A teacher covered the exterior of a rectangular prism-shaped box that measured 8 inches by 9 inches by 10 inches using one sheet of rectangular-shaped wrapping paper that measured 2 feet by 3 feet. There were no gaps or overlapping paper. How many square inches of wrapping paper were left over?

The equation of the perpendicular bisector for the line is y = 1/3(x) - 2

Given: the endpoints of the line (4,6) and (8,-6)

The bisector of the line will divide the line into two i.e. the bisector will be at the point of the line.

The coordinate of the midpoint can be calculated using the formula below:

Xm = (X1 +X2)/2  and Ym = (Y1 +Y2)/2

Where X1 = 4, Y1 =6 and X2= 8, Y2= -6

Xm = (4+8)/ 2 = 12/2 = 6  and Ym = (6+(-6))/2 = 0/2 = 0

Thus, midpoint(6, 0)

slope  = y2-y1 / x2-x1

Thus, the slope of the line segment (m₁)  = -6-6 / 8-4 = -12/4 = -3

When the two lines are perpendicular, the product of their slope is -1 i.e.

m₁ × m₂ = -1

where m₁ and m₂ represent the slope of the lines

Let the slope of the bisector be  m₂

-3 × m₂ = -1

m₂ = 1/3

Equation of perpendicular bisector with coordinate (6,0):

y - 0 = 1/3(x-6)

y = 1/3(x-6)

y = 1/3(x) - 2

Therefore, the equation for the perpendicular bisector of the line segment is y = 1/3(x) - 2

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The orthocenter of the triangle with vertices  P(-1,2), Q(5,2), R(2,1) is

Orthocenter is calculated by

formula for slope is

m = (y₂ - y₁) / (x₂ - x₁)

slope of the perpendicular = -1/m

Using side PR  P(-1,2)  R(2,1) ,

m = (1 - 2) / (2 - -1)

m = 1 / 3

slope of the perpendicular = -1/m = - 1 / (1/3) = -3

using point-slope formula for equation of line passing through Q (5, 2)

point slope formula

(y - y₁) = m (x - x₁)

(y - 5) = -3 (x - 2)

y - 5 = -3x + 6

y = -3x + 6 + 5

y = 11 - 3x

Using side PQ  P(-1, 2), Q(5, 2)

m = (2 - 2) / (5 - -1)

m = 0

slope of horizontal line is zero for horizontal line the perpendicular is a vertical line

using point-slope formula for vertical line passing through R (2, 1)

point slope formula

(y - y₁) = m (x - x₁)

0 = (x - 2)

x =  2

The two equations are

y = 11 - 3x

x = 2

solving both equations with x already known

y = 11 - 3 * 2

y = 11 - 6

y = 5

Therefore the orthocenter is (2, 5)

The triangle is attached

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If the dairy farmer wants to mix a 80% protein. The amount of pounds of each that he should use is 80% 280 pounds and 55% 1120 pounds.

Protein I 80% = x pounds

Protein II 55% = 1400 - x pounds

Mixture 60% = 1400

Hence,

80% x + 55% ( 1400 - x ) = 60% × 1400

80 x + 55 ( 1400 - x ) = 84000

80 x + 77000 - 55 x = 84000

Combine like terms

80 x - 55 x = 84000 - -77000

25 x = 7000

Divide both side by 25x

x= 7000/25

x =280 pounds ( Protein I)

Protein II

1400 - x pounds

1400 -280

=  1120 pounds

Therefore the farmer should use 280 pounds and 1120 pounds.

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Answer:

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

The degree and number of unique zeros of f(x) = (x – 5)(x + 3)(x – 1)² is:

Degree: 4; number of unique zeros: 3.

The end behavior of the polynomial is:

As x → –∞, f(x) → ∞ and as x → ∞, f(x) → ∞.

The degree of the polynomial function is given by the sum of the multiplicities of the roots.

These roots are given as follows:

Hence the degree is:

1 + 1 + 2 = 4.

The unique zeros are the roots, hence there are three unique zeros, which is the same number of linear factors of the function.

The end behavior is the limit of the function as x goes to negative infinity and to positive infinite, hence:

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Answer:

a little confused, but it should just be a horizontal line on -4 because of 4 times negative 1 = -4

Step-by-step explanation:

The probability that the mean actual weight for the 100 weights is greater than 25.2 is equal to 0.0136%.

In order to determine the probability that the mean actual weight for the 100 weights is greater than 25.2, we would have to calculate the mean and standard deviation.

In a uniform distribution, the mean of a data set can be calculated by using this formula:

Mean, E(x) = [a + b]/2

Where:

Substituting the given parameters into the formula, we have;

Mean, E(x) = [24 + 26]/2

Mean, E(x) = 50/2

Mean, E(x) = 25.

For the standard deviation, we have:

Standard deviation, S(x) = √((b - a)²/12)

Standard deviation, S(x) = √((26 - 24)²/12)

Standard deviation, S(x) = √((2)²/12)

Standard deviation, S(x) = √(4/12)

Standard deviation, S(x) = 0.5774.

For the sample standard deviation, we have:

Standard deviation = S(x)/√n

Standard deviation = 0.5774/√100

Standard deviation = 0.5774/10

Standard deviation = 0.05774.

By applying the central limit theorem, we would determine the z-score as follows:

Z-score = (x - μ)/σ

Z-score = (25.2 - 25)/0.05774

Z-score = 0.2/0.05774

Z-score = 3.64

Therefore, the p-value is equal to 0.000136.

Probability (x > z) = 0.0136%.

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Answer:

b=(cd-ax)/y

Step-by-step explanation:

b=(cd-ax)/y

Answer:

hi, I think the answer is x^2-2x+1 I don't see that option there but I'm guessing that was suppose to be option OA.

explanation:

(x-1)^2 is basically

(x-1)×(x-1)

rest of the explanation is in the photo

hope this helps

An eight pointed star have 8 rotational symmetry and 8 reflection symmetry

The rotational symmetry of a shape explains why an object's shape remains unchanged when rotated about its own axis.

The eight pointed star while standing on any of the edges will be symmetrical.

Symmetry with respect to reflections is known as reflection symmetry. Mirror or line symmetry are other names for reflection symmetry.

For a reflection symmetry to be in a figure, the figure must at least have one line dividing it into two parts, one of which is the mirror image of the other,

Each of the peak and crest in the star will make 8 reflection symmetry

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Answer:

{-9,-8,7,8,10}

Answer:

3x^2-2x+3+1/x+2

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

just click the rotate button until it matches one of the answers

The slope of a line KH if H(-4, 2) and K(2, -2) is -2/3.

A mathematical word used to define a line's direction and steepness is its slope or gradient.

If a line is rising from left to right, it is growing. The slope is positive, or m>0

If a line decreases from left to right, it is said to be diminishing. The slope is negative, indicating that m < 0

A line has zero slopes if it is horizontal. This function is constant.

The slope of a line is y - y₁ = m(x - x₁)

Slope m = (y₂ - y₁)/(x₂ - x₁)

m = (- 2 - 2)/(2 + 4)

m = - 4/6

m = - 2/3

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Expression which placed on the right side of equal sign is,

[tex]2+3^3 =2 +3\times 3\times 3[/tex]

[tex]2+3^3= 2+27[/tex]

[tex]2+3^3= 29[/tex]

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

What do you mean by 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, a expression 2 + [tex]3^3[/tex] = ?  

what can  be placed right side of the expression?

so, first we calculate the [tex]3^3[/tex] which means 3 x 3 x 3 = 27.

then , add 2 and 27 and the answer is 29.

but the answer is not present into the option.

Final answer will be 29 which placed right side of the equation 2 + [tex]3^3[/tex] = 29.

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The statement that is most likely correct for the negatively skewed data distribution given is B. The mean is less than the median.

What is a Negatively Skewed Data Distribution?

A negatively skewed data distribution has the tail to the left of the number line, and therefore its median is usually greater than its mean.

The dot plot shows a data distribution that is negatively skewed. Therefore, the statement that is most likely to be true is B. The mean is less than the median.

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The number that is closest to the mean of the distribution is 4 (option C)/

A histogram is used to represent data graphically. The histogram is made up of rectangles whose area is the product of the frequency of the rectangle and the width of the rectangle.  

Mean is the average of a set of numbers. It is determined by multiplying each bar in the histogram by its height, add the multiplication value for all the bars together and dividing it by the total frequency of the bars.

Mean = [(1 x 1) + (2 x 2) + (3 x 3) + (4 x 4) + (5 x 3) + (6 x 2) + (7 x 1)] / (1 + 2 + 3 + 4 + 3 + 2 + 1)

Mean = (1 + 4 + 9 + 16 + 15 + 12 + 7) / 16

Mean = 64 / 16

Mean = 4

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D after three rotations: 3 × 36° = 108°

F after five rotations: 5 × 36° = 180°

H after seven rotations: 7 × 36° = 252°

I after eight  rotations: 8 × 36° = 288°

Given,

In the question:

ABCDEFGHIJ is a regular decagon. It rotates clockwise about its center to form the polygon A'B'C'D'E'F G'HIJ.

To find the each angle of rotation to the point A' coincides with after that rotation.

Now, According to the question:

let's know about Decagon:

A decagon is a ten-sided polygon or 10-gon. The total sum of the interior angles of a simple decagon is 1440°. A self-intersecting regular decagon is known as a decagram.

Every regular polygon with n sides can be divided into n  congruent triangles. The angle with vertex the center of the polygon will measure

360 : n degrees.  We are given a regular decagon, therefore:

n = 10

α = 360 : n = 36°

We consider that, if the decagon is not rotated, A' coincides with A and the rotation is towards the next letter of the alphabet. This means that after one rotation of 36° A' will coincide with B, after two rotations A' will coincide with C and so on.

A' will coincide with D after three rotations: 3 × 36° = 108°

A' will coincide with F after five rotations: 5 × 36° = 180°

A' will coincide with H after seven rotations: 7 × 36° = 252°

A' will coincide with I after eight  rotations: 8 × 36° = 288°

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The graph which represents the polynomial function f(x) = x^3 - 2x^2 - 5x + 6 is in option A.

First, let us understand the polynomial function:

A polynomial function is one that uses only non-negative integer powers or positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, and so on. For example, 9y + 6 is a polynomial with an exponent of 1.

We are given:

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

We know that, when the graph intersects the x-axis, it satisfies the equation that is f(x) = 0 at that point.

Let us check the points one by one;

Option A;

The graph intersects the x-axis at -2, 1, and 3 it should satisfy the equation f(x) = 0.

Let's put x = -2 in f(x), we will get;

f(-2) = -2^3 - 2(-2)^2 - 5(-2) + 6 = -8 - 8 + 10 + 6 = -16 + 16 = 0

f(-2) = 0.

Let's put x = 1 in f(x), we will get;

f(1) = 1^3 - 2(1)^2 - 5(1) + 6 = 1 - 2 - 5 + 6 = 7 - 7 = 0

f(1) = 0.

Let's put x = 3 in f(x), we will get;

f(3) = 3^3 - 2(3)^2 - 5(3) + 6 = 27 - 18 - 15 + 6 = 33 - 33 = 0

f(3) = 0.

So, the points -2, 1, and 3 satisfy the equation f(x).

Thus, the graph which represents the polynomial function f(x) = x^3 - 2x^2 - 5x + 6 is in option A.

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There is a total of 2152 yes votes

From the question, the statement is given as

The ratio of yes votes to no votes was 4 to 7

Mathematically, this can be represented as

Ratio = 4 : 7

Alternatively, we have

Yes : No = 4 : 7

Express the ratio as fraction

Yes = Yes/Yes + No

So, we have

Yes = 4/4 + 7

Evaluate the sum

Yes = 4/11

From the question, we have

Total votes = 5918

So, we have

Yes = 4/11 * 5918

Evaluate

Yes = 2152

Hence, the number of yes votes is 2152

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Answer:

Step-by-step explanation:

We're assuming Deshaun is driving at a constant speed/at the same rate,

He drove 469 miles in 7 hours -> his speed = 469 : 7 = 67 (mph)

Therefore, it would take him 335 : 67 = 5 hours to drive 335 miles.

Omar deposited d dollars into a savings account y years ago. ... following expressions could be used to determine the zeros of the function f (x) when f (x).

Step-by-step explanation:

Martin had 6 magazines. Then m more magazines came in the mail. Write an expression that shows how many magazines Martin has now.

Martin now has: 6 + m

The Xavier is not getting better mileage with his new car .

In the question ,

it is given that

distance travelled by Xavier's new car in 25 gallons = 528 miles

the mileage can be calculated using the formula = (distance travelled)/( gallons of fuel used) .

So , mileage of the new car = 528/25 = 21.12 miles per gallon ,

the milage of Xavier's former car = 20.28 miles per gallon .

From the above data , we can see that the mileage of former car is greater than new car .

Therefore , The Xavier is not getting better mileage with his new car .

The given question is incomplete , the complete question is

Xavier's new car uses 25 gallons for 528 miles , His former car was able to travel 20.28 miles per gallon. Is Xavier getting better gas mileage in his new car?

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The time that initial investment be doubles is 20 year.

What is compound interest?

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest. It is the result of reinvesting interest, or adding it to the loaned capital rather than paying it out, or requiring payment from borrower, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.

Compound interest = principal (1+r/100)^n

compound interest = 3800.

3800 = 1900(1+3.5%)^n

3800/1900 = 1.035^n

taking natural log

ln(2) = n ln(1.035)

n = ln(2)/ln(1.035)

n = 20.15

Hence, time is 20 years.

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The answer to the algebraic expession is 10.

What is algebraic expression?

An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression.

Main Body:

We have to find the value of x²-13(x-y) at x=7 and y=4

Now substitute the value of x,y in the expression

=(7)²-13(7-4)

= 49-13(3)

= 10

Hence the answer is 10.

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Answer:

SHe got a 8 on the 8th quiz

Step-by-step explanation:

The score for eighth quiz is 8.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

The average for 5 quiz marks is 8.

So, total quiz point = 8 x 5

                                = 40

Now, for next two the score are 7 and 8

The Total quiz point= 40 + 7+ 8= 55

let x be score on the 8th quiz

55+ x /8= 7.5

52 + x = (7.5)(8)

x = 60 - 52

x= 8

Hence, the score for eighth quiz is 8.

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