Given that the four points A(1,2), B(2, -5), C(7,0) and D(p,q) are the vertices of the rhombus ABCD

calculate

a) the value of p and of q​

Answers

Answer 1

Step-by-step explanation:

Three coordinates of a Rhombus is given to us. And the fourth coordinate is D(p,q) . Weneedtofind the value of p and q . We know that the diagonals of Rhombus bisect each other at right angles . So lets find the midpoint.

• Midpoint of AC :-

[tex]\tt\to Midpoint_{(AC)}= \bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\\\\\tt\to Midpoint_{(AC)}= \bigg( \dfrac{1+7}{2},\dfrac{2+0}{2}\bigg)\\\\\tt\to Midpoint_{(AC)}= \bigg(\dfrac{8}{2},\dfrac{2}{2}\bigg)\\\\\tt\to \boxed{\orange{\tt Midpoint_{(AC)}= (4,1)}}[/tex]

_______________________________

• Midpoint of BD :-

[tex]\tt\to Midpoint_{(BD)}= \bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\\\\\tt\to \boxed{\orange{\tt Midpoint_{(BD)}= \bigg( \dfrac{2+p}{2},\dfrac{q-5}{2}\bigg)}}[/tex]

_______________________________

Now since these two coordinates must be equal, therefore ,

[tex]\tt\to \bigg( \dfrac{2+p}{2},\dfrac{q-5}{2}\bigg)= (4,1)\\\\\tt\to \dfrac{2+p}{2}=4 \qquad and \qquad \dfrac{q-5}{2}=1 \\\\\tt\to 2 + p = 8 \qquad and \qquad q-5 = 2 \\\\\tt\to p = 8 -2 \qquad and \qquad q = 2 +5 \\\\\tt\to\boxed{\orange{\tt (p,q) = (6,7) }}[/tex]


Related Questions

what is (0,3) given a slope of -2, in slope intercept form

Answers

Answer:

y=-2x + 3

Step-by-step explanation:

Answer:

y=-2x + 3

Step-by-step explanation:

(0,3) is the y intercept and

-2 is the slope

Prepare depreciation schedules using Straight-Line, Units-of-Production, and Double-Declining Balance Depreciation.

Answers

Answer:

f

Step-by-step explanation:

f

find the length of the segment. someone pls help me

Answers

Answer:

x = 7

Step-by-step explanation:

The segment from the centre at right angles to the chord, bisects the chord, so

x = 7

A coffee shop sells 40 regular coffees out of every 120 coffees they sell. Predict how many regular coffees the shop would sell if they sold 960 coffees.

Answers

Answer:

320

Step-by-step explanation:

960 ÷ 120 = 8

40 × 8 = 320

pamela is 10 years older than Jiri. the sum of their ages is 76. what is jiri age

Answers

Answer:

jiri's age is 66 years old

Step-by-step explanation:

76-10= 66 years old

use the graph f(x)=-x^2+8x+20 to determine the values of m for which m= -x^2+8x+m=0 will have two positive roots​

Answers

Answer:

first root -2 and the second is 10

Step-by-step explanation:

delta=b squared-4ac=64-4(-1)(20)=144>0

then we have 2 +roots

x1= -b+ radical delta/2a =-2

x2=-b - radical delta/2a=10

The value of m for which -x² +8x+m=0 to have two positive roots is m ≤ 0.

What is a polynomial?

A polynomial is an expression that involves the addition, subtraction and multiplication of variables.

A quadratic polynomial is a polynomial of degree 2.

Given that:

f(x)=-x² + 8x + 20

To determine the values of m for which -x² +8x+m=0 would have two positive roots​

For -x² +8x+m=0 to have two positive roots, m ≤ 0.

The value of m for which -x² +8x+m=0 to have two positive roots is m ≤ 0.

Find out more on polynomial at: https://brainly.com/question/2833285

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Answers

its not allowing me to send it. can i send somewhere else?

Step-by-step explanation:

In a park, a sidewalk is built around the edge of a circular garden as shown. The sidewalk is 5 feet wide, and the garden measures 10 feet across. Which measurement is closest to the circumference of the outer edge of the sidewalk?

Answers

Answer:

63 feet.

Step-by-step explanation:

The total diameter of the circular garden is given by 5ft+ 10 ft + 5 ft= 20 feet

As the circumference of the circle = 2πr where r = radius obtained by dividing the diameter by 2. Here the diameter = 20 feet and r= d/2 = 20/2 = 10 feet

Putting the values in the circumference formula

Then C= 2(22/7) (10)= 62.85 feet

Rounding gives almost 63 feet .

I'm stuck on this problem! A linear function that represents the number of video games purchased at an electronics store is compared to a different linear function that represents the amount of money the store made that day. Describe the key features of the functions that are needed to determine if these lines intersect.

Answers

Answer:

In order two straight lines in a coordinate plane intersect, they MUST have different slopes.

This condition is  NECESSARY  and  SUFFICIENT.

Step-by-step explanation:

The key feature of the functions that are needed to determine if the lines intersect are;

The slope; rate of changeThe y-intercept

Slope and y-intercept

From straight line geometry, we can conclude that two parallel lines whose slope are equal can never intersect.

On this note, for the functions described in the question, the functions only intersect when the slopes are different.

Additionally, the functions may intersect in the event of having equal y-intercepts.

Read more on slope and y-intercept;

https://brainly.com/question/25722412

Assume that θ is an acute angle in a right triangle satisfying the given conditions. Evaluate the 5 remaining trigonometric functions. Sketch a triangle in the correct quadrant and label.

sec θ= 17/15
sin θ<0

Answers

Answer: See step by step. Replace the x with theta

Step-by-step explanation: Since sin is less than zero, and secant is positive. This means the trig values are in Quadrant 4.

We know that secФ=17/15. We need to find sin,cos,tan,csc, and cot.

We can find tangent by using the identity

[tex]tan^{2} (x)+ 1=sec^{2} (x)[/tex] where x is theta.

[tex]tan^{2} (x)+1=\frac{289}{225}[/tex]

[tex]tan^{2} (x)+\frac{225}{225} =\frac{289}{225}[/tex]

[tex]tan^{2}(x)=\frac{64}{225}[/tex]

tan x=[tex]\frac{8}{15}[/tex], Tangent in the fourth  quadrant is negative  so  the answer is instead

[tex]tan x= -\frac{8}{15}[/tex]

We can find cotangent by taking the recipocial of tan so

[tex]cot=-\frac{15}{8}[/tex]

We can find cos by taking reciprocal of sec remeber that cosine is positive in 4th quadrant so the answer is

[tex]cos =\frac{15}{17}[/tex]

We can find sin by doing quoteint identies.

[tex]\frac{sin x}{cos x} =tan x[/tex]

[tex]\frac{ sin x}{15/17} =-\frac{8}{15}[/tex]

[tex]sin x= -\frac{8}{17}[/tex]

To find csc, take reciprocal of sine.

[tex]csc=\frac{-17}{8}[/tex]

Enter the value of the exponential expression 5 to the power 0

Answers

Answer:

1

Step-by-step explanation:

5^0 = 1.  Any base to the power 0 returns the value 1.

help pleaseeee i dont get this also show work

Answers

Answer:

AC = 2

BC = [tex]2\sqrt{2}[/tex]

CD = 4

CF = 4

BD = [tex]2\sqrt{2}[/tex]

DE = 8

EF = [tex]4\sqrt{2}[/tex]

DF = [tex]4\sqrt{2}[/tex]

Step-by-step explanation:

Since all of these are isosceles triangles, it means both legs of every triangle are congruent to each other. So,

Given: AB = 2

Find:

AC = AB = 2

BC = [tex]2\sqrt{2}[/tex]

CD = 4

CF = CD = 4

BD = BC = [tex]2\sqrt{2}[/tex]

DE = 8

EF = [tex]4\sqrt{2}[/tex]

DF = EF = [tex]4\sqrt{2}[/tex]

ANSWER FAST NO LINKS OR BAD RANDOM ANSWER OR YOU WILL BE REPORTED! Thank you, marking brainliest!

Answers

Answer:

48+25.12=73.12

Step-by-step explanation:

6 baked a cake forty eight

8*4/2=16

Answer: 73.12in

Step-by-step explanation:

Determine the area under the standard normal curve that lies to the left of
(a) Z= -1.05, (b) Z= -0.36, (c) Z= - 1.07, and (d) Z = 1.35.

Answers

Answer:

A

Step-by-step explanation:

For every 1 girl in Mr Hegarty's class there are 2 boys. What is the ratio of girls to boys in the class?
Give your answer in its simplest form.

Answers

Answer:

1:2

Step-by-step explanation:

For 1 girl there are 2 boys. This means fro 2 girls there would be 4 boys. You use the ratio girls over boys to answer this.

:)

4. Frank lives 1/2 blocks east of Mary. Mary lives 3/5 blocks east of school.
How many blocks east of school does frank live? *

Answers

Answer:

1 and 1/10 from the school

3/5=6/10

1/2=5/10

6/10+5/10= 11/10

11/10=1 1/10

Find the area of each polygon. Write the
equations and solve showing ALL the work.

a regular hexagon with an apothem of 3 ft

Answers

The answer to this hard equation of Thai hard problem of this impossible thing the answer is 3

A quadratic function has one zero (x-intercept) at x = -5 and another zero at x = 3. What is the equation of the axis of symmetry of this function?

Answers

Answer:

x = - 1

Step-by-step explanation:

The axis of symmetry is a vertical line located at the midpoint of the zeros.

Equation is then

x = [tex]\frac{-5+3}{2}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1 , that is x = - 1

Felipe built a rectangular rainwater collection tank in his garden that is 5 ft long and 3 ft wide. The volume of the tank is 75 cubic ft.

What is the height of his rainwater collection tank?

Answers

Answer:

5ft

Step-by-step explanation:

Volume = length x width x height

5 x 3 x h = 75

15h = 75

h = 5

John es mariscal de campo. Este año completo 350 pases, que representan 70% de todos los pases que lanzó este mismo año

Answers

Answer:

245

Step-by-step explanation:

70% =.07

350 × .07 =245

What is another way that you could write the ratio of pennies to quarters?

Answers

Answer:

1/100 to 25/100

or

0.01 to 0.25

Step-by-step explanation:

Pennies are also known as one per cent. Cent refers to 100 and pennies are called one per cent because they value 1 out of 100. 100 pennies equal one dollar.

Similarly, one quarter is 1/4 of a dollar and 1/4 equals 25/100 when multiplying the numerator and denominator by 25.

Water in a pool starts at a height of 200 cm and is pumped out at a constant rate so that the height decreases by 5 cm per minute.

Answers

Answer:

The answer is 40

Step-by-step explanation:

If you have to say how long it will take, it will take 40 min. 200÷5=40

Select the correct
nswer.
Which of these tables represents a function?
Х
у
Х
у
х
у
Х
у
2
3
3
2
13
-3
-2
8
4
5
5
4
12
0
o
9
6
3
3
6
10
3
1
8
7
5
5
7
13
6
- 2
9
W.
x.
Y.
Z.
OA. W
OB. X
Oc. Y
OD. Z
Type here to search
BI
1

Answers

Answer:

A. W

Step-by-step explanation:

The table in which each x-value is related to exactly one y-value is the table that represents a function.

Form the tables given, in table W, every x-value (input) has exactly one y-value (output) that is related to it.

The correct table that represents a function is table W

Functions and Tables

For a table of values to be a function, the input values also known as the domain of the function must NOT have a repeated values.

All values of the domain must have a unique values in the codomain for a table of values to be a function.

From the given table, you can see that table X, Y and z all have repeated values in the domain column. This shows that these tables do not represent a function

Hence the correct table that represents a function is table W

Learn more on functions and tables here: https://brainly.com/question/3632175

The mean of data set A is 42. The mean of data set B is 47. The mean absolute deviation (MAD) of both data sets is 25. What is the difference of the
means as a multiple of the MAD?

The difference of the means is.......? times the MAD


HELP!

Answers

Answer:

The difference of the means is 2 times the MAD

Step-by-step explanation:

Mean of data set A = 42

Mean of data set B = 47

MAD of both data sets = 2.5

Difference of their means = 47 - 42 = 5

Thus, the difference of their means = 2 × the MAD

= 2 × 2.5 = 5

Therefore:

The difference of the means is 2 times the MAD

In which pair is the value of Expression A two times the value of Expression B?

A.
Expression A: 3 × (55 + 21)
Expression B: 3 × (22 1/2 + 21)

B.
Expression A: (75 + 23)
Expression B: (75 + 23) × 2

C.
Expression A: (44 + 32) × 8
Expression B: (44 + 32) × 4

D.
Expression A: (3 × 55) + 42
Expression B: (3 × 55) + 21

Answers

Answer:

C

Step-by-step explanation:

Barry and Bernice have obtained a 30-year, fixed rate mortgage for $635,250 with a 7.35% interest rate. They purchased 2 points and their rate is now 6.925%. Factoring in the cost of points, when is the break-even point on their mortgage?

2 years, 11 months

3 years, 11 months

5 years, 10 months

2 years, 4 months

Answers

Answer: C

Explanation

A sequence is defined recursively by the formula f(n + 1) = f(n) + 3. The first term of the sequence is -4. What is the next term in the sequence?
a. -7
b. -1
c. 1
d. 7 ​

Answers

Answer:

        - 1

Step-by-step explanation:

[tex]a_1=-4\\\\a_2=a_{1+1}=a_1+3=-4+3=-1[/tex]

r= 17 cm
Please help I’ll mark Brainlest

Answers

Answer:

1. r = 2.5 mm

2. r = 12ft

3. d = 34 cm

for 4-6 you  use 2(pi) r

4. 25.1 ft

5. 40.8 cm

6. 22 mi

Answer is below. Look at the explanation in order to understand my answer.

To find the diameter, you'll have to get the radius in order to solve the diameter.

Since you said r = 17cm, we should be solving for diameter.

The formula is d = 2r

R will represent the radius.

You'll multiply the 2 by the radius.

Like i've said, R will represent the radius. The radius is 17.

With that being said, we can do the math.

The formula will be: d = 2r → d = 2 × 17

2 times 17 is 34.

The diameter would be 34.

Let me know of question or concerns about my answer.

Assume a Zip Line is a straight line. The coordinates of the line are (-7,8) and (2,-3), what is the slope of the line? (Leave your answer as a fraction

Answers

Answer:

Hi! The answer to your question is m = -[tex]\frac{11}{9}[/tex]

Step-by-step explanation:

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Hope this helps!!

- Brooklynn Deka

I also need to know what m∠cdb is

Answers

Answer:

x = 4

m<cdb = 82

Step-by-step explanation:

The exterior angle thm states that the exterior angle of a triangle is equal to the sum of the opposite interior angles:

7x + 2 + 17x = 98

24x + 2 = 98

24x = 96

x = 4

m<cdb =

y + 98 = 180

y = 180 - 98

y = 82

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