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NeTakaya
3 years ago
5

Renata wins a $20 gift card to an online music site. After Renata purchases 16 songs, the gift card has a remaining

Mathematics
1 answer:
amm18123 years ago
7 0

Answer: y=20-1.25x

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

y=mx+b

Where "m" is the slope of the line and "b" is the y-intercept.

You need to analize the information given in the exercise.

You know that gift card had a total of $20. Then, since she started to buy the songs with $20, you can identify that:

b=20

Since Renata purchased 16 songs and the gift card had a remaining  balance of $0 after this, you can find the cost of each song. This is:

\frac{20}{16}=\$1.25

Therefore, she spent $1.25 per song. This means that the slope is:

m=-1.25

Then, you get that the equation that represents the relationship between "y" (the remaining balance on Renata's gift card) and "x" (the number of songs purchased) is:

y=20-1.25x

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Nady [450]

Answer:

y = 3

Step-by-step explanation:

(5y - 3)/4 + 6 = 3y

5y - 3 + 24 = 12y

7y = 21

y = 3

Check.

(5*3 - 3)/4 + 6 = 3*3

(15 - 3)/4 + 6 = 9

12/4 + 6 = 9

3 + 6 = 9

9 = 9

7 0
2 years ago
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The curve given by x=sin(t),y=sin(t+sin(t)) has two tangent lines at the point (x,y)=(0,0). List both of them in order of increa
SOVA2 [1]

Answer:

y = 0

y =2x

Step-by-step explanation:

Given parametric equations:

x (t) = sin (t)

y (t) = sin (t + sin (t))

The slope of the curve at any given point is given by dy / dx we will use chain rule to find dy / dx

(dy / dx) * (dx / dt) = (dy / dt)

(dy / dx) = (dy / dt) / (dx / dt)

Evaluate dx / dt and dy / dt

dx / dt = cos (t)

dy / dt = cos (t + sin (t)) * (1+cos (t))

Hence,

dy / dx = (1+cos(t))*cos(t + sin (t))) / cos (t)

@Given point (x,y) = 0 we evaluate t

0 = sin (t)

t = 0 , pi

Input two values of t and compute dy / dx

@ t = 0

dy / dx = (1 + cos (0))*cos (0 + sin (0))) / cos (0)

dy / dx = (1+1)*(1) / (1) = 2 @ t = 0

@t = pi

dy / dx = ( 1 + cos (pi))* cos (pi + sin (pi)) / cos (pi)

dy / dx = (1-1) * (-1) / (-1) = 0 @ t = pi

The corresponding gradients are 0 and 2 in increasing order and their respective equations are:

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5 0
3 years ago
Length of a rectangle is 5 cm longer than the width. Four squares are constructed outside the rectangle such that each of the sq
stiv31 [10]

Answer:

18

Step-by-step explanation:

Remark

This is one of those questions that can throw you. The problem is that do you include the original rectangle or not. The way it is written it sounds like you shouldn't

However if you don't the question gives you 2 complex answers. (answers with the sqrt( - 1) in them.

Solution

Let the width = x

Let the length = x + 5

Area of the rectangle: L * w = x * (x + 5)

Area of the smaller squares (there are 2)

Area = 2*s^2

x = s

Area = 2 * x^2

Area of the larger squares = 2 * (x+5)^2

Total Area

x*(x + 5) + 2x^2 + 2(x + 5)^2 = 120                 Expand

x^2 + 5x + 2x^2 + 2(x^2 + 10x + 25) = 120     Remove the brackets

x^2 + 5x + 2x^2 + 2x^2 + 20x + 50 = 120      collect the like terms on the left

5x^2 + 25x +  50 = 120                                   Subtract 120 from both sides.

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x^2 + 5x - 14 = 0                                               Factor

(x + 7)(x - 2) = 0                                                 x + 7 has no meaning  

x - 2 =  0

x = 2                                                              

Perimeter

P = 2*w + 2*L

w = 2

L = 2 + 5

L = 7

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P = 4 + 14

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8 0
3 years ago
Find the total area the regular pyramid.
Ber [7]

Answer: 14\sqrt{3}

Step-by-step explanation:

1. You must apply the following formula for calculate  the total surface area the regular pyramid:

SA=\frac{pl}{2}+B

Where p is the perimeter of the base, l is the slant height and B is the area of the base.

2. The perimeter is, where s is the side length:

p=3s=3*4=12

3. The faces are isosceles traingles. So, to find the slant height you can divide one base into two equal right triangles and calculate the slant height with Pythagorean Theorem:

l=\sqrt{4^2-2^2}=2\sqrt{3}

4. The base is equal to any face, then both have equal areas. As previously you divide one base into two equal righ triangle to find the slant height, you can calcualte the area of one right triangle and multply it by 2 to calculate B:

B=2*\frac{bh}{2}=2*\frac{2\sqrt{3}}{2}=2\sqrt{3}

Finally substitute values:

SA=\frac{12*2\sqrt{3}}{2}+2\sqrt{3}=14\sqrt{3}

6 0
3 years ago
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geniusboy [140]

The point that Sam's house is located is at (2.5, -2)

<h3 /><h3>Midpoint of coordinate points</h3>

The formula for calculating the midpoint of coordinate is expressed as:

M(x, y) = {(x₁+x₂)/2, (y₁+y₂)/2}

Given the coordinate between their locations at (-4, 4) and (-9, 8)

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x = (-4+9)/2

x =5/2 = 2.5

Similarly

y = 4-8/2

y = -4/2

y = -2

Hence the point that Sam's house is located is at (2.5, -2)

Learn more on midpoint here: brainly.com/question/5566419
#SPJ1

6 0
1 year ago
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