A square has side lengths of 2x inches. An equilateral triangle has side lengths of (2x+1/3) inches. If the square and the triangle have the same perimeter, what is the value of x?
Answer : The value of 'x' is [tex]\frac{1}{2}[/tex]
Step-by-step explanation :
As we know that,
The perimeter of square = 4a
The perimeter of equilateral triangle = 3s
('a' is the side square and 's' is the side of equilateral triangle)
Given:
Side of square = a = 2x
Side of equilateral triangle = s = (2x+1/3)
As per question, the square and the triangle have the same perimeter. That means,
Perimeter of square = Perimeter of equilateral triangle
4a = 3s
Now put the value of 'a' and 's', we get the value of 'x'.
[tex]4\times (2x)=3\times (2x+\frac{1}{3})[/tex]
[tex]8x=6x+1[/tex]
[tex]8x-6x=1[/tex]
[tex]2x=1[/tex]
[tex]x=\frac{1}{2}[/tex]
Therefore, the value of 'x' is [tex]\frac{1}{2}[/tex]
Which of the following is the inequality −18x + 2y ≥ −13 written in slope-intercept form?
Select one:
A. y ≥ - 6.5x - 9
B. y ≥ 7x - 10
C. y ≥ 9x − 6.5
D. y ≥ 10x - 7
If you flip two coins 12 times, what is the best prediction possible for the number of times both coins will land on tails?
_____ times
Answer:
3
Step-by-step explanation:
I know I'm late by 4 years but the answer is 3. This is because if you divide 12 by the 2 coins you'll get 6. You then need to divide it in half again because it's asking for both coins not only one. This gets you the answer of 3. I'm only writing this because other people may need help, 4 years later-
Eleven is decreased by twice a number. Represent this statement using an algebraic expression.
1. 11x-2
2. 2x+11
3. 11-2x
4. 2x-11
The required algebraic expression for the given statement is 11 - 2x. Option 3 is correct.
Given that,
Eleven is decreased by twice a number. To determine the correct option that shows the represents the statement using an algebraic expression.
The algebraic expression consists of constant and variable. eg x, y, z, etc.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let the number be x,
Eleven is decreased by twice a number.
= 11 - 2x
Thus, the required algebraic expression for the given statement is 11 - 2x. Option 3 is correct.
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Rewrite y + 3 = 0 using function notation.
A) f(x) = 3
B) f(x) = -3
C) f(x) + 3 = 0
D) f(x) = y + 3
Answer:
B) [tex]\displaystyle f(x) = -3[/tex]
Step-by-step explanation:
[tex]\displaystyle y ← f(x) \\ \\ y + 3 = 0; y = -3 \\ \\ f(x) = -3[/tex]
What is the distance around a circle called?
HELP ASAP
Find the system determinant of the given matrix.
-30
-6
6
30
what sides measurements do i need to know to answer this problem?
CAN I PLZZ GET SOME HELP WITH MATHH
The line segment is reflected about the y-axis to form A'B'. Which statement describes A'B'?
A'B' is half the length of AB.
A'B' and AB are equal in length.
A'B' is greater than twice the length of AB.
A'B' and AB are perpendicular.
Jeremy is looking at two different options for a new gym membership. Plan A has a fee of $40 plus an additional fee of $19.95 per month. With this plan, the first 3 months are free. Plan B has a fee of $59.85 plus an additional fee of $29.95 per month. With this plan, the first 6 months are free. After how many months would both options cost the same amount?
Adventure Play sells an mp3 player for $18.00 and charges $3.25 per song. King Music sells a player for $23.00 and charges $2.00 per song. For how many songs will the cost be the same?
The total number of songs is 4 at which the total cost be the same and this can be determined by forming the linear equation in two variables.
Given :
Adventure Play sells an mp3 player for $18.00 and charges $3.25 per song.King Music sells a player for $23.00 and charges $2.00 per song.Let the total number of songs be 'x' and the total cost be 'y'. Now, Adventure Play sells an mp3 player for $18.00 and charges $3.25 per song sp the total cost is given by:
y = 18 + 3.25x --- (1)
Also given that King Music sells a player for $23.00 and charges $2.00 per song so, the total cost is:
y = 23 + 2x --- (2)
Given the total cost will be the same, that is, equate equations (1) and (2).
23 + 2x = 18 + 3.25x
Simplify the above equation in order to determine the value of 'x'.
23 - 18 = 3.25x - 2x
5 = 1.25x
x = 4
So, the total number of songs is 4 at which the total cost be the same.
For more information, refer to the link given below:
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What is the side length of a square with an area of 144x^2
6 more than a number c
Answer:number c + 6
Step-by-step explanation:
You're adding 6 to the number c
how to unfoil quickly try not to use a lot of steps.
Final answer:
To unfoil quickly, use the reverse foil method. Identify the first and last terms of each binomial, multiply them, and rewrite the middle term as the sum of the products. Example: (x + 2)(x - 3) = x^2 + 2x - 3x - 6.
Explanation:
To unfoil quickly, you can use a shortcut called the reverse foil method. Reverse foil allows you to quickly determine the original factors of a quadratic expression that has been expanded using the distributive property. Let's say we have the expression (x + 2)(x - 3) and we want to unfoil it. Start by identifying the first term of each binomial, which in this case is x from (x + 2) and x from (x - 3). Multiply these two terms together to get x^2. Then, identify the last term of each binomial, which is 2 from (x + 2) and -3 from (x - 3). Multiply these two terms together to get -6. Finally, rewrite the middle term of the expanded expression as the sum of the two products obtained: (x^2 + 2x - 3x - 6). In this way, you can unfoil the expression quickly and identify the original factors without having to expand it fully.
45 minus 4.5. Show work
Calculate the area of a circle with a diameter of 6cm
When you write $1.35 what does the decimal point means
Are relstioships that have an initial fee proportional or non-proportionial?
100 children attended a play on the trip 0.6 were girls. Which fraction represents the number of boys on the trip
The number of boys who attended the play is 40. Expressing this as a fraction of the total children (100), we get 40/100, which simplifies to 2/5. So, the fraction representing the number of boys on the trip is 2/5.
Explanation:The provided information suggests that 60% (or 0.6) of the children on the trip, which were 100, were girls. This means the percentage or portion of girls on the trip is 0.6*100 = 60 girls. Since we're looking for the number of boys, we have to subtract this figure from the total number of children.
So, 100 total children - 60 girls = 40 boys. To express this as a fraction of the total number of children, we get 40/100. This fraction, however, can be simplified to 2/5, which is the fraction that represents the number of boys on the trip.
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malia is at an amusement park she bought 14 tickets and each ride requires 2 tickets write an expression that gives a number of tickets malia has left in terms of x the number of rides she has already gone on find atlas one other expression that is equvalent to it
Trevor rode his bicycle 25 miles in 2 hours. Assuming Trevor rode at a constant speed, how many miles did Trevor ride in one hour
Describe a cube.use the words faces,edges,and vertices in your description
It costs 3 tickets to play a game at the fair. If you spent 21 tickets on the game, which equation could you use to solve for the number of games, g?
A. 21g=3
B. 21·3=g
C. g3=21
D. 3g=21
Answer:
Option D. 3g=21
Step-by-step explanation:
Let
g -----> the number of games
we know that
The number of games multiplied by 3 tickets to play a game must be equal to 21 tickets
so
The linear equation that represent this problem is
[tex]3g=21[/tex]
solve for g
Divide by 3 both sides
[tex]g=7[/tex]
Answer:
3g=21
Step-by-step explanation:
im smart (not really though){i got it right on imagine math}
:0
The graph below shows the number of chairs arranged with different numbers of tables in a room
A) there are 4 chairs for every 1 table in the room.
B) there are 4 tables for every 1 chair In the room.
C) the ratio of chairs to tables in the room is 5:1
D) the ratio of tables to chairs in the room 5:1
The table shows numbers of books read by students in an English class over a summer and the students’ grades for the following semester.
a) Find the line of best fit. Write in the equation for the line of best fit.
b) Use your equation to predict the grade of a student who reads 15 books. Show all your work.
A cube has a surface area of 1,014 square meters. what is the length of one side.
For which of these sets of data would all the points be displayed on a scatterplot if the window size on a regression calculator were set to 5
Answer
A is the answer
Step-by-step explanation:
I took the test
Given: ABCD is a trapezoid,
AD = 10, BC = 8,
CK
- altitude
Area of ∆ACD = 30.
Find: Area of ABCD
Therefore, the area of trapezoid ABCD is 54 square units.
To find the area of trapezoid ABCD, we can use the properties of a trapezoid and the given information.
First, let's denote the unknown base of the trapezoid as BD = b. Since AD and BC are the other two bases, we have AD = 10 and BC = 8. The height of the trapezoid is the same as the altitude of triangle ACD, which is KC = h and is given to be such that the area of triangle ACD is 30.
The area of a triangle is given by the formula:
[tex]\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
For triangle ACD, we have:
[tex]\[ 30 = \frac{1}{2} \times AD \times h \][/tex]
[tex]\[ 30 = \frac{1}{2} \times 10 \times h \][/tex]
[tex]\[ h = \frac{30 \times 2}{10} \][/tex]
[tex]\[ h = 6 \][/tex]
Now that we have the height of the trapezoid, we can calculate the area of the trapezoid using the formula:
[tex]\[ \text{Area} = \frac{1}{2} \times (\text{sum of parallel sides}) \times \text{height} \][/tex]
[tex]\[ \text{Area} = \frac{1}{2} \times (AD + BC) \times h \][/tex]
[tex]\[ \text{Area} = \frac{1}{2} \times (10 + 8) \times 6 \][/tex]
[tex]\[ \text{Area} = \frac{1}{2} \times 18 \times 6 \][/tex]
[tex]\[ \text{Area} = 9 \times 6 \][/tex]
[tex]\[ \text{Area} = 54 \][/tex]
Identify and give all the appropriate names for three different quadrilaterals or other geometric figures in this Navajo eye-dazzler design.
Answer: I don’t know
Step-by-step explanation: I don’t know
brooks planning a dinner party. he plans to give a choice of three kinds of salad: potatoe salad, tossed salad, and pasta salad, there will be three choices of meat: ham, chicken, and turkey. the dessert selections are ice cream, cake, and pie. how many salad/meat/dessert combinations are there?