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3 years ago

What is the distance between (-6. 2) and (8.10) on a coordinate grid?

Mathematics

1 answer:

nalin [4]3 years ago

7 0

Answer:

The distance between 2 points is 16.1 units.

Step-by-step explanation:

You have to apply distance formula using coordinates,

$distance = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} }$

Let (x1,y1) be (-6,2),

Let (x2,y2) be (8,10)

$distance = \sqrt{ {(8 - ( - 6))}^{2} + {(10 - 2)}^{2} }$

$distance = \sqrt{196 + 64}$

$distance = \sqrt{260}$

$distance = 2 \sqrt{65}$

$distance = 16.1 \: units \: (3s.f)$

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4.6 x 10 to the 6 power minus 8.3 x 10 to the 5th power

snow_tiger [21]

The answer is 3,770,000

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2 years ago

Which equation is y = 9x2 + 9x – 1 rewritten in vertex form?

Anastasy [175]

Answer:

$y = 9(x +\frac{1}{2}) ^ 2 -\frac{13}{4}$

Step-by-step explanation:

An equation in the vertex form is written as

$y = a (x-h) + k$

Where the point (h, k) is the vertex of the equation.

For an equation in the form $ax ^ 2 + bx + c$ the x coordinate of the vertex is defined as

$x = -\frac{b}{2a}$

In this case we have the equation $y = 9x^2 + 9x - 1$ .

Where

$a = 9\\\\b = 9\\\\c = -1$

Then the x coordinate of the vertex is:

$x = -\frac{9}{2(9)}\\\\x = -\frac{9}{18}\\\\x = -\frac{1}{2}$

The y coordinate of the vertex is replacing the value of $x = -\frac{1}{2}$ in the function

$y = 9 (-0.5) ^ 2 + 9 (-0.5) -1\\\\y = -\frac{13}{4}$

Then the vertex is:

$(-\frac{1}{2}, -\frac{13}{4})$

Therefore The encuacion excrita in the form of vertice is:

$y = a(x +\frac{1}{2}) ^ 2 -\frac{13}{4}$

To find the coefficient a we substitute a point that belongs to the function $y = 9x^2 + 9x - 1$

The point (0, -1) belongs to the function. Thus.

$-1 = a(0 + \frac{1}{2}) ^ 2 -\frac{13}{4}$

$-1 = a(\frac{1}{4}) -\frac{13}{4}\\\\a = \frac{-1 +\frac{13}{4}}{\frac{1}{4}}\\\\a = 9$

Then the written function in the form of vertice is

$y = 9(x +\frac{1}{2}) ^ 2 -\frac{13}{4}$

7 0

3 years ago

Professor Goodheart has two exams, exam 1 and exam 2. The exam 1 weights 40% and the exam 2 weights 60% of the final grades. Put

garri49 [273]

Answer:

Imperfect substitutes

explanation:

The choices above are not perfect substitutes, meaning they can not be perfectly or directly replace the other. Imperfect substitutes are close substitutes but not perfect substitutes. Unlike perfect substitutes, imperfect substitutes satisfies same utility but has different characteristics and therefore not entirely substitutable. For example, while one may want to have the 40 marks too, he'd rather have 60 marks even if the criteria for a 60 mark score was increasingly hard.

8 0

3 years ago

Simplify (-3c^-3w^5)^3 A -9w^8 B. -27cw^8 C. w^15/27c^9 D.-27w^15/c^9

kenny6666 [7]

Answer:

$\large\boxed{D.\ \dfrac{-27w^{15}}{c^9}}$

Step-by-step explanation:

$(-3c^{-3}w^5)^3\qquad\text{use}\ (ab)^n=a^nb^n\\\\=(-3)^3(c^{-3})^3(w^5)^3\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=-27c^{-3\cdot3}w^{5\cdot3}=-27c^{-9}w^{15}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=-27\left(\dfrac{1}{c^9}\right)w^{15}=\dfrac{-27w^{15}}{c^9}$

4 0

3 years ago

katie is planting a garden for her science fair project. she needs 2/3 of a cup of soil to go in 8 different pots.how many cups

Brilliant_brown [7]

Answer:

5 and 1/3 cups of soil

Step-by-step explanation:

Hello there, in this problem we can solve for the amount of soil that Katie will need by multiplying the factor for one of them by the number of pots we have, 8. We get 16/3 cups of soil, or 5 and 1/3 cups of soil.

Hope this helps!

-HM

3 0

3 years ago

Read 2 more answers