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

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 = 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

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

The total change in the amount of water in the pool is 288 gallons.

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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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:

Feel 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).

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.

An exponential function is modeled by:

[tex]y = ab^x[/tex]

In which:

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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The surface area of the triangular prism is 153 cm².

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

[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]

Answer:

42

Step-by-step explanation:

6 times 7 is 42

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

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.

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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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

Step-by-step explanation:

please mark me as brainlest

Answer: x = 4/3

Step-by-step explanation: I just answered the answer

Answer:

the answer is 49

Step-by-step explanation:

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.

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

Answer:

Second option is the correct answer

[tex]\bigodot (9a^2b^6-6ab^3c^6+4c^{12})[/tex]

Step-by-step explanation:

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 ✓

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.

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.

Answer:

- -=+ we should just add it to make the

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 !!

[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]

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.

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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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.

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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The coordinates of the 3 respective points from the given parameters are; (6, -2); (-1, 1); (2, 6)

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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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°

From 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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Answer:

C: The average of the data is a closer to the least value than it is to the greatest value

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 )

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.

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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