Mathematics Middle School

Solve the system of equations.
4x-9y - 2=0
12x-5y+38=0
x equals?
y equals?

Answers

Answer 1
I: 4x-9y-2=0
II: 12x-5y+38=0

start by eliminating x by multiplying the first equation by 3 and subtracting II:

3*(4x-9y-2)-(12-5y+38)=3*(0)-0
12x-27y-6-12x+5y-38=0
-22y-44=0
-44=22y
-2=y

-> insert y=-2 in I:

4x-9*(-2)-2=0
4x+18-2=0
4x+16=0
4x=-16
x=-4

so the solution is y=-2 and x=-4
Answer 2

Answer:(-4,-2)

Step-by-step explanation:

Related Questions

prove the identity cos(x-y)-cos(x+y)=2sinxsiny

Answers

Answer:

see the procedure

Step-by-step explanation:

we know that

[tex]cos(X - Y) = cosX cosY + sinX sinY\\cos(X + Y) = cosX cosY - sinX sinY[/tex]

so

[tex]cos(X - Y)-cos(X + Y)=cosX cosY + sinX sinY-(cosX cosY - sinX sinY)[/tex]

[tex]cos(X - Y)-cos(X + Y)=cosX cosY + sinX sinY-cosX cosY + sinX sinY[/tex]

[tex]cos(X - Y)-cos(X + Y)=sinX sinY+ sinX sinY[/tex]

[tex]cos(X - Y)-cos(X + Y)=2sinX sinY[/tex] ----> is verified

melanie's food bill at a restaurant is $28.45, the sales tax rate was 6%. if she added 20$ of the amount before tax as a tip, what was the total cost of the meal

Answers

Before tax with tip would be $48.45, without tip and with tax would be $45.52, with everything would be $65.52

Which number set has only irrational numbers?
A) {-7.4, 0, 3.14}
B) {-
5
6
,
7
8
,
π
2
}
C) {
2
,
5
, π}
D) {
8
,
9
,
10
}

Answers

The sets containing π have that as an irrational element. The other numbers in the set are rational, so NO SET contains Only Irrational Numbers.

_____
Sets A and D appear to contain Only Rational Numbers.

Answer:

The answer is D because PI is a irrational number.

Step-by-step explanation:

there are 238 juniors at a high school. the ratio of girls to boys in the junior class 3:4. how many Juniors are girls? how many are boys?

Answers

Well, for ratio problems like this, here’s what you do:

1. Add the numbers in the ratio together:

3 + 4 = 7

2. Divide that number by the quantity given:

238 / 7 =
34

3. Multiply each part of the ratio by the quotient:

4 x 34 = 136

3 x 34 = 102

102 + 136 = 238
4. Answer the problem using the information you just found:

The ratio of girls to boys in the junior class is 102 : 136.
Final answer:

The number of juniors in a class is 238 and the ratio of girls to boys is 3:4. We can use this information to calculate that there are 102 girls and 136 boys in the junior class.

Explanation:

The question provides us with the information that there are 238 juniors in the school and the ratio of girls to boys in this class is 3:4. This means for every 7 students (3 girls and 4 boys), there are 3 girls and 4 boys.

First, let's find out how many 'sets' of 7 students there are in the total number of juniors. To do this, we divide 238 by 7, which equals 34 sets.

To find out the number of girls, we multiply these 34 sets by 3 (because the ratio tells us there are 3 girls in each set). This comes to 102 girls.

Similarly, to find out the number of boys, we multiply these 34 sets by 4 (because the ratio tells us there are 4 boys in each set). This gives us 136 boys.

Therefore, in the junior class, there are 102 girls and 136 boys.

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Which type of graphs might be used to show data with qualitative categories?

Answers

Bar graphs, Pareto charts, and pie charts seem to be some forms of these graphics.

What is a histogram?

It is defined as the depiction of numerical data in a graph using a bar with no space. The histogram depicts the approximate distribution of the data.

As we know,

For the primary analysis, there are many alternative infographics that can be applied.

Bar graphs, Pareto charts, and pie charts seem to be some forms of these graphics.

The most prominent visual representations of primary analysis are pie charts and graphical representations.

Thus, bar graphs, Pareto charts, and pie charts seem to be some forms of these graphics.

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Which property justifies the following statement? If 3 ● m∠Q − 17 = 30, then 3 ● m∠Q = 47.

Answers

The addition property of equality justifies adding the same number to both sides of an equation.

Answer: Addition Property of Equality

Step-by-step explanation:

I need help on numbers 1. 2. 6. And 7. Please

Answers

i'm not sure about 1 and 2 but 6 is wrong it is a = sign and 7 is wrong.

in chemistry a mole is a unit of measure equal to 6.02x10^23 atoms of a substance. the mass of a single neon atom is about 3.35 X 10^-23 g. what is the mass of 2 moles of neon atoms?

Answers

2(6.02*10^23)(3.35*10^-23)

2*6.02*3.35

answer : 4.0334*10^1


Problem
Phil received a prize of x dollars from a poker tournament. The tournament cost him 100 dollars to enter.
What were Phil's net winnings from the tournament?
Write your answer as an expression.

Answers

you could write is this way (y+x)-100
Phil gets x dollars, but before he gets x dollars, he needs to pay 100 dollars to enter the tournament. Therefore the net winning is not x dollars but you should substract 100 dollars from x.

So, the expression of the net winning will be
[tex]\boxed{x-100}[/tex]

A news reporter wants to estimate the percentage of registered voters who will vote for a particular candidate in an upcoming election. Which statement describes a method that will help him accurately estimate this percentage?

A.) He could contact every resident in the town, ask whether the resident will vote for the particular candidate, and then calculate the percentage of residents who say they will vote for the particular candidate.

B.)He could ask employees at the newspaper which candidate each will vote for, and then calculate the percentage who will vote for the particular candidate.

C.)He could take a random sample of registered voters, and then calculate the percentage of the sample who will vote for the particular candidate.

D.)He could ask his readers to respond to a survey that asks which candidate the reader will vote for and then calculate the percentage of people who say that they will vote for the particular candidate.

Answers

A news reporter wants to estimate the percentage of registered voters who will vote for a particular candidate in an upcoming election. Which statement describes a method that will help him accurately estimate this percentage?

Answer: In order to estimate the percentage of registered voters who will vote for a particular candidate in an upcoming election, a news reporter can randomly take a sample from the registered list of voters and based on their opinion a reporter can accurately estimate percentage of registered voters who will vote for a particular candidate in an upcoming election. Therefore, the option C will be correct.

Therefore the correct method is C) He could take a random sample of registered voters, and then calculate the percentage of the sample who will vote for the particular candidate.

The other options to gather the opinion about the percentage of the sample who will vote for the particular candidate are non probabilistic and there is every possibility of introduction of bias in the estimate. The only option which is probabilistic is option c because it involves random selection of respondents. Therefore the appropriate option is c.

Simplify the expression. 8 – 3(–12x + 2)

Answers

8-3(-12x+2)
Rewrite as a sum of terms.
8+(-3)(-12x+2)
Use distributive property
8+ 36x+ (-6)
Add like terms
2+36x
Simple-
First distribute the second part of the equation.
-3(-12x + 2)
36x - 6
next- plug that into the equation.
8 + 36x - 6
Add similar ones together,
36x + 2 is your answer. 
Hope this helps!

Any number with a non-repeating and non-terminating decimal is an irrational or rational number.

Answers

Irrational number. A rational number terminates or repeats.

A bee with velocity vector

r'(t)

starts out at

(5, −5, −3)

at

t = 0

and flies around for 5 seconds. Where is the bee located at time

t = 5

if

5


0

r'(u)du = 0?

Answers

Final answer:

The bee returns to the starting point at (5, -5, -3) after 5 seconds since the integral of its velocity over that period is zero, indicating no net change in position.

Explanation:

To find where the bee is located at time t = 5, we start by looking at the given velocity vector r'(t). Since ∫05r'(u)du = 0, this implies that the integral of the velocity function over the interval from 0 to 5 seconds results in zero net displacement. Thus, the total change in position of the bee over these 5 seconds is zero.

Since the bee starts at the position (5, −5, −3) at t = 0, and there is no net change in position over 5 seconds, the bee must return to the starting point at t = 5. Therefore, the bee is located at (5, −5, −3) at time t = 5 seconds.

In a distribution, a score of X=60 has a z-score of -3.0.. A score of X=85 has a z-score of 2.0. What are the mean and standard deviation for this population?

Answers

The formula for a z-score is
[tex]z=\frac{X- \mu}{\sigma}[/tex]
We don't have μ, the mean, or σ, the standard deviation.  We can, however, set up a system of two equations with the information we do have.  We know:
[tex]-3=\frac{60- \mu}{\sigma} \text{ and } 2=\frac{85- \mu}{\sigma}[/tex]
We can make this look more like a "typical" system of equations by cancelling the fractional part of each equation.  We do this by multiplying the bottom of each equation by σ:
[tex]-3*\sigma=\frac{60- \mu}{\sigma}*\sigma \text{ and } 2*\sigma=\frac{85- \mu}{\sigma}*\sigma \\ \\-3\sigma=60- \mu \text{ and } 2\sigma=85- \mu[/tex]
Now we'll get the variables on the same side of the equation.  We'll do this by adding μ to both sides:
[tex]-3\sigma + \mu=60- \mu + \mu \text{ and } 2\sigma+ \mu =85- \mu + \mu \\ \\-3\sigma+\mu=60 \text{ and } 2\sigma+\mu=85[/tex]
Now we'll write this vertically:
[tex] \left \{ {{-3\sigma+\mu=60} \atop {2\sigma+\mu=85}} \right. [/tex]
We will "eliminate" μ by subtracting the bottom equation:
[tex] \left \{ {{-3\sigma+\mu=60} \atop {-(2\sigma+\mu=85)}} \right. \\ \\-5\sigma=-25[/tex]
Divide both sides by -5:
[tex]\frac{-5\sigma}{-5}=\frac{-25}{-5} \\ \\\sigma=5[/tex]
Our standard deviation is 5.  Substituting this into our top equation we have:
-3(5)+μ=60
-15+μ=60
Cancel the -15 by adding it to both sides:
-15+μ+15=60+15
μ=75
Our mean is 75.

Final answer:

By using the z-score formula and solving a system of linear equations, we find that the mean (μ) of the population is 75, and the standard deviation (σ) is 5.

Explanation:

To find the mean (μ) and standard deviation (σ) of the distribution based on the given z-scores, we can use the z-score formula:

z = (X - μ) / σ. Rearranging this formula, we can express X as X = zσ + μ.

For the two provided z-scores and X values:

For X = 60 and z = -3.0: 60 = (-3)σ + μ

For X = 85 and z = 2.0: 85 = (2)σ + μ

We now have a system of linear equations that can be solved to find μ and σ:

-3σ + μ = 60

2σ + μ = 85

Solving for σ and μ:

Multiplying the first equation by 2, and the second equation by 3 and adding them gives us:

(-3)(2)σ + 2μ = 120

(2)(3)σ + 3μ = 255

Adding these together yields 5μ = 375, so μ = 75.

Now, substitute the μ value into either equation to find σ:

-3σ + 75 = 60

σ = (75 - 60) / 3

σ = 5

Therefore, the mean (μ) of the population is 75 and the standard deviation (σ) is 5.

You have a credit card with a balance of $1,758.64. The interest is 12.75% APR. A late payment fee of $35.00 is added to the principal if you pay after 12/20. You make a payment for $100.00 on 12/20. How much interest did you pay? A. $224.23 B. $18.69 C. $211.48 D. $17.62

Answers

 Interest is base on 1758.64 - 100 = 1658.64 Interest for 1 month = 1658.64 x 0.1275 / 12 = 17.62 The answer is $ 17.62 2) Interest on 1758.64 = 1758.64 x 0.1275 / 12 = 18.69 Amount toward principal = 100 - 18.69 - 35 = 46.31........................ $ 35 = Late fee
The answer is 18.69 hope this helps you

The movie theater in town has 4 rooms. Each room has 58 seats on the left side and 32 seats on the right side. Which equation could be used to show the total number of seats in the theater?
A) 52 + 32= ?
B) 4 + 32 + 58= ?
C) (58 + 32) x 4= ?
D) (58 - 32) x 4= ?

Answers

Answer:

The right option is (C) (58 + 32)×4

Step-by-step explanation:

Total number of rooms = 4

Number of seats on left = 58 seats in each room

Number of seats on right = 32 seats in each room

Total number of seats in a room = 58 + 32 seats

Total number of seats in the movie theater = Number of rooms × Number of seats in each room

Total number of seats in the movie theater = 4 × (58 + 32)  = 360 seats

Hence the right option is (C) (58 + 32)×4

How can the Associative Property be used to mentally find 48 +82? i know the answer is 130. don’t answer the expression plz.❗️❗️❗️

Answers

You can look for friendly numbers such as
48 and 2, split 82 in 80 and 2 and then associate the numbers conveniently

48+ (2+80)=
(48+2)+80=
50+80 which you can do it and is 130 or

50+80=
50+50+30=
100+30 which is 130

Please help with the question above :)!!! ^^

Answers

(-1,-9) because if we substituted 1 into x y would be 9 and if we substituted 1/2 into x y would be 3 but if we substituted -1 into x y would be 1/9 so therefore that value is incorrect

Titaina reads 40 pages of her book every night. Write an expression that represents the number of pages she has read

Answers

the answer is 40x

I hope this helps

How many 4-letter code words can be made using the letters in the word pencil if : (a) Repetitions are permitted?

Answers

the answer would be six 

Final answer:

The total number of code words is 6 x 6 x 6 x 6, which is 1296 possible code words.

Explanation:

To determine how many 4-letter code words can be made using the letters in the word 'pencil' with repetitions permitted, we consider that each position in the 4-letter code word can be filled by any of the 6 letters from the word 'pencil'. Therefore, for each position, there are 6 choices.

Using the fundamental counting principle, the total number of possible 4-letter code words given that repetitions are allowed is calculated as follows:

First position: 6 possibilitiesSecond position: 6 possibilitiesThird position: 6 possibilitiesFourth position: 6 possibilities

Thus, the total number of code words is 6 x 6 x 6 x 6, which is 1296 possible code words.

an example of an equation that is a linear function explain why it is linear

Answers

One example of a linear equation is
y = 7x + 4 because the slope is a set number and the graphed version of the equation is a completely straight line.
Hope this helps!

what is the quotient of 4 2/3 divided by 4 1/5 :fraction

Answers

Write the two fractions as improper fractions 
4  2/3 is 14/3
4  1/5 is 21/5
rewrite
14/3 ÷ 21/5
since it is pretty complicated to divide two fractions, 
you change it to multiplication
keep the first fraction, change the division sign to multiplication, then flip the second fraction
(you can remember KEEP, CHANGE, FLIP whenever dealing with division of fractions :) )
14/3 * 5/21
multiply across
(14 * 5) / ( 3 * 21)
70/ 63
simplify to 10/9
this can be written as 1  1/9

Hope this helps

Answer:

1 1/9

Step-by-step explanation:

1. Use the function rule to complete the table. -10+y=4

2. What is the function rule for the second picture?

Please answer to both questions.

Answers

1)-10(x)+y=4
left to right
-16
-6
4
14
24
2)y= -1-5x

Solution:

The Given Linear Function is

   -10 x + y = 4

y= 4 + 10 x

1. x= -2

y = 4 + 10* (-2)

  = 4 - 20

  = -16

2. x= -1

y = 4 + 10* (-1)

   = 4 -10

    = -6

3. x=0

y = 4 +10* (0)

   =4

4. x=1

y= 4 +10 * (1)

  = 4+10

  =14

5. x=2

y= 4 +10*2

 = 4 +20

 = 24

2. Function Rule

Slope between two points or coordinates in two dimensional plane is

[tex]=\frac{4-9}{-1+2}=\frac{-1-4}{0+1}=\frac{-6+1}{1-0}=\frac{-11+6}{2-1}= - 5[/tex]

Slope between two points is same.

This will be linear function.

Equation of line will be

y - 9= -5 * (x+2)

y -9 = - 5 x - 10

y + 5 x+10 -9=0

5 x + y+1=0

Ms. Reynolds has a system of 10 sprinklers that water her entire lawn. The sprinklers run one at a time, and each runs for the same amount of time. The first 4 sprinklers run for a total of 50 minutes. How long does it take to water her entire lawn?
*please explain how you got the answer if possible*

Answers

you are told that sprinklers run for the same amount of time. lets refer to this time as T.
you are told that 4 sprinkles run one at a time for 50 minutes total. that means that T should be 50/4 = 12.5 minutes = 12 minutes and 30 seconds

Final answer:

To water the entire lawn with 10 sprinklers, each running for the same amount of time, it will take a total of 125 minutes.

Explanation:

Ms. Reynold's system of sprinklers is designed to run sequentially, with each sprinkler getting an equal duration of run time. We know that the first 4 sprinklers run for a total of 50 minutes.

To find out how long one sprinkler runs, we divide the total time of 50 minutes by the number of sprinklers that have run, which is 4:

50 minutes ÷ 4 sprinklers = 12.5 minutes per sprinkler.

Now that we know each sprinkler runs for 12.5 minutes, we can calculate the total time to run all 10 sprinklers by multiplying the time per sprinkler by the total number of sprinklers:

12.5 minutes per sprinkler × 10 sprinklers = 125 minutes.

Therefore, it will take 125 minutes to water her entire lawn using all 10 sprinklers.

Which type of function is represented by the table of values below?





x

y


1

4


2

16


3

64


4

256


5

1,024




exponential

linear

quadratic

square root

Answers

Answer:

Exponential :)

Step-by-step explanation:

The temperature in Bloomington on Sunday was 32.6°C. On Monday, the temperature changed by -8.25°C. What was the temperature on Monday?

Answers

Your Question;
The temperature in Bloomington on Sunday was 32.6°C. On Monday, the temperature changed by -8.25°C. What was the temperature on Monday?
My Answer;
If Monday was 8.25°C cooler than Sunday, and it was 32.6°C on Sunday.
We need to figure out the temperature on Monday, and it was 24.35°C
on Monday.
My Work;
32.6 + ( -8.25 ) = 24.35
Hope I helped,
♥ Sir Chub-Chubs.

Answer:

Temperature on monday = 24 .35°c.

Step-by-step explanation:

Given  : The temperature in Bloomington on Sunday was 32.6°C. On Monday, the temperature changed by -8.25°C.

To find :  What was the temperature on Monday.

Solution : We have given

Temperature on sunday = 32.6°C.

Temperature changed  = -8.25°C.

Temperature on monday = 32.6°C - 8.25°c )

Temperature on monday = 24 .35°c.

Therefore, Temperature on monday = 24 .35°c.

Find these measures for the number of days in the months of a leap year

Answers

Thirty days hath september April June and November
All the others have 31 
Except February which hath 28 and
29 on a year that leaps.

Use the interactive to find an expression equivalent to 4x – 4 – 2x + 3.


2x – 1

6x – 1

2x – 7

–2x + 3

Answers

Answer:

2x-1 is ur answers i got it right on edge 2020

Step-by-step explanation:

The expression equivalent to the given expression is - g(x) = 2x - 1

What are equations?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign "=".

Given is the equation as follows -

f(x) = 4x - 4 - 2x + 3

The given expression is -

4x - 4 - 2x + 3

4x - 2x - 4 + 3

2x - 4 + 3

2x - 1

Therefore, the expression equivalent to the given expression is -

g(x) = 2x - 1

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A cylinder shaped container has a radius of 20 meters and a height of 100 meters. A glass sphere with a radius of 12 meters is placed inside the cylinder shaped container and then the container is completely filled with water.

What is the approximate volume of water contained in the cylinder?

Use 3.14 for pi.


A. 24,165 m³

B. 31,400 m³

C. 118,365 m³

D. 125,600 m³

Answers

i can confirm the answer is C. i did the test and got 100%, including this answer. hope this helps u and future people
 

Answer:

CCCCCCCC

Step-by-step explanation:

Find the surface area for the given given prism

Answers

the answer is 664 in. here is an example of how to do it

Find the surface area of a rectangular prism with a length of 6 cm, a width of 4 cm, and a height of 2 cm 

SA = 2 × l × w  +  2 × l × h  +  2 × w × h 

SA = 2 × 6 × 4  +  2 × 6 × 2  +  2 × 4 × 2 

SA = 48 + 24 + 16 

SA = 88 cm2

The surface area for the given given prism is 664 square inches.

What is Three dimensional shape?

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The given figure is a rectangular prism

We need to find the surface area of the rectangular prism

The formula for surface area is  A=2(wl+hl+hw)

Where w is width

l is length

h is height

Plug in length=14, width=10 and height=8 in the given formula

A=2(140+112+80)

=2(332)

=664 square inches

Hence, the surface area for the given given prism is 664 square inches.

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