the three sides of the triangle are 42 feet, 21 feet, and 43 feet,
Let's denote the second side of the triangle as ( x ). According to the problem, the first side is twice the length of the second side, which makes it ( 2x). The third side is 20 feet less than three times the second side, so it is ( 3x - 20 ).
Now, we can write the equation for the perimeter of the triangle:
[tex]\[ \text{Perimeter} = \text{First side} + \text{Second side} + \text{Third side} \][/tex]
[ 106 = 2x + x + (3x - 20) ]
Now, combine like terms and solve for \( x \):
[ 106 = 6x - 20 ]
Add 20 to both sides:
[ 6x = 126 ]
Divide both sides by 6:
[ x = 21 ]
So, the second side is 21 feet. Using this, we can find the other two sides:
First side = [tex]\( 2x = 2 \times 21 = 42 \) feet[/tex]
Third side = [tex]\( 3x - 20 = 3 \times 21 - 20 = 63 - 20 = 43 \) feet[/tex]
Therefore, the three sides of the triangle are 42 feet, 21 feet, and 43 feet, respectively.
To recap the process:
1. Let ( x ) represent the second side of the triangle.
2. Write the equation for the perimeter using the given information.
3. Simplify the equation and solve for ( x ).
4. Substitute the value of ( x ) back into the expressions for the first and third sides to find their lengths.
5. Confirm the final answer by checking that the sum of the three sides equals the given perimeter.
complete question
Solve by making an equation
The first side of a triangle is twice the length of the second side; the third side is 20 feet less than three times the second side. The perimeter of the triangle is 106 feet. Find the three sides.
Answer:
150 students at york middle school took part in the school clean up. This is 30% of the school's total students. How many students go to he middle school?
Graph y=−56x−4 .
Use the line tool and select two points on the line.
The two points on the line y = − 56x − 4 will be (1, −60) and (−1, 52).
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
y = − 56x − 4
Let x = 1, the value of y will be
y = − 56 (1) − 4
y = − 56 − 4
y = − 60
Let x = − 1, the value of y will be
y = − 56(−1) − 4
y = 56 − 4
y = 52
The two points on the line y = − 56x − 4 will be (1, −60) and (−1, 52). Then the diagram of the line is given below.
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to rent a car,the fast company charges $75 per day plus $0.05 per mile. how many miles did mrs.kline drive if the cost of renting the car was $ 92.40?
Which phrase could be represented by this expression?
k/5 + 8
or
k over 5 + 8
eight more than a fifth of a number
five times a number plus eight
eight more than five times a number
one-fifth of the sum of a number and eight
Use the distributive property of multiplication to find 7 x 22
Hint: 22 = 20 +2
Please show all work, Thank you:)
The distributive property of multiplication is used to simplify 7 x 22. By substituting 22 with 20 + 2 and distributing the multiplication, it becomes 7 x 20 plus 7 x 2, which equals 154.
Explanation:The question is asking us to use the distributive property of multiplication to calculate 7 x 22. The distributive property allows us to multiply a single term and two or more terms inside a set of parenthesis. Here we are given the hint that 22 = 20 + 2.
Following the hint, we substitute 22 with (20 + 2) in the multiplication expression. So, 7 x 22 becomes 7 x (20 + 2). Now, by distributive property, we can take the multiplication inside the parenthesis.
7 x 20 = 140 7 x 2 = 14
By adding both these results, 140 + 14, we get the final answer 154.
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-0.3,0.5,0.55,-0.35 in least to greatest
Can I get help simplifying these three questions? Thanks!
First Question 3a–a+18–a
Second Question (a+3)–(a+2)
Third Question 43+a–2a
The scale on a map is 2cm = 15miles. Dave measures the distance to the next town at 7cm. How many miles away is the next town?
Answer:
[tex]52.5\ miles[/tex]
Step-by-step explanation:
we know that
The scale on the map is equal to
[tex]\frac{2}{15}\frac{cm}{miles}[/tex]
so
by proportion
Find how many miles are [tex]7\ cm[/tex] on the map
[tex]\frac{2}{15}\frac{cm}{miles}=\frac{7}{x}\frac{cm}{miles}\\ \\x=15*7/2\\ \\x=52.5\ miles[/tex]
Purple paint is made with a 16:3:1 ratio of white paint:blue paint:red paint. How much white paint, in gallons, is needed in order to make one gallon of purple paint? Express your answer as a common fraction.
Answer:
4/5
Step-by-step explanation:
The purple paint is split into 16+3+1=20 parts: 16 parts of white, 3 parts of blue, and 1 part of red. Thus, in one gallon of purple paint, 16 out of the total 20 parts are white paint, so there are 16/20 x 1 gallon = 4/5 gallons of white paint in one gallon of purple paint.
The amount of white paint that is needed in order to make a gallon of purple paint would be 4 / 5 gallons.
How to find the number of gallons ?The ratio of white:blue:red paint is given as 16:3:1. The sum of these ratio components gives the total parts for one 'unit' of paint.
So, 16 (for white) + 3 (for blue) + 1 (for red) = 20 total parts.
This implies that the 20 parts in this ratio make up 1 gallon of purple paint (as per the question). To find the quantity of white paint needed, we simply need to convert the 'parts' of white paint into gallons.
Since 20 parts is equivalent to 1 gallon, 1 part would be equivalent to 1/20 of a gallon. Therefore, 16 parts of white paint would be equivalent to :
= 16 * (1/20)
= 16/20
= 4/5 gallons
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Evaluate the expression 3(7 + 4)2 − 14 ÷ 7. 50 361 363 586
An interior decorator purchased a painting for $95, a sofa for $225, a chair for $275, and an end table for $155. The tax was $60 and delivery was $75. If she paid for the furniture with $50 bills, how many bills were needed?
A used-car dealer has a vehicle on the lot with a sticker price of $5999. if the dealer markup on used vehicles is 20%, how much did the dealer pay for the car?
Answer:
the correct APEX answer is $4999.17
The cost of car is $4,999.16.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
A used-car dealer has a vehicle on the lot with a sticker price of $5999.
Mark up = 20%
let the cost of Car be x.
So, x+ 20% of x = 5999
x + 20/100 x = 5999
x + 0.20 x = 5999
1.2 x= 5999
x = 5999/ 1.2
x = $4,999.16
Hence, the cost of car is $4,999.16.
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Three times the smaller of two consecutive EVEN integers IS four less than twice the larger. What are the two integers?
PLEASE HELP ME WITH THIS
The two consecutive even integers are 8 and 10.
Given that, three times the smaller of two consecutive even integers is four less than twice the larger.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let two consecutive even integers be x and x+2.
Now, 3x-4=2(x+2)
⇒ 3x-4=2x+4
⇒ 3x-2x=4+4
⇒ x=8
So, x+2=10
Therefore, the two consecutive even integers are 8 and 10.
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Solve the following system of equations algebraically for all values of x,y and z
x+3y+5z=45
6x-3y+2z=-10
-2x+3y+8z=72
The system of equations x+3y+5z=45, 6x-3y+2z=-10, -2x+3y+8z=72 can be solved algebraically to get the values x=6, y=12, z=-1.
Explanation:First, we can combine the first and the second equations and the first and third equations to cancel out y.
Doing so, we get: x+3y+5z+6x-3y+2z=45-10 and x+3y+5z-2x+3y+8z=45+72
The new equations simplify to 7x+7z=35 and -x+13z=117
Next, we can divide the first new equation by 7 to get x+z=5. Subtract x from both sides to get z=5-x.
Substitute z=5-x into the second equation to find the value of x.
Performing these substitutions gives x=6. Substituting x=6 back into the equation z=5-x gives z=-1.
Finally, we substitute x=6 and z=-1 back into the original equations to solve for y: y=(45-6-5(-1))/3 = 12
So, x=6, y=12, z=-1 are the solutions to the system of equations.
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Write an expression for the calculation subtract 10 divided into fifths from 20 divided in half.
Liz earns a salary of $2,100 per month, plus a commission of 5% of her sales. She wants to earn at least $2,400 this month. Write an inequality to find the amount of sales that will meet her goal. Identify what your variable represents.
A baseball weighs 5 ounces and the NY Yankees ordered 3,200 baseballs. How many tons do the baseballs weigh?
Answer:
dont come at me if im wrong but im pretty sure the answer is 1/2 or .5
Step-by-step explanation:
Stacy and Neil painted 280 ft2 of there living room wall with 4/5 gallon of paint. How many square feet can they paint with 3 gallons of paint?
Answer:
They can paint 1050 sq.feet with 3 gallons of paint
Step-by-step explanation:
Given :Stacy and Neil painted 280 ft2 of there living room wall with 4/5 gallon of paint.
To Find : How many square feet can they paint with 3 gallons of paint?
Solution :
Area painted with [tex]\frac{4}{5}[/tex] gallons of paint = 280
Area painted with 1 gallon of paint =[tex]\frac{280}{\frac{4}{5}} = 350 ft^2[/tex]
Area painted with 3 gallons of paint =[tex]350 \times 3 = 1050 ft^2[/tex]
Hence they can paint 1050 sq.feet with 3 gallons of paint
It costs $2.55 to make a sandwich at the local deli shop. To make a profit, the deli sells it at a price that is 140% of the cost. The sandwich sells for $___.
How can the difference 13-(-24)be rewritten as a sum with the correct solution? Explain?
A: (-13) + (-24) = -37
B: 13 + (-24) = -11
C: (-13) + 24 = 11
D: 13 + 24 = 37
The number of cows in a farm was 60% of the number of the goats. After 80 goats were taken out of the farm, the number of goats became 60% of the number of cows in the farm.
(a)how many cows were there in the farm?
(b) what is the percentage of the goats were moved out of the farm?
Which fraction expresses 36/80 in lowest terms? Please help me ;D
Eliza earns $400 per week plus $15 for each new customer she signs up. Let c represent the number of new customers Eliza signs up. Write an expression that shows how much she earns in a week. Then find how much Eliza earns in a week in which she signs up 18 customers.
Answer:
400+ (15c)
$670
Step-by-step explanation:
Eliza earns per week = $400
She earns for each new customer's signs up = $15
Let the number of new customers Eliza signs up = c
The expression that shows her earning in a week will be
400+ (15c)
If the number of customers that signs up = 18
The weekly earning of Eliza will be = 400+(15 × 18)
= 400 + 270
= $670
Eliza's earning in a week would be $670.
7/8,42/48 determine whether each pair of ratios are equivalent ratios right yes or no
You buy a movie for 19.99 and a set of earphones for 12.49 how much is the bill before taxes
Answer:32.39
Step-by-step explanation: cost of movie is 19.9
Cost of earphone is 12.49
Adding both cost is 19.9+12.49
=32.39
The cost before tax deduction is 32.39
The three seventh grade classes at Sunview Middle School collected the most boxtops for a school fundraiser. They won a $600 prize to share among them. Mr. Aceves’ class collected 3,760 box tops, Mrs. Baca’s class collected 2,301, and Mr. Canyon’s class collected 1,855. How should they divide the money so that each class gets the same fraction of the prize money as the fraction of the box tops that they collected? Explain your reasoning.
Answer: The share would be approximately $285, $175, $141 respectively.
Step-by-step explanation:
Since we have given that
Number of box tops collected by Mr. Aceves's class = 3760
Number of box tops collected by Mrs. Baca's class = 2301
Number of box tops collected by Mr, Canyon's class = 1855
We first find the ration of box tops of Mr. Aceves, Mrs. Baca and Mr. Canyon respectively:
3760:2301:1855
Total = 3760+2301+1855=7916
Total amount to be share among them as a prize = $600
Mr. Aceves's share is given by
[tex]\dfrac{3760}{7916}\times 600\\\\=284.99\\\\\approx 285[/tex]
Mrs. Baca's share is given by
[tex]\dfrac{2301}{7916}\times 600\\\\=175.08\\\\\approx 175[/tex]
Mr. Canyon's share is given by
[tex]\dfrac{1855}{7916}\times 600\\\\=140.60\\\\\approx 141[/tex]
Hence, the share would be approximately $285, $175, $141 respectively.
Ginny is studying a population of frogs. She determines that the population is decreasing at an average rate of 3% per year. When she began her study, the frog population was estimated at 1,200. Choose the function that represents the frog population after x years.
A. f(x) = 1,200(1.03)x
B. f(x) = 1,200(0.03)x
C. f(x) = 1,200(0.97)x
D. f(x) = 1,200(0.97)x
If 45 cookies will serve 15 students, how many collies are needed for 30 students?
42-24 divide 6 ; value 3
The result of the expression 42-24 divided by 6, calculated using the 'Order of Operations' rule, is 38.
Explanation:You've asked to solve this mathematical expression: 42-24 divided by 6. To do this correctly, we must follow the 'Order of Operations,' often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
In your problem, the operations are Subtraction and Division. Following the PEMDAS rule, we perform Division before Subtraction. Therefore, first perform 24 divided by 6, which is 4. Then, subtract that result from 42. In the end, 42 minus 4 gives us 38 as the final answer.
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Which equivalent fraction would you have to use in order to add 3/5 to 21/25