation:

Hope this helps!

Answer: 238 lbs

Step-by-step explanation:

x = joe's weight

y = joe's dad's weight

x + y = 336

y = x +140

Substitute for y

x + x + 140 = 336

2x + 140 =336

2x = 196

x = 98

Joe weighs 98 lbs

Now, plug that into Joe's dad's weight equation

y = 98 + 140

y = 238

Joe's dad weighs 238 lbs

(-8,-2)

Reflecting across the x-axis means leaving the x value the same but negating the y value

Answer:

(3x^2 - 1)(3x^2 + 1)(9x^4 + 1).

Step-by-step explanation:

Using the identity for the difference of 2 squares;

a^2 - b^2 = (a - b)(a + b)  

we put a^2 = 81x^8 and b^2 = 1  giving

a = 9x^4 and b = 1, so:

81x^8 − 1 =   (9x^4 - 1)(9x^4 + 1)

Applying the difference of 2 squares to 9x^4 - 1:

= (3x^2 - 1)(3x^2 + 1)(9x^4 + 1).

Answer:

The answer is (3x^2 - 1)(3x^2 + 1)(9x^4 + 1).

Step-by-step explanation:

[tex]Answer:[/tex]

x squared

x is any number, so...

[tex]x^2[/tex]  x times itself

[tex]x * x[/tex]  same here

[tex]xy[/tex]  same here

Therefore, x squared means x times itself one time.

Answer:

  add 6 unit tiles

Step-by-step explanation:

The square is completed when the algebra tile grid pattern is a square. This one will be a square when 6 more unit tiles are added to fill the empty spaces at the bottom right.

We need to add 6 to complete squares.

Here we have the expression:

x^2 + 8x + 10

By looking at the image, we can see that we need to add 6 cubes of the ones with the digit 1.

That is equivalent to adding 6 to our expression (and we also subtract 6 so we don't change it) then we have:

x^2 + 8x + 10 + 6 - 6

(x^2 + 8x + 10 + 6) - 6

(x^2 + 8x + 16) - 6

(x^2 + 2*4*x + 4^2) - 6

(x + 4)^2 - 6

So we completed squares, then we conclude that we need to add 6 to complete squares.

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Answer:

center is at (8, -1) and the radius is 9

Answer:

The time it'd take for the element to have 15 g of mass is approximately 68 min.

Step-by-step explanation:

The radioactive decay of a substance is given by the following formula:

Since the element has a half life of 12 minutes, this means that after this time the mass of the element will be half of it was originally, therefore:

Therefore the mass of the element is given by:

If the initial mass is 760 g and the final mass is 15 g, we have:

The time it'd take for the element to have 15 g of mass is approximately 68 min.

Step-by-step explanation:

Element X take 32.6 minutes to decay to 87 grams.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Element X decays radioactively with a half life of 15 minutes.

And, there are 400 grams of Element X.

Now, By the given information, we can formulate;

⇒ [tex]y = x (0.5)^{t/h}[/tex]

Substitute all the values we get;

⇒ 400 = 87 × [tex](0.5)^{t/15}[/tex]

⇒ 400 / 87 =  [tex](0.5)^{t/15}[/tex]

⇒ 4.6 =  [tex](0.5)^{t/15}[/tex]

Take log both side,

⇒ ln 4.6 = t/15 (ln 0.5)

⇒ 1.52 = t/15 x 0.7

⇒ t = 32.6 minutes

Thus, Element X take 32.6 minutes to decay to 87 grams.

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The factors of the polynomial are [tex]\rm x^2(x+11)-3(x+11)[/tex].

Factors are the integers that are multiplied to produce an original number.

Given

The factors of the polynomial are [tex]\rm x^3+11x^2-3x-33[/tex].

The factors of the polynomial are;

[tex]\rm x^3+11x^2-3x-33\\\\x^2(x+11)-3(x+11)[/tex]

Hence, the factors of the polynomial are [tex]\rm x^2(x+11)-3(x+11)[/tex].

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Answer:

$50

Step-by-step explanation:

12 x 30 = 360

960 - 360 = 600

600/12 = 50

Answer: $50

Step-by-step explanation:

All 12 of the televisions have extended warranties 12*30=360

Then subtract the amount earned from the total amount paid for extended warranties:

960 - 360 = 600

Now divide 600 by the number of months in a year:

600/12 = $50

The fixed amount Gi earns for each television he sells is $50

The triangle inequality theorem is not followed,  no triangle can be formed.

In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices.

The triangle inequality theorem describes the relationship between the three sides of a triangle.

According to the triangle inequality theorem, the sum of any two sides must be greater or equal than the length of the third side.

Here, the sides are 4.72 yds, 6.31 yds, and 1.67 yds.

4.72 + 6.31 = 11.02  >  1.67  (theorem followed)

4.72 + 1.67 = 6.39  > 6.31    (theorem followed)

6.31 + 1.67 = 7.98 > 4.72 (theorem not followed)

Since the triangle inequality theorem is not followed,

Hence, no triangle can be formed.

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Answer:

1/16

Step-by-step explanation:

Since no cards are removed between each shuffle, the chance of drawing a spade both times remains the same, meaning it is 1/4 both times. 1/4 * 1/4 =1/16

The probability of drawing two spades in two draws if the first card is returned to the deck between draws will be 1 / 16.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of samples

Given that the chance of drawing a spade from a deck of cards is 1/4. If the deck is shuffled between draws.

The probability will be calculated as,

Probability = 1 / 4 x 1/ 4

Probability = 1 / 16

Hence, the probability will be equal to 1 / 16.

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Ibrahim has 33 more stickers than Rosie

An equation is an expression used to show the relationship between two or more variable and numbers.

Given the ratio:

Rosie: Matilda: Ibrahim = 4 : 7 : 15

Let x represent the total number of stickers

Ibrahim = (15/26)x

Matilda = (7/26)x

Given:

(15/26)x = (7/26)x  + 24

x = 78

Ibrahim = (15/26)*84 = 45

Rosie = (4/26)*84 = 12

Ibrahim has 33 (45 - 12) more stickers than Rosie

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Answer: x= 6

Step-by-step explanation:

Answer:

3 11/20

Step-by-step explanation:

I need someone to talk to please

Answer:

answer is

Step-by-step explanation:

it b.

Answer:

d+22=t

d dvds plus 22 dvds equals t dvds

Answer:

The height of each step is 1957 yards

Step-by-step explanation:

we are given

Tristan is building steps up to a deck that is 15656 yards above the ground

so, total height =15656 yards

Number of steps =8

now, we can use formula

Height of each step = ( total height)/( number of steps)

now, we can plug these values

and we get

Height of each step is

Answer:

Blue

Step-by-step explanation:

Because it has the lowest likelihood, with only a 15% chance.

Answer:

B gives you the equation, A is wrong

Step-by-step explanation:

If I am incorrect in my reasoning, please let me know so that I can plan better for my future answers. Have an amazing day.

Answer:

it a

Step-by-step explanation:

I took the test

Answer: All three are correct

Step-by-step explanation:

agree with all 3 students. They are all basically the same strategy. First, stands for the area of the base. The base is a circle, so . Therefore, is the same thing as . In Andre’s strategy, all of the circular cross sections of a cylinder are congruent to its base. So finding the area of a cross section is the same as finding the area of the base. Andre then multiplied this area by the cylinder’s height, so he essentially used .

Answer:

the answer would be 21

Step-by-step explanation:

4+6 is 10 so divide 6 by 2 which is 3 and add three for each line 10+3+3+3=21

The experimental probability that Hilda pulled a red marble is 0.11752 or 11.752%.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

For a class experiment, Hilda places different colored marbles in a bag. She pulls a marble at random from the bag, records its color, and then puts the marble back in the bag. She repeats this process 25 times.

The overall results are shown in the table.

Blue, Red, Yellow, Orange Frequency 6, 4, 8, 7 respectively.

P(red) will be 1/4 and P(not red) will be 3/4.

The number of trials (n) is 25.

Frequency of the red (r) = 4

Then the probability of getting red will be

[tex]\rm P(red) = \ ^nC_r( P(red) )^r*( P(not\ red))^{n-r}\\\\P(red) = \ ^{25}C_4 * (\dfrac{1}{4})^4 * (\dfrac{3}{4})^{25-4}\\\\P(red) = 0.11752[/tex]

The experimental probability that Hilda pulled a red marble is 0.11752 or 11.752%.

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Answer:

here is ther anwser

Step-by-step explanation:

Step-by-step explanation:

b² - 4ac

= 16 - 4(3)(-2)

= 16 + 24

= 40

The graphs of parabolas are used to represent quadratic functions and equations

From the graph, we can see that the graph of the parabola opens downward

The graph crosses the x-axis at x = 2, and it crosses the y-axis at y = -4

So, the x-intercept is x = 2, and the y-intercept at y = -4

This is the maximum point on the graph.

So, the coordinate of the vertex is (2,0)

A parabola is represented as:

[tex]y = a(x - h)^2 + k[/tex]

The parabola opens downward.

So, we have:

[tex]y = -1(x - h)^2 + k[/tex]

The vertex is (2,0).

So, we have:

[tex]y = -1(x - 2)^2 + 0[/tex]

[tex]y = -(x - 2)^2[/tex]

Hence, the equation of the parabola is [tex]y = -(x - 2)^2[/tex]

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Answer:

Step-by-step explanation:

Possible number of pairs of given cards:

Number of sums with odd score, two odd numbers added to an even number from each box:

Required probability: