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dybincka [34]
3 years ago
9

Find the solution of the system of equations. −4x+5y= 13 x−5y=-22

Mathematics
1 answer:
77julia77 [94]3 years ago
5 0
The answer is (3,-2)
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Find Distance (4,6) (-4,-3)​
vampirchik [111]

Answer:

\sqrt{145}

Step-by-step explanation:

The distance formula states that the distance between two points (a,b) and (c,d) is \sqrt{(a-c)^2+(b-d)^2}.

The two points we have are (4,6) and (-4,-3). Plugging these numbers into the distance formula, we have

\sqrt{(4-(-4))^2+(6-(-3))^2.

Simplifying with order of operations, first using the distributive property, gives

\sqrt{(4+4)^2+(6+3)^2.

Squaring and adding gives

\sqrt{(4+4)^2+(6+3)^2}=\sqrt{8^2+9^2}\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~=\sqrt{64+81}\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~=\boxed{\sqrt{145}},

which is the answer in simplest form. This also rounds to about 12.04.

7 0
2 years ago
Definition: A __ is a number that makes an equation true<br> hint: first two letters: ro
laila [671]

Answer:

root

Step-by-step explanation:

A root is a number that makes an equation true

root make since in this sentce right

4 0
2 years ago
Read 2 more answers
What slope would make the lines<br> parallel?<br> y = -3x + 9<br> y = [?]x + 4
Vladimir79 [104]

Answer:

- 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x + 9 ← is in slope- intercept form

with slope m = - 3

Parallel lines have equal slopes, thus

y = - 3x + 4 ← is the equation of a parallel line

4 0
3 years ago
Consider the polynomial p(x) = x^3 + 4x^2 + 6x − 36.
Nady [450]

Answer:

a. attached graph; zero real: 2

b. p(x) = (x - 2)(x + 3 + 3i)(x + 3 - 3i)

c. the solutions are 2, -3-3i and -3+3i

Step-by-step explanation:

p(x) = x³ + 4x² + 6x - 36

a. Through the graph, we can see that 2 is a real zero of the polynomial p. We can also use the Rational Roots Test.

p(2) = 2³ + 4.2² + 6.2 - 36 = 8 + 16 + 12 - 36 = 0

b. Now, we can use Briott-Ruffini to find the other roots and write p as a product of linear factors.

2 |  1     4     6    -36

     1      6    18     0

x² + 6x + 18 = 0

Δ = 6² - 4.1.18 = 36 - 72 = -36 = 36i²

√Δ = 6i

x = -6±6i/2 = 2(-3±3i)/2

x' = -3-3i

x" = -3+3i

p(x) = (x - 2)(x + 3 + 3i)(x + 3 - 3i)

c. the solutions are 2, -3-3i and -3+3i

4 0
3 years ago
Nate has a bag containing 3 red, 2 blue, 4 yellow, and 3 green marbles. If he randomly chooses one marble from the bag, what is
SVEN [57.7K]

<u>The probability that the marble will be blue if he shakes the bag and when you puts his hand into the bag, to move it around and probably he'll get the blue marble.</u>

<em>Hopefully, it correct.... :)</em>

4 0
2 years ago
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