Mathematics High School

∠ RQS and ∠ TQS are a linear pair where m∠ RQS = 2x + 4 and m∠ TQS = 6x + 20
1. Solve for x.
2. Find m∠ RQS and m∠ TQS
3. Show how you can check your answer
I want help to understand how to solve the problem because I have others to solve also.,

Answers

Answer 1
Since the given angles are a linear pair, that means that they add up to 180 degrees (straight line). So we know that:
m∠ RQS + m∠ TQS = 180

Now let's answer the questions.
1. Solve for x
m∠ RQS + m∠ TQS = 180
2x + 4 + 6x + 20 = 180
2x + 6x + 4 + 20 = 180
(2 + 6)x + 24 = 180
8x + 24 = 180
8x = 156
x = 19.5

2. Find m∠ RQS and m∠ TQS
m∠ RQS = 2x + 4
m∠ RQS = 2*19.5 + 4
m∠ RQS = 39 + 4
m∠ RQS = 43


m∠ TQS = 6x + 20
m∠ TQS = 6*19.5 + 20
m∠ TQS = 117 + 20
m∠ TQS = 137

3. Show how you can check your answer.Verify that they do add up to 180.
So 43 + 137 = 180
This demonstrates that they do make up a linear pair.

Answer 2

Answer:

∠RQSangle r q s and ∠TQSangle t q s are supplementary angles, so the sum of the angles should equal 180.

Step-by-step explanation:

Related Questions

HELP WITH THESE SERIES OF QUESTIONS!!
1. Factor the polynomial. 3x^3 − 27x^2 + 19

2. Factor the polynomial. 15z^3 + 25z^2

3. Factor the polynomial. 9x^7 + 33x^3

Answers

1. Simplified already
2. 5x^2 x (3x+5)
3. 3x^3 x (3x^4 +11)

Michelle, Jennifer, and Betty volunteered to make cupcakes for a school fundraiser. They've been asked to make 100 cupcakes. Michelle can make 6 cupcakes in an hour. Jennifer can make 18 cupcakes in two hours. Betty can make 24 cupcakes in two hours. How long will it take to make 100 cupcakes if they work together?

A. 3 19/27 Houurs
B. 2 2/9 Hours
C. 4 1/6 Hours
D. 1 23/27 Hours

Answers

Final answer:

Michelle, Jennifer, and Betty have a combined rate of 27 cupcakes per hour. To make 100 cupcakes, it will take them 100 divided by 27, which equals 3 19/27 hours. The correct answer is A. 3 19/27 hours.

Explanation:

To determine how long it will take Michelle, Jennifer, and Betty to make 100 cupcakes together, we first need to find their individual rates of production.

Michelle makes 6 cupcakes per hour.

Jennifer makes 18 cupcakes in 2 hours, which is equivalent to 9 cupcakes per hour.

Betty makes 24 cupcakes in 2 hours, which is equivalent to 12 cupcakes per hour.

Adding these rates together gives us a combined rate of:

6 + 9 + 12 = 27 cupcakes per hour.

To find the time it takes to make 100 cupcakes, we divide the total number of cupcakes by the combined rate:

100 cupcakes ÷ 27 cupcakes/hour = 3 19/27 hours.

Therefore, the correct answer is A. 3 19/27 hours.

Solve for x.

2x = 15 + x

Answers

I did it and got x=15

The solution to the equation is x = 15.

We have,

To solve the equation 2x = 15 + x, we want to isolate the variable x on one side of the equation.

First, we can simplify the equation by subtracting x from both sides:

2x - x = 15 + x - x

This simplifies to:

x = 15

Thus,

The solution to the equation is x = 15.

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A credit card advertises an annual interest rate of 23%.

What is the equivalent monthly interest rate?

i=__^_t

Answers

 the monthly rate is:

[1 + 23%]^(1/12) =1.23^(1/12) =1.0174 - 1 x 100 =1.74%

the distance between between two distinct points on number line is always greater than zero?

true or flase,

Answers

The answer here is true. It is logically impossible to create a negative distance between two lines on a number line. Even using negative numbers, there would still be a distance between the two. This also applies to a microscopic difference. At the end of the day, there is still a difference.

Glamour runs 2/3 mile each day she wants to know how many days she has to run before she has run a whole number of miles

Answers

Hello!

2/3 × 1 = 2/3

2/3 × 2 = 4/3 (or 1 1/3)

2/3 × 3 = 2



You can also convert 2/3 to a decimal by dividing the numerator by the denominator and then multiply that to get a whole number.

ANSWER:

Glamour will have to run for 3 days to run a whole number of miles. The whole number is 2.


please help me

how many perpendicular bisectors can be constructed for a line segment?

a.) 0
b.) 1
c.) 2
d.)infinitely many,

Answers

Bisector means any line which divides the line segment is two equal parts. In this case the Perpendicular bisector will be straight in upward or downward direction from the middle of the line segment. Any line segment can have only one mid point. Hence any line segment can have only one Perpendicular bisector. Hence correct answer is B that is 1.

A scientist has 350 mg of a radioactive material. The material will cut in half every month. After how many months will there be .68mg left?

Answers

The answer would be about 9 months.

Which expression represents the total surface area, in square meters, of the rectangular pyramid below?

Answers

(2xhb)+(lb)

h= hight of triangle
b= base
l= lenght
b= breath

Answer:

B

Step-by-step explanation:

:)

A recipe cal for 2 1/2 cups of flour to make 2 dozen cookies.How many cups of flour would be required to bake 15 dozen cookies

Answers

15/2 = 7 1/2

2 1/2 * 7 1/2 = 18 3/4 cups of flour
Hello!

2 1/2 = 2.5 as a decimal

2.5 ÷ 2 = 1.25

So, it takes 1.25 (1 1/4) cups of flour for each dozen of cookies.

1.25 × 15 = 18.75

ANSWER:

18.75 (18 3/4) cups of flour would be required to bake 15 dozen cookies.

Which solid has six faces, four lateral faces, two bases, eight vertices, and 12 edges? square pyramid triangular prism rectangular prism triangular pyramid

Answers

Rectangular Prism
*********************************************

Answer:

Rectangular Prism

Step-by-step explanation:

Select the ratios whose simplest form is 8/7

Answers

48:42 
16:14
56:49
I hope this helps.

Answer:

48:42

16:14

56:49

Step-by-step explanation:

I hope I made your day

Tropical forests are being lost at the rate of 5 million hectares per year. how many hectares per day is that? how many hectares per minute?

Answers

5,000,000/365= 13,698.630137 hectatres per day /1440 = 9.5129375951388..... hectares per minute

365 days in a year
1440 minutes in a day (24hrs)


what is 62% of 25 ?
im horrible at this plz help

Answers

To do this, multiply 62% by 25 !

Convert 62% into a decimal: 0.62. Then multiply them: 0.62 · 25, which equals 15.5 !
62% of 25

'of' means multiplication.

[tex]\sf 62\%\times 25[/tex]

Convert 62% to a decimal, divide it by 100(since percentages are parts of 100):

62/100 = 0.62

[tex]\sf 0.62\times 25[/tex]

Multiply:

[tex]\sf\boxed{\sf 15.5}[/tex]

Help please, explain each step or no points.

Answers

The proportion pop/total = 5/7 is presumed to hold for the next 500 songs.

pop/500 = 5/7
pop = 500*5/7 ≈ 357

357 of the next 500 songs downloaded are expected to be pop songs.

Is the number written in scientific notation? If not, explain.
a. 0.15 x 104
b. 7.06 x 10−8
c. 3.3 x 10012

Answers

Final answer:

The second example (7.06 x 10^-8) is correctly written in scientific notation, but the first (0.15 x 10^4) and third (3.3 x 100^12) examples are not. In scientific notation, the decimal part of the number should be between 1 and 10 and the exponent of 10 should be an integer.

Explanation:

The topic is scientific notation. The number is expressed in scientific notation if it has the form a × 10^n, where 1 ≤ |a| < 10 and n is an integer.

Let's see if the given numbers are in scientific notation:

0.15 x 10^4 - No, this is not in scientific notation. The decimal part of the number, 0.15, is not between 1 and 10.7.06 x 10^−8 - Yes, this is correctly written in scientific notation. The decimal part of the number, 7.06, is between 1 and 10 and the power of 10 is an integer.3.3 x 100^12 - No, this is not in scientific notation. The power of 10 is supposed to be a straight integer, not another exponential number.

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option b (  7.06 x 10⁻⁸)

a. 0.15 x 104

No, this number is not written in proper scientific notation.

In scientific notation, the coefficient must be a number between 1 and 10.

So, 0.15 can be expressed as 1.5 by moving the decimal point one place to the right.

Hence, it should be written as 1.5 x 103.

b. 7.06 x 10-8

Yes, this number is written in proper scientific notation.

The coefficient, 7.06, is correctly between 1 and 10.

c. 3.3 x 10012

No, this number is not written correctly due to the format of the exponent.

The correct form should be 3.3 x 1012.

So, the corrected scientific notation is 3.3 x 1012.

What is the inverse of f(x) = 8x - 7

Answers

y=(x+7)/8

Work:
Y=8x-7 —> x=8y-7
Solve for y
x+7=8y
y=(x+7)/8

Final answer:

The inverse of the function f(x) = 8x - 7 can be found by switching the x and y, then solving for y. This gives the inverse function as f^-1(x) = (x + 7) / 8.

Explanation:

The inverse of a function is calculated by switching the input and output variables. Given your question, we are to find the inverse of the function f(x) = 8x - 7. To do this, we first rename f(x) as y, giving us y = 8x - 7.

Next, we switch the positions of x and y, leading to x = 8y - 7. Then, to isolate y which represents the inverse function, we should solve the equation for y: x + 7 = 8y and y = (x + 7) / 8. So, the inverse of the function f(x) = 8x - 7 is f^-1(x) = (x + 7) / 8.

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1. _____is when an asset increases in value.
~depreciation
~appreciation
~inflation
~purchasing power

2. when money loses some of its value over time, it is caused by_____
-inflation
-FICA
-purchasing power
-recalculating worth
ive tried i need help @bibby @phi someone :( @SolomonZelman,

Answers

1) Appreciation is when an asset increases in value. The increase can happen for several reasons whether it is a decreased supply or an increased demand for example. 2) When money loses some of its value over time, it is caused by inflation

1) Appreciation is when an asset increases in value.

2) When money loses some of its value over time, it is caused by         inflation

The appreciating assets is any asset which value is increasing it is a an increased demand.

Therefore,

When value of assets increases in value?

Appreciation

1) Appreciation is when an asset increases in value.

Next,

The impact inflation has on the time value of money is that decrease the value of dollar over time.

Therefore,

2) When money loses some of its value over time, it is caused by inflation

Therefore,

1) Appreciation is when an asset increases in value.

2) When money loses some of its value over time, it is caused by         inflation

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Your sock drawer has 3 pairs of black socks, 4 pairs of brown socks, 1 pair of yellow socks and 5 pairs of blue socks. you reach into the drawer in the dark and randomly pick out 2 pairs for your business trip. what is the probability your pick out in this order. 2 black pairs?

Answers

All socks together: 13
Black socks: 3

Probability to pick out black socks: 3/13

After one pick out (You picked out a pair of black socks):

Probability to pick out black socks: 2/12

Multiply them:

2/12 * 3/13 = 1/26 ≈ 0,038

The probability your pick out in this order 2 black pairs 1/26.

What is the probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Mathematics to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory.

According to the question,

The sock drawer has 3 pairs of black socks, 4 pairs of brown socks, 1 pair of yellow socks and 5 pairs of blue socks.

All socks together = 3+4+5 = 13

Black socks = 3

Probability to pick out black socks: 3/13

After one pick out (You picked out a pair of black socks),

Probability to pick out black socks: 2/12

Then, the probability = 2/12 × 3/13 = 1/26.

Hence the required probability = 2/12 × 3/13 = 1/26.

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A 3 lb bag of one brand of cat food costs $3.52. A 6 lb bag of another brand costs $6.80. Which brand is cheaper per pound?

Answers

A 6 lb bag of another brand 
For this case what we should do is find the price per pound of each of the brands of cat food.
 We have then:
 Mark 1: 
 3 lb costs $ 3.52
 P = (3.52) / (3) = 1.17 $ / lb
 Mark 2:
 6 lb costs $ 6.80
 P = (6.80) / (6) = 1.13 $ / lb
 Answer: 
 Mark 2 is cheaper per pound: 
 1.13 $ / lb

need help !!!Divide 5a^2 + 6a - 9 into 25a^4 + 19a^2 - a - 78.

Answers

Hello,

Maybe i have not understood "into".

[tex] \dfrac{25a^4+19a^2-a-78}{5a^2+6a-9} =5a^2-6a+20+ \dfrac{-175a+102}{5a^2+6a-9} [/tex]

solving the whole thing

Answers

Let
x---------------> distance from people living to the city center

we Know that
Zone 1 covers people living within three miles of the city center
Zone 1 ------------> [x < 3 miles]

Zone 2 covers those between three and seven miles from the center
Zone 2 ------------> [ 3 <= x < = 7  miles]

Zone 3 covers those over seven miles from the center
Zone 3 ------------> [  x > 7  miles]

calculate the distance between two points to find the value of x

case A) point (0,0)  point (3,4)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(4-0)² +(3-0)²]------> √[16+9]
x=√25-------------> x=5 miles

the answer Part A)
people living in (3,4)
x=5 miles -------------> covers Zone 2 [ 3 < =x <= 7  miles]


case B) point (0,0)  point (6,5)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(5-0)² +(6-0)²]------> √[25+36]
x=√61-------------> x=7.81 miles

the answer Part B)
people living in (6,5) 
x=7.81 miles -------------> covers Zone 3 [  x > 7  miles]

case C) point (0,0)  point (1,2)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(2-0)² +(1-0)²]------> √[4+1]
x=√5-------------> x=2.23 miles

the answer Part C)
people living in (1,2) 
x=2.23 miles -------------> covers Zone 1 [ x < 3  miles]

case D) point (0,0)  point (0,3)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(3-0)² +(0-0)²]------> √[9]
x=√9-------------> x=3 miles

the answer Part D)
people living in (0,3) 
x=3 miles -------------> covers Zone 2 [ 3 < =x <= 7  miles]

case E) point (0,0)  point (1,6)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(6-0)² +(1-0)²]------> √[36+1]
x=√37-------------> x=6.08 miles

the answer Part E)
people living in (1,6) 
x=6.08 miles -------------> covers Zone 2 [ 3 < = x <= 7  miles]

Stacy fails 1/2 cup measuring cup seven times to have enough flour for cake recipe how much flour does the cake recipe call for

Answers

7 times of 1/2 cup  = 7 x 1/2
7 times of 1/2 cup  = 7/2
7 times of 1/2 cup  = 3 1/2 cups.

--------------------------------------------------
The recipe called for 3 1/2 cups of flour
--------------------------------------------------

what is the inverse and then graph the function and its inverse f(×)=-5n-14

Answers

You could write the original equation as y = - 5x - 14. That's what f(x) looks to mean. In inverse interchanges x and y

The inverse is x = -5y - 14 Now solve for y
x + 14 = - 5y
y = (x + 14)/-5 I have included a graph to show these two relationships.

Red Line: y = -5x - 14
Blue Line: y = (x + 14)/-5

A total of 100 students play on the Sports Academy’s soccer, track, or basketball teams. No student plays on more than one team. 61 of the students are boys. There are 36 students on soccer teams, 19 are on the girls’ soccer team. There are 35 students on basketball teams, 18 are on the boys’ basketball team. How many boys are on the track team?

Answers

61 students are boys. 17 of them are on the soccer team and 18 of them are on the basketball team.
18+17 =35
61-35= 26

26 boys are on the track team.

There are 17 boys on the soccer team, 18 on the basketball team, and by subtracting the 35 boys playing these sports from the total of 61 boys, we find that there are 26 boys on the track team.

To find out how many boys are on the track team, we can start with the total number of boys, which is 61, and subtract the number of boys in the other two teams. We know that there are 36 students on the soccer teams, and 19 of them are girls, which means that 36 - 19 = 17 boys are on the soccer team. Next, there are 35 students on the basketball teams, and 18 of them are boys; thus we have 35 - 18 = 17 girls on the basketball team.

Now, let's add up the number of boys on the soccer and basketball teams to find out how many boys are left for the track team. The equation is 17 (soccer) + 18 (basketball) = 35 boys who are playing sports other than track. Finally, to get the number of boys on the track team, we subtract this sum from the total number of boys: 61 (total boys) - 35 (boys in other sports) = 26. This means that there are 26 boys on the track team.

1000p for an answer please

Answers

The answer is C) 3 5/12 cups.
im pretty sure its 3 5/12 sry if im wrong

I confused on how to solve these trigonometric ratios.

Answers

◆ Triangles ◆

Hey !!

8th question solved in the figure attached above ,

For 9th question's answer ,

cos 24° = 11/x = 0.913545

---> [ x=12.041 ] Ans.
.

In 10th question ,

sin 35° = x/4.1 = 0.573576

---> [x=2.352 m] Ans.

Hope it helps you :)

A system of inequalities is graphed below. The variable x represents the number of cans someone is buying, and y represents the number of bottles. Conditions on the maximum amount of total weight and volume lead to two of the inequalities.
Which descriptions correspond to solutions of this system?
7 cans and 140 bottles
12 cans and 40 bottles
8 cans and 120 bottles
9 cans and 70 bottles

Answers

we have that
We will analyze each case to verify the answer
see the attached figure

Point A) 7 cans and 140 bottles------------> (x,y)=(7,140)----> is not solution
Point B) 12 cans and 40 bottles------------> (x,y)=(12,40)----> is not solution
Point C) 8 cans and 120 bottles------------> (x,y)=(8,120)----> is a solution
Point D) 9 cans and 70 bottles------------> (x,y)=(9,70)-------> is a solution

the answer is
the solutions are
8 cans and 120 bottles
9 cans and 70 bottles

Which of the following rational numbers is equal to 3.4? (line above the four)

A: 31/9

B. 32/9

C. 33/9

D. 34/9

Answers

Hey there! :D

So, we can just divide all the numbers to figure it out. 

31/9= 3.44444444

32/9=3.5555556

33/9= 3.66666777

34/9= 3.777778

The closest number to 3.4 is 31/9. "A" is the correct answer. 

I hope this helps!
~kaikers

Answer:

I believe the answer is A, out of all numbers, it seems to be the closest to 3.4.

Step-by-step explanation:

How do I solve these trigonometric equations!!?

Find all solutions in the interval [0, 2π).

(sin x)(cos x) = 0

Find all solutions in the interval [0, 2π).

cos2x + 2 cos x + 1 = 0

Find all solutions to the equation.

cos2x + 2 cos x + 1 = 0

(I am not looking for easy answers to cheat, I just need help on how to solve them...Im a bit confused and my teacher is not avail),

Answers

1) (sin x)(cos x) = 0 This means that either sin x = 0, or cos x = 0. Sin x = 0 when x = 0 or pi. cos x = 0 when x = pi/2 or 3pi/2. 2) cos2x + 2cosx + 1 = 0 First, expand cos2x. Simple trigonometric identity states that cos2x = (cos x)^2 - (sin x)^2.Now, substituting this equation, we get cos2x + 2cosx + 1 = (cos x)^2 - (sin x)^2 + 2cosx + 1. Note that we can now utilize the identity (cos x)^2 = 1 - (sin x)^2 to obtain (cos x)^2 + 2cosx + 1 - (sin x)^2 = 2(cos x)^2 + 2(cos x) = 0. Now, we can see that 2(cos x)^2 + 2(cos x) = 2(cos x)(cos x + 1) = 0. This is true when cos x = 0 or cos x + 1 = 0. Cos x = 0 when x = pi/2 or 3pi/2. cos x = -1 when x = pi. Therefore, x = pi/2, pi or 3pi/2.
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