True OR False The lengths 45, 42, and 15 make a right triangle.

Rashal is adding the expression below. Negative 3 + left-bracket (negative 7) + (negative 6) right-bracket First, he rewrites th

diamong [38]

I think it is 3 I think I’m not sure

6 0

2 years ago

Read 2 more answers

M is the midpoint of CD. Given the coordinates of one endpoint C(10,-5) and the midpoint M(4, 0), find the coordinates of the ot

mash [69]

Answer:

D(-2, 5).

Step-by-step explanation:

We are given that M is the midpoint of CD and that C = (10, -5) and M = (4, 0).

And we want to determine the coordinates of D.

Recall that the midpoint is given by:

$\displaystyle M = \left(\frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2}\right)$

Let C(10, -5) be (x₁, y₁) and Point D be (x₂, y₂). The midpoint M is (4, 0). Hence:

$\displaystyle (4, 0) = \left(\frac{10+x_2}{2} , \frac{-5+y_2}{2}\right)$

This yields two equations:

$\displaystyle \frac{x_2 + 10}{2} = 4\text{ and } \frac{y_2 - 5}{2} = 0$

Solve for each:

$\displaystyle \begin{aligned}x_2 + 10 &= 8 \\ x_2 &= -2 \end{aligned}$

And:

$\displaystyle \begin{aligned} y_2 -5 &= 0 \\ y_2 &= 5\end{aligned}$

In conclusion, Point D = (-2, 5).

5 0

2 years ago

Katy invests a total of $26,500 in two accounts paying 4% and 9% annual interest, respectively. How much was invested in each ac

White raven [17]

A = amount invested at 4%.

b = amount invested at 9%.

we know the total amount invested was $26500, thus a + b = 26500.

whatever% of anything is just (whatever/100) * anything.

how much is 4% of a? well, is just (4/100) * a, or 0.04a.

how much is 9% of b? well, is just (9/100) * b, or 0.09b.

we know the interest yielded for both amounts adds up to $1510, thus 0.04a + 0.09b = 1510.

$\bf \begin{cases}
a+b=26500\implies \boxed{b}=26500-a\\
0.04a+0.09b=1510\\
----------------\\
0.04a+0.09\left( \boxed{26500-a} \right)=1510
\end{cases}
\\\\\\
0.04-0.09a+2385=1510\implies -0.05a=-875
\\\\\\
a=\cfrac{-875}{-0.05}\implies a=17500$

how much was invested at 9%? well, b = 26500 - a.

7 0

2 years ago

What is the equation of this line?

andrew-mc [135]

One way to write a line is y=mx+b, where b is a number, m is the slope of the line, and y and x are variables that you can plug numbers into. We know that we have two points, (0,5) and (10,0). To find the slope of a line, we can use the equation
$\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{y_{1}-y_{2}}{x_{1}-x_{2}}$
Plugging this in for our points, we get $\frac{0-5}{10-0} = -5/10=-1/2$ as our slope (we get -1/2 by dividing both -5 and 10 by 5 from the previous fraction), making our equation y=(-1/2)x+b. Plugging a point in to find out what b is, we get 0=(-1/2)10+b=-5+b. Adding 5 to both sides to separate the b, we get 5=b, making our equation y=(-1/2)x+5. To find out what x is for (x,2), since the y value comes second, we can plug in 2 into our equation to get 2=(-1/2)x+5. Since we want to solve for x, we have to separate it. Subtracting 5 from both sides, we get -3=(-1/2)x. Since we can multiply -1/2 by its reciprocal (switching the numerator and denominator) to get 1 (and therefore x on the right sides as 1*x=x), we multiply both sides by -2 to get 6=x, making the point (6,2)

Feel free to ask further questions!

4 0

2 years ago

Please help! Brainliest will be given to first to answer

Nataly_w [17]

Answer:

100 residents/km2

Step-by-step explanation:

5×4 = 20 2,000÷20 = 100

6 0

2 years ago