What is the value of (a + b) in the system of equations below?
8(a + b) + 3z = −9
a + b + z = 2

Select one:
A. -5
B. -4
C. -3
D. -2

Let the width of rectangle be X inches

Then according to question

Length of rectangle will be 3X

Also, we know that

Area of rectangle is = L×B

108 = X . 3X

3X^2 = 108

Divide both sides by 3

X^2 = 36

Taking squareroot of both sides

X=6

Therefore, width of rectangle is 6 inches

Answer:

1. 6 in.

Step by step explanation:

Let the width of our rectangle be x inches.

We have been given that the length of our rectangle is three times the width, therefore, length of our triangle will be 3x inches.

We are told that area of the rectangle is 108 square inches.

Since we know that [tex]\text{Area of a rectangle}=\text{Width}\cdot\text{Length}[/tex]

Let us substitute our given information in area formula.

[tex]108=x\cdot 3x[/tex]

Upon multiplying 3x by x we will get,

[tex]108=3x^{2}[/tex]

Let us divide both side of our equation by 3.

[tex]\frac{108}{3} =\frac{3x^{2}} {3}[/tex]

[tex]36=x^{2}[/tex]

Upon taking square root of both sides of our equation we will get,

[tex]6\pm=x[/tex]

Since width cannot be negative, therefore, width of our rectangle will be 6 inches and 1st option is the correct choice.

To solve for x, we need to get all our constants on one side of the equal sign and all our variables on the other side of the equal sign.

3x - 24 = 81

3x -24 + 24 = 81 +24

3x = 81 + 24

3x = 105

3x/3 = 105 / 3

x = 105 / 3

Answer:

[tex]x=\frac{105}{3}[/tex]

Step-by-step explanation:

To solve for x, we need to get all our constants on one side of the equal sign and all our variables on the other side of the equal sign.

[tex]3x-24=81[/tex]

[tex]3x-24+24=81+24[/tex]

[tex]3x=81+24[/tex]

[tex]3x=105[/tex]

[tex]\frac{3x}{3}=\frac{105}{3}[/tex]

Therefore, the answer is: [tex]x=\frac{105}{3}[/tex]

A, D and E are correct

given ( x - 4 ) is a factor then x =  4 is a root

the remainder on division by (x - 4 ) = 0 as indicated by the 0 on the right side of the quotient

(x - 4 ) is a factor of 3x² - 13x + 4 → A

the number 4is a root of f(x) = 3x² - 13x + 4 → D ( explained above )

thus 3x² - 13x + 4 ÷ (x - 4 ) = 3x - 1 → E

the quotient line 3 - 1 0

3 and - 1 are the coefficients of the linear quotient and 0 is the remainder

The correct options are [tex]\boxed{{\mathbf{Option A, D and E}}}[/tex].

Further explanation:

In any synthetic division, the dividend polynomial [tex]F\left( x \right) = {a_n}{x^n} + {a_{n - 1}}{x^{n - 1}} + {a_{n - 2}}{x^{n - 2}} +  \cdots {a_0}[/tex] and the divisor polynomial [tex]g\left( x \right) = x - b[/tex] can be written as,

[tex]\begin{aligned}b\left){\vphantom{1{\underline {\begin{array}{*{20}{c}}3&{ - 13}&4\\{  }&{12}&{ - 4}\end{array}} }}}\right.\!\!\!\!\overline{\,\,\,\vphantom 1{{\underline {\begin{array}{*{20}{c}}&{a}_n&{ a_{n-1}}&_\cdot_\cdot_\cdot{a_0}\\{    }&{}&{ }\end{array}} }}} \hfill \\\begin{array}{*{20}{c}}{{\text{    }}{c}_n}&_\cdot_\cdot_\cdot{ c_0}&{{\text{    }}0}\end{array} \hfill\\\end{aligned}[/tex]

Here, the monic polynomial   is divided by the polynomial   that provides the polynomial   after division that is also a factor of the polynomial  .

Given:

The synthetic division is given below.

[tex]\begin{aligned}4\left){\vphantom{1{\underline {\begin{array}{*{20}{c}}3&{ - 13}&4\\{  }&{12}&{ - 4}\end{array}} }}}\right.\!\!\!\!\overline{\,\,\,\vphantom 1{{\underline {\begin{array}{*{20}{c}}&3&{ - 13}&4\\{    }&{12}&{ - 4}\end{array}} }}} \hfill \\\begin{array}{*{20}{c}}{{\text{    }}3}&{ - 1}&{{\text{    }}0}\end{array} \hfill\\\end{aligned}[/tex]  

Step by step explanation:

We have to determine the answer among all the options.

Option A: [tex]\left( {x - 4} \right)[/tex] is a factor of [tex]3{x^2} - 13x + 4[/tex].

It can be observed from the given synthetic division the polynomial is [tex]g\left( x \right) = \left( {x - 4} \right)[/tex] that is divisible by the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].

Therefore, the polynomial [tex]g\left( x \right) = \left( {x - 4} \right)[/tex] is a factor of the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].

Therefore, the option A is correct option.

Option B: [tex]\left( {x + 4} \right)[/tex] is a factor of [tex]3{x^2} - 13x + 4[/tex].

From the option A, it has been proved that [tex]g\left( x \right) = \left( {x - 4} \right)[/tex] is a factor of the polynomial  

[tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex]

Therefore, [tex](x+4)[/tex] is a not factor of [tex]3{x^2} - 13x + 4[/tex].

Thus, the option B is not correct option.

Option C: The number [tex]-4[/tex] is a root of  [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].

From the option A, it has been proved that [tex]g\left( x \right) = \left( {x - 4} \right)[/tex] is a factor of the polynomial  

[tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex]

Now substitute 0 for [tex]g\left( x \right)[/tex] in the equation [tex]g\left( x \right) = \left( {x - 4} \right)[/tex] to find the root of the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex] as,

[tex]\begin{aligned}0&= \left( {x - 4} \right) \hfill\\x&= 4 \hfill\\\end{aligned}[/tex]  

It can be seen that the value of [tex]x[/tex] is 4 it means [tex]-4[/tex] is not a root of the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].

Therefore, the option C is not correct option.

Option D: The number [tex]4[/tex] is a root of [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].

It can be seen that the value of [tex]x[/tex] is 4 in option C it means [tex]4[/tex] is a root of the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].

Therefore, the option D is correct option.

Option E: [tex]\left( {3{x^2} - 13x + 4} \right) \div \left( {x - 4} \right) = \left( {3x - 1} \right)[/tex]  

The option E is also correct as [tex](x-4)[/tex] is the factor of the polynomial  [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].

Option F: [tex]\left( {3{x^2} - 13x + 4} \right) \div \left( {x + 4} \right) = \left( {3x - 1} \right)[/tex]  

The option F is not correct as [tex]\left( {x + 4} \right)[/tex] is not the factor of the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].

Result:  

Therefore, the correct options are [tex]\boxed{{\mathbf{Option A, D and E}}}[/tex].

Learn more:

Answer details:

Grade: Medium school

Subject: Mathematics

Chapter: Synthetic division

Keywords: Synthetic division, polynomial, monic polynomial, function, factor, real number, root, divisible, addition, remainder, quotient, divisor, dividend.

1,2,3,6,7,14,21,42

1.2,4,7,14,28

Solution

When we add 1/3 which is rational to an irrational number, we get an irrational number.

pi - is a rational number. √2, √3 are also rational numbers

So the possibilities  are pi + 1/3,

2pi + 1/3,

3pi+1/3,

√3 + 1/3,

√2 + 1/3...

I hope this will help you.

Thank you.

Given expression is

-33/-10- (-45.3+ 35.2)

Problem says that it is simplified.

After simplification it gives:

-33/-10+?

Now we need to find the unknown value that goes in place of ?.

Notice that it is expression having only constants so we will get a unique answer not the smallest or largest value.

Now let's find the value of unknown that goes in place of ?

-33/-10- (-45.3+ 35.2)= -33/-10+?

we see that -33/-10 is on both sides so we can remove that

- (-45.3+ 35.2)= ?

Now let's simplify the left side by distributing the negative sign

+45.3 - 35.2= ?

10.1 = ?

Hence the unknown value is 10.1 that goes in place of ?.

Answer:

answer is 3 on edge

Step-by-step explanation:

wwww

Answer:

The investment has doubled in worth by the start of 15th year.

Step-by-step explanation:

We are Provided a table which tells us that principal amount of $100 is invested on a interest rate of 5% for 15 years compounded annually and we are asked to find out by the start of which year our investment will be doubled.

We can see that after 14 years our amount is doubled but this can't be our answer as amount is doubled ($207.90) after 14 years not in the start of 14th year. We can see that by the start of 15 year our amount is doubled that is $207.90.

Therefore, by the start of 15th year our investment will be doubled.

[tex]8x^2 +4x-3[/tex] is divided by 2x-1

We use long division

                           4x +4 ------------> Quotient

                       ----------------------------

   2x-1             8x^2 +4x−3

                       8x^2 - 4x           (Subtract it from the top)

                      ---------------------------

                                + 8x  -3

                                   8x - 4          (Subtract it from the top)

                     ----------------------------------

                                         +1           ------------> Remainder

So , 1 is the remainder.

Answer:

1/3 of the time.

Step-by-step explanation:

This is because since the dice is being tossed 1 time, that would mean that there is only a 2 in 6 chance to roll a number under 3

The probability that the cube will show a number less than 3 is 1/3 and this can be determined by using the given data.

Given :

A number cube is labeled 1 to 6. the cube will be tossed once.

The following steps can be used in order to determine the probability that the cube will show a number less than 3:

Step 1 - According to the given data, a number cube is labeled 1 to 6. the cube will be tossed once.

Step 2 - So, the number under three is 1 or 2.

Step 3 - Therefore, the probability that the cube will show a number less than 3 is:

[tex]\rm P=\dfrac{2}{6}[/tex]

[tex]\rm P=\dfrac{1}{3}[/tex]

For more information, refer to the link given below:

https://brainly.com/question/795909

Answer-

The average U.S. public debt per American is approximately $29,400

Solution-

Given in the question,

U.S public debt as of October 2010 = $9.06×10¹²

Population of U.S in 2010 = 3.08×10⁸

We have to calculate the average U.S. public debt per American,

[tex]\text{Average debt per American}=\frac{\text{Total debt}}{\text{Population}}\\\\=\frac{9.06\times 10^{12}}{3.08\times 10^8}\\\\=2.9415\times 10^{(12-8)}\\\\=2.9415\times 10^4 \approx 2.94\times 10^4=29,400[/tex]

Therefore, the average U.S. public debt per American is $29,400 (after rounding off)

Answer:

The heights of trees

Step-by-step explanation:

Because trees vary a lot, I would say trees.

Eye color does not vary that much and this is true for new born babies.but trees on the other hand are a different story. They range from  0 to hundreds of feet so it would be a good idea to bind.

Answer:

The heights of trees

Step-by-step explanation:

I did the lesson and got 100% also the guy above explains it perfectly.

A linear function is the equation of a line. Here, you are given two points on the line, one of which is the y-intercept, and asked to write the equation. It can work reasonably well to use the 2-point form of the equation of a line.

For points (x1, y1) and (x2, y2), the equation of the line through them can be written as

... y = (y2 -y1)/(x2 -x1)·(x -x1) + y1

When it is possible to use x1 = 0, this is simplified somewhat, so we choose

... (x1, y1) = (0, -5) . . . . . . from f(0) = -5

... (x2, y2) = (5, -1) . . . . . .from f(5) = -1

Putting these values in the above formula, we get ...

... y = (-1 -(-5))/(5 - 0)·(x -0) -5

... y = 4/5x -5 . . . . . simplified

This can be put in the desired functional form using f(x) instead of y:

... f(x) = 4/5x -5

Here we're given two points on a line:  (0,-5) and (5, -1).  Going from the first point to the second, x increases by 5 and y increases by 4.  Thus, the slope of the line is

m = 4/5 = 1.         Use the point-slope formula to find the equation of this line:

                                   y-(-5) = (4/5)(x).  Thus, y = (4/5)x - 5 or f(x) = (4/5)x - 5

If rain is falling at a rate of 2.56 inches per hour, one would expect 9.6 inches of rainfall after 3.75 hours.

The question pertains to the calculation of total rainfall when the rate of rainfall and time of rainfall are known.

        So, 2.56 inches/hour * 3.75 hours = 9.6 inches total rainfall.

Hence, if rain is falling at a rate of 2.56 inches per hour, you would expect 9.6 inches after 3.75 hours

https://brainly.com/question/35125732

#SPJ2

Answer:

[tex]sin \:C =\frac{8}{17}[/tex]

Step-by-step explanation:

In a right triangle, the sine of an angle is the length of the opposite side divided by the length of the hypotenuse.

[tex]sin \:x =\frac{O}{H}[/tex]

From the formula above we know that the sine of an angle is the opposite side divided by the hypotenuse. The opposite side is AB and has a length of 8. The hypotenuse is AC with a length of 17. So we can write

[tex]sin \:C =\frac{8}{17}[/tex]

all the numbers have to equal 640

because mean is add the all up and devide by how many. Theres 8 numbers and times that by 80 to get 640

so add them all up

71

91

82

90

88

61

70

553

subtract 640 by 553

youre answer is 87

The missing value in the data set is 87.

Here,

The data set is,

{71, 91, 82, 90, 88, 61, 70, __ }

The mean of data set = 80

We have to find the missing value in data set.

What is Mean?

Mean is calculate as, Find the sum of the values by adding them all up. Divide the sum by the number of values in the data set.

Now,

The data set is,

{71, 91, 82, 90, 88, 61, 70, __ }

The mean of data set = 80

Hence,

Let the missing number in data set = x

Mean of data set = [tex]\frac{71+ 91+ 82+ 90+ 88+61+ 70+x}{8}[/tex]

[tex]80 = \frac{553+x}{8}\\\\640 = 553 + x\\\\x = 87[/tex]

Therefore, The missing value in the data set is 87.

Learn more about the mean visit:

https://brainly.com/question/1604598

#SPJ2

Answer:

$130

Step-by-step explanation:

You are given the one-step linear equation ...

... m - 75 = 55

You solve it by adding 75 to both sides.

... m -75 +75 = 55 +75

... m = 130 . . . . . . . . . . . . . simplify

A is th3e correct answer... ten hundreths thousandths

Answer:

Card 7

The hourly rate of change/slope is $75 per hour.

Card 8

Frastastic is charging $0.48 per ounce.

Step-by-step explanation:

Card 7

Lets take the set up fee as "$[tex]s[/tex]" and,

Hourly rate as $[tex]x[/tex]per hour.

Now we can write equations for 3 hour event and 5 hour event.

[tex]s+3x=275[/tex] <------- (1)

[tex]s+5x=425[/tex] <------- (2)

Now we need to solve the simultaneous equations to find [tex]s[/tex] and [tex]x[/tex].

Subtract (1) from (2)

⇒[tex]s+5x-(s+3x)=425-275[/tex]

[tex]s+5x-s-3x=150[/tex]

[tex]2x=150[/tex]

[tex]x=75[/tex]

So the hourly rate of change/slope is $75 per hour.

Therefore, Raymond is right.

Card 8

You can take Amount (oz) as x values and Cost as y values and plot a graph.

Then the Slope of the graph will give you the rate Frastastic is charging per yogurt.

Slope of a linear graph is given by the following equation;

Slope(m)=[tex]\frac{y_{1}-{y_{2}}}  {x_{1}-x_{2}   }[/tex]

Slope(m)=[tex]\frac{6.72-2.4}{14-5}[/tex]

Slope(m)=[tex]\frac{4.32}{9}[/tex]

Slope(m)=[tex]0.48[/tex]

Therefore, Frastastic is charging $0.48 per ounce.

This is less than $0.50 per ounce charged by Fromazing. Therefore, Sterling is right.

Answer:

$48

Step-by-step explanation:

1. 192/12 = 16

2. 16 * 3 = 48

3. Your answer is 48

192/12 = $16 * 3 = $48. $48 dollars was how much he was paid for 3 weeks.

The problem asks for the equations of the lines, so you use the information given in the graph to help you write the equations.

The given line has a "rise" of -4 for a "run" of 1, hence a slope of -4/1 = -4. This is the information you need from that line to write the equations of lines through the given point, (4, 3).

(a) The parallel line will have the same slope. You are asked for "an equation", so the simplest is to provide the necessary equation in point-slope form.

The equation of a line with slope m through point (h, k) is ...

... y - k = m(x - h)

For m = -4, (h, k) = (4, 3) your parallel line is ...

... y - 3 = -4(x -4)

(b) The perpendicular line will have a slope that is the negative reciprocal of that of the given line: -1/-4 = 1/4. Using the same point-slope form, your perpendicular line has equation ...

... y - 3 = (1/4)(x - 4)

It should be no surprise that the volume of a 1-inch cube is 1 cubic inch. Assuming those 36 cubes completely fill the interior volume of the figure, that figure's volume is

... 36 cubic inches

I think that this is the x-intercept method:

First of all, we set y=x^3-6x^2+11x-6.

To find x, we need to let y=0. (y is also equals to f(x))

f(x)=x^3-6x^2+11x-6

In order to make f(x)=0, what does x have to be?

f(1)=0

So then we divide x^3-6x^2+11x-6 by x-1. Why? Because that will not give us a remainder.

(x^3-6x^2+11x-6)/(x-1) = x^2-5x+6

Now, we need to factorize it.

x^2-5x+6 = (x-2)(x-3)

So x=2,3

Answer:

3.5 m

Step-by-step explanation:

The perimeter is the sum of the lengths of the three sides of the triangle, so is the sum of two legs and the base.

... 7.5 m = (2 m) + (2 m) + base

... 3.5 m = base . . . . . . subtract 4 m

base = 3.5m

Since the triangle is isosceles both legs are equal to 2m

base = 7.5 - 2 - 2 = 3.5m

you can use the formula for sample means:

[tex][tex]z(70) = \frac{70-75}{5 / \sqrt{64}} = -8[/tex][/tex]

where m stands for a value of the sample mean.

We are looking for the value, specifically for its two borderline values: 70 and 80

and their cumulative probabilities, p(z(80)) and p(z(70)). The difference p(z(80))-p(z(70))

will give the probability that m falls in the interval [70,80]

So let's get cracking at it:

[tex]z(70) = \frac{70-75}{5 / \sqrt{64}} = -8[/tex]

[tex]z(80) = \frac{80-75}{5 / \sqrt{64}} = 8[/tex]

These are very large values of z. You may notice that any z-table online won't even bother covering range that high - the probabilities for these values are virtually 0 (in the neg case) 1 (in the pos case).

This means that numerically the probability of the sample mean of 64 samples falling within the range of 1 standard deviation is very close to 1

So the answer choice  should be 1.0

Answer:

n=4/3

Step-by-step explanation:

n*(-3/8)=-0.5

n=0.5/3/8

n=1/2 / 3/8

n=4/3

Check:

4/3*-3/8=-0.5

4/3*-3/8=-1/2

-1/2=-0/5

CORRECT!

Answer:

(a) Sandra earns $15 per hour

(b) Sandra earns more per hour

Step-by-step explanation:

(a) y=15x tells Sandra's earnings for x hours. To find Sandra's earnings for 1 hour, let x=1.

... y = 15·1 = 15 . . . . Sandra earns $15 in 1 hour.

(b) To find Susan's earnings you can choose any number of hours and divide that into the corrsponding number of dollars. The math is really easy if you choose the last table entry:

... $80/(10 hours) = $8/hour

Sandra's earnings of $15 per hour are more than Susan's earnings of $8 per hour.

_____

Another way to compare the wages is to pick one of the hour numbers from the table and compute Sandra's equivalent earnings. Again, if we choose 10 hours, the math is easy

... y = 15·10 = 150

Sandra earns $150 for 10 hours' work, while Susan only earns $80 for the same time.

So based on the table, Susan's equation describing her earnings is:

y=8x   (x being the hours, y amount earned)

(a) Sandra earns $8 per hour (the factor in front of x in the equation)

(b) Sandra's equation is y=15x which means for every unit of time she adds $15, so her hourly pay is $15. Therefore Sandra earns ($7) more per hour than Susan.

16%

the percent tips is calculated as

[tex]\frac{tips}{total bill}[/tex] × 100%

total bills = 23.59 + 40.65 + 30.50 + 15.68 = 110.42

percent tips = [tex]\frac{17.67}{110.42}[/tex] × 100% = 16%

Inputs are the first number output is the second. So youre outputs are 2, -1, -1, and 3. so i would say b

The set of outputs for the function represented by the scatterplot is {-1, 2, 3}, which matches Option B from the given choices.

You are looking to identify the set of outputs (also known as the range) of a given function based on a scatterplot. The output of a function is comprised of the second element in each ordered pair, which represents the y-value on the Cartesian plane. In this case, the scatterplot includes the points (-3, 2), (-2, -1), (2, -1), and (3, 3).

To find the correct set of outputs, we need to list the y-values from each point: 2, -1, -1, and 3. When listing a set, we do not repeat values, so the set of outputs for this function would be {2, -1, 3}. Therefore, the correct answer is Option B) {-1, 2, 3}.