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\( ( {x}^{2} - 16) - (20 - x) - 4 \\ = {x}^{2} + x - 40\)

Answer:

626.71 cm^2

Step-by-step explanation:

Area of figure = area of half circle + Area of half circle + area of a rectangle

here, diameter=15 cm

radius = 15/2=7.5 cm

length=30cm

breadth=15cm

Now

Area of figure = 1/2*π*radius^2+ 1/2*π*radius^2+length*breadth

=1/2* 1/2*π*7.5^2+1/2* 1/2*π*7.5^2+30*15

=626.71 cm^2

Answer: 1.1%

Step-by-step explanation:

$9.72 - $9.61 = .11

.11/9.60 = 0.01145833 x 100 = 1.1458333 round to the nearest tenth = 1.1%

The integral\int(1/x^4 + 9x^2) dx converges by comparison to a convergent integral, and its value is 1/3

To determine whether the integral converges or diverges, we can use the limit comparison test with the integral:

Since for all x > 0, we have:

Thus, by the limit comparison test:

converges if and only if converges.

We can evaluate  using the power rule of integration:

where C is the constant of integration. Evaluating this integral from 1 to infinity, we get:

∫(1/x^4) dx from 1 to infinity = lim as b → infinity

=>

=> 0 - (-1/3)

=> 1/3

Since the integral  dx converges by comparison to a convergent integral, and its value is 1/3.

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Note: The full question is

Determine whether the integral converges or diverges; if it converges, evaluate. (If the quantity diverges, enter DIVERGES. Do not use the [infinity] symbol in your answer.) [infinity] dx x4 + 9x2 1

Check the picture below.

Answer:

-76, -12, |-29|, 34, 54

Step-by-step explanation:

I hope this helps you out...

Answer:

-76, -12, 29, 34, 54

Step-by-step explanation:

Since the 29 is in absolute value bars it turns positive.  

Answer:

x = 3

Step-by-step explanation:

2x + 12 = 18

The variable is "x" and to find the value of x we must get rid of everything on the left side of the equation.

We can easily do this by using inverse operations

To get rid of the 12, we subtract 12, because in the expression its adding and the inverse of addition is subtraction.

But remember whatever we do to one side we have to do to the other, so we subtract 12 from each side

12 - 12 cancels out

18 - 12 = 6

we now have 2x = 6

now we want to get rid of the 2

2x is the same as 2 times x which is multiplication

The inverse of multiplication is division, so to get rid of the 2 we divide each side by 2

2x / 2 = x

6 / 2 = 3

we're left with x = 3

Answer:

\({ \tt{( {x}^{4})(3 {x}^{3} - 2)(4 {x}^{2} + 5x) }} \\ = { \tt{( {x}^{4})( {12x}^{6} + 15 {x}^{4} - 8 {x}^{2} - 10x) }} \\ = { \tt{( {12x}^{24} + {15x}^{16} - {8x}^{8} - {10x}^{5} ) }}\)

Answer:

\(\left(x^4\right)\left(3x^3-2\right)\left(4x^2+5x\right)\)

\((3x^{3} -2)(4x^{2} +5x)\)

\(12x^5+15x^4-8x^2-10x\)

\(\left(x^4\right)\left(12x^5+15x^4-8x^2-10x\right)\)

\(=12x^9+15x^8-8x^6-10x^5\)

Therefore, A is your answer

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Step-by-step explanation:

(1,4)

I hope this will help you

Answer:jk;nlmlk lmStep-by-step explanation:

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Answer:

x int= -4 y int= 1

Step-by-step explanation:

intercepts refer to the place on the each axis where the line passes through

When it comes to medication or medical care, the person who would usually face the greatest impact from a discrepancy in dosage is the individual who is undergoing the treatment.

Insufficient dosage may result in a lack of intended therapeutic effects and failure to improve the patient's condition as anticipated. Also, if the amount administered is excessive, the individual may suffer from negative consequences or possible injury.

It should be noted that the effects of a difference in medication dosage can differ based on the type of medicine, the condition being treated, and personal characteristics like age, weight, general health, and specific reactions or sensitivities.

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Answer:

C) 10

Step-by-step explanation:

When we reflect triangle ABC across line l the distance BB' will be 1*2=2.

When we reflect triangle A'B'C' across line m the distance B'B" will be 4*2=8

So the distance BB" will be 2+8=10

The value of cos(2α + β) using trigonometric identities is; -1.0155

We are given;

α = sin⁻¹(4/5)

β = tan⁻¹(12/5)

Thus;

sin α = 4/5

tan β = 12/5

From trigonometric ratios, we can say that;

cos α = 3/5

sin β = 12/13

cos β = 5/13

We know from trigonometric identities that  cos (a + b) = cos a cos b - sin a sin b.

Thus;

cos(2α + β) = cos 2α cos β - sin 2α sin β

Thus;

cos(2α + β) = 2(3/5) * (5/13)) - ((2 * 4/5 * 12/13))

= 0.4615 - 1.477

= -1.0155

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The specified dimensions of the interior and exterior walls, indicates that the dimensions of the building is 28 feet 10 5/8 inches

The dimensions of a building includes the lengths, height, and width of the building.

The wall measurements for the building are;

The thickness of the interior walls = 2 × 4 (3 1/2'')

The thickness of the sheetrock on both sides of the interior walls = 1/2''

The dimensions of the exterior walls = 2 × 6(5 1/2'')

The thickness of the sheet rock on the interior of the interior walls = 1/2''

The thickness of the sheeting on the exterior of the exterior walls = 7/16''

The thickness of the brick on the exterior of the exterior wall = 3 5/8''

The specified dimension of one of the rooms = 11' 3''

The dimension of the second room = 15'7''

The outside dimension of the house, D, is therefore;

D = The sum of the dimensions of the rooms + The dimension of the inner wall + 2 × The thickness of the outer wall

Therefore;

D = 11'3'' + 15'7'' + 3 1/2'' + 1/2'' + 1/2'' + 2 × (5 1/2'' + 1/2'' + 7/16'' + 3 5/8'')

D = 11'3'' + 15'7'' + 4 1/2'' + 20 1/8'' = 28' 10 5/8''

The dimension of the building, D = 28 feet 10 5/8 inches

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The scale factor that the drawing use is 3/1000.

From the information, Colleen made a scale drawing of a house and she used the scale 3 millimeters = 1 meter.

It should be noted that 1000 millimeters = 1 meter

Therefore, the scale factor that the drawing use is:

= 3 millimeters / 1 meter

= 3/1000

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Answer:

D

Step-by-step explanation:

a local minimum is a low point in the graph, but it isn't the lowest. and If u look at the given interval choices, the only one that has a local minimum Is D.

Answer:

7y²x³

Step-by-step explanation:

when taking an exponent to an exponent multiply them

(7y²x³)² = 49y⁴x⁶

The total surface area of the solid shape made from the cube and cylinder is approximately 583.31 cm².

The side length of the cube is 8.7 cm, so the surface area of one face is A = 8.7²

= 75.69 cm²

Since there are six faces, the total surface area of the cube is 6 * 75.69 = 454.14 cm²

Since there are two circular bases, the total surface area of the bases is 2 * 22.91 = 45.82 cm².

In this case, the radius of the cylinder is 2.7 cm and the height is 4.9 cm, so the curved surface area is A_curved = 2 * π * 2.7 * 4.9 ≈ 83.35 cm².

Total surface area = surface area of the cube + surface area of the cylinder

Total surface area = 454.14 cm² + 45.82 cm² + 83.35 cm²

Total surface area ≈ 583.31 cm²

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Step-by-step explanation:

Step 3 is incorrect, it should be x - 4 + x = x(x - 3).

x - 4 + x = x(x - 3)

2x - 4 = x² - 3x

x² - 5x + 4 = 0

(x - 4)(x - 1) = 0

x = 4 or x = 1.

x = 4 is rejected as 1 / (x - 4) will become 1 / 0 which is undefined.

=> x = 1.

Answer:

C

Step-by-step explanation:

The red dotted line we see is the asymptote, which is a line that the functions will never cross.

The asymptotes we see currently is:

x = -3

and

x = 2

We can find the vertical asymptotes using the denominator of the function since the x value that makes the denominator 0 is the asymptote. Since -3 and 2 is the asymptote, the denominator of the function will be:

(x-2) (x+3)

If we look at the answer choices, we can see that C is the only option with a denominator of (x-2)(x+3), so that is our answer.

Answer:

C

Step-by-step explanation:

there are 2 vertical asymptotes at x = - 3 and x = 2

then the factors on the denominator will be (x + 3) and (x - 2)

then

f(x) = \(\frac{1}{(x-2)(x+3)}\)

Answer:

the graph shifts 3 units down

Explanation:

to move a graph up c units, add c to the whole function

so basically what you did is you subtracted 3 from the whole function the whole graph shifts 3 units down

I hope it helps.

The company cannot maximize profit because the cost of producing outweighs the revenue or profit made

The profit function is given by P(x) = R(x) - C(x), where R(x) is the revenue function and C(x) is the cost function:

P(x) = R(x) - C(x) = 180x - (65x + 13,800) = 115x - 13,800

To maximize the profit, we need to find the value of x that maximizes P(x). We can do this by finding the vertex of the parabola that represents the profit function. Since the coefficient of the x² term is negative (-115), the parabola opens downward and the vertex represents the maximum value of the function.

The x-coordinate of the vertex is given by x = -b/2a, where a and b are the coefficients of the x² and x terms, respectively. In this case, a = -115 and b = 0, so x = 0.

Therefore, the maximum profit occurs when x = 0, which means that the company should not produce any drones. This is because the cost of producing each drone (65x + 13,800) is greater than the revenue generated by selling each drone (180x) for all values of x.

In other words, the company will lose money for each drone produced, so it should not produce any at all.

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Answer:

-1/2

Step-by-step explanation:

This is because -2/3 - (-1/6) is going to equal to -1/2. (-0.5)

This transformation of the polygon ABCD to A'B'C'D' is a by a factor of 2√5.

The coordinates are given as:

First polygon: A (-3, 7), B (-4, 9), C (-7, 9), and D (-4, 5).

Second polygon: A' (3, -4), B'(3, 6), C'(8, 2.8), and D'(7.2, -1.9)

Calculate the distance AB and A'B' using:

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

⇒ AB = √ (-4 + 3)² + (9 - 7)²

⇒ AB = √1 + 4

⇒ AB = √5

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

⇒ A'B' = √ (3 - 3)² + (6 + 4)²

⇒ A'B' = 10

This gives, Divide A'B' by AB to determine the scale factor (k)

k = 10 / √5

k = 2√5

Hence, this transformation is a by a factor of 2√5

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Answer:

Reflection and 2

Step-by-step explanation:

for plato

Answer:

0

Step-by-step explanation:

7 + (-8) + 2 + (-1)

is the same as:

7 - 8 + 2 - 1

Simplify these:

-1 + 1

Solve:

0

Answer:

y=22

Step-by-step explanation:

Okay since we know x=5

we just replace x with 5 in the equation

so y=5x-3 becomes y=5(5)-3

5*5=25

25-3=22

y=22

The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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