Mathematics High School

Which of the following rules represents the set of ordered pairs?
{(1, 2), (2, 3), (4, 5), (7, 8)}

ƒ(x ) = 2x + 1
ƒ(x ) = -x + 4
ƒ(x ) = x + 1

Answers

Answer 1
sub ur points into the answer choices to see which one is true. Keeping in mind that f(x) = y

f(x) = x + 1.....u will notice that if u sub in ur answer choices into this function, it come out true. 

f(x) = x + 1.....when x = 1 and y = 2 
2 = 1 + 1
2 = 2 (correct)

f(x) = x + 1...when x = 2 and y = 3
3 = 2 + 1
3 = 3 (correct)

it works for all ur points

so ur answer is : f(x) = x + 1 <==

Related Questions

Cloverville has a population of 25,000 people and is increasing at a rate of 0.2%. The population in 3 years will be
Approximately 25,500 people
Approximately 24,8500 people
Approximately 25,150 people

Answers

The formula is
A=pe^rt
A ?
P 25000
E constant
R 0.002
T 3years

A=25,000×e^(0.002×3)
A=25,150 ...Answer

The screen aspect of a widescreen tv is 16.9. What are the width and height of a 32 inch tv? Round answer to the nearest tenth of an inch.

Answers

check the picture below.

thus


[tex]\bf 32^2=w^2+\left( \cfrac{9w}{16} \right)^2\implies 32^2=w^2+\cfrac{(9w)^2}{16^2}\implies 32^2=w^2+\cfrac{9^2w^2}{16^2} \\\\\\ 32^2=\cfrac{16^2w^2+81w^2}{16^2}\implies 32^2\cdot 16^2=337w^2 \\\\\\ (32\cdot 16)^2=337w^2\implies \sqrt{(32\cdot 16)^2}=\sqrt{337w^2} \\\\\\ 32\cdot 16=w\sqrt{337}\implies \cfrac{32\cdot 16}{\sqrt{337}}=w\implies \boxed{\cfrac{512}{\sqrt{337}}=w}\\\\ -------------------------------\\\\[/tex]

and we can rationalize that to    [tex]\bf \cfrac{512}{\sqrt{337}}\cdot \cfrac{\sqrt{337}}{\sqrt{337}}\implies \boxed{\cfrac{512\sqrt{337}}{337}}[/tex]

thus, its height is    [tex]\bf h=\cfrac{9w}{16}\implies h=\cfrac{9}{16}\cdot \cfrac{512\sqrt{337}}{337}\implies \boxed{h=\cfrac{4608\sqrt{337}}{5392}}[/tex]

A ramp leading to the freeway overpass is 200 feet long and rises 37 feet. what is the measure of the angle formed between the ramp and the freeway?

Answers

The ramp,the rise and the base, when illustrated, will form a right triangle. The hypotenuse is the ramp which measures 200 ft long. The rise is the vertical height which measures 37 feet. As you can see in the picture, the arc drawn below the ramp to the horizontal line directing to the freeways is the unknown angle that we have to find.

First, we find the angle made between the ramp and the rise (dashed line). Let's denote this is angle α. We make use trigonometric functions like cosine. Cosine of an angle is equal to the ratio of its adjacent side to the hypotenuse. In equation form:

cos α = 37/200, where α is the angle of inclination of the ramp
cos α = 0.185
α =cos^-1(0.185)
α = 79.34°

Next, let's denote the unknown angle as angle β. When you add the right angle and angle α, the sum would be angle β. Therefore,

β = 90° + 79.34°
β = 169.34°  

A ramp leading to the freeway overpass is 200 feet long and rises 37 feet. The measure of the angle formed between the ramp and the freeway is

[tex]\mathbf{ \theta = sin^{-1} \Big ( \dfrac{37}{200} \Big)}[/tex]

From the information given:

The  measure of the angle formed θ between the ramp and the freeway overpass can be determined by using the sine angle which is:

[tex]\mathbf{sin \theta = \dfrac{opposite}{hypotenuse}}[/tex]

[tex]\mathbf{sin \theta = \dfrac{37}{200}}[/tex]

[tex]\mathbf{ \theta = \dfrac{1}{sin} \Big( \dfrac{37}{200}\Big)}[/tex]

[tex]\mathbf{ \theta = sin ^{-1} \Big( \dfrac{37}{200}\Big)}[/tex]

Therefore, the measure of the angle formed between the ramp and the freeway is

[tex]\mathbf{ \theta = sin^{-1} \Big ( \dfrac{37}{200} \Big)}[/tex]

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What is the length of the hypotenuse in the triangle below ?

Answers

The answer is B. Since you know the lengths of both legs of the triangle, you can use the Pythagorean Theorem to solve. The Pythagorean Theorem says "a squared plus b squared equals c squared. The square root of c is the length of the hypotenuse." Since there is no answer that says 19.799 (This is the approximate answer), then the answer is B.
You have isosceles right triangle or 45-45-90 degree triangle. 

In 45-45-90 triangles hypotenuse = x√2   [x=leg]

If leg = 14cm, then hypotenuse = 14√2 cm.

Which of the following would best represent a cosine function with an amplitude of 3, a period of pi/2 , and a midline at y = –4? (1 point)

f(x) = –4 cos 4x + 3

f(x) = 3 cos(x – pi/2 ) – 4

f(x) = 4 cos(x – pi/2 ) + 3

f(x) = 3 cos 4x – 4

Answers

To transform the function [tex]f(x)= cos(x)[/tex] to have the amplitude of 3, we need to multiply the constant 3 to the function f(x), so we have [tex]y=3f(x)[/tex]

To transform the function [tex]f(x)=cos(x)[/tex] to have the midline [tex]y=-4[/tex] we need to subtract [tex]f(x)[/tex] by 4, so we have [tex]y=f(x)-4[/tex], 

To transform the function [tex]f(x)=cos(x)[/tex] to have period of [tex] \frac{ \pi }{2} [/tex], we need to divide the original period [tex]2 \pi [/tex] by 4, so we have [tex]y=f(4x)[/tex]. Note that it is the [tex]4x[/tex] gives the effect of dividing the points on x-axes by 4 and the period is read on x-axes

Hence, the full transformation is given [tex]y=3f(4x)-4[/tex] which is the last option

Answer:

D) f(x) 3 cos 4x-4 (I just took it)

A family has two cars. the first car has a fuel efficiency of 15 miles per gallon of gas and the second has a fuel efficiency of 20 miles per gallon of gas. during one particular week, the two cars went a combined total of 675 miles, for a total gas consumption of 40 gallons. how many gallons were consumed by each of the two cars that week?

Answers

car 1 = x

 car 2 = y

x+y =40 gallons

x=40-y

15x +20y = 675

15(40-y) +20y = 675

600-15y +20y =675

600+5y = 675

5y=75

y=75/5 = 15 gallons

x=40-15 =25 gallons

 Car 1 used 25 gallons

 Car 2 used 15 gallons


The Pyramid of Giza is one of the largest pyramid structures still standing in Egypt. It is a right pyramid with a square base, a base length of 230 m, and height of 150 m.
The area of the base is __________
The volume is _________

Answers

Refer to the diagram shown below.

The square base has a base length of a = 230 m.
The area of the base is
A = a*a = 230*230 = 52,900 m²

The height is h = 150 m.
The volume is
V = (1/3)*A*h
    = (1/3)*52900*150
    = 2,645,000 m³

Answer:
The area of the base is 52,900 m²
The volume is 2,645,000 m³

Answer:

The area of the base is 52,900 m²

The volume is 2,645,000 m³

Step-by-step explanation:

Simplify 1 over quantity x minus 3 plus 4 over x all over 4 over x minus 1 over quantity x minus 3

Answers

We can begin this problem by creating a common denominator. our fraction is:

(1/(x-3)+4/x)/(x-1)/(x-3), giving us the common denominator of x(x-3). We then take each individual fraction in the complex fraction, making it so that each one has the denominator x(x-3). 1/(x-3) becomes x/x(x-3), 4/x becomes 4(x-3)/x(x-3), and (x-1)/(x-3) becomes x(x-1)/x(x-3).

Now, our fraction is (x/x(x-3)+ 4(x-3)/x(x-3))/x(x-1)/x(x-3), or simply ((x+4(x-3)/x(x-3))/x(x-1)/x(x-3)). If we multiply the numerator and denominator by x(x-3), we get the fraction (x+4(x+3))/(x(x-1)). 

Distributing the 4, we get (x+4x+12)/(x(x-1)), or (3x+12)/(x(x-1)). (I don't know if you want the denominator factored or not, but if you want it expanded then it's (3x+12)/(x^2-x).)

I hope this was easy enough to follow! I haven't written anything like this before so I'm sorry if it wasn't very good.

Given expression: [tex]\frac{\frac{1}{x-3}+\frac{4}{x}}{\frac{4}{x}-\frac{1}{x-3}}[/tex].

[tex]\mathrm{Least\:Common\:Multiplier\:of\:}x,\:x-3:\quad x\left(x-3\right)[/tex]

[tex]\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}[/tex]

[tex]\frac{4}{x}-\frac{1}{x-3}=\frac{4\left(x-3\right)}{x\left(x-3\right)}-\frac{x}{x\left(x-3\right)}[/tex]

[tex]=\frac{4\left(x-3\right)-x}{x\left(x-3\right)}[/tex]

[tex]=\frac{3x-12}{x\left(x-3\right)}[/tex]

[tex]\frac{4}{x}-\frac{1}{x-3}=\frac{x}{x\left(x-3\right)}+\frac{4\left(x-3\right)}{x\left(x-3\right)}[/tex]

[tex]=\frac{x+4\left(x-3\right)}{x\left(x-3\right)}[/tex]

[tex]=\frac{5x-12}{x\left(x-3\right)}[/tex]

[tex]\frac{\frac{1}{x-3}+\frac{4}{x}}{\frac{4}{x}-\frac{1}{x-3}}=\frac{\frac{5x-12}{x\left(x-3\right)}}{\frac{3x-12}{x\left(x-3\right)}}[/tex]

[tex]\mathrm{Divide\:fractions}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}[/tex]

[tex]=\frac{\left(5x-12\right)x\left(x-3\right)}{x\left(x-3\right)\left(3x-12\right)}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:x[/tex]

[tex]=\frac{\left(5x-12\right)\left(x-3\right)}{\left(x-3\right)\left(3x-12\right)}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:x-3[/tex]

[tex]=\frac{5x-12}{3x-12} \ \ \ : Final Answer.[/tex]

Decide if the situation involvesâ permutations, combinations, or neither. explain your reasoning.

Answers

it needs permutations of the order does matter, like 3 people ordering from a coffee shop to see who goes first.

Combinations are when the order doesn't matter, like if you had 3 numbers behind your back and you had to guess the 3 not in order

It needs neither when you don't need to find the amount of choices you have (or something similar) for something

what type of number can be written as a fraction where p and q are intergers and q is not equal to zero

Answers

These are known as rational numbers.

Irrational numbers are the opposite.

Hope this helps!

If the tire is flat, then I will have to change it. Using the statement above, first state your variables in terms of p and q and which variable represents which statement. Then write this statement in symbolic form.

Answers

Correct Answer:

p: The tire is flat. q: I will have to change it. p -> q

I need the blue one done! please help!!

Answers

 An opposite is a person or thing that is totally different from or the reverse of someone or something else.
Examples: Night and Day, Black an White, Alive and Dead, Awake and Sleeping
Can i get branielst

Solve for x. A.x=7.5 B.x=16 C.x=17.5 D.x=27.5

Answers

You can't solve for x. There is nothing more you can do to the equation. Are you sure your solving for x?

What does it mean for an equation to have no solution or infinitely many solutions?

PLEASE GIVE ME A DETAILED RESPONSE AS IM TAKING MODULE 7 ALGEBRA DBA TOMORROW AT 7PM

Answers

If an equation has no solution, no value of x will ever make the equation true. For example, x+1=x+2.
If an equation has infinitely many solutions, all equations of x will make the equation true. For example, x+1=1+x.

No-Solution implies an inconsistent equation, while infinitely many solutions indicate a condition that holds true for any value of variable.

When an equation has No-Solution, it means that there is no value of variable that satisfies equation. In other words, equation represents an inconsistent condition, and solution set is empty. For example, equation 2x + 5 = 2x + 7 has no solution because the variable x cancels out, leaving an inconsistency (5 ≠ 7),

When an equation has infinitely many solutions, it means that any value of variable will satisfy equation. The equation represents a condition that is always true, regardless of chosen value.

For example, the equation x + 5 = x + 5 has infinitely many solutions because any value of x will make the equation true (such as x = 1, x = 2, x = 3, and so on).

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How many sides does a polygon have with an interior angle of 108?

Answers

You wanna first find the exterior angle which is 180 - 108 = 72.
360/72 = 5

What of the above terms indicates imaginary parallel lines that circle the earth?

Answers

The imaginary lines drawn all over the Earth's surface are called the latitudes and the longitudes. The purpose of these lines are mainly for navigation in aircrafts and satellite geographic locations. Each place in the Earth has a specific coordinates in terms of latitude and longitude. For example, Philippines is located 12.8797° North, 121.7740° East.

Between these two, the imaginary lines parallel to the equator of the Earth are the latitudes. Imagine a Cartesian plane that is revolved about either the x or y axis. You would form a sphere with x and y coordinates. The x-coordinates or the horizontal axis with respect to the equator of the Earth are the latitudes. The vertical axis are the longitudes.

He number of years of education of self-employed individuals in the united states has a population mean of 13.6 years and a population standard deviation of 3.0 years. if we survey a random sample of 100 self-employed people to determine the average number of years of education for the sample, what is the standard deviation of the sampling distribution of (the sample mean)

Answers

We can solve this problem by using the formula:

s = σ / sqrt(n)

where,

s = standard deviation of the sample

σ = standard deviation of the population = 3 years

n = number of samples = 100

Substituting:

s = 3 years / sqrt (100)

s = 0.3 years                       (ANSWER)

What is the r value of the following geometric sequence?
64, 48, 36. 27

2/3

3/4

5/8

3/8

Answers

It's 3/4 because 48/64=r=3/4

What is the common difference of the following arithmetic sequence?
100, 102, 104, 106,…

Answers

The common difference in the arithmetic sequence 100, 102, 104, 106,... is 2.

Arithmetic Sequence: 100, 102, 104, 106,...

Common Difference: The common difference in an arithmetic sequence is the constant value by which each term is increased or decreased. In this sequence, the common difference is 2 because each term increases by 2.

Calculation: 102 - 100 = 2, 104 - 102 = 2, 106 - 104 = 2, so the common difference is 2.

triangle pqr is a right triangle. If PQ = 8, what is PR?

Answers

The answer for this is 4.

The 30-60-90 triangle is known as a special right triangle because its angles have a unique ratio of 1:2:3. The length of the side PR in ΔPQR is 4√3 units.

What is the 30-60-90 right triangle?

The 30-60-90 triangle is known as a special right triangle because its angles have a unique ratio of 1:2:3. Furthermore, the hypotenuse is twice the length of the shorter leg, and the larger leg is √3 times the length of the shorter leg.

For the given right-angled triangle, we can use the 30-60-90 rule. The 30-60-90 triangle is known as a special right triangle because its angles have a unique ratio of 1:2:3. Furthermore, the hypotenuse is twice the length of the shorter leg, and the larger leg is √3 times the length of the shorter leg.

Therefore, we can write,

PQ = 2(RQ)

8 = 2(RQ)

RQ = 4

PR = (RQ)√3

PR = 4√3

Hence, the length of the side PR in ΔPQR is 4√3 units.

The complete question is mentioned in the image below.

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What is a variable?

a.
A variable is an unknown number or value represented by a letter
c.
A variable represents a change in value
b.
A variable always represents the total amount
d.
A variable is always represented by the letter x




 

Please select the best answer from the choices provided

Answers

A variable is an unknown number or value represented by a letter. If there was an equation x+2=19, then x would be the variable, because it is a letter representing an unknown value
hope this helps:))
A.
A variable is an unknown number or value represented by a letter.

A variable is an unknown number or value represented by a lower case letter.

what are the coordinates of a point on the unit circle if the angle formed by the positive x- axis and the radius is 45°??

Answers

On the unit circle, the radius is 1 and the trigonometric ratios are:

sin(angle( = y-coordinate / radius = y-coordinate / 1 = y-coordinate = y

cos(angle) = x-coordinate / radius = x-coordinate / 1 = x

Then:

y = sin(angle) = sin(45°) = √2 / 2

x = cos (angle) = cos (45°) = √2 / 2

=> Answer: (√2 / 2 , √2 / 2), which is the option A)

No. Of roots in eq 8sec^x-6secx+1=0

Answers

Ok, let's assume it's "sec^2 x"

[tex] 8\sec^2x-6\sec x+1=0\\ 8\sec^2x-2\sec x-4\sec x+1=0\\ 2\sec x(4\sec x-1)-1(4\sec x-1)=0\\ (2\sec x-1)(4\sec x-1)=0\\ 2\sec x-1=0\\ 2\sec x=1\\ \sec x=\dfrac{1}{2}\\ x\in\emptyset\\\\ 4\sec -1=0\\ 4\sec =1\\ \sec x =\dfrac{1}{4}\\ x\in\emptyset [/tex]

So, the number of solutions (real ones) is 0.

Help please.........,

Answers

y-6 = -4(x+1)

y-6 = -4x-4

add 6 to each side

y=-4x+2

A is the correct answer

A shoe repairman is working with his assistant, who takes twice as long to repair a pair of shoes. Together they can fix 16 pairs of shoes in an eight-hour day. How long does it take the repairman to fix one pair of shoes by himself?

Answers

[tex]\boxed{\boxed{Answer: \tex{ }$45$ minutes}}[/tex]

Hello!

The number of pairs of shoes each man can repair is its speed times the time.

Call x the repair speed of the assistant. Then, the repair speed of the repairman is 2x, and the joint speed is 2x + x = 3x.

Also, the joint speed is 16 pairs in 8 hours = 16 pairs/ 8 hours = 2 pairs/hour.

Thus, we can equate:

[tex]3x = 2 pairs/hour, \text { or } x = (2/3) pairs / hour.$\\[/tex]

That is the speed of the assistant. Then, the speed of the repairman is:

[tex]2x = 2 (2/3) pairs/hour\\2x = (4/3) pairs/hour.[/tex]

That means that the repairman takes the inverse of 4/3 of an hour to repair one pair of shoes. That is 3/4 of an hour (to repair on pair)

3/4 of an hour is 45 minutes and this is the answer.

Final answer:

To find out how long it takes the repairman alone to fix a pair of shoes, we solve a joint work rate problem. By setting equations based on their combined and individual work rates, we find out it takes the repairman 0.75 hours or 45 minutes to fix one pair of shoes by himself.

Explanation:

To determine how long it takes the repairman to fix one pair of shoes by himself, we start by establishing the rates at which both the repairman and his assistant work.

Let's denote the time it takes the repairman to repair one pair of shoes by x hours.

Since the assistant takes twice as long, their time would be 2x hours for one pair.

Working together, their combined rate allows them to fix 16 pairs in 8 hours, or 2 pairs per hour.

Now, we express their combined work rate as the sum of their individual work rates.

The repairman's rate is 1/x pairs per hour, and the assistant's rate is 1/(2x) pairs per hour.

Together, this should equal their combined rate of 2 pairs per hour:

1/x + 1/(2x) = 2

Solving this equation for x, we first find a common denominator and get:

2/2x + 1/2x = 2

3/2x = 2

3 = 4x

x = 3/4

Therefore, it takes the repairman 0.75 hours, or 45 minutes, to fix one pair of shoes by himself.

Help me please!!!!!!

Answers

Let
V1 = volume of the smaller cube (with 1/3 cm sides)
V2 = volume of the box shown

The first volume is 
V1 = (1/3)*(1/3)*(1/3)
V1 = 1/27

The second volume is 
V2 = (5/3)*(4/3)*(2)
V2 = 40/9

Now divide the two volumes
(V2)/(V1) = (40/9)/(1/27) = (40/9)*(27/1) = 120

Therefore you can fit 120 of the smaller cubes in the larger box shown.

Susie is paying $558.16 every month for her $150,000 mortgage. If this is a 30 year mortgage, how much interest will she pay over the 30 years of payments?

Answers

558.16 x 12 = 6697.92 every year

6697.92 x 30 = 200937.60 total

200937.60-150000 = $50,937.60 total interest paid

The East Bay Deli, makes 6.85 pounds of pasta salad each day. West Bay Deli makes four times that amount each day. How many combined pounds of pasta salad is made per week between the two delis? Find a fourth of their combined weekly production of pasta salad.

Answers

The daily amounts of pasta made are
East Bay Deli: 6.85 lb
West Bay Deli: 4*6.85 = 27.4 lb

Total amount made per day is 
6.85 + 27.4 = 34.25 lb

Total amount made per week is
34.25*7 = 239.75 lb
Answer: 239.8 lb (nearest tenth)

A fourth of the combined weekly production is
(1/4)*239.75 = 59.9375 lb
Answer: 59.9 lb (nearest tenth)

Given a polynomial f(x), if (x + 7) is a factor, what else must be true?

f(0)=7

f(0)=-7

f(7)=0

f(-7)=0

Answers

f(-7)=0  

Because that makes the (x+7) factor equal zero and any other factor multiplied by zero also results in zero.

Answer:

f(-7)=0 that is option 4th is correct.

Step-by-step explanation:

If we have given any polynomial  then its factor means that value is giving zero of that polynomial

And opposite sign of factor is the zero of the polynomial

For example:

x+a is factor of any polynomial f(x) then f(-a)=0

Similarly, If x+7 is a factor of any polynomial then f(-7)=0

Hence, option 4th is correct.

2x – 4y = 12 3x – 6y = 21 solve

Answers

2x - 4y = 12.....= x - 2y = 6
3x - 6y = 21..= x - 2y = 7

these are parallel lines with no solution



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