Mathematics High School

What is the distance of
CD

given that
C (5,-2) and D (-3,8)
Leave your answer as a square root.

Answers

Answer 1

Answer:

CD = [tex]\sqrt{164}[/tex]

Step-by-step explanation:

Calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = C(5, - 2) and (x₂, y₂ ) = (D(- 3, 8)

d = [tex]\sqrt{(-3-5)^2+(8+2)^2}[/tex]

   = [tex]\sqrt{(-8)^2+10^2}[/tex]

    = [tex]\sqrt{64+100}[/tex]

    = [tex]\sqrt{164}[/tex]

     = 2[tex]\sqrt{41}[/tex] ← in simplest form

Answer 2
Given :

C (5, - 2)D (- 3, 8)

To Find :

CD = ?

Solution :

As, we have C (5, - 2) and D (- 3, 8), to find CD let's use distance formula :

[tex] \underline{\boxed{\tt{Distance \: between \: two \: points = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}}}}}[/tex]

Here,

x₁ = 5x₂ = - 3y₁ = - 2y₂ = 8

So, by filling values :

[tex] \sf : \implies CD = \sqrt{(-3 - 5)^{2} + (8 - (-2))^{2}}[/tex]

[tex] \sf : \implies CD = \sqrt{(-8)^{2} + (8 +2))^{2}}[/tex]

[tex] \sf : \implies CD = \sqrt{64 + (10)^{2}}[/tex]

[tex] \sf : \implies CD = \sqrt{64 + 100}[/tex]

[tex] \sf : \implies CD = \sqrt{164}[/tex]

Hence, distance of CD is [tex] \bold{\sf \sqrt{164}.}[/tex]

Related Questions

Ratnam hired a car from a car renting agency which charges a flat amount of Rs x for travelling up to 40 kilometres and Rs. y per km for every kilometre travelled thereafter. How much should Ratnam pay the agency for a journey of 50 kilometres in Rs. ?

Answers

Answer:

Rs. X + Rs. 10y

Step-by-step explanation:

Charge for 40 km travel = Rs. x per km

Charge for every additional km traveled = Rs. y

Amount paid for 50 km

Fixed charge for 40km = Rs. X

Additional km = 50 - 40 = 10 kilometer

Total charge :

Rs. X + Rs. 10y

17.

The neighborhood park has a rectangular shape.What is the perimeter of the park?

Answers

Answer

There is not enough information given.

Explanation

All we know is that the neighborhood park has a rectangular shape. The length of each side is not defined. Without the length and width, you can't find the perimeter. There is not enough information given.

4x-9y+7x-3y-8x
.......

Answers

Answer:

3x-12y

Step-by-step explanation:

4x-9y+7x-3y-8x

group like terms

4x+7x-8x

11x-8x

=3x

-9y-3y

=-12y

combine terms

==3x-12y

Hope this helps! :)

Please solve as soon as possible

Answers

Answer:

.75

Step-by-step explanation:

Because three divided by four is .75

Answer:

Question 22: 0.75 or 75%

Question 23:   5:2

Step-by-step explanation:

Question 22: 3 divided by 4 equals 0.75

Question 23:  

2.5  = 2.5/1

2.5 × 10/10 equals 25/10

25/10 divided by 5 equals 5/2

5/2= 5:2

A wall and a tree are casting shadows as shown in the picture below. How tall is the tree?

Answers

Answer:

let my rat self say this, 24ft?

speaking:

I DON'T KNOW :,D

Please help me with this math problem.

Answers

(X+4)(x-4)

Explanation

Since both terms are perfect squares, factor using the difference of squares formula,
Hello

Donkey Kong is rolling cylindrical barrels
of different sizes at Mario.

The DIAMETER of the barrel is 16.5.

What is the circumference of the barrel?

If your answer is correct Mario will clear the barrel.

Answers

You must half the diameter to get the radius
Then you can use
2times pie times radius to get the circumference.

2 ×3.141592653589793×8.25=
51.83627878423158

Circumference of the barrel is 51.81 unit

Circumference of the circle:

Given that;

Diameter of barrel = 16.5 unit

Find:

Circumference of the barrel

Computation:

Radius of barrel = 16.5/2 unit

Radius of barrel = 8.25 unit

Circumference of the barrel = Circumference of the circle

Circumference of the barrel = 2πr

Circumference of the barrel = 2(3.14)(8.25)

Circumference of the barrel = 51.81 unit

Find out more information about 'Circumference'.

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It took Jenny 2 hours to knit 1/3 of a scarf.
How many hours will it take for her to make
one scarf?

Answers

Answer:

6 hours

Step-by-step explanation:

Bc 2hours for 1/3 so and 4 more hours and u get 6. Hope this helps u have a good day. Sorry if wrong

Answer:

6 hours

Step-by-step explanation:

Which interval on the graph could be described as linear increasing?

A

B

C

D

Answers

The right answer is B.

Christine buys a necklace that cost $18.62 and a ring that costs $7.98. She used a 35%-off coupon on the purchase. If Christine pays with a $20 dollar bill, how much change should she get back?

Answers

Christine will get $2.71 worth of change

Carter is deciding between two different movie streaming sites to subscribe to. Plan A costs $19 per month plus $2 per movie watched. Plan B costs $31 per month plus $0.50 per movie watched. Let AA represent the monthly cost of Plan A if Carter watches xx per month, and let BB represent the monthly cost of Plan B if Carter watches xx movies per month. Write an equation for each situation, in terms of x, and determine the interval of movies watched, x, for which Plan A is cheaper than Plan B.

Answers

Answer:

19x+2x=AA

31x+0.50x=BB

Step-by-step explanation:

Answer:

A  =  2x +19

B  =  0.50x + 31

Plan A is cheaper than Plan B when x < 8 movies

Step-by-step explanation:

2x + 19  =  0.50x + 31

1.5x  =  12

x  =  8

3. If RT= 5x + 8 and Rz= 4x + 1 find ZT

Answers

Answer: ZT=9

Step-by-step explanation:

5x+8=2(4x+1)

Which are vertical angles? Check all that apply. ∠EAB and ∠BAC ∠EAB and ∠CAD ∠CAD and ∠FAE ∠CAB and ∠DAE ∠DAC and ∠DAE

Answers

*See attachment for the diagram

Answer:

B. ∠EAB and ∠CAD;

D. ∠CAB and ∠DAE

Step-by-step explanation:

Vertical angles are two angles formed directly opposite each other when two straight lines crosses or intercepts each other. Vertical angles are of equal measure to each other.

Thus, from the diagram given,

<CAD is vertically opposite to <EAB, also,

<CAB is vertically opposite to <DAE.

Thus, the vertical angles are:

∠EAB and ∠CAD;

∠CAB and ∠DAE

Answer:

B and D

Step-by-step explanation:

Hope it helps ^w^

What steps would you use to solve this equations for x? *

Answers

Answer:

x=-24

Step-by-step explanation:

Multiply both sides by 4 to get x=-24

[tex]\\ \rm\hookrightarrow -6=\dfrac{x}{4}[/tex]

Multiply 4 on both sides

[tex]\\ \rm\hookrightarrow x=-6(4)[/tex]

[tex]\\ \rm\hookrightarrow x=-24[/tex]

Find the slope
Y=-x+2

Answers

Answer:

slope = -1

Step-by-step explanation:

take the equation: y = mx + b for slope-intercept

y is the input

m is the slope

x is the output

b is the y-intercept

when the slope is -1, it is seen and implied as -x.

need help will give brainlist

Answers

Answer:

40

Step-by-step explanation:

Answer:

11 is the answer.

Evaluate the expression when a=1/4
and b = 6.
-8ab=

Answers

Answer:

-12

Step-by-step explanation:

-8(1/4)(6)

-8/4=-2

-2*6=-12

select the correct answer from each dropdown menu. in the figure, the radius of the partial circle with center A is 4 feet.
The perimeter of the figure is A.____ feet, and the area of the figure is B.____ square feet. Assume =3.14, and round your answers to the nearest hundredth.​
A.- 18.84 - 24.50 - 26.84 - 75.36
B.- 11.42 - 22.84 - 45.68 - 53.68

Answers

Answer:

Step-by-step explanation:

Part A: 24.50 feet, Part B: 46.68 square feet, I just took the test and got this right!

The perimeter of the figure is [tex]24.50[/tex] and area of the figure is [tex]45.68[/tex] square feet.

What is Area of Circle?

In geometry, the area enclosed by a circle of radius r is πr². Here the Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159

According to question, the radius of the partial circle with center A is 4 feet.

We have to find the perimeter and area of the figure.

Perimeter of the figure=2πr×[tex]\frac{3}{4}[/tex] +[tex]4\sqrt{2}[/tex]

=2×[tex]3.14[/tex]×[tex]4[/tex]×[tex]0.75+4[/tex]×[tex]1.414[/tex]

[tex]=24.50[/tex]

Area of figure=[tex]\frac{3}{4}[/tex] πr²+[tex]r^{2}[/tex]×[tex]\frac{1}{2}[/tex]

=[tex]0.75[/tex]×[tex]3.14[/tex]×[tex]16[/tex][tex]+16[/tex]×[tex]0.5[/tex]

[tex]=37.68+8[/tex]

[tex]=45.68[/tex]

Hence, we can conclude that the perimeter of the figure is [tex]24.50[/tex] and area of the figure is [tex]45.68[/tex] square feet.

Learn more about area of circle  here:

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#SPJ2

What is the range of the data?
79, 52, 85, 94, 71, 82, 84, 66, 58, 98, 72, 100
A. 21
B. 48
C. 82
D. 100

Answers

Answer:

A. 21

Step-by-step explanation:

To find range you just take the highest number and subtracted by the lowest

Answer:

A

Step-by-step explanation:

what is the algebraic expression of
1 less than the quotient of 7 and a number x

Answers

Answer:

(7 ÷ x) - 1

Step-by-step explanation:

i tried, i tried

PLZ HELP I MARK U BRAINLIEST

Answers

Answer:

8/9

Step-by-step explanation:

Make 4 as a fraction. It turns to 4/1

2/9 x 4/1 = 8/9

what number lies between -2 and -3​

Answers

Answer:

-2.5?

Step-by-step explanation:

Solve for r in terms s, t, u, v.
su=rtv

Answers

Answer:

r = su/tv

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right  

Equality Properties

Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of Equality

Step-by-step explanation:

Step 1: Define

su = rtv

Step 2: Solve for r

[Division Property of Equality] Divide tv on both sides:                               su/tv = rRewrite/Rearrange:                                                                                         r = su/tv
Making r subject of formula, we get:

r = su/tv

Quadrilateral FGHI is similar to quadrilateral JKLM. Find the measure of side KL. Round your answer to the nearest tenth.

Answers

Answer:

The answer is "31.888".

Step-by-step explanation:

When their respective angles were congruent or their side lengths have a constant relation, they know that two quadrilaterals are similar

FGHI is similar to JKLM because of quadrilateral

[tex]\to \frac{FG}{JK} =\frac{GH}{KL}=\frac{HI}{LM}=\frac{FI}{JM}\\\\\to \frac{GH}{KL} =\frac{HI}{LM}\\\\\to \frac{7}{KL}= \frac{9}{41}\\\\\to KL=\frac{7 \times 41}{9}=31.888\\\\[/tex]

Answer:

12.3

Step-by-step explanation:

Trust me I got it wrong

Hey. Could you help?

Answers

Answer:

C

Step-by-step explanation:

sorry, I dont have time for a full explanation. maybe wait for the next person's answer too. just to verify mine.

hope this helps <3

Which type of function are the following equations?
1. ƒ(x) = 4x^2
2. g(x) = 1 - x
Linear, Exponential or Quadric.
(You mau choose a different answer for each equation).

Answers

Answer:

1 quadric

2 linear

Step-by-step explanation:

plz make me brainliest

1. How do the heights of the chimpanzee and gorilla habitats compare to the height of the
orangutan habitat? Round all answers to the nearest hundredth of a yard. Show your work.
2. Label a point Z that is vertical to point X and horizontal to point Y. A string of lights is being hung
from point Z to the cable that connects the gorilla and chimpanzee habitats. The string of lights
will create a right angle with the cable. Determine the distance between point Y and the point
where the string of lights attaches to the cable. Round all answers to the nearest hundredth of a
yard. Show your work.

Answers

Answer: im confused on what your asking can u give me more detail.

Step-by-step explanation:

please help me on this will give you brainliest!!

Answers

36!!
18/2= 9
45/5= 9
9 x 4 = 36

Answer:

AC = 36

Step-by-step explanation:

since these triangles are similar, we can use the triangle similitary theorem. This means that the sides are proportional to each other.

ef/bc = 5/45 (1/9) = ed/ba =  2/18 (1/9)

we can see the sides are in a ratio of 1:9, and plug it in the proportion

df/ac = 1/9

4/ac = 1/9

cross multiply and we get that ac = 36

Which is the correct way to find the length of a line segment with endpoints (0,4) and (7,-9)?

Answers

Answer:

0 is Y 7 is X 4 is Y and -9 is X

Step-by-step explanation:

you can use Y and X to pin point the spots

Will give, Branliest for anyone who answers.​

Answers

4,6,20

150,75
70,35
120,60
110,56

5/2

10/4

15/6

50/20

300 G  150 G 75 G

140 G 70 G 35 G

420 G 210 G 105 G

220 G 110 G 55 G

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