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

Answers

Answer 1
Answer: 11x - 16

Explanation:
Distribute (8x - 16) by 1.
3x + 8x - 16.
Add 3x and 8x.
11x - 16

Related Questions

A is the set of integers greater than or equal to -9 and less than or equal -2
B = {-30, -27, 20, 24, 28}
a) Find the cardinalities of A and B.
n(A)=
n(B) =

Answers

Answer:

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

SET :an organized collection of objects

Cardinality : It is defined as how many elements make in a set or other grouping.

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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Which of the following linear equations represents the data chart?

X Y
1 6
2 5
3 4
4 3

y=x+5
y=x+3
y = -x + 7
None of these choices are correct.

Answers

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

A swimming pool is to be constructed in a 1,408-ft2 backyard. There is to be a fence that will surround a 12-by-24-foot pool. The pool builder wants to build a concrete paver deck of a uniform width, x, surrounding the pool and filling the entire area of the backyard. What is the width of the pool deck?

Answers

The width of the pool is 10 feet.

What is area of rectangle?

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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Find g(32) for g(x) = x+4−−−−√.
A. 3
B. 5
C. 6
D. 10

Answers

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]

Which equation has roots of 3 ± √2?

Answers

Answer:

D.

Step-by-step explanation:

I need help on this I’m stuck

Answers

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 .

HOPE IT HELPS

PLEASE GIVE BRAINLIEST

Which sequences are arithmetic sequences? Select all that apply.
a) 100, 95, 90, 85, ...
b) 10, 20, 40, 80, ...
c) 5, 17, 29, 41, 53, ...
d) -1, 1, -1, 1, -1, 1, ...
e) 42, 52, 62, 72, 82, ...


Answers

Answer:

state Avogadro's hypothesis and prove that molecular weight

a single card is drawn from a standard 52-card deck calculate the probability and odds for the following event a jack or club is drawn

Answers

                                          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.

determine if x-3 is a factor of f(x)=x^3-x^2-5x-3

Answers

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.

Plot the complex number and find its absolute value 2−i

Answers

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

What is the complex number?

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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Given market demand Qd=50-p, and market supply p=Qs+5.what would be the state of the market if market price was fixed at Birr 25 per unit?​

Answers

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

Quantity demanded

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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F
10
A. 18
B. 28
C. 38
D. 48
G
8
H
If ZG ZH, find the perimeter of AFGH.

Answers

The answer is 28

If angle g and angle h are the same, this means it’s an isosceles triangle. Since the side opposite of the angle is what the angle correlates to, line segment FH= line segment GF. Now we have FH=10.
Finally we add all sides 10+10+8 and arrive at 28.
Hope this helps!

Answer:

The answer is 28

Step-by-step explanation:

ms..s.s..snskkzkzklzlzls

Simplify the following expression to its simplest form

Answers

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]

need help with this please

Answers

Answer:

no lo sé no lo sé

Step-by-step explanation:

solo se que nada se

Please help me answer this question

Answers

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]

What is the length ?

Answers

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

Jaxon is flying a kite, holding his hands a distance of 3.25 feet above the ground and letting all the kite’s strings play out. He measures the angle of elevation from his hand to the kite to be 24∘. If the string from the kite to his hand is 105 feet long, how many feet is the kite above the ground? Round your answer to the nearest tenth of a foot if necessary.

Answers

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]

Math: One to One function...help!

Answers

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]

the stream frontage is 800 feet in length and the property line is 3900 feet in length

The lot has an area of about ___ acres

Answers

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

What is the Pythagorean Theorem?

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.

What is the area of a right triangle?

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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Given: a || b, transversal k
Prove <3 = <6

Answers

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

What is transversal line?

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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Assume that BK Call Center receives 2 phone calls in one hour on average. If the department works 10 hours a day receiving the class, find the probability,
A. Exactly 20 calls will be received at a particular day
B. No call is received in a particular hour
C. At least 1 call will be received in a particular hour

Answers

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%.

What is the Poisson distribution?

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:

x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.

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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Jack has a rectangular piece of land, the area of which is represented by a₁ = 9.5%. His brother has a different rectangular piece of land, the area of which is represented by a2 = 14-). Let a represent the area in square meters and /represent the length in meters of the pieces of land. The two equations plotted on a graph meet at a point as shown in the image.​

Answers

Answer:

yea that’s right

Step-by-step explanation:

Write each of the following numerals in base 10. For base twelve, T and E represent the face values ten and eleven, respectively.
a. 421 five
b. 11101 two
c. 13Ttwelve

Answers

(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

What is the solution set of -xl = -10?

Answers

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

PLEASE GIVE BRAINLIEST

No solution since it can’t be equal to negative numbers

Which expression is equivalent to this quotient?

Answers

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]

$30 is taken off the price of a dress. If the new price is now 60% off the original price, what was the original price of the dress.

Answers

the original price of the dress is $75

1
0/1 point
A student wants to write an expression for, "all of the elements which are not in set A but are in set B".

Answers

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

How to solve for the expression

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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Which number line could help you find the distance between (7,4) and (3,4)?

Answers

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

If f(x) = sin(x) and g(x) = sin(2x), then the derivative of f(x) + g(x) is

Answers

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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if someone could please help that would be great!

Please graph it!!!

Answers

The graph is attached with the answer.

What are Piecewise Function ?

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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