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
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]
1). What are the vertices of the hyperbola whose equation is:
( y + 6 ) ² ( x + 8 ) ²
_____ - _____
81 49
2). What are the foci of the hyperbola whose equation is:
( x - 6 ) ² ( y + 7 ) ²
_____ - _____
16 9
Answer:
1) The vertices of the hyperbola are (-8, -15), (-8, 3)
2) The foci of the hyperbola are (11, -7) or (1, -7)
Step-by-step explanation:
1) The vertices of a hyperbola given in the form [tex]\dfrac{\left (y - k\right)^2}{a^2} -\dfrac{\left (x - h\right)^2}{b^2} = 1[/tex] is (h, k ± a)
Therefore, for the given hyperbola with the following equation;
[tex]\dfrac{\left (y + 6\right)^2}{81} -\dfrac{\left (x + 8\right)^2}{49} = 1[/tex], we have;
[tex]\dfrac{\left (y + 6\right)^2}{9^2} -\dfrac{\left (x + 8\right)^2}{7^2} = 1[/tex]
Therefore the vertices are;
(-8, -6 ± 9) = (-8, -15), (-8, 3)
2) The equation of the given hyperbola is presented as follows;
[tex]\dfrac{\left (x - 6\right)^2}{16} -\dfrac{\left (y + 7\right)^2}{9} = 1[/tex]
The given hyperbola is of the form;
[tex]\dfrac{\left (x - h\right)^2}{a^2} -\dfrac{\left (y - k\right)^2}{b^2} = 1[/tex]
We get;
[tex]\dfrac{\left (x - 6\right)^2}{4^2} -\dfrac{\left (y + 7\right)^2}{3^2} = 1[/tex]
The foci is then (h ± c, k)
Therefore, by comparison, the foci of the given hyperbola is (6 ± c, -7)
Where c² = a² + b²
∴ c² = 4² + 3² = 25
c = √25 = 5
∴ The foci; (6 ± 5, -7) = (11, -7) or (1, -7).
If the sum of a number and six is doubled, the result is three less than the number. Find the number.
Answer:
n = -15
Step-by-step explanation:
Represent the number by n.
Then 2(n + 6) = n - 3
Performing the indicated multiplication, we get:
2n + 12 = n - 3
Combining like terms, we get n = -15
5,111 ÷ 3 it wont show up on calculator
Answer:
Step-by-step explanation:
In calculator the answer is 1703.66666667
Answer:
1,703.6
Step-by-step explanation:
What is the volume of the cone to the nearest cubic millimeter? (Use π = 3.14)
Answer:
V = 183.16666666667 m3
Step-by-step explanation:
https://www.calculatorsoup.com/calculators/geometry-solids/cone.php
This calculator might help with other problems you have like this one and no this isn't a scam
Write an equation of a line in slope-intercept form that has a slope of -5 and passes through the point (-3, -4).
Answer:
y = -5x - 19
Step-by-step explanation:
y = -5x + b
-4 = -5(-3) + b
-4 = 15 + b
-19 = b
Would you use the median or mean to describe the center of each data set? Explain your reasoning. Heights of 50 basketball players
Answer:
Median is used to describe the center of the data of heights of 50 basketball players.
Step-by-step explanation:
The median divides the data into two equal parts.
It can be used to describe the center of the data.
The mean gives the average where most data lies.
The advantages of median are
1)it is located even when the values are not capable of quantitative measurements.
2) It is not affected by extreme values > It can be computed even when a frequency distribution involves open end classes like those of income and prices.
3) In a highly skewed distribution median is appropriate average to use.
The disadvantages of the mean are
1) it is greatly affected by extreme values.
2) It sometimes gives fallacious conclusions.
3) In a highly skewed distribution mean is not an appropriate average to use.
4) It cannot be computed even when a frequency distribution involves open end classes like those of income and prices.
Anna's car requires 5 1/2 gallons of gasoline to make 4 round trips to work and back. If her car can travel 24 miles per gallon of gasoline, how far, in miles is one round trip to work and back?
Answer:
33 miles
Step-by-step explanation:
5.5÷4= 1.375 gal per round
1.375×24= 33 miles
If a wheel of a bicycle covers 440m in 200 rotation. find the area of a wheel.
Answer:
7/22
Step-by-step explanation:
Area = 400/200 × 400/200 ×1/4 × 7/22 = 7/22
Step-by-step explanation:
Total distance covered in 200 rotation = 440 m
Distance covered in 1 rotation
= 440 / 200
= 2.2 m
Distance covered in 1 rotation = Circumference of circle so
circumference = 2πr
2.2 = 2 * 22/7 * r
2.2 = 6.28 r
r = 2.2 / 6.28
r = 0.35 m
Now Area of the wheel
= πr²
= 22 /7 * 0.35 * 0.35
= 0.385 m²
Hope it will help :)❤
(5)
A table cost $275. An LCD television set cost $325 more than the table.
Find the ratio of the cost of the LCD television set to the cost of the table.
Express the ratio in its simplest form.
Answer:
table cost=275
LCD television cost=325+275
= 600
[tex]ratio = \frac{600}{275} \\ = \frac{120}{55} \\ = \frac{24}{11} [/tex]
What is the slope for a line containing the following points? (-3,5) (3,1)
Step-by-step explanation:
[tex]y2- y1 \x2 - x1[/tex]
please help!! I’m doing 13 points since it’s sorta tricky!!
Answer:
c 10
Step-by-step explanation:
2units each and there are five spaces , this 10
Find the area of the triangle. If necessary, round the answer to two decimal places.
a = 12, b = 15, C = 52°
A)35.46
B)70.92
C)88.80
D)141.84
Answer:
B) 70.92
Step-by-step explanation:
a = 12
b = 15
C = 52°
[tex] area = \dfrac{ab \sin C}{2} [/tex]
[tex]area = \dfrac{12(15) \sin 52^\circ}{2}[/tex]
[tex] area = 70.92 [/tex]
Answer:
c
Step-by-step explanation:
because 15 x 12 is 180 so multiply by .5 and you get 90 and 88.80 is the closest thing to 90
Solve 5x + 2y = 7 10x + 4y = 14 (1 point) (1,1) (2,3) No solution Infinitely many solutions
Step-by-step explanation:
if you do 14 divided by 7 gives you 2 am I right
Josh drops his phone from a height of 50 feet. The situation is best modeled by h = -16t^2 +50, where h is the height in feet and t is the time in seconds. How long will it take for the phone to hit the ground? Round to the nearest tenth.
It will take approximately 1.8 seconds for the phone to hit the ground.
What is meant by an Equation?A mathematical statement which includes two sides, namely, left and right hand side consisting of numbers or variables, which are connected by an "equal to" sign is called an equation.
Given in the question that,
Equation representing the situation of the height of the phone in t seconds, is,
h = -16t² + 50
where h is the height in feet and t is the time in seconds.
The phone hits the ground means that the height is 0 there.
Substituting h = 0,
-16t² + 50 = 0
-16t² = -50
t² = 50 / 16
t² = 3.125
t = 1.767 ≈ 1.8 seconds
Hence the time taken is 1.8 seconds to the nearest tenth.
To learn more about Equations, click here :
https://brainly.com/question/29538993
#SPJ2
Please help tysm! will mark brainily for whoever answers first and correct ^^
What is the volume of the cylinder below?
A. 98pi units3
B. 784pi units3
C. 112pi units3
D. 196pi units3
Answer:
D) 196π
Step-by-step explanation:
Volume of a cylinder formula:
V = πr²h
Given:
r = 7
h = 4
Work:
V = πr²h
V = π7²(4)
V = 49(4)π
V = 196π
A bucket with 35 chips has a ratio of 2 blue chips for every 3 red chips. How many red chips are in the
bucket?
Answer:
10
Step-by-step explanation:
Help please no links please
Answer:
10ft × 7ft = 70sq ft
Step-by-step explanation:
The width of the Bed is = The width of the study corner = 10ft
https://northeast.schoolobjects.com/eduphoria_webcontrols/attachmentwriter.aspx?orgguid=0cdcd836-79e1-43fd-b1f1-87815cd304ec&attid=b57be0e4-768f-4f58-b615-ebd56e104099 FIND SQ
Answer:
Links are never trusted sir
Step-by-step explanation:
copy and paste (●'◡'●)
For a party, Tyler gets four different kinds of soda. He buys a 6-pack of each
kind. At home, he divides the sodas evenly among three coolers. How many
sodas are in each cooler?
Answer:
8 sodas/cooler
Step-by-step explanation:
4 · 6 = 24
24/3 = 8
what is the quadraic formula? i dont know.... plz help!
Answer:
The quadratic formula is:
-b +/- √b² - 4(a)(c)
2a
Pretend the underline is a division line.
The square root symbol (√) counts for everything after it, not just b² btw.
Step-by-step explanation:
I know this video is cheesy, but the song helped me memorize it so I didn't have to look it up every time.
https://youtu.be/VOXYMRcWbF8
Step-by-step explanation:
Quadratic Formula :-
[tex]\sf{ x = \dfrac{ - b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]
Which works according to :-
[tex]\rm{ax^2 + bx + c}[/tex]
In case you do not know, this is also called Sridhar Acharya's formula.
Hope it helps :)
Write an explicit formula to represent the sequence:
{8, 11, 16, 23, 32,...}
You start at (2, 8). You move up 1 unit. Where do you end?
Answer:
2,9 should be your answer
Answer:2 Answers By Expert Tutors ... You end at (-2, 1-4+8), which is point (-2,5). ... Moving down and up would indicated that we are moving along the y- ...
You start at (4, 5). You move right 1 unit. Where do you end ...
Jan 29, 2020
You start at (-4, 2). You move right 8 units and down 4 units ...
Sep 25, 2019
If you start at (10,9) . Move left 2 units and right 1 unit where do ...
May 22, 2020
you start at (3,0) . you move right 2 units. where do you end ...
Apr 5, 2020
More results from www.wyzant.com
Step-by-step explanation:
Can anyone help me with these two questions
I’ll mark you as a brainliest.
No links please :( .
Answer:
Step-by-step explanation:
I don’t know what they talking about or asking
Answer:
purple
Step-by-step explanation:
systems of equations involves lines that cross
I need this Done tonight. Plz help me.
Answer is 15 miles
This is because:
1 inch- 5 miles
3 inches- 15 miles
3x5=15 miles
Hope this helps!
A natural gas company charges a $21.08 connection fee plus $2.21 per 8 cubic feet of gas used. In the winter peak usage months,
November through February, they charge each customer a peak usage surcharge of $25.90. If a family uses 176 cubic feet of gas,
how much will their bill have increased because of the peak usage surcharge?
OA. $46.98
OB. $569.80
OC. $25.90
OD
$95.60
Juan gets paid $13.75 for walking his neighbor's dog. This week he has walked the dog 7 times. Juan did such a good job that his neighbor gave him a $23.45 tip. How much money has Juan made?
Answer:
The answer is 119.7 hope this helped! Also please mark me as brainliest.
Which functions is nonlinear
Answer:
the 3rd one
Step-by-step explanation:
Answer:
last one
Step-by-step explanation:
need help just need the answer need asap
Answer:
about 236.715 ft²
Step-by-step explanation:
area of a circle = πr²
so π7.5² = 176.7145868
area of a rectangle is b × h
so 15 × 4 = 60
60 + 176.7145868 = 236.7145868 ft² ≈ 236.715 ft² (for the nearest thousandths)
