Up and Running Auto Shop keeps track of their regular customers' data to see if there is a relationship between the life of a car's engine (y) and the number of times the oil is changed (x). When the data is shown on a scatter plot, the equation for the line of best fit is y = 0.4125x + 0.1576. What is the relationship between 0.4125 and the life of the car's engine?

Answer:

see the attachment for a table

Step-by-step explanation:

A. The table is shown in the attachment. The solution to h(t) = g(t) is at a value of t that lies between 6 and 7. At t=6, h(t) > g(t). At t=7, h(t) < g(t). Since both functions are continuous, they must have equal values somewhere between t=6 and t=7. (Intermediate value theorem.)

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B. The solution means the cannon balls will have the same height at a value of t between 6 and 7.

Answer:

b

Step-by-step explanation:

Answer:

the factors of x^3-1 are [tex]x^3 -1 = (x-1) (x^2 +x+1)\\[/tex]

Step-by-step explanation:

We need to find factors of x^3 -1

[tex]x^3-1 \\(x)^3 -(1)^3\\We \,\, know\,\, a^3 -b^3 = (a-b) (a^2 +ab + y^2) \\So, \,\, using\,\, the \,\, formula\,\,\\Here\,\, a= x \,\,and\,\, b= 1\\(x)^3 -(1)^3 = (x-1) (x^2 +x+1)\\[/tex]

So, the factors of x^3-1 are [tex]x^3 -1 = (x-1) (x^2 +x+1)\\[/tex]

the answer to this problem is 15

I believe 15 is correct ^^

Answer:  [tex]A)\quad \dfrac{x^6\ z}{y^{10}}[/tex]

Step-by-step explanation:

[tex].\quad \dfrac{(x^{2}\cdot y^{-3}\cdot z^{4})^2}{x^{-2}\cdot y^{4}\cdot z^{7}}\\\\\\= \dfrac{x^{2\cdot 2}\cdot y^{-3\cdot 2}\cdot z^{4\cdot 2}}{x^{-2}\cdot y^{4}\cdot z^{7}}\\\\\\=\dfrac{x^{4}\cdot y^{-6}\cdot z^{8}}{x^{-2}\cdot y^{4}\cdot z^{7}}\\\\\\=\dfrac{x^{4+2}\cdot y^{-6+6}\cdot z^{8-7}}{x^{-2+2}\cdot y^{4+6}\cdot z^{7-7}}\\\\\\=\large\boxed{\dfrac{x^6\ z}{y^{10}}}[/tex]

Answer:

y=(-5/12)x+(95/12)

Step-by-step explanation:

step 1

Find the slope of the line AB

m=(3-8)/(2+10)=-5/12

step 2

Find the slope of the line parallel to AB

we know that

If two lines are parallel then their slopes are the same

so

the slope is m=-5/12

step 3

Find the equation of the line l parallel to AB that passes through Point X

The equation of the line into point slope form is equal to

y-y1=m(x-x1)

substitute

y-10=(-5/12)(x+5)

y=(-5/12)x-(25/12)+10

y=(-5/12)x+(95/12)

[tex]A=\frac{ab}{2}=\frac{25\cdot12}{2}=\boxed{150}[/tex]

Answer:

x=30

Step-by-step explanation:

Answer:

[tex]\large\boxed{7x^2-15x+5-2x-8x^2=-x^2-17x+5}[/tex]

Step-by-step explanation:

[tex]7x^2-15x+5-2x-8x^2\qquad\text{combine like terms}\\\\=(7x^2-8x^2)+(-15x-2x)+5\\\\=-x^2-17x+5[/tex]

Answer:

option A.

Step-by-step explanation:

We know that the volume of a rectangular prism is the product of its base area and height. That is to say:

Volume = Base Area x Height

Where: x^3-3x^2 +5x-3

Height: x^2-2

Volume =

Solving for "Height" we have:

Height = Volume / Base Area

Height = (x^3-3x^2 +5x-3) / (x^2-2)

Using ruffinis law we have that the solution is:

x-3 with a remainder of 7x-9

That is to say:

x-3 + (7x-9)/(x^2 - 2)

That is option A.

Answer:

4

Step-by-step explanation:

The general equation of a circle with center (a, b) and radius r is given by the equation;

[tex](x-a)^{2}+(y-b)^{2}=r^{2}[/tex]

The constant in the right hand side of the equation is simply the square of the radius;

We have been given the following equation;

(x-3)^2 + (y+1)^2 = 16

Comparing this with the general equation above;

[tex]r^{2}=16\\\\r=\sqrt{16}=4[/tex]

Answer: C

Step-by-step explanation:

25,230 x .15= 3,784.50

25,230- 3,784.50= 21,535

21,535/36= 598.20833

598.20833 x 1.0671= 638.348109

638.348109 x 36= 22,980.5319

Answer:

Letter C $23,735.84.The result varies a few dollars, because during the solution an adjustment was made to the decimals.

Step-by-step explanation:

1. Define the price of the vehicle you are going to buy with the dealer or seller

Principal: $25230

Rate= 6.71%

N= 36 months

Down payment=15% of the cost of the vehicle= (25230*0.15)=$3784.50

25230-3784.50=21445.5

2. Apply the amortization formula to determine the monthly payments. With this taxation, you will determine the payments applied to the principal and the copper of interest.

A=P*(r(1+r)^{n})/((1+r)^{n}-1).

A= amortization or monthly payments.

P=Principal

R=interest rate

N= the total number of months

a. Calculate the monthly interest rate. The annual interest rate is 6.71% percent. Divide it by 12 to get the monthly interest rate. The monthly interest rate is 0.5592 percent (6.71/12 = 0.5592)  

A=21445.5*(0,005592 (1+0,005592)^{{36}})/(1+0,005592)^{{36}}-1.

A=21445.5*(0,00683/0,2223)

A=21445.5*0,03072=658.90

Total of the payment= 658.90*36=23720.40

Answer:

The perimeter of the triangle ABC is 22.8 units

Step-by-step explanation:

* Lets study the information in the problem

- There is Δ ABC with vertices:

  A (-2 , 2) , B (6 , 2) , C (0 , 8)

- The perimeter of the triangle is the sum of the length of its

  three sides

* We must to find the lengths of AB , BC and CD

- The rule to find the distance between 2 points (x1 , y1) and (x2 , y2) is

  √[(x2 - x1)² + (y2 - y1)²]

* Lets find the lengths of the three sides

- Length of AB

∵ A = (-2 , 2) and B = (6 , 2)

∴ AB = √[(6 - -2)² + (2 - 2)²] = √8² = 8 units

- Length of BC

∵ B = (6 , 2) and C = (0 , 8)

∴ BC = √[(0 - 6)² + (8 - 2)²] = √[6² + 6²] = √72 = 6√2 units

- Length of AC

∵ A = (-2 , 2) and C = (0 , 8)

∴ AC = √[(0 - -2)² + (8 - 2)²] = √[2² + 6²] = √40 = 2√10 units

* Now lets find the perimeter of the triangle

∵ The perimeter = AB + BD + AC

∴ The perimeter = 8 + 6√2 + 2√10 = 22.8 units

* The perimeter of the triangle ABC is 22.8 units

Answer:

The perimeter of triangle ABC = 22.78 units

Step-by-step explanation:

Formula:-

The length of line segment with end points (x₁, y₁) and (x₂, y₂) is given by,

Length = √ [(x₂ - x₁)² + (y₂ - y₁)²]

To find the each side of triangle

We have  A(-2,2), B(6,2), and C(0,8).

AB =  √[(6 - -2)² + (2 - 2)²] =  √64 = 8

BC = √[(0 - 6)² + (8 - 2)²] = √(36 + 36) = 8.48

AC = √[(0 - -2)² + (8 - 2)²] = √(4 + 36) = 6.3

To find the perimeter of triangle ABC

Perimeter = AB + BC + AC

 = 8 + 8.48 + 6.3 = 22.78 units

Answer:

[tex]y=\$360(1+0.03x)[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]y=P(1+rx)[/tex]

where

y is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

x is Number of Time Periods

in this problem we have

[tex]P=\$360\\r=0.03[/tex]

substitute in the formula above

[tex]y=\$360(1+0.03x)[/tex]

Answer:

y = 360(0.03)x

Step-by-step explanation:

incorrect and how do i erase a answer

Answer:

The answer is D. For every girl in the reading club, there are four girls in the drama club. It is not B. For every boy in the drama club, there are six boys in the reading club.

Pls make me brinlyest .

Hope this helped

The correct statement is, C. For every girl in the reading club, there are three girls in the drama club.  

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given,  8 boys in reading club 4 girls in reading club 2 boys in drama club 12 girls in drama club.

Going through the given options (given statements so multiple options would be correct).

For every girl in the reading club, there are three girls in the drama club,

As 12 is a multiple of 4 and 3.

learn more about proportion here :

https://brainly.com/question/7096655

#SPJ2

Answer:

[tex]NQ=24\ units[/tex]

Step-by-step explanation:

we know that

Triangles ABM and CDN are congruent

so

CD=AB

AB=2AL ----> because the diameter divide the circle into two equal parts

CQ=AL=140/2=70 units

NC----> is the radius

NC=148/2=74 units ----> the radius is half the diameter

Applying Pythagoras Theorem find the value of NQ

[tex]NC^{2}=NQ^{2}+CQ^{2}[/tex]

substitute the values

[tex]74^{2}=NQ^{2}+70^{2}[/tex]

[tex]NQ^{2}=74^{2}-70^{2}[/tex]

[tex]NQ^{2}=576[/tex]

[tex]NQ=24\ units[/tex]

Answer:

The surface area is equal to [tex]203\ m^{2}[/tex]

Step-by-step explanation:

step 1

Find the height of the prism

we know that

The volume of the prism is equal to

[tex]V=Bh[/tex]

where

B is the area of the base of the prism

h is the height of the prism

we have

[tex]V=160\ m^{3}[/tex]

[tex]B=64\ m^{2}[/tex]

substitute in the formula and solve for h

[tex]160=64h[/tex]

[tex]h=160/64=2.5\ m[/tex]

step 2

Find the surface area

The surface area of the prism is equal to

[tex]SA=2B+Ph[/tex]

where

B is the area of the base of the prism

P is the perimeter of the base

h is the height of the prism

we have

[tex]B=64\ m^{2}[/tex]

[tex]P=30\ m[/tex]

[tex]h=2.5\ m[/tex]

substitute in the formula

[tex]SA=2(64)+(30)(2.5)=203\ m^{2}[/tex]

Answer:

u = 16

Step-by-step explanation:

Given

[tex]\frac{3}{4}[/tex] u = 12

Multiply both sides by 4 to eliminate the fraction

3u = 48 ( divide both sides by 3 )

u = 16

Answer:

k is 2/3 and y is -1/3 when x is -0.5.

Step-by-step explanation:

The direct variation relationship is y = kx, where k is the const. of var.

Subbing 3 for x and 2 for y, 2 = 3k, or k = 2/3.

Now, if x = -0.5, y = (2/3)(-1/2) = -1/3

k is 2/3 and y is -1/3 when x is -0.5.

Answer:

2/3 and y is -1/3 when x is -0.5.

Step-by-step explanation:

Hope I helped

Answer:

40

Step-by-step explanation:

12x4 = 48

3x2 = 6

2x1 = 2

6+2 = 8

48-8= 40

HOPE THIS HELPS!

Answer:

20

Step-by-step explanation:

Since we are told that line a is parallel to line b, even if it's not visible in the image, we can say that ∠5 = ∠1, since they are formed by the same line crossing parallel lines.

So, we have

∠4 = 3x

∠5 = ∠1 = 6x

Since ∠4 and ∠5 are complementary angles formed by line t, we know their sum is 180 degrees. So,

∠4 + ∠5 = 180

3x + 6x = 180

9x = 180

x = 20

Answer is 20.

(4, 2) and (4, -5)

(Look at the photo. They have the same x-coordinates, but different y-coordinates; one is positive the other is negative, resuting in different quadrants)

I hope this helps!

Answer:

you'll find lots of clouds over tropical climates and practically no clouds over desert clmates.

Answer:

encontrará muchas nubes sobre climas tropicales y prácticamente ninguna nube sobre climas desérticos.

Step-by-step explanation:

1. 428 pages: There are a total of 428 pages that you can flip to.

2. 1/428: Page 45 is only one page out of the total sample space.

3. 1/2: Since the last page is 428, there is an even number of pages. That means that there are 214 page numbers that are even. 214/428 = 1/2.

Answer:

1. What is the sample space for this experiment?

A: 1 to 428

2. What is the probability that you will turn to page 45?

A: There is a 1 out of 428 chance you will turn to page 45.

3. What is the probability that you turn to an even numbered page?

A: There is a 1 out of 2 chance you will turn to an even numbered page.

C, because you distribute the 1/6 to x and 18 which ends up being 1/6x - 3

[tex]\frac{1}{6}(x-18)[/tex]   Distribute 1/6(multiple 1/6 to x and -18)

[tex]\frac{1}{6}(x) -\frac{1}{6} (18)[/tex]     Simplify

[tex]\frac{1}{6}x -3[/tex]       Your answer is C

It’s A. Hope you already got it✨

The answer is actually D or C

Answer:

The equation that can be used to find d is [tex]2d+17=41[/tex]

[tex]d=12\ dogs[/tex]

Step-by-step explanation:

Let

d -----> the number of dogs

we know that

The linear equation that represent this situation is

[tex]2d+17=41[/tex]

Solve for d

Subtract 17 both sides

[tex]2d=41-17[/tex]

[tex]2d=24[/tex]

Divide by 2 both sides

[tex]d=12\ dogs[/tex]

Final answer:

The equation to find the number of dogs at the shelter is 2d + 17 = 41, where 2d represents the total cups of food eaten by the dogs and 17 represents the cups eaten by the cats per day.

Explanation:

To find d, the number of dogs at the animal shelter, we can use the information provided to set up an equation. We know the shelter uses 41 cups of food each day in total, and that cats eat 17 cups in total per day. Since each dog eats 2 cups per day, we can represent the number of cups dogs eat as 2d, where d is the number of dogs. We can then express the total food used as the sum of the food eaten by the cats and the food eaten by the dogs, which gives us the equation:

2d + 17 = 41

This equation can be used to find the number of dogs at the shelter since solving for d would give us the total number of dogs based on their food consumption.

Final answer:

Classifying functions involves identifying whether a population is experiencing growth, depicted by exponential or J-curve growth models, or decay, which is often described through logistic or S-curve models. Exponential growth shows unrestricted rapid increases, while logistic growth accounts for environmental limits and a carrying capacity. Age structure diagrams provide further context for the type of population change being observed.

Explanation:

Growth and Decay in Biological Functions

When classifying functions as growth or decay, one must consider the nature of the function in relation to the context of time and population size. For instance, when discussing bacterial growth, Curve A depicting exponential growth is characterized by a population size that increases rapidly over time, often without any constraints. This curve represents a J-curve model on a graph where population size skyrockets as time progresses. On the other hand, Curve B illustrates logistic growth, which follows an S-curve model where the population grows rapidly at first and then slows down as it reaches carrying capacity, a point where growth rate starts to decline.

Different time intervals on a growth curve represent various phases, such as the lag phase, where growth is slow or negligible; the log phase or exponential phase, where the number of cells increases dramatically; the stationary phase, where growth rate is zero due to resource depletion or waste accumulation; and the death phase, where the number of live cells declines.

Various types of growth in organisms can be identified by their structural adaptations or ecological contexts, such as whether they are terrestrial or aquatic, or whether they are deciduous or evergreen plants. Additionally, age structure diagrams for populations can reveal if a population is rapidly growing, growing slowly, stable, or in decline.

Answer:

x = 61.3°

Step-by-step explanation:

We are given the radius r = 9 cm and arc length l = 9.7 cm. We need to find the angle x in degrees.

The formula used is:

l = rФ

In our case Ф = x. So re writing the formula:

l= rx

9.7 = 9 x

=> x = 9.7 / 9

x = 1.07 radians

Converting radians into degree we need to multiply the value of x by

180/π where π = 3.14

x = 1.07 * 180/3.14

x = 61.3°

Answer:

A. 3, 4, 5

Step-by-step explanation:

Option A:

LHS = 3² + 4² = 9 + 16 = 25

RHS = 5² = 25

(3, 4, 5) is a right triangle.

Option B:

LHS = 7² + 8² = 49 + 64 = 113

RHS = 9² = 81

(7, 8, 9) is NOT a right triangle.

Option C:

LHS = 3² + 9² = 9 + 81 = 90

RHS = √95² = 95

(3, 9, √95)  is NOT a right triangle.

Hope this help!!!

Have a nice day!!!

Answer:

2 and a half

Step-by-step explanation:

To solve this, divide the total amount of free time [5/6] by the time it takes to play one video game [1/3]

Remember that dividing 5/6 by 1/3 is the same as multiplying 5/6 by 3/1.

Multiply the numerators

5 x 3 = 15

Multiply the denominators

6 x 1

15/6 = 2 3/6

So, Lamar can play 2 and a half video games

I hope this helps!

The answer is 2 and a half.