Find the values of x and y that make the quadrilateral a parallelogram.
The values of x and y that make the quadrilateral a parallelogram are x=3 and y=1.
What is parallelogram and its properties?A parallelogram is a four-sided flat shape with opposite sides that are parallel and equal in length.
Properties are:-
Opposite sides if parallelogram are equal.
The consecutive angles of a parallelogram are supplementary (their sum is 180 degrees).
The diagonals of a parallelogram bisect each other (they intersect at their midpoint).
The slope of the line between the points (4x+6, 4y-3) and (7x-3, 3y+1) is:
slope = (3y+1 - 4y+3) / (7x-3 - 4x-6)
= (-y + 4) / (3x-9)
The slope of the line between the points (7x-3, 3y+1) and (3y+1, 4y-3) is:
slope = (4y-3 - 3y-1) / (3y+1 - 7x+3)
= (y-4) / (7x-3 - 3y-1)
= (y-4) / (7x-3 - 3y-1)
Setting these two slopes equal to each other, we have:
(-y + 4) / (3x-9) = (y-4) / (7x-3 - 3y-1)
Simplifying this equation, we get:
(7x-3 - 3y-1)(-y+4) = (3x-9)(y-4)
-7xy + 28x + 3y^2 - 13y - 7 = 3xy - 12x - 9y + 36
Rearranging and simplifying, we get:
3x + 2y = 11 ... (1)
Similarly, we can find the slope of the line between the points (4x+6, 4y-3) and (3y+1, 4y-3) and the slope of the line between the points (7x-3, 3y+1) and (4x+6, 4y-3) and set them equal to each other. We get another equation:
4x - 3y = 9 ... (2)
We now have two equations with two variables. Solving for x and y, we get:
x = 3
y = 1
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(2x-3)(2x+7) trinomial
[tex]4[/tex][tex]x^{2}[/tex][tex]+8x-21[/tex]
Step-by-step explanation:
Find the measure of each missing angle explain work
does anyone know the answer by any chance?
can I get some help somebody? reward brainiest
Answer:
Step-by-step explanation:
1). x² - 8x
To convert this expression into a perfect square trinomial,
x² - 2(4x) + 4² = (x - 2)²
Therefore , 4² = 16 should be added.
Option (4) is the answer.
2). x² + 2x = 3
x² + 2(1)(x) = 3
x² + 2(1)(x) + 1 = 3 + 1 [By adding 1 on both the sides]
(x + 1)² = 4
x + 1 = ±2
x = -3, -1
Option (1) is the answer.
3). 3x²- 18x = 21
x² - 6x = 7
x² - 2(3x) = 7
x² - 2(3x) + 3² = 7 + 3²
(x - 3)² = 7 + 9
(x - 3)² = 16
x - 3 = ±4
x = -1, 7
The graph of f(x) = x2 − 3x − 28 is shown. Which of the following describes all solutions for f(x)?
a parabola passing through negative 4 comma zero, zero comma negative 28, and 7 comma zero
(−4, 0), (0, −28), (7, 0)
(−4, 0), (−1, −24), (0, −28), (3, −28), (7, 0)
(x, x2 − 3x − 28) for all real numbers
(x, y) for all real numbers
Answer:
C. (x, x2 − 3x − 28) for all real numbers
Function graphs are graphs of solution equations for y! In this instance, f(x) = x² -3x -28 is the graph.
Constructing a Function Graph:⇒f(x) = x² − 3x − 28
A group of all points in the plane of the form (x, f(x)) constitutes the diagram of a function f. The graph of f can also be defined as the graph of an equation y = f(x). As a corollary, a function's graph is a subset of an equation's graph.
Solving equation:
⇒f(x) = x² − 3x − 28
⇒f(x) = x² − (7−4)x − 28
⇒f(x) = x² − 7x+4x − 28
⇒f(x) = x(x −7) +4(x −7)
⇒f(x) = (x −7) (x+4)
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I need help on this question :/
Answer: 50-50
Step-by-step explanation:
What is the volume of the rectangle pyramid below 5 m 3 m 3 m
Answer: 3(5)(1/2)(3) = 45/2
Step-by-step explanation:
Answer:
15 cubic meters
Step-by-step explanation:
V = 1/3 · Area of Base x Height
V = 1/3 ·3² · 5
V = 3 · 5
8.
50 in.
Write an expression for the perimeter in simplest radical
form
V8 in.
V8 in.
V18 in.
I a) 2V21 in.
I b) 12v2 in.
I c) 218 + 8V2 in.
d) They aren't like terms
Answer:
Do you want the perimeter of this shape?
Can you help me solve this please
9514 1404 393
Answer:
180 days
Step-by-step explanation:
The formulas for the volume of a cone and a cylinder are ...
V = πr²h . . . . . volume of a cone
V = (1/3)πr²h . . . . . volume of a cylinder
Comparing these formulas, you can see that the 6' high cone at the top will have the same volume as a cylinder of the same radius that is 2' high. So, we can simplify the problem to finding the volume of a cylinder that is 66+2 = 68' high.
V = π(12 ft)²(68 ft) = 9792π ft³ ≈ 30752.5 ft³
When the corn is used at the rate of 170 ft³/day, it will last ...
(30752.5 ft³)/(170 ft³/day) ≈ 180.96 days
The corn will last 180 days.
_____
Additional comment
In scenarios like this, it is inappropriate to round up. There will be about 162 ft³ of corn left after 180 days, which is not enough for an additional day.
What percent of $44 equals $11
Answer:
Step-by-step explanation:
11/44 = 1/4 = 0.25 = 25%
25% of $44 = $11
find the slope
5x -3y = 18
Answer:
m=5/3
Step-by-step explanation:
Pls help with the first one thank you
Answer:
1) 54 is the answer
2) The shape is cube
Need help will give you the brainliest
Answer:
8q+2r
since all of the terms are to the first power, you can add them if they have the same term (so there are 5 indivudal q's and 3q so 8q)
Answer:
8q+2r
Step-by-step explanation:
please mark brainliest
11 of 14
A train leaves at 14.54 and arrives at its destination at 15.47.
If the train travelled 66 km, what was it's average speed in km/h?
Give your answer rounded to 1 dp.
km/h
Answer:
74.7 km/h
Step-by-step explanation:
The computation of the average speed is shown below:
As we know that
Speed = Distance ÷ Time
where
Distance = 66 km
And, the time is from 14.54 to 15.47 is 53 minutes
So, the speed is
= 66 km ÷ 53 minutes
= 74.71698 kilometers per hour
= 74.7 km/h
Mark bought a car for x dollars. One year later the car was 0.85x. What was the percent decrease.
Answer:
[tex]Let~the~percentage~decrease~be~equal~to~y.\\Then,\\0.85x = x-\frac{y}{100}(x)\\or, 0.85x = x-0.01xy\\or, 0.85x = x(1-0.01y)\\or, 0.85 = 1-0.01y\\or, 0.01y = 1-0.85 = 0.15\\or, y =15\\So, ~the~decrease~of~the~price~is~15%.[/tex]
Alternative method:
[tex]Percentage~decrease = \frac{Initial~Rate-Final~rate}{Initial~Rate}(100) \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=\frac{1-0.85}{1}(100) = 0.15(100)=15[/tex]
Answer:
thr percent decrease is 15%
Step-by-step explanation:
you get 1.00 which represent beginning price u subtract the current price 1.00-0.85 you get0.15 which is 15%
Solve the system by graphing. x + y = 27 and y=x+3. The solution is ( , ).
Answer:
X=12 Y=15
Step-by-step explanation:
X+Y=27 (1)
Y=X+3 (2)
substitute (2) into (1)
X+X+3=27
2X=24
X=12
substitute X=12 into (2)
Y=12+3
Y=15
4x - 12 = 36 *
pls helppppppppppppppppp
PLEASE HELP !!
An advertising company charges $100 each time an advertisement is shown. It costs $200 to create the
advertisement. The cost to create the advertisement and show it x times is given by the function
C(x) = 100x+ 200.
Answer:
30
Step-by-step explanation:
1 plus 2 is 6 x 2 plus 5
Answer:
3
Step-by-step explanation:
500=100×+200
500-200=100×
300=100×
300/100=×
3=×
Complete the table for the given rule
Solve for c.
2(2c + 9) = C
c = [?]
Hint: Use the Distributive Property first, to
simplify the left side of the equation.
Enter
Answer:
c= -6
Step-by-step explanation:
2(2c+9)=c
4c+18=c
4c+18-18=c-18
4c=c-18
4c-c=c-c-18
3c=-18
3c/c=-18/3c
c= -6
Please find x and a
Answer:
x = 36
a = 25
Step-by-step Explanation
By Pythagoras Theorem:
[tex]x = \sqrt{ {39}^{2} - {15}^{2} } \\ \\ x = \sqrt{1,521 - 225} \\ \\ x = \sqrt{1,296} \\ \\ x = 36 \\ \\ a = \sqrt{ {20}^{2} + {15}^{2} } \\ \\ a = \sqrt{400 + 225} \\ \\ a = 25 \sqrt{625} \\ \\ a = 25[/tex]
If takes 660 metres of fence to enclose a rectangular field. if one side is 30 metres less that twice the other side, find the dimensions of this field (Please help)
Answer:
210 by 120
Step-by-step explanation:
perimeter=2l+2w
length= 2w-30
width= w
2(2w-30+w) = 660
6w-60= 660
6w= 720
w=120
length= 2*120-30 = 210
I need help I can't find the answer.
Evaluate the function: f(x)= 3x - 5; f(-1)
Answer:
-8
Step-by-step explanation:
f(x)=3x-5
f(-1)=3(-1)-5=-3-5=-8
Malala is following this recipe for bread rolls.
She uses 500 mL of water.
How much of each of the other ingredients does she use?
Recipe: Makes 15 bread rolls
480 g flour
12 g salt
6 g yeast
30 mL oil
600 mL water
Answer:
500ml water
400 g flour
2 g salt
5 g yeast
25ml oil
Step-by-step explanation:
FH = 48
QH = 2x + 4
a)9
b)10
c)6
d)4
Answer:
b.10
Ddssssssssssssss
Check
Use the diagram to answer the question.
If m Z1 = 45°, which other angles have a measure of
45°? Check all that apply.
t
22
O 23
a
1
2
m 24
25
3
4
b
>>
26
5
6
Answer:
<5 and <4
Step-by-step explanation:
Corresponding angles are congruent.
<1=<5
Opposite Interior angles are also congruent.
Answer:
∠4 and ∠5
Step-by-step explanation:
Opposite interior and corresponding angles have the same measurement.
Which expressions are equal?
A. 2(x+3)+2x and 4x+3
B.3(x+2)+4xand 6x+6
C.5x+2(x+4) and 6x+8
D.4+5(x+2) and 5x+14
Answer:
Step-by-step explanation:
2(x + 3) + 2x
2x + 6 + 2x
4x + 6 and 4x + 3 not equal
3(x + 2) + 4x
3x + 6 + 4x
7x + 6 and 6x + 6 not equal
5x + 2(x + 4)
5x + 2x + 8
7x + 8 and 6x + 8 not equal.
4 + 5(x + 2)
4 + 5x + 10
5x + 14 and 5x + 14 are equal
does anyone know how to do this math problem?
Answer:
1,-2
Step-by-step explanation:
Multiply top equation by 3 and bottom by 2
6p+9q=-12
6p+10q=-14
Do bottom - top
(6p+10q)-(6p+9q)= (-14) - (-12)
q = -2
6p + 9(-2)=-12 = 6p=18
6p=18-12=6
p=1