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belka [17]
3 years ago
11

In a right triangle, the hypotenuse has endpoints P(–3, 2) and Q(1, –3). On a coordinate plane, line P Q has points (negative 3,

2) and (1, negative 3). If R represents the third vertex in the triangle and R is located in the third quadrant, what is the length of PR?
Mathematics
2 answers:
Marina CMI [18]3 years ago
6 0

<u><em>Answer:</em></u>

<u><em>The length of PR is 5 units.</em></u>

<u><em>Step-by-step explanation:</em></u>

<u><em></em></u>

mrs_skeptik [129]3 years ago
4 0

Answer:

The length of PR is 5 units

Step-by-step explanation:

Here, we want to calculate the length of PR

Since PQ is the hypotenuse, it means that the right-angle would be between lines PR and RQ

Also, since R is on the third quadrant, then its coordinates are (-x,-y)

To get the coordinates of R since we know that we need a right angle, we drop a straight vertical line through P and a straight horizontal line through Q

What this mean is that the coordinates of R will take the x-coordinate of the point P and the y-coordinate of the point Q

Hence, we have that the coordinates of the point R is (-3,-3)

Now, we want to calculate the length of PR

PR will be the distance between the points P and R

Mathematically, to get this, we use the distance formula

That will be;

√(y2-y1)^2 + (x2-x1)^2

Thus, we have

√(2-(-3)^2 + (-3-(-3))^2

= √5^2 + 0^2

= √25 = 5 units

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Mrs.Smith has two similiar recycling bins in her office. The dimension of the smaller bin can be found by dilating the dimension
nikklg [1K]

Answer:

The dimension of the larger bin is x and the smaller bin is 0.75x.

Step-by-step explanation:

Let the dimension of the larger bin is x.

It is given that the dimension of the smaller bin can be found by dilating the dimension of the larger bin by a scale factor of 0.75

In order to find the dimension of the smaller bin multiply the dimension of the larger bin by 0.75

(x)(0.75)=0.75x

Hence, the dimension of the larger bin is x and the smaller bin is 0.75x.

8 0
2 years ago
If one gallon of whole milk cost $3.84 at this rate how much does a cup of whole milk cost ​
timama [110]

Answer:

$0.24 for one cup of whole milk

Explanation:

One Gallon is 16 cups, so if you divide the amount of a whole gallon by the amount of cups, you get 0.24 which will be your answer.

Hope this helps! ^^

6 0
3 years ago
if you think that Andy solved the problem correctly, explain how you can tell he is correct. If not, identify and explain all er
nasty-shy [4]

Answer:

25 lol

Step-by-step explanation:

4 0
3 years ago
8. Solve X=Students &amp; Y=Teachers<br> X+Y=24<br> X=3Y
Len [333]

Answer:

x=18, y= 6

Step-by-step explanation:

if x+y=24

x= 24- y

in second case

x= 3y

24_ y = 3y

24=4y

y= 6

hence x = 24 _6 = 18

5 0
3 years ago
Graph f(x) =-2x^+16x-30 by factoring to find the solutions, then find the coordinates of the vertex, and the axis of symmetry. I
fredd [130]

Answer:

<em>Observe attached image</em>

<em>Function zeros:</em>

(3, 0), (5, 0)

<em>Vertex:</em>

(4, 2)

<em>Axis of symmetry:</em>

<em>x =4</em>

Step-by-step explanation:

<u>First factorize the function</u>

f (x) = -2x ^ 2 + 16x-30

<em>Take -2 as a common factor.</em>

-2(x ^ 2 -8x +15)

<em>Now factor the expression x ^ 2 -8x +15</em>

You must find two numbers that when you add them, obtain the result -8 and multiplying those numbers results in 15.

These numbers are -5 and -3

Then we can factor the expression in the following way:

f (x) = -2(x-5)(x-3)

<em><u>The quadratic function cuts the x-axis at </u></em><em>x = 3 and at x = 5.</em>

Now we find the coordinates of the vertex.

For a function of the form ax ^ 2 + bx + c the x coordinate of its vertex is:

x = \frac{-b}{2a}

In the function f (x) = -2x ^ 2 + 16x-30

a = -2\\b = 16\\c = 30

<u>Then the vertice is:</u>

x = \frac{-16}{2(-2)}\\\\x = 4

The y coordinate of the symmetry axis is

y = f (4) = -2 (4) ^ 2 +16 (4) -30\\\\y = 2

The axis of symmetry is a vertical line that cuts the parabola in two equal halves. This axis of symmetry always passes through the vertex.

<u>Then the axis of symmetry is the line</u>

x = 4

<u>The solutions and the vertice written as ordered pairs are:</u>

<em>Function zeros:</em>

(3, 0), (5, 0)

<em>Vertex:</em>

(4, 2)

6 0
3 years ago
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