Coordinates of Z if Y is the midpoint of XZ, X(10,9) and Y(-4,8)

Answers

Answer 1

Answer:

[tex]Z(x,y) = (-18,7)[/tex]

Step-by-step explanation:

Given

[tex]X = (10,9)[/tex]

[tex]Y = (-4,8)[/tex]

Required

Determine the coordinates of Z

From the question, we understand that Y is the midpoint

And the midpoint is calculated as:

[tex](x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

In this case:

[tex]Y(x,y) = (-4,8)[/tex]

[tex]X(x_1,y_1) = (10,9)[/tex]

[tex]Z = (x_2,y_2)[/tex]

So: This gives

[tex](x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

[tex](-4,8) = (\frac{10+x_2}{2},\frac{9+y_2}{2})[/tex]

Multiply through by 2

[tex](-8,16) = (10 + x_2,9+y_2)[/tex]

By comparison:

[tex]-8 = 10 + x_2[/tex] and [tex]16 = 9 + y_2[/tex]

Solving for x2

[tex]-8 = 10 + x_2[/tex]

[tex]-8 - 10 = x_2[/tex]

[tex]-18 = x_2[/tex]

[tex]x_2 = -18[/tex]

Solving for y2

[tex]16 = 9 + y_2[/tex]

[tex]16 - 9 = y_2[/tex]

[tex]7 = y_2[/tex]

[tex]y_2 = 7[/tex]

Hence, the coordinates of Z is:

[tex]Z(x,y) = (-18,7)[/tex]


Related Questions

help find the missing lengths round to nearest tenth

Answers

Answer:

x = 20.8y = 22.3

Step-by-step explanation:

Theta is 21 degreesx is the adjacent side8 is the opposite sidey is the hypothenuse

SOH - CAH - TOA

Since the opposite side is given and we need to find the length of the adjacent side, we can use tangent to solve for x.

[tex]tan 21=\frac{opposite}{adjacent} \\tan 21 =\frac{8}{x} \\0.384 =\frac{8}{x} \\0.384x =8 \\x=\frac{8}{0.384} \\x=20.84[/tex]

Since the opposite side is given and we need to find the length of the hypotenuse, we can use sine to solve for y.

[tex]sin 21=\frac{opposite}{hypotenuse} \\sin21 =\frac{8}{y} \\0.358 =\frac{8}{y} \\0.358y=8 \\y=\frac{8}{0.358} \\y=22.32[/tex]

what is the difference between (4,4) and (1,-3)

Answers

Answer:

7/3

Step-by-step explanation:

If I solved it correctly, you use  y2-y1 / x2-x1. From here you get -3-4/1-4=-7/-3 which when you divide equals 7/3. LMK IF its wrong and ill figure it out champ!

9. Which of the following equations has NO solution?

A. a + 2 = a + 2
B. a = -a + 2
C. a + 2 = a - 2
D. a + a = 2​

Answers

Answer:

C. a +2 = a - 2

Step-by-step explanation:

a + 2 = a - 2

a + 4 = a

4 = 0

find the output when x = 6

Answers

Answer:

5

Step-by-step explanation:

the points is also given on graph

(6,5)

Pretty sure it’s 5.

Based on the position vs. time graph, which velocity vs. time graph would correspond to the data? A graph with horizontal axis time (seconds) and vertical axis position (meters). A line runs straight upward from 0 seconds 0 minutes.

Answers

Answer:

C or the graph with continuous acceleration (straight line)

Step-by-step explanation:

It's the right answer on edguinity

Answer:

c

Step-by-step explanation:

What is the slope of the line?

-2

1/2

1

2

Answers

Going to be number two becaus

APQR is an equilateral triangle. One side measures 5x - 7 and another side 3x + 11. Find the length of each
side.

Answers

Step-by-step explanation:

x=9

therefore,

each sides length is 9

5x-7=3x+11

=5x-3x=7+11

=2x=18

=x=9

See the attachment plsss

Find log1/4 rounded to the nearest hundredth.

Answers

Answer:

-log_4

Step-by-step explanation:

The value of log1/4 rounded to the nearest hundredth is -0.60

Given the parameter which is needed for our Calculation:

log1/4

Using a calculator, the value of log1/4 is -0.602059

Rounding to the nearest hundredth, is two digits after the decimal point.

Hence, we have ;

-0.60 (since the value after 0 is less than 5)

Therefore, log1/4 is -0.60

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Solve for the value of c.​

Answers

Answer:

c = 11

Step-by-step explanation:

2c+8+6c-6 = 90 ( the angle measure of the two angles)

8c+2 = 90

8c = 88

c = 11

what's the sum of 6+y

Answers

Answer:

6y?

It's probably wrong but off the top of my head, 6y

13 is 26%of what number

120 is 30% of what number

Answers

50 and 400 do you need me to explain

Answer:

1. 50%

2. 400

Write an equation that passes through the point (1, 3) and is perpendicular to x – 2y = -8.

Answers

Answer:

y = -2x + 5

Step-by-step explanation:

Given:

Passes through point (1, 3)

Perpendicular to x – 2y = -8

Solve:

x – 2y = -8

y = 1/2x + 4

The slope is m = 1/2

The slope of the perpendicular line is the inverse of the slope of the original equation.

The slope of the inverse equation is m = -2.

Making an inverse equation of y = -2x + a

Find a:

Use point, (1, 3) where (x, y):

3 = (-2)*(1) + a

a = 5

y = -2x + 5

Answer:

y=½x+5

Step-by-step explanation:

Passes through, (1,3)

Perpendicular to x-2y=-8.

Step 1

write the equation in form of y=mx+c

x-2y=8

-2y=-x+8

Dividing both sides of the equation by -2 we get;

y=-x/2+8

y=-½x+8

Thus the gradient is -½. Call it M1

Recall, The product of the gradients(slopes) of perpendicular lines is -1 i.e

M1 × M2= -1

Solve for M2

-½×M2=-1.

Dividing both sides by -½ we get

M2=-1×-2

M2=2

Now, use this slope(M2) with the points (1,3) to find the new equation that is perpendicular to x-2y=-8

Note: Given two points (x1,y1) and (x2,y2) the the slope would be ∆x/∆y i.e (x1-x2)/(y1-y2).

Therefore, identify new point (x,y). Use this new point with point (1,3) and the slope M2 to get the new equation.

Slope=∆x/∆y

M2=(x-1)/(y-3)

but M2 is 2

2=(x-1)/(y-3)

2/1=(x-1)/(y-3) Note: 2= 2/1

Cross multiplying we get:

2(y-3)=1(x-1)

Open the brackets

2y-6=x-1

Solve for y so as to write the equation in form of y=mx+c

2y=x-1 +6

2y=x+5

Divide both sides of the equation by 2

y=x/2+5

y=½x+5

7. In the drawing below, identify the following. (This is NOT multiple choice!)
A) Alternate Interior Angles
B) Alternate Exterior Angles
C) Consecutive Interior Angles
D) Corresponding Angles

Answers

I think answer should be d. Please give me brainlest I hope this helps let me know if it’s correct or not okay thanks

Which expression is equivalent to sqrt(80)?

Answers

Answer:

b on edg

Step-by-step explanation:

second part

a=4

b=5

Find the percent increase from the first number to the second in the following pairs.
A. 100, 140
B. 80, 125
C. 60, 80
D. 9,1

Answers

A. 40%
B. 56.25%
C. 33.3333%
D. -88.8888%

a) Show that x² - 8x + 20 can be written in the form (x - a)² + a where a is an integer.
b) Hence explain how you know that x² - 8x + 20 is always positive.

I have worked out the first bit of the question and the answer is:
x²-8x+20
x²-8x+16-16+20
(x-4)²+4
(x-a)²+a
a= 4

I just need help with part b and I'm struggling to do it. Please help.

Answers

b) x^2 - 8x + 20 is always positive because in part a, you figured out that it could also be written as (x-4)^2 + 4.
You know that (x-4)^2 is greater than or equal to 0 so by adding 4, the result will always be positive.

Answer:

Step-by-step explanation:

b) x^2 - 8x + 20 is always positive because in part a, you figured out that it could also be written as (x-4)^2 + 4.

You know that (x-4)^2 is greater than or equal to 0 so by adding 4, the result will always be positive

Nov 27, 8:06:26 PM
Find the Area of the figure below, composed of a rectangle and a semicircle. Round to
the nearest tenths place.
14
10
Answer:
Submit Answer

Answers

Answer:

The area of given figure is: 179.3

Step-by-step explanation:

The figure consists of a rectangle and a semi-circle

The length of rectangle is 14 and width is 10.

The width of rectangle is also the diameter of the semi-circle.

So,

d = 10

[tex]r = \frac{d}{2} = \frac{10}{2} = 5[/tex]

Area of Semi-Circle:

[tex]C =\frac{ \pi r^2}{2}\\= \frac{3.14 * (5)^2}{2}\\=\frac{3.14*25}{2}\\=\frac{78.5}{2}\\= 39.25[/tex]

Area of Rectangle:

[tex]R = Length * Width\\R = 10*14\\R = 140[/tex]

The total area will be the sum of area of rectangle and the area of semi-circle

So,

[tex]Total\ Area = C + R\\= 39.25 + 140\\=179.25[/tex]

Rounding off to nearest tenth

The total area is: 179.3

The sum of 4 thirteens and 16 thirteens, need answer ASAP :(

Answers

Answer:

260?

Step-by-step explanation:

I used the equation (4)13+(16)13 and plugged it into my calculator and got 260.

The sum of 4 thirteens and 16 thirteens is 260.

What is the meaning of sum?

You add up all the numbers to arrive at the sum. When you summarise something, you pay attention to all of its crucial components. A specific sum of money can also be referred to using the word sum. You might have to spend a sizable sum of money on a new car. However, you might be able to justify spending so much if you add up or total all of its advantages. When you add up the costs of everything you ordered, the total on a restaurant bill is determined. Sum need not be restricted to numbers. When you summarise something, you're providing a summary or overarching statement about it.

Here, 4 thirteens = 4 × 13 = 52

16 thirteens = 16 × 13 = 208

Sum of 4 thirteens and 16 thirteens = 52 + 208 = 260

Hence, 260 is the correct answer.

Learn more about sum from the link.

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If the r-value, or correlation coefficient, of a data set is 0.841, what is the
coefficient of determination to three decimal places?

Answers

Answer: 0.707

Step-by-step explanation:

Answer: 0.707 is the correct answer!!

Step-by-step explanation:

A building is 1ft from an 11 ft fence that surrounds the property. A worker wants to wash a window in the building 14ft from the ground. He plans to place a ladder over the fence so it rests against the building. He decided he should place the ladder 11ft from the fence for stability. To the nearest tenth of a foot, how long a ladder will he need?

Answers

Answer:

L = 18,4 ft

Step-by-step explanation:

The building, the ground, and the ladder make up a right triangle, with legs:

The distance (a) between the bottom of the ladder and the building 12 ft

The distance (b) between the gound and the window 14 ft up

The hypothenuse is the length of the ladder (L)

According to Pythagoras theorem

L²  = a²  + b²

L  = √  (12)²  +  (14)²

L = √ 144 + 196

L = √ 340

L = 18,4 ft

Describe the relationship between angles f, b, and a in the diagram.
PLEASE HELP ME IM GIVING 30 POINTS !!

Answers

The exterior angle of a triangle is equal to the sum of the two interior opposite angles, so : f° = a° + b° .

A triangle is a polygon which has 3 sides. The triangles can be divided into 3 types based on the value of the angles: Equilateral, isosceles ,scalene and right angled.

One of the internal angles of a right triangle (also known as a right-angled triangle) measures 90 degrees (a right angle). The hypotenuse, the triangle's longest side, is the side that faces the right angle. The triangle's other two sides are referred to as its legs. Right triangles adhere to the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.

We know when we add all the angles of any given triangle it is 180°

∴ a° + b° + c° = 180°

or, a° + b° = 180° - c°

Now we know that a linear pair the sum of the angles is 180°.

∴c° + f° = 180°

or, f° = 180° - c°

So from the above two equations we can say that

f° = a° + b°

Therefore in the triangle the exterior angle of the triangle is equal to the sum of the two interior opposite angles.

To learn more about triangle visit:

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What is the equation of the parabola with
vertex (4, -2) and y-intercept 6?

Answers

Answer:

Step-by-step explanation:

N sei

y+x2÷2 when x=4 and y=−3.

Answers

Answer:

The answer is 1.

Step-by-step explanation:

Plug in the values to make the equation -3+4*2/2

According to the order of operations, you should multiply what you can first.

so 4*2 = 8

Then 8 divided by 2 = 8/2=4

Then -3+4=1

Answer:

5

Step-by-step explanation:

y + x²÷2 when x=4 and y=-3

-3 + 4² ÷ 2

-3 + 16 ÷ 2

-3 + 8

5

I hoped this helped :)

(WHO EVER HELPS ME GETS BRAINLIEST AND EXTRA POINTSSSSS :D )

Answers

Answer:d

D. 9 and 46/180

Step-by-step explanation:

Answer:

Ok thank you for your efforts

Step-by-step explanation:

The answer is D 9 46/180

Kennedy draws 12 circles she shades 3/4 how many circles does jennedy shade

Answers

Answer:

9

Step-by-step explanation:

12 / 4 = 3

3 x 3 = 9

A store buys lawnmowers from the manufacturer and marks

up the price by 40% to arrive at a retail price. Fill in the

blank: The wholesale price is times the retail price.

Answers

Answer:

0.7142857

Step-by-step explanation:

Let wholesale price = x

Retail price = 40% Markup of wholesale price

Retail price = (100 + 40)% of x

Retail price = 140% of x

Retail price = 140/100 * x

Retail price = 1.4x

Hence,

Wholesale price / retail price

x / 1.4x

= 0.7142857

Hence, wholesale price is 0.7142857 of the retailer price

What is the sum of the first 10 terms of the sequence:
10,5, 0, -5, -10...
A. 100
B. -125

Answers

Answer:

-125

Step-by-step explanation:

The answer is B . -125

In a diagram of a landscape plan, the scale is 1 cm = 10 ft. In the
diagram, the trees are 4.2 cm apart. How far apart should the actual trees
be planted?

Answers

Answer:

42 ft

Step-by-step explanation:

4.2/1=4.2

4.2*10=42 ft

PLS GIVE BRAINLIEST

Answer:

42

Step-by-step explanation:

1 cm=10ft on the diagram

so the only thing we have to do is multiply.

4.2x10=42 make sure your answer is in FT not CM

so for example

42ft. Units are important XD

What is 3,350,000 in scientific notation?

Answers

Answer:

10^4 or 3.5

Step-by-step explanation:

what expression gives the solution to -5+2x^2=-6x

Answers

Answer:

Step-by-step explanation:

2x² + 6x - 5 = 0

D = 36 + 40 = 76 = (2√19)²

[tex]x_{1}[/tex] = ( - 6 - 2√19) / 4 = ( - 3 - √19) / 2

[tex]x_{2}[/tex] = ( - 3 + √19) / 2

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