PART A: Maria rented a coat at $285 for 3 days. If she rents the same coat for 60 days, she has to pay a total rent of $510. Write an equation in standard form to represent the total rent (y) that Maria has to pay for renting the coat for x days.
PART B: Write the equation obtained in Part A using function notation.
PART C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals.

Answers

Answer 1

1) Name the variables

Number of days: x

rent: y

2) state the initial points

   x           y
days        $

3           285

60           510

3) assume linear relation:

=> (y - yo) / (x - xo) = (y1 - yo) / (x1 - xo)

=> (y - 285) / (x - 3) = (510 - 285) / (60 - 3)

=> (y - 285) / (x - 3) = 225 / 57 = 75 / 19

=> 19 (y - 285) = 75 (x - 3)

=> 19y - 19*285 = 75x - 75*3

=> 19y - 75x = 5415 - 225

=> 19y - 75x = 5190

=> standar form = -75x + 19y = 5190

PART B: Write the equation obtained in Part A using function notation.

-75x + 19y = 5190

=> 19y = 5190 + 75x

=> y = 5190/19 + (75/19)x

=> function notation = f(x) = (75/19)x + 5190 / 19

PART C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals.

1) Coordinate axes:

x: number of days

y: rent

2) draw the two given points: (3,285) and (60, 510)

3) draw the line that joins those points from the interception of the y-axis until some points further (60, 510).

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Answer: The original area of the square is 64 square feet

-------------------------------------
-------------------------------------

Let x be the original side length of the square. The original area is therefore going to be x*x = x^2. For now we don't know the area but once we figure out x, we can compute the area.

The original side length x is increased by 7 ft to jump up to (x+7) ft
At the same time, the other dimension is reduced to (x-2) ft, which is a decrease of 2 ft

The old square is x ft by x ft with area x*x = x^2

The new rectangle is (x+7) ft by (x-2) ft

Let's find the area of this rectangle

Have a look at the image attachment to see how to multiply out (x+7)*(x-2) using the box method

The terms in red are x^2, 7x, -2x and -14 which are found by multiplying the headers

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The like terms are 7x and -2x which combine to 5x

Overall the result of multiplying out (x+7)*(x-2) is x^2+5x-14

Note: we can get the same result if we use the FOIL or distribution rule. The box method is a handy way to visually keep track of all the terms.

-------------------------------------

The area of the rectangle, in terms of x, is x^2+5x-14

We are told that the area is 90 square feet

So equate the two expressions and solve for x

x^2+5x-14 = 90
x^2+5x-14-90 = 90-90
x^2+5x-104 = 0
(x-8)(x+13) = 0 ... see note below
x-8 = 0 or x+13 = 0
x = 8 or x = -13

note: find two numbers that multiply to -104 and add to 5. Those numbers are -8 and 13 which helps us factor

We ignore x = -13 as a negative side length makes no sense

The only practical root is x = 8

The side length of the original square is 8 feet

The area is
x*x = 8*8 = 64 square feet

We can check the answer by adding 7 to 8 to get 15, and subtracting 2 from 8 to get 6. The 8 by 8 square turns into a 15 by 6 rectangle. Since 15*6 = 90, we have confirmed the right answer.

A trail is 2940 miles long. it begins in city a and ends in city
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Answers

Final answer:

Manfred has hiked 1260 miles of the trail, which is calculated by multiplying the total length of the trail (2940 miles) by the fraction of the trail he has completed (3/7).

Explanation:

To calculate the distance Manfred has hiked on the trail, we multiply the total length of the trail by the fraction of the trail he has completed. In this case, Manfred has hiked three sevenths (3/7) of the trail. The total distance of the trail is 2940 miles.

Distance Hiked = (Total Distance of Trail) × (Fraction of Trail Completed)

Distance Hiked = 2940 miles × (3/7)

Distance Hiked = 2940 miles × 0.4286

Distance Hiked = 1260 miles

Therefore, Manfred has hiked 1260 miles of the trail.

Johnny is reading a novel for the read-a- Thon. The ratio of the number of pages she read to the pages that remain to be read is 7:3. If the book contains 500 pages in all, how many pages did Johnny reed and how many pages remain left?

Answers

There are several ways to answer this question and I will use this approach. Since Johnny reads at a ratio of 7:3 it can be stated that for every 10 pages in a book containing 500 pages Johnny will read 7 of those pages. There are 50 groups of 10 in a 500-page book (50 x 10). Take the ration 7:3 times 50 and use the distributive property: 7:3(50) = (7 x 50):(3 x 50) = 350:150. Based on this Johnny has read 350 pages and has 150 pages remaining.

$40 is discounted into $32 what is the percent decrease

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about 28.5 percent is the decrease I hope this helps :)

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In all there would be 17 guests. Including Cindy.

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it would be graph W because the cost will increase, so that gets rid of Y... It has to start at 40 for the original cost, getting rid of Z and X

W is correct. the red line starts at 40 which is the initial fee

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The answer is C. 6. I hope this helps!

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empire state building

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HELP PLEASE:

What is the point-slope form of the line with slope 25 that passes through the point (−4, −7)?

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Answers

y - y1 = m(x - x1)
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Answer:

Correct option is:

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Step-by-step explanation:

The point-slope form of the line with slope m and passing through the point (x1,y1) is given by:

y-y1=m(x-x1)

Here, we are given line with slope m=2/5

and passing through (x1,y1)=(-4,-7)

i.e. x1= -4 and y1= -7

[tex]y-(-7)=\dfrac{2}{5}(x-(-4))[/tex]

[tex]y+7=\dfrac{2}{5}(x+4)[/tex]

Hence, Correct option is:

y+7=2/5(x+4)

PLZ HELP
Mrs. Kuss received a $50 Itunes gift card for her birthday. She bought one album for $9.99 and would like to see how much money she has left to buy single songs. If each song costs $1.29, how many songs can Mrs. Kuss buy with her remaining money? Show your work.

Answers

Mrs kiss can buy about 31 songs

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She initially has $50 and she bought an album of $9. 99 so you subtract those $9.99 from $50 and you are left with $40.01, now you can either divide it by $1.29 to skip the long process or subtract $1.29 at a time. Once you do so, you will get an answer of 31 more songs with $0.02 left. YOU'RE WELCOME :D

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Answers

11 / 3 = 55 / 15;
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The mass of biscuits left after Jason eats 2/5 of the packet is approximately 0.8 kg.

To find the mass of the biscuits left after Jason eats 2/5 of the packet, we need to calculate the mass of the biscuits he ate and then subtract it from the initial mass of the packet.

Given:

Mass of the packet of biscuits = 1 1/3 kg

First, let's convert 1 1/3 kg to an improper fraction:

1 1/3 = 3/3 + 1/3 = 4/3 kg

Now, to find the mass of the biscuits Jason ate, we can use the fact that he ate 2/5 of the packet:

Mass of biscuits Jason ate = (2/5) * (4/3) kg

Now, perform the multiplication:

Mass of biscuits Jason ate = (8/15) kg

To find the mass of biscuits left, we subtract the mass Jason ate from the initial mass of the packet:

Mass of biscuits left = 4/3 kg - 8/15 kg

To subtract fractions, we need to find a common denominator, which is 15 in this case:

Mass of biscuits left = (20/15) kg - (8/15) kg

Now, perform the subtraction:

Mass of biscuits left = 12/15 kg

Finally, let's simplify the fraction:

Mass of biscuits left = (12/15) * (1/3) kg

Mass of biscuits left ≈ 0.8 kg

Therefore, the mass of biscuits left after Jason eats 2/5 of the packet is approximately 0.8 kg.

For more details of mass :

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Please Help With This. What is the equation of the line shown in this graph? Answer your answer in the box.

Points are:
(-2,-3) (3,-3)

Answers

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -2}}\quad ,&{{ -3}})\quad % (c,d) &({{ 3}}\quad ,&{{ -3}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-3-(-3)}{3-(-2)} \\\\\\ \cfrac{-3+3}{3+2}\implies \cfrac{0}{5}\implies 0[/tex]

[tex]\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-3)=0[x-(-2)] \\\\\\ y+3=0\implies y=-3[/tex]

What is the next term in the sequence 1/2 1/6 1/18 1/54

Answers

1/162
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1. Can √72 be completely simplified if it is broken up as √72=√9x8, explain why or why not?

2. How do you determine the result of taking the square root of a variable raised to an even power? For example √x∧28?

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sqrt72 = sqrt(9x8) = 3sqrt8 = 3(sqrt(4x2)) = 3(2sqrt2) = 6 sqrt(2)

2. sqrt x = x^½. Rules of indices states for a power of a power, you times them.
so (x^28)^½ = x^14

For an arithmetic sequence where a1 = 13 and the common difference is 3, find s7.

A. 162
B. 157
C. 154
D. 151

Answers

sn=n/2[2a+(n-1)d]
s7 means n=7

a7=7/2[2(13)+(7-1)(3)]=7/2(44)=154

Ans:C

Answer:

C. 154

Step-by-step explanation:

Here we have given that,

First Term a₁ = 13

Common Difference d = 3

Term (n ) = 7

so, we have arithmetic sequence: 13, 16, 19, 22,... and so on

Thus Sum of first 7 terms = [tex]\frac{n}{2} [2a+(n-1)d][/tex]

= 7÷2 [2*13 + (7 - 1)*3 ]

= 3.5 [ 26 + 21 ]

= 154

When the function f(x) is divided by x-2 the quotient is 3x^2+8x-4 and the remainder is 9 find the function f(x) and write the result in standard form?

Answers

dividend ÷ divisor = quotient + remainder
∴ dividend = divisor(quotient) + remainder ... there is a reason why I am not multiplying the remainder by the divisor in this case... your remainder is not represent as a fraction with the divisor as the denominator..

[tex]f(x)=(x-2)(3x^2+8x-4)+9=3x^3+8 x^{2} -4x-6 x^{2} -16x+8+9[/tex]
[tex]f(x)=3x^3+2x^2-20x+17[/tex]

The expression for the function f(x) in standard form is f(x) = 3x³ + 2x² - 20x + 17 if the function f(x) is divided by x-2.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

When the function f(x) is divided by (x - 2) the quotient is 3x² + 8x - 4 and the remainder is 9

By using the division algorithm:

f(x) = (x - 2)(3x² + 8x - 4) + 9

After simplification:

f(x) = 3x³ + 8x² - 4x - 6x² - 16x + 8 + 9

f(x) = 3x³ + 2x² - 20x + 17

Thus, the expression for the function f(x) in standard form is f(x) = 3x³ + 2x² - 20x + 17 if the function f(x) is divided by x-2.

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Maybelle looked at a hotel. She waited a week before she decided to book nights at that hotel, and now the prices have increased. The original price was $1195. The price for the same room and the same number of nights is now $2075. What is the percent increase? Round to the nearest whole percent. Explain and Show your work.

-20 points. Better yet, 30 points!! Please help!

Diff in price = %
_________ _________ thats the formula i think...
original price 100

Answers

The formula for percent increase is (final-initial)/initial*100
Plug in to get (2075-1195)/1195*100
880/1195*100
.7364*100
73.64% rounding we get
74%

if MN = PQ AND PQ = RS then MN = RS

Answers

The answer for this problem would be : true

hich is an example of a proportional relationship?

A.The yogurt shop charges .30 per pound.
B.The yogurt shop charges .30 per pound plus $1.00 for the cup.
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B im sure plz like and put 5star

is (3,4) a solution of y=-x+5

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3=x
4=y

4=-3+5

So no it’s not.

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