Solve the equation 1/t-2=t/8

Answer:  She has 525 costumers.

Step-by-step explanation:

We know that the costumer base is  [tex]\frac{2}{3}[/tex] residential and  [tex]\frac{1}{3}[/tex] business. This means that:

[tex]\frac{2}{3}=350[/tex] residential customers

Let be "x" the total costumers Athy has and "y" the number of business costumers.

Then "x" must be:

[tex]x=350+y[/tex]

Then, in order to find "y" , we need to multiply the number of residential costumers by  [tex]\frac{1}{3}[/tex] and divide the product by [tex]\frac{2}{3}[/tex] :

[tex]y=\frac{(350)(\frac{1}{3})}{\frac{2}{3} }\\\\y=175[/tex]

Substituting we get that "x" is:

 [tex]x=350+175=525[/tex] costumers

Answer:

Step-by-step explanation:

The slope-intercept form of an equation 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, 5) and (1, -3).

Substitute:

[tex]m=\dfrav{-3-5}{1-1}=\dfrac{-8}{0}\ \bold{!}[/tex]

Dividing by zero is not possible.

The slope does not exist.

Conclusion: this is a vertical line with the equation x = a

From the points

(1, 5) → x = 1, y = 5

(1, -3) → x = 1, y = -3

we have the equation x = 1.

Answer : The correct answer is, [tex]29\frac{62}{7}[/tex]

Step-by-step explanation :

The given expression is:

[tex]10\frac{3}{7}+19\frac{5}{9}[/tex]

Step 1 : Convert mixed fraction into fraction.

[tex]\frac{73}{7}+\frac{176}{9}[/tex]

Step 2 : Taking L.C.M

[tex]\frac{(9\times 73)+(176\times 7)}{63}[/tex]

[tex]\frac{(657)+(1232)}{63}[/tex]

[tex]\frac{1889}{63}[/tex]

Step 3 : Convert fraction into mixed fraction.

[tex]=29\frac{62}{7}[/tex]

Thus, the correct answer is, [tex]29\frac{62}{7}[/tex]

Answer:

(2, 2), (3, 1), (4, 2)

Step-by-step explanation:

y ≥-1/3 x + 2

y < 2x + 3

(2, 2), (3, 1), (4, 2)

(2, 2), (3, –1), (4, 1)

(2, 2), (1, –2), (0, 2)

(2, 2), (1, 2), (2, 0)

I will assume which we determining which set of points is a solution

(2,2) is in all the sets, so we ignore it

Looking at the graph, we do not have negative solutions for y when x >0 so (3,-1) cannot be a solution and (1,-2) cannot be a solution

(2, 2), (3, 1), (4, 2)

(2, 2), (3, –1), (4, 1)   x

(2, 2), (1, –2), (0, 2)   x

(2, 2), (1, 2), (2, 0)

Again looking at the graph (2,0) is not a solution

(2, 2), (3, 1), (4, 2)

(2, 2), (3, –1), (4, 1)   x

(2, 2), (1, –2), (0, 2)   x

(2, 2), (1, 2), (2, 0)  x

Answer:

(2, 2), (3, 1), (4, 2)

Step-by-step explanation:

Answer:

Before Tax: $240

After Tax: $259.20

Step-by-step explanation:

If we are trying to find the original price then here:

216/1.08 = 200

This took away the tax now we need to take away the discount:

200 x 1.2 = 240

Before Tax: $240

After Tax: $259.20

The original after tax price of the flute is $259.20.

The first step is to remove tax from the sales price.  In order to remove tax, divide the sales price by (1 + tax): $216 / 1.08 = $200

The second step is to remove the effect of discount. In order to do this multiply 200 by (1 + discount): 200 x 1.2 = $240.

The after tax original price = $240 x 1.08 = $259.20

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Answer:

15.79%

Step-by-step explanation:

do 95-80 which is 15

then do 15/95 as a fraction then multiply that number by 100 to get 15 15/19 then turn that into a decimal and you get 15.79%

Jillian's percent error in estimating the time it would take her to run 7 miles is 15.79%.

Jillian's percent error in her run can be calculated by taking the absolute value of the difference between her estimated time and actual time, divided by the estimated time, and then multiplied by 100 to get the percentage. Here is the calculation step-by-step:

Therefore, Jillian's percent error in her estimation is 15.79%.

Answer:

48.28

Step-by-step explanation:

2800:58 = 48.28

Answer:

54 is x

Step-by-step explanation:

Sounds like you describing vertical angles. Vertical angles are congruent so that means 2x+2=3x-52

2=1x-52. Subtracted 2x on both sides

54=1x. Added 52 on both sides

54=x. Since 1 times x is x

Answer:

total cost = 150 + 25n

Step-by-step explanation:

total cost = flat fee + cost per person* number of people

total cost = 150 + 25n

Answer:

Step-by-step explanation:

a

Answer:

4/x14y8     -    Last Option

Answer:

Step-by-step explanation:

a - number of lawn that Tim needs to mow

310 < 120 + 30a

190 < 30a

6.333 < a

a > 6.333

Tim needs to mow at least 7 lawns to earn more than $310

Answer:

C

Step-by-step explanation:

The easiest way to determine this is to realize that time is the independent variable (n) and temperature is the dependent variable (a).

From the table, we can plug in the two points (n) into n of each equation and see if that equals the temperature values (a).

A little thinking would get us to plug the numbers in C first.

[tex]a(n)=46-(n-1)*4\\46-(5-1)*4=30[/tex]

Works!!

Now, second number:

[tex]a(n)=46-(n-1)*4\\46-(6-1)*4=26[/tex]

Works!!

Hence, C is the correct answer.

Answer:

[tex]a(n)=46-(n-1) \times 4[/tex]

Step-by-step explanation:

It's important to know that the graph is showing a linear function, which means its equation cannot be exponential. So, choices A and B are not correct here.

To find the correct equation, we could find the slope first with the following formula and the two given points

[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\\ m=\frac{26-30}{6-5}=4[/tex]

Now, we use the point-slope formula to find the equation

[tex]y-y_{1} =m(x-x_{1} )\\y-30=4(x-5)\\y=4x-20+30\\y=4x+10[/tex]

Notice that choice C has the same coefficient of 4, which is the slope of the line. Therefore, that's the right answer.

Let's prove it for [tex]n=6[/tex]

[tex]a(n)=46-(n-1) \times 4\\a(6)=46-(6-1) \times 4=46-20=26[/tex]

As the table shows.

Therefore, choice C is correct.

Step-by-step answer:

Step 1:

find out the amount and direction of the vertical translation.

+3 means translating 3 units up, and -6 means translating 6 units down.

Step 2:

to each of the coordinate pairs, add the value of the translation to the y-coordinate (i.e. the second number of the pair).

For example, if the translation is +3, and if one of the vertices is (4,1), then the image of the vertex is (4,1+3) = (4,4).

Repeat for the rest of the vertices.

Step 3:

Check by graphing both image and preimage to see if the shapes are identical.  If not, look for a mistake in the translation process.

To translate a figure vertically, add the translation value to the y-coordinates of each vertex. For a translation of 'k' units, the new vertices will be (x, y + k). This keeps the shape the same and only changes its position vertically.

To find the coordinates of the image vertices when a figure is translated vertically,

you need to follow these simple steps:

This method ensures that the shape of the figure remains unchanged and it is only shifted up or down vertically.

Answer:

8 pages/ minute

Step-by-step explanation:

To find the rate, we take the pages and divide by the minutes

368 pages / 46 minutes

8 pages/ minute

Answer:

C

Step-by-step explanation:

recall the property [tex]a^{1/b}= \sqrt[b]{a}[/tex]

if we apply this to this case,

[tex]x^{1/4} = \sqrt[4]{x}[/tex]

- [tex]x^{1/4} = - \sqrt[4]{x}[/tex]

Answer:

Heya mate here's the answer

let the 4th angle be x

so 75°+ 75°+75° +x= 360°

=> x= 360 - 225

=> x = 135°  

therefore the 4th angle= 135°

hope this helps

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The y-intercept is the number or constant at the end of the equation.

D sets both of their y-intercepts to -6, so it's correct.

=============================================

Explanation:

Plug x = 0 into f(x)

f(x) = 4x + 1

f(0) = 4(0) + 1

f(0) = 1

The y intercept of f(x) is 1

----------

Now plug x = 0 into g(x)

g(x) = 3^x - 2

g(0) = 3^0 - 2

g(0) = -1

The y intercept of g(x) is -1

----------

Note how the y intercepts are 2 units apart.

Each of the answer choices are in the form of f(x) + M and g(x) + N. The goal is to see which M and N values will be 2 units apart. In this case, that would be choice C where M = -1 and N = 1

We see that f(x) - 1 = f(0) - 1 = 1 - 1 = 0 and g(x) + 1 = g(0) + 1 = -1 + 1 = 0

Therefore, f(x) - 1 and g(x) + 1 have the same y intercept of 0.

Answer:

=13.73 ft²

Step-by-step explanation:

The diameter of the largest possible circle that can be cut out of  a square is equal to the length of the side of the square.

Therefore the diameter of the circle cut from a square of side 8ft =8ft

r=4ft

Area of the remaining board= Area of square- area of circle

=side²-πr²

=8²-π×4²

=64-16π

=13.73 ft²

Answer:

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = (x - h)² + k (h, k) are the coordinates of the vertex

Given y = x² + 7x - 5

To express in vertex form use the method of completing the square

add/subtract ( half the coefficient of the x- term )²

y = x² + 2( [tex]\frac{7}{2}[/tex] )x +[tex]\frac{49}{4}[/tex] - [tex]\frac{49}{4}[/tex] - 5

y = (x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{49}{4}[/tex] - [tex]\frac{20}{4}[/tex]

y = (x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{69}{4}[/tex]

Hence

a = [tex]\frac{7}{2}[/tex] and b = - [tex]\frac{69}{4}[/tex]

Answer:

[tex]-2\dfrac{1}{4}\div\left(-\dfrac{2}{3}\right)=\dfrac{27}{8}=3\dfrac{3}{8}}[/tex]

Step-by-step explanation:

[tex]-2\dfrac{1}{4}\div\left(-\dfrac{2}{3}\right)\qquad\text{the quotient of two negative numbers is positive}\\\\=2\dfrac{1}{4}\div\dfrac{2}{3}\qquad\text{convert the mixed number to the improper fraction}\\\\=\dfrac{2\cdot4+1}{4}\div\dfrac{2}{3}=\dfrac{9}{4}\div\dfrac{2}{3}\\\\\text{dividing by a fraction is the same as multiplying by its reciprocal.}\\\\=\dfrac{9}{4}\cdot\dfrac{3}{2}=\dfrac{9\cdot3}{4\cdot2}=\dfrac{27}{8}\qquad\text{convert to the mixed number}\\\\=3\dfrac{3}{8}[/tex]

Answer: 324π units²

Step-by-step explanation:

The formula for the surface area of a sphere is: A=4πr²

Now we just plug in 9 for r:

A = 4π(9)²

A = 4π*81

A = 324π

Answer:

1018 units^2

Step-by-step explanation:

The surface area of a sphere is given by A = 4pi(r)^2, where r is the radius.

Here, A = 4(3.14159)(9 units)^2 = 1018 units^2, to the nearest integer.

Jerod will need 19 pages to display all his 112 photos.

If you divide 112 by 12 you get 18.6667.

Since Jerod cannot break his paper into a half for the .6667 space, he would need to use 19 pages in total. All his 18 pages will have 6 photos each but his last 19th will have 1 photo left on it.

Hope this helps!!!

Mark as Brainliest Please!!!

Answer: 120 different ways. It is a permutation.

Step-by-step explanation:

Because 1st, 2nd, and 3rd are different positions and the order of placing matters, this is a permutation. (In Combinations, the order doesn’t matter, like in choosing people to be on a team without any positions). The calculation is 6x5x4 because there are 6 competitors who could get first, 5 who could get second (the 6th already has first place), and 4 who could get 3rd ( the other two already have 1st and 2nd place).

The number of ways to award the medals in 120 different ways.

When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.

Given

Because 1st, 2nd, and 3rd are different positions and the order of placing matters, this is a permutation. (In Combinations, the order doesn’t matter, like in choosing people to be on a team without any positions). The calculation is 6x5x4 because there are 6 competitors who could get first, 5 who could get second (the 6th already has a first place), and 4 who could get 3rd ( the other two already have 1st and 2nd place).

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[tex]\bf f(x)=x-1\qquad \qquad g(x)=3\cdot f(x)\implies g(x)=\underline{3(x-1)} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} x&g(x)\\ \cline{1-2} 1&0\\2&3\\3&6 \end{array}\qquad \qquad (\stackrel{x_1}{1}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{6})[/tex]

[tex]\bf slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{6-0}{3-1}\implies \cfrac{6}{2}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=3(x-1)\implies y=\underline{3(x-1)}[/tex]

The table that represents g(x) = 3⋅f(x) when f(x) = x − 1 is that of Option D;

x g(x)

1 0

2 3

3 6

f(x) = x − 1

We want to find; g(x) = 3⋅f(x)

This means that; g(x) = 3(x - 1)

Looking at the options, the input values to be used are x = 1, 2 3.

When x = 1; g(x) = 3(1 - 1 )

g(x) = 0

When x = 2; g(x) = 3(2 - 1)

g(x) = 3

When x = 3; g(x) = 3(3 - 1)

g(x) = 6

Looking at the options, only the table in option D is correct.

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That is true for sure!!!

The statement 1/5⁻² =25 is true.

The statement 1/5⁻² = 25 is true.

To simplify the expression, we can rewrite 1/5⁻² as 5²/1. When we have a negative exponent in the denominator, it moves to the numerator and becomes positive.

Therefore, 1/5⁻² is equivalent to 5²/1.

Since 5² equals 25, we can conclude that 1/5⁻² is indeed equal to 25.

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Answer:

-316

Step-by-step explanation:

Each operation shown in bold is done on the next line.

(-5+1)(((3+6)*2-2)(5)-1) =

= (-4)((9*2-2)(5)-1)

= (-4)((18-2)(5)-1)

= (-4)(16(5)-1)

= (-4)(80-1)

= (-4)(79)

= -316

Answer:

a

Step-by-step explanation:

[tex]\bf Py+qy=-4y+8\implies Py+qy+4y=8\implies \stackrel{\textit{common factor}}{y(P+q+4)}=8 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=\cfrac{8}{P+q+4}~\hfill[/tex]

Answer:

y =  8 / (P + q + 4)

Step-by-step explanation:

Group ALL y terms on the left side:  Py + qy + 4y = 8.

Factor y out of the left side:              y(P + q + 4) = 8

Divide both sides by (P + q + 4):        y =  8 / (P + q + 4)

Answer:

124

Step-by-step explanation:

Answer:

124

Step-by-step explanation:

32 goes into 39 one time, 39-32= 7

bring down the 6

32 goes into 76 two times, 76 - 64= 12

bring down the 8

32 goes into 128 four times, 128 - 128 = 0

So 3968/32 = 124