Find the values of sine, cosine, tangent, cosecant, secant, and cotangent for the angle θ in standard position on the coordinate plane with the point (−3,−5) on its terminal side.

sinθ=

cosθ=

tanθ=

cscθ=

secθ=

cotθ=

The probability of not landing on that colour or the complement is 3/4.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that, the probability of landing on a certain colour is p, we are asked to write an expression for the probability of not landing on that colour or the complement, and also suppose the probability of p is 1/4.

We know that, p(not an event) = 1 - p(E)

Therefore, the if the probability of landing on a certain colour is p, then the probability of not landing on that colour = 1 - p

Also,

If the probability of p is 1/4,

Then, p(not an event) = 1 - 1/4 = 3/4

Hence, the required expression is p(not an event) = 1 - p(E)

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Using the concept of proportion and substitution with the total money to be divided given, The answer is Carl gets $480, Stacy gets $720, and Peter gets $240.

Proportion refers to the relationship between two or more quantities or values, often represented as a ratio or fraction. It can also refer to the relative size or scale of something in relation to something else. In mathematics, a proportion is an equation that states that two ratios are equal. For example, "the ratio of apples to oranges is 2:3" can be written as the proportion "2/3 = x/y," where x and y represent the number of apples and oranges. In statistics, a proportion is a measure of the frequency with which an event occurs, often expressed as a decimal or percentage.

The substitution method is a technique used to solve systems of equations, which are sets of two or more equations containing multiple variables. The basic idea behind the substitution method is to solve for one variable in terms of the others in one equation, and then substitute that expression into the other equations. This can be done by isolating one variable by adding or subtracting other variables from both sides of the equation, and then using the resulting equation to express that variable as a function of the others. Once one variable is expressed in this way, it can be substituted into the other equations, allowing us to solve for the other variables.

S = 3P (Stacy gets three times as much as Peter)

P = C/2 (Peter gets half the amount that Carl gets)

C + S + P = 1200

We can substitute the first equation into the second one to get:

S = 3(C/2)

Now we can substitute the second equation into the first one to get:

C + 3(C/2) + C/2 = 1200

We can simplify this equation by multiplying out the 3(C/2) term and combining like terms to get:

5C/2 = 1200

Now we can solve for C by multiplying both sides by 2/5:

C = 480

Now that we know C = $480, we can use the earlier equations to find S and P:

S = 3P = 3(480/2) = $720

P = C/2 = 480/2 = $240

So Carl gets $480, Stacy gets $720, and Peter gets $240.

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The inequality that best represents the purchase made by Gabriela, given the number of hand soaps and lotions purchased, is x + y > 12

Gabriela bought more than 12 bottles of hand soaps and lotions which simply means that the total number of these items that Gabriela bought as more than  12 bottles when added together.

The inequality would therefore be:

Number of hand soaps + Number of lotions > 12

Assuming the number of hand soaps is x and the number of lotions is y, the inequality would be:

x + y > 12

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Answer:

reciprocal

Step-by-step explanation:

Reciprocal just means to turn it upside down.

Answer:

-2\x^2-1

Step-by-step explanation:

4q² + 8q +4 = (4q+4)(q+1) = 4(q+1)²

Given, 4q² + 8q +4

Factorization of the given equation takes place as follows:

the equation is a function of q

or f(q) = 4q² + 8q +4

we can write 8q = 4q + 4q

f(q) = 4q² + 4q+ 4q +4

now we can take (q+1) as common

f(q) = 4q(q+1) + 4(q+1)

or f(q) = (4q+4)(q+1) = 4(q+1)²

4q² + 8q +4 = (4q+4)(q+1) = 4(q+1)²

Therefore, the factors of 4q² + 8q +4 are (4q+4)(q+1) or 4(q+1)².

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Answer: 4 (q + 1)²



Step-by-step explanation:

I did the attached solution through middle term breaking meothod, but you could apply the whole square formula as well and get the same answer. i.e (a + b)² = a² + 2ab + b²

hope that helps...

The values of m in the graph of y = mx²-5x-2 have no x-intercepts are

m< 25/8.

A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed. We find it easier to graph linear equations when we consider intercepts.

Given a function y = mx²-5x-2 for not having the x-intercepts means that at any value of m function can not have the value zero or in other words function would not have any roots.

Thus for not having any root b² - 4ac < 0

For our function

a = m

b = -5

c = -2

substituting the values in the general formula

(-5)² - 4 * m * -2 < 0

25 + 8m< 0

m < 25/ 8

Therefore, The values of m are m 25/8 on the graph of y = mx2-5x-2, which has no x-intercepts.

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Width is 50 on each side and length.

Find the dimensions of the field if the length ?

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The equation of the line that represents the graph will be y = - 1.6x + 3.4.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

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

From the graph, the two points are (-1, 5) and (4, -3). Then the equation of the line is given as,

(y - 5) = [(- 3 - 5) / (4 + 1)](x + 1)

y - 5 = - 1.6(x + 1)

y = - 1.6x - 1.6 + 5

y = - 1.6x + 3.4

The equation of the line that represents the graph will be y = - 1.6x + 3.4.

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Answer:

Step-by-step explanation:

All triangle's angles have a sum of 180 degrees.

56 + 61 = 117

180 - 117 = 63

x = 63

Answer: x = 0, 16

Step-by-step explanation:

First square both sides

(sqrt2x+4 - sqrtx)^2 = 4

now distribute the inside using the (a-b)^2 = a^2 -2ab + b^2 property to get

2x+4 - (2sqrt 2x^2 +4x) + X = 4

3x=2sqrt 2x^2 +4x

9x^2 = 4(2x^2+4x)

9x^2 = 8x^2+16x=0

x^2-16x=0

x(x-16)=0

x=0, 16

Answer: Yes

Step-by-step explanation:

Answer:

Iniko's part is 4/15

Allea had the highest score

Step-by-step explanation:

Use the LCD 15 and convert the fractions:

Allea: 2/5 = 6/15

Loki:   1/3 = 5/15

Iniko score = 15/15 - 6/15 - 5/15 = 4/15

The solution to the expression -6.15/-8.2 is 0.75

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

-6.15/-8.2

Next, we cancel out the negative sign

So, we have the following representation

-6.15/-8.2 = 6.15/8.2

Using a calculator, we have the following result

So, we have the following representation

-6.15/-8.2 = 0.75

Hence, the solution is 0.75

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Answer:

-0.04 = decrease of 4%

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Average rate of change of function $f(x)$}\\\\$\dfrac{f(b)-f(a)}{b-a}$\\\\over the interval $a \leq x \leq b$\\\end{minipage}}[/tex]

Given interval:

Therefore:

Given values:

Substitute the values into the formula:

[tex]\begin{aligned}\textsf{Average rate of change}&=\dfrac{f(1940)-f(1920)}{1940-1920}\\\\&=\dfrac{45.3-46.1}{1940-1920}\\\\&=\dfrac{-0.8}{20}\\\\&=-0.04\end{aligned}[/tex]

Therefore, the average rate of change was -0.04 which is a decrease of 4%.

The probability that the student is absent is 3/20

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

The probability that the student will be absent and it will be on Monday is 3 /100.

The probability that it will be Monday is 1/5

Therefore the probability that the student will be absent any day is 3/100÷1/5 = 3/20

Since it is certain that it is Monday , the probability that it is Monday is 1.

Therefore, the probability that the student is absent on that Monday is 1 × 3/20 = 3/20

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Answer:

  B.  15, 20, ...

Step-by-step explanation:

You want to know which sequence of numbers has the steepest graph.

The slope (steepness) of the graph is the ratio of the change in y to the change in x. Here, we presume the x-values for each of these sets of points are 1, 2, 3, 4, ....

That means the slope will be the difference of adjacent y-values. Subtracting the first from the second, we get ...

  8 -4 = 4

  20 -15 = 5

  52 -50 = 2

  7 -4 = 3

The sequence in which the values differ by 5 has the largest difference, so will have the steepest graph:

  15, 20, 25, 30, ...

Answer:

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

Step-by-step explanation:

I am not sure if you wanted it in exactly 4 steps, But this is the way to do it.

If in exactly 4 steps, omit the third step. Then we would get:

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

Hope that helps ya

Answer:

10.12

Step-by-step explanation:

100%+6.5%=106.5%

106.5% divided by 100=1.065

155.75 multiplied by 1.065=165.87375..

165.87375-155.75=10.12375

which equals 10.12

a. The system of inequalities for this situation can be represented as:

x (number of snacks) ≥ 0

y (number of bottles of water) ≥ 0

2x + 2.25y ≤ 70 (total amount of money remaining)

y ≤ 4 (maximum number of bottles of water that can be carried on a tray)

7x + 7y ≤ 70 (total cost of tickets and snacks/drinks cannot exceed the amount given)

b. To graph the system, we can start by plotting the inequality 2x + 2.25y ≤ 70. This represents all the points that satisfy the inequality and forms a boundary line for the feasible region. The line will be a boundary line because it is less than or equal to 70.

We can plot the inequality y ≤ 4 as a horizontal line at y = 4. This represents the maximum number of bottles of water that can be carried.

Finally, we can plot the inequality 7x + 7y ≤ 70 as a boundary line. This represents the total cost of tickets and snacks/drinks that cannot exceed the amount given.

The feasible region will be the area between these lines, above the x-axis and y-axis, and below the line y=4.

The vertices of this feasible region will be the intersection points of the three lines, which are (10,0), (0,10) and (8,4)

c. The combinations of snacks and drinks that are possible are the ones that fall within the feasible region. Any point within the feasible region represents a valid solution in this context, because it satisfies all the constraints and is within the budget.

d. Every point within the feasible region represents a valid solution in this context, because it satisfies all the constraints and is within the budget.

e. One possible combination is (8,4) which is 8 snacks and 4 bottles of water, this combination is possible because it's within the feasible region and satisfies all the constraints. One combination that is not possible is (12,3), it's not possible because it's not within the feasible region and doesn't satisfy the constraint y ≤ 4.

f. To prove that the combination (8,4) is possible, we substitute these values into the system of inequalities:

2(8) + 2.25(4) = 35 ≤ 70 (total amount of money remaining)

4 ≤ 4 (maximum number of bottles of water that can be carried)

7(8) + 7(4) = 56 ≤ 70 (total cost of tickets and snacks/drinks cannot exceed the amount given)

To prove that the combination (12,3) is not possible, we substitute these values into the system of inequalities:

2(12) + 2.25(3) = 30.5 > 70 (total amount of money remaining)

3 > 4 (maximum number of bottles of water that can be carried)

7(12) + 7(3) = 63 > 70 (total cost of tickets and snacks/drinks cannot exceed the amount given)

As all the inequalities are not satisfied, the combination (12,3) is not possible.

A system of inequalities is a set of two or more inequalities that must be satisfied simultaneously. It is a way to represent a set of constraints using mathematical equations. These constraints can be related to a problem in a specific area, such as finance, engineering, or operations research. The solution set of a system of inequalities is the common set of solutions that satisfy all the inequalities in the system. The solutions can be represented graphically as a region in a coordinate plane called the feasible region, which is the set of all possible solutions.

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Answer:

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

Initial area is 2400 km².

Decrease rate is 8.5% per year.

The area after 8 years will be:

The area of the forest after 8 years will be 1,179 km².

The forest decreases exponentially each year. Each year, the forest would decline by 8.5% each year.

The exponential equation that would be used to determine the area of the forest in 8 years is:

Area of the forest = initial area x (1 - percent decrease/100)^number of years

Area of the forest = 2,400 x (1 - 8.5%/100)^8

Area of the forest = 2,400 x (91.5/100)^8

Area of the forest = 2,400 x 0.915^8

Area of the forest = 1,179 km²

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Answer:

-5a

Step-by-step explanation:

Think of it as 5-10 since both of them have "a"

5-10=-5

-5a

Answer:

-5a

Step-by-step explanation:

Algebra are algebraic expressions that can be used as variables and is subjected to BODMAS rule just like numerical expressions.

Example: 5b + 9b = 14b

Given from the question:

5a - 10a = -5a

The equation of the variation is y =7x.

When we are discussing about the idea of variation then on specie is changing with respect to the other. If the change is such that the both variables are increasing at the same time then we could say that we have a direct variation.

Now, we know that;

y=8.4 when x=1.2

Given that;

y α x

If we add k;

y = kx

8.4 = k 1.2

x = 8.4/1.2

x = 7

Then the equation is;

y =7x

This is the equation that has been used to produce the graph in the image attached to the answer given here.

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The sum of the sequence ∑₀⁵⁰⁰(2i - 312) is 94500

The sum of a sequence is the sum of terms of the sequence.

Given the sum ∑₀⁵⁰⁰(2i - 312).

To evaluate the sum, we expand the brackets.

So, we have that

∑₀⁵⁰⁰(2i - 312) = ∑₀⁵⁰⁰2i -  ∑₀⁵⁰⁰312

= 2∑₀⁵⁰⁰i -  ∑₀⁵⁰⁰312

Now, ∑₀⁵⁰⁰i is the sum of natural numbers

So, ∑₀⁵⁰⁰i = n(n + 1)/2 where n = 500

Also, ∑₀⁵⁰⁰312 = 312n where n = 500

Thus substituting these into the equation for the sum, we have that

∑₀⁵⁰⁰(2i - 312) = 2∑₀⁵⁰⁰i -  ∑₀⁵⁰⁰312

= 2n(n + 1)/2 - 312n

Given that n = 500, substituting n = 500 into the equation, we have that

∑₀⁵⁰⁰(2i - 312) = n(n + 1) - 312n

= 500(500 + 1) - 312 × 500

= 500(501) - 312 × 500

= 250500 - 156000

= 94500

So, the sum is 94500

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The solution of |2x - 1|= 5  are x=-2 and x=3.

Two or more expressions with an Equal sign is called as Equation.

The given equation is |2x - 1| = 5

2x-1=+5

Add 1 on both sides

2x=6

Divide both sides by 2

x=3

Now take 2x-1=-5

Add 1 on both sides

2x=-4

x=-2

The solution of |2x - 1|= 5  are x=-2 and x=3.

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Answer: If you're on the test, the answer should be B

Step-by-step explanation:

Answer:

[tex]\left(\frac{\pi}{4}, 0 \right), \left(\frac{3\pi}{4}, 0 \right), \left(\frac{5\pi}{4}, 0 \right), \left(\frac{7\pi}{4}, 0 \right)[/tex]

Step-by-step explanation:

The [tex]x[/tex]-intercepts are when [tex]y=0[/tex].

[tex]0 \leq x \leq 2\pi \implies 0 \leq 2x \leq 4\pi \\ \\ \cos 2x=0 \implies 2x=\frac{\pi}{2}, \frac{3\pi}{2}, \frac{5\pi}{2}, \frac{7\pi}{2} \\ \\ \implies x=\frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4} \\ \\ \therefore \left(\frac{\pi}{4}, 0 \right), \left(\frac{3\pi}{4}, 0 \right), \left(\frac{5\pi}{4}, 0 \right), \left(\frac{7\pi}{4}, 0 \right)[/tex]