Use the functions m(x) = 4x + 5 and n(x) = 8x − 5 to complete the function operations listed below. Part A: Find (m + n)(x). Show your work. (3 points) Part B: Find (m ⋅ n)(x). Show your work. (3 points) Part C: Find m[n(x)]. Show your work. (4 points)

Answer:

a) [tex]1.19 \times 10^{-2} + 1.07\times 10^{-2}[/tex] is larger than [tex]1.19\times 10^{-2}[/tex]; b) [tex]1.19 \times 10^{-2} - 1.07\times 10^{-2}[/tex] is smaller than [tex]1.19\times 10^{-2}[/tex]; c) [tex](1.19\times 10^{-2})\cdot (1.07\times 10^{-2})[/tex] is smaller than [tex]1.19\times 10^{-2}[/tex]; d) [tex](1.19\times 10^{-2})/ (1.07\times 10^{-2})[/tex] is greater than [tex]1.19\times 10^{-2}[/tex].

Step-by-step explanation:

a) Is [tex]1.19 \times 10^{-2} + 1.07\times 10^{-2}[/tex] smaller or larger?

1) [tex]1.19 \times 10^{-2} + 1.07\times 10^{-2}[/tex] Given.

2) [tex](1.19+1.07)\times 10^{-2}[/tex] Distributive property.

3) [tex]2.26 \times 10^{-2}[/tex] Addition/Result.

[tex]1.19 \times 10^{-2} + 1.07\times 10^{-2}[/tex] is larger than [tex]1.19\times 10^{-2}[/tex].

b) Is [tex]1.19 \times 10^{-2} - 1.07\times 10^{-2}[/tex] smaller or larger?

1) [tex]1.19 \times 10^{-2} - 1.07\times 10^{-2}[/tex] Given.

2) [tex](1.19-1.07)\times 10^{-2}[/tex] Distributive property.

3) [tex][1.19+(-1.07)]\times 10^{-2}[/tex] Subtraction.

4) [tex]0.12\times 10^{-2}[/tex] Addition/Result.

[tex]1.19 \times 10^{-2} - 1.07\times 10^{-2}[/tex] is smaller than [tex]1.19\times 10^{-2}[/tex].

c) Is [tex](1.19\times 10^{-2})\cdot (1.07\times 10^{-2})[/tex] smaller or larger?

1) [tex](1.19\times 10^{-2})\cdot (1.07\times 10^{-2})[/tex] Given.

2) [tex](1.19\times 1.07)\cdot (10^{-2}\times 10^{-2})[/tex] Associative property/Commutative property.

3) [tex]1.27\times 10^{-4}[/tex] Multiplication/ ([tex]a^{b}\cdot a^{c} = a^{b+c}[/tex])/ [tex](-x)\cdot (-y) = x\cdot y[/tex] /Result.

[tex](1.19\times 10^{-2})\cdot (1.07\times 10^{-2})[/tex] is smaller than [tex]1.19\times 10^{-2}[/tex].

d) Is [tex](1.19\times 10^{-2})/ (1.07\times 10^{-2})[/tex] smaller or larger?

1) [tex](1.19\times 10^{-2})/ (1.07\times 10^{-2})[/tex] Given.

2) [tex](1.19\times 10^{-2})\cdot (1.07\times 10^{-2})^{-1}[/tex] Division.

3) [tex](1.19\times 10^{-2})\cdot (1.07\times 10^{2})[/tex] ([tex](a^{b})^{c} = a^{b\cdot c}[/tex]; [tex](-x)\cdot (-y) = x\cdot y[/tex])

4) [tex](1.19\times 1.07)\cdot (10^{-2}\cdot 10^{2})[/tex] Associative property/Commutative property.

5) [tex]1.27[/tex] Multiplication/([tex](a^{b})^{c} = a^{b\cdot c}[/tex]; [tex]a^{0} = 1[/tex])/Modulative property/Result.

[tex](1.19\times 10^{-2})/ (1.07\times 10^{-2})[/tex] is greater than [tex]1.19\times 10^{-2}[/tex].

It would have to have a positive slope and the bottom needs to be shaded, since -2y is negative it means we will be dividing by a negative. The inequality sign will switch.

also if it is < then the line is dotted, if it’s the “greater or equal to sign” then the line is not dotted.

dunno if I explained it very well

The shaded region common to both the inequalities represents the solution set of the inequality → x - 2y² < 12.

An inequality is used to compare two or more expressions or numbers.

For example -

2x > 4y + 3

x + y > 3

x - y < 6

Given is the inequality as -

x - 2y² < 12

The given inequality is -

x - 2y² < 12

2y² - x < - 12

2y² < x - 12

y² < (x/2) - 6

[tex]$y < \pm\sqrt{\frac{x}{2}-6 }[/tex]

[tex]$y < \sqrt{\frac{x}{2}-6 }[/tex]        

and

[tex]$y < -\sqrt{\frac{x}{2}-6 }[/tex]

Refer to the graph of the equation attached. The shaded region common to both the inequalities represents the solution set of the inequality.

Therefore, the shaded region common to both the inequalities represents the solution set of the inequality → x - 2y² < 12.

To solve more questions on inequality, visit the link-

https://brainly.com/question/11897796

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Answer:

 [tex]x_3 = \left[\begin{array}{c}4&3&1\\0\end{array}\right][/tex]

Step-by-step explanation:

According to the given situation, The computation of all x in a set of a real number is shown below:

First we have to determine the [tex]\bar x[/tex] so that [tex]A \bar x = 0[/tex]

[tex]\left[\begin{array}{cccc}1&-3&5&-5\\0&1&-3&5\\2&-4&4&-4\end{array}\right][/tex]

Now the augmented matrix is

[tex]\left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\2&-4&4&-4\ |\ 0\end{array}\right][/tex]

After this, we decrease this to reduce the formation of the row echelon

[tex]R_3 = R_3 -2R_1 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\0&2&-6&6\ |\ 0\end{array}\right][/tex]

[tex]R_3 = R_3 -2R_2 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\0&0&0&-4\ |\ 0\end{array}\right][/tex]

[tex]R_2 = 4R_2 +5R_3 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&4&-12&0\ |\ 0\\0&0&0&-4\ |\ 0\end{array}\right][/tex]

[tex]R_2 = \frac{R_2}{4}, R_3 = \frac{R_3}{-4} \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&1\ |\ 0\end{array}\right][/tex]

[tex]R_1 = R_1 +3 R_2 \rightarrow \left[\begin{array}{cccc}1&0&-4&-5\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&-1\ |\ 0\end{array}\right][/tex]

[tex]R_1 = R_1 +5 R_3 \rightarrow \left[\begin{array}{cccc}1&0&-4&0\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&-1\ |\ 0\end{array}\right][/tex]

[tex]= x_1 - 4x_3 = 0\\\\x_1 = 4x_3\\\\x_2 - 3x_3 = 0\\\\ x_2 = 3x_3\\\\x_4 = 0[/tex]

[tex]x = \left[\begin{array}{c}4x_3&3x_3&x_3\\0\end{array}\right] \\\\ x_3 = \left[\begin{array}{c}4&3&1\\0\end{array}\right][/tex]

By applying the above matrix, we can easily reach an answer

Answer:

560 km

Step-by-step explanation:

350x8/5=

350x1.6=

560

Answer:

x = 64

Step-by-step explanation:

A circle equal 360 degrees

180 + 90 + x + 26 = 360

Combine like terms

296+x = 360

Subtract 296 from each side

296+x-296 = 360-296

x = 64

Answer:

[tex]\theta=\frac{n\pi}{5}[/tex]

Step-by-step explanation:

You have the following function:

[tex]r=2sin5\theta[/tex]          (1)

In order to find the zeros of the function you equal to zero the equation (1), and then you solve for θ:

[tex]2sin5\theta=0\\\\sin5\theta=0\\\\5\theta=sin^{-1}(0)=n\pi;\ \ \ \ n=0,1,2,3,..\\\\\theta=\frac{n\pi}{5}[/tex]

Then, there are infinite zeros for the function of the equation (1), because n has infinite positive integers values.

Answer:

θ = 0, pi/5, 2pi/5, 3pi/5, 4pi/5 ,pi

Step-by-step explanation:

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

The tank for a car holds 17 gallons. The gasoline gauge shows the tank is 3/4 full. How much gas is still in the tank?

Give your answer as a whole number or as a mixed fraction reduced to lowest terms.

Answer:

[tex]Gas \: \:left = 12 \frac{3}{4} \: \:gallons \\\\[/tex]

Step-by-step explanation:

The tank for a car holds 17 gallons.

The gasoline gauge of the car shows that the tank is 3/4 full.

We are asked to find the remaining gasoline in the tank.

[tex]Gas \: \:left = \frac{3}{4} \times 17 \\\\Gas \: \:left = \frac{51}{4} \\\\Gas \: \:left = 12 \frac{3}{4} \: \:gallons \\\\[/tex]

Therefore, the remaining gas in the tank is [tex]12\frac{3}{4}[/tex] gallons.

Alternatively:

[tex]1 - \frac{3}{4} = \frac{1}{4}[/tex]

Amount of gasoline consumed = [tex]\frac{1}{4} \times 17 = \frac{17}{4}[/tex]

Amount of gasoline left = total - consumed

Amount of gasoline left = [tex]17 - \frac{17}{4} = 12\frac{3}{4} \:\: gallons[/tex]

approximately 36.633 cm if you use pi = 3.14

approximately 36.6519 cm if you use the calculator's stored value of pi

Work Shown:

L = arc length, r = radius, x = central angle in degrees

L = (x/360)*2*pi*r

L = (300/360)*2*pi*7

L = (35/3)pi .... exact arc length in terms of pi

L = (35/3)*3.14

L = 36.633 .... approximate arc length

Keep in mind that I used pi = 3.14 which isn't that great an approximation for pi. If you want to use more digits of pi, then use your calculator's built in version of it to get (35/3)*pi = 36.6519; of course it will depend on which option your teacher prefers.

Answer: 4 miles

Step-by-step explanation:

If Ashley ran 1 mile 4 times, she ran 1+1+1+1, or 1*4, or 4 miles.

Hope it helps <3

Answer:

25 and 30

Step-by-step explanation:

Let the smaller consecutive multiples of 5 be x. Therefore, other consecutive multiples will be x + 5.

Now as per statement the sum of two consecutive multiples of 5 is 55. To find the multiples. Thus

x + x + 5 = 55

2x + 5 = 55

2x = 55 - 5

2x = 50

x = 50/2

x = 25

This the smaller consecutive multiples of 5 is 25, the other consecutuve multiple is x+ 5, 25 + 5 = 30.

The consecutive multiple numbers of 5 are 25 and 30

Answer the two consecutive multiples of 5 are 25 and 30

Answer:

25 and 30.

Step-by-step explanation:

Let the smaller consecutive multiple of 5 be 'x'. So, the other multiple will be x + 5.

Now, the statement is the sum of two consecutive multiples of 5 is 55. To find the multiples, we must simplify as below.

x + x + 5 = 55

2x + 5 = 55

2x = 55 - 5

2x = 50

x = 50/2

x = 25

We observe that the smaller consecutive is 25, so the other multiple is x+ 5, 25 + 5 = 30.

(Hope this helps and please mark as the brainliest)

Answer:

x = -3 and x = 9.

Step-by-step explanation:

2|x - 3| - 5 = 7

2|x - 3| = 12

|x - 3| = 6

x - 3 = 6

x = 9

-(x - 3) = 6

-x + 3 = 6

-x = 3

x = -3

Hope this helps!

Answer:

x=9            x=-3

Step-by-step explanation:

2|x-3|-5=7

Add 5 to each side

2|x-3|-5+5=7+5

2|x-3|=12

Divide by 2

2/2|x-3|=12/2

|x-3|=6

There are two solutions to an absolute value equation, one positive and one negative

x-3 =6           x-3 = -6

Add 3 to each side

x-3+3 = 6+3      x-3+3 = -6+3

x=9                     x = -3

Working backwards, on Wednesday morning we have 60 / (1/2) = 120 pounds of ice.

2/3 melts on Tuesday so 120 pounds must be 1/3 of the ice.

120 / (1/3) = 360

Answer: D. 360

Answer:

Step-by-step explanation:

t1=2

t2=-8

r=t2/t1=-8/2=-4

t10=t1*r⁹

t10=2*(-4)⁹= -2*(2²)⁹

t10= -2¹⁹= -524288

Answer:

-524288

Step by step

so use the formula

ar^n-1

so

a is first term

r is common ratio

n is number of terms

so

get r which is -8/2=-4

then apply

2×(-4^9)=answer

not sure

Answer:

8lb of the cheaper Candy

17.5lb of the expensive candy

Step-by-step explanation:

Let the cheaper candy be x

let the costly candy be y

X+y = 25.5....equation one

2.2x +7.3y = 25.5(5.7)

2.2x +7.3y = 145.35.....equation two

X+y = 25.5

2.2x +7.3y = 145.35

Solving simultaneously

X= 25.5-y

Substituting value of X into equation two

2.2(25.5-y) + 7.3y = 145.35

56.1 -2.2y +7.3y = 145.35

5.1y = 145.35-56.1

5.1y = 89.25

Y= 89.25/5.1

Y= 17.5

X= 25.5-y

X= 25.5-17.5

X= 8

Answer: 54 mL

Step-by-step explanation:

Simply do 9(number of containers)*6(Syrup per container) to get 54 mL of syrup.

Hope it helps <3

Answer:

x>3

Step-by-step explanation:

Answer:

The null hypothesis is ;

H0 ≥ 12

While the alternative hypothesis H1 is ;

H1 < 12

Step-by-step explanation:

Here, we want to correctly identify the null hypothesis H0 and the alternative hypothesis H1

The null hypothesis is as follows ;

H0 ≥ 12

While the alternative hypothesis H1 is ;

H1 < 12

Complete question:

If x = –3 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?

a) The discriminant is negative.

b) The discriminant is –3.

c) The discriminant is 0.

d) The discriminant is positive.

Answer:

c) The discriminant is 0.

Step-by-step explanation:

Here, x = -3 is the only x intercept of graph of a quadrant equation.

In this case the determinant of the quadrant equation will be 0.

i.e, x = 0

The determinant of the quadrant equation will be zero because, since x = -3 is the only x intercept of the graph, the quadrant equation will have equal roots. Also, when there are equal roots in a quadrant equation, the discriminant tends to zero.

Therefore the correct answer is (c) The discriminant is 0.

D = 0

Answer:

C

Step-by-step explanation:

taking the quiz rn

Answer:

x = [tex]\frac{3}{4}(n-1)[/tex]

Step-by-step explanation:

It's given in the question that '' The number is 75% of one less than a number n"

Let the number is 'x'.

One less than a number 'n' will be = (n - 1)

75% of one less than a number will be = 75% of (n -1)

                                                                = [tex]\frac{75}{100}(n-1)[/tex]

                                                                = [tex]\frac{3}{4}(n-1)[/tex]

Therefore, the desired expression to get the number 'x' will be,

x = [tex]\frac{3}{4}(n-1)[/tex]

Answer:

3/4(n-1)

Step-by-step explanation:

did it in rsm

Answer: 25 square units

Step-by-step explanation:

We mark the points, A(2,0), B(7,0), C(10,3), D (5,3). on a graph and then joined them to make parallelogram ABCD as provided in the attachment.

Area of parallelogram  = Base x corresponding height

From the figure, base AB = 7 - 2 units = 5 units

corresponding height: h= 5 units

Now , Area of parallelogram  ABCD = base AB x corresponding height

= 5 x 5 square units

= 25 square units

Hence,  the area of parallelogram  ABCD is 25 square units .

Answer:

The geometric mean of the measures of the line segments AD and DC is  60/13

Step-by-step explanation:

Geometric mean: BD² = AD×DC

BD = √(AD×DC)

hypotenuse/leg = leg/part

ΔADB: AC/12 = 12/AD

AC×AD = 12×12 = 144

AD = 144/AC

ΔBDC: AC/5 = 5/DC

AC×DC = 5×5 = 25

DC = 25/AC

BD = √[(144/AC)(25/AC)]

BD = (12×5)/AC

BD= 60/AC

Apply Pythagoras theorem in ΔABC

AC² = 12² + 5²

AC² = 144+ 25 = 169

AC = √169 = 13

BD = 60/13

The geometric mean of the measures of the line segments AD and DC is BD = 60/13

Answer:

x = 80

y = 130

Step-by-step explanation:

The 2 angles are supplementary. so, x-30 + x+50 = 180.

We solve and get 2x = 180-20

x = 80

y = x+50, because of parallel rules.

y = 130

Answer:

x = 80

y = 130

Step-by-step explanation:edge 2020

Answer:

x=3 or/and x= -7/3

Step-by-step explanation:

+1= +1

3x = 9

9 divided by 3 is x= 3

+1= +1

3x = -7

-7 divided by 3 is x= -7/3

Answer:

[tex]\huge\boxed{x=3\ \vee\ x=-\dfrac{7}{3}}[/tex]

Step-by-step explanation:

[tex]|a|=\left\{\begin{array}{ccc}a&\text{for}\ a\geq0\\-a&\text{for}\ a<0\end{array}\right\\\\|a|=k\to a=k\ \vee\ a=-k\ \text{for}\ k>0\\==========================\\\\|3x-1|=8\iff3x-1=8\ \vee\ 3x-1=-8\\\\\begin{array}{cccc}3x-1=8&\vee&3x-1=-8&\text{add 1 to both sides}\\3x-1+1=8+1&\vee&3x-1+1=-8+1\\3x=9&\vee&3x=-7&\text{divide both sides by 3}\\\dfrac{3x}{3}=\dfrac{9}{3}&\vee&\dfrac{3x}{3}=\dfrac{-7}{3}\\x=3&\vee&x=-\dfrac{7}{3}\\\end{array}[/tex]

Answer:

If we have two functions g(x) and f(x)

I suppose that the functions here are:

f(x) = 2 - √(4*x)

g(x) = -3*x

First, let's analyze the functions:

g(x) as not any problem for any value of x, so the domain is the set of all the real numbers.

f(x) has a square root on it, and we know that the square root of a negative number is equal to a complex number, so here we can not have negative values of x.

The domain of f is D = x ∈ {0, ∞}

Then (gof)(x) = g(f(x)) = -3*(2 - √(4*x)) = -6 + 3*√(4*x)

We can see that g(x) does not have any problem, and the problems with f(x) remain there, so the domain of the composition is equal to the domain of f(x):

D =  x ∈ {0, ∞}

Answer:

Side a^2 = 49 + 16

Side a^2 = 65

Side a = 8.062

sin (B) = 4 / 8.062

cos (B) = 7 / 8.062

tan (B) = 4 / 7

cot (B) = 7 / 4

sec (B) = 8.062 / 7

csc (B) = 8.062 / 4

Step-by-step explanation:

Answer: Monomial.

Step-by-step explanation:

Ok, when we have a polynomial with only one term, this is a monomial.

If the polynomial has two terms, this is a binomial.

If the polynomial has 3 terms, this is a trinomial.

And so on.

In this particular case we have:

52*c^2*y^4

Where c and y may be variables.

We can see that here we have only one term, so this would be a monomial.

(notice that the number of variables does not affect the type of polynomial in this case, only the number of terms)

Answer:

binomial.

Step-by-step explanation:

The polynomial −50c3z3−41y220z4 has 2 terms, so it is a binomial.

Answer:

5/3

Step-by-step explanation:

3/8 + 1/8 + 2/3 + 1/2

=> [ 3/8 + 1/8 ] + [ 2/3 + 1/2 ]

=> 1/2( or 4/8 ) + 7/6

=> 10/6 or 5/3

Answer:

[tex] \frac{3}{8} + \frac{1}{8} + \frac{2}{3} + \frac{1}{2} [/tex]

Add the fractions with the same common denominator

That's

[tex] \frac{3}{8} + \frac{1}{8} = \frac{4}{8} = \frac{1}{2} [/tex]

So we have

[tex] \frac{1}{2} + \frac{2}{3} + \frac{1}{2} [/tex]

Add the fractions with the same common denominator

That's

[tex] \frac{1}{2} + \frac{1}{2} = \frac{2}{2} = 1[/tex]

We have

[tex] 1 + \frac{2}{3} [/tex]

That's

[tex] \frac{1}{1} + \frac{2}{3} [/tex]

Find the common denominator

The common denominator is 3

[tex] \frac{1}{1} + \frac{2}{3} = \frac{3 + 2}{3} [/tex]

[tex] = \frac{5}{3} \: \: \: \: \: \: or \: \: \: \: \: \: \: 1 \frac{2}{3} [/tex]

Hope this helps you

Answer:

72.4%

Step-by-step explanation:

The essay is 25% of your grade, and the rest is 75% of your grade.

25 (3.3/4) + 75 (0.69) ≈ 72.4

Answer:

-4,4,16

Step-by-step explanation:

They are all even integers.

-4^2=16

4^2=16

16^2=256

the square of the third,16 is 256 which is more than the square of the second,4=16

The three consecutive even integers such that the square of the third is 60 more than the square of the second are -18, -16 and -14.

Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."

Given:

Let the three even consecutive integers are 2n-2, 2n and 2n + 2.

According to the question,

So,

(2n + 2)² = (2n)² - 60

4n² + 4 + 8n = 4n² -60

8n = -64

n = -8

That means, the integers are -18, -16 and -14.

Therefore, the required even integers are -18, -16 and -14.

To learn more about the integers;

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Answer:

csc B = 13/12

Step-by-step explanation:

csc B = 1 / sin B

The sin B is

sin B = opp/ hyp  so

csc B = hyp /opp

csc B = 26 / 24

csc B = 13/12

Answer:

13/12

Step-by-step explanation:

sin θ = opposite/ hypotenuse

csc θ = 1/sinθ

csc θ  = hypotenuse/opposite

csc (B)  = 26/24

csc (B)  = 13/12