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1 year ago

Pls help will mark as brainliest

Mathematics

1 answer:

Nata [24]1 year ago

6 0

Answer:

12.

Step-by-step explanation:

I attached my answerrrrr

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write an equation for the perpendicular bisector of the line joining the two points. PLEASE do 4,5 and 6

myrzilka [38]

Answer:

4. The equation of the perpendicular bisector is y = $\frac{3}{4}$ x - $\frac{1}{8}$

5. The equation of the perpendicular bisector is y = - 2x + 16

6. The equation of the perpendicular bisector is y = $-\frac{3}{2}$ x + $\frac{7}{2}$

Step-by-step explanation:

Lets revise some important rules

The product of the slopes of the perpendicular lines is -1, that means if the slope of one of them is m, then the slope of the other is $-\frac{1}{m}$ (reciprocal m and change its sign)
The perpendicular bisector of a line means another line perpendicular to it and intersect it in its mid-point
The formula of the slope of a line is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
The mid point of a segment whose end points are $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$
The slope-intercept form of the linear equation is y = m x + b, where m is the slope and b is the y-intercept

∵ The line passes through (7 , 2) and (4 , 6)

- Use the formula of the slope to find its slope

∵ $x_{1}$ = 7 and $x_{2}$ = 4

∵ $y_{1}$ = 2 and $y_{2}$ = 6

∴ $m=\frac{6-2}{4-7}=\frac{4}{-3}$

- Reciprocal it and change its sign to find the slope of the ⊥ line

∴ The slope of the perpendicular line = $\frac{3}{4}$

- Use the rule of the mid-point to find the mid-point of the line

∴ The mid-point = $(\frac{7+4}{2},\frac{2+6}{2})$

∴ The mid-point = $(\frac{11}{2},\frac{8}{2})=(\frac{11}{2},4)$

- Substitute the value of the slope in the form of the equation

∵ y = $\frac{3}{4}$ x + b

- To find b substitute x and y in the equation by the coordinates

of the mid-point

∵ 4 = $\frac{3}{4}$ × $\frac{11}{2}$ + b

∴ 4 = $\frac{33}{8}$ + b

- Subtract $\frac{33}{8}$ from both sides

∴ $-\frac{1}{8}$ = b

∴ y = $\frac{3}{4}$ x - $\frac{1}{8}$

∴ The equation of the perpendicular bisector is y = $\frac{3}{4}$ x - $\frac{1}{8}$

∵ The line passes through (8 , 5) and (4 , 3)

- Use the formula of the slope to find its slope

∵ $x_{1}$ = 8 and $x_{2}$ = 4

∵ $y_{1}$ = 5 and $y_{2}$ = 3

∴ $m=\frac{3-5}{4-8}=\frac{-2}{-4}=\frac{1}{2}$

- Reciprocal it and change its sign to find the slope of the ⊥ line

∴ The slope of the perpendicular line = -2

- Use the rule of the mid-point to find the mid-point of the line

∴ The mid-point = $(\frac{8+4}{2},\frac{5+3}{2})$

∴ The mid-point = $(\frac{12}{2},\frac{8}{2})$

∴ The mid-point = (6 , 4)

- Substitute the value of the slope in the form of the equation

∵ y = - 2x + b

- To find b substitute x and y in the equation by the coordinates

of the mid-point

∵ 4 = -2 × 6 + b

∴ 4 = -12 + b

- Add 12 to both sides

∴ 16 = b

∴ y = - 2x + 16

∴ The equation of the perpendicular bisector is y = - 2x + 16

∵ The line passes through (6 , 1) and (0 , -3)

- Use the formula of the slope to find its slope

∵ $x_{1}$ = 6 and $x_{2}$ = 0

∵ $y_{1}$ = 1 and $y_{2}$ = -3

∴ $m=\frac{-3-1}{0-6}=\frac{-4}{-6}=\frac{2}{3}$

- Reciprocal it and change its sign to find the slope of the ⊥ line

∴ The slope of the perpendicular line = $-\frac{3}{2}$

- Use the rule of the mid-point to find the mid-point of the line

∴ The mid-point = $(\frac{6+0}{2},\frac{1+-3}{2})$

∴ The mid-point = $(\frac{6}{2},\frac{-2}{2})$

∴ The mid-point = (3 , -1)

- Substitute the value of the slope in the form of the equation

∵ y = $-\frac{3}{2}$ x + b

- To find b substitute x and y in the equation by the coordinates

of the mid-point

∵ -1 = $-\frac{3}{2}$ × 3 + b

∴ -1 = $-\frac{9}{2}$ + b

- Add $\frac{9}{2}$ to both sides

∴ $\frac{7}{2}$ = b

∴ y = $-\frac{3}{2}$ x + $\frac{7}{2}$

∴ The equation of the perpendicular bisector is y = $-\frac{3}{2}$ x + $\frac{7}{2}$

8 0

3 years ago

Help me out please and thank you

faust18 [17]

<h3>Answer: 1</h3>

========================================================

Explanation:

We're given the height in relation to base BC, so we need to find the length of this base. This is the same as finding the distance from B to C.

Turn to the distance formula

$d = \text{Distance from B to C}\\\\d = \sqrt{(x_1-x_2)^2+(y_1-y^2)^2}\\\\d = \sqrt{(-2-(-3))^2+(-1-(-2))^2}\\\\d = \sqrt{(-2+3)^2+(-1+2)^2}\\\\d = \sqrt{(1)^2+(1)^2}\\\\d = \sqrt{1+1}\\\\d = \sqrt{2}\\\\$

Coincidentally, the base and height are the same. This won't always be the case.

Now we can find the area of the triangle

$A = \text{Area of triangle}\\\\A = \frac{1}{2}*\text{Base}*\text{Height}\\\\A = \frac{1}{2}*\sqrt{2}*\sqrt{2}\\\\A = \frac{1}{2}*\sqrt{2*2}\\\\A = \frac{1}{2}*\sqrt{4}\\\\A = \frac{1}{2}*2\\\\A = 1\\\\$

The area of the triangle is 1 square unit.

See diagram below.

5 0

3 years ago

Solve for the variable p Write the equation 4l +26p= 210. Write the equation in the form p = an expression.

Fittoniya [83]

Answer:

p = (105-2l)/13

Step-by-step explanation:

4l + 26p = 210

Isolate 26p by subtracting 4l from both sides

26p = 210-4l now divide by 26

p = (210-4l)/26 you can simply

p = (105-2l)/13

8 0

3 years ago

In approximately two to three sentences, explain how you would convert<br> 14/ 25<br> to a percent

Darina [25.2K]

Divide 14 by 25. Then you should get a decimal number. take the decimal number and multiply by 100 and done!

7 0

3 years ago

If a is (-8, 3) and c is (12, -4), find b if it is 2/5 the distance from a to c

ohaa [14]

Answer:

(0, 1/5)

Step-by-step explanation:

Since b is 2/5 of the distance from a to c, it is ...

b = a + 2/5(c -a) = 3/5a +2/5c

b = (3a +2c)/5 = (3(-8, 3) +2(12, -4))/5 = (-24+24, 9-8)/5 = (0, 1/5)

Point b is (0, 1/5).

4 0

3 years ago

Pls help will mark as brainliest​

Pls help will mark as brainliest