Peter is 2 years older than Winnie. Peter's age is 16 years less than seven times Winnie's age. The equations below model the relationship between Peter's Age (p) and Winnie's age (w):
p=w+2
p=7w-16
Which is a possible correct method to find Peter's and Winnie's ages?
A. Solve w+2 = 7w-16 to find the value of w
B. Solve p+2 =7p-16 to find the value of p
C. Write the points where the graphs of the equations intersect the x axis
D. Write the points where the graphs of the equations intersect the y axis
Answers
P=w+2
p=7w-16
Compare both equations
7w-16=w+2
Add 16 to both sides.
7w=w+18
Subtract w from both sides.
6w=18
Divide both sides by 6.
w=3, which is the age of Winnie.
Now Peter's age=3+2=5 years
Option A is the correct method to find the age of Peter and Winnie.
Answer:
A. Solve w+2 = 7w-16 to find the value of w.
Step-by-step explanation:
Here p represents the age of Peter and w represents the age of Winnie,
Given,
Peter is 2 years older than Winnie.
⇒ p = w + 2 -----(1)
Also, Peter's age is 16 years less than seven times Winnie's age.
⇒ p = 7w - 16 -----(2),
By equating right sides of equation (1) and (2),
We get,
w + 2 = 7w - 16,
Since, this equation is only in the variable w,
Thus, we can find the value of w with help of the above equation,
After putting this value in either of equation (1) or (2),
We can find the value of p.
Hence, option A is correct.
Note : From equation (1) and (2),
w = p - 2 and [tex]w=\frac{p+16}{7}[/tex]
[tex]\implies p-2=\frac{p+16}{7}[/tex]
⇒ Option B is incorrect.
Now, let x represents w and y represents p in the graph,
Then, the solution will be the intersection point of lines y=x+2 and y=7x-16,
Which is shown below,
⇒ Options C and D are incorrect.
Related Questions
Which describes a parameter of a population?
A) all the golf balls produced last Monday by the Acme Company
B) 63% of Rains County agree with the latest U.S. foreign policy
C) 88% of students at Emory High School have been to a football game
D) 45% of Jacksonville, Florida residents have been to the beach last summer
Answers
Answer:
A) all the golf balls produced by the Acme Company
Step-by-step explanation:
what is the circumference of a circle with a diameter of of 8.4 cm?
Answers
Hope this helps!
- Juju
3.14•8.4= 26.376. :)
C= 26.376
Samuel needs $29 to download some songs and movies on his MP3 player. His mother agrees to pay him $6 an hour for raking leaves in addition to his $5 weekly allowance. What is the minimum number of hours Samuel must work in one week?
Answers
so just do 4 hours and just 1 week
So you’d do 4 hours, and get your weeks allowance :)
find two consecutive odd integers such that 36 more than the lesser is three times the greater
Answers
x= first integer
x+2= second integer
x + 36= 3(x + 2)
multiply 3 by everything in parentheses
x + 36= 3x + 6
subtract x from both sides
36= 2x + 6
subtract 6 from both sides
30= 2x
divide both sides by 2
15= x
x= 15 first consecutive odd integer
x+2= second consecutive odd integer
15+2= 17
ANSWER: 15, 17
Hope this helps! :)
Final answer:
To find two consecutive odd integers such that 36 more than the lesser is three times the greater, set up an equation and solve for the variable x. The two consecutive odd integers are 15 and 17.
Explanation:
To find two consecutive odd integers such that 36 more than the lesser is three times the greater, we can set up an equation:
x + 36 = 3(x + 2)
Simplifying this equation, we get:
x + 36 = 3x + 6
Subtracting x from both sides, we get:
36 = 2x + 6
Subtracting 6 from both sides, we get:
30 = 2x
Dividing both sides by 2, we get:
15 = x
Therefore, the two consecutive odd integers are 15 and 17.
The distance between Rosa’s house and her school is 3/4 mile. She ran 1/4 mile.What fraction of the way to school did she run?
Answers
.25
25%
She ran 1 forth of the distance.
Suppose the population of a town is 15,200 and is growing 2% each year. Write an equation to model the population growth. Predict the population after 10 years. y = 15,200 ∙ 2x; about 15,564,800 people y = 2 ∙ 15,200x; about 304,000 people y = 15,200 ∙ 1.02x; about 18,529 people y = 15,200 ∙ 2x; about 18,529 people
Answers
y = A * (b) ^ t
Where:
A: initial population.
b: growth rate.
t: time.
Substituting values we have:
y = 15200 * (1.02) ^ t
After 10 years we have:
y = 15200 * (1.02) ^ 10
y = 18529
Answer:
An equation to model of the population growth is:
y = 15,200 ∙ 1.02 ^ x
the population after 10 years is:
about 18,529
PLEASE HELP ME PLSSSSSSSSSSSSS
The scatter plot below shows the number of pizzas sold during weeks when different numbers of coupons were issued. The equation represents the linear model for this data. y = 3.4x + 43
According to the model, what is the average number of pizzas sold in one night if no coupons are issued?
Question 5 options:
A 43
B 0
C 11
D 21
Answers
Answer:
option: A is correct.
Step-by-step explanation:
We are asked to find the average number of pizzas sold in one night if no coupons are issued.
i.e. we have to find the value of y such that x=0 i.e. no coupon was issued.
We are given a equation which represents the linear model for this data:
y = 3.4x + 43
where y denotes the average number of pizza sold and x denotes the number of coupons issued.
Hence when x=0 we have value of y from the above linear equation as:
y=3.4×0+43=0+43=43
i.e. y=43.
Hence, average number of pizzas sold in one night if no coupons are issued are 43.
(80z) to the 3/4 power
Answers
6. How could you change the simulation to generate data for three pets? Result Frequency Heads, Heads 9 Heads, Tails 14 Tails, Heads 18 Tails, Tails 9 Total 50
PLEASE HELP WILL GIVE BRAINLYEST
Answers
Answer: what i did was put "change one of the tails, heads or heads, tails to add the data for the 3 pets" because you couldn't tell if it was heads tails or tails heads
Final answer:
To generate data for three pets in a simulation, expand the outcome possibilities to include all combinations of Heads and Tails for three entities, and then record the frequency of each outcome to analyze probabilities or patterns.
Explanation:
To determine how to change a simulation to generate data for three pets when you currently have data for two, you need to expand the number of possible outcomes to account for the additional pet. For the current two-pet scenario, there are four outcomes: Heads-Heads, Heads-Tails, Tails-Heads, and Tails-Tails. When adding a third pet, each of these outcomes would branch into two further outcomes, representing the two possibilities for the third pet (let's call it Pet C).
The possible outcomes would be:
Heads-Heads-HeadsHeads-Heads-TailsHeads-Tails-HeadsHeads-Tails-TailsTails-Heads-HeadsTails-Heads-TailsTails-Tails-HeadsTails-Tails-TailsFor each outcome, you would simulate or record the frequency as you did with the two-pet scenario, totaling the number of trials to ensure you have complete data for analysis. You would then use this data to analyze the probabilities or patterns of outcomes involving three pets.
Make a conjecture about the position, size and shape of a figure if a composition of transformation included a dilation
Answers
What is the length of the diagonal of a 10cm by 15com rectangle
Answers
a2 + b2 = c2
102 + 152 = c2
100 + 225 = c2
√325 = c
5√13 = c
The diagonal measures 5√13 cm.
To write f(x) = 2x2 – 44x + 185, factor out from the first two terms. Next, form a perfect square trinomial keeping the value of the function equivalent: f(x) = 2(x2 – 22x + 121) + 185 – 242 The function written in vertex form is f(x) = (x – )2 + .
Answers
To write f(x) = 2x2 – 44x + 185, factor out
2
from the first two terms.
Next, form a perfect square trinomial keeping the value of the function equivalent:
f(x) = 2(x2 – 22x + 121) + 185 – 242
The function written in vertex form is f(x) =
2
(x –
11
)2 +
-57
.
Answer:
f(x) = 2(x-11)^2 - 57
Step-by-step explanation:
To write f(x) = 2x^2 – 44x + 185, factor out from the first two terms.
Next, form a perfect square tri nomial keeping the value of the function equivalent: f(x) = 2(x^2 – 22x + 121) + 185 – 242
To get vertex form we factor x^2 -22x+121
product is 121 and sum is -22
-11*-11= 121 and sum -11+(-11)= -22
x^2 -22x+121
(x-11)(x-11)
f(x) = 2(x^2 – 22x + 121) + 185 – 242
f(x) = 2(x-11)(x-11)+ 185 – 242
f(x) = 2(x-11)^2 - 57
HELP WILL MARK BRAINLIEST!!!!!!!!!!!Cindy has to write an 18-page report. If she has written 1/3 of a report so far, how many pages has she written?
A. 4 pages
B. 6 pages
C. 8 pages
D. 9 pages
Answers
1/3 of 18 = 6
Cindy has written 6 pages of her report so far.
Also: This means she has 12 pages left.
6 x 1= 6
The answer is 6 pages, or B.
What value of k makes the equation true?
a.2
b.3
c.4
d.8
Answers
Its C. 4
Correct on edge :D
Think this belongs to math, I'm not sure though, anyway, what is the width and length of a wooden plank if the dimension is 12,5 x 8,5cm?
Answers
You can infer from this problem that the shape of the wooden plank is a rectangle based on the dimensions given. The length of a rectangle is usually the longest side of the rectangle so you can conclude that the length of the rectangle is 12.5 cm. Therefore, the width is 8.5 cm.
Write a real-world problem that can be represented by a rule and a table using division
Answers
Expand the polynomial:
(5a+1/5 b)^2
Answers
(5 a + b/5)^2
(5 a + b/5) (5 a + b/5) = (5 a) (5 a) + (5 a) (b/5) + (b/5) (5 a) + (b/5) (b/5):
5×5 a a + (5 a b)/5 + (5 b a)/5 + (b b)/(5×5)
(5 a b)/5 = 5/5×a b = a b:
5×5 a a + a b + (5 b a)/5 + (b b)/(5×5)
(b×5 a)/5 = 5/5×b a = b a:
5×5 a a + a b + b a + (b b)/(5×5)
Combine powers. (b b)/(5×5) = (b^(1 + 1))/(5×5):
5×5 a a + a b + b a + (b^(1 + 1))/(5×5)
1 + 1 = 2:
5×5 a a + a b + b a + (b^2/5)/5
5 a×5 a = 5×5 a^2:
5×5 a^2 + a b + b a + (b^2/5)/5
5×5 = 25:
Answer: 25 a^2 + a b + b a + (b^2/5)/5
(25x^2)+(2xy)+(y^2/25)
Help! How do i find a solution set? (I have a texas ti graphing calculator if that helps) An example is
(x - a)(x + b) = 0
How would I find the solution set for this?
Please explain to me in an easy to understand, step by step way.
If you know how to use a texas TI calculator, you can also explain to me how to do it on the calculator, but that is not required
Answers
Answer:
The solution set is given by {a, -b}.
Step-by-step explanation:
We have the equation,
[tex](x - a)(x + b) = 0[/tex]
Equating the factors to 0 gives,
[tex](x - a)=0[/tex] and [tex](x + b)=0[/tex]
i.e. x = a and x = -b
So, the solutions of the equation [tex](x - a)(x + b) = 0[/tex] are x= a and x= -b.
Thus, the solution set is given by {a, -b}.
I need help with my assignments on these two questions
Answers
a. Using properties of exponents, the value of the expression is 10⁰
b. The equation has no solution
What are properties of exponents?a. Properties of exponents are mathematical rules that allow us to simplify and manipulate expressions involving exponents. These properties help us perform operations such as multiplication, division, and raising to a power more efficiently.
In the given problem, we have to solve and simplify using properties of exponents.
Given that; [tex]\frac{10^-^3}{10^-^3}[/tex];
we can apply quotient rule when dividing exponents here;
[tex]\frac{10^-^3}{10^-^3} = 10^-^3 ^+^3 = 10^0[/tex]
The answer is 10⁰
b. To simply the equation, we just need to use basic mathematical operation to find the value of x.
3x - 2x + 4 = 5x - 4x - 8
Simplify;
x + 4 = x - 8
Collect like terms
x - x = -8 - 4
0 = -12
No solution
Learn more on properties of exponents here;
https://brainly.com/question/3187898
#SPJ1
Help please! 10 points!
10: Gavin builds furniture for a living. he Sells chairs for $45 and tables for $70 each. It takes Gavin 4 hours and $10 worth of supplies to build each chair. A table requires 10 hours and $15 worth of supplies to make. Gavin wants to work for no more than 40 hours per week and spend no more than $80 on materials. Write a system of inequalities and state 3 possible combos.
Answers
Let's assume
number of chairs =x
number of tables =y
we are given
Gavin builds furniture for a living. he Sells chairs for $45 and tables for $70 each
So, we can find objective function as
[tex] Z=45x+70y [/tex]
now, we can find inequalities
A table requires 10 hours and $15 worth of supplies to make
so, total hours to make table =10y
amount spent on table =15y
It takes Gavin 4 hours and $10 worth of supplies to build each chair
so, total hours to make chair =4x
amount spent on chair =10x
total number of hours to make chair and table =4x+10y
Gavin wants to work for no more than 40 hours per week
so, we get
[tex] 4x+10y\leq 40 [/tex]
spend no more than $80 on materials
so, we get
[tex] 10x+15y\leq 80 [/tex]
so,
objective function:
[tex] Z=45x+70y [/tex]
Constraints:
[tex] 4x+10y\leq 40 [/tex]
[tex] 10x+15y\leq 80 [/tex]
o decorate his bedroom, Mike spent $41.64 on new bedding, $36.84 on paint, and $72.49 on accessories. About how much did he spend to decorate his bedroom?
Answers
Answer:
Mike spent $150 on his decorations.
Step-by-step explanation:
In order to find the amount of money Mike spent on his decorations you must add all the costs together.
$41.64 + $36.84= $78.48
$78.48 + $72.49= $150.97
Then you round 150.97 to 151, which is also close to 150.
Hope this helps :)
Trent is fishing from a pier. ●The tip of his fishing rod is 53 ¾ feet above the surface of the water. ●The hook on the end of the fishing line is directly below the tip of the fishing rod 12 ⅔ feet below the surface of the water. Trent estimates that the distance between the tip of his fishing rod and the hook is less than 65 feet. Is Trent’s estimate reasonable? Explain your answer. HELP Please
Answers
Hope this helped :)
HELP THIS IS URGENT HELLPP
Answers
Between which two consecutive integers does ???147 lie?
A.
146 and 148
B.
12 and 13
C.
11 and 12
D.
10 and 11
Answers
The consecutive numbers where the square root of 147 will lie are between 12 and 13.
Consecutive numbers simply mean the numbers that follow each other. Examples of consecutive numbers are 2,3, 4.
It should be noted that the square root of 147 is 12.12. Therefore, 12.12 can be found between 12 and 13. In conclusion, the numbers will be 12 and 13.
Read more about consecutive numbers on:
https://brainly.com/question/7382233
in a first aid kit the ratio of large bandages to small bandages is 5 to 2. Based on this ratio, how many large bandages are in the kit if there are total of 60 bandages?
Answers
what is the mean median and mode
Answers
to calculate add all the numbers and divide by how many numbers there are
4,600,000+4,500,000+4,000,000+4,600,000+10,200,000 and since there are 5 numbers divide that by 5
median-find the middle number
put numbers in order from least to greater and find the number in the middle
4,000,000x 4,500,000x 4,600,000 4,600,000 10,200,000x so your answer should be 4,600,000
mode-if a number appears more than once
4,600,000
Would (j^-13)(j^4)(j^6) equal to j^-312?
Answers
[tex](j^{-13})(j^{4})(j^{6}) = j^{(-13+4+6)} = j^{-3}[/tex]
The equation b=540−30m gives the balance b (in dollars) that you owe on a drum set after m monthly payments. What is the balance after 9 monthly payments?
Answers
b=540-30m
b=540-30(9)
b=540-270
b=270
So the answer is b=270
800 hm = _____ cm
8
0.08
8,000,000
80,000
Answers
We know that 1 hectometer= 100 meters, so our first conversion factor expressed as a fraction is [tex] \frac{100m}{1hm} [/tex]
We also now that 1 meter = 100 centimeters, so our second one is [tex] \frac{100cm}{1m} [/tex]
Now that we have our fractions, lets multiply our original quantity by them to get our answer in the required units:
[tex]800hm( \frac{100m}{1hm} )( \frac{100cm}{1m})=8000000cm [/tex]
We can conclude that 800hm are 8,000,000cm
Answer:
Exactly what they said (the answer is i bold at the bottom)
Step-by-step explanation:
Prove it is rational by writing it as a quotient of two integers. Please answer these problems, I need to check my answers. Ignore the blank ones, I was able to check them. Thank you!
1. 2.4
2. 74
3. 17.3333333…
4. π
5.
6. –18
7.
8. 87.125
9. –30
10. –8.3
11. 58.25
12. 121
13. 4.5
14.
Answers
2. 74 = 74/1
3. 17.3333333… = 52/3
4. π - not rational
6. –18 = -18/1
8. 87.125 = 87125/1000
9. –30 = -30/1
10. –8.3 = -83/10
11. 58.25 = 5825/100
12. 121 = 121/1
13. 4.5 = 45/10
Most of the decimals can be reduced to lower terms by removing at least one factor of 2 or 5. If all you want is a ratio of integers, that is irrelevant.