What is the simplified form of this expression? 3x + (8x − 16)

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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The correct answer is the last choice .

The parent quadratic function is f(x) = x² it's just like the image above .

if you look at the graph horizontal translation has happened two units to right , it means we have -2 inside a bracket next to x , then vertical translation has happened 4 units to up it means we have +4 outside the bracket and after x

there's also a reflection on the graph which means there's a negative before the bracket .

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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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Answer:

state Avogadro's hypothesis and prove that molecular weight

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

Step-by-step explanation:

please mark me as brainlest

Answer:

(x - 3) is a factor of the given function

Step-by-step explanation:

Given function:

[tex]\implies f\:\!\:(x)=x^3-x^2-5x-3[/tex]

If (x - 3) is a factor of the given function then [tex]f\:\!\:(3) = 0[/tex]

Substitute x = 3 into the function and solve:

[tex]\implies f\:\!\:(3)=(3)^3-(3)^2-5(3)-3[/tex]

[tex]\implies f\:\!\:(3)=27-9-15-3[/tex]

[tex]\implies f\:\!\:(3)=0[/tex]

Therefore, as  [tex]f\:\!\:(3) = 0[/tex] then (x - 3) is a factor of the given function.

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]

No solution since absolute value can't be equal to negative numbers

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Answer:

no lo sé no lo sé

Step-by-step explanation:

solo se que nada se

Answer:

yea that’s right

Step-by-step explanation:

The derivative of f(x) + g(x) is cosx+2cos2x

Derivative : In mathematical calculus, the derivative is the rate of change of a function at a instant point.

Derivative of a function is denoted by dy/dx, where derivative of y is happening with respect to x.

We have to add f(x) and g(x), then differentiate the whole addition with respect to x.

Given that, f(x) = sin(x) & g(x) = sin(2x)

So, f(x) + g(x) = sin(x) + sin(2x)

Now, differentiating with respect to x we get,

(f(x)+g(x))' = d/dx(sinx) + d/dx(sin 2x)

               = cosx+2cos2x

Derivative of  f(x) + g(x) = cosx+2cos2x

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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:

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:

The answer is 28

Step-by-step explanation:

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The graph is attached with the answer.

When function has different behaviour at different intervals , then it is called a piecewise function.

It is given that

f(x) = - 3x -5 at x ≤ -1

f(x) = -2x +3 at -1 <x<4

f(x) = 2 at x ≥ 4

All the piecewise Function are a straight line.

The table for functions is

f(x) = 3x -5

-1  -8

-2  -11

-3   -14

f(x) = -2x +3

0  3

1    1

2    -1

3   -3

f(x) = 2

4     2

5      2

6     2

7     2

The graph is attached with the answer.

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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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Answer:

AC = 2x - 13 Cm

BC = 3x + 4 Cm

AB = 36 Cm

AB = AC + BC

BC = AB - AC

= 36 - (2x - 13)

= 36 - 2x + 13

= 49 - 2x

but, BC = 3x + 4

so equating both the equation we get

3x + 4 = 49 - 2x

3x + 2x = 49 + 4

5x = 53

x = 53/5

x = 10.6

BC = 49- 10.6*2

= 49- 21.2

= 27.8 CM

Answer:

BC = 31 cm

Step-by-step explanation:

from the diagram

AC + CB = AB ( substitute values )

2x - 13 + 3x + 4 = 36

5x - 9 = 36 ( add 9 to both sides )

5x = 45 ( divide both sides by 5 )

x = 9

then

BC = 3x + 4 = 3(9) + 4 = 27 + 4 = 31 cm

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]

The way to write this expression in mathematics is A'∩B

In order to get the right way to write this expression we have to break it down in two parts.

First we are told that some of the elements are not in A.

This is represented as A'.

Then we are told that they are in the set B. Hence we have it written as B.

Then the expression  not in set A but are in set B would be written as

A'∩B.

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(a)

421₅ = 4×5² + 2×5¹ + 1×5⁰

… = 100 + 10 + 1

… = 111

(b)

11101₂ = 1×2⁴ + 1×2³ + 1×2² + 0×2¹ + 1×2⁰

… = 16 + 8 + 4 + 0 + 1

… = 29

(c)

13T₁₂ = 1×12² + 3×12¹ + 10×12⁰

… = 144 + 36 + 10

… = 190

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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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]

                                          17/52

Step-by-step explanation: There are 13 clubs in a deck of fifty-two cards and there are four jacks in a fifty-two deck.  So adding that up it's 17 out of 52 = 17/52.   And you can not reduce it.

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

Answer:

D.

Step-by-step explanation:

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]