what is the volume of this triangular prism?

Answer:

x=6

Step-by-step explanation:

Isolate the x variable.

3+6x=2x+27

3+4x=27

4x=24

x=6

The area of the shaded portion in the equilateral triangle with sides 6 is 9√3 - 36π.

To find the area of the shaded portion in the equilateral triangle, we need to determine the area of the three arcs and subtract it from the area of the equilateral triangle.

First, let's find the area of one arc. Each arc has a radius equal to the length of the side of the equilateral triangle, which is 6. The formula for the area of a sector is A = (θ/360)πr², where θ is the central angle in degrees.

In an equilateral triangle, each interior angle measures 60 degrees, so the central angle of the arc is 120 degrees (360 degrees divided by 3). Plugging these values into the formula, we get A_arc = (120/360)π(6)² = (1/3)π(6)² = 12π.

Since there are three identical arcs, the total area of the arcs is 3 times the area of one arc, which is 3(12π) = 36π.

Now, let's find the area of the equilateral triangle. The formula for the area of an equilateral triangle is A_triangle = (√3/4)s², where s is the length of a side.

Plugging in the value of the side length, we have A_triangle = (√3/4)(6)² = (√3/4)(36) = 9√3.

Finally, we subtract the area of the arcs from the area of the equilateral triangle to find the shaded portion's area: A_shaded = A_triangle - A_arc = 9√3 - 36π.

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The length of the hypotenuse in this problem is given as follows:

h = 10.6 m.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

The side lengths for this problem are given as follows:

7m and 8m.

Hence the hypotenuse is obtained as follows:

h² = 7² + 8²

\(h = \sqrt{7^2 + 8^2}\)

h = 10.6 m.

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Answer:

D) y= + 0.8x + 46

Step-by-step explanation:

Hope it helps

The required answers are 1) \($$A = x^2 + 28x + 192$$\) 2) 300000 3) \($$x^2 + 28x + 192 = (x + 14 - 2\sqrt{19})(x + 14 + 2\sqrt{19})$$\).

area of the land purchased is given as 480m², and the dimensions of the land are (x+12)mx(x+16)m. Therefore, the area of the land can be expressed as:

\($$A = (x+12)(x+16)$$\)

Expanding this expression, we get:

\($$A = x^2 + 28x + 192$$\)

Hence, the area of the land purchased is given by the polynomial expression \($x^2 + 28x + 192$\).

The total budget for the expenses is Rs. 5,00,000. If Mr. Chand's daughter is ready to share 3/5 of the expenses, then the fraction of the expenses she will pay is:

\($\frac{3}{5}=\frac{x}{500000}$$\)

Simplifying this expression, we get:

\($x = \frac{3}{5}\times 500000 = 300000$$\)

Therefore, Mr. Chand's daughter will pay Rs. 3,00,000 towards the expenses.

We can solve the polynomial \($x^2 + 28x + 192$\) into different factors by using the quadratic formula:

\($x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$\)

Here, the coefficients of the polynomial are:

\($$a = 1, \quad b = 28, \quad c = 192$$\)

Substituting these values in the quadratic formula, we get:

\($x = \frac{-28 \pm \sqrt{28^2 - 4\times 1 \times 192}}{2\times 1}$$\)

Simplifying this expression, we get:

\($$x = -14 \pm 2\sqrt{19}$$\)

Therefore, the polynomial \($x^2 + 28x + 192$\) can be factored as:

\($$x^2 + 28x + 192 = (x - (-14 + 2\sqrt{19}))(x - (-14 - 2\sqrt{19}))$$\)

or

\($$x^2 + 28x + 192 = (x + 14 - 2\sqrt{19})(x + 14 + 2\sqrt{19})$$\)

So, we have factored the polynomial into two factors.

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Answer:

A. f(25) = 15

Step-by-step explanation:

there are three functions given,

1st.

3√x  .............replace x with 25 cause f(25)

3√25

3*5

15 ......given that x≥9, so 15 falls above 9 and is correct

2nd.

-| 2x |

-| 2(25) | .....replace x here as well

- |50|

-50 .......given that 0<x<9, but it doesn't fall between 0 and 9 so wrong.

3rd.

13 .......given x≤0, 13 doesn't fall under or equal to 0 but is above so wrong.

Therefore can be concluded answer is 15

Answer:

A 15

Step-by-step explanation:

Answer:

y=-2x+2

Step-by-step explanation:

We use the formula

y=mx+b, where m is the slope, b is the y intercept, and x&y are the coordinates.

We know that one point is (-1, 4)

and the slope is -2.

We are trying to find b.

In order to do that, we plug in what we know:

so,

4=-2(-1)+b

4=2+b

4-2=b

b=2

So now we go back to the original equation and use b as our value'

y=-2x+2

Answer:

30.25 is the answer..........m

Answer:

hold yo ablo espanol

Step-by-step explanation:

h(x) is a translation upwards of 2 units of f(x), and the new range of the function h(x) will be [2, ∞)

We know that f(x) is the parent absolute value function:

f(x) = |x|

It is transformed so we get:

h(x)=  |x| + 2

Remember that a vertical translation of N units is written as:

h(x) = f(x) + N

Then h(x) is a translation upwards of 2 units of f(x), and the new range of the function h(x) will be [2, ∞)

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Answer:

\( p(x)= x^3-2x^2+x-2 \)

Step-by-step explanation:

Here we are given that a polynomial has zeros as 2 , i and -i . We need to find out the cubic polynomial . In general we know that if \(\alpha , \ \beta \ \& \ \gamma \) are the zeros of the cubic polynomial , then ,

\(\sf \longrightarrow p(x)= (x -\alpha )(x-\beta)(x-\gamma) \)

Here in place of the Greek letters , substitute 2,i and -i , we get ,

\(\sf\longrightarrow p(x)= (x -2 )(x-i)(x+i) \)

Now multiply (x-i) and (x+i ) using the identity (a+b)(a-b)=a² - b² , we have ,

\(\sf \longrightarrow p(x)= (x-2)\{ x^2 - (i)^2\} \)

Simplify using i = √-1 ,

\(\sf \longrightarrow p(x)= (x-2)( x^2 + 1 ) \)

Multiply by distribution ,

\(\sf \longrightarrow p(x)= x(x^2+1) -2(x^2+1) \)

Simplify by opening the brackets ,

\(\sf\longrightarrow p(x)= x^3+x-2x^2-2 \)

Rearrange ,

\(\sf\longrightarrow \underline{\boxed{\blue{\sf p(x)= x^3-2x^2+x-2}}}\)

equation has infinitely many solutions has the same number on both sides of the equal sign

-3x -21 + x + 5 = -20x -16

-2x -16 = -20x -16

so either you have -18x on the left or +18x in the right

Answer:

cancel y 's 5x=-10

Step-by-step explanation:

The number of coins Mark have is 48.

Joey has 25 collectible coins which is 9 more than 1/3 the number Mark has. Therefore, the number of coins Mark have can be calculated as follows:

Let's write the equation for the word problem before solving.

Hence,

let

x = number of coins Mark has

Therefore,

Number of coins Joey have = 9 + 1  /3 x

Hence,

25 = 9 + 1  / 3 x

25 - 9 = 1 / 3 x

16 = 1 / 3 x

cross multiply

x = 16 × 3

x = 48 coins

Therefore,

number of coins Mark have = 48 coins

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Answer:

C. (x-3)(x+2)(x+1)

Step-by-step explanation:

We can use the rational roots test to help factor out the original equation.

The leading term is 1 and the constant is 6

p/q= 6/1

Now we find factors (all these are plus and minus)

1,2,3,6

1

We find the common ones (+1 and -1) and use -1 because it ends up being the root of the function

Factor, (x+1)

Now we have (x+1)(x^2-x-6)

Factor this with whatever method you perfer, I use AC method

Find two that are a product of -6 and add to -1 (-3 and 2)

We get (x+1)(x-3)(x+2)

C

Answer:

\(\boxed{C}\)

Step-by-step explanation:

Let's solve all of the option and see which equals x³-7x-6

Option A)

\((x-4)(x-2)(x+1)\)

=> \((x^2-6x+8)(x+1)\)

=> \(x^3+x^2-6x^2-6x+8x+1\\x^3-5x^2+2x+1\)

So, A is not correct

Option B)

\((x-6)(x-1)(x+1)\\(x+6)(x^2-1)\\x^3-x+6x^2-6\\x^2+6x^2-x-6\)

This is also not correct

Option C)    ← Correct

\((x-3)(x+2)(x+1)\\(x^2-x-6)(x+1)\\x^3+x^2-x^2-x-6x-6\\x^3-7x-6\)

This equals to x³-7x-6, So, this is the correct option. No need to do Option D since we have the right option now!

For supporting bars are two pieces of wood, one that is 36 inches and another that is 54 inches. The length of the diagonal of the kite would be approximately 64.90 inches.

Assuming that the supporting bars represent two adjacent sides of the kite, we can use the Pythagorean theorem to find the length of the third side (the diagonal or the kite's spine) and the area of the kite.

Now,

If we let the length of the shorter supporting bar be "a" and the length of the longer supporting bar be "b", then the length of the diagonal (d) can be found using the Pythagorean theorem:

⇒ d² = a² + b²

Plugging in the values given in the problem, we have:

d² = 36² + 54²

d² = 1296 + 2916

d² = 4212

d ≈ 64.90 inches

So, the length of the diagonal of the kite would be approximately 64.95 inches.

As for a possible relationship between the sides of the kite, we can see that the diagonal is always longer than either of the supporting bars. Additionally, the difference between the squares of the diagonal and each supporting bar is always a perfect square. In this case, we have:

d² - a² = 2916

d² - b² = 1296

Therefore, we can predict that the longer the supporting bars of the kite, the larger the area of the kite will be, since the area of a kite is directly proportional to the product of its diagonals. We can also predict that the diagonal of the kite will be closer in length to the longer supporting bar than to the shorter one.

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Answer:

5

Step-by-step explanation:

2 + 4 +3 - 6 +2

5

plz mark me brainliest

Answer:

The correct answer is D. the increase in area of the new frame.

Step-by-step explanation:

Hope this helps you!!

9514 1404 393

Answer:

  warmer by 30.2 degrees

Step-by-step explanation:

It might help to think of these values plotted on a number line. Both temperatures will be left of zero, with -63°C being farther to the left (colder).

The difference can be found by subtracting the colder temperature from the warmer one:

  -32.8 -(-63) = -32.8 +63 = 63 -32.8 = 30.2 . . . degrees

The South America temperature -32.8°C is 30.2° warmer than the North America temperature.

Answer:

20.52 cm²

area of semi-circle - area of triangle

\(\dashrightarrow \sf \dfrac{1}{2} \ \pi (radius)^2 \ - \ \sf \dfrac{1}{2} *base*height\)

\(\rightarrow \sf \dfrac{1}{2} (3.14)(6)^2 - \dfrac{1}{2} *12*6\)

\(\hookrightarrow \sf 56.52 \ - \ 36\)

\(\hookrightarrow \sf 20.52 \ cm^2\)

Answer:

-3x^2 -5x +2

Step-by-step explanation:

-2x(x+3)-(x+1)(x-2)=

Distribute

-2x^2 -6x  -(x+1)(x-2)

Foil

-2x^2 -6x  -(x^2 -2x +x -2)

Combine like terms

-2x^2 -6x  -(x^2 -x  -2)

Distribute the minus sign

-2x^2 -6x  -x^2  +x +2

Combine like terms

-2x^2  -x^2  -6x +x +2

-3x^2 -5x +2

Answer:

\(\huge\boxed{-2x(x+3)-(x+1)(x-2)=-3x^2-5x+2}\)

Step-by-step explanation:

\(-2x(x+3)-(x+1)(x-2)\)

Use the distributive property: a(b + c) = ab + ac

and FOIL: (a + b)(c + d) = ac + ad + bc + bd

\(=(-2x)(x)+(-2x)(3)-\bigg[(x)(x)+(x)(-2)+(1)(x)+(1)(-2)\bigg]\\\\=-2x^2-6x-\bigg(x^2-2x+x-2\bigg)=-2x^2-6x-x^2-(-2x)-x-(-2)\\\\=-2x^2-6x-x^2+2x-x+2\)

Combine like terms:

\(=(-2x^2-x^2)+(-6x+2x-x)+2=-3x^2+(-5x)+2\\\\=-3x^2-5x+2\)

The expression or equation to represent the number of hat each shelter will receive is h = 1600 / 4

Algebraic expressions are the mathematical statement that we get when operations such as addition, subtraction, multiplication, division, etc. are operated upon on variables and constants.

To represent the amount each local shelter will receive, we can write an expression for that while the variable is present

The number of hats can be found by dividing the total number of hats collected by the number of local shelters.

Estimating the number of hats

1596 ≅ 1600

Number of hats (h) = 1600 / 4

h = 400

Each local shelter will receive 400 hats

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Answer:

Step-by-step explanation:

The graph on the left represents Firm Aleph’s cost curves. The horizontal axis represents quantity (Qe) and the vertical axis represents average total cost (ATC). The graph shows that at Qe, ATC is at its minimum. The graph also shows that at Qe, price (PE) is equal to average total cost (ATC).

The graph on the right represents the market demand and supply curves. The horizontal axis represents quantity (QE) and the vertical axis represents price (PE). The graph shows that at QE, price (PE) is equal to marginal cost (MC). It also shows that at QE, price (PE) is equal to average total cost (ATC).

When the market moves to long-run equilibrium, both market equilibrium quantity and price remain constant3.

If the product that Firm Aleph produces has a positive externality, then there is a difference between private marginal cost (PMC) and social marginal cost (SMC). The marginal social benefit (MSB) curve lies above the demand curve. The socially optimal quantity is where MSB equals SMC. In an unregulated market, however, firms produce where PMC equals demand. Therefore, an unregulated market produces less than the socially optimal quantity3.

Here’s a graph showing marginal social benefit (MSB) on the market graph from part (b):

Answer:

This statement would be true.

Step-by-step explanation:

The equation that models the product is 5 × 5 = 25

In mathematics, a numerical expression is a combination of numbers or integers combined using mathematical operators like addition, subtraction, multiplication, division, etc. In this, we don't use variables like x, y, etc., or any unknown quantity.

Here we have

Jonathan uses the area model to show the product of two mixed numbers  

The equation that models the product can be formed as follows

Here number of units along length = 5 units

Number of units along breadth = 5 units

Area = 5 × 5 = 25

Therefore,

The equation that models the product is 5 × 5 = 25

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Answer:

Yup you get it! (Probability doesn't change, it is constant for all trials)

Step-by-step explanation:

In binomial experiments, you have two conditions, a success and failure is how they often put it. In this experiment, the probability of success has to be the same for each trial to constitute it as a binomial experiment.

Basically there's 4 rule you need to satisfy for an experiment to be considered binomial:

1) Has to have fixed number of trials. Eg, n=1,2,3.....x x= finite number (we cannot have infinte trials)

2) Each trial is independent of one another. (One trial doesn't influence another trials probability/outcome)

3) Only two outcomes (very important) because as name suggests bi- (bi usually means two)

4) Probability of each outcome/condition is constant from one trial to another

The solution for variables x, y, and z are -

The given linear equation are-

x - 6y - 2z = -8   .......equation 1.

-x + 5y + 3z = 2 ......equation 2.

3x - 3y - 4z = 15 .......equation 3.

Add equation 1 and 2; gives

-y + z = -6   .....equation 4

multiply equation 2 and subtract it with equation 3;

12y + 5z = 21 ......equation 5

multiply equation 4 with 5 and subtract it from equation 5.

17 y = 51

y = 3.

Put y = 3 in equation 4 and find z.

z = -6 + 3

z = -3

Put the value of y and z in equation 1 and find x.

x = -8 + 18 + 6

x = 100

Therefore, the solution for variables x, y, and z are -

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To find the polar equation of a conic with focus at the pole, directrix y=3, and eccentricity of 2, we can use the definition of a conic in polar coordinates.

The general form of the polar equation for a conic with focus at the pole is given by:

r = \(\frac{ed}{1+e\cos(\theta-\theta_0)}\)

Where:

- r is the distance from the origin (pole) to a point on the conic.

- e is the eccentricity.

- d is the distance from the pole to the directrix.

- θ is the angle between the polar axis and the line connecting the pole to a point on the conic.

- θ_0 is the angle between the polar axis and the line connecting the pole to the focus.

In this case, the focus is at the pole, so θ_0 = 0. The directrix is y = 3, which means its distance from the pole is d = 3. The eccentricity is given as 2, so e = 2.

Substituting these values into the general equation, we get:

r =\(\frac{2\cdot3}{1+2\cos(\theta-0)}\)

Simplifying further:

r =\(\frac{6}{1+2\cos(\theta)}\)

Therefore, the polar equation of the conic with focus at the pole, directrix y=3, and eccentricity of 2 is:

r =\(\frac{6}{1+2\cos(\theta)}.\)

This equation describes the shape of the conic in polar coordinates, where r represents the distance from the origin to a point on the conic, and θ represents the angle between the polar axis and the line connecting the origin to the point.

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