Add the polynomials?

Answer:

180=x+42

collect like terms

x=180-42

x=138

The principal amount is $693.33.

Simple interest is a quick and simple approach to figure out how much money has accrued interest. Interest is always applied to the original principal amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount.

The formula is

Simple Interest = P x R x T/100

Given:

Interest = 78

Rate= 7.5%

Time= 1 and half year = 1.5 year

Now, Simple Interest= P x R x T / 100

                             78 = P x 7.5 x 1.5 / 100

                             7800= P x 11.25

                             P = 7800/11.25

                              P = 693.33

Hence, the principal amount is $693.33.

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Answer:

37.2 rotations

Step-by-step explanation:

35 / (3.14 x .3) = 37.15499

Rounded = 37.2 rotations

Yes (3,0) is the solution of the given equation.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Given Data

Equation

3x - 2y-9=0

X + 8y-3 = 0

Solution(3, 0)

Finding the values of x,

x + 8y - 3=0

x = 3 + 8y...(1)

Substituting x in the equation

3x - 2y = 9

3(3+ 8y) -2y = 9

9 + 24y - 2y = 9

22y = 0

y = 0

Substituting the value in (1)

x = 3 + 8(0)

x = 3

Yes (3,0) is the solution of the given equation.

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E = 38.33 the margin of error at a 98% confidence level by standard deviation mean.

What does standard deviation mean ?

Given that,

bar x = 36

s = 9

n = 12

Degrees of freedom = df = n - 1 =12 - 1 = 11

At 98% confidence level the t is ,

∝ = 1 - 98% = 1 - 0.98  ⇒ 0.02

∝/2 = 0.02/2 = 0.01

t∝/2 df = t0.01 ,11 = 1.231

Margin of error = E = t∝/2, df * ( s/n/sqrtn)

                             E = 1.231 * ( 9 /0.01/sqrt12)

                              E = 38.33

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Answer:Note that at least means greater than or equal to (≥) . It was stated that you must be at least 48 inches tall to ride the roller coaster. Hence, the inequality is h≥48 h ≥ 48

Step-by-step explanation: poopity poop UWU UWU UWU oodfijdisfioahgioahiodfhipodioajhierfia           MUSIC MUSIC MUSIC MUSIC MUSIC MUSIC HACKER HACKER HAKER HACKER HACKER OMG UWU UWU UWU YOUR 13 LOL YOUR FATHERLESS GT DELETED TRASH KID

m∠2 = m∠7

and

m∠4 = m∠8

Both are correct answers and should be ticked

Here, we want to select which of the statements must be correct based on the diagram given

a) m∠2 = m∠7

This is correct

m∠2 = m∠3 as they are vertically opposite angles

However, m∠3 = m∠7 as they are vertically opposite angles

b) m∠7 = m∠10

We cannot compare the relationship between b and c as the pair are not parallel lines

c) m∠8 = m∠9

This is not correct also as the pair of lines are not parallel

d) m∠4 = m∠8

These two are corresponding angles, so they are congruent and thus equal in value

Yes, the triangle is a right-angle triangle.

Right angle triangle is a triangle in which one of the angles as 90 degree.

For the triangle to be right angle triangle

perpendicular² + base² = hypotenuse²

The three sides of a triangle are 6, 8 and 10

So,

6² + 8² = 10²

36 + 64 = 100

100 = 100

Therefore the triangle is a right-angle triangle.

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The owner loses the figure and the $70 that gives back, so the total amount he loses is $90.

We know that the owner initially has a figure whose price is $20, and he sells it for $30.

Then, he sells it for a $100 bill, so he gives $70 back.

The problem is that the $100 bill was fake, so at this point the total amount that he loses is:

The value of the action figure (which is $20) plus the $70 that he gives back.

Adding these two we get:

$20 + $70 = $90

The owner loses $90 in total.



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Answer:

The small box price is 6.5 and The large box price is 16.5

Step-by-step explanation:

I did the question with a simultaneous equation

let's say the price of the small box = x and the price of the large box = y

Then, I just subtract downward;

18x+25y=529.50

- 18x+10y=282.00

_____________

0+15y=247.50

15y=247.50

— ————

15 15

I just canceled 15 by 15:

Then, y=247.50÷15=16.5

so I just find the value of Y which is 16.5, then I insert it into the second equation:

18x+10y=282

18x+10(16.5)=282

18x+165=282

18x=282-165

18x=117

— —

18 18

Cancel 18 by 18

finally x=6.5

Insert x and y into both equations, it works

Using proportions, the costs for the boats are given as follows:

Factory A:

Factory B:

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of the problem using the standard operations such as addition, subtraction, multiplication and division with the unit rates to find the equivalent amounts.

Considering the costs per hour and the number of hours needed, the cost of a small boat at Factory A is given by:

15 x 1  + 11 x 0.5 + 12 x 0.2 = $22.9.

For example, 15 x 1 is because it requires one hour of cutting, and each hour of cutting pays of $15.

The cost of a medium boat at Factory A is given by:

15 x 1.6  + 11 x 1 + 12 x 0.2 = $37.4.

The cost of a large boat at Factory A is given by:

15 x 2.5 + 11 x 2 + 12 x 1.4 = $76.3.

The cost of a small boat at Factory B is given by:

13 x 1  + 11 x 0.5 + 10 x 0.2 = $20.5.

The cost of a medium boat at Factory B is given by:

13 x 1.6  + 11 x 1 + 10 x 0.2 = $33.8.

The cost of a large boat at Factory B is given by:

13 x 2.5 + 11 x 2 + 10 x 1.4 = $68.5.

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Answer: x= 13/2 or 6 1/2

Step-by-step explanation:

2(x+4)-3(2x-5)=-3

Simplify the equation,

2x+8-6x+15 = -3

-4x+23= -3

-4x = -26

Cancel the minus sign, now we get

2x = 13

i.e., x= 13/2

The system of equations for the given conditions in question includes equation: 3.40 = 0.05x + 0.1y + 0.25z, and 2x = z. and we have 2 nickels, 23 dimes, and 4 quarters.  

What is system of equations?

A system of equations is a collection of some equations with one or more numbers of variables. Systems of equations have solutions that are either the variable mappings that satisfy each component equation or the intersections of all of these equations.

Let the quantities of nickels, dimes, and quarters are x, y, and z respectively.

We know that, 1 nickel = $0.05, 1 dime = $0.1, and 1 quarter = $0.25

So, the values of nickels, dimes, and quarters would be value of one times total quantity.

Nickels = 0.05x, dimes = 0.1y, and quarters = 0.25z

As given in the question, the total value is 3.40

So, we get equation:

3.40 = 0.05x + 0.1y + 0.25z

Also it is given that there are twice as many nickels than quarters.

2x = z

Combining above two equations

3.40 = 0.05x + 0.1y + 0.25(2x)

3.40 = 0.05x + 0.1y + 0.5x

3.40 = 0.55x + 0.1y

Lets put 2 in place of x, we get y

(3.40 - 1.1)0.1 = y

y = 23.

Now, putting values of x, y in equation to get value of z

3.40 = 0.05(2) + 0.1(23) + 0.25z

3.40 = 0.1 + 2.3 + 0.25z

(3.40 - 2.4)/0.25 = z

z = 4

Therefore, we have 2 nickels, 23 dimes, and 4 quarters.  

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The inverse function of one-to-one function f(x)= 7x - 2 is [tex]f^{-1}=\frac{x}{7}+\frac{2}{7}[/tex].

The graphs of f and [tex]f^{-1}[/tex] are symmetric with respect to the line defined by y = x.

Given that:-

f(x)= 7x - 2

Let f(x) = y

Hence,

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

Hence, we can write,

y = 7x - 2

y + 2 = 7x

x = y/7 + 2/7

[tex]f^{-1}(y) = y/7 + 2/7[/tex]

Replacing y by x, we get,

[tex]f^{-1}(x) = x/7 + 2/7[/tex]

Hence, the inverse function of f(x) is [tex]f^{-1}(x) = x/7 + 2/7[/tex].

The graph of inverse is always the mirror image of the function's graph in the line y = x. It is because they're basically 100% similar but in reverse just like you in a mirror.

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The linear equation 20x + 35(60-x) = 1500 can be solved to find the number of tickets.

What is an equation?

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. The word equation and its related terms in various languages may have somewhat different definitions; for example, in French, an equation is described as including one or more elements, but in English, an equation is any well-formed formula that includes two expressions linked by an equals sign.

Let the number of advance tickets sold = x

And then, the number of same-day tickets sold = 60 - x

Then, the equation formed is

20x + 35(60-x) = 1500

=> 20x + 2100 - 35x = 1500

=> -15x = 1500 - 2100

=> x = -600/ -15 = 40

Hence, the number of advance tickets sold = 40

And the number of same-day tickets sold = 60 - 40 = 20

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THE MIDPOINT FORMULAR IS GIVEN BY

[tex]( \frac{x1 + x2}{2} . \frac{y1 + y2}{2} ) \\ \\ = (\frac{ - 2 + ( - 4)}{2} . \frac{ - 3 + 10}{2} ) \\ = ( \frac{ - 6}{2} . \frac{7}{2} ) \\ = ( - 3. \frac{7}{2} )[/tex]

ATTACHED IS THE SOLUTION

The exponent is 81[tex]m^{} 4[/tex] [tex]n^{20}[/tex]

Here we have to determine the sign for exponential or radical expression

(-3m[tex]n^{5}[/tex])^4

Simplify using the exponent rule with the same exponent [tex](ab)^{n}[/tex] = [tex]a^{n}[/tex] . [tex]b^{n}[/tex]

Similarly

(-3m[tex]n^{5}[/tex])^4

= [tex](-3)^{4}[/tex] . [tex]m^{4}[/tex]. [tex](n^{5} )^{4}[/tex]

Now using the exponent  power rule [tex](a^{n} )^{m}[/tex] = [tex]a^{nm}[/tex]. We get

= 81 . [tex]m^{4}[/tex].[tex]n^{20}[/tex]

Therefore the exponent as a product of power is 81[tex]m^{4} n^{20}[/tex].

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The most appropriate choice for average will be given by-

Shureka Washburn must get 78 or higher in her final exam to make her average 76 or higher.

What is  average?

In a data set, there are many numbers. Average is the single number which acts as a representative of all the numbers in the data set.

Average is calculated by sum of all observations divided by total number of observations.

Here,

Let the score of Shureka Washburn in her last test be x

Score of Shurek Washburn on first test = 86

Score of Shurek Washburn on second test = 84

Score of Shurek Washburn on third test = 83

Score of Shurek Washburn on fourth test = 49

Total sum of all her scores = 86 +  84 + 83 + 49 + x

                                           =  302 + x

Average = [tex]\frac{302 + x }{5}[/tex]

By the problem,

                          [tex]\frac{302 + x}{5} \geq 76[/tex]

                          [tex]302 + x \geq 76[/tex] [tex]\times 5[/tex]

                          [tex]302 + x \geq 380[/tex]

                          [tex]x \geq 380 - 302[/tex]

                          [tex]x \geq 78[/tex]

Shureka Washburn must get 78 or higher in her final exam to make her average 76 or higher.

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Given the following question:

Part A:

Your answer is option B, you can find this by checking the values. We are given 107, 128, 163, 212, 275 if you check the values on the graph, you can see that they are exact. So, your answer is option B.

The distance between the two points is 5.

The formula to find the distance between two points (x1, y1) and (x2, y2)

distance = [tex]\sqrt{(x2-x1)^{2} + (\\ y2-y1)^{2} }[/tex]

Substituting points A(2,9) and B(-2,6), we get

distance = [tex]\sqrt{(-2-2)^{2} + ( 6-9)^{2} }[/tex]

              =[tex]\sqrt{(-4)^{2} + (-3)^{2} }[/tex]

              = [tex]\sqrt{16 + 9}[/tex]

              =[tex]\sqrt{25}[/tex]

             = 5

Therefore the distance between the two points is 5.

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With regards to the rigid transformations, Yes, it is true to state that ∠ABD is congruent to ∠EFM. This can be justified by translating ∠ABD by superimposing it on ∠EFM.

It is also true to state that ∠ ABD is congruent to ∠GFHG. To justify this, rotate ∠ABD by 180°

A rigid transformation in mathematics is a geometric transformation of a Euclidean space that retains the Euclidean distance between each pair of points. Rotations, translations, reflections, and any combination of these are examples of rigid transformations.

Hence, the above statements are true. Note that rigid transformations do not modify the distance angles, size or shape.

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Step-by-step explanation:

Answer:

-18

Step-by-step explanation:

-xy^2 =

Let x=2 and y = -3

-(2) (-3)^2

-2 (9)

-18

Answer:

18.

Step-by-step explanation:

(2)(-3)^2

Parentheses first. There's nothing to do so, the exponent is next. -3^2 is 9. 9 * 2 = 18.

Hope this helps! :)

So if i have a bag of rice of 3.5 pounds, that means that it weighs:

since

that means that you will have enough rice for the recipe

Answer: Less than 470 minutes

Step-by-step explanation:

This equation represents this problem.

0.04x + 44.4 = 0.06x + 35

Solve,

0.02x = 9.4

1 / .02 = 50

x = 470

At 470 minutes they're equal and we are looking for when Plan A is cheaper then Plan B, so x < 470

Use m instead of x in this problem, sorry didn't read the last line.

Based on the number of dice rolled, the probability of getting the sum of 6, and 4 and 6 or 4 can be found to be:

Probability of getting sum of 6:

(1 and 5) (2 and 4) (3 and 3) (4 and 2) ( 5 and 1)

= 5 / (6 x 6)

= 5 / 36

The number of sums of 4 are:

= (1 and 3), (2 and 2), (3 and 1)

= 3 / (6 x 6)

= 1 / 12

The probability of getting sums of 6 and 4 are:

= (5 + 3) / (6 x 6)

= 8 / 36

= 2 / 9

These events are mutually exclusive because they cannot roll a sum of 6 or 4.

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The features of the graphs are

Function 1

The equation of the function is given as

f(x) = 3(x - 4)^2 + 3

A quadratic equation can be represented as

f(x) = a(x - h)^2 + k

Where, the vertex is

Vertex = (h, k)

And the axis of symmetry is

x = h

By comparing the equations, we have

Vertex = (4, 3)

Axis of symmetry: x = 4

See attachment 1 for the graph of the function

Function 2

The equation of the function is given as

f(x) = 5x^2 + 4x - 1

Differentiate the function

f'(x) = 10x + 4

Set to 0

10x + 4 = 0

This gives

x = -0.4

Substitute x = -0.4 in f(x) = 5x^2 + 4x - 1

f(-0.4) = 5(-0.4)^2 + 4(-0.4) - 1

Evaluate

f(-0.4) = -1.8

This means that

Vertex = (-0.4, -1.8)

Axis of symmetry: x = -0.4

See attachment 2 for the graph of the function

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y ≤ 16 - x (option A)

let the total number of pieces Luke ate at a time = y

Let the total number of pieces James ate at a time = x

They have never eaten more than 16 pices of pizza

This is written as:

maximum 16 : ≤ 16

number of pieces Luke ate at a time + total number of pieces James ate at a time ≤ 16

y + x ≤ 16

rewritting to make y subject of formula:

y ≤ 16 - x (option A)

Answer:

-8, -10i, 10i

Step-by-step explanation:

x^3 + 8x^2 + 11x = -800

I just plugged it into my calculator

The standard deviation of the discrete distribution of the number of defects in a day is of 0.75 defects.

From the distribution at the end of the answer, the mean is:

E(X) = 0.1667 x 4 + 0.3333 x 5 + 0.5 x 6 = 5.3333.

Hence the standard deviation is of:

S(X) = sqrt(0.1667 x (4-5.3333)² + 0.3333 x (5 - 5.3333)² + 0.5 x (6 - 5.3333)²) = 0.75 defects.

The distribution is missing, and is given as follows:

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