Given:
The three vertices of parallelogram are (0,6),(5,-4),(-1,-5).
To find:
The fourth vertex of the parallelogram.
Solution:
Consider the given vertices of parallelogram are A(0,6), B(5,-4), C(-1,-5).
Let the fourth vertex be D(a,b).
Midpoint formula:
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
We know that the diagonal of parallelogram bisect each other. It means their midpoints are same.
Midpoint of AC = Midpoint of BD
[tex]\left(\dfrac{0+(-1)}{2},\dfrac{6+(-5)}{2}\right)=\left(\dfrac{5+a}{2},\dfrac{-4+b}{2}\right)[/tex]
[tex]\left(\dfrac{-1}{2},\dfrac{1}{2}\right)=\left(\dfrac{5+a}{2},\dfrac{-4+b}{2}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{5+a}{2}=-\dfrac{1}{2}[/tex]
[tex]5+a=-1[/tex]
[tex]a=-1-5[/tex]
[tex]a=-6[/tex]
And,
[tex]\dfrac{-4+b}{2}=\dfrac{1}{2}[/tex]
[tex]-4+b=1[/tex]
[tex]b=1+4[/tex]
[tex]b=5[/tex]
Therefore, the coordinates of fourth vertex are (-6,5).
10.6-10.7 quiz big ideas question 9
Answer:
-4.7
Step-by-step explanation:
Given the following perfect square trinomial, fill in the missing term. (2 points)
4x^2+16x+____
Please help me with this homework
Answer:
502.65 cubic feet
Step-by-step explanation:
volume of cylinder = πr²j
=π(4)²(10)
=502.65
Find the square root.
-
[tex]\sqrt{x} 9/25[/tex]
Answer:
1.4
Step-by-step explanation:
............... ..............
0 0
Which of the following has zero width and an infinite length? A. a point B. a line segment C. a line D. a plane
Answer:line
Step-by-step explanation: the section between any two points on a line is called a line segment a line segment can be very long or very short or somewhere in between the difference between a line and a line segment is that a line segment has two endpoints and a line goes on forever
There are three colors of jellybeans in a jar: Red, orange, and yellow. On a random pick, the probability of getting a red jellybean is 1/8 and the probability of getting an orange jellybean is 1/4. What is the probability of getting a yellow jellybean?
Answer: 5/8
Step-by-step explanation:
Probability of getting a red jellybean = 1/8
Probability of getting an orange jellybean = 1/4
Probability of getting a yellow jellybean = 1 - (⅛ + ¼)
= 1 - (1/8 + 2/8)
= 1 - 3/8
= 5/8
Therefore, the probability of getting a yellow jellybean is 5/8
Critique the reasoning of others. Sally states that the equation g(x) = x2 + 3x − 10 represents a quadratic function that is the product of the expressions that define the two linear functions a(x) = x + 2 and b(x) = x − 5. Is Sally correct? Explain.
Answer:
Step-by-step explanation:
No, not quite. She's close.
The middle term (often called the linear term) is + which means that the absolute value of the factors must be plus.
(x + 5)(x - 3) is what should should think.
x + 5 = 0
x = - 5
x + 2 = 0
x = - 2
(x + 5)(x - 2)
x^2 - 2x + 5x - 10
x^2 + 3x - 10
if x/6 = 6/9 whats the value of x and pls give explanantion
Answer:
x=4
Step-by-step explanation:
[tex] \frac{x}{6} = \frac{6}{9} = > 9x = 6 \times 6 = > x = \frac{36}{9} = > x = 4[/tex]
If (3,2) —> (2, -3) represents a counter clockwise rotation of the point on a coordinate plane, how many degrees is the rotation?
A. 90°
B. 180°
C. 270°
D. 360°
Rami designed a small pond for a restaurant. The diagram below shows the measurements of the pond. How many cubic feet of water are needed to fill the pond?
Answer:
426
Step-by-step explanation:
The diameter is 7.2. What is the circumference?
Answer:
22.62 cm exactly or limited to de precision of this calculator (13 decimal places). Note: for simplicity, the operations above were rounded to 2 decimal places and π was rounded to 3.14.
Answer:
22.6
Step-by-step explanation:
circumference is pi x diamter so:
7.2 x pi (3.142)
=22.61
round it so 22.6
How many possible combinations of desserts are there if I get can order
three out of 10 possible choices without duplicates? *
Answer: 3
Step-by-step explanation:
What’s the answer?!!!!!!
Answer:
no
Step-by-step explanation:
Using the converse of Pythagoras' identity.
If the square of the longest side is equal to the sum of the squares of the other 2 sides then the triangle is right.
longest side = 30 , then 30² = 900
20² + 23² = 400 + 529 = 929 ≠ 900
Then the triangle is not right.
help me pls very much appreciated luvs <33
Answer:
18
Step-by-step explanation:
Since this is a multiple choice question, I will employ the guess and check method - meaning I will check each answer one by one.
Variable x = dimes = $0.10
Variable y = quarters = $0.25
Set up a system of equations:
x + y = 38
x(0.10) + y(0.25) = 6.80
Plug in each choice into the second equation. You can find the number of quarters that correspond to each number of dimes by using the first equation.
20 dimes:
20 + y = 38
y = 18
20(0.10) + 18(0.25) = 6.80
2 + 4.5 = 6.80
6.5 does not equal 6.80
Because dimes (x) are worth less than quarters (y), this result tells us the answer will be less than 20 dimes as with 20 or more we have less than $6.80. Another example just to show this is true:
38 dimes:
38 + y = 38
y = 0
38(0.10) + 0(0.25) = 6.80
3.8 + 0 = 6.80
3.8 does not equal 6.80.
Since x is worth less than y, we need more of y rather than x. Adding more x will only mean we will get a lower price. Adding more y will mean we get a higher price which is what we need. So only solve for x that is less than 20.
6
6 + y = 38
y = 22
6(0.10) + 32(0.25) = 6.80
0.60 + 8 = 8.60
8.60 does not equal 6.80.
This result is higher than what we wanted (6.80) which means we need more x. Now we only have to solve for x numbers that are greater than 6 and less than 20.
18
18 + y = 38
y = 20
18(0.10) + 20(0.25) = 6.80
1.8 + 5 = 6.8
6.8 does equal 6.8.
Correct!
Find c.
Round to the nearest tenth:
8 cm
82
55°
b
c = [? ]cm
Law of Sines:
sin A
sin C
sin B
b
Please help asap
Answer:
9.7cm
Step-by-step explanation
According to the sine rule;
a/sinA = c/sinC
8/sin55 = c/sin82
Cross multiply
csin55 = 8sin82
c(0.8192) = 8(0.9903)
c = 8(0.9903)/0.8192
c = 7.9221/0.8192
c = 9.67
Hence the value of c to the nearest tenth is 9.7cm
qual é o resultado dessa conta 28+X=50?
Answer:
x=22
Step-by-step explanation:
Answer:
x=22
Step-by-step explanation:
help please!
integrate the following:
[tex] \displaystyle \int \frac{ \cos(2x) - \cos(2a) }{ \cos(x) - \cos( \alpha ) } dx[/tex]
Answer:
[tex] \displaystyle 2 \sin(x) + 2x \cos( \alpha ) + \rm C[/tex]
Step-by-step explanation:
we would like to integrate the following integration:
[tex] \displaystyle \int \frac{ \cos(2x) - \cos(2 \alpha ) }{ \cos(x) - \cos( \alpha ) } dx[/tex]
notice that you can simplify the integrand
recall that,
[tex] \displaystyle \cos(2 \theta) = 2 \cos(\theta) ^{2} - 1[/tex]
thus substitute:
[tex]\displaystyle \int \frac{ 2\cos^{2} (x)- 1 - \{2\cos ^{2} (\alpha ) - 1 \} }{ \cos(x) - \cos( \alpha ) } dx[/tex]
remove parentheses:
[tex]\displaystyle \int \frac{ 2\cos^{2} (x)- 1 - 2\cos ^{2} (\alpha ) + 1}{ \cos(x) - \cos( \alpha ) } dx[/tex]
[tex]\displaystyle \int \frac{ 2\cos^{2} (x) - 2\cos ^{2} (\alpha ) }{ \cos(x) - \cos( \alpha ) } dx[/tex]
factor out 2:
[tex]\displaystyle \int \frac{ 2(\cos^{2} (x) - \cos ^{2} (\alpha )) }{ \cos(x) - \cos( \alpha ) } dx[/tex]
we can use algebraic identity i.e
a²-b²=(a+b)(a-b) to factor the denominator
[tex]\displaystyle \int \frac{ 2(\cos^{} (x) + \cos ^{} (\alpha ))( \cos(x) - \cos( \alpha ) ) }{ \cos(x) - \cos( \alpha ) } dx[/tex]
reduce fraction:
[tex]\displaystyle \int \frac{ 2(\cos^{} (x) + \cos ^{} (\alpha ))( \cancel{\cos(x) - \cos( \alpha ) ) }}{ \cancel{\cos(x) - \cos( \alpha ) }} dx[/tex]
[tex] \displaystyle \int 2( \cos(x) + \cos( \alpha ) )dx[/tex]
distribute:
[tex] \displaystyle \int 2 \cos(x) + 2\cos( \alpha ) dx[/tex]
use sum integration formula:
[tex] \rm \displaystyle \int 2 \cos(x) dx+ \int2\cos( \alpha ) dx[/tex]
recall integration rules:
[tex] \displaystyle 2 \sin(x) + 2x \cos( \alpha ) [/tex]
and we of course have to add constant of integration
[tex] \displaystyle 2 \sin(x) + 2x \cos( \alpha ) + \rm C[/tex]
Pls help
Pls help
Pls help
Answer:
600ft²
Step-by-step explanation:
Oh boy, this is gonna be a long one, so proceed with caution:
So we're gonna start with the one to the very left, we can split this into three different rectangles:
So we got the length of the bottom minus the length we don't want there because we're doing the big rectangle:
35 - 10 = 25
25 x 20 = 500
So we're just gonna keep that on a back burner, cause now we gotta do the two smaller ones:
So we got the measure from the one side, but we gotta subtract the 10 from the other side:
20 - 10 = 10
10 x 10 = 100
Now we gotta add that all up:
500 + 100 = 600
So the area of the first shape is 600ft²
I gotta go, but hope this helps a little bit
Mrs. Washer filled the gas tank of her car, She used 2/3 of a tank of gasoline
while driving to the beach. She used another 1/6 of the tank driving to her
hotel How much gasoline is left in the tank?
Answer: She has 1/6 of gasoline left in the tank.
Hope this helps!
A 5-pound bag of dog food costs $2.10. What is the unit price?
per pound
Submit
Answer:
.42 per pound
Step-by-step explanation:
The triangle and the trapezoid share a 15 inch base and height of 10 inches.
The area of the trapezoid is less than twice the area of the triangle. Find the value of x. Explain your reasoning.
Can the area of the trapezoid be exactly twice the area of the triangle? Explain your reasoning.
Answer:
15 ; yes
Step-by-step explanation:
Base = 15 inches
Height = 10 inches
Area of triangle = 1/2* base * height
Area of triangle = 0.5 * 15 * 10
Area of triangle = 75 in²
Area of trapezium < 2(75)
Area of trapezium, A
A = 1/2*(x+b)h
x = top base ; b = bottom base ; h = 10
1/2*(x + 15)10 < 150
5x + 75 < 150
5x < 150 - 75
5x < 75
x < 15
Hence, Area of trapezoid :
A = 1/2 * (15 + 15)10
A = 1/2 * (30)10
A = 1/2 * 300
A = 150
Hence, Area of trapezium can be twice the area of triangle.
2(75) = 150
What is the volume of the cone to the nearest whole number?
HELP PLZ
Answer:
167.467mm^3
Step-by-step explanation:
Volume of cone:1/3hpir^2
1/3(10)(pi)(4)^2
=160/3(pi)
(Pi=3.14)
160/3pi=167.467mm^3
Matt tossed a coin 30 times. The results were 12 heads and 18 tails. What is the experimental probability of tossing heads?
Answer:
25%
Step-by-step explanation:
You can't determine what it is going to land on but this is the answer!
Ps.Im not completely sure no hate please :)
solve 3(2x-5)-2x=3(X+7)
Answer:
x = 36
Step-by-step explanation:
Given
3(2x - 5) - 2x = 3(x + 7) ← distribute parenthesis on both sides
6x - 15 - 2x = 3x + 21
4x - 15 = 3x + 21 ( subtract 3x from both sides )
x - 15 = 21 ( add 15 to both sides )
x = 36
.......................................
Answer:
150
Step-by-step explanation:
A helicopter flies from the airport on a course with a bearing of 21 degrees. After flying for 99 miles, the helicopter flies due east for some time. The helicopter flies back to the airport with a bearing of 227 degrees. How far did the helicopter fly on the final leg of its journey?
Answer:
Step-by-step explanation:
From the question we are told that:
Initial bearing [tex]\angle _1=21 \textdegree[/tex]
Initial distance [tex]d_1=99miles[/tex]
Final bearing [tex]\angle _2=227 \textdegree[/tex]
Let [tex]\triangle OAB[/tex] be the perimeter travailed
[tex]\angle OAB=90+21=111 \textdegree\\\angle ABO=270-227=43 \textdegree[/tex]
Generally the equation for OB using sine rule is mathematically given by
[tex]OB=99*\frac{sin111}{sin43}[/tex]
[tex]OB=135.52miles[/tex]
Therefore the helicopter flight on the final leg of its journey is
[tex]OB=135.52miles[/tex]
The graph shows the population of a city from 1900 to 2000. What is the average rate of change of the population between 1950 and 1980?
Please help! I attached a photo of the graph.
Answer:
-15
Step-by-step explanation:
in 1950 it was 45 and in 1980 it was 30 so it is -15
The average rate of change can be define as the value of something is changing with respect to another thing is tinging. The average rate of change of the population between 1950 and 1980 is 500 per year. It means the population is decreasing with 500 per year.
Given information-The given graph shows the population of a city between the year 1900 to 2000.
Average rate of change-The average rate of change can be define as the value of something is changing with respect to another thing is tinging.
Form the given graph,
The year 1950 is between the year 1940 and year 1960. The value at the y axis where the population (in thousand) shown is 45,000 for the year 1950.
The year 1980 is shown in graph at the x axis and the value of the population in the y axis is 30,000.
Thus the population is decreasing from year 1950 to 1980. The difference in the population of the year 1950 and 1980 is,
[tex]d=45000-30000[/tex]
[tex]d=15000[/tex]
Thus the change in the population between 1950 and 1980 is 15,000.
Average rate of change of the population between 1950 and 1980 -
As the population and the year both are changing. The rate of change for the population with respect to the year can be calculating by dividing the difference of the population between two year to the total years between the 1950 to 1980.
There is total 30 year from 1950 to 1980, thus the average rate of change is,
[tex]A(x)=\dfrac{15000}{30} \\ A(x)=500[/tex]
Thus the average rate of change of the population between 1950 and 1980 is 500 per year. It means the population is decreasing with 500 per year.
Learn more about the average rate of change here;
https://brainly.com/question/2530409
Simplify:3x×2x×x⁴ plz help me I am confuse I think the answer is 6x⁶ It is or not plz help me❤️❤️
Answer:
6x^2^x^2+x^4
Step-by-step explanation:
Answer:
Yes your answer is correct
Step-by-step explanation:
First of all you multiply 3x with 2x which equals 6x power 2 because we sum the power. Then we multiply 6x power 2 with x power 4 which equals 6x power 6 because X is 1X so the answer is 6X power 6
the radio of used cars at a dealership is 7:5. if the dealership has 156 cars on the lot , how many are new ?
Answer:
91 used
65 new
Step-by-step explanation:
7 + 5 = 12
156/12 = 13
7(13) = 91
5(13) = 65
Consider the net of a prism below. Describe the prism that the net models.
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete, as the net of the prism is not shown.
However, I will give a general explanation on how to determine the net of the three popular prisms.
(1) Rectangular prism.
It is made up of 6 rectangles
(2) Triangular prism
It consists of 3 rectangles and 2 triangles
(3) Square prism
It is made up of 6 squares
See attachment for the net of each prism