To solve this problem, establish an algebraic equation that equates the sum of the lengths of the three pieces to the total length of the board. Solving this equation reveals that the first piece of wood is 5 inches, the second piece 20 inches and the third piece 25 inches.
Explanation:This question represents a simple algebraic equation. Since the second piece is 4 times the length of the first piece and the third piece is 5 times the length of the first piece, the sum of these lengths should equal the total length of the board, which is 50 inches. Given that 'x' represents the length of the first piece, we can establish the following equation:
x + 4x + 5x = 50
This is because '4x' is the length of the second piece and '5x' is the length of the third piece. When you combine like terms, the equation simplifies to:
10x = 50
Upon solving this simplified equation, we find that 'x' or the length of the first piece of wood equals 5 inches. Therefore, based on the information provided, the length of the second piece would be 20 inches (4 times 'x') and the third piece would be 25 inches (5 times 'x').
Learn more about Solving Algebraic Equations here:https://brainly.com/question/31303181
#SPJ3
Which transformation of f(x)=3^x does h(x)=-3^x-7 represent?
solve for x
4x - 3 / 3 = 7
I
A cell phone plan has a monthly cost that is shown in the table below. What is the correct statement regarding the average rate of change during the 40-minute time of talk? Total minutes of talk time Monthly cost of cell phone 0 $9.95 10 $10.65 20 $11.35 30 $12.05 40 $12.75
Answer:
The correct statement regarding the average rate of change during the 40-minute time of talk is that the average rate of change of the monthly cost with respect to the talk time is $0.07 per minute.
Explanation:
To find the average rate of change during the 40-minute time of talk, we can calculate the average rate of change of the cost with respect to the number of minutes of talk time.
We can use the formula for average rate of change, which is:
[tex]\[ \text{Average rate of change} = \frac{\text{Change in cost}}{\text{Change in talk time}} \][/tex]
Given the following data:
- At 0 minutes of talk time, the monthly cost is $9.95.
- At 40 minutes of talk time, the monthly cost is $12.75.
Using the formula, we can calculate the average rate of change:
[tex]\[ \text{Change in cost} = 12.75 - 9.95 = 2.80 \][/tex]
[tex]\[ \text{Change in talk time} = 40 - 0 = 40 \][/tex]
[tex]\[ \text{Average rate of change} = \frac{2.80}{40} = 0.07 \][/tex]
Line segment EF has a length of 5 units. it is translated 5 units to the right on a coordinate plane to obtain line segment E'F. What is the length of E'F? A. 5 units B.6 units C.10 units D.25 units
Answer:
Step-by-step explanation:
Its 5 units
What does y equal 1/3z+y=4
the length is 19.25 M the width is 14.75 M and the height is 10.25 M which is the best estimate of its surface area using 2lw + 2lh + 2 Wh
Suppose that 5 customers arrive, and each orders a different appetizer to share from a choice of 12 appetizers. In how many ways can this be done?
The number of ways to choose a different appetizer for each of the 5 customers from a choice of 12 appetizers is 95,040.
Explanation:The number of ways to choose a different appetizer for each of the 5 customers from a choice of 12 appetizers can be calculated using permutations. In this case, the order in which the appetizers are chosen does matter, and repetition is not allowed since each customer must choose a different appetizer.
To calculate the number of ways, we can use the formula for permutations:
P(n, r) = n! / (n-r)!
Where n is the total number of items and r is the number of items to be chosen.
So, in this case, the number of ways to choose the appetizers is:
P(12, 5) = 12! / (12-5)! = 12! / 7!
Using a calculator simplifies to:
P(12, 5) = 95,040
Which number line represents all the values of x for the equation x^2=16?
Solve for x.
-4x = -6 + 2x
Can someone check this please
Your mom has sent you to buy a new suit, and will let you get new shoes too if you keep it under $200. The suit you want to buy is $230. If you are getting 20% off the price, will you get the shoes?
use the number line to add -2/5+1/2
-2/5 = -4/10
1/2 = 5/10
-4/10 + 5/10 = 1/10
What is the average of 1,2,4,and 9
r -7 times r to the 3rd power
What are 2 phrases for the expression 85-y
What is 15.839 rounded to the nearest tenth
Which number is greater 87 or 13.688? How do you know?
Sam is doing his math homework. Hey completes 10 probelms every 30 minutes. How many porbelms can sam complete in 60 minutes?
. The width of a rectangle is 16 feet less than 3 times the length. If the area is 35 square feet, find
the dimensions of the rectangle.
The dimensions of the rectangle are approximately 8.93 feet for the length and 10.8 feet for the width. This solution involves setting up and solving a quadratic equation based on the given conditions.
Explanation:The subject of this question is Mathematics and it requires algebraic reasoning to solve. Here's step-by-step how to find the dimensions of the rectangle:
Let the length be denoted by 'x' (in feet).According to the question, the width is 16 feet less than three times the length, which can be written algebraically as '3x - 16'.The area of a rectangle is calculated by length times width, so in this example we would multiply 'x' by '3x - 16', and set that equal to the total area of 35 square feet.This set-up results in the equation 'x(3x - 16) = 35' or '3x^2 - 16x - 35 = 0'.Solving this quadratic equation for 'x', we find that the length (x) is approximately 8.93 feet.Substituting this value back into the equation for width, we find that the width is approximately 10.8 feet.Learn more about Solving Quadratic Equations here:https://brainly.com/question/30398551
#SPJ2
Carlotta subscribes to the HotBurn music service. She can download no more than 11 song files per week. Carlotta has already downloaded 8 song files this week. Write, solve, and graph an inequality to show how many more songs Carlotta can download.
The number of songs that can be downloaded is no more than 3.
i.e
Number of songs ≤ 3
What is inequality?It is a statement of an ordered relationship
- greater than,
- greater than or equal to,
- less than,
- less than or equal to between two numbers or algebraic expressions.
We have,
The number of songs that can be downloaded per week = S
S = No more than 11 songs.
This can be written as:
S ≤ 11
The number of songs already downloaded = 8
The number of songs that can be downloaded per week is:
S ≤ 11 - 8
S ≤ 3
Thus,
The number of songs that can be downloaded is no more than 3.
i.e
Number of songs ≤ 3
Learn more about inequality here:
https://brainly.com/question/22010462
#SPJ2
Sarah has $20 saved. If she will save her allowance for the next 3 weeks, and she gets $10 per week for her allowance. At the end of the week, she gets $150 in birthday money. How much money will she have after the 3 weeks?Which of the following sets of equations represents this problem?
After a 85% reduction, you purchase a new soft drink machine for $90. What was the original price?
The original price of the soft drink machine was $600, obtained by using the percentage reduction formula to find that $90 represents 15% of the original price.
Explanation:To find the original price of the soft drink machine before the 85% reduction, we first need to understand what a percentage reduction means. An 85% reduction implies that the final price is only 15% of the original price, as 100% - 85% = 15%. Therefore, the $90 you paid is 15% of the original price.
Next, we will step through the following calculation to determine the original price:
Let the original price be represented by P.15% of P is equal to $90, which can be written as (15/100) × P = $90.To find P, we divide both sides of the equation by 15 and then multiply by 100 to isolate P on one side. This gives us P = (90 ÷ 15) × 100.Performing the calculation P = 6 × 100, we find that P = $600.Therefore, the original price of the soft drink machine was $600.
26.891 to the nearest ten thousands place
the number isn't large enough to round to the nearest ten thousandths.
that would be the 4th digit to the right of the decimal point, so we would need the 4th and 5th numbers to the right in order to round the answer.
Using the numbers 3, 5, and 8, can you write nine proper fractions and nine improper fractions? You may use each number only once within a fraction.
Answer: yes we can write nine proper and nine improper fraction with help of these given numbers.
Explanation: Since, a proper fraction is a fraction which has the value less than 1, that is, the value of numerator is less than the value of denominator.
For example p/q is a proper fraction if p<q.
On the other hand, In Improper fraction numerator is greater than denominator.
Since, given numbers are 3,5 and 8
So, the possible proper fractions= [tex]\frac{3}{5},\frac{3}{8} \frac{5}{8},\frac{3}{5.8},\frac{5}{3.8}, \frac{8}{5.3},\frac{3}{5+8},\frac{5}{3+8}, \frac{5-3}{8}[/tex]⇒[tex]\frac{3}{5},\frac{3}{8} \frac{5}{8},\frac{3}{40},\frac{5}{24}, \frac{8}{15},\frac{3}{13},\frac{5}{11}, \frac{1}{4}[/tex]
Similarly, the possible improper fraction= [tex]\frac{5}{3},\frac{8}{3} \frac{8}{5},\frac{40}{3},\frac{24}{5}, \frac{15}{8},\frac{13}{3},\frac{11}{5}, \frac{19}{3}[/tex] ( Here, [tex]8-\frac{5}{3}=\frac{19}{3}[/tex] )
More math help please!
Each Child Receives a meal which consists of a hamburger, a bag of pretzels, and a drink for the children ages 6-10 and a hamburger , two bags of pretzels, and a drink for the children that are older than 10. It costs the club 80 cents for each hamburger, 35 cents for each bag of pretzels, and 60 cents for each drink. Calculate the cost to feed each age group
Suppose v varies directly as g , and v = -36 when g = 4. Find v when g = 12.
PLEASE HELP A paperweight in the shape of a rectangular prism is shown: A right rectangular prism is shown with length 10 cm, width 4 cm, and height 4 cm. If a cross section of the paperweight is cut perpendicular to the base, which shape describes the cross section? Parallelogram Triangle Square Hexagon
Answer: Square
Step-by-step explanation:
Since, the dimension of the given rectangular prism is 10 × 4 × 4
If a cross section of the paperweight is cut perpendicular to the base,
Then the dimension of the resultant quadrilateral is, 4 × 4
That is, the length and breadth is equal,
And the angles are of 90° each,
Which is the condition of a square,
Therefore, the resultant shape will be square.
⇒ Third Option is correct.
The cross section of the paperweight when cut perpendicularly to the base is a square.
Given the following data:
Length of rectangular prism = 10 cm.Width of rectangular prism = 4 cm.Height of rectangular prism = 4 cm.How to determine the resultant shape.We know that the shape of this paperweight is a right rectangular prism. Also, the base area of the paperweight is cut perpendicularly.
This ultimately implies that, the paperweight's length would be removed while its height and width remains, which corresponds to the dimensions (length and width) of a four-shaped object or quadrilateral with an angle of 90 degrees each.
In conclusion, the cross section of the paperweight when cut perpendicularly to the base is a square.
Read more on a square here: https://brainly.com/question/25092270
Which names are other ways to name ∠2? Select each correct answer. ∠H ∠G ∠KGH ∠HKG ∠K ∠GHK ∠HGK angle 2 with vertex h. one ray has point G on it. The other ray has point k on it.
Answer:
Angle GHK and Angle H
Step-by-step explanation:
None of the others are correct I took the test
Find the common ratio, r, in the following geometric sequence. 27, 9, 3, 1,…
3
-3
1/3
-9