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-Dominant- [34]
4 years ago
7

Find the distance between the two points. (−4, 7), (4, 0)

Mathematics
1 answer:
soldi70 [24.7K]4 years ago
8 0
Use the distance formula to determine the distance between the two points.<span><span>Distance=<span>√<span><span><span>(<span>x2</span>−<span>x1</span>)</span>2</span>+<span><span>(<span>y2</span>−<span>y1</span>)</span>2</span></span></span></span><span>Distance=<span><span><span>(<span>x2</span>-<span>x1</span>)</span>2</span>+<span><span>(<span>y2</span>-<span>y1</span>)</span>2</span></span></span></span>Substitute the actual values of the points into the distance formula.<span><span>√<span><span><span>(<span>(4)</span>−<span>(0)</span>)</span>2</span>+<span><span>(<span>(7)</span>−<span>(4)</span>)</span>2</span></span></span><span><span><span>(<span>(4)</span>-<span>(0)</span>)</span>2</span>+<span><span>(<span>(7)</span>-<span>(4)</span>)</span>2</span></span></span>Simplify.Subtract <span>00</span> from <span>44</span> to get <span>44</span>.<span><span>√<span><span><span>(4)</span>2</span>+<span><span>(<span>(7)</span>−<span>(4)</span>)</span>2</span></span></span><span><span><span>(4)</span>2</span>+<span><span>(<span>(7)</span>-<span>(4)</span>)</span>2</span></span></span>Remove parentheses around <span>44</span>.<span><span>√<span><span>42</span>+<span><span>(<span>(7)</span>−<span>(4)</span>)</span>2</span></span></span><span><span>42</span>+<span><span>(<span>(7)</span>-<span>(4)</span>)</span>2</span></span></span>Raise <span>44</span> to the power of <span>22</span> to get <span>1616</span>.<span><span>√<span>16+<span><span>(<span>(7)</span>−<span>(4)</span>)</span>2</span></span></span><span>16+<span><span>(<span>(7)</span>-<span>(4)</span>)</span>2</span></span></span>Multiply <span><span>−1</span><span>-1</span></span> by <span>44</span> to get <span><span>−4</span><span>-4</span></span>.<span><span>√<span>16+<span><span>(7−4)</span>2</span></span></span><span>16+<span><span>(7-4)</span>2</span></span></span>Subtract <span>44</span> from <span>77</span> to get <span>33</span>.<span><span>√<span>16+<span><span>(3)</span>2</span></span></span><span>16+<span><span>(3)</span>2</span></span></span>Remove parentheses around <span>33</span>.<span><span>√<span>16+<span>32</span></span></span><span>16+<span>32</span></span></span>Raise <span>33</span> to the power of <span>22</span> to get <span>99</span>.<span>√<span>16+9</span></span>Add <span>1616</span> and <span>99</span> to get <span>2525</span>.<span><span>√25</span>25</span>Rewrite <span>2525</span> as <span><span>52</span><span>52</span></span>.<span><span>√<span>52</span></span><span>52</span></span>Pull terms out from under the radical, assuming positive real numbers.<span>5
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In math, prime numbers are whole numbers greater than 1, which have only two factors – 1 and the number itself. Prime numbers are divisible only by the number 1 or itself. For example, 2, 3, 5, 7, and 11 are the first few prime numbers.

Step-by-step explanation:

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Step-by-step explanation:

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Question 2
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Please show all steps and explain what you did thoroughly, thank you for your time and help.
Makovka662 [10]

Answer:

Step-by-step explanation:

1) x² + 6x + 11 = 0

a = coefficient of x² = 1

b = coefficient of x = 6

c = Constant = 11

Roots = (-b ± √b² - 4ac)/2a

D = \sqrt{b^{2}-4ac}\\\\=\sqrt{6^{2}-4*1*11}\\\\=\sqrt{36-44}\\\\=\sqrt{-8}\\\\=\sqrt{8i^{2}}\\\\ = 2i\sqrt{2}

Roots = \dfrac{-6 \± 2i\sqrt{2}}{2}\\

          = \dfrac{2(-3 \± i\sqrt{2})}{2}\\\\=-3 \± i\sqrt{2}

2) 2x² - 16x = 50

Divide the whole equation by 2

x² - 8x = 25

Divide the coefficient of x  (i. e 8 ) by 2 = 8/2 = 4, Now add 4 to both sides of the equation

x² - 8x + 4 = 25 + 4

x² - 2*4*x + 2² = 29

(x - 2)² = 29

Take square root both side

x - 2 = \± \sqrt{29}\\\\x = 2 \± \sqrt{29}

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