Triangle DEF, with vertices D(9,-8), E(8,-3), and F(2,-5), is drawn inside a rectangle,
as shown below.
What is the area, in square units, of triangle DEF?
[
Answer: A=?
units²
Answers
The area of the triangle DEF is 2 square units
How to determine the area?The given parameters are:
D(9,-8), E(8,-3), and F(2,-5),
The area of the triangle is calculated using:
Area = 0.5|x1 * (y2 -y3) + x2 * (y1 -y3) + x3 * (y2 -y1) |
This gives
Area = 0.5|9 * (-3 + 5) + 8 * (-8 + 5) + 2 * (-3 + 8) |
Evaluate
Area = 0.5|4|
Expand
Area = 2
Hence, the area of the triangle DEF is 2 square units
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Related Questions
The one-to-one functions g and h are defined as follows.
g = {(-4, 0), (-1, 1), (0, -5), (3,-1)}
h(x) = 2x-13
Answers
what is the value of u ?
Answers
Step-by-step explanation:
you do know that the sum of all angles in a triangle is always 180° ?
so,
3u + 6u - 18 + u + 18 = 180
10u = 180
u = 18
Please help me with this
Answers
Answer:
42
Step-by-step explanation:
6 times 7 is 42
If 8n = 128, n equals:
Answers
n = 128 / 8 = 16
Answer:
8n is the same as 8 times a number.
That means...
Continuation:
[tex]8 * n = 128[/tex]
[tex]128 \div 8 = n[/tex]
[tex]128 \div 8 = 16[/tex]
Therefore, n is 16.
Which pairs of events describe independent events? Select all that apply.
O Rolling a six-sided die and having it land on a 4, and then choosing a blue marble from a jar of marbles.
O Rolling a six-sided die and having it land on a 3,
and then rolling a six-sided die and having it land on a 2.
O Choosing a blue marble from a jar of marbles, not replacing it, and then drawing a red marble.
O Entering a raffle 3 times and winning one prize, and then winning another prize in the same raffle.
O Drawing a 3 from a deck of cards, not replacing it, and then drawing a 4 from the same deck of cards.
Answers
When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events. The correct options are A and B.
Which pair of events are called independent events?When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events.
Symbolically, we have:
Two events A and B are said to be independent iff we have:
[tex]P(A \cap B) = P(A)P(B)[/tex]
Comparing it with chain rule will give
[tex]P(A|B) = P(A)\\P(B|A) = P(B)[/tex]
Thus, showing that whether one occurred or not, the other one doesn't care about it (independence).
Two events are known to be independent even if the result of one event does not affect the result of the second event.
Rolling a dice in an independent event and choosing a blue marble is another independent event. The two events are independent and the result of one does not affect the other.
Thus, A is correct.
Rolling a dice in an independent event, and rolling it again won't affect the result of the second roll. Therefore, rolling a dice twice or for n number of times is an independent event.
Thus, B is correct.
Hence, the correct options are A and B.
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Without using the formula, work out the gradient of the graph shown.
Answers
Reason:
Start at the y intercept (0,4) which is where the red line crosses the y axis.
Then move up 2 units, and to the right 1 unit to arrive at (1, 6) which is another point on this red line.
The motion of "up 2, right 1" means:
rise = 2run = 1gradient = slope = rise/run = 2/1 = 2Feel free to use any other two points you prefer and you should get the same result. For instance, you could have started at the x intercept (-2,0) and did the "up 2, right 1" motion to arrive at (-1, 2).
Pls Help :(((
If a^x=b^y=c^z is a system of exponential expression where b^2=ac
Prove that 1/x + 1/z = 2/y
Answers
[tex]\text{Let,}\\\\~~~~~~~a^x =b^y = c^z = k\\\\\text{So,}\\ \\a = k^{\dfrac 1x}\\\\b=k^{\tfrac 1y}\\\\\ c = k^{\tfrac1z}\\\\\text{Now, given that,}\\\\~~~~~~~~~b^2 = ac\\\\\implies \left( k^\tfrac 1y \right)^2 = k^{\tfrac 1x} \cdot k^{\tfrac 1z}\\\\\implies k^{\tfrac 2y} = k^{\tfrac 1x + \tfrac 1z} ~~~~~~~~~~;[a^m \cdot a^n = a^{m+n}]\\\\\implies \dfrac 2y = \dfrac 1x + \dfrac 1z\\\\\implies \dfrac 1x + \dfrac 1z = \dfrac 2y \\\\\text{Proved.}[/tex]
A Circular pie with a diameter of 10” Is cut into six equal pieces. What is the surface area of two slices of pie?
Answers
To solve this question, let's find the surface area of the entire pie and then divide it by 6 for each slice.
The area of a circle is pi*r^2. We are given the diameter, so divide that by 2 to get the radius.
Now that you have the area, divide by 6. That is the area of each slice. The problem asks for the area of 2 slices though, so multiply that by 2.
math quarterly
8th grade
Answers
kindly check the attachment.
Answer:
the answer is 49
Step-by-step explanation:
Keisha pumped 6 gallons of water into her pool each minute for 48 minutes what was the total change in the amount of water in the pool
Answers
The total change in the amount of water in the pool is 288 gallons.
What is Volume?Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.
Here, Rate of water pumped into her pool = 6 gallons / minute.
Total Duration = 48 minutes
Total amount of water = Rate X Time
= 6 X 48
= 288 gallons
Thus, the total change in the amount of water in the pool is 288 gallons.
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28.4.2 Test (CST): Transformations, Congruence, and Similarities, Part 2
Quadrilateral RUST has a vertex at R (1,5).
T
S
What are the coordinates of R'after the translation (x, y) → (x+1, y-1),
Answers
Answer:
R'(2,4)
Step-by-step explanation:
When doing translations you subtract or add within the coordinates like a normal problem.
If it helps you, write it as seperate equations like:
1-1 and 5-1
Hope that helps ✓
A pyramid and a cone are both 12 centimeters tall and have the same
volume. What statement must be true about the two solids?
AA
OA. The horizontal cross-sections of the prisms at the same height
must have the same area.
OB. The vertical cross-sections of the prisms at the same width must
have the same area.
C. The area of the cross-sections of the prisms are multiples of each
other.
D. The cross-sections of the prisms are the same shape.
Answers
Answer:
The horizontal cross-sections of the prisms at the same height must have the same area.
Step-by-step explanation:
A pyramid and a cone are both 12 centimeters tall and have the same volume.... What is the volume?
Volume is the quantification of the three-dimensional space a substance occupies.
We have to determine the true statement, and it is
The horizontal cross-sections of the prisms at the same height must have the same area cone and given pyramid are looks like same in two-dimensional.
The horizontal cross-sections of the prisms at the same height must have the same area thus the correct option is A.
What is the volume?A pyramid and a cone are both 12 centimeters tall and have the same volume, we know that Volume is the quantification of the three-dimensional space a substance occupies.
We have to determine the true statement, and it is the horizontal cross-sections of the prisms at the same height must have the same area cone and given pyramid are looks like same in two-dimensional.
If we cross-section the figures at the same height, it won't get the same shape but we should get the same area, as the area of the cross-section will be proportional to the base area, and the base area of both figures are the same.
Thus, the correct option is A.
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How many solutions does the system of equations have?
y=-2x+3
y = x² - 6x +3
Answers
Answer:
2 solutions
Step-by-step explanation:
y = - 2x + 3 → (1)
y = x² - 6x + 3 → (2)
substitute y = x² - 6x + 3 into (1)
x² - 6x + 3 = - 2x + 3 ( subtract - 2x + 3 from both sides )
x² - 4x = 0 ← factor out x from each term on the left side
x(x - 4) = 0
equate each factor to zero and solve for x
x = 0
x - 4 = 0 ⇒ x = 4
substitute these values into (1)
x = 0 : y = - 2(0) + 3 = 0 + 3 = 3 ⇒ (0, 3 )
x = 4 : y = - 2(4) + 3 = - 8 + 3 = - 5 ⇒ (4, - 5 )
the 2 solutions are (0, 3 ) and (4, - 5 )
Using the net below, find the surface area
of the triangular prism.
3cm
6 cm
9 cm
5 cm
9 cm
4 cm
Surface area= [?] cm²
Answers
The surface area of the triangular prism is 153 cm².
What is a triangular prism?Suppose you've got a triangle. Now, stretch it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.
Usually, when we talk about a triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.
The area of the triangular prism is the sum of the area of the rectangle and the area of the triangle, therefore, the area of the prism will be,
Area = A + B + C
=(9 × 15) + (0.5×6×3) + (0.5×6×3)
= 135 + 9 + 9
= 153 cm²
Hence, the surface area of the triangular prism is 153 cm².
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Answer:
9*5 + 6*9 + 9*4 + 1/2*6*3 + 1/2*6*3
=1872+1/2*6*3+1/2*6*3
=1872+18
=1890cm²
Surface area= 1890cm²
Wyatt analyzed the data from his science experiment and found that the MAD was greater than the IQR.
What does this tell you about the variability of the data?
A: The middle 50% of the data is
spread out more than the
average variation.
B: The average variation is spread
out more than the middle 50%
of the data.
C: The average of the data is closer to the
least value than it is to the greatest
value.
D: The average of the data is closer to the
greatest value than it is to the least value.
Answers
Answer:
C: The average of the data is a closer to the least value than it is to the greatest value
The Chesapeake Bay holds about 18 trillion gallons of water. The bay covers 4,480 square miles or 2,867,200 acres. Each acre can hold 750,000 oysters. Each oyster can filter 50 gallons of water each day. Can there be enough oysters to filter the whole Chesapeake Bay in one day? How is this number impacted by the bay's conditions?
Answers
There are enough oysters to filter the whole Chesapeake Bay in one day.
The numbers can be affected by the water temperature and the cleanliness of the water.
Are there enough oysters?The total number of water that can be filtered by the oysters is a function of the total amount of oysters in the bay and the quantity of water they can filter.
Total amount of water they can filter = oysters per acre x total acre x total gallons they can filter each day
(2.9 x[tex]10^{6}[/tex]) x (7.5 x [tex]10^{5}[/tex]) x (5 x 10) = 1.0875 x [tex]10^{14}[/tex]
The gallons of water in the bay in standard form = 1.8 x [tex]10^{13}[/tex]
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PLEASE HELP ASAP!!
The graph below is the solution for which set of inequalities?
1) x-2y ≤ 4
x+y ≤ 5
x ≥ 0
y ≥ 0
2) 3x-y ≤ 12
2x+y ≤ 10
x ≥ 0
y ≥ 0
3) 2x-y ≤ 8
x+y ≤ 5
x ≥ 0
y ≥ 0
4) x+y ≤ 5
x+y ≤ 4
x ≥ 0
y ≥ 0
Answers
Answer:
Hi,
Step-by-step explanation:
x>=0
y>=0
x+y-5<=0 line passing through (0,5) and (5,0) with (0,0) in minus region
2x-y-8<=0 line passing trough (0,-8) and (4,0) with (0,0) in minus region
Answer C
1.) Line segment AB has endpoints A(1,8) and B(7,−4). What are the coordinates of the point located 5/6 of the way from A to B?
O (-4, 11 1/3)
O (3, -2 1/3)
O (6, -2)
O (12, -14)
2.) Line segment AB has endpoints B (-3, 0) and A(5, 4). What are the coordinates of the point located 1/4 of the way from B to A?
O (1, -1)
O (1, 2)
O (3, 3)
O (-1, 1)
3.) Line segment AB has endpoints A(1, 8) and B(7, -4). What are the coordinates of the point located 1/6 of the way from A to B?
O (0, 8 2/3
O (2, 6)
O (8 2/3, -3 1/3)
O (6, -3 1/3)
^Please help, ASAP. These were due yesterday, however I am trying to get this done.
BRAINLIEST AND 5 STARS TO CORRECT RESPONSES ONLY! LOTS OF PTS AVAILABLE TO THOSE WHO PARTICIPATE HOWEVER.
Answers
The coordinates of the 3 respective points from the given parameters are; (6, -2); (-1, 1); (2, 6)
How to find the length of Line Segment?1) The coordinates of the point located 5/6 of the way from A to B is;
x = ⁵/₆(7 - 1) + 1
x = 6
y = ⁵/₆(-4 - 8) + 8
y = -2
x, y = (6, -2)
2) The coordinates of the point located ¹/₄ of the way from A to B is;
x = -3 + ¹/₄(5 - (-3))
x = -1
y = 0 + ¹/₄(4 - 0)
y = 1
x, y = (-1, 1)
3) The coordinates of the point located ¹/₆ of the way from A to B is;
x = ¹/₆(7 - 1) + 1
x = 2
y = ¹/₆(-4 - 8) + 8
y = 6
x, y = (2, 6)
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[tex]y=1-sqrt(1-2/x)[/tex]
make x the subject
Answers
[tex]~~~~~~~~y = 1- \sqrt{ 1- \dfrac 2x}\\\\\\\implies \sqrt{ 1- \dfrac 2x} = 1 - y\\\\\\\implies 1 - \dfrac 2x = (1 -y)^2~~~~~~~~~~~~~;[\text{Square on both sides}]\\\\\\\implies \dfrac 2x = 1-(1-y)^2\\\\\\\implies \dfrac{1}{x} = \dfrac{1-(1-2y+y^2)}{2}\\\\\\\implies x = \dfrac{2}{1-1+2y-y^2}\\\\\\\implies x = \dfrac{2}{2y-y^2}\\\\\\\implies x = -\dfrac{2}{y(y-2)}~~~~~~~~~~~~~~~~~;[y\neq 0,~ y \neq 2]\\[/tex]
please help with all of question 4.
Answers
Answer:
Step-by-step explanation:
Combine like terms: Like terms have same variable with same power and to combine the like terms, add/subtract the co efficient of the variables.
Perimeter:Perimeter = sum of all sides
a) Perimeter of ΔABC = AB + BC + CA
= x + 14 + x + 14 + x + 14
= x + x + x + 14 + 14 + 14 {Combine like terms}
= 3x + 42
b) EF = DI - GH
= 2x + 3 - x
= 2x - x + 3
= x + 3
c) FG = HI - ED
= 12 + 2x - (x + 5)
= 12 + 2x - x - 5 {To open the brackets, (-1) is distributed to x and 5}
= 12 - 5 + 2x - x
= 7 + x
d) Perimeter of DEFGHI = DE + EF + FG + GH + HI + ID
= x + 5 + x + 3 + 7 +x + x + 12 +2x + 2x + 3
= x +x + x + x + 2x + 2x + 5 + 3 + 7 + 3 + 12
= 8x + 30
Find CD.
A) 5
B) 28
C) 56
D) 96
Answers
Answer:
C) 56
Step-by-step explanation:
. What is the length of BC¯¯?
2. What is the length of AC¯¯?
3. What is the length of AD
A certain population of bacteria has an initial population of 225. the bacteria triples every hour. determine the multiplier that would allow you to predict the population of bacteria after 2 hours.
Answers
Using an exponential function, it is found that the multiplier that would allow you to predict the population of bacteria after 2 hours is of 9.
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex]
In which:
a is the initial value.b is the growth rate.In this problem, the bacteria triples every hour, hence the rate of change is b = 3, and the equation is:
[tex]y = a(3)^x[/tex]
Hence, after 2 hours:
[tex]y = a(3)^2 = 9a[/tex]
Which means that the multiplier is of 9.
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Which of the following transformations will result in an image that maps onto itself?
A. rotate 180 degrees counterclockwise and then reflect across the y-axis
B. reflect across the y-axis and then reflect again across the y-axis
C. rotate 90 degrees counterclockwise and then rotate 270 clockwise
D. reflect across the y-axis and then reflect across the x-axis
Answers
If we reflect across the y-axis and then reflect again across the y-axis , it will give result an image that maps onto itself , Option B is the right answer.
What are the rules of Transformations ?The reflection of the point (x,y) across the x-axis is the point (x,-y), across the y-axis is the point (-x,y). , across the line is the point (y, x)
The 90 degree counterclockwise rotation of a point (x, y) is the point (-y, x)
The 180 degree counterclockwise rotation of a point (x, y) is the point (-x, -y)
The 270 degree clockwise rotation of a point (x, y) is the point (-y, x)
Therefore on application of these rules
For Case A
The point will be (-y , x)
For Case B
The point will be (x,y)
Therefore Option B is the answer.
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Which statement about the angles in the figure is true?
m/3+m/5= 180°
m/7+m/10 = 180°
m/8+m/9 = 90°
m/1+m/8= 90°
Answers
The true statement about the angles in the figure is m∠1 + m∠8 = 90°. The correct option is the last option m∠1 + m∠8 = 90°
Determining the measures of anglesFrom the question, we are to determine the statement that is true about the angles in the given figure
In the given diagram, we can observe that
m∠3 + m∠8 + m∠9 + m∠10 = 180° (Sum of angles in a triangle)
Also,
m∠3 = m∠1 (Vertically opposite angles)
m∠9 + m∠10 = 90° (Vertically opposite angles)
∴ m∠1 + m∠8 + 90° = 180°
m∠1 + m∠8 = 90°
Hence, the true statement about the angles in the figure is m∠1 + m∠8 = 90°. The correct option is the last option m∠1 + m∠8 = 90°
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liz wants to determine which sport students like to play the most at her school.which method will most likely produce a random example.
Answers
Answer:
Random sampling
Step-by-step explanation:
Random sampling is a method of choosing a sample of observations from a population to make assumptions about the population. It is also called probability sampling.
which of the following number lines shows the correct sum of the number above and 4?
Answers
Answer:
c.
Step-by-step explanation:
because on you have to add 4 to the number above. so 3+4 equals 7 so you move 4 spaces to the right on the number line to get you 7. so C is the correct answer
quadratic equation y= (x+4)^2 -2
I need to know if it’s Max or min
Domain
Range
Increasing interval
Decreasing interval
Whoever the first correct answer belongs to gets a crown :) tysmmm
Answers
Answer:
Max or Min: min
Domain: (−∞, ∞)
Range: (−2, ∞)
Increasing interval: (−4, ∞)
Decreasing interval: (−∞, -4)
Step-by-step explanation:
Max or Min: You determined that the curve opens upwards meaning that the vertex is at the min. If it opened down then it would be at the max.
In mathematical terms: if a > 0, the parabola opens upward and the vertex is a minimum. If a < 0, the parabola opens downward, and the vertex is a maximum.
Domain: This is all possible x values, since the parabola is upwards its going to have any possible x values
Range: this is all possible y values. we know that the vertex point (min) doesn't go less than the value of -2 for y but anything above is possible hence -2 is the lowest possible y value and anything beyond above
Increasing interval: The derivative of a function may be used to determine whether the function is increasing or decreasing on any intervals in its domain. If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I.
Decreasing interval: The derivative, then set it equal to 0, and then find between which zero values the function is negative.
visual representation attached as well
Hope it helps :)
If you have any questions or anymore help lmk, happy to help with any school work!!
Have a nice day, you got this !!
What is the solution for x in the equation?
x-3/7=2x-25/7
Answers
Step-by-step explanation:
please mark me as brainlest
Answer: x = 4/3
Step-by-step explanation: I just answered the answer
Janine sketched a quick graph. "Looks like the solution is (-30, -91)." Is she right? How do you know? Be
clear and complete.
Answers
Answer:
- -=+ we should just add it to make the
Factor 27a^{3}b^{9} + 8c^{18}.Which of the following is one of the factors
Answers
Answer:
Second option is the correct answer
[tex]\bigodot (9a^2b^6-6ab^3c^6+4c^{12})[/tex]
Step-by-step explanation:
[tex]27a^{3}b^{9} + 8c^{18}[/tex][tex]=(3ab^{3} )^3+ (2c^{6})^3[/tex][tex]=(3ab^{3} +2c^{6})[(3ab^3)^2-(3ab^3)(2c^6)+(2c^6)^2][/tex][tex]=(3ab^{3} +2c^{6})\orange{\bold{(9a^2b^6-6ab^3c^6+4c^{12})}}[/tex]