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1 year ago

What are the solutions of 2|x-6|=10

1 answer:

8 0

$\begin{gathered} 2|x-6|=10 \\ \frac{2\left|x-6\right|}{2}=\frac{10}{2} \\ \mleft|x-6\mright|=5 \\ x-6=-5\quad \mathrm{or}\quad \: x-6=5 \\ \end{gathered}$

then

$\begin{gathered} x-6=-5 \\ x-6+6=-5+6 \\ x=1 \end{gathered}$

$\begin{gathered} x-6=5 \\ x-6+6=5+6 \\ x=11 \end{gathered}$

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Use the formula d = ( r − c ) t to find c if d = 6 , r = 4 , and t = 2 . c=

Minchanka [31]

First, we are going to want to plug in the values we are given. In this case, we will end up with the equation:

$6 = (4 - c) 2$

From here, we can solve the equation to find $c$ :

$6 = 2(4 - c)$

Apply the commutative property to rearrange the terms on the right-side of the equation to make the distributive property more apparent

$6 = 8 -2c$

Apply the distributive property

$-2 = -2c$

Subtract 8 from both sides of the equation

$1 = c$

Divide both sides of the equation by -2

We have found that c = 1.

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3 years ago

Round to the nearest tenth.

laila [671]

Answer:

8.2 units

Step-by-step explanation:

Given that the only information for our triangle are 2 sides and 1 angle, we must use the Law of Cosines to find side BC

Recall the Law of Cosines

$a^2=b^2+c^2-2bc\cdot cos(A)$

Identify angles and sides

$m\angle A=23^\circ\\a=BC=?\\b=AC=14\\c=AB=6$

Solve for side "a"

$a^2=b^2+c^2-2bc\cdot cos(A)\\\\a^2=14^2+6^2-2(14)(6)\cdot cos(23^\circ)\\\\a^2=196+36-168cos(23^\circ)\\\\a^2=222-168cos(23^\circ)\\\\a=\sqrt{222-168cos(23^\circ)}\\ \\a\approx8.2$

Therefore, the length of line segment BC is about 8.2 units

8 0

2 years ago

3. Given the following functions f(x) and g(x), solve f[g(7)] and select the correct answer below:

antoniya [11.8K]

Hello,
f(g(x))=f(2x+2)=4(2x+2)+21=8x+29
f(g(7))=8*7+29=56+29=85

8 0

3 years ago

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Simplify the expression

baherus [9]

2*7b =

use the distributive property

14b

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3 years ago

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Find the x and y intercepts of the following function. g(x)=x^2-5x-84

Ahat [919]

Answer:

see explanation

Step-by-step explanation:

To find the y- intercept let x = 0 in the function

g(0) = 0 - 0 - 84 = - 84 ← y- intercept

To find the x- intercepts let y = 0, that is

x² - 5x - 84 = 0

To factor the quadratic

Consider the factors of the constant term (- 84) which sum to give the coefficient of the x- term

The factors are - 12 and + 7, since

- 12 × 7 = - 84 and - 12 + 7 = - 5, thus

(x - 12)(x + 7) = 0

Equate each factor to zero and solve for x

x - 12 = 0 ⇒ x = 12

x + 7 = 0 ⇒ x = - 7

x- intercepts are x = - 7 and x = 12

8 0

3 years ago