Find the values of x and y that satisfy both equations below.
[tex]27 ^{x - 2} = 9^{y} \\ 32 ^{y - \frac{3}{5} } = \frac{1}{8 ^{2x} } [/tex]
​

Answer:

  t = 36

Step-by-step explanation:

If one of the roots is "a", the equation can be factored as ...

  (5x -a)(x -a) = 0

  5x^2 -6ax +a^2 = 0

Comparing terms to the given equation, we see that ...

  -6ax = -36x

  a = 6 . . . . . . . . divide by -6

Then ...

  a^2 = t

  36 = t . . . . . . . substitute 6 for a

_____

The roots are 6 and 6/5.

Answer:

56x² + 6x - 36

Step-by-step explanation:

(8x-6)(7x+6) = 8x*(7x + 6) - 6*(7x + 6)

= 8x*7x + 8x*6 - 6*7x - 6*6

=56x² + 48x - 42x - 36

= 56x² + 6x - 36

Answer:

The ratio of food costs to take home is 1 : 6.

Step-by-step explanation:

Given:

Carol's monthly take home pay is 1500$. She spends $250 a month on food.

Now, to find the ratio of food costs to take home pay.

Take home pay = $1500.

Cost of food = $250.

So, getting the ratio:

Cost of food : take home pay

$250 : $1500

[tex]=\frac{250}{1500}[/tex]

[tex]=\frac{1}{6}[/tex]

[tex]=1:6[/tex]

Therefore, the ratio of food costs to take home is 1 : 6.

Final answer:

Carol's food costs to take home pay ratio is 1:6, meaning for every six dollars she takes home, she spends one dollar on food.

Explanation:

To calculate the ratio of Carol's food costs to her take home pay, we compare the amount she spends on food to her total monthly take home pay. This can be represented by the ratio 250:1500 or simplified by dividing both numbers by the common factor of 250, which results in the simplified ratio of 1:6. Hence, for every dollar Carol takes home, she spends about one-sixth of it on food.

Answer:

4

Step-by-step explanation:

Because the fact the quits are ll feet there are 6 feet left over but that can not make 11 feet quilt

Answer:y = (19 - 8x)/3

Step-by-step explanation:

add 8x to both sides ,

-3y = -19+8x

dividing both sides by -3

y = (19 - 8x)/3

Answer:

36 apples

Step-by-step explanation:

First, divide 72 by 6 to find out how many apples are in 1 basket.(Answer 12)

There will be 12 apples in one basket.

Mrs. Doolan wants 3 baskets so multiply 12 by 3 to get 36.

72/6= 12

12X3=36

Answer:36 apples

Step-by-step explanation: dividing that will each be 12 apples in a basket. mrs. doolan will recieve three baskets so 12x3. that will equal 36

Answer:

D

Step-by-step explanation:

Put this in statistics in my graphing calculator.

Min Value = 6

Max Value = 30

Q1 = 9

Median = 21

Q3 = 28

Box and whisker plot in D represents this data: 6, 7, 8, 10, 18, 20, 22, 25, 28, 28, 30, 30.

GIven that,
To determine which box-and-whisker plot represents this data: 6, 7, 8, 10, 18, 20, 22, 25, 28, 28, 30, 30.

Statistic is the study of mathematics that deals with relations between comprehensive data.

Here,
A number is given they are arranged in ascending order already,
the median of the data is given as,
Median = [ n / 2 th term + n / 2 + 1 th term] / 2
Median = [ 12 / 2 + 12 / 2 + 1 term] / 2
Median = [6th term + 7 th term] /2
Median = 20 + 22 / 2 = 42/ 2 = 21
Median = 21

Now,

Min Value = 6                     ; Max Value = 30

Q1 = [8 + 10]/2 = 9               ;  Q3 = [28 + 28] / 2 = 28

The data calculated above is represented by the Box and whisker plot in D.

Thus, box and whisker plot in D represents this data: 6, 7, 8, 10, 18, 20, 22, 25, 28, 28, 30, 30.

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Answer:

Step-by-step explanation:

9x+3y=420  ---------- (eq1)

1x+6y=296 -----------(eq2)

to solve by elimination, we first multiply (eq 1) by 2

(eq1) x 2

2(9x+3y)=2 (420)

18x + 6y = 840 -----(eq 3)

eliminate y term by subtracting (eq2) from (eq3)

(eq 3) - (eq 2)

(18x + 6y) - (1x+6y) = 840 - 296

18x + 6y - 1x-6y = 544

18x - 1x = 544

17x = 544 (divide both sides by 17)

x = 544/17 = 32

Since you said that you are not looking for the answer, i will stop here, but to get the y value, subtitute the value of x which we found, back into eq 1 or 2 to find y

Both Adam's expression, d - 0.75d, and Rena's expression, 0.25d, yield the same sale price for the video game, offering different perspectives on calculating the discounted amount.

Adam's expression:

d: represents the original price of the video game in dollars.

-0.75: represents the discount of 75% as a decimal. A negative sign is used to indicate a decrease in price.

d - 0.75d: This expression subtracts the discount (0.75d) from the original price (d) to find the sale price of the video game.

Rena's expression:

0.25: represents the remaining price after the discount, which is 100% - 75% = 25%. This is also expressed as a decimal.

d: represents the original price of the video game in dollars.

0.25d: This expression multiplies the remaining price (0.25) by the original price (d) to find the sale price of the video game.

Both expressions, d - 0.75d and 0.25d, arrive at the same sale price for the video game. They simply represent different mathematical approaches to achieve the same result.

y = -5x + 29 is the equation of line in slope intercept form for the line that passes through (5, 4) and (6,-1)

Solution:

Given that, line that passes through (5, 4) and (6,-1)

To find: Equation of line in slope intercept form

Let us first find the slope of line

The slope of line is given by formula:

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Here given points are (5, 4) and (6, -1)

[tex](x_1, y_1) = (5,4)\\\\(x_2,y_2) = (6, -1)[/tex]

Substituting the values in formula,

[tex]m =\frac{-1-4}{6-5}\\\\m = \frac{-5}{1}\\\\m = -5[/tex]

The equation of line in slope intercept form is given as:

y = mx + c ------------ eqn 1

Where, "m" is the slope of line and "c" is the y - intercept

To find y - intercept, substitute m = -5 and (x, y) = (5, 4) in eqn 1

4 = -5(5) + c

4 = -25 + c

c = 29

Substitute m = -5 and c = 29 in eqn 1 to get equation of line

y = -5x + 29

Thus equation of line in slope intercept form is found

a = –5

Solution:

Given data: [tex]y=-\frac{1}{2}ax[/tex], [tex]m=\frac{5}{2}[/tex]

The standard equation of a line is y = mx + c.

In the line [tex]y=-\frac{1}{2}ax[/tex] can be written as [tex]y=-\frac{1}{2}ax+0[/tex].

The slope of the line [tex]y=-\frac{1}{2}ax+0[/tex] is [tex]m=\frac{-1}{2}a[/tex].

Given [tex]m=\frac{5}{2}[/tex].

Both are slopes of the line. So,we can equate the both slopes.

⇒ [tex]\frac{-1}{2}a=\frac{5}{2}[/tex]

⇒ [tex]a=\frac{5}{2}\times\frac{-2}{1}[/tex]

⇒ a = –5

Hence the value of a is –5.

Answer: 1) 56 cents. 2) 30 CDs

Step-by-step explanation:

1.68 ÷ 3 = 56 cents

60 x 7 = $420

$420/ 14 = 30 CDs

The price per ounce of tomato sauce is 56 cents. Edward can buy 30 CDs for $14 each with the same amount that would buy 60 CDs for $7 each.

To calculate the price per ounce, we take the total cost of the can in cents, which is $1.68 or 168 cents, and divide it by the number of ounces, which is 3 ounces. Thus, the price per ounce is: 168 cents / 3 ounces = 56 cents per ounce.

Edward wants to spend the same amount to buy CDs at $14 each as he would buying 60 CDs at $7 each. The total cost for 60 CDs at $7 each is: 60 CDs x $7/CD = $420. We divide this total cost by the price of one CD at $14: $420 / $14/CD = 30 CDs. Therefore, Edward can buy 30 CDs for $14 each with the same amount of money.

Fraction of students left-handed: [tex]\frac{3}{25}[/tex]

There are more right-handed students

Step-by-step explanation:

To solve the problem, we call:

[tex]p(L)[/tex] the fraction of students in the class that are left-handed

[tex]p(R)[/tex] the fraction of students in the class that are right-handed

We know that:

[tex]p(L) = 12\%[/tex] is the fraction of students which are left-handed

we can convert this value into fractional form dividing by 100:

[tex]p(L)=\frac{12}{100}[/tex]

Simplifying by 4,

[tex]p(L)=\frac{3}{25}[/tex]

We also know that

[tex]p(L)+p(R)=1[/tex], because the fraction of students that are either left or right-handed must be 100%

Therefore, the fraction of students that are right-handed is

[tex]p(R)=1-p(L)=1-\frac{3}{25}=\frac{22}{25}[/tex]

Therefore, there are more right-handed than left-handed students.

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Answer:

The height of the triangle is: [tex]H = (5x^2 + x +3)[/tex]

Step-by-step explanation:

Here, the area the triangle  is given as: [tex]15x^4 + 3x^3 + 4x^2 - x - 3[/tex]

Also, base of the triangle  = [tex](6x^2 -2)[/tex]

Let us assume the height of the triangle = H units

Now, AREA of TRIANGLE =  [tex]\frac{1}{2} \times B \times H[/tex]

[tex]\implies (15x^4+3x^3+4x^2-x-3 ) = \frac{1}{2} \times ( 6x^2-2) \times H\\\implies H =\frac{ (15x^4+3x^3+4x^2-x-3 )}{(3x^2-1)}[/tex]

Solving by LONG DIVISION, we get:

[tex]H = (5x^2 + x +3)[/tex]

Hence, the height of the triangle is: [tex]H = (5x^2 + x +3)[/tex]

Answer:

$13,287

Step-by-step explanation:

As per question, Soft Shoes has sold blue slippers last week for $1,528 which is 11.5% of total sales, In order to find their total sales let us assume that their total sales is 'y'. Now in the form of an equation we write the above statement as:

11.5% of y = $1,528

or

[tex]\frac{11.5}{100}y[/tex] = $1,528

or

0.115 y = $1,528

Dividing the equation by 0.115, we get:

y = [tex]\frac{1528}{0.115}[/tex]

y = $13,286.96

Rounding to the nearest dollar we get:

y = $13,287

Hence their Total Sales will be $13,287.

Margot needs 3/4 pounds of turkey to make 1 liter of turkey chili. To make 4 liters of turkey chili, which is 4 times the recipe, she will need 3 pounds of turkey.

Margot used 1/2 pound of turkey to make 2/3 liters of turkey chili. To find out how much turkey she will need for 4 liters of turkey chili (4 times the 1-liter recipe), we need to calculate the amount of turkey needed per liter first and then multiply it by 4.

First, we determine the amount of turkey needed for 1 liter by setting up a proportion. Since 1/2 pound of turkey makes 2/3 liters, we have:

1/2 pound / (2/3) liter = x pounds / 1 liter

By cross-multiplication, we find that x = (1/2) * (3/2) = 3/4. Therefore, Margot needs 3/4 pounds of turkey for 1 liter of chili.

To make 4 times the recipe, or 4 liters, Margot will need 4 * 3/4 pounds of turkey = 3 pounds of turkey.

Answer:

40%

Step-by-step explanation:

First, divide 100 by 20. You do this because you need something out of 100 to equal a percent. (Example- 50 out of 100 is 50%)

Next you need to take the number you got from dividing (5) and multiply that with 8. This leaves you with 40/100 or 40%.

Hope this helps!

-Coconut;)

Answer:

40%

Step-by-step explanation:

The total number of students are '20'. Moreover the number of boys out of that 20 students are '8'.

So to find the percentage of the number of boys, take 8 (number of boys) divided by 20 (the total) and times that by 100, which will give you the percentage.

This is how it goes...

[tex]\frac{8}{20}[/tex] × 100 = 40%

∴ 40% of the class is made up of boys.

8 : 1 is the ratio of the areas of these similar rectangles

Solution:

Given that, rectangle has an area of 25 square feet

A similar rectangle has an area of 200 square feet

To find: Ratio of the areas of these similar rectangles

Ratio of the areas of these similar rectangles can be found dividing the area of rectangles

[tex]\rightarrow \frac{\text{ Area of rectangle}}{\text{Area of similar rectangle}} = \frac{200}{25}[/tex]

Reduce the fraction to lowest term

[tex]\rightarrow \frac{\text{ Area of rectangle}}{\text{Area of similar rectangle}} = \frac{200}{25} = \frac{8}{1}[/tex]

In ratios we get,

Area of rectangle : Area of similar rectangle = 8 : 1

Thus 8 : 1 is the ratio of the areas of these similar rectangles

Answer:

Part 1) [tex]y=650(1.1^x)[/tex]

Part 2) Approximate 1,152 monkeys

Step-by-step explanation:

Part 1) Write an exponential function to model the monkey population

we know that

The exponential function is of the form

[tex]y=a(b^x)[/tex]

where

y is the population of monkeys

x is the number of years

a is the initial value or y-intercept

b is the base of the exponential function

r is the percent rate of change

we have

[tex]a=650\ monkeys\\r=10\%=10/100=0.10[/tex]

[tex]b=1+r=1+0.10=1.10[/tex]

substitute

[tex]y=650(1.1^x)[/tex]

Part 2) What will the approximate population be after 6 years?

For x=6 years

substitute the value of x in the exponential equation

[tex]y=650(1.1^6)=1,151.5\ monkeys[/tex]

Approximate 1,152 monkeys

Answer:

[tex]p(Not\ 5) = \frac{8}{9}[/tex]

Step-by-step explanation:

Given:

Txo six-sided dice are rolled.

Total number of outcomes n(S) = 36

We need to find the probability that the sum is not equal to 5 p(Not 5).

Solution:

Using probability formula.

[tex]P(E)=\frac{n(E)}{n(S)}[/tex]  ----------------(1)

Where:

n(E) is the number of outcomes favourable to E.

n(S) is the total number of equally likely outcomes.

The sum of two six-sided dice roll outcome is equal to 5 as.

Outcome as 5: {(1,4), (2,3), (3,2), (4,1)}

So, the total favourable events n(E) = 4

Now, we substitute n(E) and n(s) in equation 1.

[tex]P(5)=\frac{4}{36}[/tex]

[tex]p(5) = \frac{1}{9}[/tex]

Using formula.

[tex]p(Not\ E) + p(E) = 1[/tex]

[tex]p(Not\ 5) + p(5) = 1[/tex]

Now we substitute p(5) in above equation.

[tex]p(Not\ 5) + \frac{1}{9} = 1[/tex]

[tex]p(Not\ 5) = 1-\frac{1}{9}[/tex]

[tex]p(Not\ 5) = \frac{9-1}{9}[/tex]

[tex]p(Not\ 5) = \frac{8}{9}[/tex]

Therefore, the sum of two six-sided dice roll outcome is not equal to 5.

[tex]p(Not\ 5) = \frac{8}{9}[/tex]

Answer:

A force is a vector quantity. As learned in an earlier unit, a vector quantity is a quantity that has both magnitude and direction. To fully describe the force acting upon an object, you must describe both the magnitude (size or numerical value) and the direction.

Step-by-step explanation:

Answer:

(x , 1/2x - 5/2)  where x is a real number.

Step-by-step explanation:

-2x + 4y = -10 ⇔ 4y = 2x - 10 ⇔ y = 1/2x - 5/2

then any couple of the form (x , 1/2x - 5/2) is a solution to the equation

example :

let x = 7 then 1/2x - 5/2 = 1/2(7) - 5/2 = 1

in this case  -2x + 4y = -2(7) + 4(1) = -14 + 4 = -10

then (7,1) verify the equation

Answer:

40.5

Step-by-step explanation:

[tex] \frac{35 + 39 + 39+ 43 + 43 + 44}{6} = \frac{243}{6} = 40.5[/tex]

Answer:

Step-by-step explanation:

1/2 (6x-10) - x

Opening bracket

= 6x/2 - 10/2 - x

= 3x - 5 - x

= 2x - 5

Following are the solution to the given expression:

Given:

[tex]\to \frac{1}{2} (6x-10) - x \\\\ [/tex]

To find:

solve x or find the value.

Solution:

[tex]\to \frac{1}{2} (6x-10) - x \\\\ \to \frac{6x}{2} - \frac{10}{2} - x \\\\ \to \frac{6x-10-2x}{2}\\\\ \to \frac{4x-10}{2}\\\\ \to \frac{2(2x-5)}{2}\\\\ \to (2x-5) [/tex]

The final answer is "(2x-5)".

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Answer:to find the difference between 6/8 and 1/7, you need to make the denominators (the bottom numbers) the same. turn 6/8 into 42/56. then turn 1/7 into 8/56. you’ll then do 42/56-8/56. so it’ll be 42-8=36. so it will come out to 36/56, which is (when simplified) is 9/14. your answer will be 9/14.

Step-by-step explanation:

Answer:

Sasha's dad expects to have between 23 and 24 cupcakes with flaw design

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Flaw prediction in the design by the manufacturer = 1 out of 50 cupcakes

Last week production = 98 dozens

2. Approximately how many cupcakes would be expected to have a flaw design?

For answering this question we have to find out the exact number of last week production, this way:

Last week production = 98 dozens

Last week production = 98 * 12 = 1,176

Now, we can calculate the number of cupcakes that would be expected to have a flaw design:

Number of cupcakes with a flaw design = 1,176/50 = 23.52

Sasha's dad expects to have between 23 and 24 cupcakes with flaw design

Answer:

Therefore the store which has the lowest price after discount is Wal-Mart.

Step-by-step explanation:

i) W-Mart       $230       12% off  

After discount the price will be = $230 - ($230 × 0.12) = $202.40

ii)XYZ sports      $255       $50 off  

After discount the price will be = $255 - $50 = $205

iii)Bike City      $270       25% off  

After discount the price will be = $270 - ($270 × 0.25) = $202.50

Therefore the store which has the lowest price after discount is Wal-Mart.

Answer:

  Emma

Step-by-step explanation:

Emma ran (3 1/2)×(1000 m) = 3500 m compared to Grace's 380 m. 3500 m is farther, so Emma ran farther.

Answer:

Option D) B and C          

Step-by-step explanation:

we know that

To find out the percentage of high school teachers that have a second job, divide the number of teachers that have a second job by the total number of teachers

Survey A

[tex]\frac{28}{110}=0.2545[/tex]

Convert to percentage

[tex]0.2545(100)=25.45\%[/tex]

Survey B

[tex]\frac{27}{90}=0.3[/tex]

Convert to percentage

[tex]0.3(100)=30\%[/tex]

Survey C

[tex]\frac{21}{70}=0.3[/tex]

Convert to percentage

[tex]0.3(100)=30\%[/tex]

Survey D

[tex]\frac{32}{80}=0.4[/tex]

Convert to percentage

[tex]0.4(100)=40\%[/tex]

Compare the percentages

Surveys B and C have the same percentage

therefore

Surveys B and C show proportional results, because the ratio of the number of teachers that have a second job by the total number of teachers is equal (this number is the constant of proportionality k in a proportional relationship between two variables)

Answer:

it's A and D :| the other person was incorrect.

Step-by-step explanation:

Answer:

the answer is option D. 52 feet^2