1) Castel and Rob are selling cheesecakes for a school fundraiser. Customers can buy New York style
cheesecakes and apple cheesecakes. Castel sold 5 New York style cheesecakes and 6 apple cheesecakes
for a total of $85. Rob sold 6 New York style cheesecakes and 6 apple cheesecakes for a total of $90.
What is the cost each of one New York style cheesecake and one apple cheesecake?

Answer:

[tex]V(x) = -\frac{340}{3}x +2220[/tex]

[tex]V(8) = 1313.3[/tex]

Step-by-step explanation:

Given

Let x represent years and V represents the value.

So, we have:

[tex](x_1,v_1) = (0,2220)[/tex]

[tex](x_2,v_2) = (6,1540)[/tex]

Solving (a): The linear function

First, we calculate the slope (m)

[tex]m = \frac{v_2 - v_1}{x_2 - x_1}[/tex]

This gives:

[tex]m = \frac{1540-2220}{6-0}[/tex]

[tex]m = \frac{-680}{6}[/tex]

[tex]m = -\frac{340}{3}[/tex]

The linear function is calculated using:

[tex]v - v_2 = m(x - x_2)[/tex]

Where:

[tex](x_2,v_2) = (6,1540)[/tex]

[tex]m = -\frac{340}{3}[/tex]

So, we have:

[tex]v - 1540 = -\frac{340}{3}(x - 6)[/tex]

Open bracket

[tex]v - 1540 = -\frac{340}{3}x +\frac{340}{3}* 6[/tex]

[tex]v - 1540 = -\frac{340}{3}x +680[/tex]

Make v the subject

[tex]v = -\frac{340}{3}x +680+1540[/tex]

[tex]v = -\frac{340}{3}x +2220[/tex]

So, the function is:

[tex]V(x) = -\frac{340}{3}x +2220[/tex]

Solving (b): When x = 8

Substitute 8 for x in [tex]V(x) = -\frac{340}{3}x +2220[/tex]

[tex]V(8) = -\frac{340}{3}*8 +2220[/tex]

[tex]V(8) = -\frac{340*8}{3} +2220[/tex]

[tex]V(8) = -\frac{2720}{3} +2220[/tex]

Take LCM

[tex]V(8) = \frac{-2720+2220*3}{3}[/tex]

[tex]V(8) = \frac{-2720+6660}{3}[/tex]

[tex]V(8) = \frac{3940}{3}[/tex]

[tex]V(8) = 1313.3[/tex]

Hence, its value after 8 years is 1313.3

Answer:

Alexandram has greater weekly expenses

They charge the same price

Step-by-step explanation:

I got this answer for khan academy!

Answer:

Alexandram

They charge the same price

Step-by-step explanation:

It is the time it takes Amy to hike to the waterfall.

The term [tex]\frac{6}{x}[/tex]  describes the time it takes Amy to hike to the waterfall.

The correct answer is an option (C)

"It is defined as the distance traveled per unit times."

"It defines a relation between input values and output values."

For given example,

Amy hikes 6 miles from a ranger station to a waterfall and back again. She hikes 1 mile/hour faster on the way back.

we have been given a function [tex]T(x)=\frac{6}{x}+\frac{6}{x+1}[/tex]

This function represents Amy's total time spent hiking,

and x represents Amy's hiking speed in miles/hour.

Let 't' be the time required to reach Amy from ranger hills to a waterfall.

As 'x' represents Amy's hiking speed in miles/hour and Amy hikes 6 miles from a ranger station to a waterfall.

Using the formula of speed,

⇒ x = 6/t

⇒ t = 6/x

Therefore, the term [tex]\frac{6}{x}[/tex]  describes the time it takes Amy to hike to the waterfall.

The correct answer is an option (C)

Learn more about the speed here:

https://brainly.com/question/4926312

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Answer:

D

Step-by-step explanation:

y=-x-4

First, we can match the graphs with the y-intercept of -4 given from the equation.

Only graphs C and D crosses the y-axis at -4.

The slope from the equation is -1.

If the slope is a negative number, the line should be negative as well, meaning the line should be going downwards (left to right always)

Out of graphs C and D, only graph D has a line going downwards and a y-intercept of -4.

Hope I was able to help! Good Luck!

Answer:

$25

Step-by-step explanation:

5% of 500 = 0.05 × 500 = 25

Answer:

25$

Step-by-step explanation:

500*.05=25

Hope this helps :0

Answer:

64 degree and 116 degree

Step-by-step explanation:

4y-44+3y+35=180(Linear pair)

7y=189

y=27

4(27)-44=64

3(27)+35=116

Answer:

The inequality describes all possible value of x is 14 < x < 32 ⇒ D

Step-by-step explanation:

In any triangle:

In the given figure

∵ ABC is a triangle

∵ AC = 9 and BC = 21

∵ AB is the third side of the triangle

→ By using the rules above

∴ BC - AC < AB < BC + AC

∵ AB = x - 2

→ Substitute their values in the inequality above

∵ 21 - 9 < x - 2 < 21 + 9

∴ 12 < x - 2 < 30

→ Add 2 to the 3 terms

∴ 12 + 2 < x - 2 + 2 < 30 + 2

∴ 14 < x < 32

∴ The inequality describes all possible value of x is 14 < x < 32

Answer:

answer is C

average speed=distance÷time=120÷4=30

Answer:

(3,-5)

Step-by-step explanation:

its the last answer

Answer:

(3,-5)

Step-by-step explanation:

Hi there!

Since the dot is in the fourth quadrant, our x value will have to be positive. If the value was negative, it would be in the third quadrant.

If you think about the dot’s relation to the y axis, it is below the point of origin, or y = 0, so the y-value will have to be negative.

The only answer that fits this criteria is (3,-5)

I hope this helps!

Answer:

b

Step-by-step explanation:

becuse

Answer:

top right

Step-by-step explanation:

Answer:

≈ 77 cm²

Step-by-step explanation:

The area of the shaded portion is calculated as

area of outer sector - area of inner sector

= (πR² - π r²) × [tex]\frac{60}{360}[/tex] ( R is the outer radius, r is the inner radius )

= (π × 14² - π × 7² ) × [tex]\frac{1}{6}[/tex]

= (196π - 49π ) ÷ 6

= 147π ÷ 6

≈ 77 cm² ( nearest whole number )

Answer:

[tex]A_s=76.97\ cm^2[/tex]

Step-by-step explanation:

Circular Sector

It's the portion of a circle enclosed by two radii and an arc. The area of a sector is calculated as follows:

[tex]\displaystyle A=\frac {r^{2}\theta }{2}[/tex]

Where r is the radius and θ is the central angle expressed in radians. The central angle will be converted to radians:

[tex]\theta=60*\frac{\pi}{180}=1.0472\ rad[/tex]

The shaded region in the figure can be obtained by subtracting the smaller sector A2 area from the larger sector area A1:

[tex]A_s=A_1-A_2[/tex]

The larger area is calculated with a radius of r1=14 cm:

[tex]\displaystyle A_1=\frac {14^{2}*1.0472 }{2}[/tex]

[tex]\displaystyle A_1=102.626\ cm^2[/tex]

The smaller area is calculated with r2=7 cm:

[tex]\displaystyle A_2=\frac {7^{2}*1.0472 }{2}[/tex]

[tex]\displaystyle A_2=25.656\ cm^2[/tex]

The shaded area is:

[tex]A_s=102.626\ cm^2-25.656\ cm^2[/tex]

[tex]\boxed{A_s=76.97\ cm^2}[/tex]

Answer:

y = 10

Step-by-step explanation:

Use the substitution method since you already know what x equals.

4y - 9(y - 3) = -23

Simplify:

4y - 9y + 27 = -23

Combine like terms:

-5y + 27 = -23

Isolate y by subracting 27 from both sides:

-5y = -50

Divide by -5 to get y by itself:

-5/-5 = y

-50/-5 = 10

Answer:   The slope is 5/4  and the  y intercept will  be 2

Step-by-step explanation:

First convert the equation to slope intercept form ( y = mx+b)  where m will be the slope and b will be the y intercept.

5x - 4y = -8      Subtract 5x from both sides

-5x             -5x

  -4y =  -5x - 8     Divide both sides by -5

y =  5/4x  + 2

Answer:

50

Step-by-step explanation:

p/5=10

Your main goal is to isolate p

p/5 = 10, in order to eliminate the 5, multiply 5 on both sides, since it's the inverse of division.

(5)p/5 = 10(5)

p=50

Answer:

Option C

Step-by-step explanation:

[tex]3\frac{1}{5} \times 2\frac{1}{5}[/tex]

Lets convert it into improper fraction.

[tex]\frac{16}{5} \times \frac{11}{5} = \frac{16 \times 11}{5 \times 5} = \frac{176}{25}[/tex]

Lets convert [tex]\frac{176}{25}[/tex] into a mixed fraction.

[tex]=> \frac{176}{25} = 7\frac{1}{25} = 7.04[/tex]

Rounding off 7.04 gives 7 and rounding 7 further gives 10.

So , the estimate of the product is 10

Answer

8

Step-by-step explanation:

8=3+5

Answer:

y=8

Step-by-step explanation:

If x =3 the you would plug 3 into x

y=3+5

3+5=8

y=8

hope this helps

Answer:

5

Step-by-step explanation:

20/5=4

45/5=9

cant simplify farther

Answer:

the answer is 5.

Step-by-step explanation:

Factors for 20: 1, 2, 4, 5, 10, and 20.

Factors for 45: 1, 3, 5, 9, 15, and 45.

Same numbers is 5.

the answer is 5.

Answer:

A)

Side DF=3

Side EF=6/5

Bye

The values of DF and EF are 3 and 6/5 respectively. (option A)

When two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Given that, Δ ABC ~ Δ DEF

The proportion = AB/DE = BC/EF = AC/DF = 5/3

2/EF = 5/3

EF = 6/5

5/DF = 5/3

DF = 3

Hence, The values of DF and EF are 3 and 6/5 respectively. (option A)

For more references on similar triangles, click;

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Answer: need pictures

Step-by-step explanation

9514 1404 393

Answer:

  2 1/12 days

Step-by-step explanation:

Time is the ratio of distance to speed.

  (1200 mi)/(24 mi/h) × (1 day)/(24 h) = 25/12 day = 2 1/12 days

Answer:

0.8= 2.1448=2.1379

Step-by-step explanation:

Answer:

0.8/2.1448/2.1379

Step-by-step explanation:

I got right(Plato/Edmentum

Complete question :

A, B, C and D are four towns. B is 30 kilometres due east of A. C is due 30 kilometres north of A. D is due 45 kilometres due south of A. Work out the bearing of B from C.

Answer:

44°

Step-by-step explanation:

From the diagram sketched, we have a right angled d triangle, thus we can apply Pythagoras ;

Using the relation :

Tanθ = opposite / Adjacent

Tan θ = 30 / 30

Tanθ = 1

θ = tan^-1(1)

θ = 45°

Hence, bearing of B from C is 45°

Answer:

x=200

substitute 15 for y and then solve and get X to the other side

Answer:

She's  3 years old.

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

12/4=3

Answer:

A

Step-by-step explanation:

If 7 out of 9 voted to plant, that means 2 voted against

so the ratio we are looking at here for vote for and vote against is 7:2

So let the total that voted be x

7/9 * x = 119

x = (9 * 119)/7

x = 153

Answer:

Its 0

Step-by-step explanation:ur not smart if u dont know that

Answer:

He spend 75.12

Step-by-step explanation:

First determine the amount of the tip

62.60 * 20%

62.60 *.20

12.52

Add this to the cost of the sandwiches

62.60+ 12.52

75.12

Answer:

He spent  75.12! hope this helps :)

Step-by-step explanation:

Answer:

cant see from the light retake the photo

Step-by-step explanation:

We learnt this way in Turkey.