Solving Systems and Missing Angles

*Show your work and write the rule used to solve each problem

The linear equation of f(n) would be -3/2 n + 4.

What is linear function f(n) ?

A linear function is one with the equation f(x) = ax + b, where a and b are real values. The gradient of the line is represented by a, while the y-axis intercept is represented by b. (which is sometimes called the vertical intercept).

A linear equation can be represented as f(n) = mn + b, where m is the slope and b is the y-intercept.

To find m and b, we can use two points from the table.

Let's use the points (6, -1) and (4, 2).

The slope, m, can be found using the formula:

m = (f(n2) - f(n1)) / (n2 - n1)

Plugging in the values from the points, we get:

m = (2 - (-1)) / (4 - 6)

m = 3 / (-2)

m = -3/2

Now that we have m, we can use one of the points and the slope to find b. Let's use the point (6, -1).

f(n) = mn + b

-1 = (-3/2)(6) + b

Solving for b, we get:

b = -1 + (3)(3) = 4

So the linear equation of f(n) is:

f(n) = -3/2 n + 4

Thus, The linear equation of f(n) would be -3/2 n + 4.

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If the distance to a star was suddenly cut in half, it would appear four times brighter.

The brightness of a star is directly proportional to the inverse square of its distance from us. This means that if the distance to a star is halved, its brightness will increase by a factor of four.

The relationship between brightness and distance can be expressed as follows:

B = k / d^2

where B is the brightness, k is a constant of proportionality, and d is the distance.

If the distance to the star is halved, it can be expressed as:

d' = d / 2

Plugging this into the equation for brightness, we get:

B' = k / (d / 2)^2

Expanding this and simplifying, we get:

B' = 4 * k / d^2

Since k is a constant, it cancels out and we are left with:

B' = 4 * B

This means that if the distance to a star was suddenly cut in half, it would appear four times brighter. In astronomical terms, this is equivalent to an increase of 2 magnitudes on the logarithmic magnitude scale.

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Answer:

(f•g)(-4) = f(g(-4)) = f(-21) = -43

The area bounded by the curve y = sin(x) and y = cos(x) for sin(x) = cos(x) as point of intersection is equal to 2√2.

Area bounded by the curve y = sin(x) and y = cos(x).

Point of intersection for sinx = cosx

⇒  x = π/4 and 5π/4

Required area

= [tex]\int_{\frac{\pi }{4} }^{\frac{5\pi }{4}}[/tex]( sinx - cosx)dx

= ( -cosx - sinx ) [tex]|_ {\frac{\pi}{4} }^ {\frac{5\pi}{4} }[/tex]

= [ -cos(5π/4) - sin(5π/4) ] - [ -cos(π/4) - sin(π/4) ]

= [ -( -1 / √2 ) - (-1 / √2 ) ] - [ -1 /√2 - 1 /√2 ]

= ( 1 + 1 ) / √2 + ( 1 + 1 ) / √2

=  ( 2 + 2 ) / √2

= 4 /√2

= 2√2

Therefore, the area bounded by the given curve is equal to  2√2.

The given question is incomplete, I answer the question in general according to my knowledge:

find the area of the region bounded by the curves y = sin(x), y = cos(x), where solution the points of intersection occur when sin(x) = cos(x), that is, when x = π/4 and 5π/4.

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Answer: Using the distributive property, an expression equivalent to 34 + 16 is

2 (17 + 8)

Answer:

Lin originally had 4 bags * the same amount of apples per bag = 4 * x apples.

After eating 1 apple from each bag, she was left with 4 * x - 4 apples = 28 apples.

Therefore, each bag originally contained x = 28 + 4 = 32 apples.

Effect of switching the explanatory response variables have on the regression line is E) The sign and value of m and the value of b all change.

The y-axis dependent variables and x-axis independent variables are shown as a regression line to show their linear relationship. By examining the data pattern the variables' effects have created, the correlation is established.

In a regression graph, the line closest to the data points is shown. By changing the value of x in the regression equation, his statistical tool assists in analyzing the behavior's of a dependent variable y when there is a change in the independent variable x.

Hence, The sign and value of m and the value of b all change.

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The equation that represents the given sitution is 3a-6 = 69. Rita saved $25.

What is an epression?

A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.

Assume that Rita saved $a.

Given that the cost of a skateboard is $6 less than three times what she has saved.

The mathematical expression of $6 less than three times what she has saved is 3a-6

The actual cost is $69.

According to the question,

3a-6 = 69

Add 6 on both sides:

3a = 69 + 6

3a = 75

Divide both sides by 3:

a = 75/3

a = 25

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The probability of rain in a place during a long weekend (Friday, Saturday, and Sunday) is 65% . The risk of rain is between 10% and 30% on all three days.

a) The risk of rain in the destination throughout the long weekend may be calculated by adding the chance of rain on each day, which is 10% + 25% + 30% = 65%. As a result, the probability of rain at the destination throughout the long weekend is 65%.

b) The notion of conditional probability may be used to calculate the likelihood that it will rain in the destination on all three days of the long weekend. It is the likelihood of rain on Sunday given that it has already rained on:

Friday and Saturday × (the probability of rain on Saturday given that it has already rained on Friday) × (probability of rain on Friday) ×( the probability of rain on Friday).

The best lower bound for this probability is the 10% chance of rain on any given day, and the best upper bound is the 30% chance of rain on any given day.

As a result, the likelihood of rain at the destination on all three days of the long weekend is between 10% and 30%.

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A linear inequality that forms a system of linear inequalities with y > x - 1, whose solution set is the empty set, is y < x - 1.

When taken together, y > x - 1 and y < x - 1 form a system of linear inequalities, but these two inequalities are contradictory and cannot both be true at the same time. Therefore, the solution set of this system is the empty set, meaning there are no solutions that satisfy both inequalities.

To explain in detail, consider the line y = x - 1. When x = 1, y = 0. If y > x - 1, then y must be greater than 0 when x = 1. But if y < x - 1, then y must be less than 0 when x = 1. These two inequalities cannot both be true at the same time, so the solution set of the system is the empty set.

This shows that when two contradictory linear inequalities are taken together, their solution set is the empty set. In this case, y > x - 1 and y < x - 1 are contradictory, and so their solution set is the empty set.

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--The given question is incomplete; the complete question is

"Write a linear inequality that, when taken with y > x - 1, forms a system of linear inequalities whose solution set is the empty set."

I would implement a random sampling approach to determine the rate of smoking among teenagers.

Simple random sampling is a form of probability sampling in which a selection of participants is chosen at random from a population. Each person in the population has an equal probability of getting chosen. The data is then collected from as big a percentage of this random selection as feasible.

The Simple Random Sampling method is a dependable way of gathering information in which every member of a population is picked at random, purely by chance.

Random sampling guarantees that the findings received from your sample are close to those obtained if the full population was surveyed. The simplest random sample gives each unit in the population an equal probability of being chosen.

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The measure of arc KT be 49 and the measure of arc LN be 17 then the measure of ∠M be 30°.

Simply put, the arc measure is the diameter of the arc relative to the circle. Since they both describe the same thing, it is literally the same as the central angle. The arc length is what you were presumably thinking about because it refers to both the length and the distance of the arc.

Divide the arc length by the circle's circumference, then multiply the result by 360 degrees to find the angle's measurement.

Any straight line connecting two places is considered an arc in general. The arc length is the measurement of an arc's length. An ordered pair of adjacent vertices is referred to as a graph arc in a graph. Any section of the circle's circumference (other than the complete curve) is referred to as an arc.

Let the measure of arc KT = 49 and the measure of arc LN = 17

measure of ∠M = 30°.

Therefore, the measure of ∠M be 30°.

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this is hard

Step-by-step explanation:

I think its 3.89 p/s

The probability that a person who passes through the security system is without any security hazards is 0.99.

Let A be the event that the person passed through the checkpoint

Let X be the event of a person being a hazard

Now, according to the problem,

P(X) = 0.023

P(not A/not X) = 0.015

P(A/X) = 0.01

We need to find P(A/not X)

Now we know that the conditional probability P(Q/R)

= P(Q ∩ R) / P(R)

We need to find P(A/not X) we need to know P(A ∩ not X) and P(not X)

We know that

P(Q/notR) = 1 - P(Q/R)

Hence P(A/ not X) = 1 - p(A/X)

= 1 - 0.01

= 0.99

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-3.6<- 10/3 is the answer for above question. -3.6 is lesser than -10/3.

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Your lack of cogscitis has a previous probability of 0.5 according to Dr. B.

Prior probability quantifies how likely a theory is to be correct before any supporting data are taken into account. Your lack of cognitis has a previous probability of 0.5 according to Dr. B. This means that according to Doctor B, there is a 50/50 likelihood that you do not have cognitis before any supporting evidence is considered. This impartial viewpoint is frequently employed in scientific research and medical diagnostics. Prior probability is a crucial component of Bayesian inference, which is used to update a hypothesis' probability after all available data has been considered. Prior probability can help scientists and medical practitioners make better decisions.

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The area of the region which is common after rotation of 45 degrees between the two squares is equal to 7.46 cm² and area of the blue region which is swept out by interior region is 1.5442cm².

Measure of the side of the square = 3cm

Degrees of rotation of the square by keeping center fixed = 45 degrees

The region which is swept out by the interior of the square

= Four isosceles right triangles formed at the corners

Sides of the each  isosceles right triangle be 's'

Hypotenuse = s√2

Side of the square ABCD is :

s + s√2 + s = 3

⇒ s = 3 / ( 2 + √2 )

⇒ s= 0.8787

Area of the isosceles right triangle formed at the corner

= s² /2

= 0.8787² /2

Area of four triangles = 4 (0.8787² /2)

                                   = 1.5442cm²

Area of the left octagon

= Area of square ABCD - Area of four triangles at the corners

= 3² - 1.5442

= 9 - 1.5442

= 7.456 cm²

=7.46 cm²

Therefore, the area of the region swept out of the square is 1.5442cm² and the area of the region common between two squares is 7.46cm².

The given question is incomplete, I answer the question in general according to my knowledge:

A square ABCD, with sides of 3 cm, is rotated by 45 degrees keeping its center fixed to result into another square, PQRS. What is the area of the region common to the two squares? what is the area of the blue region swept out by the interior of the square shown below?

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The amount compounded after 16 years is $641.88. Therefore, option D is the correct answer.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].

Given that, principal =$400, time period = 16 years and the rate of interest = 3%.

Here, Amount =400(1+3/100)¹⁶

= 400(1.03)¹⁶

= 400×1.605

= $641.88

Therefore, option D is the correct answer.

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Answer:

85%

Step-by-step explanation:

17 divided by 20, times 100 = 85%

So, 85% of the sheep had black wool.

Answer:

A

Step-by-step explanation:

Mateo has a balance of 1,460.89 dollars, and he knows that check 354 was for 25.79 dollars. Therefore, to find the amount, in dollars, X, of check 353, Mateo needs to subtract the known amount of check 354 from his current balance.

So, the equation that can be used to find the amount of check 353 is:

1,460.89 - 25.79 = X

Thus the correct answer is:

A. 1,225.70 + x = 1,460.89

Answer:

yes youre right its 1

Step-by-step explanation:

2% of 50 is

2/100 = x/50

it simplifies to 1/50 = x/50

so x = 1

Answer:

1

Step-by-step explanation:

2%=2/100=0.02

of means multiply

0.02*50=1

u were correct

In finance, a dividend is a portion of a company's profits that is distributed to its shareholders. Dividends can be paid in cash or in the form of additional shares of stock. It is a way for a company to return some of its profits to its shareholders.

The information provided for Windwept, Inc. for 2017 includes its income statement and balance sheet. The income statement shows the company's net sales, cost of goods sold, depreciation, earnings before interest and taxes, interest paid, taxable income, taxes, and net income.

The balance sheet provides information on the company's assets, liabilities, and equity, including cash, accounts receivable, inventory, and long-term debt.

However, the information provided does not include the total amount of dividends paid by the company. Therefore, it is not possible to determine the total dividends paid by Windwept, Inc. for 2017 based on the information given.

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Answer: There are 850 students total

Step-by-step explanation: First step is to analyze, 34 brought lunch which makes up 4% so to find total we will divide because dividing percentages gives you bigger numbers.

We will do 34/4%= 850

Therefore there are 850 students attending Ridgewood Junior High School

The volume of paper in the recycling bin is 6800 cubic inches.

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same. Volume of a rectangular prism = Area of a base × Height.

Given that, the area of the bottom of the bin is 400 square inches. Paper completely fills the bin to a height of 17 inches.

So, the volume of recycling bin is 400×17

= 6800 cubic inches

Therefore, the volume of paper in the recycling bin is 6800 cubic inches.

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Answer:

see below

Step-by-step explanation:

The circumference of a circle is 12πcm. = 2πr

so radius =6

diameter =2r =12

area = πr² =36π

The radius of the circle be 6 cm and diameter be the double of radius, diameter be 12 cm then the area of the circle be 36π cm².

A circle is round with no sides or corners. Circles can be big and small. Circles can be any color. Being round with no sides or corners is the defining attribute of a circle.

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”.

A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The points of circle are at a fixed distance from the center.

Let r be the radius of a circle, then its circumference of the circle be [tex]$2 \pi r$[/tex] and area of the circle be [tex]$\pi r^2$[/tex].

Circumference exists given to be [tex]$12 \pi$[/tex], we get

[tex]$$2 \pi r=12 \pi$$[/tex]

simplifying the above equation, we get

[tex]$r=\frac{12 \pi}{2 \pi}[/tex] = 6 cm

The radius of the circle be 6 cm and diameter be the double of radius, diameter exists 2 × 6 = 12 cm.

Area of the circle be [tex]$\pi \times 6^2=36 \pi \mathrm{cm}^2$[/tex].

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Using right triangle properties, The length of the guy wire, to the nearest foot is 11√(37) ft.

A triangle in which one of the interior angles is 90° is called a right triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the height and the base.

Here, 2 right triangles are formed. One between stake and pole and second between stake and cell tower.

The height of pole = 12 ft.

The distance between stake and pole = 2 ft.

The distance between pole and tower = 9 ft. so the The distance between stake and tower = 2 + 9 = 11 ft.

Let x is the angle between wire and ground.

from first right angled triangle,

tan x = 12/2

tan x = 6

from second right angled triangle

tan x = height of tower/(11)

6 = height of tower/11

height of tower = 66 ft

So, length of wire = √(66² + 11²)

⇒ length of wire = √[(11*6)² + 11²]

⇒ length of wire = √[11²(6²+1)]

⇒ length of wire = √[11²(36+1)]

⇒ length of wire = 11√(37) ft.

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Answer:

Graph B represents an increasing function

Step-by-step explanation:

If you look at the other graphs, they are either stagnant on one line or going downwards.

Graph B, on the other hand, is growing on both the x and y axis.

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When the larger number is divided by the smaller, the quotient is 2 and the remainder is 4 then the two numbers are 18 and 7.

The first number would be x, leaving the other number to be x+11 (which would make it the bigger number) the quotient is:

[tex]$\frac{x+11}{x}[/tex]

Since it had a remainder of 4, it meant that the numerator was 4 more than having the divisor going in evenly ( had 4 left over) or it would have gone in exactly 2 times

It will take away 4 from the number being divided into (for it was just 4 too big for the divisor going in evenly) making

[tex]$\frac{x+11-4}{x}=2$$[/tex]

combine on top

[tex]$\frac{x+7}{x}=2$$[/tex]

Multiply both sides by x so it cancels on the left side with the denominator, giving

x + 7 = 2 x

subtract the x from both sides leaving

7 = x

So 7 was the first number and 18(x+11) is the second number

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En 3 años Carlos ganará $12,724 de intereses.

If Carlos deposits $8000 at a monthly interest rate of 2%, he will earn 1440 in interest over the course of three years. This amount is calculated by first multiplying the amount of the deposit (8000) by the interest rate (2%) to determine the amount of interest earned each month (160).

La formula para calcular el interes compuesto es:

I = P(1+r/n)^(nt)

Donde:

I = Interes

P = Cantidad inicial

r = Tasa de interes

n = Numero de periodos por año

t = Numero de periodos

En este caso:

I = 8000 (1+ 0.02/12)^(12 x 3)

I = 8000 (1.0016667)^36

I = 8000 (1.5905350)

I = 12,724

En 3 años Carlos ganará $12,724 de intereses.

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