a 56 inch board is to be cut into three pieces so that the second piece is three times as long as the first piece and a third piece is four times as long as the first piece if x represents the length of the first please find the length of all three pieces
Greg started with a certain number of quarters. He then decided on a number of quarters he would save each day. He added the quarters he saved to the amount with which he started. At the end of day 2, Greg had a total of 26 quarters saved. At the end of day 5, he had a total of 35 quarters saved.
A. How many quarters does Greg start with? Show or explain your work.
B. Write an equation to model the number of quarters Greg has saved, y, after x days.
C. Using the rate at which Greg is saving, explain why he can never have exactly 100 quarters saved by the end of any given day.
Final answer:
Greg started with 20 quarters. The equation for the number of quarters saved after x days is y = 20 + 3x. With Greg's savings rate of 3 quarters per day, he cannot have exactly 100 quarters on any day since 100 is not a multiple of 3 plus the 20 starting quarters.
Explanation:
To determine how many quarters Greg started with, let 's' be the number quarters Greg started with, and 'd' be the number of quarters he saves each day. After 2 days, he had a total of 26 quarters saved, and after 5 days, he had a total of 35 quarters saved. These can be written as two equations:
s + 2d = 26s + 5d = 35Subtracting the first equation from the second gives:
3d = 9
From which we find that d = 3 (Greg saves 3 quarters a day). Plugging this value back into the first equation:
s + 2(3) = 26
s + 6 = 26
s = 20
Greg started with 20 quarters.
B. The equation to model the number of quarters Greg has saved, y, after x days is:
y = 20 + 3x
C. With the savings rate of 3 quarters a day, Greg's total will always be a multiple of 3 plus the 20 he started with. 100 is not a multiple of 3, meaning he can never save exactly 100 quarters by the end of any given day since 100 minus the 20 quarters he started with leaves 80, which is not divisible by 3.
Final answer:
Greg started with 20 quarters and saves 3 quarters every day afterward. The equation to model the number of quarters saved after x days is y = 20 + 3x. It is impossible for Greg to have exactly 100 quarters saved by the end of any given day because 100 cannot be reached by adding multiples of 3 to the starting amount of 20 quarters.
Explanation:
To solve for the number of quarters Greg started with and the number of quarters he saves each day, we can set up a system of equations. Let's designate q as the number of quarters Greg started with and d as the number of quarters he saves each day. From the problem, we have two points of data: On day 2, Greg has 26 quarters, and on day 5, he has 35 quarters.
The equations representing these two data points are:
q + 2d = 26q + 5d = 35Subtracting the first equation from the second gives us:
3d = 9
Dividing both sides by 3 gives us:
d = 3
Now that we have the value for d, we can substitute it back into the first equation:
q + 2(3) = 26
q + 6 = 26
Subtracting 6 from both sides gives us:
q = 20
Greg started with 20 quarters.
For the equation to model the number of quarters saved, y, after x days, we have:
y = q + dx
This simplifies to:
y = 20 + 3x
To address part C, let's analyze the possibility of Greg having exactly 100 quarters saved. If we set y to 100 in the equation y = 20 + 3x and solve for x, we get:
100 = 20 + 3x
80 = 3x
x = 80/3
x ≈ 26.67
Since x must be an integer because Greg cannot save a fraction of a day, he cannot have exactly 100 quarters by the end of any given day. This is because 100 is not a multiple of 3 (the daily amount Greg saves) when starting from 20. Thus, it's impossible for Greg to have exactly 100 quarters saved by the end of any given day.
what is the answer to Divide 2800 by 10
Solve the quadratic equation by completing the square.
x^2 - 10x + 18 = 0
What is the circumference of the circle? Round your answer to the nearest foot
−2x+15y=−24
2x+9y=24
what do y and x equal?
Double a penny every day for 30 days. How many dollars do you have
The two triangles below are similar. Which pair are corresponding sides?
LN and MN
MN and QR
LM and QR
LM and PQ
Answer:
2) MN correspond to QR .
Step-by-step explanation:
Given : The two triangles below are similar.
To find : Which pair are corresponding sides
Solution : We have given that Triangle LMN is similar to triangle PQR.
Then Sides
MN correspond to QR .
Therefore, 2) MN correspond to QR .
What is the square of 2/3 I really need help I’m so confused
Two cars are traveling along the same highway. The distance, d, in miles, from San Francisco after h hours spent driving is described for each car below.
Car A:
d = 60h + 20
Car B: h d
0 60
2 160
4 260
Select three statements that are true.
A.Car A is traveling at the same rate, in miles per hour, as Car B.
B.Car A is traveling at a faster rate, in miles per hour, than Car B.
C. Car A is traveling at a slower rate, in miles per hour, than Car B.
D.Car A is originally closer to San Francisco than Car B.
E .Car A is originally at the same distance from San Francisco as Car B.
F.Car A and Car B are at the same distance away from San Francisco after 4 hours.
Car A is traveling faster at the checkpoint because it must go past the speed of car B to reach the same distance.
Explanation:Car A is traveling faster at the checkpoint because it must go past the speed of car B to reach the same distance.
To determine which car is traveling faster at the checkpoint, we need to compare their velocities. Car A has a positive, constant acceleration, which means its velocity is increasing. Car B, on the other hand, travels at a constant speed, which means its velocity remains the same.
Therefore, Car A is traveling faster at the checkpoint than Car B.
What is the average speed in miles per hour of a car that’s travels 956.4 miles in 15.9 hours? Round the answer to nearest tenth , explain step by step how to solve it
Sarah folds this pattern into a square pyramid. What is the surface area of Sarah's pyramid?
A. 161 sq. Inches
B.224sq.inches
C. 112sq.inches
D.273sq.inches
I need the answer really fast gets a brain list plz
HELP MEEEEEEEEEEEEEEEEEEE @Louli Just give the answer!!
The line plot shows the number of hours two groups of teens spent studying last week.
How does the data compare for the two groups of teens?
A)The range for the hours spent studying last week for the 13- to 15-year olds is the same as the range for the hours spent studying last week for the 16- to 18-year olds.
B)The median value for the hours spent studying last week for the 13- to 15-year olds is greater than the median value for the hours spent studying last week for the 16- to 18-year olds.
C)The mode for the hours spent studying last week for the 13- to 15-year olds is less than the mode for the hours spent studying last week for the 16- to 18-year olds.
D)The 13- to 15-year olds spent an average of 14 hours studying last week.
Which relationship describes angles 1 and 2?
Select each correct answer.
adjacent angles
vertical angles
complementary angles
supplementary angles
using the distributive property to find the product (y-4)(y^2+4y+16) results in a polynomial of the form y^3 + 4y^2 + ay - 4y^2 - ay - 64 what is the value of a in the polynomial
Answer:d
Step-by-step explanation:
Convert 3 feet to inches.
A) 4 inches
B) 9 inches
C) 12 inches
D) 36 inches
what is the answer to this question ?
Smoked salmon is being sold for $15.50 per pound. What is the cost of 6 ounces of salmon?.
PLEASE HELP!!!!
Beth’s final exam is worth 140 points. It consists of 40 questions. Each multiple choice question is worth 2 points, and each word problem is worth 5 points. How many of each kind of question are on the test?
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(3, -2), B(6, -2), C(6, 5), and D(3, 5). What is the area of rectangle ABCD?
Answer:
21
Step-by-step explanation:
a = 6-3 = 3
b = 5 -(-2)= 7
Area = a*b = 3*7 = 21
The area of rectangle ABCD which is graphed in the coordinate plane with vertices A(3, -2), B(6, -2), C(6, 5), and D(3, 5) is 21 unit².
What is the area of a rectangle?Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,
[tex]A=a\times b[/tex]
Here, (a)is the length of the rectangle and (b) is the width of the rectangle.
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(3, -2), B(6, -2), C(6, 5), and D(3, 5).
The shortest distance(length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
[tex]D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]
The distance from A to B is the length of the rectangle. The distance of line segment AB is,
[tex]W= \sqrt{(3-6)^2 + (-2-(-2))^2}\\W = \sqrt{(-3)^2 + (0)^2}\\W=\sqrt{9}\\W=3\rm\; units[/tex]
The distance from B to C is the width of the rectangle. The distance of line segment BC is,
[tex]L = \sqrt{(6-6)^2 + (-2-5)^2}\\L = \sqrt{(0)^2 + (-7)^2}\\L=\sqrt{49}\\L=7\rm\; units[/tex]
Thus, the area of rectangle ABCD is,
[tex]A=7\times3\\A=21\rm\; unit^2[/tex]
Hence, the area of rectangle ABCD which is graphed in the coordinate plane with vertices A(3, -2), B(6, -2), C(6, 5), and D(3, 5) is 21 unit².
Learn more about the area of rectangle here;
https://brainly.com/question/11202023
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i need this rotated 270 degrees clockwise
What is the total cost or sale price to the nearest cent 20$ haircut; 15% tip
what she got to school she saw that the school has nine buildings each Heaven 30 classrooms how many classrooms does the school have
Final answer:
To find the total number of classrooms in the school, we multiply the number of buildings (9) by the number of classrooms in each building (30), resulting in a total of 270 classrooms.
Explanation:
The question asks how many classrooms are there in total if a school has nine buildings, each with 30 classrooms. To find the answer, we need to multiply the number of buildings by the number of classrooms in each building. This calculation is straightforward:
Multiply the number of buildings (9) by the number of classrooms in each building (30).
This gives us: 9 buildings x 30 classrooms/building = 270 classrooms in total.
Therefore, the school has a total of 270 classrooms.
What will be the perimeter and the area of the rectangle below if it is enlarged using a scale factor of 5.5? A rectangle is shown. The length of the rectangle is labeled as 8 cm, and the width is labeled as 6 cm. Perimeter = 50 cm, area = 155.25 cm2 Perimeter = 50 cm, area = 1,452 cm2 Perimeter = 154 cm, area = 155.25 cm2 Perimeter = 154 cm, area = 1,452 cm2
Cougar Park is shaped like a parallelogram and has an area of 1/10 square mile. It’s base is 3/8 mile. What is its height?
HELP ASAP!!!
1: What is the surface area of a sphere with a radius of 4 meters rounded to the nearest square meter
A: 50 m^2
B: 101 m^2
C: 201 m^2
D: 268 m^2
2: What is the volume of a sphere with a radius of 6 meters rounded to the nearest square meter?
A: 905 m^3
B: 679 m^3
C: 452 m^3
D: 226 m^3
Help ASAP!!
[tex]3 - 1 \times \frac{3}{5} = [/tex]
the gift shop at a science museum sells lollipops that are made to look like the plants. Each lollipop is shaped like a sphere and has a radius of 12 mm
What is the volume of each lollipop?
The answer is 2304pi
The volume of the lollipop having the radius of 12 mm is 7241.14 [tex]mm^{3}[/tex].
What is volume?Volume is the capacity of a container to hold something in its capacity. Like a drum can hold water.
How to calculate the volume of lollipop?The radius is given as 12 mm. The lollipop is having shape of sphere. The formula of volume of sphere is 4/3π[tex]r^{3}[/tex].
Volume =4/3π[tex]r^{3}[/tex].
Volume of lollipop is 4/3π[tex]12^{3}[/tex]
=4/3*22/7*576
=(88*1728)/21
=152064/21
=7241.14[tex]mm^{3}[/tex].
Hence the volume of lollipop having radius of 12 mm is 7241.14[tex]mm^{3}[/tex].
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107=5x+17 simplify your answer as much as possible