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4 years ago

14

On Tuesday, a local retail store is offered an additional 20% off all school supplies. Before you handed cashier the 20% off cou

pon, your receipt total was $54. What discounted amount will the coupon offer you?

1 answer:

inysia [295]4 years ago

6 0

I think it would be $8.64

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Point A is at (2,-8) and the point C is at (-4,7). Find the coordinates of point B on AC such that the ratio of AB to BC is 2:1.

pentagon [3]

Answer:

The coordinates of point B are (-2, 2)

Step-by-step explanation:

We have two points: A and C.

The coordinates for A are (2, -8) and the coordinates for C are (-4, 7).

We have to find the coordinates of the point B, that satisfies the condition that the distance AB is 2 times the distance BC.

We also know that B is a point of the line AC.

We can calculate the line AC as a linear function y=mx+b.

The slope m is:

$m=\dfrac{y_c-y_a}{x_c-x_a}=\dfrac{7-(-8)}{-4-2}=\dfrac{15}{-6}=-2.5$

Then, the y-intercept b can be calculated using the coordinates of one of the points, in this case point A:

$y=-2.5x+b\\\\b=y_a+2.5x_a=-8+2.5*2=-8+5=-3$

Then, we know that B is a point of the linear function y=-2.5x-3, within the range x ∈ (-4; 2).

To have a ratio AB to BC of 2 to 1, we can divide the length of the line AC in 3 parts, and the point B will be located in the end of the segment nearer to point C.

In the picture attached, you can see the division of the segment AC in three parts and the location of point B=(x, y).

Applying the Thales theorem, we can divide the segment in the y-axis in three and calculate y, and the same for the x-axis.

Then, the coordinate y for the point B is:

$y=y_c-(y_c-y_a)/3\\\\y=7-[7-(-8)]/3=7-15/3=7-5=2\\\\\\x=x_c-(x_c-x_a)/3\\\\x=-4-(-4-2)/3=-4-(-6)/3=-4+2=-2$

Then, the point B has coordinates (-2, 2).

We can verify the distances as:

$AB=\sqrt{(2-(-2))^2+((-8)-2)^2}=\sqrt{16+100}=\sqrt{116}\\\\\\BC=\sqrt{((-2)-(-4))^2+(2-7)^2}=\sqrt{4+25}=\sqrt{29}\\\\\\\dfrac{AB}{BC}=\dfrac{\sqrt{116}}{\sqrt{29}}=\sqrt{\dfrac{116}{29}}=\sqrt{4}=2$

4 0

3 years ago

I think of a number I add 16 subtract 30 and my answer Is 36 what was my number

sp2606 [1]

36+30=66 66-16=50 so your answer is 50

8 0

3 years ago

Read 2 more answers

Anybody good in pre Calculus and know how to do #3 or #4?

lys-0071 [83]

Answer:

3. 0

4. n = -2

Step-by-step explanation:

I haven't taken pre-calc but this looks a lot like algebra.

For #3, just plug in -2 for the x values, so:

x^2 + 4x +4

(-2)^2 + 4(-2) + 4

= 4 - 8 + 4

= 0

For #4, move the variables to one side and solve( im not sure what the pi is for tho, or is that a n?):

5n + 6 = -3n - 10

add 3n to both sides

8n + 6 = -10

subtract 6 from both sides

8n = -16

divide both sides by 8

n = -2

7 0

3 years ago

Please help me answer the question

Rufina [12.5K]

Answer:

y=-x+2

Step-by-step explanation:

The slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.

From the graph, we can see that the y-intercept is at (0,2) so the equation becomes y=mx+2.

Other points on the graph include (1,1) and (2,0). Plugging (1,1) into the slope-intercept equation, we get 1=(m)1+2. Solving this will give us m=-1.

We can confirm this by plugging m=-1 into the equation along with the point (2,0); 0=(-1*2)+2. It checks out!

So our final equation in slope-intercept form will be y=-x+2

4 0

3 years ago

Can anyone help me?<br>

Travka [436]

Answer:

find by using formula that 1/2×base×height

8 0

2 years ago