Kim's furniture store is offering a 30% discount on all its armchairs. Using a proportion, find the discount of the price of an armchair that originally cost $266.00.

Answer:

2(4x - 3)

Step-by-step explanation:

Factor 3(x-2) + 5x

8x - 6

= 2(4x - 3)

Answer:

(a)

let m represents renting movie and c represents the total cost of buying a rental card.

As per the given statement: A video store charges $10 for a rental card plus $2 per movie.

⇒ c(m) = 2m + 10                      ......[1]

which implies that this equation represents the slope intercept form(i.e y = ax+b) where 2 is the slope and a y-intercepts of 10.

(b)

Graph of the given equation:

c(m) = 2m + 10

you can see in the figure given below.

(c)

now, to find the cost of buying a rental card and renting 6 movies.

⇒ m = 6 [ as m represents renting movie]

Substitute this m =6 in equation [1];

c(6) = 2(6) + 10

c(6) = 12 + 10

c(6) = 22.

Therefore, the total cost of buying a rental card and renting 6 movies is, $22.

Answer:

a ≠ 2b

Step-by-step explanation:

The given expression is

[tex]\frac{8ab^{2}x}{4a^{2}b-8ab^{2}}[/tex]

[tex]=\frac{8ab^{2}x}{4ab(a-2b)}[/tex]

Simplifying it, we have

[tex]\frac{8ab^{2}x}{4a^{2}b-8ab^{2}} = \frac{bx}{a-2b}[/tex]

For the above fraction to exist, the denominator must not be equal to zero.

i.e, a-2b ≠ 0

=> a≠2b

∴ The algebraic fraction exists when a≠2b.

Answer:

A valid exclusion for the algebraic fraction is when a=2b

Step-by-step explanation:

You have:

[tex]8ab^2x/4a^2b-8ab^2[/tex]

First you must to simplify:

Taking out common factor 4ab

[tex]4ab(2bx)/4ab(a-2b)[/tex]

[tex]2bx/a-2b[/tex]

The fraction can be written only if  the denominator is different to zero, then

a-2b[tex]\neq[/tex]0

the excluded values are where  

a-2b=0

this expression is equal to 0 when a=2b

Answer:

10.8

Step-by-step explanation:

7.2 X 1.5 = 10.8

Assuming  two houses are 1.5 inches apart on the map. The actual distance between the houses is 10.8 miles.

Let x represent the actual distance

Given:

1 inch = 7.2 miles

1.5 inch =? miles

Hence:

1/ 7.2 = 1.5/ x

x= 7.2×1.5

x=10.8 miles

Inconclusion assuming  two houses are 1.5 inches apart on the map. The actual distance between the houses is 10.8 miles.

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Answer: Option 'c' is correct.

Step-by-step explanation:

Since we have given that

Number of students who are interested in being on the team = 9

Number of positions to fill on his basket ball team = 3

So, the combinations of the three positions he can choose for the team is given by

[tex]3\times 9=27[/tex]

Hence, Option 'c' is correct.

The coach can choose 84 different combinations of the three positions from 9 interested students for the basketball team.

The coach needs to choose 3 out of 9 students to fill the positions on his basketball team. This is a combination problem, and the number of ways to choose [tex]\( r \)[/tex] items from [tex]\( n \)[/tex] items is given by the combination formula:

[tex]\[ C(n, r) = \frac{n!}{r!(n-r)!} \][/tex]

Here, [tex]\( n = 9 \) (number of students) and \( r = 3 \)[/tex] (number of positions to fill).

[tex]\[ C(9, 3) = \frac{9!}{3!(9-3)!} \][/tex]

[tex]\[ C(9, 3) = \frac{9!}{3!6!} \][/tex]

[tex]\[ C(9, 3) = \frac{9 \times 8 \times 7}{3 \times 2 \times 1} \][/tex]

[tex]\[ C(9, 3) = \frac{504}{6} \][/tex]

[tex]\[ C(9, 3) = 84 \][/tex]

So, the coach can choose from 84 different combinations for the team positions.

The correct answer is:

B: 84

Final answer:

The equation of the line with an x-intercept of -4 and a y-intercept of 2 is y = 0.5x + 2. We found this by calculating the slope using the two given points and then using the slope-intercept form to construct the equation.

Explanation:

To write the equation of the line with an x-intercept of -4 and a y-intercept of 2, we can use the two intercepts as points on the line: (-4,0) and (0,2). We can find the slope using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are points on the line. For our points this would be:

m = (2 - 0) / (0 - (-4)) = 2 / 4 = 0.5

Once we have the slope, we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. Since the y-intercept is given as 2, we can write:

y = 0.5x + 2

This is the equation of the line with the given intercepts.

[tex]\dfrac{o+4m+p}{6}=e\qquad\text{multiply both sides by 6}\\\\o+4m+p=6e\qquad\text{subtract o and 4m from both sides}\\\\\boxed{p=6e-o-4m}[/tex]

First find the difference

160-40=120

Take the difference and divide it by the original number

120/160=0.75

Multiply by 100

75

The point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

We have the slope m = 4 and the point (-1, -3). Substitute:

[tex]y-(-3)=4(x-(-1))\\\\\boxed{y+3=4(x+1)}[/tex]

Answer:

Step-by-step explanation:

About Point Slope Form:

Y - 3 = 4 (x - -1)

Answer:

[tex]A=8.2 cm^2[/tex] or [tex]A=\frac{81}{\pi }[/tex]

Step-by-step explanation:

Since the the formula for the circumference of a circle is [tex]C=2\pi r[/tex] and C is 18, we can substitute and solve for r. After we solve for r, we substitute it into the area formula.

[tex]18=2\pi r\\\frac{18}{2\pi } =\frac{2\pi r}{2\pi }\\2.866=r[/tex]

The formula for the area is [tex]A=\pi r^{2} \\A=\pi 2.866^{2} \\A=8.2 cm^2[/tex]

As a fraction, we would not simplify to a decimal and the solution would be:

[tex]A=\pi r^{2} \\A=\pi (\frac{9}{\pi }) ^{2} \\A=\frac{81}{\pi }[/tex]

Answer:

6-y

Step-by-step explanation:

Six less than y means you take away y from six.

Hope this helps

Answer:

The answer is 8 1/3.

The answer will be 8 1/3

To find the perimeter of a rectangle in terms of x, add up the length and width and multiply by 2.

The perimeter of a rectangle can be found by adding up all four sides. In this case, the length and width of the rectangle are represented by the factors of the area measure:

10x² + 13x - 3 = (2x - 1)(5x + 3)

So the length is (2x - 1) and the width is (5x + 3). The perimeter can be calculated using the formula:

Perimeter = 2(length + width)

Substituting the values, the perimeter in terms of x is:

Perimeter = 2((2x - 1) + (5x + 3))

Simplifying further:

Perimeter = 2(7x + 2)

Perimeter = 14x + 4

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Answer:

Greece had a larger difference ($7.07)

Step-by-step explanation:

Brazil -

18.33 - 12.25 = 6.08

Greece-

16.55 - 9.48 = 7.07

Answer:

Greece has the larger difference between categories

Step-by-step explanation:

Difference in categories of Brazil

[tex]= 18.33 - 12.25\\= 6.08\\[/tex]

Difference in categories of Greece

[tex]= 16.55 - 9.48\\= 7.07\\[/tex]

Thus, Greece has the larger difference between categories

Answer:

The width of the rectangle is [tex]5xy^3[/tex].

Step-by-step explanation:

The area of a rectangle is the product of length and width of the rectangle.

[tex]A=length\times width[/tex]

It is given that the area of the rectangle is [tex]15x^3y^4[/tex] square meters and the length of the rectangle is [tex]3x^2y[/tex].

[tex]15x^3y^4=3x^2y\times width[/tex]

[tex]width=\frac{15x^3y^4}{3x^2y}[/tex]

[tex]width=\frac{3\times 5\times x^2\times xy^3\times y}{3x^2y}[/tex]

Cancel out common factors 3x²y.

[tex]width=5xy^3[/tex]

Therefore the width of the rectangle is [tex]5xy^3[/tex].

Answer:

she has a 70 percent chance of getting a yellow one

Step-by-step explanation:

Answer:

7/10 is your answer.

Answer:

Linear

Step-by-step explanation:

This can be written in slope intercept form (y=-5x+7) and there are no exponents.

Answer:

[tex]\frac{C}{2\pi } =r[/tex]

Step-by-step explanation:

Recall to find the circumference of a circle the formula is [tex]C=\pi d[/tex] or [tex]C=2\pi r[/tex]. Since we need r, we will use the second formula for circumference.

We start by solving for r in the Circumference formula. using inverse operations. We divide both sides (as the inverse of multiply) by 2pi.

[tex]C=2\pi r\\\frac{C}{2\pi } =r[/tex].

Answer: C

Step-by-step explanation:

Answer:

12.=0.06

13. =-5.12

14. =0.5

Step-by-step explanation:

12. .1 + .2 -.3 x.4/.5

.1+.2 -.12/.5

.1+.2-.24

.3-.24=.06

13. 3.2^2

10.24-15.36=-5.12

14. 4.2 x5/6 /10 +3/20

3.5 / 10 + 3/20

0.35+3/20

7/20+3/20=10/20

0.5

Answer: If the rate of change is $1 = 78p, then if you have 160p, how much dollars you will get?

(if p are penys)

100p = 1 pound

if $1 = 78p = 0.78 pound

→ 1  pound = $1/0.78 = $1.28

→ 160*1 pound = $160/0.78 = $205.13

So if you change 160 pounds, you will get 205 dollars and 13 cents.

The number of dollars when 160 pounds is exchanged will be 205.13.

You may multiply the pounds by the exchange rate to get how many dollars you will receive for 160 pounds if the exchange rate is $1 = 78p.

160 pounds multiplied by the 78p to the dollar conversion rate results in:

160 pounds multiplied by 100 pence equals 16,000 pence.

Since there are 100 pence in a pound, we divide the amount in pence by 100 to get dollars:

16,000 p divided by 78p is $205.13

Consequently, if you convert 160 pounds to dollars at the current exchange rate of $1 = 78p, you will get around 124.80 dollars in return.

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Answer:

The cost of soft pretzel is $1.25

Step-by-step explanation:

Let $x be the price of one slice of pizza and $y be the price of one soft pretzel.

1. 9 slices of pizza cost $9x and 5 soft pretzels cost $5y. Together they cost $33.25, then

9x+5y=33.25.

2. 4 slices of pizza cost $4x and 6 soft pretzels cost $6y. Together they cost $19.50, then

4x+6y=19.50.

3. Solve the system of two equations:

[tex]\left\{\begin{array}{l}9x+5y=33.25\\4x+6y=19.50\end{array}\right..[/tex]

Multiplythe first equation by 4, the second equation by 9 and subtract them:

[tex]4(9x+5y)-9(4x+6y)=4\cdot 33.25-9\cdot 19.50,\\ \\36x+20y-35x-54y=133-175.5,\\ \\-34y=-42.5,\\ \\y=\$1.25.[/tex]

Then

[tex]4x+6\cdot 1.25=19.50,\\ \\4x=19.50-7.50,\\ \\4x=12,\\ \\x=\$3.[/tex]

Answer: Each soft pretzel cost $1.25

Step-by-step explanation:

Hi, we have to write an equation for each case:

9 x + 5 y = 33.25

4x +6 y = 19.50

Where x is the price of 1 slice of pizza, and y is the price of each soft pretzel.

Multiplying the first equation by 4, and the second equation by 9

36x +20y =133

36x +54y =175.5

And subtracting the first equation to the second equation

36x +54y =175.5

-

36x +20y =133

____________

34 y = 42.5

Solving for y  

y =42.5/34

y = $1.25

Each soft pretzel cost $1.25

Answer:

X^2 y

Step-by-step explanation:

So now you can make this x^2 y because the ^3 cancels it out

Answer:

x^6/27y

Step-by-step explanation:

(x^2/3y^1/3)^3

x^2 ^3/  (3^3 y^1/3 ^3)

Using the power of power rule, when a power is raised to a power, we multiply the powers.

x^ (2*3)/ (3^3 y^(1/3*3))

x^6/(27 y^1)

x^6/27y

Answer:

24 total students

Step-by-step explanation:

multiply 25 times 18 to get 450 then divide 450 by 75 then you get 6, which is the total amount of girls, so 6 + 18 = 24

x = number of students

75% of x = number of boys

(75/100)*x = 18

0.75x = 18

x = 18/0.75 <--- divide both sides by 0.75 to isolate x

x = 24

So there are 24 students in the class

Note how 18/24 = 3/4 = 0.75 = 75% represents the percentage of boys

Answer:$5.1

Step-by-step explanation: so since theres the 1 in 1.2 we know we have $3.40 right?, yeah so, half of $3.40 is 1.7 so jus add $1.7 to $3.40 wich is $5.1

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (3, 5) and (4, 6). Substitute:

[tex]d=\sqrt{(4-3)^2+(6-5)^2}=\sqrt{1^2+1^2}=\sqrt{1+1}=\sqrt2\approx1.4[/tex]

The distance between the two points is 1.4.

Option D is the correct answer.

The distance between two points of a line is given as:

Distance =  √(c - a)² + (d - b)²

We have,

To find the distance between the two points (3, 5) and (4, 6)

We can use the distance formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Substituting the given values, we get:

d = √((4 - 3)² + (6 - 5)²)

d = √(1² + 1²)

d = √2

To the nearest tenth, the distance is approximately 1.4.

Therefore,

The distance between the two points is 1.4.

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20 cents per apple

1/5=.20

Answer:

976 421; 124 679

Step-by-step explanation:

Part A. Largest number

Leslie's number was 976 421.

This is because the largest numbers are in the positions of largest value.

For example, 9 in the hundred thousands place, the next largest number in the ten thousands place, and so on.

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

Part B. Smallest number

The smallest possible number is 124 679.

The value of the 4 is greater than the value of the 6 because the 4 is in the thousands place and the 6 is only in the hundreds place.

4000 > 600.

Answer:

Estimate is 150 and actual product is 138.

Step-by-step explanation:

To estimate products, we round the numbers to nearest unit place, 10th, 100th, 1000th, and so on.

Given are the numbers 3 and 46.

We can round 46 ≈ 50.

So Estimation would be 3 x 46 ≈ 3 x 50

3 times 5 is 15 and we can add zeros after it.

So estimation is 3 x 46 ≈ 150.

Now actual product would be...

3 times 6 is 18, so we note down 8 and 1 goes to carry over 4.

3 times 4 is 12 and carry 1 will be added in it, so 12 + 1 = 13.

It means the actual product is 3 x 48 = 138.

Answer: (B) a=3, b=3

Step-by-step explanation:

   [tex]\dfrac{(2xy)^4}{4xy}[/tex]

[tex]=\dfrac{2^4x^4y^4}{4xy}[/tex]

[tex]=\dfrac{16x^4y^4}{4xy}[/tex]

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

[tex]=4x^3y^3[/tex]

Answer:

b

Step-by-step explanation:

Answer: D) y = - 1 /2 x + 1

Step-by-step explanation:

Got this right on USA test prep

The equation of the perpendicular line that passes through (6, -2) will be y = - (1/2)x + 1. Then the correct option is D.

If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation of the line is given as,

y = 2x + 8

Then the slope of the line is 2, then the slope of the perpendicular line will be - 1/2. Then the equation is given as,

y = - (1/2)x + c

The equation of the line is passing through (6, -2). Then we have

- 2 = - (1/2)6 + c

- 2 = - 3 + c

c = 1

Then the equation of the line is given as,

y = - (1/2)x + 1

The equation of the perpendicular line that passes through (6, -2) will be y = - (1/2)x + 1. Then the correct option is D.

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