Sue has 100 dimes and quarters. If the total value of the coins is $21.40, how many of each kind

Let A=(-6,7), B=(-4,11), and C=(-2.10) be three points in the coordinate plane (A) Verify that the three points form a right tri

faust18 [17]

Answer:

(A) see below

(B) the right angle is at vertex B(-4,11)

(1) 3x -4y = -46

(E) the midpoint is (-4, 8.5)

Step-by-step explanation:

(A) The slope of line AB is Δy/Δx = (11-7)/(-4-(-6)) = 4/2 = 2. The slope of line BC is (10-11)/(-2-(-4)) = -1/2. The slopes of AB and BC have a product of 2(-1/2) = -1, so are the slopes of perpendicular lines. The points are distinct, and lines joining two pairs of them are at right angles, so the points form a right triangle.

(B) Point B(-4,11) is the point of intersection of perpendicular segments AB and BC, so is the location of the right angle.

(1) The slope of the hypotenuse AC is ...

Δy/Δx = (10-7)/(-2-(-6)) = 3/4

In point-slope form, the equation for the line through point A with this slope is ...

y -7 = 3/4(x +6) . . . . point-slope form of the equation of the hypotenuse

4y -28 = 3x +18 . . . . multiply by 4

-46 = 3x -4y . . . . . . subtract 18+4y

3x -4y = -46 . . . . . . . standard form equation of the hypotenuse

(E) The midpoint of the hypotenuse is the average of the endpoint coordinates:

M = (A + C)/2 = (-6-2, 7+10)/2 = (-4, 8.5)

The midpoint of the hypotenuse is M(-4, 8.5).

8 0

3 years ago

3 over 5 to the power of 2 + 4 × 3 − 2

dsp73

2

( ---- )^2 + (4*3) - 2

5

becomes

9

---- + 12 -2 following order of operations rules (PEMDAS)

25

Combining the last 2 terms, we get 10. The final answer is

9/25 + 10, or 10 9/25, or 10.36.

6 0

3 years ago

Read 2 more answers

Which statement is true for the equation 3x − 3x − 2 = −2? It has no solution. It has one solution. It has two solutions. It has

Sergio039 [100]

Answer:

it has infinitley solutions .

Step-by-step explanation:

Any value of x makes the equation true.

All real numbers

Interval Notation:

(−∞,∞)

hope i helped :) !! brianilest ?!??!

4 0

3 years ago

Is there a way to simplify the process of plugging in factors through synthetic division to find the zeros of a polynomial? I am

Iteru [2.4K]

Yes you can use the discriminant of a quadratic/polynomial. For instance, if
$b^2 - 4ac = 0$ there is one real root. If $b^2 - 4ac > 0$ there are two real roots and i $b^2 - 4ac < 0$ there are no real roots

The discriminant comes from the quadratic equation, which is the following.
$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

4 0

3 years ago

X^100+1 divide by x+1

timofeeve [1]

Answer:

x=-1

Step-by-step explanation:

$\frac{x ^{100} + 1 }{x + 1}$

$x + 1 = 0$

$x = - 1$

7 0

2 years ago