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4 years ago

If a line segment contains one endpoint at (2,3) and has a midpoint of (-2,6) what is the second endpoint of the line segment

Mathematics

1 answer:

olchik [2.2K]4 years ago

4 0

Answer:

Step-by-step explanation:

The coordinates of the midpoint M are the average of the coordinates of the two endpoints:

$M_x = \dfrac{2+x}{2},\quad M_y = \dfrac{3+y}{2}$

Plug the known coordinates of the midpoint:

$-2 = \dfrac{2+x}{2},\quad 6 = \dfrac{3+y}{2}$

Solve for x and y:

$-4 = 2+x,\quad 12 = 3+y$

$x=-6,\quad y = 9$

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Can somebody help me on 23 and 24, it’s geometry

Luda [366]

Question 23:

x = 4

DE = 44

Question 24:

x = 25

SE = 28

Step-by-step explanation:

As RS is the perpendicular bisector of DE, it will divide DE in two equal parts DS and SE

Question number 23:

Given

DS = 3x+10

SE = 6x-2

As the two segments are equal:

$DS = SE\\3x+10 = 6x-2$

Subtracting 10 from both sides

$3x+10-10 = 6x-2-10\\3x = 6x-12$

subtracting 6x from both sides

$3x -6x = 6x-6x-12\\-3x = -12$

Dividing both sides by -3

$\frac{-3x}{-3} = \frac{-12}{-3}\\x = 4$

Now

$DS = 3x+10\\= 3(4)+10\\= 12+10\\=22$

And

$SE = 6x-2\\= 6(4)-2\\= 24 - 2\\=22\\DE = DS+SE\\= 22+22\\=44$

Question No 24:

Given

DS = x+3

DE = 56

We know that:

$DS = \frac{1}{2}DE\\x+3 = \frac{56}{2}\\x + 3 = 28\\x = 28-3\\x = 25$

DS = $25+3 = 28$

As DS is 28, SE will also be 28

Hence,

Question 23:

x = 4

DE = 44

Question 24:

x = 25

SE = 28

Keywords: Bisector, Line segment

Learn more about line segments at:

#LearnwithBrainly

4 0

3 years ago

2/5 of a number is what percantage of that number

iragen [17]

Answer:

40% of that number

8 0

3 years ago

Read 2 more answers

Is the relationship shown by the data linear? If so, model the data with an equation.

Marina CMI [18]

Answer:

4th option

Step-by-step explanation:

The relationship is linear,

putting the value of x in the right side of the equation of option 4, you'll get the value of the left side

putting, x=1

y+4=-1/2(x-1)

y=-1/2(1-1)-4

y=-4

putting, x=7

y+4=-1/2(7-1)

y=-1/2(6)-4

y=-6/2-4

y=-3-4

y=-7

8 0

3 years ago

⦁ In a simple random sample of 1219 US adults, 354 said that their favorite sport to watch is football. Construct a 95% confiden

fomenos

Answer:

95% confidence interval for the proportion of adults in the United States whose favorite sport to watch is football is [0.265 , 0.316].

Step-by-step explanation:

We are given that in a simple random sample of 1219 US adults, 354 said that their favorite sport to watch is football.

Firstly, the pivotal quantity for 95% confidence interval for the proportion of adults in the United States whose favorite sport to watch is football is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = proportion of adults in the United States whose favorite sport to watch is football in a sample of 1219 adults = $\frac{354}{1219}$

n = sample of US adults = 1291

p = population proportion of adults

Here for constructing 95% confidence interval we have used One-sample z proportion statistics.

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%

significance level are -1.96 & 1.96}

P(-1.96 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }$ < ${\hat p-p}$ < $1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }$ ) = 0.95

P( $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }$ < p < $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }$ ) = 0.95

95% confidence interval for p = [ $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }$ , $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }$ ]

= [ $\frac{354}{1219}-1.96 \times {\sqrt{\frac{\frac{354}{1219}(1-\frac{354}{1219})}{1219} }$ , $\frac{354}{1219}+1.96 \times {\sqrt{\frac{\frac{354}{1219}(1-\frac{354}{1219})}{1219} }$ ]

= [0.265 , 0.316]

Therefore, 95% confidence interval for the proportion of adults in the United States whose favorite sport to watch is football is [0.265 , 0.316].

5 0

3 years ago

I know the answer is 324 but can someone tell me step by step how to solve it?

love history [14]

Do what is in brackets first, then the multiplication.

5 0

3 years ago