f(x) = 3x² + 5; find f(x + 3) - [f(x) + 3]

Answer:

The cardinality Of Set A= 8, Set B = 5

Step1: Integers greater than or equal to -9 and less than or equal to -2 are

      =   -9,-8,-7,-6,-5,-4,-3,-2

Step 2: Form a set using given elements, we have

Set A = {-9,-8,-7,-6,-5,-4,-3,-2}

Step 3: Count the no. of elements

we have, no. of elements is 8.

For given Set B = {-30, -27, 20, 24, 28}

we have, no. of elements is 5.

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Answer: C

Step-by-step explanation:

[tex]\frac{3x^{2}-3}{x^{2}+3x}=\frac{3(x^{2}-1)}{x(x+3)}=\frac{3(x-1)(x+1)}{x(x+3)}[/tex]
So, the original fraction is equal to

[tex]\frac{\frac{3(x-1)(x+1)}{x(x+3)}}{\frac{x+1}{x(x+3)}}=\boxed{3(x-1)}[/tex]

Perpendicular lines have slopes that are negative reciprocals of each other, so since the slope of the given line is 1, the slope of the line we want to find is -1.

Substituting into point-slope form,

[tex]y+4=-1(x-5)\\\\y+4=-x+5\\\\\boxed{y=-x+1}[/tex]

The length of the kitchen in the drawing using the scale factor is: B. 5/6.

We are given a scale factor of 1:24.

Let the length of the kitchen in the drawing = x

Actual length of kitchen = 20 ft.

Using the scale factor, we have:

1/24(20) = 20/24

= 5/6

The length of the kitchen in the drawing is: B. 5/6.

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To calculate the distance between two points we use this formula:

[tex] \boxed{ \boxed{{d \: = \: \sqrt{(x_2 \: - \: x_1)^{2} \: + \: (y_2 \: - \: y_1)^{2} } }}}[/tex]

______________________

We apply the values already obtained to the formula to get the distance:

[tex]d \: = \: \sqrt{( - 3 \: - \:( - 5))^{2} \: + \: (0 \: - \: 8)^{2} }[/tex]

[tex]d \: = \: \sqrt{( - 3 \: - \: ( - 5))^{2} \: + \: ( - 8)^{2} }[/tex]

[tex]d \: = \: \sqrt{( - 3 \: + \: 5) ^{2} \: + \: 64 } [/tex]

[tex]d \: = \: \sqrt{ {2}^{2} \: + \: 64 } [/tex]

[tex]d \: = \: \sqrt{4 \: + \: 64} [/tex]

[tex]d \: = \: \sqrt{68} [/tex]

[tex]d \: = \boxed{ \bold{ \: 2 \sqrt{17} \: units}}[/tex]

[tex] \huge{\boxed{ \bold{2 \sqrt{17} \: units }}}[/tex]

By the property of corresponding angles  ∠3 ≅ ∠5.

In geometry, a transversal is any line that intersects two straight lines at distinct points.

If two parallel lines are cut by a transversal, then each pair of corresponding angles are equals.

That is, ∠3 = ∠5 and ∠4 = ∠6.

Therefore the given angles ∠3 and ∠5 are equal.

Hence  ∠3 ≅ ∠5 .

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Step-by-step explanation:

[tex] \sin(\pi - x) + \tan(x) \cos(x) (x - \frac{\pi}{2} [/tex]

[tex] \sin( - x + \pi ) + \tan(x) ( \cos(x - \frac{\pi}{2} ) )[/tex]

Sin is odd function, so if you add pi to it, it would become switch it sign.

[tex] - \sin( - x) + \tan(x) \cos(x - \frac{\pi}{2} ) [/tex]

Also since sin is again, a odd function, we can just multiply the inside and outside by -1, and it would stay the same.

[tex] \sin(x) + \tan(x) \cos(x - \frac{\pi}{2} ) [/tex]

Cosine is basically a sine function translated pi/2 units to the right or left so

[tex] \sin(x) + \tan(x) \sin(x) [/tex]

[tex] \sin(x) ( 1 + \tan(x) )[/tex]

Answer: 46.0 ft

Step-by-step explanation:

[tex]\sin 24^{\circ}=\frac{x}{105}\\\\x=105\sin 24^{\circ}[/tex]

So, the distance above the ground is [tex]105\sin 24^{\circ}+3.25 \approx \boxed{46.0 \text{ ft}}[/tex]

Answer:

D.

Step-by-step explanation:

Answer:

The answer is 28

Step-by-step explanation:

ms..s.s..snskkzkzklzlzls

Answer:

x² - 4 = 0

x² = 4

x =± √4

x = +2 or x = -2.

Answer:

2 and -2 (±2)

Step-by-step explanation:

Step 1: Move -4 to the other side of the equal sign; we get x² = 4.

Step 2: A lot of people miss the negative answer! The square root of 4 is equal to both positive 2 and negative 2.

Answer:

state Avogadro's hypothesis and prove that molecular weight

Answer:

Liz

Step-by-step explanation:

if the chart is correct only 3 people spent more than 2 1/2 hours on homework when 9 people spent less than 2 1/2 hours on homework

Using the Pythagorean Theorem, it is found that the lot has an area of about 35 acres.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

Researching the problem on the internet, the lot has one leg of 800 feet and the hypotenuse is of 3900 feet, hence the other leg is found as follows:

[tex]800^2 + l^2 = 3900^2[/tex]

[tex]l = \sqrt{3900^2 - 800^2}[/tex]

l = 3817 feet.

The area of a right triangle is given by half the multiplication of it's legs. Hence, the area of the lot, in square feet, is given by:

A = 0.5 x 800 x 3817 = 1,526,800 square feet.

Each square feet is equivalent to 0.000029568 acres, hence the area in acres is given by:

Aa = 0.000029568 x 1,526,800 = 35 acres.

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Answer:

6

Step-by-step explanation:

I presume you meant

[tex]g(x) = \sqrt{x + 32} \\ g(32) = \sqrt{32 + 4} \\ g(32) = \sqrt{36} \\ g(32) = 6[/tex]

The absolute value of the complex number is √2. The graph is plotted and attached.

A complex number is one that has both a real and an imaginary component, both of which are preceded by the letter I which stands for the square root of -1.

The given complex number as;

2−i

The absolute value is found as;

[tex]\rm R = \sqrt{1^2 +(-1)^2 } \\\\ R = \sqrt 2[/tex]

The graph for the complex number is attached.

Hence the absolute value of the complex number is √2.

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Answer:

yea that’s right

Step-by-step explanation:

The minimized value is 50 and the maximized value is 130

The objective function is:

P = 10x + 5y

Subject to

2x+3y ≤30

2x+y ≤ 26

-2x+3y ≤ 30

x, y >0

Next, we plot the graph of the constraints (see attachment)

From the graph, the vertices of the feasible regions are:

(0, 10),(12, 2) and (6,14)

Substitute these values in P = 10x + 5y

P = 10(0) + 5(10) = 50

P = 10(12) + 5(2) = 130

P = 10(6) + 5(14) = 130

Hence, the minimized value is 50 and the maximized value is 130

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1. The value of x in the equilateral triangle is: 12

2. x = 25; y = 14

If a triangle has three sides that are marked congruent, then the triangle is an equilateral triangle.

1. Since triangle ABC is an equilateral triangle and its sides are equal, therefore:

5x - 22 = 3x + 2 [congruent sides]

Solve for x

5x - 3x = 22 + 2

2x = 24

2x/2 = 24/2

x = 12

The value of x is: 12.

2. Base angles of an isosceles triangle are congruent, therefore:

2x = 50

x = 50/2

x = 25

Thus, using the triangle sum theorem, we have:

2x + 50 + 5y + 10 = 180

Plug in the value of x and find y

2(25) + 50 + 5y + 10 = 180

50 + 50 + 5y + 10 = 180

110 + 5y = 180

5y = 180 - 110

5y = 70

y = 70/5

y = 14

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Answer:

Step-by-step explanation:

We know that, 252 = 625

And, 262 = 676

Now, 676 - 625 = 51

So, there are 51 - 1 = 50 numbers lying between 252 and 262

Answer:

Zeros: 0, 1, and 7

Step-by-step explanation:

Given function: f(x) = 3x(x - 1)²(x - 7)²

To find the zeros (also known as the x-intercepts) of the function, first substitute f(x) = 0 into the equation and simplify.

1. Substitute f(x) = 0:

[tex]\sf f(x) = 3x(x - 1)^2(x - 7)^2\\\\\Rightarrow 0 = 3x(x - 1)^2(x - 7)^2[/tex]

2. Divide both sides by 3:

[tex]\sf \dfrac{0}{3} = \dfrac{3x(x - 1)^2(x - 7)^2}{3}\\\\\Rightarrow 0=x(x-1)^2(x-7)^2[/tex]

3. Separate into possible cases:

[tex]\sf a)\ x = 0\\b)\ (x - 1)^2 = 0\\c)\ (x - 7)^2 = 0[/tex]

4. Simplify:

[tex]\sf a)\ x = 0\ \textsf{[ already simplified ]}[/tex]

[tex]\sf b)\ (x - 1)^2=0\ \textsf{[ take the square root of both sides ]}\\\\\sqrt{(x - 1)^2}=\sqrt{0}\\\\\Rightarrow x-1=0\ \textsf{[ add 1 to both sides ]}\\\\x-1+1=0+1\\\\\Rightarrow x=1[/tex]

[tex]\sf c)\ (x - 7)^2=0\ \textsf{[ take the square root of both sides ]}\\\\\sqrt{(x - 7)^2}=\sqrt{0}\\\\\Rightarrow x-7=0\ \textsf{[ add 7 to both sides ]}\\\\x-7+7=0+7\\\\\Rightarrow x=7[/tex]

Therefore, the zeros of this function are: 0, 1, and 7.

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Step-by-step explanation:

look at the attachment above

Answer:

[tex]\textsf{1)} \quad -\dfrac{1}{16}e^{-4x}\left(4x+1\right)+\text{C}[/tex]

[tex]\textsf{2)} \quad - \cos x+\dfrac{2}{3} \cos^3 x - \dfrac{1}{5} \cos^5 x +\text{C}[/tex]

Step-by-step explanation:

Question 1

[tex]\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Integration of $e^{ax}$} \\\\$\displaystyle \int e^{ax}\:\text{d}x=\dfrac{1}{a}e^{ax}+\text{C}$\\\\for $a\neq 0$\\\end{minipage}}[/tex]

Given integral:

  [tex]\displaystyle \int xe^{-4x}\:\text{d}x[/tex]

Using Integration by parts:

[tex]\textsf{Let }\:u=x \implies \dfrac{\text{d}u}{\text{d}x}=1[/tex]

[tex]\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=e^{-4x} \implies v=-\dfrac{1}{4}e^{-4x}[/tex]

Therefore:

[tex]\begin{aligned}\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x & =uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x\\\\\implies \displaystyle \int xe^{-4x}\:\text{d}x & =-\dfrac{1}{4}xe^{-4x}-\int -\dfrac{1}{4}e^{-4x}\: \text{d}x\\\\& =-\dfrac{1}{4}xe^{-4x}+\int \dfrac{1}{4}e^{-4x}\: \text{d}x\\\\& =-\dfrac{1}{4}xe^{-4x}-\dfrac{1}{16}e^{-4x}+\text{C}\\\\& =-\dfrac{1}{16}e^{-4x}\left(4x+1\right)+\text{C}\end{aligned}[/tex]

Question 2

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\\ \end{minipage}}[/tex]    

[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating a constant}\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\\(where $n$ is any constant value)\end{minipage}}[/tex]

Rewrite the given integral:

[tex]\begin{aligned}\displaystyle \int \sin^5 x \: \text{d}x & =\int (\sin x)^4 \cdot \sin x \: \text{d}x\\& =\int (\sin^2 x)^2 \cdot \sin x \: \text{d}x\end{aligned}[/tex]

Use the trig identity  [tex]\sin^2x+\cos^2x \equiv 1[/tex]  to rewrite  [tex]\sin^2x[/tex] :

[tex]\implies \displaystyle \int \sin^5 x \: \text{d}x = \int (1-\cos^2 x)^2 \cdot \sin x \: \text{d}x[/tex]

Integration by substitution

[tex]\textsf{Let }\:u=\cos x \implies \dfrac{\text{d}u}{\text{d}x}=-\sin x \implies \text{d}x=-\dfrac{1}{\sin x}\: \text{d}u[/tex]

Therefore:

[tex]\begin{aligned}\implies \displaystyle \int \sin^5 x \: \text{d}x & = \int (1-u^2)^2 \cdot \sin x \cdot -\dfrac{1}{\sin x}\: \text{d}u\\& = \int -(1-u^2)^2 \: \text{d}u\\ & =\int -1+2u^2-u^4 \: \text{d}u\\& =-u+\dfrac{2}{3}u^3-\dfrac{1}{5}u^5+\text{C}\end{aligned}[/tex]

Finally, substitute  [tex]u = \cos x[/tex]  back in:

[tex]\implies \displaystyle \int \sin^5 x \: \text{d}x=- \cos x+\dfrac{2}{3} \cos^3 x - \dfrac{1}{5} \cos^5 x +\text{C}[/tex]

Answer: y = -x + 7

Step-by-step explanation:

The slope is [tex]\frac{5-6}{2-1}=-1[/tex], so we know the equation is of the form [tex]y=-x+b[/tex].

Substituting in the coordinates (1,6) to find b,

[tex]6=-1+b\\\\b=7[/tex]

Thus, the equation is y = -x + 7

The width of the pool is 10 feet.

The area of rectangle is product of length and breadth.

Let the width be x.

length = 24 + 2x. and breadth =  12 + 2x

We know, area= 1408 ft².

(12 + 2x)(24 + 2x) = 1408

12*24 + 12*2x + 24*2x + (2x)² = 1408

288 + 72x + 4x² = 1408

4x² + 72x + 288 - 1408 = 0

4x² + 72x - 1120 = 0

x² + 18x - 280 = 0

x² - 10x + 28x - 280 = 0

x(x - 10) + 28(x - 10) = 0

(x - 10)(x + 28) = 0

So, x=10, -28.

Hence, the width be 10 feet.

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A one-to-one function has an inverse. The inverse is another function that undoes the action of the first one, so if we evaluate a function [tex]f[/tex] at some point [tex]x[/tex] to get the number [tex]f(x)[/tex], evaluating the inverse at [tex]f(x)[/tex] will recover the original input [tex]x[/tex]. In other words,

[tex]f^{-1}(f(x)) = x[/tex]

The process works in the opposite direction, too:

[tex]f\left(f^{-1}(x)\right) = x[/tex]

From the given definition of [tex]g[/tex], we have [tex]g(-4) = 3[/tex], so taking inverses on both sides, we find

[tex]g(-4) = 3 \implies g^{-1}(g(-4)) = g^{-1}(3) \implies \boxed{g^{-1}(3) = -4}[/tex]

Given [tex]h(x)=2x-13[/tex], evaluating [tex]h[/tex] at its inverse will recover [tex]x[/tex], so that

[tex]h\left(h^{-1}(x)\right) = x \implies 2h^{-1}(x) - 13 = x \implies \boxed{h^{-1}(x) = \dfrac{x+13}2}[/tex]

[tex](h\circ h^{-1})(x)[/tex] is another way of writing the compound function [tex]h\left(h^{-1}(x)\right)[/tex]. As already discussed, this reduces to [tex]x[/tex], so

[tex]\boxed{\left(h\circ h^{-1}\right)(-9) = -9}[/tex]

Answer:

2nd one

as the y is both 4, the points are on the same plane. As such, we care about the distance of x which is between 3 and 7

The state of the market if market price was fixed at Birr 25 per unit is excess demand

Qd = 50 - p

p = Qs + 5

p - 5 = Qs

if market price was fixed at Birr 25 per unit?

Qd = 50 - p

= 50 - 25

Qd = 25

Qs = p - 5

= 25 - 5

Qs = 20

The state of the market if market price was fixed at Birr 25 per unit is excess demand (demand greater than supply) leading to an increase in price.

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Using the Poisson distribution, the probabilities are given as follows:

A. 0.0888 = 8.88%.

B. 0.1354 = 13.54%.

C. 0.8646 = 86.46%.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

Item a:

10 hours, 2 calls per hour, hence the mean is given by:

[tex]\mu = 2 \times 10 = 20[/tex].

The probability is P(X = 20), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 20) = \frac{e^{-20}20^{20}}{(20)!} = 0.0888[/tex]

Item b:

1 hour, hence the mean is given by:

[tex]\mu = 2[/tex]

The probability is P(X = 0), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-2}2^{0}}{(0)!} = 0.1354[/tex]

Item c:

The probability is:

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1354 = 0.8646[/tex]

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