Christina buys coffee for her office mates everyday. Normally she buys just three coffees for $5.55. on special days there are five people in the office who drink coffee. How much will five cost?

Applying the area of square and triangle, the amount of paper needed is:  180 inches².

The area of a square shape = (side length of the shape)².

The area of a triangular shape = 1/2(base)(height)

The diagram that illustrates the problem given is shown in the image attached below, where the triangular paper to cover the triangular plank and the square paper for the square plank are shown also with their dimensions.

Therefore, the amount of paper that would cover the piece of art = area of the square shape + area of the triangular shape.

Area of the square shape = 12² = 144 inches²

Area of the square shape = 144 inches²

Area of the triangular shape = 1/2(12)(6)

Area of the triangular shape = 36 inches²

Amount of paper needed = 36 + 144

Amount of paper needed = 180 inches²

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Complete Question:

Theresa created a piece of art by attaching a square plank to a triangular plank. The square plank has a perimeter of 48 inches. The triangular plank has a base length of 12 inches and a height of 6 inches. She wants to cover the piece of art with colored paper.

How many square inches of paper are needed to cover Theresa's art piece?

The maximum weight that could be supported by a beam that is 6 inches wide, 2 inches high, and 24 feet long is 3.33.

G = C×(w×h²/l)

Where,

C = constant

C = G×l/(w²h²)

Weight (w) = 6 in

Height (h) = 2 in

Length (l)= 10 ft

Maximum ton (G) = 8 t

C = 8×10/(6×2²)

C = 80/24

C = 10/3

G = (10/3)×(w×h²/l)

So, Maximum weight

G = (10/3)×(6×2²/24)

G = 10/3 t

G = 3.33 tones

The maximum weight is 3.33 tones.

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The correct factorization of the expression, [tex]64x^{3} +8[/tex], is 4[tex](2x-1)^{2}[/tex] (8x+2).

According to the question,

We have the following information:

[tex]64x^{3} +8[/tex]

The factors of this expression can be found using identity because 64[tex]x^{3}[/tex] is the whole cube of 4x and 8 is the cube of 2.

So, we have the following expression:

[tex](4x)^{3} + 2^{3}[/tex]

Now, we can use the following identity to factor the given expression:

[tex]a^{3} +b^{3} = (a+b) (a^{2} -ab+b^{2} )[/tex]

We have a = 8x and b = 2:

(8x+2) {[tex](4x)^{2}[/tex]-16x+[tex]2^{2}[/tex]}

(8x+2) (16[tex]x^{2}[/tex]-16x+4)

Taking 4 as the common factor from the second bracket:

4(8x+2) (4[tex]x^{2}[/tex]-4x+1)

Now, finding the factors of second bracket:

4(8x+2) ([tex]4x^{2}[/tex]-2x-2x+1)

4(8x+2) {2x(2x-1)-1(2x-1)}

4(8x+2) (2x-1) (2x-1)

4[tex](2x-1)^{2}[/tex] (8x+2)

Hence, the correct factorization of the expression, [tex]64x^{3} +8[/tex], is 4[tex](2x-1)^{2}[/tex] (8x+2).

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Answer:

5736

Step-by-step explanation:

calculator

Answer:          5736

Step-by-step explanation:

The division that can match the model is that 6 ÷ 1/5 = 30.

Division is one of the four fundamental mathematical operations, along with addition, subtraction, and multiplication. It is defined as the splitting of a large group into smaller groups so that each group has an equal number of items. In mathematics, it is an operation used for equal grouping and equal sharing.

It is a process of repeated subtraction. It is the inverse operation of multiplication. It is defined as the formation of equal groups. When we divide numbers, we break them down into smaller numbers so that the multiplication of those smaller numbers equals the larger number taken.

In this case, the division will be:

= 6 ÷ 1/5

= 6 × 5

= 30

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y = -18(x-7)² + 1 is the vertex form of the given equation.

y = a (x − h) 2 + k, y is the y -coordinate, x is the x -coordinate, and a is the constant that tells you whether the parabola is facing up (+a) or down (-a).

Given that y = -18x² + 252x - 881, where a = -18, b = 252 and c = -881

h = -b/2a

h = -252/2*(-18) = 7

k = ah² + bh + c = -18*49 + 252*7 - 881 = 1

Therefore, putting the values in y = a (x − h) 2 we get,

y = -18(x-7)² + 1

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The completion of the trend analysis for sales with 2010 as the base year is as follows:

                             2013           2012           2011           2010

Sales            $ 620,000   $ 580,000   $ 450,000   $ 600,000

Trend Analysis      103%             97%              75%             100%

Trend analysis is a technical analysis that uses historical data over some periods to predict and monitor future developments in a particular topic.

To undertake a trend analysis for sales, a base year is chosen and the sales account for the base year is set at 100% and used to check how sales have changed during the review periods.

The other years' results are compared to the base year's by dividing each year's result by the base year's.

Percentages are used to depict trend analysis so that the resulting increases and decreases can be easily compared to the base year.

2013 (D) = 103% ($620,000/$600,000 x 100)

2012 (C) 97% ($580,000/$600,000 x 100)

2011 (B) 75% ($450,000/$600,000 x 100)

2010 (A) = 100% ($600,000/$600,000 x 100)

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Answer:

5q + 5q + 5 is equivalent to 10q + 5

Answer:

A.

Step-by-step explanation:

The Required Factors   (x + 1) (x - 3 ) (x + 2) (x - 2).

Given equation.
x^4 - 2x^3 - 7x^2+8x+12 = 0

Factors : factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.

polynomial : an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable

Now, factorize the polynomial of degree 4 as follows.

= (x + 1) (x - 3) (x^2 - 4)

Then, again factorize polynomial of degree 2.

Therefore  (x + 1) (x - 3 ) (x + 2) (x - 2)

This is the required factors.

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Step-by-step explanation:

f(x) = 2x - 3

f(m) = 5

that means

5 = 2m - 3

8 = 2m

m = 4

f(-2) = n

that means

n = 2×-2 - 3 = -4 - 3 = -7

so,

m + n = 4 + -7 = -3

Answer:

1.3000

Step-by-step explanation:

To Round Numbers...

1 ) Decide which is the last digit to keep ( In this case it would be the hundredths )

2 ) Leave it the same if the next digit is less than 5 (this is called rounding down)

3 ) But increase it by 1 if the next digit is 5 or more (this is called rounding up)

Hope this helps! :)

The equation of line passes through the point (6, 4) with a slope 2/3 is, y = 2/3x

Given,

The points which the line passes through = (6, 4)

Slope = 2/3

We have to find the equation of line;

Linear equation;

Y = mx + b is one way to represent a linear equation.

Here,

x is 6 and y is 4

Slope, m is 2/3

Then,

Substitute the values in y = mx + b

Here,

y = mx + b

4 = 2/3 (6) + b

4 = 12/3 + b

4 = 4 + b

b = 4 -4

b = 0

Then,

The equation of line is, y = 2/3x + 0

That is,

The equation of line passes through the point (6, 4) with a slope 2/3 is, y = 2/3x

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Answer:

99

Step-by-step explanation: 99

Answer:

y = 8 [tex](\frac{1}{2}) ^{x}[/tex]

Step-by-step explanation:

an exponential function can be expressed in the form

y = a [tex]b^{x}[/tex]

to find a and b use points that lie on the graph

using (0, 8 ) , then

8 = a[tex]b^{0}[/tex] [ [tex]b^{0}[/tex] = 1 ] , then a = 8

y = 8[tex]b^{x}[/tex]

using (1, 4 ) , then

4 = 8[tex]b^{1}[/tex] = 8b ( divide both sides by 8 )

[tex]\frac{4}{8}[/tex] = b , that is b = [tex]\frac{1}{2}[/tex]

y = 8 [tex](\frac{1}{2}) ^{x}[/tex] is the exponential function

Answer: 13

Step-by-step explanation:

Here is what i did

I used a graphing calculator

Option A is the correct answer g(x) = |x+3| by using the relation with the parent function.

Explain absolute value function.

A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function. Remember that a number's distance from 0 on the number line represents its absolute value.

The definition of the absolute value parent function, f(x)=| x |, is as follows:

f(x) = [tex]\left \{ {{x ~, ~ x > 0} \atop {0 ~ , ~x = 0}} \atop {-x ~, ~x < 0} \right.[/tex]

Given parent function is f(x) = |x|

g(x) is obtained by stretching the graph of f(x) by a factor of 3.

Use the function g(x)=f(x−h) to translate the absolute value function f(x)=| x | horizontally.

The graph of f(x) is moved h units to the right to obtain g(x) for h>0

The graph of f(x) is translated h units to the left to obtain g(x) when h>0

Therefore, g(x) = |x+3|

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Answer:  x = 8   y = 21

Step-by-step explanation:

7x + 12 = 12x - 28

40 = 5x

x = 8

180 = 12(8-28) + 9y - 77

180 = 96 - 28 - 77 + 9y

180 = -9 + 9y

189 = 9y

y = 21

Answer:

x=8

y=21

Step-by-step explanation:

9y-77+12x-28=180

9y+12x=285

7x+12=12x-28

5x=40

x=8

9y+96=285

9y=189

y=21

The proof to the above diagram is ∠1 + ∠3 = 180

Supplementary angles are angles whose sum equals 180°

If angle A + angle B = 180°, then both angles are said to be supplementary, meaning angle A is the supplement of Angle B.

∠2 ≅ ∠3. This means ∠2 is approximately equal to ∠3

Also ∠1 + ∠2 = 180°( sum of angles on a straight line)

making ∠2 the subject of the equation

∠2 = 180 - ∠1

But ∠2 ≅ ∠3, which we can say that ∠2 = ∠3

substituting ∠2 for ∠3 in the equation, we have

∠3 = 180 - ∠1

which is further simplified as,

∠1 + ∠3 = 180°

Which  means both angles are also supplementary.

In conclusion,  both angles are supplementary as ∠1 + ∠3 = 180

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Given polynomial with descending degrees of x would be,

x^4z^4 + x^3 - x^2z + z^3

In this question we have been given a polynomial x^3 + z^3 - x^2z + x^4z^4

We need to write given polynomial by descending degrees of x.

The highest degree of x in above polynomial is 4

x^3 + z^3 - x^2z + x^4z^4

then the second term would be x with degree 3.

x^3 + z^3 - x^2z + x^4z^4

the third term would be x with degree 2

x^3 + z^3 - x^2z + x^4z^4

and the last term is the term x with degree 0:

x^3 + z^3 - x^2z + x^4z^4

Therefore, given polynomial with descending degrees of x would be, x^4z^4 + x^3 - x^2z + z^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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Answer:

Answer would be $3.25

Step-by-step explanation:

First you would have to divide 19.5 by 6 to get 3.25 then check your answer by multiplying 3.25 by 6 which would be 19.50 .

Answer:

g(x)=−x−5, find g(1)g(1)

Step-by-step explanation:

g(x)=−x−5, find g(1)g(1)

Answer: 2012

Step-by-step explanation: biggest shift in pop

Answer: Read explanation

Step-by-step explanation: Observations of setting: Humanoid beings. Earth-like world. A human base to collect information. Forest like setting. Bird-like transportation creatures.

Theme ideas: Man a part of research group enters an avatar of beings to collect information on this world. Research group makes an invasion on these creatures home land.  

Make any corrections if you want! Make it more comfortable to your style!

DT is congruent to TD.

A line segment is always equal to itself.

Given,

The figure;

We have to find the segments which are congruent because of the reflexive property of congruence.

Reflexive property of congruence;-

An angle, line segment, or shape is always congruent to itself, according to the reflexive characteristic of congruence in geometry. If angle A is an angle, then angle A is a congruent angle of angle A

Here,

DT = TD,

A line segment is always equal to itself.

So, DT is congruent to TD.

Congruence;-

If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent, or to be in the relation of congruence.

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The midpoint of the line joining (6,-5) and (-1,-6) is (-5/2,-11/2).

How to determine the midpoint of the line joining two points (a,b) and (p,q)?

To get the midpoint of the line joining two points (a,b) and (p,q), we first have to add the x coordinates of two points and divide it by 2. So the midpoint's x coordinate will be (a+p)/2 . Similarly, we have to do the same with y. Then the midpoint of the line joining two points (a,b) and (p,q) will be [(a+p)/2,(b+q)/2}.

To get the midpoint of (6,-5) and (-1,-6) , first, we have to add the x coordinates and divide it by 2 . And have to do the same with y.

so, the midpoint will be [(6+(-5)]/2,[-5+(-6)]/2.

Hence ans will be ,(-5/2,-11/2)

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If each day a player of climbing shoes cost 84 it cost 169 to buy six days of climbing one pair of climbing shoes and one harness. The amount that the harness cost is $25.

Cost of climbing = ( $10×6)

Cost of climbing = $60

Harness cost = Total cost  - (Cost of climbing  + Cost of shoes)

Harness cost =$169 - ($60 + $84)

Harness cost =$169 - $144

Harness cost =$25

Therefore $25 is the harness cost.

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