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3 years ago

Solve for x write the smaller solution first and the larger solution second. Round to two decimal places (x+8)^2-7=0

Mathematics

1 answer:

siniylev [52]3 years ago

4 0

Answer:

x ≈ - 10.65, x ≈ - 5.35

Step-by-step explanation:

Given

(x + 8)² - 7 = 0 ( add 7 to both sides )

(x + 8)² = 7 ( take the square root of both sides )

x + 8 = ± $\sqrt{7}$ ( subtract 8 from both sides )

x = - 8 ± $\sqrt{7}$ , thus

x = - 8 - $\sqrt{7}$ ≈ - 10.65

x = - 8 + $\sqrt{7}$ ≈ - 5.35

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Find x - and - y intercepts of the following equation. a. 4x - 3y = 12 b. y = 1/3x c. y = 2x + 5 d. y = 6

saw5 [17]

✒️ Equation

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A. To find the x - intercept, let y = 0.

$\tt \: \: \large \tt \: \begin{array}{|c|} \hline \tt \: 4x \: - \: 3y \: = \: \tt\underline{\green{ 12 }} \\ \tt 4x \: - \: 3(0) \: = \: \tt\underline{\blue{ 12 }} \\ \tt4x \: - \: 0 \: = \: \tt\underline{\pink{ 12 }} \\ \tt \tt\underline{\red{ \: x \: = \: 3 }} \\ \\ \tt \: x ↬\: the \: intercept\\ \tt\\ \hline\end{array} \: \\$

$\\$

To find the y - intercept, let x = 0

$\large \tt \: \begin{array}{|c|} \hline \tt 4x \: - \: 3y \: = \: \tt\underline{\green{ 12 }} \\ \tt 4(0) \: - \: 3y \: = \: \tt\underline{\blue{ 12 }} \\ \tt \: 0 \: - \: 3y \: = \: \tt\underline{\pink{ 12 }} \\ \tt \tt\underline{\red{ y \: = \: - 4 }} \\ \\ \tt \: x ↬\: the \: intercept \\ \ \\ \hline\end{array} \:$

$\\$

B. Replace x with 0 and solve for y. Then replace y with 0 and solve for x.

$\large \tt \: \begin{array}{|c|} \hline \tt y \: - \: intercept: \: y \: = \: \frac{1}{3}(0) \\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \tt = \tt\underline{\red{ 0 }} \\ \\ \tt \: x \: and \: y ↬ intercepts: (0,0)\\ \\ \tt \: x \: ↬ \: intercepts: \: 0 = \: \frac{1}{3} x \\ \quad\quad \quad \quad\quad\quad\quad\quad\quad \: \tt \tt\underline{\red{ \: 0 \: = \: x }} \ \\ \\ \hline\end{array} \\$

$\\$

The equation in b is a linear equation in the form y = mx, where m is any real number. the graph of any equation in the form y = mx is always a line that passes through the origin, which means that both the x - and - y - intercepts are (0,0).

$\large \tt \: \begin{array}{|c|} \hline \tt intercept \: for \: m \: of \: y \: = \: \tt\underline{\red{ mx }} \\ \hline\end{array}$

$\\$

C. Replace y with 0, then solve for the x.

$\large \tt \: \begin{array}{|c|} \hline \tt x ↬ \: intercept : \: 0 \: = \: 2x \: \ + 5 \\ \\ \tt - 5 \: = \: 2x\\ \\ \tt \: \frac{ - 5}{2} \: = \: x\\ \\ \tt \: x \: ↬ \: intercept \ \\ \hline\end{array}$

Now, replace x with 0, and then solve for y.

$\large \tt \: \begin{array}{|c|} \hline \tt y ↬ \: intercept: \: y \: = \: 2(0) \: + \: 5 \\ \\ \tt \: y \: = \: 0 \: + \: 5 \\ \\ \tt \: y \: = \: 5 \\ \\ \tt y ↬ \: intercept \ \\ \\ \hline\end{array}$

The equation in 11c is written in the form y = mx + b. note than in the form, when x is replaced by 0 to find the y↬intercept. you are left with the constant b.

$\large \tt \: \begin{array}{|c|} \hline \tt \: the \: y ↬ intercept \: of \: y \: = \: mx \: + \: b \\ \hline\end{array}$

If the equation is in the form y = mx + b, where m and b are real numbers, then the y ↬intercept is b.

$\\$

D. Remember that the graph of y = 6 is horizontally line parallel to the x axis that passes through the y axis at (0,6). since the line is parallel to x axis, it will not incest tha x-axis. Hence, there is no x ↬ intercept.

$\\ \\ \\$

$\pmb{(ノ‥)ノ}\qquad\qquad\qquad\qquad\boxed{\tt{[05-12-2022]}} \\ \qquad\qquad\qquad\qquad\qquad\qquad\boxed{\tt{[03:11 \: am]}}$

7 0

2 years ago

<img src="https://tex.z-dn.net/?f=10%7B%20-%201%7D%5E%7B2%7D%20%7B%20-%202%7D%5E%7B%20-%202%7D%20" id="TexFormula1" title="10{ -

AVprozaik [17]

$\bf ~~~~~~~~~~~~\textit{negative exponents}
\\\\
a^{-n} \implies \cfrac{1}{a^n}
\qquad \qquad
\cfrac{1}{a^n}\implies a^{-n}
\qquad \qquad 
a^n\implies \cfrac{1}{a^{-n}}
\\\\
-------------------------------\\\\
10-1^2-2^{-2}\implies 10-1-\cfrac{1}{2^2}\implies 9-\cfrac{1}{4}\implies \cfrac{36-1}{4}\implies \cfrac{35}{4}$

8 0

4 years ago

Find the domain and range of the function represented by the graph.

True [87]

Answer:

Step-by-step explanation:

The domain of this function is $[-4,2]$ , as it is shown in the graph that $x$ is only within this interval. The range of this function is $[-4,4]$ , as the smallest value of $y$ is -4 and the largest value of $y$ is 4, and $y$ takes every possible values between them.