Four students in an art class mixed red and blue paint to make purple. The amounts they used are shown in the table. Which student made a different shade of purple than the other students.

The height of a triangle with a hypotenuse of 23 and angle between base and hypotenuse of 75° is h= 23sin(75)

An equation is an expression that shows the relationship between two or more variables and numbers.

Trigonometric ratio shows the relationship between the sides and angles of a right angle triangle.

Let us assume that the right triangle has a altitude h, hypotenuse of 23 and angle between base and hypotenuse is 75°, hence:

sin(75) = h/23

h= 23sin(75)

The height of a triangle with a hypotenuse of 23 and angle between base and hypotenuse of 75° is h= 23sin(75)

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Answer:

x=0

Step-by-step explanation:

You can combine the equation to get 2sin(3/2 +x) = -2

divide both sides by 2 and you get the equation equal to -1. sin is equal to -1 when the value inside is 3/2 so this is the answer.

The system of equation that will represent her purchase is as follows:

1.39b + 2.49m = 50.73

1.29b + 2.69m = 51.63

At store A she will pay a total sum of $50.73 for bread and milk.

At store B she will pay a total sum of $51.63  for bread and milk.

Therefore, the system of equation that will represent her purchase is as follows:

where

b = number of bread

m = number of milk

Therefore,

1.39b + 2.49m = 50.73

1.29b + 2.69m = 51.63

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From the given information, the measure of DEF is 81°

From the question, we are to determine the measure of DEF

From the given information,

DEF and RST are complementary angles. This means they sum up to 90°

Thus,

(3(-5 + 2x)) + (x - 7) = 90

(3(-5 + 2x)) + (x - 7) = 90

(-15 + 6x) + (x - 7 ) = 90

-15 + 6x + x - 7 = 90

6x + x = 90 + 15 + 7

7x = 112

x = 112/7

x = 16

Then, substitute the value of x to determine the measure of DEF

(3(-5 + 2x))

= (3(-5 + 2(16)))

= (3(-5 + 32))

= (3(27))

= 81°

Hence, the measure of DEF is 81°

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the effects of the given transactions on the accounting equation are:

an investment would increase assets (cash) and also increase equity. every expense such as salaries would decrease assets and equity.

incurring debt would increase assets and liabilties while paying off debt would decrease both asset (cash) and liabilities.

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Answer:

no

Step-by-step explanation:

you have done your part by helping in their study session,if you help them cheat you will suffer the consequences if he/she is caught,

This is an academic integrity violation because it is against honesty rules, the best would be to offer assistance to your friend.

Academic integrity encompasses principles of honesty, fairness, and trustworthiness in academic pursuits. It generally includes a commitment to originality and independent work. Assisting someone in completing an exam, especially a take-home exam, where individual effort and understanding are expected, would likely violate academic integrity policies.

Handling the situation ethically and responsibly would involve respecting the academic rules and ensuring fairness for all students. Instead of directly completing the exam for your friend, you can offer assistance by explaining concepts, providing guidance on problem-solving approaches, or reviewing their completed work to identify errors or areas for improvement. This way, you can help your friend learn the material and develop their own understanding, without compromising academic integrity.

Encourage your friend to seek additional help from their professor, teaching assistants, or tutoring services provided by the institution. They can also engage in group study sessions or form study groups with classmates, which promote collaborative learning while maintaining individual effort.

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Answer:

3.25 years (nearest hundredth)

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for t:

[tex]\implies \sf 4916=4000\left(1+\frac{0.064}{4}\right)^{4t}[/tex]

[tex]\implies \sf 4916=4000\left(1.016\right)^{4t}[/tex]

[tex]\implies \sf \dfrac{4916}{4000}=\left(1.016\right)^{4t}[/tex]

[tex]\implies \sf \dfrac{1229}{1000}=\left(1.016\right)^{4t}[/tex]

[tex]\implies \sf \ln \left(\dfrac{1229}{1000}\right)=\ln \left(1.016\right)^{4t}[/tex]

[tex]\implies \sf \ln \left(\dfrac{1229}{1000}\right)=4t \ln \left(1.016\right)[/tex]

[tex]\implies \sf t=\dfrac{\ln \left(\frac{1229}{1000}\right)}{4\ln \left(1.016\right)}[/tex]

[tex]\implies \sf t=3.247594892...[/tex]

Therefore, it will take 3.25 years (nearest hundredth) for the account to grow to $4916.

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Step-by-step explanation:

1) 3 + 4 = 7

2) 6 - 6 = 0

3) 1 + 3 = 4

4) 6 + 9 = 15

5) 10 - 14 + 2 = -2

6) 2 + 3 - 5 = 0

Answer:

sqrt(172) = hypotenuse

Step-by-step explanation:

IF those are the leg lengths (sides) and not the hypotenuse, then use Pythagorean theorem

c^2 = 7^2 + sqrt (123) ^2

c = sqrt (172)

If sqrt 172 is the hypotenuse :

(sqrt123)^2 = 7^2 + x^2

then  x = sqrt (74 )

The perimeter of the rectangle as a function of its base is P = 2(b + 235/b)

The perimeter of a shape is the sum of the side lengths of the shape For all regular quadrilaterals, you add up the side lengths to determine the area

The given parameters are

Area = 235 sqare inches

The area of a rectangle is calculated using

Area = Base * Height

Note that the area of a shape is the amount of space on the shape

Recall that the area of a rectangle is calculated using

Area = Base * Height

Rewrite the above equation as

A = bh

So, we have

bh = 235

Make h the subject of the formula

h = 235/b

The perimeter of the rectangle is

P = 2(b + h)

So, we have

P = 2(b + 235/b)

Hence, the perimeter of the rectangle as a function of its base is P = 2(b + 235/b)

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Answer:

OA

Step-by-step explanation:

Answer:

6x-18

Step-by-step explanation:

6*(x-3)

multiply 6 with x and 3

Answer: Option 1

Step-by-step explanation:

The domain is the set of x values that make the radicand non-negative. Since the radicand is a perfect square, it will always be non-negative for any real value of x.

The equations that represent linear relationship is y – 5 = 2(x – 1)

Linear functions are functions that has a leading degree of 1. According to the question, we need to determine the function that represents linear equation.

The required equation must have a degree of 1 and must contain both dependent and independent variables.

The equations that represent linear relationship is y – 5 = 2(x – 1)  

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Answer:

The anser is:

A

C

D

E

Step-by-step explanation:

I hope this helps, have a blessed day :)

The equation of line that passes through a pair of points: (2, 3), (4, -2).is option B. y = -5/2 x + 8.

Suppose the given points are (x_1, y_1) and (x_2, y_2),

then the equation of the straight line joining both two points is given by

[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]

We need to find the equation of the line that passes through a pair of points: (2, 3), (4, -2).

So, the equation would be

[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]

[tex](y - 3) = \dfrac{-2 - 3}{4- 2} (x -2)\\\\\\(y - 3) = \dfrac{-5}{2} (x -2)\\\\\\2(y - 3) = -5 (x -2)\\\\2y - 6 = -5x + 10\\\\2y = -5x + 16\\\\y = -5/2 x + 8[/tex]

Hence, the equation of line is option B. y = -5/2 x + 8.

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Answer:B

Step-by-step explanation:

The value of x according to the equation in the task content is; -5.35 or -10.65.

The equation given in the task content is; (x + 8)² -7 = 0.

Hence, the equation can be solved as follows;

(x + 8)² - 7 = 0

x² + 16x +64 -7 = 0

x²+ 16x +57 = 0

By solving by means of the quadratic formula, we have;

x = -5.35

x = -10.65

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Answer:

a) 60,000 cubic cm; b) 60,000 mL; c) 60 L

Step-by-step explanation:

a) V = l x w x h

V = 50 cm x 40 cm x 30 cm = 60,000 cubic cm

b) 1 cubic cm = 1 mL, therefore 60,000 cubic cm = 60,000 mL

c) 1000 mL = 1 L; 60,000 mL = 60 L

Answer:

Step-by-step explanation:

We use the known identity:

sin (A + B)  sin A cos B + cos A sin B.

8 sin x cos 3x + 8 sin 3x cos x

= 8 (sin x cos 3x + sin 3x  cos x)

= 8sin (x + 3x)

= 8 sin 4x

Identity :

sin (A + B)  sin A cos B + cos A sin B

= 8 sin x cos 3x + 8 sin 3x cos x

= 8 (sin x cos 3x + sin 3x  cos x)

= 8sin (x + 3x)

= 8 sin 4x

The amount Barbara earned this month is  $1512.

Percentage can be described as a fraction of an amount expressed as a number out of hundred.

Barbara's earnings = percentage commission x worth of goods sold

7% x 21,600

0.07 x 21,600 = $1512

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Answer:

[tex]y = -\frac{x}{6} + \frac{14}{3}[/tex]

Step-by-step explanation:

So when you're solving for y you want to get y by it self meaning there should be nothing with y, including any coefficients. The first step is to usually move any terms to the other side and then divide by the coefficient of y so y "technically doesn't" have a coefficient, while it does, but that coefficient 1, so it doesn't really mean much.

Subtract x from both sides

[tex]6y = -x+28[/tex]

Divide both sides by 6

[tex]y = -\frac{x}{6} + \frac{14}{3}[/tex]

The given equation solved for y as y = (28 - x)/6.

The given equation is x+6y=28.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation can be solved for y as follows

Here, x+6y=28

⇒ 6y = 28 - x

⇒ y = (28 - x)/6

Therefore, the given equation solved for y as y = (28 - x)/6.

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It would take 2 hours for me at level 6 to be on the same level with my friend which is initially at level 5.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let t represent the time it would take to be on the same level with your friends. I am at level 6 and my friend is on level 4, hence:

5t = 4t + 2

t = 2 hours

It would take 2 hours for me at level 6 to be on the same level with my friend which is initially at level 5.

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Answer: 319.74 square mm

Step-by-step explanation:

[tex]6(7.3)^2=319.74[/tex]

Answer:

its the same as increasing x by 5 percent

Answer:

1.05x is the answer

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

I think it’s a trick question because “legs” can also mean like chair legs that hold it up. Therefore:

2 dogs = 8 legs

4 horses = 16 legs

1 giraffe = 4 legs

And a bed: 4 legs(things that hold it up)

And a chair: 4 legs (things that hold it up)

This is assuming that the bed is a normal bed with stools holding it up

And the chair has 4 piles aswell as no missing legs in the animals… lol

Cost of bench = x

Cost of garden table = x - 50

x - 50 + x = 700

2x - 50 = 700

2x = 750

x = 325

Answer:

x = 3

Step-by-step explanation:

We can use the following equation to solve for x:

[tex]315=9x-27+8x+24+5x-17+2x+23\\315=(9x+8x+5x+2x)+(-27+24-17+23)\\315=24x+3\\312=24x\\13=x[/tex]

The equation for the profit from selling the items is P =  40x-0.5x²-300. The values of x are 10 and 70.

We have the cost function in this question to be

Cx = 60x+300

Revenue = 100x−0.5x²

A. The revenue function is stated as the revenue - cost

= (100x−0.5x²)-60x+300

We have to open the equation

40x-0.5x²-300

B. when profit is 50 dollars

50 = 40x-0.5x²-300

We have to multiply both sides by 10

500 = 400x - 5x² - 3000

We have to collect like terms and form a quadratic equation

5x² - 400x - 3500 = 0

We have to solve the quadratic equation above using a quadratic calculator.

Hence

x = 10, 70

So the two values that would create a profit of 50 dollars is 10 and 70.

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