When you own a pet, there are one-time costs, such as a leash, and continuing costs, such as food. Suppose the one-time costs for owning a small dog are $180, and the continuing costs are $400 per year Which function models the average annual cost of owning a small dog for x years?

The slope-intercept form of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (-1, -2) and (-2, 7). Substitute:

[tex]m=\dfrac{7-(-2)}{-2-(-1)}=\dfrac{9}{-1}=-9[/tex]

Therefore we have [tex]y=-9x+b[/tex].

Put the coordinates of the point (-1, -2) to the equation of a line:

[tex]-2=(-9)(-1)+b[/tex]

[tex]-2=9+b[/tex]     subtract 9 from both sides

[tex]-11=b\to b=-11[/tex]

Answer:

3 fancy shorts

4 plain

Step-by-step explanation:

By setting up equations for the total cost and the number of shorts purchased, we find that Kristin bought 2 fancy shorts at $28 each and 5 plain shorts at $15 each.

To solve the problem, let's denote the number of fancy shorts Kristin bought as F and the number of plain shorts as P. The problem gives us two conditions: Kristin spent a total of $131 on shorts, and she bought a total of 7 shorts. Fancy shorts cost $28 each, and plain shorts cost $15 each.

Now, we can set up two equations based on this information:

Using equation (2), we can express P as P = 7 - F and substitute this into equation (1) to solve for F:

28F + 15(7 - F) = 131

Simplify the equation:

28F + 105 - 15F = 131

13F = 26

F = 2

Now that we have the value for F, we can use it to find P:

P = 7 - F

P = 7 - 2

P = 5

Kristin bought 2 fancy shorts and 5 plain shorts.

Answer:

1526.0 cubic units

Step-by-step explanation:

Rotating rectangle AKLM you will get cylinder with height KA and base radius KL.  From the given data

[tex]KA=\sqrt{(6-0)^2+(0-0)^2}=6,\\ \\KL=\sqrt{(0-0)^2+(9-0)^2}=9.[/tex]

The volume of the cylinder is

[tex]V_{cylinder}=\pi r^2\cdot H.[/tex]

Then

[tex]V_{cylinder}=\pi \cdot 9^2\cdot 6=486\pi \approx 1526.0\ un^3.[/tex]

Answer:

2,-2

Step-by-step explanation:

Answer:

$7.20

Step-by-step explanation:

I got u bro, Divide the price of the stickers by the number of stickers ($3/5=$.60) multiply the price of one sticker by the number of stickers ($.60x12=) :)

Final answer:

The cost of 12 stickers can be found by writing the proportion 5 stickers/3 dollars = 12 stickers/c dollars and solving for c, which yields c = 7.2. Thus, 12 stickers cost $7.20.

Explanation:

The student is asked to write a proportion to determine the cost c if they buy 12 stickers when the known price is 5 stickers for $3. To set up the proportion, we can compare the number of stickers to the cost. We have one ratio of 5 stickers to $3, and we need to find the equivalent ratio for 12 stickers to $c. The proportion can be represented as:

5 stickers / 3 dollars = 12 stickers / c dollars

Now we cross-multiply to solve for c:
5 * c = 3 * 12

c = (3 * 12) / 5

c = 36 / 5

c = 7.2

Therefore, the cost c of 12 stickers is $7.20.

Answer:

3598 (or 3600 to 2.s.f)

Step-by-step explanation:

You need to recall that the circumference is π * d

So if we have the circumference, we can divide by π to get d:

11,304 ÷ π = 3598 or 3600  to 2.s.f

Answer:

[tex]D\approx 3600[/tex]

Step-by-step explanation:

Circumference is given by this formula below. What gives us the radius.

[tex]C=2\pi R \Rightarrow 11304=6.28R \Rightarrow R=1800[/tex]

The diameter of the circle is calculated by dividing the Circumference, 11304 in this case by [tex]\pi[/tex]

[tex]C=2\pi R \Rightarrow C=\pi D \Rightarrow D=\frac{C}{\pi} \Rightarrow D=\frac{11304}{\pi} \Rightarrow D\approx 3600[/tex]

Answer:

A) [tex]x=\frac{h-6}{1.5}[/tex]

B)[tex]26[/tex]

Step-by-step explanation:

A)Let's call the height of the plant [tex]h[/tex] and this height will be 6 inches on the day 0 like this:

[tex]h=6[/tex]

on the day 1 of the month the plant will have the original 6 inches plus the height it grew the first day  which will be 1.5 inches

[tex]h=6+1.5[/tex]

on the day 2 of the month the plant will have the original 6 inches plus the height it grew the first day plus the height it grew the second day which will be again 1.5 inches

[tex]h=6+1.5+1.5[/tex]

we can see that on the day 1 we add 1.5 inches one time, on the day 2 we add 1.5 inches two times. it is possible to say now that the height will be the original 6 inches plus 1.5 times the days of the month like this:

[tex]h=6+1.5x[/tex]

We will solve for x because we need to find the number of days for a given h like this:

[tex]h=6+1.5x\\h-6=1.5x\\x=\frac{h-6}{1.5}[/tex]

and this will be our equation that trent can use to find the number of days (x), it will take the sunflower to a given height.

B)to know how many days it will take for he sonflower to grow to a height of 45 inches we replace h in the equation with 45 like this:

[tex]x=\frac{h-6}{1.5}\\x=\frac{45-6}{1.5}\\x=26[/tex]

The sunflower will take 26 days to grow to a height of 45 inches

Substitute the values of a nad b to the expression:

[tex]125a^0b^4=(125)\left(\dfrac{5}{7}\right)^0\left(-\dfrac{1}{5}\right)^4=(125)(1)\left(\dfrac{1^4}{5^4}\right)\\\\=(125)\left(\dfrac{1}{625}\right)=\dfrac{125}{625}=\dfrac{125:125}{625:125}=\dfrac{1}{5}[/tex]

[tex]Use\\\\a^2-b^2=(a-b)(a+b)\\\\i=\sqrt{-1}\to i^2=-1\\------------------------\\\\x^2+25=x^2+5^2=x^2-(-5^2)=x^2-(5i)^2\\\\\boxed{x^2+25=(x-5i)(x+5i)}[/tex]

Answer:

It is a rational number and real number

Explanation:

it is a real number because it can become .75 and that is a real number.

it is a rational number because assume that 3/4 is a rational number. Since every rational number can be expressed as a/b form which do not have any common factor so we can say that a/b = 3/4 Squaring both side we get: a2/b2 = 9/16 a2 = (9/16) b2 Or we can say b2 = a2(16/9) a2 is divided by 9. So we can say that a is divided by 9. It implies that there exist some number c such that a/9 = c a = 9c By squaring both side we get a2 = 81 c2 Put the value of a2 from the equation a2 = (9/16) b2 we get: (9/16)b2 = 81c2 this tends to b2/ 9 = 16 c2 It implies that b2 is divided by 9. So we can say that b is divided by 9. This implies that a and b have a common factor 9. Since a and b have common factor therefore 3/4 is not a irrational number. Hence 3/4 is a rational number.

Good luck

Please mark me brainliest

Answer:

3/4 is a rational number and also a real number

Step-by-step explanation:

to prove 3/4 is real

3/4 is a fraction. It is a proper fraction since denominator  is grater than numerator.

3/4 can be written as 0.75 which is terminating decimal.

Therefore 3/4 is a real number

To prove 3/4 is a rational number

3/4 is the form of p/q.

Therefore 3/4 is a rational number.

Answer:

Perimeter of the paperboard that remains after the semicircle is removed = 94.26 in

Step-by-step explanation:

Watch the attached figure of how the semi circle is cut out of the rectangular paperboard.

Length = 24 in

Width = 18 in

Radius of the semi circle = Half of the width of the paperboard = [tex]\frac{18}{2}[/tex] = 9 in

1) Circumference of the semi circle = π*radius

= 3.14*9

= 28.26 in

2) Perimeter of the paperboard that remains after the semicircle is removed

= Top + Left + Bottom + Right Circumference of the semi circle

= 24 + 18 + 24 + 28.26

= 94.26 in

Answer:

the answer is 304.84 in2 I just had the question

Answer:

C. greater than 90 and less than 180 degrees.

Step-by-step explanation:

An obtuse angle is angle in the second quadrant.

This angle is more than [tex]90\degree[/tex] but less than [tex]180\degree[/tex].

Therefore the correct answer is option C.

Note however that a [tex]90\degree[/tex] angle is called a right angle and an angle greater than [tex]0[/tex] but less than [tex]90\degree[/tex] is called an acute angle.

Answer:

C-Greater than 90 and less than 180

Step-by-step explanation:and obtuse angle can go over 180 my rule is if its over 90 its obtuse

Answer:

Step-by-step explanation:

The key and the most critical step is to draw the line first. Don't do anything else before that.

(2,-8) (-2,-8)

What you find out is that the y value is always - 8.

So the line has no slope and any x value

y = 0*x + b

y = - 8 is the equation of the line.

Final answer:

The function y=230(0.98)ˣ is an exponential decay model depicting how a quantity decreases over time. The graph starts at 230 (the initial value) and decreases at a decay rate of 0.98 each step. To express small or large numbers succinctly, standard exponential form is used.

Explanation:

The exponential equation given, y=230(0.98)ˣ, represents a mathematical function known as an exponential decay model. To draw the appropriate graph for this function, you would plot the y-value against x on a Cartesian plane. The x-axis would indicate the time or trial number, and the y-axis would represent the value of y at that time. The decay rate in this equation is 0.98, which means that with each step in x (assuming x is a time interval), the quantity y decreases to 98% of its previous amount. The initial value, or mean, of the equation is 230, which is the starting point of the graph at x=0.

The mentioned exponential curve would start at y=230 and decrease gradually as x increases. If you were to shade the area for the probability that a student has less than $0.40 in his or her pocket, you would first need to solve for x when y=0.40, and then shade under the curve to the left of the corresponding x-value on your graph. This would visually represent P(x < 0.40).

To express numbers in standard exponential form, you use a coefficient between 1 and 10 multiplied by a power of 10. For example, converting 9.3 times 10 to the power of 7 is an example of expressing a very large number in exponential form. For small values of x, the exponential curve will show slower change, which increases rapidly for larger values of x.

The image of the triangle after a dilation with a scale factor of 5/6 is similar to the original triangle. The Option C

No, a dilation with a scale factor of 5/6 does not change the similarity of a triangle. Dilations involve scaling the size of the original figure, but the shape and angles remain unchanged.

In this case, the sides of the triangle will be uniformly reduced by a factor of 5/6, maintaining the proportional relationships between the sides. As a result, the dilated triangle will still be similar to the original triangle and the angles will retain their measurements, just as in the initial triangle.

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Answer:

The tree is 20 ft tall.

Step-by-step explanation:

We can use ratio's to solve this problem.   Take the height of the object over the shadow length.

5 ft                  x ft

----------- = ----------------

3ft                  12 ft

Using cross products

5*12 = 3*x

60 = 3x

Divide by 3 on each side

60/3 = 3x/3

20 =x

The tree is 20 ft tall.

a)

very straighforwards, a rectangle of 24 in x18 in has an area of simply that product.

however, that gives us in², so we firstly need to convert those inches to cm, so since 1 inch is 2.54 cm, then 24 inches is just 24*2.54, and likewise 18 inches is just 18*2.54.

so the tabletop is (24*2.54) * (18*2.54) = 2787.09 cm².

b)

each bag can cover 260 cm², she can't buy any partials, half a bag or a quarter of a bag, is a whole bag or nothing.

well, if she only buys one, she'll be able to cover 260 cm², however the tabletop is 2787.09 cm², so, how many times does 260 go into 2787.09?  2787.09 ÷ 260 ≈ 10.72.

so she needs 10 bags plus 0.72 of another, the store doesn't sell partials, so she'll need to buy another bag, namely 11 bags.

c)

well, each bag is 3.76, for eleven bags that'll be 11*3.76 = 41.36.

Answer:

x = 5 and y = -2

Step-by-step explanation:

Here you have given what y is equal to, this means you can sub this into the first equation:

3x - 2(x - 7) = 19

Expand the brackets:

-2 * x = -2x

-2 * -7 = 14

3x -2x +14 = 19

Move the +14 over to the other side making it a -14:

3x - 2x = 19 - 14

3x - 2x = 5

3x - 2x = x

So x = 5

Now sub this into the first equation:

3(5) - 2y = 19

15 - 2y = 19

Move the -2y over to the other side making it a +2y, and move the +19 over to the other side making it a -19:

15 - 19 = 2y

-4 = 2y

Divide both sides by two:

y = -2

So x = 5 and y = -2

Answer:

D[tex]_o[/tex] of Y = (-3/2, -1)

Step-by-step explanation:

We are given three points on the graph:

X (4, 0)

Y (3, 2)

Z (2, 2)

and the scale factor of dilation which is [tex]-\frac{1}{2}[/tex].

Given that, we are to find the coordinates of Y after dilation. To find that, we will multiply the coordinates of the point Y with the scale factor.

Y =  [tex](-\frac{1}{2}[/tex] × [tex]3[/tex] , (-\frac{1}{2}[/tex] × [tex]2)[/tex]

Y = [tex](-\frac{3}{2} , -1)[/tex]

Answer:

105.42

Step-by-step explanation:

       259.63

        154.21

         105.42

[tex]\mathsf{\heartsuit\;\; (\sqrt{8})^2 = \sqrt{64}}\\\\\mathsf{\heartsuit\;\; [(8)^\frac{1}{2}]^2 = \sqrt{(8)^2}}\\\\\mathsf{\heartsuit\;\; (8)^\frac{2}{2} = [(8)^2]^\frac{1}{2}}\\\\\mathsf{\heartsuit\;\; 8 = [8]^\frac{2}{2}}\\\\\mathsf{\heartsuit\;\; 8 = 8}\\\\\mathsf{\heartsuit\;\; Option\;(A)\;is\;the\;Answer}[/tex]

The number which will make the equation true, when placed in the box is: A. √8.

In order to determine the unknown number, we would assign a variable (x) to the unknown number and then evaluate the resulting algebraic equation as follows:

x² = √64

x² = 8

Taking the square root of both sides, we have:

x = √8.

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Answer:

Given the statement: The length of an aquarium, which has the form of a rectangular solid, is equal to 5 decimeters, and the width is 4/5 the length.

Since, aquarium is in the form of a rectangular solid.

Length of an aquarium(l) = 5 dm

Width of an aquarium(w)= [tex]\frac{4}{5}\times 5 = 4 dm[/tex]

It is also given that when you put 40 liters of water into the aquarium, it was full to [tex]\frac{2}{3}[/tex] its volume.

Volume of Rectangular solid(V) is given by;

[tex]V = l \times b \times h[/tex] where l is the length , w is the width and h is the height of the rectangle respectively.

Volume(V) of an aquarium = [tex]\frac{3}{2} \times 40 = 60[/tex] liter.

Using volume formula to calculate the height(h);

[tex]60 = 5 \times 4 \times h[/tex]

[tex]60 = 20h[/tex]

Divide both sides by 20 we get;

h =  3 dm                      [ 1 liter = 1 cubic dm]

We have to find the what part of length makes up the height of the aquarium.

[tex]h = \frac{3}{5} l[/tex]       where l = 5 dm

therefore, [tex]\frac{3}{5}[/tex] part of the length makes up the height of the aquarium.

[tex](a)\\\\\triangle HFG\sim\triangle HGE\sim\triangle GFE\\\\(b)\\\\\dfrac{FE}{GE}=\dfrac{GE}{HE}\qquad\qquad\dfrac{HF}{HG}=\dfrac{HG}{HE}[/tex]

Answer:

20

Step-by-step explanation:

20 x 10 = 200

10% = 0.10

200 x 0.10 = 20

Answer:

Step-by-step explanation: first of all u have to do the $20 per hour which she worked 10 hours so 20 x 10 which equals $200. 10% of $200 would be $20 because u divide 200 by 0.10 which is 20. so I think the answer would be $180 or $20 for Madeline. (I’m not a pro at math sorry)

Answer: 45%

Step-by-step explanation:

[tex]\underline{\qquad \qquad\quad|\text{Quantity}|\quad\%\quad|\text\quad{Qty } \times\text{\%}\qquad}\\\underline{\text{Solution A }|\text{5 liters}\quad|\text{0.20}\quad|5\times0.20=1.00}\\\underline{\text{Solution B }|\text{5 liters}\quad|\text{0.70}\quad|5\times0.70=3.50}\\\text{Mixture }\quad|\text{ 10 liters }|\quad\text{x}\quad|\qquad\text{4.50}[/tex]

10x = 4.50

  x = .45

    = 45%

Answer:82,600

Step-by-step explanation:

round down, as 19 is closer to than 100, so keep the 100's place there and take out the 10's and 1's and change them to 0. Please mark my answer as brainliest!

Answer:82700

Step-by-step explanation:

The weight of the 747 airplane, when expressed in tons, is approximately 300 tons.

The calculation is as follows:

[tex]\text{Weight in tons} = \frac{\text{Weight in pounds}}{2000}[/tex]

Substitute the values:

[tex]\text{Weight in tons} = \frac{600,000}{2000}[/tex]

Perform the division:

[tex]\text{Weight in tons} = 300[/tex]

The most reasonable value of [tex]n[/tex] is 300 tons.

Answer:

the answer is the last one

Step-by-step explanation:

i drew all the example and i would say that the last one came out having a proportional relationship.

tell me if i got it right!

Answer:

um i think its 1.42

Step-by-step explanation:

Answer: 372.6 miles

Step-by-step explanation:

81 miles/5 hours = 16.2 mph

Distance traveled in 23 hours = 16.2*23 = 372.6 miles

Sorry this is 4 years late.

Answer:

The approximate distance between the points is 38.2

Step-by-step explanation:

The distance between these two points is a diagonal line. In order to solve this problem, you need to plot your points and form a right triangle.  The overall distance from one point to another on the x-axis is 26 (12-(-14)), and the overall distance from one point to another on the y-axis is 28 (20-(-8)).  These two distances will form a right angle at (-14,-8).  The distances on the x and y axis are the 'legs' of the triangle and the distance between the given points in the problem represents the hypotenuse.  Using the pythagorean theorem (a^2 +b^2 = c^2), we can substitute in our values of 'a' and 'b' to get 28^2 + 26^2 = c^2, or 784 + 676= 1460, therefor the square root of 1460 is approximately 38.2.

So to find the distance between these two points, we are going to be plugging them into the Distance Formula and solving as such:

[tex]D=\sqrt{(12-(-14))^2+(-8-20)^2}\\D=\sqrt{(26)^2+(-28)^2}\\D=\sqrt{676+784}\\D=\sqrt{1460}[/tex]

Now, with this radical we can simplify it using the product rule of radicals (√ab = √a × √b) as such:

[tex]\sqrt{1460}=\sqrt{10*146}=\sqrt{5*2*2*73}=2*\sqrt{73*5}=2\sqrt{365}[/tex]

In short: