Alvin is 12 years younger than Elga. The sum of their ages is 28. What is Elga's age?

The simplified expression of x(3x + 5)-5(2x - 1) is 3x² - 5x + 5

From the question, we have the following parameters that can be used in our computation:

x(3x + 5)-5(2x - 1)

Open the brackets

So, we have

3x² + 5x - 10x + 5

Evaluate the like terms

So, we have

3x² - 5x + 5

Hence, the simplified expression is 3x² - 5x + 5

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The solution that is the closest estimate of the amount of glass Maria will need to construct her pyramid would be =5289.25 cm squared. That is option C.

To calculate the area of a square based pyramid, the formula that should be used would be given below as follows:

\(area = {a}^{2} + 2a \sqrt{ \frac{a2}{4} } + {h}^{2} \)

Where:

a= 44cm

height= 44²-22²= 38.1cm

Area= 44²+ 2(44) × √44²/4 + 38.1²

= 1936+88 × √ 484+1452

= 2024× √1936

= 5807.61 cm².

Therefore the closest estimate to the final answer would be 5289.25 cm squared

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Answer:

\(m_{perpendicular}\) = 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

x + 6y = - 24 ( subtract x from both sides )

6y = - x - 24 ( divide through by 6 )

y = - \(\frac{1}{6}\) x - 4 ← in slope- intercept form

with slope m = - \(\frac{1}{6}\)

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-\frac{1}{6} }\) = 6

Answer

Total cost of labor = 8 hours x $7 = $56

The cost to make party trays is $14 and sold for $35,

∴ Profit per tray = $35 - $14 = $21

Now, to know how many trays must be sold to cover all costs including labor, we divide the total cost of labour by the profit per tray, that is;

$56/$21 = 2.67 trays.

Answer:

Note: The full question is attached as picture below

a. Slope of 0.536 means that when there is an increase in carbohydrate content, there will be sn increase in 0.536 grams of sugar content.

b. Coefficient of Determination, R^(2) = 0.544^(2) = 0.295936 = 0.296. Percent of variation = 29.6

c. For carbohydrate content of 29 grams,

Predicted amount of sugar per cup for Raisin Bran = -5.10 + 0.536*29 = 10.444 gram

d. Residual value= Actual value - Predicted value

8.556 = Actual sugar content - 10.444

Actual sugar content = 8.556 +10.444

Actual sugar content = 19

So, the Raisin Bran actually have 19 grams of sugar per cup.

Answer:

62

Step-by-step explanation:

The graph of the linear equation is on the image at the end.

Here we want to graph a linear equation. To do so, we need to find two points in the line. Then graph the points, and then find a line that connects these two points.

Here the equation is:

y = 3x

if we evaluate in x = 0 we will get:

y = 3*0 = 0

So we have the point (0, 0)

if x = 1

y = 3*1 = 3

So we have the point (1, 3)

Then the graph of the linear equation is the one at the end of the answer.

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Answer:

$0.64 per cup

Step-by-step explanation:

There are 16 cups in 1 gallon, so the number of cups in 2 gallons is:

1 gallon: 16 cups

2 gallon = 2 x 1 gallon = 2 x 16 cups = 32 cups

So we need to find the price of each cup:

1 cup = ($20.48 / 32 cups) = $0.64 per cup.

The gardner is correct Because the total distance traveled by the roller is greater than the length of the bowling green.

A diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle.

For the gardener to be correct,

8×Perimeter of the roller = Length of the bowling green

Therefore,

Let use first find the perimeter of the roller

Where:

Substitute these values into equation 1

For 8 full rotation,

Comparing the distance for 8 revolution of the roller with the length of the bowling green,

Therefore, the gardner is correct

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Jerrica would have to win 40 additional games in a row to have an 80% winning record. This would bring her total wins to 20 + 40 = 60, and her total games played to 35 + 40 = 75.

To determine how many games Jerrica would have to win in a row in order to have an 80% winning record, we need to calculate the number of games she needs to win out of a certain total.

Let's denote the number of games she needs to win in a row as x. If she wins x additional games, her total wins would be 20 + x, and her total games played would be 35 + x.

To have an 80% winning record, she would need to win 80% of the total games played. Mathematically, this can be expressed as:

(20 + x) / (35 + x) = 80 / 100

Cross-multiplying, we get:

100(20 + x) = 80(35 + x)

Expanding and simplifying:

2000 + 100x = 2800 + 80x

Subtracting 80x from both sides:

20x = 800

Dividing by 20:

x = 40

Jerrica would have to win 40 additional games in a row to have an 80% winning record. This would bring her total wins to 20 + 40 = 60, and her total games played to 35 + 40 = 75.

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Sara and Ashton both have the same number of comic books after 10 months

From the question, we have the following parameters that can be used in our computation:

Sara

Initial = 12 comic books

Books at the fourth month = 20

Ashton

Initial = 2 comic books

Books each month = 3

The equations can be represented as

Total number of books = Initial + Books each month * Number of months

Rewrite as

y = Initial + Books each month * x

For Ashton, the equation is

y = 2 + 3x

For Sara, we have

y = 12 + Books each month * Number of months

So, we have

20 = 12 + Books each month * 4

This gives

Books each month = 2

So, the equation is

y = 12 + 2x

Substitute y = 2 + 3x in y = 12 + 2x

2 + 3x = 12 + 2x

Evaluate the like terms

x = 10

This means that

Number of months = 10

Hence, the number of months is 10

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Complete question

Sara started with 12 comic books in her collection. She collected the same number of comic books each month until she had 20 comic books in the 4th month. Ashton started with 2 comic books in his collection and continues to collect 3 comic books each month.

Calculate when they both have the same number of books

Answers:

===========================================

Explanation:

Side MO is twice as long as the midsegment XY. Note how XY and MO are parallel.

This makes

MO = 2*XY = 2*10 = 20

Side MO breaks into two equal halves MZ and ZO

Each of MZ and ZO are 20/2 = 10 units long.

Put another way: XY, MZ and ZO are all the same length (all 10 units long).

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

The diagram shows that segment NO is 18 units long, which cuts in half to 18/2 = 9. This is the length of NY, YO and XZ

Also, MN = 14 which cuts in half to 7. This means MX, XN and YZ are all 7 units each.

The graph which represents the polar curve r = -4 sin ( 3θ ) is plotted

Polar coordinates describe the position of a point P in the plane by its separation from the origin, r, and the angle formed between the positive x-axis and the line segment leading to P.

To graph the polar curve, we make use of the following representations:

r represents the y-axis

θ represents the x-axis

Polar coordinates can also be extended into three dimensions using the coordinates (ρ, φ, θ), where ρ is the distance from the pole, φ is the angle from the z-axis ( called the co-latitude or zenith and measured from 0 to 180° ) and θ is the angle from the x-axis ( as in the polar coordinates ).

Given data ,

Let the polar curve be represented as A

Now , the polar coordinates is given as

r = -4 sin ( 3θ )

And , To graph the polar curve, we make use of the following representations:

r represents the y-axis

θ represents the x-axis

So , on simplifying , we get

The graph which represents the polar curve r = -4 sin ( 3θ ) is plotted

Hence , the polar curve is r = -4 sin ( 3θ )

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Answer:

D

Step-by-step explanation:

Answer:

0.46 pounds of honey

Step-by-step explanation:

0.58 - 0.12 = 0.46

thanks fr the points

Answer:

$0.12

Step-by-step explanation:

cost of one bag of puppy treats after using the coupon: 10.24-2.80=$7.44

cost per puppy treat= 7.44/62=$0.12

To know the area of a figure, you would like to know its shape and estimations. The steps to take on how to draw a figure with the use of a ruler and a pencil is given below.

Begin by selecting the kind of figure you need to draw. Make use of a ruler to draw the sides of the figure. Make sure that the lines are straight and have the right length.

E.g. If the figure may be a rectangle or a parallelogram, you wish to create beyond any doubt that inverse sides are parallel to each other. If the figure is triangle, you would like to draw three lines that shows at three distinctive points. At last, name the sides and vertices of the figure.

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Answer:

40i²-5i+45

Step-by-step explanation:

The Length is 5 inches and the Breadth is 15 inches

What is Perimeter?

A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter. There are various practical applications for calculating the perimeter.

Solution:

Perimeter of Rectangle = 2*(Length + Breadth)

According to the question

Breadth = 3*Length

Perimeter = 40

40 = 2*(Length + 3*Length)

20 = 4*Length

Length = 5 inch

Breadth = 15 inch

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Answer:

Step-by-step explanation:

1)  DE = 6/sin63 = 6.7

DF = 6/tan63 = 3.1

m∠E = 180 - 90 - 63 = 27°

2)  tan30 = 1/√3 = UV / (27√10)

UV = (27√10) / √3 · (√3/√3) = (27√30) / 3 = 9√30

3)  cosV = 3/8

cos⁻¹(3/8) = 68

m∠V = 68°

The volume of a gas as 100 degrees temperature given at constant pressure is 20 degrees

According to the question;

Since, the proportion is an inverse proportion as described, it follows that;

where,

20 = k/50

20 × 50 = k

1000 = k

If

temperature is 100 degrees?

V = 10 degrees

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Answer:

V = 40

T = 100

Answer:

Step-by-step explanation:

4 : 2

8 : 4

12 : 6

16:8

The ratio in the form of n: 1 will be 2: 1.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The ratio is given below.

⇒ 4: 2

Simplify the ratio in the form of n: 1, then we have

⇒ 4: 2

⇒ 2: 1

The ratio in the form of n: 1 will be 2: 1.

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Answer:

u > 7

Step-by-step explanation:

-2u -6 < -20  Add 6 to both sides

-2u - 6 + 6 < -20 + 6

-2u < -14  Divide both sides by -2.  When you multiply or divide both sides by a negative number, you must flig the sign.

\(\frac{-2u}{-2}\) > \(\frac{-14}{-2}\)

u > 7

Helping in the name of Jesus.

The answer is:

u > 7

In-depth explanation:

You haven't told me what the values of u are, but I'll solve the equation for u.

Add 6 on each side:

\(\bf{-2u-6 < -20}\)

\(\bf{-2u < -14}\)

Divide each side by -1 and reverse the sign:

\(\bf{2u > 14}\)

Now divide each side by 2

\(\bf{u > 7}\)

The perimeter of the semicircle is 6π

From the question, we have the following parameters that can be used in our computation:

Diameter, d = 12 cm

The perimeter of the semicircle. is calculated as

P = πd/2

Substitute the known values in the above equation, so, we have the following representation

P = π * 12/2

Evaluate

P = 6π

Hence, the perimeter is 6π

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Answer: -2.5

Step-by-step explanation:

-10/20 = -1/2

5/-10 = -1/2

So the ratio is -1/2 and the next term is 5 * -1/2 = -2.5

Answer:

To graph the line with slope -1 passing through the point (-2,4), we can use the point-slope form of the equation of a line, which is:

where m is the slope of the line, and (x1, y1) is the given point on the line. Substituting the given values, we get:

Simplifying this equation, we get:

Now we can graph this line by plotting the given point (-2,4), and then using the slope of -1 to find one or more additional points on the line. We can do this by starting at the given point and then moving one unit down (since the slope is negative) and one unit to the right (since the slope is -1). This gives us the point (-1,3). We can then connect these two points to graph the line.

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