The equation 5x - 7(x-1) = ax+b has exactly one solution.

Answer:

For 0 hours = $40

For 1 hours = $75

For 2 hours = $110

For 3 hours = $145

For 4 hours = $180

For 5 hours = $215

Step-by-step explanation:

Given equation is:- [tex]C=35n+40[/tex]

where, C=Cost in dollars, n=hours.

Now, Amy charge $40 for service call and $35 for per hour service.

So,

For 0 hours:

[tex]C=35n+40[/tex]

[tex]C=(35\times 0)+40[/tex]

[tex]C=0+40[/tex]

[tex]C=40[/tex]

Therefore for 0 hours Amy charge $40.

For 1 hours:

[tex]C=35n+40[/tex]

[tex]C=(35\times 1)+40[/tex]

[tex]C=35+40[/tex]

[tex]C=75[/tex]

Therefore for 1 hours Amy charge $75.

For 2 hours:

[tex]C=35n+40[/tex]

[tex]C=(35\times 2)+40[/tex]

[tex]C=70+40[/tex]

[tex]C=110[/tex]

Therefore for 2 hours Amy charge $110.

For 3 hours:

[tex]C=35n+40[/tex]

[tex]C=(35\times 3)+40[/tex]

[tex]C=105+40[/tex]

[tex]C=145[/tex]

Therefore for 3 hours Amy charge $145.

For 4 hours:

[tex]C=35n+40[/tex]

[tex]C=(35\times 4)+40[/tex]

[tex]C=140+40[/tex]

[tex]C=180[/tex]

Therefore for 4 hours Amy charge $180.

For 5 hours:

[tex]C=35n+40[/tex]

[tex]C=(35\times 5)+40[/tex]

[tex]C=175+40[/tex]

[tex]C=215[/tex]

Therefore for 5 hours Amy charge $215.

Answer:

We will buy it at $9.95 plus  5% tax because it is slightly cheaper than other price

Step-by-step explanation:

$9.95 x 18 = 179.10 + 5% sales tax(8.95) = 188.055

$9.75 x 18 = 175.50 + 15 = 190.50

hence sales tax can be get back by submitting monthly return file. so the first method is cheaper than second one,

The first shop offers a better price for 18 rolls of film. You will pay [tex]$179.10[/tex]for 18 rolls of film at the first shop.

Let's calculate the total cost for each shop:

For the first shop:

- The price per roll is [tex]$9.95[/tex].

- There is a 5% sales tax.

- The total cost without tax for 18 rolls is [tex]18 rolls * $9.95/roll = $179.10[/tex].

- The sales tax on this amount is 5% of [tex]$179.10[/tex], which is [tex]0.05 = $8.955.[/tex]

- The total cost including tax is [tex]$179.10[/tex][tex]+ $8.955[/tex] [tex]=$188.055.[/tex]

 For the second shop:

- The price per roll is [tex]$9.75.[/tex]

- There is no sales tax.

- The shipping cost is a flat rate of [tex]$15.00.[/tex]

- The total cost for 18 rolls, excluding shipping, is 18 rolls *[tex]$9.75/roll[/tex] [tex]= $175.50.[/tex]

- Adding the shipping cost, the total cost is [tex]$175.50[/tex][tex]+ $15.00 = $190.50[/tex].

 Comparing the two total costs:

- First shop: [tex]$188.055[/tex] (approximately [tex]$179.10[/tex] without rounding the tax)

- Second shop: [tex]$190.50[/tex]

 The first shop offers a better price for 18 rolls of film. You will pay approximately [tex]$179.10[/tex] for 18 rolls of film at the first shop, which is less than the [tex]$190.50[/tex] you would pay at the second shop.

Well, let's see. The problem gave you an ordered pair. In other words, you have an 'x' and a 'y' coordinate. All you need to do is put them into the equation.

Step-by-step explanation:

This means that instead of --

-3x - 3y = 125 + 5y = -20

We would have:

-3(-5)-3(-5) = 125(-5) + 5(-5) = -20

From here, you just simplify it into:

30 = -650 = -20

Since the values are not the same, the ANSWER is NO. The ordered pair does not satisfy the following system of equations.

Final answer:

The ordered pair (-5, -5) does not satisfy either of the two given equations, thus it does not satisfy the system of equations.

Explanation:

To determine if the ordered pair (−5,−5) satisfies the given system of equations, we substitute x with −5 and y with −5 into each equation and check if the left-hand side equals the right-hand side.

For the first equation −3x−3y=12, substituting x and y gives us:

−3(−5) −3(−5) = 15 + 15 = 30 which does not equal 12. Therefore, the pair does not satisfy the first equation.

For the second equation 5x+5y=−20, substituting x and y gives us:

5(−5) + 5(−5) = −25 + −25 = −50 which does not equal −20. Therefore, the pair does not satisfy the second equation either.

Since the ordered pair does not satisfy both equations, we can conclude that (−5,−5) does not satisfy the system of equations.

Answer:

1/4

Step-by-step explanation:

The probability of pulling a blue marble is 5/10 = 1/2

The probability of pulling a blue marble twice is 1/2 * 1/2 = 1/4

Answer:

36

Step-by-step explanation:

when you multiply 2x9 you get 18 and since 2 is half of 4 that means you have to do that twice so do 2x9 again and add both of them up to get a product of 36

The solution to the expression 4 × 9 using 2's facts is;

36

For example; 2 × 5 means double of 5 which is 10.

We are given; 4 × 9

Now, we know that 4 is a double of 2 and so we have;

2 × 2 × 9

Since we want to express the result as a double, let us multiply one of the 2 by 9 and retain the other 2.

2 × 9 means double of 2 and it is 18

Then we now have 2 × 18 which implies double of 18 which is 36.

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Answer for the question No.17

Answer:

[tex]x=28.11\ degree[/tex]

[tex]m\angle\ ABC=28.11\ degree[/tex]

Step-by-step explanation:

Answer for the question No.17

Given:-

[tex]\angle\ BAD=(5x+10)\ degree[/tex]

[tex]\angle\ ADC=(87)\ degree[/tex]

[tex]\angle\ DCB=(3x+10)\ degree[/tex]

Let,[tex]m\angle\ ABC=x[/tex]

In quadrilateral ABCD,

[tex]\angle\ BAD+\angle\ ABC+\angle\ DCB +\angle\ ADC =360\ degree[/tex] ---(sum of angle of quadrilateral is 360 degree)

[tex]\therefore\ (5x+10)+x+(3x+10)+87=360[/tex]

[tex]9x+107=360[/tex]

[tex]9x=360-107[/tex]

[tex]9x=253[/tex]

[tex]x=\frac{253}{9}[/tex]

[tex]\therefore\ x=28.11\ degree[/tex]

SInce x=[tex]m\angle ABC[/tex]

[tex]\therefore\ m\angle\ ABC=28.11\ degree[/tex]

Answer:

$1080 annual

Step-by-step explanation:

200(# of thousands) x 5.4

1080

Answer:

7 erasers

Step-by-step explanation:

Since we know that she bought the same exact amount of pencils and erasers, we can assume that they are the same price. So, to find how many things she can purchase, divide 252 by 18, which will give you 14.

Then, since she bought the same number of pencils and erasers, divide 14 by 2, which is 7. So, Krista bought 7 pencils and 7 erasers.

You can check your work by multiplying 7 by 18 and adding that to 7 multiplied by 18. You'll get 252, which is the amount Krista started with.

Hope this helps! :)

Answer:

14 erasers.

Step-by-step explanation:

Just simple division!

252/18=14

Answer:

4 cuts

Step-by-step explanation:

you first do a vertical cut

then a horizontal cut

then two diagonal cuts

Answer:

4 cuts

Step-by-step explanation:

Answer:

6:24

12:48

Step-by-step explanation:

3 : 12  

 x2

6:24

 x2

12:48

:)

Answer: 1 : 4 and 2 : 8

Step-by-step explanation: To find 2 different ratios that are equal to the ratio 3:12, we first rewrite the ratio 3:12 as the fraction 3/12. Notice that we can find 1 of our equal ratios by simply writing this fraction in lowest terms. if we divide both the numerator and denominator of 3/12 by their greatest common factor of 3, we get the equal ratio 1/4.

Now we can use 1/4 to find another equal ratio. If we multiply both the numerator and denominator of 1/4 by 2, we get the equal ratio 2/8.

Finally, remember to write these ratios using the same form as the original problem. 1 : 4 and 2 : 8.

[tex]\bf G(\stackrel{x_1}{-3}~,~\stackrel{y_1}{7})\qquad H(\stackrel{x_2}{4}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-3)}}}\implies \cfrac{-9}{4+3}\implies -\cfrac{9}{7}[/tex]

Final answer:

After subtracting the manufacturing costs of the computer, monitor, and scanner from the selling price for one unit and multiplying by 408 customers, the approximate total profit is $247,050.00, which rounds to option C. $240,000.00.

Explanation:

To calculate the profit the company makes for each computer sold at $1,196.91 after giving away a monitor and a scanner, we need to subtract the cost of manufacturing the computer, monitor, and scanner from the selling price, and then multiply it by the number of customers. The costs for the computer, monitor, and scanner are $393.29, $151.44, and $46.39 respectively. Therefore, the total cost of manufacturing one set is:

Total cost = Cost of computer + Cost of monitor + Cost of scanner

Total cost = $393.29 + $151.44 + $46.39 = $591.12

The profit for one computer set would then be:

Profit per computer = Selling price - Total cost

Profit per computer = $1,196.91 - $591.12 = $605.79

To find the total profit for 408 customers, we multiply the profit per computer by the number of customers:

Total profit = Profit per computer × Number of customers

Total profit = $605.79 × 408 ≈ $247,060.32

When rounding to the nearest 50 dollars, we get:

Total profit ≈ $247,050.00

The closest answer to this would be option C. $240,000.00.

Answer:

Step-by-step explanation:

The cyclist's speed is 0.35 kilometers per minute. She will travel 0.7 kilometers in 2 minutes.

The question deals with converting speed from kilometers per hour to kilometers per minute, and also calculating distance given a certain time and speed.

First, we convert speed from kilometers per hour to kilometers per minute. There are 60 minutes in an hour, so we divide the speed of the cyclist (21 kilometers per hour) by 60: 21/60 = 0.35 kilometers per minute.

Next, we calculate the distance the cyclist will travel in 2 minutes. Distance equals rate times time, so we multiply the cyclist's speed by the time: 0.35 kilometers per minute * 2 minutes = 0.7 kilometers.

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Answer:

756

Step-by-step explanation:

8(90 +6)-4b

Plug in known values

8(90 + 6) - 4(3)

Solve

720 + 48 - 12

768 - 12

756

Hope this helps :)

n = 15 when p=$213.75 and r=$9.50

Step-by-step explanation:

Given

p = overtime pay

n = number of hours

r = hourly pay rate

It is also given that the pay for working hours varied directly with Number of hours and hourly pay rate jointly

So

It can be denoted as:

p ∝ nr

It can also be written as:

[tex]p = knr[/tex]

where k is the constant of proportionality

Putting the given values of p,n and r in the equation

[tex]103.44 = k * 8 * 8.62\\103.44 = 68.96k\\k = \frac{103.44}{68.96}\\k = 1.5[/tex]

So the equation is now,

p = 1.5nr

Putting

p = 213.75

r = 9.50

[tex]213.75 = 1.5 * n * 9.50\\213.75 = 14.25n\\n = \frac{213.75}{14.25}\\n = 15[/tex]

Hence,

n = 15 when p=$213.75 and r=$9.50

Keywords: Proportion variation

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Answer: 99.

Step-by-step explanation: To answer this, you must reverse the operation to find the number being multiplied. The operation done: multiplication. Multiplication in reverse: division. 495 divided by 5 is 99.

Answer:

The other number is 99.

Step-by-step explanation:

"Ian multiplies a number by 5. The product of the two numbers is 495".

Therefore que know that 5 · x (a number we don't know yet) = 495.

This is an equation.

[tex]5*x=495\\[/tex] - To solve it we need to clear the equation.

Thus,

[tex]x=\frac{495}{5}[/tex]

x = 99

Answer:

[tex]\displaystyle y = -2\frac{1}{2}x + 20\frac{1}{2}[/tex]

Step-by-step explanation:

First, find the rate of change [slope]:

[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-8 + 3}{-5 + 7} = -\frac{5}{2} = -2\frac{1}{2}[/tex]

Then plug these coordinates into the Slope-Intercept Formula instead of the Point-Slope Formula since you get it done swiftly that way. It does not matter which ordered pair you choose:

3 = −2½[7] + b

−17½

[tex]\displaystyle 20\frac{1}{2} = b \\ \\ y = -2\frac{1}{2}x + 20\frac{1}{2}[/tex]

_______________________________________________

8 = −2½[5] + b

−12½

[tex]\displaystyle 20\frac{1}{2} = b \\ \\ y = -2\frac{1}{2}x + 20\frac{1}{2}[/tex]

** You see? I told you it did not matter which ordered pair you choose because you will always get the exact same result.

I am joyous to assist you anytime.

Percent increase in attendance is 42.85% (Approx.)

Given that;

Number of people in first season = 840

Number of people in last season = 1200

Find:

Percent increase in attendance

Computation:

Percent increase in attendance = [(1200 - 840)/840]100

Percent increase in attendance = [360/840]100

Percent increase in attendance = [0.4285]100

Percent increase in attendance = 42.85% (Approx.)

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Final answer:

To find the percent increase in attendance from the first to the last basketball game, the number of people at the beginning is subtracted from the number at the end, the result is divided by the initial number, and then multiplied by 100 to get the percentage, which in this case is approximately 43%.

Explanation:

To calculate the percent increase in attendance from the first to the last basketball game, you subtract the initial number of attendees from the final number of attendees, divide the result by the initial number and then multiply by 100 to get it in percentage form.

The formula for percent increase is:
Percent Increase = ((Final Value - Initial Value) / Initial Value) * 100

Using the provided numbers:

Initial attendance = 840

Final attendance = 1,200

Subtract the initial attendance from the final attendance: 1,200 - 840 = 360

Divide the change in attendance by the initial attendance: 360 / 840 = 0.4286 (approximately)

Multiply by 100 to find the percent: 0.4286 * 100 = 42.86%

Round to the nearest percent: 43% increase.

Therefore, the percent increase in attendance was 43%.

Answer:

y+2=2(x+1)

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(4-(-2))/(2-(-1))

m=(4+2)/(2+1)

m=6/3

m=2

y-y1=m(x-x1)

y-(-2)=2(x-(-1))

y+2=2(x+1)

Answer:

See below

Step-by-step explanation:

Parent function is:

Transformations are:

shifts f(x) 4 units down

stretches f(x) by a factor of 4 away from the x-axis

shifts f(x) 4 units right

compresses f(x) by a factor of toward the y-axis (must be 4)

Answer:

The rate of change in number of subscriber for the six years is 3.62%

Step-by-step explanation:

Given as :

The initial subscriber of newspaper = p = 10225

The subscriber of newspaper after 6 years of publish = P = 8200

The time period = t = 6 years

Let The average yearly rate of change = r%

Now, According to question

The subscriber of newspaper after n years = initial subscriber × [tex](1-\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, P = p × [tex](1-\dfrac{\textrm r}{100})^{\textrm t}[/tex]

Or, 8200 = 10225 × [tex](1-\dfrac{\textrm r}{100})^{\textrm 6}[/tex]

Or, [tex]\dfrac{8200}{10225}[/tex] =  [tex](1-\dfrac{\textrm r}{100})^{\textrm 6}[/tex]

Or, 0.80195 =  [tex](1-\dfrac{\textrm r}{100})^{\textrm 6}[/tex]

Taking power [tex]\dfrac{1}{6}[/tex] both side

So, [tex](0.80195 )^{\frac{1}{6}}[/tex] = [tex]((1 - \frac{r}{100} )^{6})^{\frac{1}{6}}[/tex]

Or, 0.9638 = 1 - [tex]\dfrac{r}{100}[/tex]

Or,  [tex]\dfrac{r}{100}[/tex] = 1 - 0.9638

Or,  [tex]\dfrac{r}{100}[/tex] = 0.0362

Or, r = 0.0362 × 100

i.e r = 3.62

So, The rate of change in subscriber = 3.62%

Hence, The rate of change in number of subscriber for the six years is 3.62% . Answer

Answer:

c. Cos 52 = 17/c

Step-by-step explanation:

sin(x) = cos(90-x)

Based on the given figure if sin52=17/c if trigonometric ratio then the correct option is C)cos38=17/c

The trigonometric functions are the ratio of the sides of a right angled triangle. Sin, cos, tan, cosec, sec,cot are the trigonometric functions.

We have been given sin 52=17/c

We know that sin x= cos(90-x)

sin52=cos(90-52)=cos 38

So the value will be cos38=17/c

Hence the correct answer is cos38=17/c.

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Answer:

Step-by-step explanation:

parallelogram, because the figure has exactly one pair of parallel sides

Answer:

0.8

Step-by-step explanation:

We begin with the expression: [tex]0.5+(-\frac{3}{4} )+0.25-(-\frac{4}{5} )[/tex]

First, we need to convert the fractions into decimals to make this easier.

[tex]-\frac{3}{4}=-0.75[/tex] and [tex]-\frac{4}{5} =-0.8[/tex]

Once we have this, we can simplify it

[tex]0.5-0.75+0.25-(-0.8)\\\\0.5-0.75+0.25+0.8\\\\0.75-0.75+0.8\\\\0.8[/tex]

Kyle will have more time to play video games

Solution:

From given question,

Kyle’s parents told him that for every 5 hours of homework or reading he completes, he will be able to play 3 hours of video games.

5 hours of homework = 3 hours of video games

Victor’s parents told their son that he can play 30 minutes for every hour of homework or reading time he completed.

1 hour of homework = 30 minutes of playtime

Suppose if victor spends 5 hours doing homework or reading, then he could play,

5 hours of victor homework = 30 minutes x 5 = 150 minutes of play

That is,

150 minutes = 120 + 30 = 2 hours 30 minutes

This 2 hours 30 minutes playtime of victor is less than kyle playtime (which is 3 hours )

So Kyle gets more play time

Answer:

369/10

Step-by-step explanation:

10 1/4=41/4

3 3/5=18/5

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

(41/4)(18/5)=738/20

simplify

369/10

Answer:

36 9/10

How to Solve:

First you must convert 10 1/4 into an improper fraction. To do that you must multiply ten by four and add one. The total of that will become the new numerator and the denominator will stay the same.

10 1/4 → 41/4

Next you should also convert 3 3/5 into an improper fraction. To do that you must multiply three by five and add three. The total of the will become the new numerator and the denominator will stay the same.

3 3/5 → 18/5

Now multiply the numerators.

41 × 18= 738

Now multiply the denominators.

4 × 5 = 20

Apply the new numerator and denominator into a fraction.

738/20

Now you simplify the fraction by dividing both the numerator and denominator by two.

738/20 ÷ 2/2 = 369/10

Finally, the improper fraction must be converted into a mixed fraction.

369/10 → 36 9/10

Therefore, 10 1/4 times 3 3/5 equals 36 9/10

Answer:

Step-by-step explanation:

If the sides are all equal to each other, the figure is a regular octagon. one is given to you below.

Answer:

$104.12

Step-By-Step Explanation:

First divide $416.48 by 4 ↓

                                         $416.48÷4= $104.12

Callie will have $104.12 less than what she earned each month once you take away the money she is paying for car repairs.

Callie will have $104.12 less than what she earned each month once you take away the money she is paying for car repairs.

Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

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Answer: if a=9, b=3, and c=1/3 then...

a^2 ÷ 3 = 9^2÷3

= 27

a^2 + 30 - 18 = 9^2+30-18

= 93

4b^2 · 3 = 4×3^2×3

= 108

ac ÷ (2b) = 9×1/3÷ (2×3)

= 1/2

3c ÷ (2b^2) = 3×1/3 ÷ (2×3^2)

= 1/18

Step-by-step explanation:

With a^2 ÷ 3, you would replace any letters with the number it says to replace it with. so, "a" would be replaced with 9, since it says that a=9. So, once your done with all of that, the equation would become, 9^2÷3.

With a^2 + 30 - 18, you would also, replace any letters with the number it says to replace it with. So, "a" would be replaced with 9, since it says that a=9. So, then after you do all of that, the equation would be, 9^2+30-18.

With 4b^2 · 3, you would do the same thing, you would replace any letters  with the number it tells you to replace it with. So, "b" would be replaced with the number, 3. And if you don't already know... when "b" turns into 3, the number doesn't become 43. When "b", gets changed to 3, it becomes 4×3. So, after all that is done, then the equation would turn into, 4×3^2×3.

With ac ÷ (2b), you would do the same thing that was done above. Start by replacing any letters with the numbers that, it says to replace it with. Which you would replace "a" with 9, "c" with 1/3, and "b" with 3. And like I said above if the letters change to a number the numbers don't just stay as numbers, they get multiplied by each other. like when you change "a" to 9 and "c" to 1/3... it becomes 9×1/3. Same thing with b, when "b" gets changed to 3... since the number 2 is right next to it... it becomes, 2×3. So, after all that is done, the equation turns out to be, 9×1/3 ÷ (2×3).

And last but not least, to solve 3c ÷ (2b^2)... To solve 3c ÷ (2b^2), you would change any letters with the numbers that it says to replace it with. Like changing "c" to 1/3, and "b" to 3. And when changing "c" to 1/3, you'd notice that since 3 is right next to "c", you would multiply them together, 3×1/3. Same thing when changing "b" to 3, you would multiply it by the number it is next to. So, it would be 2×3. So, after all of that is done the equation turns into, 3×1/3 ÷ (2×3^2).

Final answer:

Using the given values (a=9, b=3, c=1/3), the expressions evaluate to 27, 93, 108, 0.5, and 1/18 respectively, after calculation.

Explanation:

To evaluate each expression with the given values a=9, b=3, and c=1/3, we substitute these values into each expression and perform the appropriate arithmetic operations:

[tex]a^2[/tex] ÷ 3 = 92 ÷ 3 = 81 ÷ 3 = 27

[tex]a^2[/tex] + 30 - 18 = 92 + 30 - 18 = 81 + 30 - 18 = 93

[tex]4b^2[/tex] · 3 = [tex]4(3)^2[/tex] · 3 = 4(9) · 3 = 36 · 3 = 108

ac ÷ (2b) = (9)(1/3) ÷ (2(3)) = 3 / 6 = 1/2= 0.5

3c ÷ (2b2) = (3)(1/3) ÷ (2(3)2) = 1 / (2(9)) = 1 / 18 = 0.0556

[tex]y = 1.3x + 3[/tex]