Shannon and Kelly spent $135 on gift certificates for their friends during the holidays. If this amount is 5/7 their total spending money, how much spending money did they originally have? Set up an equation and solve.

Here's my step-by-step explanation:

Let's get two facts straight: f(x) is a linear function. It's a line. g(x) is an exponential function. It's a curve.

Method 1: Elimination using f(x)

For f(x), the y-intercept (where on the y-axis it coincides with) in {f(x) = 7/3x - 3} is -3. And the only graph that has that is Graph 2.

Alright, so the first obvious solution, according to that graph, is (0, -3). And since we're speaking in terms of x (thus f(x) and g(x)), we pick the x-value from that coordinate and get 0.

The second solution is not as obvious; it's supposed to be (3,4) but the graph is kinda off. I attached a Desmos graph so you can see what I'm talking about a little more clearly.

Anyway, since we're speaking in terms of x we pick the x-value from that coordinate and get 3. Nice, we've got the solutions 0 and 3.

Hope this helps, let me know if I made a mistake.

Answer: C. 3.2 × 10^4

Step-by-step explanation:

for this case the multiplication of the values with exponent are summed, as the exponent are the 6 and -3

6 - 3 = 3

this will be the exponent of the common value which is the 10.

after you only need to multiply 8 and 4 by separate the

8 * 4 = 32.

then we only need to place the values one by one

32 × 10^3

3 is the result of the sum of the exponent.

10 is the common value.

32 is the result of the product.

if we add another zero to the multiplication we get 3.2 and exponent finish with one more zero, then we get this result

3.2 × 10^4

because of that the C is the correct answer, keep in mind that the other answers do not apply correctly the rule of the exponent, because the rest of answer give us wrong answer with final result of the exponent.

To simplify the expression (8 × 10^6) × (4 × 10^-^3) in scientific notation, we multiply the numbers (8 x 4) and add the exponents (6 + -3) resulting in 32 x 10^3. To represent the coefficient within the range of 1 and 10, we revise 32 as 3.2 x 10 yielding the answer 3.2 x 10^4.

To answer the question, 'Which shows the expression below in simplified form? (8 × 10^6) × (4 × 10^-^3)', we need to understand the rules for multiplying numbers in scientific notation. To multiply two numbers in scientific notation, we multiply the coefficients (the numbers) first and separately add the powers of ten.

Here, the coefficients are 8 and 4 which multiply to give 32. The powers of ten are 10^6 and 10^-3. When multiplying powers of 10, we add the exponents, so 6 + -3 = 3. Therefore, the simplified form of the expression is 32 × 10^3. However, in scientific notation, we usually want the coefficient to be a number between 1 and 10. Therefore, we rewrite 32 as 3.2 x 10 to get the final answer: 3.2 x 10^4. So, the correct answer is option D. 3.2 x 10^4

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Answer:

Step-by-step explanation:

To find the equation of a parallel line, we first need to find the slope of 3y + 7 = 2x.

We need to find it because, if two lines are parallel, then that means they have the same slope.

The best way to do this is solve for y:

[tex]3y+7=2x\\3y=2x-7\\y=\frac{2}{3}-\frac{7}{3}[/tex]

Due to the rule that in y = mx + b, m = the slope, we find that the slope is 2/3.

Now we use that slope in the same formula to find b of the line we're trying to find the equation for, and then we'll have our answer. We find b by plugging in (2, 6) for x and y:

[tex]y = mx+b\\y=\frac{2}{3}x+b\\6=\frac{2}{3}(2)+b\\18=4+3b\\ 14=3b\\\frac{14}{3} = b[/tex]

So our line is:

[tex]y=\frac{2}{3}x+\frac{14}{3}[/tex]

To find the equation of a line parallel to a given line and passing through a given point, first find the slope of the original line. Then, using the slope-intercept form of a line, substitute the given point's coordinates and the slope to find the equation of the parallel line.

To find an equation of the line parallel to 3y+7=2x and passing through point (2,6), we need to find the slope of the original line and then use it to create the equation of the parallel line. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.

The given equation 3y+7=2x can be rearranged to y = (2/3)x + 7/3.

The slope of this line is 2/3. Since a line parallel to another line has the same slope, the slope of the parallel line is also 2/3.

Using the point (2,6) and the slope 2/3, we can use the slope-intercept form to find the equation of the parallel line: y = (2/3)x + b. Plugging in the coordinates of the given point, we get 6 = (2/3)(2) + b.

Solving for b, we find that b = 5/3. Therefore, the equation of the line parallel to 3y+7=2x and passing through (2,6) is y = (2/3)x + 5/3.

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Answer:

75

Step-by-step explanation:

1200+9X=25X

1200=25X-9X

1200=16X

X=1200/16

X=75

To find the number of tote bags a company needs to sell in order to cover its costs, we need to set its daily costs equal to its daily revenue and solve for the number of bags. In this case, the solution to the equation indicates that the company needs to sell 80 tote bags each day to break even.

The subject of this question is business mathematics, specifically the mathematical concept of break-even point. The break-even point is the point at which total revenue equals total expenses, and the business is neither losing nor making money. In this case, the fixed costs, or overhead expenses, total $1200 per day, while the variable costs are $9 per tote bag. We can express daily costs, C, as C = $1200 + $9x, where x represents the number of tote bags. The daily revenue, R, is R = $25x. To find the number of tote bags needed to break even, you set C equal to R and solve the resulting equation $1200 + $9x = $25x. Solving this equation yields x = 80. Therefore, the company needs to sell 80 tote bags each day in order to break even.

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Answer:

(p×2)+3

Step-by-step explanation:

I'm not too sure, I've only just started practicing this stuff?

Answer:

11:16

Step-by-step explanation:

The ratio cannot be simplified any further.

Final answer:

The slope of the line represented by the equation 2x + 5y = 10, passing through points (5, 0) and (0, 2), is calculated as -2/5, meaning the slope is negative two-fifths.

Explanation:

The slope of the line represented by the equation 2x + 5y = 10 can be calculated by using the coordinates of two points through which the line passes. In this case, the points are (5, 0) and (0, 2). According to the slope formula, slope (m) is defined as the change in y (the rise) over the change in x (the run). Therefore, the slope is:

The slope of the line is negative two-fifths (-2/5). Since the slope is negative, this indicates that as the x-value increases, the line moves down the y-axis.

Answer:

Jamie has 14 dimes and 26 nickels

Step-by-step explanation:

nickels : x

dimes : y

[tex]x + y = 40 \\ x = y + 12 \\ \\ replace \: x \:in \: the \: first \: equation \\ y + 12 + y = 40 \\ 2y = 28 \\ y = 14[/tex]

Jamie has a total of 40 coins out of which there are 14 dimes and 26 nickels.

Let x represent the number of dimes. Since Jamie has 12 more nickels, the number of nickels is x + 12.

The total number of coins is 40, so x + x + 12 = 40.

Solve for x:

2x + 12 = 40, 2x = 28

x = 14.

Answer: 12x3−21x2+67x−15

Step-by-step explanation:

(3x−5)(4−9x)+(2x+1)(6x2+5)

=12x+−27x2+−20+45x+12x3+10x+6x2+5

=12x+−27x2+−20+45x+12x3+10x+6x2+5

=(12x3)+(−27x2+6x2)+(12x+45x+10x)+(−20+5)

=12x3+−21x2+67x+−15

Answer:

12x^3 - 21x^2 + 67x - 15!

Step-by-step explanation:

Answer: B is the answer

Step-by-step explanation:

Why? It is equal to 0

Answer:

d. -24/-6 - 4​

Step-by-step explanation:

Use order of operation (PEMDAS) to solve.

There are no parentheses.

There are no exponents.

There is multiplication and/or division. Do this first, from left to right.

There is addition and/or subtraction. Do this second, from left to right.

Solve. Remember that a negative times (or divided by) a negative makes a positive.

-24 / -6 = 4

4 - 4 = 0

Check your work. None of the other expressions are equal to 0.

a. -24 / 6 - 4 = -4 - 4 = -8

b. -24 / -6 + 4 = 4 + 4 = 8

c. 24/6 + 4 = 4 + 4 = 8

Answer: 12 inches cubed

Step-by-step explanation:

volume=length x width x height

volume=1.5 in x 2 in x 4 in

volume=12 in^3

Answer:

36

Step-by-step explanation:

Number of boys = 30

also, Number of boys = 10(number of girls/2)

∴ 30 = 10(number of girls/2)

30×2 = 10(number of girls)

⇒ number of girls = [tex]\frac{60}{10}[/tex]

⇒ number of girls = 6

Total number of girls and boys = 30 + 6 = 36

The missing digit in this numbers are 11

Answer:

see explanation

Step-by-step explanation:

64x + 27 ← is not a sum of cubes. We would require

64x³ + 27 ← sum of cubes and factors as

64x³ + 27 = (4x + 3)(16x² - 12x + 9)

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

3 divided by 1 is 0.33 repeating

Answer: 10 : t = 16   11 : x = -8   13 : x = 0

Step-by-step explanation: Im sure about 10 and 11 but not too sure about 13 and explanations are too hard for me to explain

Answer:

384

Step-by-step explanation:

If 48 is 50% of something, that means

48 + 48 = 96. Now, what number is 96 25% of? well 96 • 4 = 384. Now let's do the math backwards!

25 % of 384 is 96. 50 % of 96 is 48! so your answer is 384! Hope this helps!!!

Answer:

384

Step-by-step explanation:

If 48 is 50% of something, that means

48 + 48 = 96. Now, what number is 96 25% of? well 96 • 4 = 384. Now let's do the math backwards!

25 % of 384 is 96. 50 % of 96 is 48! so your answer is 384! Hope this helps!!!

Step-by-step explanation:

Answer:

[tex]-\frac{5}{14}[/tex]

Step-by-step explanation:

When you add fractions, sometimes you have to raise a number to make it more easier for you.

As in this case, we have two fractions in which seem to not be the same, but note this.

7 is multiple of 14, meaning to make our life easier, we can do this method:

[tex]\frac{2 * 2}{7 * 2}  = \frac{4}{14}[/tex]

Whoa! Now we have the same denominator for both fractions, now we made this problem way more easier than it was before.

Do the math:

[tex]\frac{-9 }{14} + \frac{4}{14}[/tex]

==> [tex]-\frac{5}{14}[/tex]

The fraction in the simplest form is -5/4.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

Operators who let do a basic mathematical calculation.

* Multiplication operation: Multiplies values on either side of the operator

For example 12*2 = 24

We have been given that expression of fraction as

⇒ -9/14 + 2/7

We have to determine the fraction in the simplest form.

⇒ -9/14 + 2/7

Take the LCM,

⇒ (-9 + 2×2)/7

⇒ (-9 + 4)/7

⇒ -5/4

Therefore, the fraction in the simplest form is -5/4.

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Answer:

x = 31

Step-by-step explanation:

Let x: total amount of questions in the Chemistry test.

Then 52% represents the ratio of questions properly answered vs total questions:

[tex]\frac{Correct}{Total} = 52%[/tex]

The number of correct questions is the number of total questions take the number of missed questions.

[tex]Correct questions = Total questions - missed questions[/tex]

Since, missed questions = 15

[tex]\frac{x-15}{x} = 52%[/tex]

Also, 52% can be expressed as 0.52. Then, the expression can be rewritten as:

[tex]\frac{x-15}{x} = 0.52[/tex]

Then, rearranging:

[tex] x - 15 = 0.52x [/tex]

[tex] x - 0.52x = 15 [/tex]

[tex] 0.48x = 15 [/tex]

[tex] x = 15/0.48 [/tex]

[tex] x = 31.25 [/tex]

Rounding to the nearest unit: x = 31

Answer:

[4, -1]

Step-by-step explanation:

Using the Elimination Method:

3x + y = 11

5x - y = 21

__________

8x = 32

__ ___

8 8

x = 4 [Plug this back into both equations to get the y-coordinate of -1]; -1 = y

The y's are already additive inverses [result in 0], canceling each other out.

I am joyous to assist you anytime.

Answer:

67.5 seconds

Step-by-step explanation:

I can run faster :D

Find the mean of the runner's speeds as (72 + 63)/2 = 67.5

The runners take 67.5 seconds to cover 1/4 mi if Joel can run around a 1/4 mi track in 72 sec and Jason can run around the track in 63 seconds.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

It is given that:

Joel can run around a 1/4 mi track in 72 sec and Jason can run around the track in 63 seconds.

The runners start at the same spot and run in opposite directions.

The runner's speeds = (72 + 63)

The time they take = 135/2        

The time they take = 67.5 seconds

Thus, the runners take 67.5 seconds to cover 1/4 mi if Joel can run around a 1/4 mi track in 72 sec and Jason can run around the track in 63 seconds.

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Answer:

1.256637061 x 10 (to the power of 20)

Step-by-step explanation:

Just apply these digits into your calculator.

Answer:

see the picture 8.1 is answer

Answer:

H

Step-by-step explanation:

The total cost of the call is $2.50

Since the first three minutes cost $0.60

x minutes = $2.50 - $0.60

x minutes = $1.9

Each additional minutes cost $0.17

So: $1.9 / $0.17 = 11

To find the total minutes

$0.60 + $1.9 = $2.50

3 + 11 = total minutes

14 = total minutes

Answer:

1. False

2. c. (1, -7)

3. Input= 1 and 4; Output=6, 12 and 18. The rule is the input×3

Step-by-step explanation:

1. 8+4=±5+7

8+4= 12 & ±5+7= 2

The left side  12  does not equal to the right side  2 , which means that the given statement is false.  

2. I'm not sure how to show my work.

3.

Input: 0, 1, 2, 3, 4, 5, 6

Output: 0, 3, 6, 9, 12, 15, 18

0×3=0; 1×3=3; 2×3=6; 3×3=9; 4×3=12; 5×3=15; 6×3=18

1. The equation is false.

2. The ordered pair that is a solution of the equation y = -11x + 4 is (-1, -7).

3. The rule for the table is to square the input and add 3.

1. Given

8 + 4 = -5 + 7

12 = 2

The left side of the equation is 12, and the right side of the equation is 2. 12 is not equal to 2, so the equation is false.

2. The ordered pair that is a solution of the equation y = -11x + 4 is (-1, -7).

To see this, we can substitute the x-value of -1 into the equation and solve for y:

y = -11(-1) + 4

y = 11 + 4

y = 15

We can also substitute the y-value of -7 into the equation and solve for x:

-7 = -11x + 4

-11x = -11

x = 1

Therefore, the ordered pair (-1, -7) satisfies both sides of the equation, so it is a solution.

The other ordered pairs do not satisfy both sides of the equation. For example, if we substitute the x-value of 0 into the equation, we get y = 4, which does not equal -7.

3. The rule for the table is square the input and add 3.

To see this, we can look at the first few rows of the table:

Input | Output

-------|--------

0      | 3

3      | 12

9      | 28

We can see that squaring the input and adding 3 gives us the output for each row. For example, squaring the input of 0 gives us 0, and adding 3 gives us 3, which is the output for the first row.

We can also see that this rule works for all of the rows in the table. Therefore, the rule for the table is to square the input and add 3.

Here is the completed table:

Input | Output

-------|--------

0      |    3

3      |    12

9      |    28

16     |    45

25    |    64

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Answer:

5/6

Step-by-step explanation:

Let x = 0.8333.....

Then 10x = 8.333...

Now we subtract x from 10x.

               10x = 8.333...

       -           x = 0.833...

    -----------------------------

                  9x = 7.5

9x = 7.5

9x/9 = 7.5/9

x = 7.5/9 = 15/18 = 5/6

Answer: 5/6

The repeating decimal .83 repeating is equal to the fraction 83/99 in simplest form. A repeating decimal can be expressed as a fraction using the method of setting up equations, exploiting the fact we know which digits are repeating.

To express the repeating decimal .83 repeating as a fraction in simplest form, we first need to understand what a repeating decimal is. A repeating decimal is a decimal fraction in which a digit or group of digits repeats infinitely. In the case of .83 repeating, the group of digits that is repeating is '83'. This means that the decimal can be written out as .838383..., and so on, infinitely.

To represent this as a fraction, we can use the method of setting up a pair of equations. Let's define the repeating decimal like this: x = .8383... . Now, multiply x by 100 since there are two repeating digits, yielding the equation: 100x = 83.8383... . Subtract the first equation from this to give 99x = 83, or x = 83/99 when simplified. So, the decimal .83 repeating is equal to the fraction 83/99 in simplest form.

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Answer:

3

Step-by-step explanation:

1 Donut, 4 Bagels/2 donuts, 3 bagels/3 donuts, 2 bagels, 3 combinations that are possible

The answer is choice A.

Answer:

the answer is A that stuff is real easy