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Eddi Din [679]
3 years ago
11

Just number 7 would be fine but if you could also number 8 would help a lot​

Mathematics
2 answers:
BlackZzzverrR [31]3 years ago
8 0

Answer:

7. r = -5

8. x = -1

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

Step-by-step explanation:

<u>Step 1: Define</u>

r + 2 - 8r = -3 - 8r

<u>Step 2: Solve for </u><em><u>r</u></em>

  1. Combine like terms:                    -7r + 2 = -3 - 8r
  2. Add 8r to both sides:                   r + 2 = -3
  3. Subtract 2 on both sides:            r = -5

<u>Step 3: Check</u>

<em>Plug in r into the original equation to verify it's a solution.</em>

  1. Substitute in <em>r</em>:                    -5 + 2 - 8(-5) = -3 - 8(-5)
  2. Multiply:                              -5 + 2 + 40 = -3 + 40
  3. Add:                                    -3 + 40 = -3 + 40
  4. Add:                                    37 = 37

Here we see that 37 does indeed equal 37.

∴ r = -5 is a solution of the equation.

<u>Step 4: Define equation</u>

-4x = x + 5

<u>Step 5: Solve for </u><em><u>x</u></em>

  1. Subtract <em>x</em> on both sides:                    -5x = 5
  2. Divide -5 on both sides:                      x = -1

<u>Step 6: Check</u>

<em>Plug in x into the original equation to verify it's a solution.</em>

  1. Substitute in <em>x</em>:                    -4(-1) = -1 + 5
  2. Multiply:                               4 = -1 + 5
  3. Add:                                     4 = 4

Here we see that 4 does indeed equal 4.

∴ x = -1 is a solution of the equation.

djverab [1.8K]3 years ago
8 0
Yeah I think whatever that dude just said was right
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A rotation is a transformation that preserves figure shape, figure sizes, angles and lengths.

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Question 15 (5 points)<br> Find the angle between u = &lt;7, -2&gt; and v= (-1,2&gt;.
Tema [17]

Answer:

Approximately 2.3127 radians, which is approximately 132.51^{\circ}.

Step-by-step explanation:

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Magnitude of the two vectors:

\begin{aligned} \| u \| &= \sqrt{{7}^{2} + {(-2)}^{2}} \\ &= \sqrt{53} \end{aligned}.

\begin{aligned} \| v \| &= \sqrt{{(-1)}^{2} + {2}^{2}} \\ &= \sqrt{5} \end{aligned}.

Let \theta denote the angle between these two vectors. By the property of dot products:

\begin{aligned} \cos(\theta) &= \frac{u \cdot v}{\|u\| \, \| v \|} \\ &= \frac{(-11)}{(\sqrt{53})\, (\sqrt{5})} \\ &= \frac{(-11)}{\sqrt{265}}\end{aligned}.

Apply the inverse cosine function {\rm arccos} to find the value of this angle:

\begin{aligned} \theta &= \arccos\left(\frac{u \cdot v}{\| u \| \, \| v \|}\right) \\ &= \arccos\left(\frac{(-11)}{\sqrt{265}}\right) \\ & \approx \text{$2.3127$ radians} \\ &= 2.3127 \times \frac{180^{\circ}}{\pi} \\ &\approx 132.51^{\circ}\end{aligned}.

8 0
2 years ago
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