Mona wants to buy carpet for a floor in her house.
The floor is rectangular with a width of 8 m and a length of 9 m.
Two shops sell carpet with the prices shown below.
How much will Mona save by going to Carpet World ?

The equation of the line that is parallel and perpendicular to y = -8x + 6 and passes through the point (7, 5) are y = -8x + 61 and  \(y = \frac{1}{8}x + \frac{33}{8}\) respectively.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the original line:

y = -8x + 6

Using the slope intercept:

Slope m = -8

Since the desired line is parallel, it will have the same slope.

Therefore, the slope of the parallel line is also -8.

Plug in the slope m = -8 and the poin (7,5) into the point-slope form:

( y - y₁ ) = m( x - x₁ )

( y - 5) = -8( x - 7 )

Simplify

y - 5 = -8x + 56

y = -8x + 56 + 5

y = -8x + 61

The equation of the parallel line is y = -8x + 61.

For the perpendicular line:

The slope of the perpendicular line will be the negative reciprocal of -8, which is 1/8.

Hence, plug slope m = 1/8 and point (7,5) into the point-slope form:

( y - y₁ ) = m( x - x₁ )

\(y - 5 = \frac{1}{8} ( x + 7 )\\\\y - 5 = \frac{1}{8}x + \frac{7}{8} \\\\y = \frac{1}{8}x + \frac{7}{8} + 5\\\\y = \frac{1}{8}x + \frac{33}{8}\)

Therefore, the perpendicular line is \(y = \frac{1}{8}x + \frac{33}{8}\).

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Answer:

That is a linear function

Step-by-step explanation:

A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.

If you try to graph that function on a graphing calculator, you will get a straight line.

Therefore, it is a linear function.

mark brainliest please!

Answer:

I think it's a linear one(function)

y=6x÷19

Answer:

x=4

Step-by-step explanation:

The value of x from the given similar triangles is 7 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

The given triangles ABC and DEF are similar triangles.

Here, AB/DE =AC/DF =BC/EF

4/12 =8/3(x+1)

8/3(x+1) =1/3

24=3x+3

3x=24-3

3x=21

x=7

Therefore, the value of x is 7 units.

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The slope of the equation is equal to -3.

The missing values in table should be completed with the ordered pairs below.

In order to use the given linear function to complete the table, we would have to substitute each of the values of x (x-values) into the linear function and then evaluate as follows;

When the value of x = -2, the y-value is given by;

y = -3x

y = -3(-2)

y = 6 ⇒ (-2, 6).

When the value of x = 1, the y-value is given by;

y = -3x

y = -3(1)

y = -3 ⇒ (1, -3).

At data point (-4, 3), a linear function in standard form for this line can be calculated by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 3 = (0 - 3)/(0 + 4)(x + 4)

y - 3 = -3/4(x + 4)

y = -3x/4

At data point (3, 2), a linear function in standard form for this line can be calculated by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 2 = (4 - 2)/(6 - 3)(x - 3)

y - 2 = 2/3(x - 3)

y = 2x/3

When the value of x = -3, the y-value is given by;

y = 2x/3

y = 2(-3)/3

y = -2 ⇒ (-3, -2).

When the value of x = 3, the y-value is given by;

y = 2x/3

y = 2(3)/3

y = 2 ⇒ (3, 2).

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When teaching an 8th grade lesson on problem solving, Sylvia begins by utilizing a short video clip. Sylvia uses this video clip as a discrepant event because students attached with science it would look like magic for them.

A discrepant occurrence is an unexpected, counterintuitive result that differs from what an observer would typically anticipate. Oobleck is a classic illustration of a discrepant event.

Most kids (who have never seen it before) wouldn't anticipate that it would have both solid and liquid qualities. They didn't anticipate it to spread out right away once the "ball" was placed on the table instead of rolling into a ball and taking shape.

The main factor is that pupils will develop an obsession with science. They will see this as "magic," and they will be very interested in learning how it worked. After that, they'll be prepared to "amaze" their friends with both the "trick" and their subsequently displayed "smarts."

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Answer:

  angle PQS = 53°

Step-by-step explanation:

You want the measure of angle PQS given that right angle PQR is divided into angles PQS = 4+7a and SQR = 9+4a.

The angle addition theorem tells you the whole is the sum of the parts:

  ∠PQR = ∠PQS +∠SQR

  90° = (4 +7a)° +(9 +4a)°

  0 = -77 +11a . . . . . . . . . . divide by ° and subtract 90

  7 = a . . . . . . . . . . . . . . add 77 and divide by 11

The measure of angle PQS is ...

  ∠PQS = (4 +7·7)° = 53°

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Answer:

1500t and 2500l

Answer:

15 laptops.

Step-by-step explanation:

You need to find the money earned by selling 10 tablets which is:

1500 x 10 = 15 000

After that, minus the amount of money needed for the goal from the amount of money earned from selling 10 tablets.

52 500 - 15 000 = 37 500

The remaining amount of money is the amount of money you get after finding out how much you make from selling 10 tablets. Use the remaining and divide it with the amount of money needed for each laptop:

37 500 ÷ 2500 = 15

Answer: 15

The x-intercepts are:

t = (15 + √(385)) / 8 ≈ 1.94

t = (15 - √(385)) / 8 ≈ -0.819

To find the x-intercepts of the function, we set f(t) equal to zero and solve for t:

-16t² + 60t + 16 = 0

Dividing both sides by -4 (to simplify the equation) gives:

4t² - 15t - 4 = 0

Using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

with a = 4, b = -15, and c = -4, we have:

t = (-(-15) ± √((-15)² - 4(4)(-4))) / 2(4)

Simplifying:

t = (15 ± sqrt(385)) / 8

Therefore, the x-intercepts are:

t = (15 + √(385)) / 8 ≈ 1.94

t = (15 - √(385)) / 8 ≈ -0.819

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Question: A trucking company operates in three regions of the country. The table below depicts the probability that each  company truck is in the region and the fuel prices per gallon. What amount should the company budget on average  for a gallon of fuel across its operations? Round your answer to the nearest cent.

Answer:

A. $3.53

B. $3.55

C. $3.68

D. $3.70

The amount that the company should put on average for a gallon across the operations is $ 3.70. This option D is correct.

The company of trucks runs operations in several countries as per the table each region has distinct scores of probability and as the company that is farthest from the market has more wages as compared to that is the nearest

The percentage is 100 and probability counts as compared to one. Thus 50% is 0.50. If assuming X is the cost of fuel then using the formula we get.

\(Mean = E (X) = f(xi) xi\)

E(X) = 3.10 x 0.2 +3.5 x 0.3 +4.05 x 0.5 = 3.69 that is 3.70 dollars.

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The complete question is :

A trucking company operates in three regions of the country. The table below depicts the probability that each  company truck is in the region and the fuel prices per gallon. What amount should the company budget on average  for a gallon of fuel across its operations? Round your answer to the nearest cent.

A. $3.53

B. $3.55

C. $3.68

D. $3.70

Answer:

The circle's circumference is approximately 106.81 centimeters.

Explanation:

The formula for the circumference of a circle is C = 2πr, where C is the circumference, π is pi (approximately 3.14), and r is the radius of the circle.

So, for a circle with a radius of 17 centimeters, its circumference can be found by:

C = 2πr

C = 2 x 3.14 x 17

C ≈ 106.81 cm

Therefore, the circumference of the circle is approximately 106.81 centimeters.

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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that log4x=2log16x. (ii)Show that log x=3logb³ x. (iii) Show that log₂x=(1+log₂3)logix

Answer:

1. S

2. G

3. I

4. O

5. P

6. D

7. C

8. F

9. J

10. Q

11. E

12. K

13. R

14. A

15. B

16. N

17. M

18. L

19. H

Step-by-step explanation:

4. O

→ 3 is a coefficient of 3x

5. P

→ 3 is a common factor in the expression 3x+9

6. D

→example of a constant term is 1,3,10

7. C

→ \(cosx=\frac{adjacent}{hypotenuse} =\frac{A}{H}\)

8. F

→\(x^{2} -4\) will be factorised as (x-2)(x+2)

9. J

→ example of an expression is \(2x+9\)

10. Q

→ factors of 3 are 3×1.

11. E

→ example of factoring is \((x+2)(3x+4)\)

12. K

→ example of a factored completely is \(2x(x+y)\)

14. A

→example of a polynomial is \(3yx^{3} +xy^{2} -2x+9\).

15. B

→ example of a quadratic expression is \(x^{2} +6x-9\).

17. M

→ \(sinx=\frac{opposite}{hypotenuse} =\frac{O}{H}\)

18. L

→ \(tanx=\frac{opposite}{adjacent} =\frac{O}{A}\)

19. H

→ example of a term is 2x,3,40

\(\\ \sf\longmapsto z1w2=z2w1\)

\(\\ \sf\longmapsto 15(10)=4z_2\)

\(\\ \sf\longmapsto 4z_2=150\)

\(\\ \sf\longmapsto z_2\approx 38\)

⟼4z

jshsujsjajajenxjnxjde

⟼z

2

≈38

Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.

To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.

For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.

For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.

Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.

Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.

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Garage B is more cost-effective for any parking duration exceeding 2 hours.

When comparing Garage A and Garage B based on their pricing structure, it's important to consider both the flat fee and the hourly rate to determine which option is more cost-effective.

Garage A charges a flat fee of $5, regardless of the duration of parking, and an additional $2 for every hour parked. This pricing structure benefits those who need to park for shorter durations, as the flat fee is relatively low.

However, for longer parking durations, the hourly charge can accumulate significantly, making it less favorable for extended stays.

On the other hand, Garage B follows a different approach by charging a rate of $4.50 per hour with no flat fee. This pricing structure is more suitable for those who require shorter parking times, as they only pay for the exact duration of their stay. In such cases, Garage B would likely be more cost-effective compared to Garage A.

However, for longer stays, Garage A might offer better value. For example, if someone needs to park for 6 hours, Garage A would charge $17 ($5 flat fee + 6 hours * $2/hour) while Garage B would charge $27 ($4.50/hour * 6 hours). In this scenario, Garage A would be the more affordable option.

Ultimately, the choice between Garage A and Garage B depends on the individual's specific parking needs. If the stay is anticipated to be short, Garage B's hourly rate is preferable.

However, for longer durations, Garage A's combination of a flat fee and hourly rate may result in lower overall costs. It's essential to consider the anticipated length of stay to make an informed decision.

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The table that represents a linear equation is the first one, and the line can be:

y = -4x - 1

A general linear function can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Now, notice that if we evaluate the line in x + 1, we will get:

y = a*(x + 1) + b

y = a*x + a + b

So, for an increase of one unit on the variable x, we have a constant increase in the y value.

Now, if you look at the first table, you can see that for each increase of 1 unit on the value of x, the value of y decreases by 4.

So that is the table that can represent a linear function.

And the line is:

y = -4x - 1

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Answer:

The Answer is 45x >200 +20x, I just took A Quiz with this question and got it correct.

Step-by-step explanation:

Answer:

the answer is 45x > + 20x

Step-by-step explanation:

Answer:

y = 1/4x

Step-by-step explanation:

lmk if you want an explanation

The equation of the line that is parallel to a given line and passes through the point (-8,-2) is y = x/4.

A straight line on the coordinate plane is represented by a linear function.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

Let's say the equation of an unknown line in slope y-intercept form is

y = mx + c

Since this is parallel to a line whose slope is 1/4

m  = 1/4

y = x/4 + c

It is passing through (-8,-2)

-2 = -8/4 + c

c = 0

So y = x/4 will be the equation.

Hence "The equation of the line that is parallel to a given line and passes through the point (-8,-2) is y = x/4".

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Step-by-step explanation:

sorry I don't know the answer I want some points so because I do this I really really sorry. and thanks for point

Answer: (a) x = -1

Step-by-step explanation:

Given

x - 8 = - 9

Add 8 on both sides to isolate x

x - 8 + 8 = - 9 + 8

\(\boxed{x=-1}\)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

6.4

Step-by-step explanation:

multiply

Answer:

6.43

Step-by-step explanation:

You are given:

1 mile = 1.6 kilometers

but you want 4 miles so you multiply both of them by 4 so...

1*4 = 1.6*4

That gives you ------> 4 miles = 6.4 kilometers

to solve for m

distribute into parentheses

176 = -16 - 24m

get m on one side

176 + 16 = -24m

192 = -24m

divide by -24

-8 = m

m = -8

Answer: Answer choice B

Step-by-step explanation:

9514 1404 393

Answer:

  B. infinite set of points on the line

Step-by-step explanation:

The lines are identical, so the set of points they have in common is an ...

  infinite set of points on the line

Answer:

uhhh 21

Step-by-step explanation:

19

Answer:

Step-by-step explanation:

g(2)= 5-9(2)

= -13

f(g(2))= 5+3(-13)

= -34

Answer:

g(2) = -13

f(g(2)) = -34

Explanation:

For g(2), just substitute 2 in for the x, multiply, and simplify.

g(x) = 5-9(x)

g(2) = 5-9(2) = 5-18 = -13

For f(g(2)), substitute this output in for x, multiply, and simplify.

f(x) = 5 + 3(x)

f(g(2)) = 5 + 3(g(2)) = 5 + 3(-13) = 5-39 = -34