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3 years ago

Triangle PQR hAS vertices P (4,-1),Q(-2,7), and R (9,9). find an equation of the median from R

1 answer:

7 0

A median intersects at the midpoint of the opposite length. The midpoint is:

x,m = (4+-2)/2 = 1
y,m = (-1+7)/2 = 3

The midpoint is at (1,3). With this point and point R(9,9), the equation would be:

y = mx + b, where
m = (9 - 3)/(9 - 1) = 0.75
b is the y-intercept
Substituting any point,
3 = 0.75(1)+b
b = 2.25

Thus, the equation for the median is:

y = 0.75x + 2.25

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Can someone help me with these

Stolb23 [73]

Answer:

Problem 2) : the gradient is "-2", and the y-intercept is "3"

Problem 3)

A is $y=2x+2$

B is $y=x+2$

Step-by-step explanation:

Problem 2)

In the line given by the equation: $y=-2x+3$

the "gradient" (also known as "slope") is the numerical coefficient that multiplies the variable "x". So in this case the gradient is "-2"

the y-intercept is the numerical term "+3" because that is the y-value result of evaluating the expression for x = 0

$y=-2x+3\\y=-2\,(0)+3\\y=3$

Problem 3)

Consider the two lines :

$y=x+2$ and $y=2x+2$

notice that both have the same y-intercept (that is the numerical term "2" at the end of both expressions. That means that both lines cross the y-axis at the point y=2.

Now notice that the gradient of one of them is "1" (for $y=x+2$ ) that is the coefficient that multiplies the variable "x". While for the other line ( $y=2x+2$ ) the gradient is "2" and therefore steeper than the previous one.

Then, the line identified as "A" which is the one with steeper gradient, corresponds to the equation $y=2x+2$ , and the line identified with "B" is the one with smaller gradient $y=x+2$ .

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3 years ago

A company's revenue (in dollars) can be modeled by the function

Tju [1.3M]

R(p) = -15p² + 200p + 10,000
To find the maximum of the function, we take the first derivative and equate to 0:

R'(p) = -30p + 200
0 = -30p + 200
p = 6.67

A price of $6.67 will maximize revenue.

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3 years ago

How many solutions exist for the given equation?

katrin2010 [14]

$1(x + 12) = 4x - 1\\x+12=4x-1\\13=3x\\x=\frac{13}{3} \\x=4\frac{1}{3}$

This equation has only one solution

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P.S. Hello from Russia

7 0

2 years ago

Read 2 more answers

Kim is 5 years older than her brother Jack. If the sum of their ages is 21, find each of their ages.

yarga [219]

9514 1404 393

Answer:

Kim is 13
Jack is 8

Step-by-step explanation:

Let k represent Kim's age. Then Jack's age is k-5 and the total of their ages is ...

k + (k -5) = 21

2k = 26 . . . . . . . add 5, collect terms

k = 13 . . . . . . . . . divide by 2; Kim's age

k -5 = 8 . . . . . . . Jack's age

Kim is 13; Jack is 8.

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2 years ago

Please help! Billy just received $10 for his birthday and immediately spent $2.50 on a pack of baseball cards. He then wants to

Oduvanchick [21]

Answer:

1.5x = 7.5 (a)

Step-by-step explanation:

If Billy has $7.50 remaining, then he can buy x no. of boxes.

Each box costs $1.50

So, 1.5x = 7.5

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2 years ago