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vovikov84 [41]
3 years ago
10

Given that f(x) = 9x2 − 180, find x

Mathematics
2 answers:
timurjin [86]3 years ago
7 0
-162
Because 9 x 2 = 18
18 - 180 = -162
expeople1 [14]3 years ago
7 0

Answer:

The values of x are x=\sqrt{20},\:x=-\sqrt{20}.

Step-by-step explanation:

We have the function f(x) = 9x^{2} - 180.

To find the value of x, you must set the function to zero

9x^2\:-\:180=0

Next, add 180 to both sides

9x^2-180+180=0+180

Simplify

9x^2=180

Divide both sides by 9

\frac{9x^2}{9}=\frac{180}{9}

Simplify

x^2=20

\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}

x=\sqrt{20},\:x=-\sqrt{20}.

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The length of a rectangle is 3 centimeters less than four times its width. Its area is 10 square centimeters. Find the dimension
Kay [80]

Answer:

W = 2 cm

L = 5 cm

Step-by-step explanation:

A rectangle is a four sided shape with 4 perpendicular angles. It has two pairs of parallel sides which are equal in distance: width and length. Its area, the amount of space inside it, can be found using the formula A = l*w. If the area is 10 cm² and the length is "3 cm less than 4 times the width" or 4w - 3, you can substitute and solve for w.

A = l*w

10 = (4w - 3)(w)

10 = 4w² - 3w

Subtract 10 from both sides to make the equation equal to 0. Then solve the quadratic by quadratic formula.

4w² - 3w - 10 = 0

Substitute a = 4, b = -3 and c = -10.

w = \frac{3 +/- \sqrt{(-3)^2 - 4(4)(-10)} }{2(4)} = \frac{3 +/- \sqrt{9 +160)} }{8} =  \frac{3 +/- \sqrt{169} }{8} = \frac{3+/-13}{8}

There are two possible solutions which can be found.

3 + 13 / 8 = 16/ 8 = 2

3 - 13 / 8 = -10/8 = -5/4

Since w is a side length or distance, it must be positive so w = 2 cm.

If the width is 2 cm then the length is 4(2) - 3 = 8 - 3 = 5 cm.

8 0
2 years ago
Hi again I’ll appreciate it if you help me
BartSMP [9]

Answer:

answer is in the picture with work, just know your formulas and plug the numbers in and you'll be fine

7 0
3 years ago
In Geometry what is the meaning of the following symbol?
BartSMP [9]

Answer:

D. Is congruent to

Step-by-step explanation:

This symbol is used when two figures have exactly same lengths and angles, which means they are congruent

6 0
2 years ago
How do I solve this problem. I have to find the missing side lengths and lease my sender as radicals in simplest form
nlexa [21]

Answer:

x = y = 2√2

Step-by-step explanation:

Find the diagram attached

To get the unknown side x and y, we need to use the SOH CAH TOA identity

Opposite side = x

Adjacent = y

Hypotenuse = 4

Sin theta = opposite/hypotenuse

sin 45 = x/4

x = 4 sin 45

x = 4 * 1/√2

x = 4 * 1/√2 * √2/√2

x = 4 * √2/√4

x = 4 * √2/2

x = 2√2

Similarly;

cos theta = adjacent/hypotenuse

cos 45 = y/4

y = 4cos45

y = 4 * 1/√2

y = 4 * 1/√2 * √2/√2

y = 4 * √2/√4

y = 4 * √2/2

y = 2√2

4 0
2 years ago
5) x - 4y = 28<br> -4x - y = 7<br> Solve each system by elimination
dexar [7]

Answer:

x = 0, y = -7

Step-by-step explanation:

x - 4y = 28

-4x - y = 7

____________

x - 4y = 28

-16x - 4y = 28

____________  _

17x = 0

x = 0

0 - 4y = 28

y = -7

3 0
3 years ago
Read 2 more answers
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