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2 years ago

Find the distance between the points given. (-3, -6) and (3, 2)

Mathematics

1 answer:

vlada-n [284]2 years ago

5 0

Answer:

10 units

Step-by-step explanation:

Moving from (-3, -6) to (3, 2), x increases by 6. Draw a triangle and use this 6 as the length of the base. y increases by 8. Label the height of the triangle with this 8. Then find the hypotenuse (which is also the desired distance) by using the Pythagorean Theorem:

6^2 + 8^2 = d^2, where d is that distance:

36 + 64 = 100 = d^2, and so d = 10. The distance in question is 10 units.

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2v^2-12 =-12v Would really appreciate it loves❤️

Black_prince [1.1K]

For this case we have the following equation:

$2v ^ 2-12 = -12v$

Rewriting we have:

$2v ^ 2 + 12v-12 = 0$

Dividing by 2 to both sides of the equation:

$v ^ 2 + 6v-6 = 0$

We apply the quadratic formula:

$x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}$

We have to:

$a = 1\\b = 6\\c = -6$

Substituting:

$x = \frac {-6 \pm \sqrt {6 ^ 2-4 (1) (- 6)}} {2 (1)}\\x = \frac {-6 \pm \sqrt {36 + 24}} {2}\\x = \frac {-6 \pm \sqrt {60}} {2}\\x = \frac {-6 \pm \sqrt {4 * 15}} {2}\\x = \frac {-6 \pm2 \sqrt {15}} {2}$

Thus, we have two roots:

$x_ {1} = - 3+ \sqrt {15}\\x_ {2} = - 3- \sqrt {15}$

ANswer:

$x_ {1} = - 3+ \sqrt {15}\\x_ {2} = - 3- \sqrt {15}$

7 0

2 years ago

Represent each sum as a single rational number. 7 + (1/9)

Nady [450]

Answer:

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Step-by-step explanation:

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3 years ago

A jar containing only nickels and dimes contains a total of 60 coins. The value of all the coins in the jar is $4.45. Solve by e

borishaifa [10]

Answer: 31 nickels and 29 dimes

Step-by-step explanation:

Nickels (.05): x

Dimes (.10): y

Value: .05x + .10y = 4.45 → -20(.05x + .10y = 4.45) → -x - 2y = -89

Quantity: x + y = 60 → 1(x + y = 60) → x + y = 60

-y = -29

y = 29

Next, substitute "29" for "y" into either equation and solve for "x":

x + y = 60

x + 29 = 60

x = 31

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3 years ago

What are the answers to these aswell mb?

docker41 [41]

Answer:

4 is D = 23

Step-by-step explanation:

the coefficient is the number before the letter

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3 years ago

Find all values of x that make the triangles congruent. Explain your reasoning.

RSB [31]

Answer:

x = $\frac{4}{5},5$

Step-by-step explanation:

If both the triangles ΔABC and ΔBCD are congruent,

Corresponding sides of both the triangles will be proportional.

$\frac{AB}{BD}=\frac{AC}{CD}$

$\frac{5x}{3x+10}=\frac{5x-2}{4x+3}$

5x(4x + 3) = (5x - 2)(3x + 10)

20x² + 15x = 15x² + 50x - 6x - 20

20x² + 15x = 15x² + 44x - 20

20x² - 15x² = 44x - 15x - 20

5x² = 29x - 20

5x² - 29x + 20 = 0

5x² - 25x - 4x + 20 = 0

5x(x - 5) - 4(x - 5) = 0

(5x - 4)(x - 5) = 0

$x=\frac{4}{5},5$

3 0

2 years ago