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Digiron [165]
3 years ago
9

Constance wants to purchase an school jacket. She saw the same jacket at a few stores. Store A had the jacket for 15% off the or

iginal price of $59.60. Store B has it on sale for $50.99. Determine which is the better buy? What is the total price after 6% sales tax at this store?
Mathematics
1 answer:
GREYUIT [131]3 years ago
3 0

Answer:

Store A is better buy.

$53.70

Step-by-step explanation:

We have been given that Constance wants to purchase an school jacket. Store A had the jacket for 15% off the original price of $59.60.

Let us find price offered by store A by finding 85% of $59.60 as because 100% minus 15% is equal o 85%.

\text{Price offered by store A}=\frac{85}{100}\times \$59.60

\text{Price offered by store A}=0.85\times \$59.60

\text{Price offered by store A}=\$50.66

Store B has the same jacket at a price of $50.99 and price of jacket at store A after discount is $50.66, therefore, store A is a better buy.

Let us find total price of jacket after adding 6% of $50.66 to $50.66 as:

\text{Total price of jacket}=\$50.66+\$50.66\times \frac{6}{100}

\text{Total price of jacket}=\$50.66+\$50.66\times0.06

\text{Total price of jacket}=\$50.66+\$3.0396

\text{Total price of jacket}=\$53.6996

\text{Total price of jacket}\approx \$53.70

Therefore, the total price of jacket after 6% sales tax would be $53.70.

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Match the parabolas represented by the equations with their foci.
Elenna [48]

Function 1 f(x)=- x^{2} +4x+8


First step: Finding when f(x) is minimum/maximum
The function has a negative value x^{2} hence the f(x) has a maximum value which happens when x=- \frac{b}{2a}=- \frac{4}{(2)(1)}=2. The foci of this parabola lies on x=2.

Second step: Find the value of y-coordinate by substituting x=2 into f(x) which give y=- (2)^{2} +4(2)+8=12

Third step: Find the distance of the foci from the y-coordinate
y=- x^{2} +4x+8 - Multiply all term by -1 to get a positive x^{2}
-y= x^{2} -4x-8 - then manipulate the constant of y to get a multiply of 4
4(- \frac{1}{4})y= x^{2} -4x-8
So the distance of focus is 0.25 to the south of y-coordinates of the maximum, which is 12- \frac{1}{4}=11.75

Hence the coordinate of the foci is (2, 11.75)

Function 2: f(x)= 2x^{2}+16x+18

The function has a positive x^{2} so it has a minimum

First step - x=- \frac{b}{2a}=- \frac{16}{(2)(2)}=-4
Second step - y=2(-4)^{2}+16(-4)+18=-14
Third step - Manipulating f(x) to leave x^{2} with constant of 1
y=2 x^{2} +16x+18 - Divide all terms by 2
\frac{1}{2}y= x^{2} +8x+9 - Manipulate the constant of y to get a multiply of 4
4( \frac{1}{8}y= x^{2} +8x+9

So the distance of focus from y-coordinate is \frac{1}{8} to the north of y=-14
Hence the coordinate of foci is (-4, -14+0.125) = (-4, -13.875)

Function 3: f(x)=-2 x^{2} +5x+14

First step: the function's maximum value happens when x=- \frac{b}{2a}=- \frac{5}{(-2)(2)}= \frac{5}{4}=1.25
Second step: y=-2(1.25)^{2}+5(1.25)+14=17.125
Third step: Manipulating f(x)
y=-2 x^{2} +5x+14 - Divide all terms by -2
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4(- \frac{1}{8})y= x^{2} -2.5x-7
So the distance of the foci from the y-coordinate is -\frac{1}{8} south to y-coordinate

Hence the coordinate of foci is (1.25, 17)

Function 4: following the steps above, the maximum value is when x=8.5 and y=79.25. The distance from y-coordinate is 0.25 to the south of y-coordinate, hence the coordinate of foci is (8.5, 79.25-0.25)=(8.5,79)

Function 5: the minimum value of the function is when x=-2.75 and y=-10.125. Manipulating coefficient of y, the distance of foci from y-coordinate is \frac{1}{8} to the north. Hence the coordinate of the foci is (-2.75, -10.125+0.125)=(-2.75, -10)

Function 6: The maximum value happens when x=1.5 and y=9.5. The distance of the foci from the y-coordinate is \frac{1}{8} to the south. Hence the coordinate of foci is (1.5, 9.5-0.125)=(1.5, 9.375)

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Answer:

68 inches

Step-by-step explanation:

P = 2 (L + W)

P = 2(4x+5 + 4x+5)

P = 2(8x + 10)

P = 16x + 20

If x= 3

P = 16(3) + 20

P = 48 + 20

P = 68 inches

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Slope 1/3 passing through the points (-3,-4)
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Answer:

y=1/3x-3

Step-by-step explanation:

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plug in slop as m and points as x and y

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7. Is it proportional?
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Answer:

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The rate of change is the ratio between the x and y (or input and output) values in a relationship.  Another term for the rate of change for proportional relationships is the constant of proportionality.

If the rate of change is yx, then so is the constant of proportionality.  To simplify things, we set  yx=k, where k represents the constant of proportionality.  

If you solve a yx=k equation for y, (like this: y=kx), it is called a direct variation equation. In a direct variation equation, y varies directly with x. When x increases or decreases, y also increases or decreases by the same proportion.

To find y in a direct variation equation, multiply x by the constant of proportionality, k.

For example: Given the relationship y=7x, the constant of proportionality k=7,  so if x=3,  then y=3×7 or 21.

Given the same relationship, if x=7,  then y=7×7, or 49.  

Step-by-step explanation:

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