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3 years ago

Solve the following equation -2|x-4|+7=-3

Mathematics

1 answer:

algol [13]3 years ago

7 0

-2|x-4|+7 = -3

-2|x-4| = -10

|x-4| = 5

Two forms:

x-4 = 5 : x = 9
or
x-4 = -5 : x = -1

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Which equation has the same solution as 4-2 (1-5) = 1 – 19?

lesya [120]

The answer will be D

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3 years ago

How is the Distributive Property used to simplify operations with scientific notation

Citrus2011 [14]

Answer:

See explanation

Step-by-step explanation:

Let a,b, and c be real numbers.

The distributive property says that:

$a(b + c) = ab + ac$

Assuming we want to simplify:

$10(5*10^{-1}+150*10^{-3})$

We apply the distributive property to get:

$10(5*10^{-1}+150*10^{-3}) = 5*10^{-1} \times 10+150*10^{-3} \times 10$

We can now use rules of exponents to simplify further:

$10(5*10^{-1}+150*10^{-3}) = 5*10^{-1} \times 10^{1} +150*10^{-3} \times 10^{1}$

$10(5*10^{-1}+150*10^{-3}) = 5*10^{-1 + 1} +150*10^{-3 + 1}$

$10(5*10^{-1}+150*10^{-3}) = 5*10^{0} +150*10^{-2}$

$10(5*10^{-1}+150*10^{-3}) = 5*1+1.50*10^{-2}x {10}^{2}$

$10(5*10^{-1}+150*10^{-3}) = 5*1+1.50*10^{-2 + 2}$

$10(5*10^{-1}+150*10^{-3}) = 5+1.50*10^{0} = 6.5 \times {10}^{0}$

4 0

3 years ago

Show all steps please

OLga [1]

$9-8x\geq0\ \ \ |subtract\ 9\ from\ both\ sides\\\\-8x\geq-9\ \ \ \ |change\ signs\\\\8x\leq9\ \ \ \ |divide\ both\ sides\ by\ 8\\\\x\leq9\\\\ |9-8x|=\left\{\begin{array}{ccc}9-8x&for\ x\leq9\\8x-9&for\ x \ \textgreater \ 9\end{array}\right$

$1^o\ x\in(-\infty;\ 9]\to|9-8x|=9-8x\\\\9(9-8x)=2x+3\\81-72x=2x+3\ \ \ \ |subtract\ 81\ from\ both\ sides\\-72x=2x-78\ \ \ \ |subtract\ 2x\ from\ both\ sides\\-74x=-78\ \ \ \ |divide\ both\ sides\ by\ (-74)\\\\x=\dfrac{-78:2}{-74:2}\\\\\boxed{x=\frac{39}{37}}\in(-\infty;\ 9]$

$2^o\ x\in(9;\ \infty)\to|9-8x|=8x-9\\\\9(8x-9)=2x+3\\72x-81=2x+3\ \ \ \ |add\ 81\ to\ both\ sides\\72x=2x+84\ \ \ \ |subtract\ 2x\ from\ both\ sides\\70x=84\ \ \ \ \ \ |divide\ both\ sides\ by\ 70\\\\x=\dfrac{84:14}{70:14}\\\\x=\dfrac{6}{5}\notin(9;\ \infty)\\\\\\Answer:\boxed{x=\frac{39}{37}}$

6 0

4 years ago

Solve The System<br> -5x-5y=0<br> 6x+5y=12

Naddik [55]

9514 1404 393

Answer:

(x, y) = (12, -12)

Step-by-step explanation:

The two equations can be added to solve for x.

(-5x -5y) +(6x +5y) = (0) +(12)

x = 12 . . . . . . . . simplify

-5(12) -5(y) = 0 . . . substitute into the first equation