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3 years ago

What is the only solution of 2x2 + 8x = x2 – 16?

Mathematics

2 answers:

Lemur [1.5K]3 years ago

8 0

i think its x = 10, -2

Tamiku [17]3 years ago

7 0

Answer:

The answer to your question is -4

Step-by-step explanation:

You might be interested in

Factor completely the given polynomial

kherson [118]

I like to always factor out the negative first, so that we will have our first term be positive:
So it can be rewritten as this: -(x^2-3x-28)

Then we need to find two numbers that multiply to -28, but add up to -3.
Those two numbers are -7 and +4.

So we can rewrite as: -(x-7)(x+4)

6 0

3 years ago

Find the domain and range of f(x). Please explain your answer. f(x) = √(x^2+5x+6)

timama [110]

Answer:

Domain:— [ x ≥ -2, x ≤ -3 ]

Range:— [ y ≥ 0 ]

Step-by-step explanation:

You may use graphing calculator to draw a graph and examine the graph’s domain and range. However, I’ll explain further about the graph of quadratic in a surd.

First, factor the quadratic expression in the surd:—

$\displaystyle \large{f(x)=\sqrt{(x+3)(x+2)}}$

We can find the x-intercepts by letting f(x) = 0.

I’ll be separating in two parts — one for finding x-intercept and one for finding y-intercept.

__________________________________________________________

Finding x-intercepts

Let f(x) = 0.

$\displaystyle \large{0=\sqrt{(x+3)(x+2)}}$

Solve for x, square both sides:—

$\displaystyle \large{0^2 = (\sqrt{(x+3)(x+2)})^2}\\\displaystyle \large{0=(x+3)(x+2)}$

Simply solve a quadratic equation:—

$\displaystyle \large{x=-3,-2}$

Therefore, x-intercepts are:—

$\displaystyle \large{\boxed{x=-3,-2}}$

__________________________________________________________

Finding y-intercept

Let x = 0.

$\displaystyle \large{f(x)=\sqrt{(0+3)(0+2)}}\\\displaystyle \large{f(x)=\sqrt{3 \cdot 2}}\\\displaystyle \large{f(x)=\sqrt{6}}$

Therefore, y-intercept is:—

$\displaystyle \large{\boxed{\sqrt{6}}}$

__________________________________________________________

However, I want you to focus on x-intercepts instead. We know that the square root only gives you a positive value. That means the range of function can only be y ≥ 0.

For domain, first, we have to know how or what the graph looks like. You can input the function in a graphing calculator as you’ll see that when x ≥ -2, the graph heads to the right while/when x ≤ -3, the graph heads to the left. This means that the lesser value of x-intercept gets left and more value get right.

See, between -3 < x < -2, there is no curve, point or anything between the interval. Therefore, -3 < x < -2 does not exist in function.

Hence, the domain is:—

x ≥ -2, x ≤ -3

4 0

2 years ago

Unit4: Congruent Triangles Hw 1: Classifying Triangles Gina Wilson (All things algebra) 2014

anastassius [24]

Answer:

12. x = 6, side = 83
13. x = 18, side = 29
14. x = 11, sides = 74, 74 and 37
15. x = 23, sides = 95, 95 and 108

Step-by-step explanation:

11 is incomplete, can't solve

The triangle is equilateral, so all sides are equal, using one pair to find x:

13x + 5 = 17x - 19
17x - 13x = 5 + 19
4x = 24
x = 6

Each side is:

13*6 + 5 = 78 + 5 = 83

13.

Sides are equal as triangle is equilateral

QR = 2x - 7
RS = 5x - 61
QS = x + 11

Finding x by comparing two sides

2x - 7 = 5x - 61
5x - 2x = 61 - 7
3x = 54
x = 18

Sides are equal

18 + 11 = 29

14.

Equal sides of isosceles triangle:

CD = DE
9x - 25 = 6x + 8
9x - 6x = 8 + 25
3x = 33
x = 11

Sides are

CD = DE = 9*11 - 25 = 99 - 25 = 74
CE = 10*11 - 73 = 110 - 73 = 37

15.

Equal sides of isosceles triangle WXY, WX = WY

WX = 4x + 3
WY = 7x - 66
XY = 5x - 7
4x + 3 = 7x - 66
7x - 4x = 3 + 66
3x = 69
x = 23

Sides are:

WX=WY = 4*23 + 3 = 95
XY = 5*23 - 7 = 108

6 0

3 years ago

Read 2 more answers

Select all of the following functions that are quadratic.

wlad13 [49]

1st,2nd,3rd,4th that is your answer

7 0

2 years ago

Question 2 of 10 Which describes the graph of y = (x-4)2 - 1?

WITCHER [35]

$y=(x-4)^2-1:$ $y=-\frac{4}{5}$

Sure hope this helps you

y = -4/5

4 0

2 years ago