Given: 3x + 2y + 7 = 5x +3y +10
Prove: m = -2
please help im very confused :)
also make sure to include the statements and reasonings as shown in the screenshot!
Answers
3x + 7 = 5x + y + 10
Subtract 3x from both sides
7 = 2x + y + 10
Subtract 10 from both sides
2x + y = -3
Subtract 2x from both sides
y = y = -2x -3
m = -2
Answer:
See Below.
Step-by-step explanation:
1) Given:
[tex]3x+2y+7=5x+3y+10[/tex]
2) Subtraction Property of Equality (subtract 2y from both sides):
[tex]3x+7=5x+y+10[/tex]
3) Subtraction Property of Equality (subtract 5x from both sides):
[tex]-2x+7=y+10[/tex]
4) Subtraction Property of Equality (subtract 10 from both sides):
[tex]-2x-3=y[/tex]
5) Symmetric Property:
[tex]y=-2x-3[/tex]
6) Slope-intercept form:
[tex]y=mx+b\text{, where $m$ is slope and $b$ is y-intercept.}[/tex]
7) Substitution:
[tex]m=-2[/tex]
Related Questions
Decide whether Equation A or B would be used to solve the problem.
You had $1.65. After a friend returned the money you had loaned her, you
had $3.50. How much did she give you?
a. n + 1.65 = 3.50
b. n - 1.65 = 3.50
Answers
Answer:
The correct answer is B because you had less when the friend did not give you the money. Therefore before you had 3.50-1.65
Step-by-step explanation:
A line passes through (1, –5) and (–3, 7). a. Write an equation for the line in point-slope form. b. Rewrite the equation in slope-intercept form.
Answers
Answer:
Point-slope form: y + 5 = 13/-4 (x-1)
Slope-intercept form:
Step-by-step explanation:
Ok, so first to find the equation in point-slope form, you need to find the slope. So, the slope would be 7- (-5)/-3-1 , which is 13/-4. That is your slope, or m. Now, for point-slope form, you have the equation y - y1 = 13/-4 (x-x1). Now, you take one of your points, say (1, -5), and you put it into the equation. So your point-slope form equation would be y - (-5) = 13/-4 (x - 1). This would simplify to y + 5 = 13/-4(x - 1).
Now for slope-intercept form, you have m, the slope, which is 13/-4. Substituting that into the equation, you have y = 13/-4x + b. To find b, you substitute one of your coordinates into the equation. For example, (1, -5). Then you have -5 = (13/-4 * 1) +b. Simplify this, and you have b = -5+ 13/-4, which is -20/4 + 13/-4, which is -20/4 - 13/4 = -33/4. So your final equation is y = 13/-4x - 33/4.
Hope that helped.
At a real estate agency, an agent sold a house for $397,000. The commission rate is 4.5% for the real estate agency and the commission rate for the agent is 20% of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
Answers
Answer:
1. $97,265
2. $17,865
Step-by-step explanation:
Step one:
given data
cost of the house= $397,000.
we are told that the commission is 4.5% real estate agency
and also the agent commission is 20%
Step two:
1. How much did the agency make on the house?
this amount is 20% plus 4.5% together.
=20/100*397,000 +4.5/100*397,000
=0.2*397,000. +0.045*397,000.
=79400+17865
=97,265
The agent made a total of $97,265 on the house
2. How much did the agent earn in commission?
in commission, the rate is 4.5% which amounts to $17,865
Express this ratio in its simplest form.
240cm : 3.6m
Answers
convert 3.6m into cm :
3.6 x 100 = 360cm
240cm : 360cm
2 : 3
help please this is also do very very soon thank you!!!
Answers
Answer:
700
Step-by-step explanation:
100:2
???:14
14*100
=1400
1400/2
=700
Answer:
The answer is 650
Step-by-step explanation:
You need to find the slope.
i took the points (2, 100) and (4, 200)
Then i put it into the slope formula which is y2 - y1/ x2- x1
I got that the slope is 50. So every two hours 5o millmeters for water drops. So now at 12 hours on the graph it says 600 millimeters of wate has already dropped. The graph is at intervals of two. Now at the next point it will be 14. So just add 50 to 600 and you get 650. So at 14 hours 650 water should have dripped
pls mark brainlest
[tex]log_{9}log_{2}log_{2}256[/tex]
Answers
Answer:
I hope it will help you...
A random sample of 400 voters in a certain city are asked if they favor an additional 4% gasoline tax to provide badly needed revenues for street repairs. If more than 220 but fewer than 260 favor the sales tax, we shall conclude that 60% of the voters are for it.a.) Find the probability of committing a type I error if 60% of the voters favor the increased tax.b.) What is the probability of committing a type II error using this test procedure if actually 48% of the voters are in favor of the additional gasoline tax?
Answers
Answer:
A) α = 0.04136
B) β = 0.00256
Step-by-step explanation:
We are given;
Sample size; n = 400
Proportion; p = 60% = 0.6
Formula for mean is;
μ = np
μ = 400 × 0.6 = 240
Standard deviation is given by;
σ = √npq
Where q = 1 - p = 1 - 0.6 = 0.4
σ = √(400 × 0.6 × 0.4)
σ = √96
σ = 9.8
A) our null hypothesis is at p = 0.6
Probability of making a type I error means we reject the null hypothesis when it is true.
This can be expressed in reference to the question as;
α = P(x < 220) + P(x > 260) all at p = 0.6
Now,
P(x < 220) = z = (x¯ - μ)/σ = (220 - 240)/9.8 = -2.04
Also;
P(x > 260) = z = (260 - 240)/9.8 = 2.04
Now, from z-distribution table probability of a z-score of -2.04 is 0.02068.
Also, probability of z-score of 2.04 is (1 - P(z < 2.04) = 1 - 0.97932 = 0.02068
Thus;
α = 0.02068 + 0.02068
α = 0.04136
B) Type II error occurs when we fail to reject the null hypothesis even though it's false.
In this case our alternative hypothesis is at p = 48% = 0.48
Thus;
μ = np
μ = 400 × 0.48 = 192
Standard deviation is given by;
σ = √npq
Where q = 1 - p = 1 - 0.48 = 0.52
σ = √(400 × 0.48 × 0.52)
σ = √99.84
σ = 9.992
Type II error would be given by;
β = [((x1¯ - μ)/σ) < z > ((x2¯ - μ)/σ)]
β = [((220 - 192)/9.992) < z > ((260 - 192)/9.992)]
β = (2.8 < z > 6.81)
Rearranging this gives us;
β = P(z < 6.81) - P(z < 2.8)
From z-distribution tables, we have;
β = 1 - 0.99744
β = 0.00256
In this exercise, we have to calculate the gasoline rates, and the answer will be:
A)[tex]\alpha= 0.04136[/tex]
B)[tex]\beta= 0.00256[/tex]
We are given that the sample size; n = 400, proportion; p = 60% = 0.6 so the formula for mean is;
[tex]\mu= np\\\mu=(400)(0.6)= 240[/tex]
Standard deviation is given by;
[tex]\sigma= \sqrt{npq}[/tex]
Where:
[tex]q = 1 \\p= 0.6\\q-p=0.4[/tex]
[tex]\sigma= \sqrt{(400)(0.6)(0.4)} \\=\sqrt{96} = 9.8[/tex]
A)Our null hypothesis is at p = 0.6. Probability of making a type I error means we reject the null hypothesis when it is true. This can be expressed in reference to the question as:
[tex]\alpha= P(x<220)+P(x>260)[/tex]
Now,
[tex]P(x < 220) = z = (x^-- \mu)/\sigma = (220 - 240)/9.8 = -2.04\\P(x > 260) = z = (260 - 240)/9.8 = 2.04[/tex]
Now, from z-distribution table probability of a z-score of -2.04 is 0.02068. Also, probability of z-score of 2.04 is:
[tex](1 - P(z < 2.04) = 1 - 0.97932 = 0.02068[/tex]
Thus;
[tex]\alpha= 0.02068+0.02068\\\alpha= 0.04136[/tex]
B) Type II error occurs when we fail to reject the null hypothesis even though it's false. In this case our alternative hypothesis is at p = 48% = 0.48. Thus:
[tex]\mu= np\\\mu= (400)(0.48)=192[/tex]
Standard deviation is given by;
[tex]\sigma= \sqrt{npq} \\=\sqrt{(400)(0.48)(0.52)} = 9.992[/tex]
Type II error would be given by:
[tex]\beta= [((x^{-1} - \mu)/\sigma) < z > ((x^{-2} - \mu)/\sigma)]\\= [((220 - 192)/9.992) < z > ((260 - 192)/9.992)]\\= \beta = (2.8 < z > 6.81)\\[/tex]
Rearranging this gives us:
[tex]\beta = P(z < 6.81) - P(z < 2.8)\\= 0.00256[/tex]
See more about statistics at : brainly.com/question/7412334
Sal needs 3 quarts of blue paint and 2 quarts of white paint to paint his room. How many quarts of blue paint will he need to paint his parent's room, if he needs 6 quarts of white paint?
Answers
Answer:
9 quarts of blue paint
Step-by-step explanation:
the ration is 3:2
2 times 3 is 6, so multiply the 3 from the blue paint to 3 as well
A digital thermometer costs $599.99. The company offers a $200 rebate. What percent of the cost is
the rebate?
Answers
Answer:
33.33%
Step-by-step explanation:
600/3 is 200 which means 1/3 of it is rebated
(please i need help)
Tiya flipped a coin 40 times. The coin landed heads up 16 times and tails up 24 times.
Part A: Based on the results, what is the experimental probability of the coin landing heads up? Show your work. (5 points)
Part B: What is the theoretical probability of the coin landing heads up? Show your work
Answers
Answer:
A) 16/40
B) P(H)= 0.4
Step-by-step explanation:
A) 16+24=40 is your denominator.
16 times it landed heads up, so 16/40
B) 16/40 as decimal (16 divided by 40) = 0.4
P= probability
(h)= (Heads up)
Si a un numero "X" le sumo 3 y al resultado lo multiplico por 2, me da 14 ¿cual es ese numero?
Answers
The domain for the equation y = 3x + 14 is listed below. Find the range for the given domain.
D:{-5,0,4}
R:
Answers
Answer:
R:{-1,14,26}
Step-by-step explanation:
The domain of a function is all the x-values of the function. The range of a function is all the y-values of the function. Therefore, we must plug in every x-value in the function to get our outputs to create our range:
Given: y=3x+14
When x=-5:
y=3(-5)+14
y=-15+14
y=-1 (this is the first point of the range)
When x=0:
y=3(0)+14
y=0+14
y=14 (this is the second point of the range)
When x=4:
y=3(4)+14
y=12+14
y=26 (this is the last point of the range)
Therefore, our range is R:{-1,14,26}
The range for the given domain {-5, 0, 4} in the equation y = 3x + 14 is
{ -1, 14, 26 }.
We have,
To find the range for the given domain of {-5, 0, 4} in the equation
y = 3x + 14, we substitute each value of the domain into the equation and determine the corresponding range values.
When x = -5:
y = 3(-5) + 14
y = -15 + 14
y = -1
When x = 0:
y = 3(0) + 14
y = 0 + 14
y = 14
When x = 4:
y = 3(4) + 14
y = 12 + 14
y = 26
Therefore,
The range for the given domain {-5, 0, 4} in the equation y = 3x + 14 is
{ -1, 14, 26 }.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ4
whats 10 divided by 489
Answers
Answer:
0.02044989775
Step-by-step explanation:
Mrs. Johnson earned $31,500.00 in salary this year. Her salary will increase by 10% next year. Mrs. Johnson is paid on a monthly basis. By how much will her monthly salary increase when she receives her raise?
Answers
Answer:
34650 dollars by next year
Step-by-step explanation:
Answer:
Step-by-step explanation31500x.10. 3150. 31500+3150. 34650. 34650/12 2887.50. 31500/12. : 2625. Difference per month 262.50
8300 dollars is placed in an account with an annual interest rate of 6.5%. How much will be in the account after 14 years , to the nearest cent?
Answers
Answer:
bruh
Step-by-step explanation:
42
A carpenter has 183 doorknobs in his workshop. Of those doorknobs, 95 are round and the rest are square. If he wants to place 9 square doorknobs in each bin, about how many bins would he need? The carpenter will need about bins.
Answers
Answer:
10 bins needed approximately
Step-by-step explanation:
Total door knobs = 183
Round door knobs = 95
Square door knobs = x
Total door knobs = Round door knobs + Square door knobs
183 = 95 + x
183 - 95 = x
88 = x
Square door knobs = x = 88
If he wants to place 9 square doorknobs in each bin, about how many bins would he need?
Divide total square knobs by square knobs in each bin
Total bins needed = Total square knobs / knobs in each bin
= 88 / 9
= 9.78
Approximately 10 to the nearest number of bins
Bins needed is approximately 10
can someone please help me
Answers
Answer
7 or 5 or both
Step-by-step explanation:
so first, you know it has to be 7 or 5 because all the other numbers are already on the chart and it M was that then you would get the same output value. now you figure out the equation. thats all I can help you with because I am dumb but hope you can figure out the equation.
If f(x) = 2x - 5, then f(4) is _____.
Answers
8-5= 3
Answer is 3
Convert 2x + 37y = 18 to point-slope form.
Answers
Answer:
x=−37/2 y+9
Step-by-step explanation:
2x+37y=18
2x+37y+−37y=18+−37y
2x=−37y+18
2x2=−37y+18/2
x=−37/2 y+9
Anyone know the answers???
Answers
Answer:
A. -80
B. 60
C. 98
D. -54
Step-by-step explanation:
ez give brainliest pls
Simplify.
[tex]\sqrt{44}[/tex]
Answers
hope this helps :)
Superman needs to save Lois from the clutches of Lex Luthor. After flying for 7 seconds, he is 1708 meters
from her. Then at 11 seconds he is 1484 meters from her.
What is Superman's average rate?
meters per second
How far does Superman fly every 13 seconds?
meters
How close to Lois is Superman after 24 seconds?
meters
Answers
Step-by-step explanation:
1) rate = ( 1484 - 1708) ÷ ( 11 - 7) = - 56 m/ s
2) rate × 13 = - 56 × 13 = - 728 m per 13 s
3) rate = - 56
t = 24 s
d = - 56 × 24 = 1344 m
whole distance = 2100
7 × 56 = 392
and he flay till 1708 then whole distance = 392 + 1708
so the remaining distance between him and her
2100 - 1344 = 756 m
True or False: A check is a document that directs the bank to deduct money from your account and make a payment
Answers
Answer:true
Step-by-step explanation: An order to a bank to pay a stated sum from the drawer's account, written on a specially printed form.
Traveling along a path from A to B, what is the ratio of the change in y to the change in x?
A. 5/3
B. 4/7
C. 3/5
D. 2/3
Answers
Answer:
Option C. is correct
Step-by-step explanation:
Slope of a Line
Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Please note the slope measures the ratio of the change in y to the change in x.
The points of the graph are A=(-3,-2) B=(7,4). Calculating the slope:
[tex]\displaystyle m=\frac{4-(-2)}{7-(-3)}[/tex]
[tex]\displaystyle m=\frac{6}{10}[/tex]
Simplifying by 2:
[tex]\displaystyle m=\frac{3}{5}[/tex]
Option C. is correct
Does this look good I made it this morning
Answers
Answer:
looks delicious
Step-by-step explanation:
Answer:
Man looks so good!
Step-by-step explanation:
Send me some in the mail. lol ☺☻♥
A gas station had two pumps. Pump A dispensed 241,752 gallons. Pump B dispensed 113,916 more gallons than Pump A. About how many gallons did both pumps dispense?
Answers
Answer:
Total gallons= 597,420
Step-by-step explanation:
Giving the following information:
Pump A dispensed 241,752 gallons.
Pump B dispensed 113,916 more gallons than Pump A.
First, we will calculate the number of gallons dispensed by Pump B:
Pump B= Pumb A + 113,916
Pump B= 241,752 + 113,916
Pump B= 355,668 gallons
Now, in total:
Total gallons= 241,752 + 355,668
Total gallons= 597,420
the function f(x) is defined by the set of ordered pairs {(5,-2),(-6,-2),(3,-2),(4,-2)
Answers
Answer:
Assuming it is a constant function.
[tex]f(x)=0x-2[/tex]
Step-by-step explanation:
(5,-2)
(-6,-2)
(3,-2)
(4,-2)
From the points, we can see that for any value of [tex]x[/tex], the function will give -2. The graph of this function will be a horizontal line, parallel to the [tex]x[/tex]-line passing the y-intersect point -2.
So the function might be
[tex]f(x)=0x-2[/tex]
If it is a constant function.
I'm considering that there are no discontinuities.
Answer:
Domain: x>=-6
Range: y=-2
Step-by-step explanation:
I think this is the one but I’m not entirely sure
Pls help i reall need help with this
Simplify Each
1. 3 - {7 - [8 + (7 - 3)] }
2. 12 - ( 3 - 4) - [8 - 6] + 5
3. - {2 - [7 - 8] + 2 - (1 - 3)}
4. 6 + 3
2 + 3
5. 4+5
- [ 8 - (245)]
1 - 4
Answers
Answer:
1.8
2.16
3.-7
5.-702
I didn't understand the 4th one
Answer:
1) 8
2) 16
3) -7
4) 14
5) 243
Step-by-step explanation:
For number 4 i just assumed you meant 6 + 3 + 2 + 3
Benny went to his local zoo that featured 6 lion exhibits. If these lion exhibits make up 25% of the zoo's exhibits, then how many exhibits does the zoo have in total?
Answers
Answer:
24
Step-by-step explanation:
if 6 exhibits are 25% of the entire zoo. You would need four times that amount to get the total number of exhibits because 25% × 4 = 100%. So, if you multiply 6 × 4 the total number of exhibits would be 24.
AB = 3x + 5, AC = 9x - 13
Solve for x . I’ll give brainliest to the first person who answers:)
Answers
Answer:
x = 2
Step-by-step explanation:
I assumed that you wanted me to set them equal to each other, so that is what I did. I wasn't given any other number to go by so hopefully this is correct.