The parallelogram ABCD formed by vertices A(x, y) = (0, 0), B(x, y) = (3, 6) and C(x, y) = (11, 2) has a point D with the following coordinates: D(x, y) = (14, 8).
How to determine the missing vertex of a parallelogram
In this question we know only three vertices of the parallelogram. To determine the missing point we must understand the properties of parallelograms. Vectorially speaking, we can find the missing vertex by using the following property:
[tex]\overrightarrow{AB} = \overrightarrow {CD}[/tex]
[tex]\vec B - \vec A = \vec D - \vec C[/tex]
[tex]\vec D = \vec C + (\vec B - \vec A)[/tex]
D(x, y) = (11, 2) + [(3, 6) - (0, 0)]
D(x, y) = (11, 2) + (3, 6)
D(x, y) = (14, 8)
The parallelogram ABCD formed by vertices A(x, y) = (0, 0), B(x, y) = (3, 6) and C(x, y) = (11, 2) has a point D with the following coordinates: D(x, y) = (14, 8).
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The Student Council at High School A held a Student Body President election. There are 940 students in enrolled and 625 students voted for a Student Body President. Approximately what percentage of the student body voted for Student Body President?
Answer:
65 %
Step-by-step explanation:
625 out of 940 is what % ?
625/940 x 100% = 66.49%
Paula has buttons. she gives away 28 buttons. choose the expression that shows the number of buttons paula has left.
Answer:
y = 28 - x
Step-by-step explanation:
The variable x represents how many buttons Paula had before giving 28 away and the variable y represents how many buttons she has now.
What is the equation of a line parallel to y=(3)/(4)x-5 and passes through (12,-2)?
A parallel line has the same slope as the original line. So in this case the slope of the line is also 3/4. Now how do we know if it intersects the point? We need to adjust the y intercept.
Currently, we know the equation of the line is y= 3/4 x + b, where b is the thing we are looking for. We also have a point, which supplies the x and y. Plug that in and solve for b
-2 = (3/4)*(12) + b
You'll get b= -11
So the equation of the parallel line intersecting the point given is y= 3/4x -11.
I am assuming that the slope is 3/4 based on the way you formatted the original equation, but it's the same steps if the slope is different.
The heights of 150 oak trees are normally
distributed with a mean of 84 feet and a
standard deviation of 3 feet. about how
many trees fall within two standard
deviations of the mean?
Using the Empirical Rule, it is found that about 143 trees fall within two standard deviations of the mean.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.95% of the measures are within 2 standard deviations of the mean, hence, out of 150 trees, the amount is:
A = 0.95 x 150 = 142.5, rounded to 143.
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Find the volume.
Area = 16.4 cm²
8.1 cm
cm³
The area of the given figure is 16.4 cm² and the Length of the side is 8.1 cm. therefore, the volume of the given figure is 132.84 cm³.
When can we find the volume of a considered figure?For finding the volume of the considered figure, we somehow need measurement of its correct dimensions by which we would be able to recreate the figure.
By any means, if we could get enough measurement, then we'd be able to characterize the figure, and thus, get its volume.
Area = 16.4 cm²
Length of side = 8.1 cm
The volume of the given figure
= Area x side
= 16.4 x 8.1
= 132.84 cm³
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If e : f is 3 : 7 and f : g is 2 : 3 what is e : g ? please answer asap!
Answer:
e: f=3 : 7 and f : g= 2 : 3
Step-by-step explanation:
here's the answer
Does anybody know the answer to this
substitute 3 in X's place
-2x + 5 = -2(3) + 5 = -6 + 5 = -1
hope it helps...!!!
A
4
Find the value of x.
B
6
X+1
D
x = [?]
E
X
C
A timer is started and a few moments later a swimmer dives into the water and then comes back up. The swimmer's depth (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=t2−12t+27
Rewrite the formula in factored form and select each true statement below.
The swimmer is underwater for 12 seconds.
The swimmer dives into the water 3 seconds after the timer was started.
The swimmer comes back up 9 seconds after the timer was started.
The swimmer dives to a maximum depth of 27 feet.
The swimmer dives into the water 12 seconds after the timer was started.
The formula in factored form is (t - 3)(t - 9) and the swimmer dives into the water 3 seconds after the timer was started also, the swimmer comes back up 9 seconds after the timer was started.
Analysis:
at h(t) = 0 that is when the diver has not dived or at height 0 foot
the equation becomes [tex]t^{2}[/tex] -12t + 27 = 0
by factorizing,
[tex]t^{2}[/tex] -9t -3t + 27 = 0
(t-9)(t-3) = 0, this is the equation in factored form.
t = 3 or 9
These are the times, the height h(t) = 0
Which means the swimmer dived 3 seconds later or got to the top of water after 9 seconds in which case h(t) = 0
In conclusion, the swimmer dives 3 seconds later after the timer was started and the swimmer comes back up after 9 seconds are the true statements for this problem.
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Answer:
The swimmer comes back up 9 seconds after the timer was started.
The swimmer dives into the water 3 seconds after the timer was started.
Step-by-step explanation:
Which expressions are equivalent to the given expression.
y^-8y^3x^0x^-2
[tex]y^{-8} y^3 x^0 x^{-2}[/tex] is equivalent to [tex]y ^{-5} x ^{-2}\\[/tex].
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
Given;
[tex]y^{-8} y^3 x^0 x^{-2}[/tex]
Simplify
[tex]y^{-8} y^3 x^0 x^{-2}\\\\y ^{-8+3} x ^{0-2}\\ \\y ^{-5} x ^{-2}\\[/tex]
Hence, [tex]y^{-8} y^3 x^0 x^{-2}[/tex] is equivalent to [tex]y ^{-5} x ^{-2}\\[/tex].
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Question 16(Multiple Choice Worth 1 points)
(02.03 LC)
Triangle ABC is transformed to triangle A' B' C', as shown below:
B
C
-2-10
1 2 3 4
-2
3
Which equation shows the correct relationship between the measures of the angles of the two triangles?
2
Answer:
What is this supposed to mean even?
Step-by-step explanation:
helpppp pleaseeeeeee
Answer:
3.) (5,2), (5,5), and (9,2)
Step-by-step explanation:
The triangle currently has the coordinates (2,0), (6,0), and (2,3).
If you want to translate the triangle up 2 units, you need to add 2 to each "y" value.
(2,0) -----------> y = 0 ------------> new y = 2
(6,0) -------> y = 0 --------------> new y = 2
(2,3) ----------> y = 3 -----------> new y = 5
If you want to translate the triangle 3 units to the right, you need to add 3 to each "x" value.
(2,0) -----------> x = 2 ------------> new x = 5
(6,0) -------> x = 6 --------------> new x = 9
(2,3) ----------> x = 2 ----------> new x = 5
Therefore, the new coordinates are (5,2), (9,2), and (5,5).
Which values of x and y would make the following expression represent a real number?
The complete question is
"Which values of x and y would make the following expression represent a real number? (4 + 5i)(x + yi)"
The value of x and y are all points that satisfy the equation would be,(4,-5).
How to find the simplify the expression?Use the distributive property to simplify the expression.
The given expression is,
(4 + 5i)(x + yi)
4(x + yi)+ 5i (x + yi)
4x + 4yi + 5xi + 5yi^2
We know that i^2 = -1
4x + 4yi + 5xi - 5y
(4x - 5y) +i ( 4y + 5x)
In x+iy, x is the real part and y is the imaginary part.
If the given expression represents a real number it means the imaginary part must be zero.
4y + 5x= 0
All the points which satisfy the above equation are the values of x and y for which the given expression is a real number.
For eg. (4,-5)
4y + 5x
4(-5) + 5(4)
= 0
LHS=RHS, which means the point satisfies the equation and the value of x and y are (4,-5).
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Answer:
x = 4, y = -5 or the 3rd option
Step-by-step explanation:
just took the test
what is the slope of (4, −6) and (0, 2)
Step-by-step explanation:
please mark me as brainlest
[tex]1. \frac{1}{3} + \frac{3}{2} + \frac{6}{5} - \frac{1}{2 = } [/tex]
[tex]2. \frac{7}{5} - \frac{4}{2} + \frac{4}{5} - \frac{3}{2} = [/tex]
[tex]3. \frac{9}{8} + \frac{7}{8} - \frac{6}{7} + \frac{8}{7} + \frac{1}{3} = [/tex]
[tex]4. \frac{11 }{8} + \frac{11}{5} + \frac{8}{5} - \frac{9}{6} - \frac{5}{3} = [/tex]
can you please solve it
Answer:
1. 3.33333333333
2. -1.3
3. 2.61904761905
4. 2.00833333333
In a coin box there are 20-cent, 50-cent and $1 coins. The number of 20-cent coins is 2x, the number of 50-cent coins is y and the number of $1 coins is 4x. If the total value of the coins is $58.80, what is the total number of coins?
A limited-edition poster increases in value each year with an initial value of $18. After 1 year and an increase of 15%
per year, the poster is worth $20.70. Which equation can be used to find the value, y, after x years? (Round money
values to the nearest penny.)
O y = 18(1.15)
Oy=18(0.15)
Oy=20.7(1.15)*
Oy= 20.7(0.15)
The equation that can be used to find the value of the poster after x years is y = 18(1.15)^x.
What is the equation that can be used to find the future value of the poster?The formula for calculating future value:
FV = P (1 + r)^n
Where:
FV = Future value P = initial valueR = rate of increaseN = number of yearsy = 18(1.15)^x.
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Which pattern below does not follow the same rule as the other three patterns? A $2$ , $4$ , $8$ , $16$ , $32$ 2, 4, 8, 16, 32, B $5$ , $10$ , $20$ , $40$ , $80$5, 10, 20, 40, 80 C $15$ , $25$ , $35$ , $45$ , $55$15, 25, 35, 45, 55 D $25$ , $50$ , $100$ , $200$ , $400$
Answer:
C. 15, 25, 35, 45, 55
Step-by-step explanation:
Each number in A, B, and D are double the previous number but C adds 10.
Can somebody help me find the surface area
To calculate the area of the complex shape:
⇒ must separate the shape into simpler shape
2 rectangles with a length 9ft and a width 6ft1 rectangle with a length of 9 ft and a width 3ft2 triangles with a base of 3 ft and a height 5.4ftLet's calculate:
2 rectangles with a length 9ft and a width 6ft[tex]Area = 9*6+9*6=54+54=108[/tex]
1 rectangle with a length of 9 ft and a width 3ft[tex]Area= 9*3=27[/tex]
2 triangles with a base of 3 ft and a height 5.4ft[tex]Area = \frac{1}{2}* 3*5.4+\frac{1}{2}* 3*5.4=8.1+8.1=16.2[/tex]
Total Area = [tex]108+27+16.2= 151.2[/tex]
Answer: 151.2 ft²
Hope that helps!
Find the mean of a student test scores if he earned 5, 93, 85, 90 and 91 points on five tests
Answer:
72.8
Step-by-step explanation:
What is the total number of different 10-letter arrangements that can be formed using the letters in the word FORGETTING?
Answer:
1814400
Step-by-step explanation:
A jar contains 8 red marbles, 6 blue ones, and 6 yellow ones. One marble is chosen at random. The color is
recorded in the table, and then it is returned to the jar. This is repeated 40 times.
Red Blue Yellow
11
11
18
Answer:
Step-by-step explanation:
Comment
The theoretical probabilities are
Red: 8/20 = 0.4
Blue:6/20 = 0.3
yellow:6/20 = 0.3
The experimental Probabilities are
Red: 11/40 = 0.275
blue: 11/40 = 0.275
Yellow: 18/40=0.45
Both probabilities add to 1 as they should
The yellow is the highest disproportionate answer and it really shouldn't be. If anything it should be red. (0.45 > 0.4 comparing yellow experimental with red theoretical. The yellow is way more than it should be)
The number of trials is double the number of marbles in the jar. The number of trials would be double for each color in the jar. Both blanks are double.
The equation of a circle is given below:
x squared minus 8 x plus y squared plus 6 y minus 11 equals 0
Identify the center and radius of the circle.
Group of answer choices
center: left parenthesis 4 comma minus 3 right parenthesis
radius: 6
center: left parenthesis negative 8 comma 6 right parenthesis
radius: 6
center: left parenthesis 4 comma minus 3 right parenthesis
radius: 36
center: left parenthesis negative 8 comma 6 right parenthesis
radius: 36
The center of the circle will be (4, -3) and the radius of the circle will be 6 units. Then the correct option is A.
What is an equation of a circle?A circle can be characterized by its center's location and its radius's length.
Let the center of the considered circle be at the (h,k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
(x - h)² + (y - k)² = r²
The equation is given below.
x² - 8x + y² + 6y - 11 = 0
x² - 8x + y² + 6y = 11
Then the center and the radius of the circle will be
x² - 8x + 16 + y² + 6y + 9 = 11 + 16 + 9
(x - 4)² + (x + 3)² = 36
(x - 4)² + (x + 3)² = 6²
Thus, the center and the radius of the circle will be (4, -3) and 6 units respectively.
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please help me please
Answer:
detailed explanation is in image
Step-by-step explanation:
ans is 60 unit²
MARK ME THE BRAINLIEST !
Answer:
60 cm2
Step-by-step explanation:
Formula for finding out the area of the figure -
Area of full rectangle - Area of unshaded rectangle = Area of shaded region
Area of full rectangle =
Length (l) = 9+3 = 12 cmBreadth (b) = 4+4 = 8cm Area of full rectangle = l*b = 12*8 = 96cm2Area of unshaded rectangle =
Length (l) = 9 cmBreadth (b) = 4 cmArea of unshaded rectangle = l*b = 4*9 = 36cm2Putting the formula = 96-36 = 60cm2
Hence the area of shaded region = 60cm2
I gave the answer first !
Which rule describes a translation 3 units down?
A (x, y) → (x+3, y + 3)
B (x, y) → (x, y - 3)
(x, y) → (x, y + 3)
D (x, y) → (x, -3y)
B; the y axis is what moves up and down
Can someone please help? This is sooooooooo hard!!! :(
Answer:
BD = BE
Step-by-step explanation:
If BD = BE , angle BED = angle BDE.
Because they are in a same triangle.
And also they are congruent.
The radius of a circle is 7 mm. What is the area.
Answer:
A= 153.94 mm
Step-by-step explanation:
A = πr²
A=π(7)²
A= 153.94 mm
Joe started 125 miles in 5 hours. How many miles would travel in 1 hour
Answer:
Hope this helps :D
Step-by-step explanation:
Explanation on picture
please help... The triangle represents a cross section from a 3D prism. Draw or describe the 3D prism that produced this cross section.
The 3D prism that produced the cross-section of a triangle is a triangular prism.
How to describe the 3D prism?From the given figure, we can see that the cross-section is a triangle
One of the faces of a triangular prism is a triangle.
This means that when the triangular prism is cut vertically, a triangle face is created
Hence, the 3D prism that produced the cross-section of a triangle is a triangular prism.
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20 divided by tann(45°)
Answer:
20
Step-by-step explanation:
as we know
[tex] \tan {45}^{0} = 1 \\ [/tex]
20/ 1=20
is correct answer