Question 3 of 12 , Step 1 of 1 Find three consecutive integers whose sum is 360.

The system of inequalities is correctly graphed on Shannon's graph.

Here we have the following system of inequalities:

y ≥ (1/2)*x - 1

x - y > 1

We can rewrite the second inequality as:

y < x - 1

Then the system becoimes:

y ≥ (1/2)*x - 1

y < x - 1

The first line will be one with positive slope, it is solid (due to the symbol ≥) and the shaded area is above the line.

For the second we will have a dashed line, and now the shaded area is below the dashed line.

From that, we caonclude that Shannon's graph is the correct one.

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The optimal solution for the given linear programming problem is x = 20 and y = 80

The given linear programming problem is:

Minimize g = 44x + 13y

Subject to:  

x + y ≥ 100

-x + y ≤ 20

-2x + 3y ≥ 30

Where x, y ≥ 0

To solve this problem, we need to determine the feasible region for x and y. The first constraint is x + y ≥ 100, which gives the inequality x + y - 100 ≥ 0.

The second constraint is -x + y ≤ 20, which gives the inequality x - y + 20 ≥ 0.

The third constraint is -2x + 3y ≥ 30, which gives the inequality 2x - 3y + 30 ≥ 0. The feasible region for x and y can be represented by the three inequalities x + y - 100 ≥ 0, x - y + 20 ≥ 0 and 2x - 3y + 30 ≥ 0.

To minimize g = 44x + 13y, we need to use the graphical method. First, draw the feasible region. Then, we draw the line corresponding to the objective function g = 44x + 13y. We will be looking for the point where the line intersects the feasible region with the lowest possible value of g. The intersection point is the optimal solution.

In conclusion, the optimal solution for the given linear programming problem is x = 20 and y = 80, with the minimum value of g being g = 44*20 + 13*80 = 3200.

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Answer:

Please review the trigonometric proof below

Step-by-step explanation:

Given

[tex]\csc x -\sin x=\cos x \cot x[/tex]

Apply the reciprocal identity to [tex]\csc x[/tex].

[tex]\frac{1}{\sin x} -\sin x=\cos x \cot x[/tex]

Write [tex]-\sin x[/tex] as a fraction then multiply by [tex]\frac{\sin x}{\sin x}[/tex].

[tex]\frac{1}{\sin x} + \frac{-\sin x}{1} =\cos x \cot x[/tex]

[tex]\frac{1}{\sin x} + \frac{-\sin x}{1} *\frac{\sin x}{\sin x}=\cos x \cot x[/tex]

[tex]\frac{1}{\sin x} + \frac{-\sin x\sin x}{\sin x}=\cos x \cot x[/tex]

Combine the numerators over the common denominator.

[tex]\frac{1-\sin x\sin x}{\sin x}=\cos x \cot x[/tex]

Multiply [tex]\sin x[/tex] by [tex]\sin x[/tex].

[tex]\frac{1-\sin^2 x}{\sin x}=\cos x \cot x[/tex]

Apply the Pythagorean identity [tex]1-\sin^2 x=\cos^2 x[/tex]

[tex]\frac{\cos^2 x}{\sin x}=\cos x \cot x[/tex]

Factor [tex]\cos x[/tex] out of [tex]\cos^2 x[/tex].

[tex]\frac{\cos x\cos x}{\sin x}=\cos x \cot x[/tex]

Separate into two fractions.

[tex]\frac{\cos x}{1} *\frac{\cos x}{\sin x}=\cos x \cot x[/tex]

Apply the quotient identity [tex]\frac{\cos x}{\sin x}=\cot x[/tex].

[tex]\frac{\cos x}{1} *\cot x=\cos x \cot x[/tex]

Anything over 1 is just itself.

[tex]\cos x\cot x=\cos x \cot x[/tex]

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, = space

Answer:

csc x − sin x

= [tex]\frac{1}{sin, x}[/tex] - sin x

= [tex]\frac{1 - sin^{2}, x }{sin, x}[/tex]

= [tex]\frac{cos^{2}, x }{sin, x}[/tex]

= [tex]\frac{cos, x}{sin, x}[/tex] * cos x

= cot x cos x

∴csc x - sin x - cot x cos xQED

It is the most " explanation " I can think of.

Thus the answer is shown above..

Answer:

Step-by-step explanation:

W = w

L = 3w

H = w+4

Now V = LHW

          = (3w)(w+4)(w)

         = (3w²+12w)(w)

        = 3w³+12w²

Answer:

The possible number of hours Yolanda could rent the boat is 6 hours. I hope this isn't too late, and it's not incorrect lol

Step-by-step explanation:

7t - 3 ≤ 39

*We add 3 to both sides, which will cancel out the 3.*

7t ≤ 42

*We divide 42 by 7 to isolate the variable*

t ≤ 6

Claire will be 20 years old in 16 years. To solve this problem, we use algebra.

Let's represent Claire's current age with the variable x. According to the problem, in 8 years, Claire will be three times her current age. We can write this as an equation:

x + 8 = 3x
Next, we can rearrange the equation to solve for x:

8 = 2x
x = 4
This means that Claire is currently 4 years old. To find out when she will be 20 years old, we can subtract her current age from 20:

20 - 4 = 16

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Answer:

  100°

Step-by-step explanation:

You want the missing arc measure in the geometry where two chords cross at 85° and they intercept one arc of measure 70°.

The angle where chords cross is the average of the two arcs that they intercept. Here, that means ...

  85° = (AE +BC)/2

Solving for BC, we get ...

  2(85°) = AE +BC

  BC = 170° -AE = 100°

The missing arc measure is 100°.

McKenzie would take 6 hours to complete the landscaping job alone if Lindy calls in sick.

If McKenzie and Lindy can complete the landscaping job in 4 hours working together, it means their combined work rate is 1/4 of the job per hour. Let x be the number of hours it takes Lindy to complete the job alone, then McKenzie can complete the job in x-6 hours.

Using the formula for their individual work rates, we have:

[tex]1/x + 1/(x-6) = 1/4[/tex]

Multiplying both sides by [tex]4x(x-6)[/tex], we get:

[tex]4(x-6) + 4x = x(x-6)[/tex]

Expanding and simplifying, we get:

[tex]2x^2 - 12x - 48 = 0[/tex]

Dividing both sides by 2 and using the quadratic formula, we get:

[tex]x = (12 ± \sqrt{12^2 + 4248}) / (2*2)[/tex]

x = (12 ± 18) / 4

x = 7.5 or -1.5

Since we cannot have a negative time, the answer is that it would take Lindy 7.5 hours to complete the job alone, and McKenzie would take 1.5 hours less, or 6 hours, to complete the job alone if Lindy calls in sick.

Therefore, McKenzie would take 6 hours to complete the landscaping job alone if Lindy calls in sick.

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The 42 grams of aluminum implies that the chemist has 0.06429ml of aluminum

The density of material shows the denseness of that material in a specific given area. A material’s density is defined as its mass per unit volume. Density is essentially a measurement of how tightly matter is packed together. It is a unique physical property of a particular object. The principle of density was discovered by the Greek scientist Archimedes. It is easy to calculate density if you know the formula and understand the related units The symbol ρ represents density or it can also be represented by the letter D.

How to determine the amount of aluminum?

The mass is given as:  Mass = 42 grams

The density of aluminum is: Density = 2.7 g/cm³

So, we have: Volume = Density/Mass

This gives, Volume = 2.7/42

Evaluate : Volume = 0.06429cm³

Convert to ml

Volume = 0.06429ml

Hence, the chemist has 0.06429ml of aluminum

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The man has 7 shirts in total, so he can take 3 of those shirts on his 3-day trip without repetition. This means that he can make 7 different combinations of shirts, since each shirt has only one choice. For example, he could take shirts A, B, and C; or he could take shirts D, E, and F; or he could take shirts G, A, and B. In total, he has 7 different combinations of shirts to choose from.
The number of combinations of shirts that the man can take without repetition can be found using the formula for combinations, which is:
C(n, r) = n! / (r! * (n-r)!)

In this case, n = 7 (the total number of shirts) and r = 3 (the number of shirts he will take with him).

Plugging in these values into the formula, we get:

C(7, 3) = 7! / (3! * (7-3)!)

C(7, 3) = 7! / (3! * 4!)

C(7, 3) = 5040 / (6 * 24)

C(7, 3) = 5040 / 144

C(7, 3) = 35

Therefore, the man can take 35 different combinations of shirts without repetition.

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The midpoint of the line segment whose endpoints are the given points is (8.1 , -21.7).

To find the exact distance between the points (9.6,-19.7) and (6.6,-23.7), we can use the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the given values:

distance = sqrt((6.6 - 9.6)^2 + (-23.7 - (-19.7))^2)

Simplifying:

distance = sqrt((-3)^2 + (-4)^2)

distance = sqrt(9 + 16)

distance = sqrt(25)

distance = 5

Therefore, the exact distance between the points is 5.

To find the midpoint of the line segment whose endpoints are the given points, we can use the midpoint formula:

midpoint = ((x1 + x2)/2 , (y1 + y2)/2)

Substituting the given values:

midpoint = ((9.6 + 6.6)/2 , (-19.7 + (-23.7))/2)

Simplifying:

midpoint = (16.2/2 , -43.4/2)

midpoint = (8.1 , -21.7)

Therefore, the midpoint of the line segment whose endpoints are the given points is (8.1 , -21.7).

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The graph of this function is a sine curve with amplitude 3√2 and phase shift π/4.

The k cos(ϕ) would be 3 and k sin(ϕ) would be 3.

The combined sound is given by:

f(t) = f1(t) + f2(t)

f(t) = 3 sin(t) + 3 cos(t)

To find k and ϕ, we can use the following trigonometric identity:

k sin(t + ϕ) = k sin(t) cos(ϕ) + k cos(t) sin(ϕ)

Comparing this with the equation for f(t), we can see that:

k cos(ϕ) = 3

k sin(ϕ) = 3

Squaring both equations and adding them gives:

k^2 = 3^2 + 3^2 = 18

k = √18 = 3√2

Dividing the two equations gives:

tan(ϕ) = 3/3 = 1

ϕ = π/4

Therefore, the combined sound has the form:

f(t) = 3√2 sin(t + π/4)

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The value of the constant of variation for the direct variation is k = -1/2.

Variation depicts the relationship between two variables and how it changes. Often, a ratio is used to illustrate this connection. When we remark that a variation is continuous, we are referring to how consistently the ratio changes. Hence, whenever you read the phrase "constant of variation," just keep in mind that it refers to the stability of the relationship between the variables.

The direct variation is given by the following relations:

y = kx

Now, using the table substitute the value of y = f(x) and x:

y = kx

-2 = k(4)

k = -2/4

k = -1/2

Hence, the value of the constant of variation for the direct variation is k = -1/2.

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Answer:

See below.

Step-by-step explanation:

This is the correct formula for simple interest, but be careful with the numbers.

a = 6 000(1 + 0. 028t)

0.028 means 2.8% interest rate.

For 2.9% interest rate it should be

a = 6 000(1 + 0. 029t)

Answer:

3.5 * 10²

Step-by-step explanation:

In standard form, the number before the point has to be less than ten so

0.035 = 3.5 *10²

Yes, the binomial 2x+3 is a factor of the given polynomial P(x)=2x^(3)+3x^(2)-2x-3. We can verify this by using synthetic division.

First, we need to find the zero of the binomial, which is -3/2. Then, we can use synthetic division to divide the polynomial by the binomial.

Here are the steps for synthetic division:

1. Write the coefficients of the polynomial in a row: 2  3  -2  -3
2. Write the zero of the binomial to the left of the row: -3/2 | 2  3  -2  -3
3. Bring down the first coefficient: -3/2 | 2  3  -2  -3
               0  -3   6  -6
               ---------------
               2  0   4   -9
4. Multiply the zero by the first coefficient and write the result below the second coefficient: -3/2 * 2 = -3
5. Add the second coefficient and the result: 3 + (-3) = 0
6. Repeat steps 4 and 5 for the remaining coefficients: -3/2 * 0 = 0, -2 + 0 = -2; -3/2 * -2 = 3, -3 + 3 = 0
7. The final row of numbers represents the coefficients of the quotient: 2x^(2) + 0x + 4, with a remainder of -9.

Since the remainder is not zero, the binomial is not a factor of the polynomial. However, if we divide the polynomial by the binomial using long division, we get the following:

2x^(2) + 4 - (9/(2x+3))

This means that the polynomial can be written as: P(x) = (2x+3)(2x^(2) + 4) - 9

So, the binomial 2x+3 is a factor of the polynomial P(x)=2x^(3)+3x^(2)-2x-3.

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Answer:

Below

Step-by-step explanation:

The graph of the linear inequality y ≥ −2x − 1 is the region _______ the graph of the line y= - 2x -1

≥  is greater than or equal to and translates to 'on or above'

Answer:

1/4

Step-by-step explanation:

Fractions have two parts, the numerator and the denominator. The denominator is the bottom number and it tells us what unit of fraction we are working with (ie: it denotes fourths, halves, etc.)

Hope it helps! :D

The polygon with an interior angle

sum of 1080° is an octagon, or

polygon with 8 sides.

We are given that the interior angle

sum of our polygon is 1080°. We also

know that the sum of the interior

angle of any polygon with "n" sides is

given by the formula (n - 2) × 180°.

Therefore, to determine the number

of sides that our polygon has, we set

this formula equal to 1080°, and solve

for "n".

Divide both sides of the equation by

180°.

Add 2 to both sides of the equation.

We get that our polygon has 8 sides,

and the name of a polygon with 8 sides

is an octagon. Therefore, the polygon

that has an interior angle sum of 1080°

is an octagon, or an 8 sided polygon.

The most accurate comparison is that a gamma ray has more energy than a radio wave because it has a shorter wavelength and higher frequency.

The most energetic and high frequency particles are gamma rays. On the other side, radio waves are the EM radiation types with the lowest energies, longest wavelengths, and lowest frequencies.

All electromagnetic radiation travels in a vacuum at the speed of light (c), which is the same for all electromagnetic radiation types, including microwaves, visible light, and gamma rays.

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if we take a peek at the tickmarks on the sides, that means that the line that cuts the side is the median, so we have three medians meeting at the centroid of the triangle, bearing in mind that the centroid cuts all three medians in a 2 : 1 ratio, then we can say that line AC is being cut by it in a 2 : 1 ratio, the hell all that means?  well, it means

[tex]\cfrac{AB}{BC}=\cfrac{2}{1}\implies \cfrac{10}{BC}=\cfrac{2}{1}\implies 10=2BC\implies \cfrac{10}{2}=BC\implies \boxed{5=BC} \\\\\\ \stackrel{AB+BC}{10+5}\implies \stackrel{ AC }{\boxed{15}}[/tex]

Answer:

See below.

Step-by-step explanation:

We are asked to identify BC and AC.

Before we start, we should know that this triangle has a center called a Centroid.

A Centroid is a point that is formed by 3 concurrent medians.

A Median is a line segment that connects the vertex of a triangle to the midpoint of the opposite side.

The top part of a Median is 2/3 of the entire line segment. The bottom part of a Median is 1/3 of the entire line segment.

Using the information from above, we can identify that AB (10) is 2/3 of AC, and that BC is 1/3 of AC.

Divide 10 by [tex]\frac{2}{3}[/tex] to find AC.

[tex]10 \div ( \frac{2}{3} )=15 \ (AC)[/tex]

Since we know AC, we can now find BC by simply subtracting AC - AB.

[tex]15-10=5 \ (BC)[/tex]

Therefore, AC = 15; BC = 5.

The coordinates of the centroid (,)(△) of triangle ABC are (-1, 8/3).

To find the coordinates of the centroid, we can use the formula:

(x, y) = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3)

where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices A, B, and C, respectively.

Plugging in the coordinates of A (0, 4), B (0, 2), and C (-3, 2), we get:

(x, y) = ((0 + 0 - 3)/3, (4 + 2 + 2)/3) = (-1, 8/3)

In a two-dimensional plane, the centroid of a triangle is the point where the three medians of the triangle intersect. A median is a line segment drawn from a vertex of the triangle to the midpoint of the opposite side. The centroid divides each median into two segments, with the ratio of the length of the segment closer to the vertex to the length of the segment closer to the opposite side being 2:1.

In a three-dimensional space, the centroid of a solid can be found by dividing the solid into smaller parts, finding the centroid of each part, and then averaging them. The centroid of a solid is the point where the lines connecting the centroids of each part intersect.

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Complete Question: -

Give the coordinates of the centroid of triangle ABC, which is denoted by (,)(△) and is the point where the medians of the triangle intersect for a (0 , 4) , b (0 ,2) , and C  (-3 ,2 ).

Debra's two area baking plates are 17 square inches different in size.

The area surrounding a shape forms its perimeter. Area is a unit of measurement for interior space. Surface area is a measurement of a solid shape's exposed surface, whereas area is a two-dimensional measurement of the size of a flat surface (three-dimensional).

The square baking dish has the following surface area with an 8-inch side length:

Area of first square = (side length)² = 8² = 64 square inches

Similarly, the surface area of a square baking dish with 9-inch sides is:

Area of second square = (side length)² = 9² = 81 square inches

Difference in area = |Area of second square - Area of first square|

Difference in area = |81 - 64|

Difference in area = 17 square inches

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Answer:

y - 8 ≤ -27

Step-by-step explanation:

The difference of y and 8 is less than or equal to -27

y - 8 ≤ -27

Below, you will learn how to solve the problem.

(a) To find the linear relationship y = mx + b between x = year and y = profit, we first need to find the slope (m) and the y-intercept (b).

The slope (m) is the change in y (profit) divided by the change in x (year):
m = (17 - 5)/(6 - 2)

m = 12/4

m = 3

Next, we can use one of the data points (2, 5) and the slope (3) to find the y-intercept (b):
5 = 3(2) + b
b = 5 - 6

b = -1

So the linear relationship between x = year and y = profit is:

y = 3x - 1

(b) To find the company's profit at the end of 3 years, we can plug in x = 3 into the equation:
y = 3(3) - 1

y = 8

So the company's profit at the end of 3 years is $8 million.

(c) To predict the company's profit at the end of 8 years, we can plug in x = 8 into the equation:

y = 3(8) - 1 = 23

So the company's profit at the end of 8 years is predicted to be $23 million.

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The value of the expression a + 4 when a = 7 is 11.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

Function= a+4

Now,

By algebra

If a = 7, then we can substitute this value into the expression a + 4 to get:

=a + 4

= 7 + 4

= 11

Therefore, by algebra the answer will be 11.

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The complete question is;

Evaluate the expression a+4 when a=7?

(5g^(2)+6g-10)-(2g^(2)+2g+9) = 3g^(2) + 4g - 19

To subtract the two polynomials, we will use the vertical form. This means that we will line up the like terms and subtract them.

Step 1: Line up the like terms in the vertical form.

5g^(2) + 6g - 10

- (2g^(2) + 2g + 9)

Step 2: Distribute the negative sign to each term in the second polynomial.

5g^(2) + 6g - 10

- 2g^(2) - 2g - 9

Step 3: Subtract the like terms.

5g^(2) - 2g^(2) = 3g^(2)

6g - 2g = 4g

-10 - 9 = -19

Step 4: Write the final answer.

3g^(2) + 4g - 19

Therefore, the answer is 3g^(2) + 4g - 19.

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Answer:

y = -1/35x + 71/35

Step-by-step explanation:

slope of the perpendicular line = -1/35  (the negative reciprocal of 35)

use the point (1,2) and the point-slope form:

y - 2 = -1/35(x - 1)  now put it in slope-intercept form

y = -1/35x + 1/35 + 2

y = -1/35x + 71/35

0r,  y = -1/35(x - 71)

The equation of the line perpendicular to y = 35x − 4 and passing through the point (1, 2) is y = (-1/35)x + 71/35.

To find the equation of the line perpendicular to y = 35x − 4 and passing through the point (1, 2), we need to follow these steps:

y - 2 = (-1/35)(x - 1)

y - 2 = (-1/35)x + 1/35
y = (-1/35)x + 1/35 + 2
y = (-1/35)x + 71/35

So, the equation of the line perpendicular to y = 35x − 4 and passing through the point (1, 2) is y = (-1/35)x + 71/35.

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The number of stamps given for the books in question are :

To find the number of stamps needed for 1 book, the formula is :

= Stamps needed for 19 books / Number of books

= 380 / 19

= 20 stamps

For 7 books :

= 7 books x 20 stamps per book

= 140 stamps

For 12 books :

= 12 books x 20 stamps per book

= 240 stamps

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