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2 years ago

find the distance between the points. give an exact answer and an approximation to three decimal places

Mathematics

1 answer:

Fudgin [204]2 years ago

7 0

7.21 units is the distance between the two points.

<h3>How to find the distance between the points?</h3>

The length of the line segment connecting any two points is referred to as their distance. In coordinate geometry, the distance between two points can be computed by measuring the length of the line segment connecting the two points.

The formula distance between the points is

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

the points are (x1 , y1) = (-6,-5)

(X2 , y2) = (-12,-9)

now, place the values of x and y in formula

$d = \sqrt{ {( - 9- ( - 5))}^{2} + {( - 12-( - 6))}^{2} } \\ d = \sqrt{ {( - 9 + 5)}^{2} + {( - 12 + 6)}^{2} }$ $d = \sqrt{ {( - 4)}^{2} + ( - 6) {}^{2} } \\ d = \sqrt{16 + 36} \\ d = \sqrt{52} \\ d = 7.21 \: units$

Hence, 7.21 units is the distance between the two points.

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Disclaimer: The question is incomplete on portal. This is complete question.

Question: Find the distance between the points. give an exact answer and an approximation to three decimal places (-6,-5)&(-12,-9)

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Is 3.14 a rational or irrational

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Answer:

Rational

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3 years ago

Elliott has some yarn that she wants to use to make hats and scarves. Each hat uses 0.2, point, 2 kilograms of yarn and each sca

sp2606 [1]

Answer:

Elliot will make 4 hats and 16 scarves

Step-by-step explanation:

Let x be the number of hats and y be the number of scarves Elliot will make.

Elliott wants to make a total of 20 items, then

x + y = 20

Each hat uses 0.2 kilograms of yarn, so x hats use 0.2x kilograms of yarn and each scarf uses 0.1 kilogram of yarn, then y scarves use 0.1y kilograms of yarn. Elliott wants to use twice as much yarn for scarves as for hats, then

0.1y = 2(0.2x)

Thus,

0.1y = 0.4x

y = 4x

Substitute it into the first equation:

x + 4x = 20

5x = 20

x = 4

y = 20 - 4

y = 16

Hence, Elliot will make 4 hats and 16 scarves

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3 years ago

washington high school's head tennis coach, ms. racket, runs a tennis camp for middle school students every summer. the students

Kaylis [27]

Your question was incomplete. Please refer the content below:

Washington high school's head tennis coach, Ms. racket, runs a tennis camp for middle school students every summer. the students bring their own lunches, but Ms. racket provides them with snacks. there is a proportional relationship between the number of students who enroll in Ms. racket's tennis camp, x, and the total number of snacks she buys, y. what is the constant of proportionality? write your answer as a whole number or decimal. snacks per student.

X Y

10 30

13 39

14 42

21 63

The constant of proportionality is 3 as for 1 student she buys 3 snacks.

The constant of proportionality means the ratio between the terms x and y.

It is calculated by dividing y by x.

Here we get that:

X Y constant of proportionality(Y/X)

10 30 3

13 39 3

14 42 3

21 63 3

Therefore, we get the constant of proportionality as 3.

Learn more about constant of proportionality here:

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2 years ago

HELP PLZZZ I NEED ANSWERS

asambeis [7]

Answer:

Step-by-step explanation:

y = (x - 5)^2 + 16

= x^2 - 5x - 5x + 25 + 16

= x^2 - 10x + 41

That corresponds with answer choice D.

Hope this helps!

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3 years ago

Help me asap! I will give you marks

Law Incorporation [45]

Recall the binomial theorem.

$(a+b)^n = \displaystyle \sum_{k=0}^n \binom nk a^{n-k} b^k$

1. The binomial expansion of $\left(1+\frac x3\right)^7$ is

$\left(1 + \dfrac x3\right)^7 = \displaystyle\sum_{k=0}^7 \binom 7k 1^{7-k} \left(\frac x3\right)^k = \sum_{k=0}^7 \binom 7k \frac{x^k}{3^k}$

Observe that

$k = 1 \implies \dbinom 71 \left(\dfrac x3\right)^1 = \dfrac73 x$

$k = 2 \implies \dbinom 72 \left(\dfrac x3\right)^2 = \dfrac73 x^2$

When we multiply these by $8-9x$ ,

• $8$ and $\frac73 x^2$ combine to make $\frac{56}3 x^2$

• $-9x$ and $\frac73 x$ combine to make $-\frac{63}3 x^2 = -21x^2$

and the sum of these terms is

$\dfrac{56}3 x^2 - 21x^2 = \boxed{-\dfrac73 x^2}$

2. The binomial expansion is

$\left(2a - \dfrac b2\right)^8 = \displaystyle \sum_{k=0}^8 \binom 8k (2a)^{8-k} \left(-\frac b2\right)^k = \sum_{k=0}^8 \binom 8k 2^{8-2k} a^{8-k} b^k$

We get the $a^6b^2$ term when $k=2$ :

$k=2 \implies \dbinom 82 2^{8-2\cdot2} a^{8-2} b^2 = 28 \cdot2^4 a^6 b^2 = \boxed{448} \, a^6b^2$

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1 year ago