Lukas is running a lemonade stand on a hot summer day. He spent $14 for the materials and earns $1.50 for each cup of lemonade sold. What is an equation that relates the number of cups of lemonade sold, c and the profit earned, P, and explain whether Lukas selling 19.5 cups is a viable solution.

Answer:

y = -3/2x + 3

Step-by-step explanation:

Answer:

y= 3 - 2x

Step-by-step explanation:

Answer:

The equation of the parallel line is

y = 3x + 9

Step-by-step explanation:

The general equation of a straight line is given as;

y = mx + c

where m is the slope and c is the intercept

If two lines are parallel, their slopes are equal

So the slope of the new line too is 3

Using the point-slope formula

y-y1 = m(x-x1)

y-12 = 3(x-1)

y-12 = 3x-3

y = 3x-3 + 12

y = 3x + 9

Answer:

375 paying customers

Step-by-step explanation:

First you need to find how much the fee was increased from $5.00 to $7.50

7.5 - 5 = 2.5

Then how many times the pay increase goes into that number to find your X value

2.5/.5 = 5

Now that we have found our x value lets plug it into the equation to find the money the park will make in increments of 1

500 - 25(1) = 475

500 - 25(2) = 450

500 - 25(3) = 425

500 - 25(4) = 400

500 - 25 (5) = 375

Answer:

375

Step-by-step explanation:

Answer:

10

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Answer:

10 meters

Step-by-step explanation:

You can count each unit since each unit equals 1 meter

Answer:

see explanation

Step-by-step explanation:

(a)

9n = [tex]\frac{15}{7}[/tex] - 2 ( multiply through by 7 to clear the fraction )

63n = 15 - 14 = 1 ( divide both sides by 63 )

n = [tex]\frac{1}{63}[/tex]

(b)

[tex]\frac{1}{3}[/tex] = k - 4 ( multiply through by 3 to clear the fraction )

1 = 3k - 12 ( add 12 to both sides )

13 = 3k ( divide both sides by 3 )

[tex]\frac{13}{3}[/tex] = k

(c)

g - [tex]\frac{2}{5}[/tex] g = 3 ( multiply through by 5 to clear the fraction )

5g - 2g = 15

3g = 15 ( divide both sides by 3 )

g = 5

(d)

[tex]\frac{3}{7}[/tex] w + 2w = 3 ( multiply through by 7 to clear the fraction )

3w + 14w = 21

17w = 21 ( divide both sides by 17 )

w = [tex]\frac{21}{17}[/tex]

Answer:3

Step-by-step explanation: it’s exactly 3

Sandra purchased three t-shirts

65-23=42

42/3=14

Answer:

128

Step-by-step explanation

Turn 40% into a decimal by placing a decimal point 2 places to the left making it 0.40. Then, calculate using 320 multiplied by 0.40 which is 128.

Answer:

the answer is 128.

40% of 320 = 128 :)

Answer:

Thus the surface area of this cylinder involving pie is:

[tex]A=750\pi[/tex] ft²

or

[tex]A\approx 2356.19[/tex] ft²

Step-by-step explanation:

Given

radius = r = 10 ft

height = h = 15 ft

The surface area of a cylinder formula is:

[tex]A=2\pi rh+2\pi r^2[/tex]

substituting the value = r = 10 ft and h = 15 ft

[tex]\:A=\left(2\times \:\pi \:\times \:15\times 10\right)+\left(2\times \pi \:\times \:15^2\right)\:[/tex]

[tex]A=750\pi[/tex] ft²

Thus the surface area of this cylinder involving pie is:

[tex]A=750\pi[/tex] ft²

or

[tex]A\approx 2356.19[/tex] ft²

Answer:

5x+x=132

Step-by-step explanation:

132/6=22

22*5=110

Charlie weighs 110 pounds and Tali weighs 22 pounds.

Answer:

I don't have any favorites. There is a reason for this, i don't read a lot of books but when i do, i usually like a mashup of different types of text styles. I guess i do have a favorite of a mashup. When i do read i usually pick a book that has an argument between different characters, a type of fiction memoir? And autobiography.

This mashup usually leads up to Wonder which is one of my all-time favorites. But there is another one i like and it is Diary of a Wimpy Kid. The only thing about that one is that doesn't have the whole autobiography part.

I like these styles because most of the books that i read have either funny traits or intense traits which, i love both of them.

Step-by-step explanation:

Answer:

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 3

Step-by-step explanation:

The recursive formula lets us find a term in the sequence by adding the common difference d to the previous term.

Here d = a₂ - a₁ = - 9 - (- 6) = - 9 + 6 = - 3 , thus

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 3 with a₁ = - 6

Answer:

the length of each piece is 4.8 feet

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

I'm not sure how to answer this. How you need to do is take the two smaller sides and add them. If they are greater than the largest side, you can make a triangle.

I would say that the statement is false. If you subtract, you could get a minus number, and that would be an absurd result.

Answer:

KILOLITER

Step-by-step explanation:

Answer milliletres

Step-by-step explanation:

Answer:

[tex]t = 4[/tex]

Step-by-step explanation:

Baxter Tree Service:

Per tree trimming charges = $42

Additional charges for removing the trimmings from the property = $75.50

Number of trees trimmed = [tex]t[/tex]

Total charges = Additional charges + cost of trimming [tex]t[/tex] trees

Total charges = $75.50 + $42[tex]t[/tex]

Barron and Son:

Per tree trimming charges = $37

Additional charges for removing the trimmings from the property = $95.50

Number of trees trimmed = [tex]t[/tex]

Total charges = Additional charges + cost of trimming [tex]t[/tex] trees

Total charges = $95.50 + $37[tex]t[/tex]

Now, the total charges need to be same and we have to find the value of [tex]t[/tex].

[tex]75.50+42t = 95.50+37t\\\Rightarrow 42t-37t=95.50-75.50\\\Rightarrow 5t=20\\\Rightarrow \bold{t =4}[/tex]

[tex]t = 4[/tex] number of trees must be trimmed.

Answer:

Step-by-step explanation:

Y+6=3y-30

Subtract y from the left

6=2y-30

Add 30 to both sides

36=2y

Divide by 2

18=y

2x+29=4x-47

Subtract 2x

29=2x-47

Add 47

76=2x

Divide by 2

38=x

Answer:

The dimensions of the carpet are 15 inches and 82 inches

Step-by-step explanation:

Assume that the width of the carpet is x inches

∵ The width of the carpet is x inches

∵ The length of the carpet is 67 inches more than the width

∴ The length of the carpet is (x + 67) inches

∵ The perimeter of the rectangle = 2(length + width)

∵ The perimeter of the carpet = 194 inches

→ Equate the two right sides of the perimeter

∴ 2(length + width) = 194

→ Divide both sides by 2

∴ length + width = 97

→ Substitute the value of the length and width in the equation above

∵ x + 67 + x = 97

→ Add the like terms in the left side

∴ (x + x) + 67 = 97

∴ 2x + 67 = 97

→ Subtract 67 from both sides

∵ 2x + 67 - 67 = 97 - 67

∴ 2x = 30

→ Divide both sides by 2

∴ x = 15

∵ x represents the width of the carpet

∴ The width of the carpet is 15 inches

∵ The length of the carpet = 15 + 67

∴ The length of the carpet is 82 inches

∴ The dimensions of the carpet are 15 inches and 82 inches

Answer:

About 50% percent

Step-by-step explanation:

20 is 50 percent of 40, so 21 is about 50 percent (52.5 %)

~theLocoCoco

Answer:

52.5%

Step-by-step explanation:

21/40 = 52.5/100

52.5/100= 52.5%

im not sure but you can try :<

Answer:

5 hot dogs packs at least and 4 buns packs at least

Step-by-step explanation:

Answer:

x = -8.4 and -223.6

Step-by-step explanation:

I 'foiled' and simplied, then graphed; x-intercepts (listed above) were the x-intercepts

Answer:

Domain = [tex](-\infty,6)\;\cup\;(6,\infty)[/tex]

Range = [tex](-\infty,1)\;\cup\;(1,\infty)[/tex]

vertical asymptote is at [tex]x=6[/tex]

Step-by-step explanation:

Domain is all the x values, with an asymptote, it is just a line that approaches a number but never reaches it. The vertical asymptote if you look at x, the lines look like the come from infinity on the left and right, try to reach 6 but can't.

Range is all the y values, with an asymptote, it approaches a number but never reaches it. The horizontal asymptote if you look at y, the lines look like the come from infinity on the top and bottom, try to reach 1 but can't.

Answer:

None of the options match

Step-by-step explanation:

First let's check option 1: lines 2 and 3.

line 2 in mx+b form: y=-1/16x -5

line 3, already in mx+b form: y=-6x-7

if it was perpendicular, the slopes should have been -1/16 and 16 or -6 and 1/6.

now for the 2nd option: lines 1 and 2.

line 1 in mx+b form: y=-8x-5

line 2 in mx+b form: y=-1/16x-5

Again, the slopes do not match, they should have been -8 and 1/8 or -1/16 and 16.

For the 3rd option: all lines

this is obviously wrong since lines 1, 2 and 2, 3 are not perpendicular themselves. No need to bother checking this option.

Lastly, 1 and 4.

line 1 in mx+b form: y=-8x-5

line 4 --> y+3=18x-18 --> y=18x-21

This is also wrong since the slopes should have been -8 and 1/8 or 18 and -1/18.

To conclude, I think the answer is none. None of the combinations on here are perpendicular anyways...

Answer:

D

Step-by-step explanation:

We have the four lines:

[tex]\displaystyle\text{Line 1: }y+8x&=-5 \\\\ \text{Line 2: } x+\frac{1}{6}y&=-5\\\\\text{Line 3: } y&=-6x-7 \\\\\text{Line 4: } y+3&=\frac{1}{8}(x-1)[/tex]

Remember that for two lines to be perpendicular, their slopes are negative reciprocals of each other.

So, let’s determine the slope of each line.

For Line 1, we can rewrite our equation as:

[tex]y=-8x-5[/tex]

So, the slope of Line 1 is -8.

We can rewrite Line 2 as:

[tex]\displaystyle \begin{aligned} \frac{1}{6}y&=-x-5\\y&=-6x-30\end{aligned}[/tex]

So, the slope of Line 2 is -6.

The slope of Line 3 is also -6.

And the slope of Line 4 is 1/8.

So, the slopes of perpendicular lines must be negative reciprocals.

The negative reciprocal of -8 (slope of Line 1) is 1/8. We multiply by a negative and then take the reciprocal.

Since the slope of Line 4 is 1/8, this means that Lines 1 and 4 are perpendicular.

For Lines 2 and 3, they have the same slope, not negative reciprocals of each other.

So, they will instead of parallel instead of perpendicular.

And Line 1 is perpendicular only to Line 4, and no other line.

Therefore, our answer is D.

Answer:

542

Step-by-step explanation:

-3, 2, 7, 12

-3 + x = 2 x = 5

2 + x = 7 x = 5

7 + x = 12 x = 5

If you want to find the 3rd term in the sequence and you start with the first number, then you do this:

-3 + (2 * 5) = -3 + (10) = 7

The same goes for the 110th term:

-3 + (109 * 5) = -3 + (545) = 542

The formula to find the nth term is:

f(n) = n(0) + (n-1) * 5

Suppose n(0) = -3 then

f(110) = -3 + {(110-1) * 5}

f(110) = -3 + {(109) * 5}

f(110) = -3 + (545) = 542

You can simplyfy f(n) = n(0) + (n-1) * 5

f(n) = n(0) + (n-1) * 5

f(n) = n(0) + (5n-5)

f(n) = n(0) + 5n - 5

f(110) = -3 + (5 * 110) - 5

f(110) = -3 -5 + (550)

f(110) = - 8 + 550

f(110) = 542

Answer:

Option (C) is correct.

Step-by-step explanation:

The given options of the possible equation for the graph are as follows:

[tex](A) y=2\left(\frac{3}{2}\right)^x \\\\(B) y=-2\left(\frac{3}{2}\right)^{-x} \\\\(C) y=2\left(\frac{2}{3}\right)^x \\\\(D) y=-2\left(\frac{2}{3}\right)^{-x} \\\\[/tex]

The given graph is decreasing and at x=0, y=2.

So, first checking the value of the given options for x=0

[tex](A) y=2\left(\frac{3}{2}\right)^0=2\times 1= 2 \\\\(B) y=--2\left(\frac{3}{2}\right)^{-0}= -2\times 1= -2 \; (not\; possible) \\\\(C) y=2\left(\frac{2}{3}\right)^0= 2\times 1= 2 \\\\(D) y=2\left(\frac{2}{3}\right)^{-0} = -2\times 1= -2 \; (not\; possible)[/tex]

As, for x=0, y=2, so options (C) and (D) are not possible, so rejected.

Now, checking the nature (increasing or decreasing) of the given equation by differentiating it.

For option (A),

[tex]\frac{dy}{dx}=2\left(\frac{3}{2}\right)^{x}\times \ln\left(\frac{3}{2}\right)[/tex]

As [tex]\ln \left(\frac{3}{2}\right)=\ln(1.5)>0 \;and\; \left(\frac{3}{2}\right)^{x} >0[/tex]

So, [tex]\frac{dy}{dx}>0[/tex]

Therefore, the function in option (A) is increasing function.

Similarly, for option (C),

[tex]\frac{dy}{dx}=2\left(\frac{2}{3}\right)^{x}\times \ln\left(\frac{2}{3}\right)[/tex]

As [tex]\ln \left(\frac{2}{3}\right)=\ln(0.67)<0 \;and\; \left(\frac{3}{2}\right)^{x} >0[/tex]

So, [tex]\frac{dy}{dx}<0[/tex]

Therefore, the function in option (C) is decreasing function.

As the given graph is decreasing, so, (C)  represents[tex]y=2\left(\frac{2}{3}\right)^x[/tex] the given graph.

Hence, option (C) is correct.

The equation [tex](C) y = 2(\dfrac{2}{3})^{x[/tex] could be the equation to represent the given graph is decreasing.

We have to determine, Which of the following equations could be the equation to represent the given graph.

According to the question,

The given options of the possible equation for the graph are as follows:

The given graph is decreasing and at x = 0, y = 2.

Then,

First checking the value of the given options for x = 0.

For x = 0, y = 2, so options (C) and (D) are not possible, so the options are rejected.

Therefore,

To check the nature (increasing or decreasing) of the given equation by differentiating it.

[tex]\dfrac{dy}{dx} = 2(\dfrac{2}{3})^x \times ln(\dfrac{3}{2})\\\\ln(\dfrac{3}{2}) = ln(1.5) >0 \ and\ (\dfrac{3}{2})^{x} >0\\\\So, \dfrac{dy}{dx}>0\\\\[/tex]

Therefore, The function in option A  is increasing function.

For function c;

[tex]\dfrac{dy}{dx} = 2(\dfrac{2}{3})^x \times ln(\dfrac{2}{3})\\\\ln(\dfrac{3}{2}) = ln(0.67) <0 \ and\ (\dfrac{3}{2})^{x} >0\\\\So, \dfrac{dy}{dx}<0\\\\[/tex]

Therefore, The function in option c is decreasing function.

The given graph is decreasing, so, the function c represents the given graph decreasing.

Hence, option (C) is correct.

To know more about the Graphs click the link given below.

https://brainly.com/question/16351335

Answer:

-3 ( D )

Step-by-step explanation:

Logarithm base 3 of 1/27 is -3.

Answer:

the number is 4

Step-by-step explanation:

we can write this as

x + 15 = 19

now we transpose

x= 19-15

x= 4

Answer:

7 is the answer

Step-by-step explanation:

6 + 1 - 3 of a number = 11

1 - 3 = -2

6 - 2 = 4

so 4 + 7 is 11

Hope it helps!

Answer:

(a) 7 : 5

(b) 19 : 5

Hope this helps :)

Answer:

(a) 5:7 ( 5 new to 7 used). (B) 12:7   (12 books to 7 used ones). You are welcome :)

Step-by-step explanation:

7/16

Steps:

[tex]\frac{1}{2} /\frac{8}{7} =\frac{1}{2} *\frac{7}{8} =\frac{7}{16}[/tex]