Mathematics High School

Solve for x.5(x – 10) = 30 – 15x

Answers

Answer 1

[tex]5(x-10)=30-15x [/tex]
[tex]5x-50=30-15x [/tex]
[tex]20x=30+50 [/tex]
[tex]x=4.[/tex]

Answer 2

Answer:

x=4

Step-by-step explanation:

Related Questions

Sean used candle molds, as shown, to make candles that were perfect cylinders and spheres:
What is the approximate difference in the amount of wax needed to make a candle from each of these molds? Use π = 3.14.

18.0 cubic inches
28.26 cubic inches
37.0 cubic inches
56.52 cubic inches

Answers

We calculate for the volumes of each of the wax needed for the candles through the equations presented below.

For cylinder:
V = πr²h
where V is volume, r is radius and h is height.

Substituting the known values,

V = (3.14)(3 in)²(6 in)
V = 169.56 in³

For sphere:

V = 4πr³/3
Substituting the known values,
V = 4(3.14)(3 in)³ / 3 = 113.04 in³

The difference between the two volumes,

difference of volumes = 169.56 in³ - 113.04 in³
difference of volumes = 56.52 in³

Thus, the answer to this item is the last choice.

Jared is in charge of production in a factory that makes lightbulbs. The factory made 2,648 lightbulbs over the weekend. Jared wants to pull a sample of these bulbs for testing. Which sample would give Jared the most-accurate test results? a sample consisting of every 20th lightbulb a sample consisting of every 40th lightbulb a sample consisting of every 50th lightbulb a sample consisting of every 100th lightbulb

Answers

Ideally, the smaller the sample population, the more accurate is the sampling result, but it will take longer time if the number of samples is huge.

The answer to the above question is ideally 20 light bulbs per sampling.

if the reserve rate is 3% and a bank receives a deposit of 16,000 how much of the 16,000 is the bank free to loan out?

Answers

that means the bank keeps 3% and can loan out 97% of the total

16000*0.97 = $15,520 can be loaned out

2x+7=12x-6 looking for x

Answers

Hey!

Let's start by writing the problem:
[tex]2x+7=12x-6[/tex]
Subtract 7 from both sides.
[tex]2x+7-7=12x-6-7[/tex]
[tex]2x=12x-13[/tex]
Subtact 12x from both sides.
[tex]2x-12x=12x-13-12x[/tex]
[tex]-10x=-13[/tex]
Divide both sides by -10.
[tex]\frac{-10x}{-10}=\frac{-13}{-10}[/tex]
[tex]x=\frac{13}{10}[/tex]

Let me know if you have any questions regarding this problem!
Thanks!
-TetraFish

2x+7=12x-6 subtract 12x from both sides

-10x+7=-6 subtract 7 from both sides

-10x=-13 divide both sides by -10

x=13/10

x=1.3

What is the length of a diagonal of a cube with a side length of 3 cm? (ALL OF THE ANSWERS ARE SQUARE ROOTED) 18,27,33,38

Answers

The three dimensional diagonal of a rectangular prism is:

d^2=x^2+y^2+z^2, and since this is a cube, x=y=z=s, and we are told that s=3

d^2=3s^2 and s=3

d^2=3(3^2)

d^2=3(9)

d^2=27

d=√27

Answer:

Step-by-step explanation:

i just took the test

Find the value of x to the nearest tenth. See linked picture below. Thanks!

Answers

Answer: Choice D) 11

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

Work Shown:

cos(angle) = adjacent/hypotenuse
cos(35) = 9/x
x*cos(35) = 9
x = 9/cos(35)
x = 10.9869712988531 ... make sure your calculator is in degree mode
x = 11 ... rounding to the nearest tenth

Angle C is an inscribed angle of circle P. Angle C measures (5x-7) degrees and arc AB measures (2x) degrees. Find x.

Answers

This is the concept of geometry, the vale of x can be found as follows;
angle C and arc BC are supplementary angles, therefore:
(5x-7)+2x=180
7x-7=180
7x=187

x=187/7
x=26 5/7

There are 5273 students in school. There are 231 more girls than boys. List the number of boys that attend this school.

A.5042
B.231
C.2752
D.2521

Answers

B + G = 5273
G = B + 231
B + B + 231 = 5273
2B + 231 = 5273
subtract 231 from both sides
2B = 5042
divide both sides by 2
B = 2521
G = 2521 + 231
G = 2752

There are 2752 girls and 2521 boys LETTER D

Two trucks leave a warehouse at the same time. one travels due north at an average speed of 4747 miles per hour, and the other travels due south at an average speed of 5050 miles per hour. after how many hours will the two trucks be 388388 miles apart?

Answers

the combined speed are 47 + 50 = 97 mph

required number of hours = 388/97 = 4 hours

Let f(x) = 27x5 − 33x4 − 21x3 and g(x) = 3x2. Find f of x over g of x

Answers

The answer is 9x3 − 11x2 − 7x

Answer: 9x^3 − 11x^2 − 7x

Find the take home percent of the gross pay: net pay $298.76, gross pay $402.38. round to the nearest percent.

Answers

298.76 / 402.38 = 0.742 = 74%

An automobile engineer is redesigning a conical chamber that was originally specified to be 12 inches long with a circular base of diameter 5.7 inches. In the new design, the chamber is scaled by a factor of 1.5. The volume of the original chamber is cubic inches. This is cubic inches less than the volume of the new chamber. NextReset

Answers

Original chamber:
Length, L = 12 in.
Base diameter, d = 5.7 in.
The volume is
V = (1/3)*(πd²/4)*L = (1/3)*(π/4)(5.7 in)²*(12 in) = 102.07 in³

Scaled chamber:
Because the scale factor is 1.5, obtain
Length = 1.5*12 = 18 in.
Base diameter = 1.5*5.7 = 8.55 in
The new volume is
V (1/3)*(π/4)*(8.55 in)²*(18 in) = 344.49 in³

Differenc in volumes = 344.49 - 102.07 = 242.42 in³

Answer: 242.4 in³ (nearest tenth)

Answer:

added pictures of all the questions on this test

Step-by-step explanation:

2. A ski resort is building a new ski lift that will transport tourists from the base of the mountain to its highest point. This mountain has a vertical height of 200 yards, and the ski lift will rise at an angle of 40 degrees. When the project is completed, how many yards, d, will a tourist travel from the base of the mountain to its peak?
Part I: Sketch a figure to illustrate the scenario above. Label the vertices and the lengths that are given in the question. (3 points)

Part II: Using your sketch from Part I, write an equation using a trigonometric ratio to find the distance a tourist will travel from the base of the mountain to its peak. Round your answer to the nearest 100th. Show your work. (2 points)

3. Darcy mounted a motion sensor so it would light a path to the door on her deck. If you know AB = 10 feet, and BE and BD trisect ∠ABC, what is the perimeter of the deck area to the right of the beam of light (△BDC)?

Part 1: What other angles or sides of △BDC can you label given that side AB is 10 feet, BE and BD trisect ∠ABC? Label the diagram accordingly, and explain your reasoning. (4 points)

Part 2: Use the trigonometric ratios 30° and 60° to calculate and label the remaining sides of △BDC. Show your work. (3 points)

Part 3: Use the Pythagorean Theorem to calculate the length of side BD. Does this method verify the length you found using trigonometric ratios? (2 points)

Part 4: What is the perimeter of the area to the right of the beam of light on Darcy's deck (△BDC)? Show your work. Use your calculator to round your final answer to the nearest foot. (3 points)

4. Two cars are starting from positions that are 20 miles apart. They are both headed for the same intersection, as depicted in the diagram below. Car A is traveling at 30 mph, and Car B is traveling at 45 mph. Which car will reach the intersection first?

Part I: Use the law of cosines to determine how far Car B has to travel to reach the intersection. (2 points

Part II: Use to determine the time necessary for Car A to reach the intersection. Round your answer to the nearest hundredth of an hour. (1 point)

Part III: Use to determine the time necessary for Car B to reach the intersection. (1 point)

Part IV: Which car reaches the intersection first, and by how many hours? (2 point

5. Solve for the missing length and the other two angles in the triangle below.

Part I: Use the law of cosines to find the missing third side. (2 points)

Part II: Use either the law of cosines or the law of sines to find the measure of angle C. (2 points)

Part III: Use any method you like to find the measure of angle B. (1 point)

6. Solve the triangle below.

Part I: Use the law of cosines to find the measure of angle B. (2 points)

Part II: Use the law of sines to find the measure of angle C. (2 points)
Part III: Use any method you like to find the measure of angle A. (1 point)

7. Assume two people, Swanson and Suzie, are standing 35 feet apart and are watching a boat race. At a given moment, Swanson approximates the angle formed by the lead boat, himself, and Suzie to be . Suzie approximates the angle formed by the lead boat, herself, and Swanson to be . How far is the boat from Swanson?

Part I: What is the missing angle in this triangle? (1 point)

Part II: Use the law of sines to find the distance from Swanson to the boat. (2 points)

8. Solve the following triangle for all missing sides and angles.

Part I: Find the measure of angle B. (1 point)

Part II: Use the law of sines to find the length of side a. (2 points)

Part III: Use any method to find the length of side c. (2 points)

Answers

You are given the mountain that has a vertical height of 200 yards, and the ski lift will rise at an angle of 40 degrees. You are asked to find how many yards will a tourist travel from the base of the mountain to its peak. You can solve this using trigonometric function. More importantly, imagine that the mountain has a 90 - degree vertical height so that when you connect the peak of the mountain down to its base and then connected to the ski, you can form a right triangle.

Use the sine function.
sine β = opposite side / hypotenuse side
the opposite side will be the height of the mountain and the hypotenuse side will be the distance of the ski from the bottom going to the peak of the mountain

sine 40° = 100 yards / hypotenuse side
hypotenuse side = 100 yards / sine 40°
hypotenuse side = 156 yards

Answer:

156

Step-by-step explanation:

Use the sine function.

sine β = opposite side / hypotenuse side

the opposite side will be the height of the mountain and the hypotenuse side will be the distance of the ski from the bottom going to the peak of the mountain

sine 40° = 100 yards / hypotenuse side

hypotenuse side = 100 yards / sine 40°

hypotenuse side = 156 yards

In triangle abc, the measure of angle b is 29 degrees° more than three times the measure of angle

a. the measure of angle c is 61 degrees° more than the measure of angle

a. find the measure of each angle.

Answers

Answer:

∠a = x

∠b = 3x + 29

∠c = x + 61

x + 3x + 29 + x + 61 = 180

5x = 180 - 29 - 61

5x = 90

x = 90/5

x = 18° ← ∠a

∠b = 3x + 29 = 3*18 + 29 = 83°

∠c = x + 61 = 18 + 61 = 79°

Step-by-step explanation:

What is another name for angle 2?

Answers

The rays MR and MP intersects at the point M, this means the point M is the vertex of the ∠2.

Another name for ∠2 is ∠PMR.

Final answer:

Angle 2 could refer to different things, such as an angular velocity, a direction angle, or a contact angle, depending on its context within a mathematical or physical scenario.

Explanation:

In mathematical terms, angle 2 refers to a particular position or orientation, typically specified in degrees. For instance, if points 1 and 2 rotate through the same angle (AO), angle 2 might move through a greater arc length because it is farther from the center of rotation. This concept is related to the mathematical definition of angular velocity, defined as radians per unit time.

Alternatively, angle 2 could also refer to the direction angle, which is the angle measured counterclockwise from the positive direction on the x-axis to a vector. This term is often used when calculating vector components. In this context, a positive angle indicates a counterclockwise rotation, whereas a negative angle implies a clockwise rotation.

Finally, angle 2 might specify the contact angle, which is the angle between the tangent to the liquid surface and the surface itself. To figure out the precise name for angle 2 in your particular context, I would need further information about the specific scenario or diagram you're referring to.

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A normal distribution has a meaning of 50 and a standard deviation of 6. What is the probability that a value selected at random from this data is in the interval from 50 to 62 ? Express your answer as a percent rounded to the nearest 10th

Answers

We first need to standardise the value X=50 and X=62, in other words, find the z-scores.

The formula to find z-score is (X-μ)/σ

Where μ is the mean score which in this case is 50 and σ is the standard deviation = 6

Z-score for X = 50 ⇒ (50-50)÷6 = 0÷6 = 0
Z-score for X = 62 ⇒ (62-50)÷6 = 12÷6 = 2

Presenting this information on a normal distribution bell curve, the area we need is in between z = 0 and z = 2

P(0<z<2) = P(z<2) - P(z<0)
P(0<z<2) = 0.9772 - 0.5
P(0<z<2) = 0.4772

As a percentage, the probability is 0.4772 × 100 = 47.72%

Suppose x=10 and y=10. what is x after evaluating the expression (y>= 10)||(x++ >10)? java

Answers

Suppose x=10 and y=10. what is x after evaluating the expression (y>= 10)||(x++ >10)? java
Answer is 10

Final answer:

The value of x remains 10 after evaluating the Java expression (y >= 10)||(x++ > 10) due to short-circuit evaluation, as the first condition y >= 10 is true.

Explanation:

The student is asking about the value of x after evaluating the Java expression (y >= 10)||(x++ > 10) given that x=10 and y=10. The double pipe || represents a logical OR operator, which evaluates to true if at least one of the operands (conditions) is true. Since y >= 10 is true because y is equal to 10, the OR expression is true, and Java does not evaluate the second operand due to short-circuit evaluation. Short-circuit evaluation means that in an OR expression, if the left-hand side is true, the right-hand side is not evaluated, which in this case means that x++ is not executed. Therefore, x remains 10.

Which correlation should be used to measure the relationship between gender and grade point average for a group of college students??

a. ?point-biserial correlation

b. ?pearson correlation

c. ?phi-coefficient

d. ?spearman correlation?

Answers

I believe the correct answer would be A. The best correlation to use to measure the relationship between gender and grade point average for a group of college students would be the point-biserial correlation. It is coefficient that is used when a variable is dichotomous or that the variable is part of a whole set. It is used in measuring the direction of the correlation that is present between a dichotomous variable and a continuous variable. From the question, the dichotomous variable would be the grade point average for a group of college students while the other variable is the continuous one.

Two mechanics worked on a car. the first mechanic worked for 20 hours, and the second mechanic worked for 5 hours. together they charged a total of $1900 . what was the rate charged per hour by each mechanic if the sum of the two rates was $155 per hour?

Answers

20x + 5y = 1900
x + y = 155....multiply by -20
----------------
20x + 5y = 1900
-20x - 20y = - 3100 (result of multiplying by -20)
--------------add
-15y = -1200
y = -1200/-15
y = 80 <== 80 per hr for the mechanic that worked 5 hrs

x + y = 155
x + 80 = 155
x = 155 - 80
x = 75 <== 75 per hr for the mechanic that worked 20 hrs

BARNEY'S BICYCLE SHOP IS SELLING T-SHIRTS AT THE LOCAL HEALTH FAIR. THEY PLAN ON SELLING SHIRTS FOR $8 EACH. TO HAVE THE SHIRTS MADE, BARNEY'S BICYCLE SHOP PAYS THE SHIRT MAKER $3.50 PER SHIRT PLUS AN INITIAL FEE OF $63. HOW MANY SHIRTS MUST BARNEY'S BICYCLE SHOP SELL BEFORE THEY CAN MAKE A PROFIT?

A. 9 SHIRTS
B. 8 SHIRTS
C. 14 SHIRTS
D. 11 SHIRTS

Answers

STOP SHOUTING, WHOSE SHOUTING, I'M NOTTTTT

so

shirts are being sold 8 doolars each
shirts cost 3.5 to make plus initial fee of 63

how much to make a profit

ok, amount they make=cost per shirt times number of shirts=8 times x where x is number of shirts of 8x

cost he needs to pay=3.5x+63

when will his profit be more than what he's paying

8x>3.5x+63
solve
mnus 3.5x both sides
4.5x>63
divide both sides by 4.5
x>14

needs to sell at least 14 shirts
hmm, ok, 14 is the answer then

C is answer

Barney's Bicycle Shop must sell at least 14 shirts before they can make a profit. Among the given options, the correct answer is C. 14 shirts.

To determine the number of shirts Barney's Bicycle Shop must sell before making a profit, we need to consider the cost of producing the shirts and the revenue generated from selling them.

For each shirt sold, the shop earns $8 in revenue. However, they incur costs to have the shirts made. The shirt maker charges $3.50 per shirt and an initial fee of $63.

Let's calculate the total cost per shirt:

Cost per shirt = $3.50 + ($63 / number of shirts)

To break even or make a profit, the revenue from selling the shirts must exceed the cost per shirt.

Let's calculate the revenue per shirt:

Revenue per shirt = $8

Now we can set up the equation to find the number of shirts needed to break even or make a profit as inequality:

Revenue per shirt ≥ Cost per shirt

$8 ≥ $3.50 + ($63 / number of shirts)

To solve this inequality, we can subtract $3.50 from both sides:

$4.50 ≥ $63 / number of shirts

Multiplying both sides by the number of shirts:

$4.50 x number of shirts ≥ $63

Simplifying the equation:

Number of shirts ≥ $63 / $4.50

Number of shirts ≥ 14

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Today Javier put a cabinet on layaway by making a down payment of $80 and agreeing to pay $24 a month starting next month for 36 months. When will Javier receive the cabinet ?
A. 1 month
B. Today
C in 24 months
D in 36 months

Answers

Answer:

Option D is the answer.

Step-by-step explanation:

A layaway is a system of paying a deposit to secure an item that is meant to be purchased later. In this purchasing method, a buyer places a deposit on an item to lay it away. He can pick the item later when he pays the balance. The balance can also be paid in smaller installments until the full amount is paid.

So, here Javier will be paying for 36 months, hence, he will get the cabinet after 36 months.

PLEASE HELP ME AND TRY TO ANSWER THIS PLS PLS PLS AND IF YOU CAN DO THIS ONE AND HELP ME CAN YOU PLEASE GO BACK TO MY LAST PROBLEM AND TRY TO SOLVE IT IF IT HASNT ALREADY BEEN SOLVED I AM RUSHING SO FAST RIGHT NOW PLEASE TRY TO HELP AND ANSWER IT ASAP IT WOULD BE A HUGE HELP!

Answers

The solution is (4.75,-22)

Jerome earns $200 per month plus $12 for bike he sells at the bike shop.This month, he wants t6o earn at least $400. Whats the least bikes that jerome can sell to reach his goal.

Answers

The total amount that Jerome would earn is the sum of the basic salary and the commission he gets based on the number of bikes he is able to sell.

Let x be the number of bikes he sold. With this representation, the total commission he will get is 12x.

The sum of 200 and 12x should be greater than 400. The equation that best represent the given is scenario is,
200 + 12x > 400
Transposing 200 to the other side of the equation,
12x > 400 - 200
Simplifying,
12x > 200
Dividing the equation by 12 will give us the final answer of,
x > 16.67

ANSWER: 17 bikes

Statistics??? Construct a 95% confidence interval for the population mean. Assume the population has a normal distribution. A sample of 20 college students had mean annual earnings of $3120 with a standard deviation of $677.

Answers

Given:
μ = $3120, population mean
σ = $677, population standard deviation.
The population is normally distributed.
n = 20, sample size.

At the 95% confidence level, the confidence interval is
[tex]( \mu - 1.96\frac{\sigma}{ \sqrt{n} } ,\, \mu + 1.96\frac{\sigma}{ \sqrt{n} }) [/tex]

1.96(σ/√n) = 1.96(677/√20) = 296.71
Th confidence interval for the mean is
($2823.29, $3416.71)

Answer: ($2823.29, $3416.71)

At a certain university the student to teacher ratio is 16:1. If there are 2,000 students enrolled, how many teachers must be employed to maintain this ratio?

A. 28,000 B. 200 C. 215 D. 125

Mark for review (Will be highlighted on the review page)

Answers

Answer:

D. 125

Step-by-step explanation:

Ratio between students and teacher = 16:1 , 16/1 =2000 /x , x = 2000/16 = 125 teachers

The number of teachers in the school will be 125. The correct option is D.

What are ratios and proportions?

A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio could be written as 1: 3.

Given that at a certain university the student-to-teacher ratio is 16:1. If there are 2,000 students enrolled.

The number of teachers will be calculated as,

16 / 1 = 2000 / t

t = 2000 / 16

t = 125 teachers

Therefore, the count of teachers in the school is 125.

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An aquarium tank holds 169 gallons of water. How much is this in liters? Use the following conversion: 1 gallon is 3.8 liters.

Answers

There are 642.2 Liters of water

Final answer:

To convert gallons to liters, you multiply the number of gallons by the conversion factor 3.8. Therefore, an aquarium tank holding 169 gallons contains 641.2 liters of water.

Explanation:

The question is asking about converting gallons to liters. The process involves simple multiplication using the conversion rate.

Given that the volume of water in the aquarium tank is 169 gallons and that 1 gallon is equivalent to 3.8 liters, you can find the volume in liters by multiplying the number of gallons by the conversion rate. Therefore, 169 gallons * 3.8 liters/gallon equals 641.2 liters.

This means there are 641.2 liters of water in the aquarium tank.

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What is the inverse of f(x)=70x^3/4 ?

Answers

y/70=x^3/4
x=(y/70)^(4/3)

Final answer:

The inverse of the function [tex]f(x) = 70x^{(3/4)[/tex] is [tex]f^{(-1)}(x) = (x/70)^{(4/3)[/tex].

Explanation:

The inverse of the function [tex]f(x) = 70x^{(3/4)}[/tex] can be found by interchanging the roles of x and y and solving for y. The goal is to isolate y on one side of the equation.

Step 1: Replace f(x) with y: [tex]y = 70x^{(3/4)}[/tex]

Step 2: Swap x and y: [tex]x = 70y^{(3/4)}[/tex]

Step 3: Solve for y: Divide both sides of the equation by 70 and raise both sides to the power of 4/3 to undo the exponent: [tex]y = (x/70)^{(4/3)}[/tex]

Therefore, the inverse of [tex]f(x) = 70x^{(3/4)}[/tex] is [tex]f^{(-1)}(x) = (x/70)^{(4/3)}[/tex].

On a recent trip, I took a cab from the airport to my hotel. These were the cab fares posted on the door of the cab: $2.20 for the first 1⁄2 mile and 30 cents for each additional 1/5 mile. How far did I travel if my fare was $17.20? What would my fare be if I were to travel 16.8 miles? What would my fare be if I were to travel n miles? What kind of relationship is this? Justify your response and provide a visual representation (a graph) of the relationship.

Answers

We have the fixed cost of $2.20
For every mile travelled the fare is 5 × 30cents = $1.50

If the fare was $17.20, the number of miles travelled is [tex] \frac{17.20-2.20}{1.50} = 10 [/tex] miles

The fare for travelling 16.8 miles is [tex]2.20+1.5(16.8)=$27.40[/tex]

The fare for travelling n miles is [tex]C=2.20+1.5n[/tex]

The relationship is a linear relationship as there is a constant increase of $1.50 for every mile travelled. The graph of the relationship is shown below

5inches is what fraction of a foot?

Answers

One foot is equal to 12 inches. The question is asking: 5 inches is what fraction of 12 inches. This is the same thing as 5 being the numerator and 12 being the denominator. This is 5/12. Therefore your answer is: 5 inches is 5/12 of a foot. Hope this helps! Please rate, leave a thanks, and mark a brainliest answer (not necessarily mine). Thanks, it really helps! :D

AB and BC are tangent to circle D. Find x if AB = 2x + 9 and BC = 3x + 6. Find x.

Answers

it woulds be x+15 because if you take 2x and subtracted from the 3x then you get x and then you add the 9 and 6 witch you get 15

Answer:

the value of X comes out to be equal to 3

Step-by-step explanation:

since AB and BC are tangent to the circle D

then the length of the tangent will be same

AB will be equal to BC

where,

AB = 2 x + 9

and

BC = 3 x + 6

2 x + 9 = 3 x + 6

3 x - 2 x = 9 - 6

x = 3

hence, the value of X comes out to be equal to 3

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