Answer:
the answer is
Step-by-step explanation:
2/3
The figure shown is an equilateral triangle. Calculate the length of each side and give your answer in cm.
First side:2x-7
Second side:x+y-9
Third side:y+5
From the sides length of given equilateral triangle,
Length of each side = 21 cm
Given :
In an equilateral triangle , the length of sides are given by
First side:2x-7
Second side:x+y-9
Third side:y+5
All the sides are equal in equilateral triangle .
second side = third side length
[tex]x+y-9=y+5\\Subtract \; y \\x+y-y-9=y-y+5\\x-9=5\\x=5+9\\x=14[/tex]
first side =third side
[tex]2x-7=y+5\\\2(14)-7=y+5\\21=y+5\\21-5=y\\y=16[/tex]
Now we find length of the side
[tex]2x-7\\2(14)-7\\21[/tex]
All sides are equal in equilateral triangle
Length of each side = 21 cm
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order each set of integers from least to greatest -221, 63, 54, -89, -71, -10
8000 divided by 17000
Which ordered pairs are solutions to the inequality. 3x+4y greater than or equal to 12
(8,-3)
(-5,2)
(0,5)
(3,2)
Choose any that apply
The ordered pairs that are solutions to the inequality 3x + 4y ≥ 12 are (8, -3), (0, 5), and (3, 2). The pair (-5, 2) does not satisfy the inequality and is not a solution.
To determine which ordered pairs are solutions to the inequality 3x + 4y ≥ 12, we can substitute the x and y values from each pair into the inequality and see if it holds true.
For (8, -3), we check if 3(8) + 4(-3) ≥12, which gives 24 - 12 ≥ 12, so 12 ≥ 12. This pair is a solution because the inequality is satisfied.For (-5, 2), we check if 3(-5) + 4(2) ≥ 12, which gives -15 + 8 ≥ 12, so -7 ≥ 12. This pair is not a solution because the inequality is not satisfied.For (0, 5), we check if 3(0) + 4(5) ≥ 12, which gives 0 + 20 ≥ 12, so 20 ≥ 12. This pair is a solution because the inequality is satisfied.For (3, 2), we check if 3(3) + 4(2) ≥ 12, which gives 9 + 8 ≥ 12, so 17 ≥ 12. This pair is a solution because the inequality is satisfied.Therefore, the solution pairs are (8, -3), (0, 5), and (3, 2).
identify and explain the error why GCF for 28, 42, 56 is 736
Ms. Winter makes homemade bath soaps and bottles of lotion. In her inventory, she has 48 bath soaps and 64 bottles of lotion. She wants to use all of her inventory to make as many gift baskets as she can using the same number of bath soaps and the same number of lotion bottles in each gift basket. QUESTION: HOW MANY GIFT BASKETS CAN SHE MAKE AT THE MOST? EACH BASKET WILL CONTAIN HOW MANY BOTTLES OF LOTION AND HOW MANY BOTTLES OF BATH SOAPS???? pls
Write 10x - 5y = 30 in slope intercept form
The required equation in slope-intercept form is y = 2x - 6.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + b
Where:
m is the slope or rate of change.x and y are the points.b is the y-intercept or initial value.Based on the information provided about this line, a linear equation in standard form that models it is given by;
y = mx + b
10x - 5y = 30
By making y the subject of formula, we have the following:
10x - 5y = 30
2x - y = 6
y = 2x - 6
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Which fraction is equivalent to negative 4 over 6?
6 over negative 4
negative 6 over 4
4 over negative 6
4 over 6
The fraction that is equivalent to -4/6 is 4/-6. so the correct option is C.
To find an equivalent fraction, we need to divide both the numerator and denominator by their greatest common factor.
In this case, the greatest common factor of 4 and 6 is 2.
Dividing -4 by 2 gives -2, and dividing 6 by 2 gives 3.
Since we have given the option as 4 over negative 6
Thus, -4/6 = 4/-6
Therefore, the fraction equivalent to -4/6 is 4/-6.
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what is 35% of $100?
Each day at lunchtime, at least 53 people buy food from a food truck.
Using the variable p, an inequality that represents that situation is...
Answer:
p≥ 53
Step-by-step explanation:
Given that, at least 53 people buy food from the food truck. It means minimum 53 people buy the food, and number greater than 53 is quite possible; however, the possibility of people buying food less than 53 is not possible.
Since the number of people is alway 53 or greater than 53 therefore we may represent this condition using the greater and equal sign.
Lets use the variable p for people who buy the food.
Now the inequality can be written as
p≥ 53
So our desired inequality is p≥ 53 .
A packing machine can pack 4,000 boxes in 5 hours. At what rate does the machine work?
Find the solution to the system of equations graphed here.
A)
(-1, -3)
B)
(1, -3)
C)
(1, 3)
D)
(3, 1)
The solution of the given system of equations is (1,3) and this can be determined by using the given data.
Given :
The pink line in the graph passes through the point (0,5) and (2.5,0).The blue line in the graph passes through the point (0,4) and (4,0).The equation of a pink line that passes through the point (0,5) and (2.5,0) is:
[tex]\dfrac{y-5}{x-0}=\dfrac{0-5}{2.5-0}[/tex]
Simplify the above equation.
(y - 5) = -2x
y + 2x = 5 --- (1)
The equation of a blue line that passes through the point (0,4) and (4,0) is:
[tex]\dfrac{y-4}{x-0}=\dfrac{0-4}{4-0}[/tex]
Simplify the above equation.
y - 4 = -x
y + x = 4
y = 4 - x --- (2)
Substitute the value of 'y' in equation (1).
4 - x + 2x = 5
x = 1
Substitute the value of 'x' in equation (2).
y = 4 - 1
y = 3
Therefore, the correct option is C).
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The longest bridge in the world is located in China. It is164,800 meters long. Another bridge in China is 69,732 meters long. Round each length to the nearest ten thousand to find the answer. What is the approximate difference between the lengths of the two bridges?
5/4, 9/10, 4/5, 13/20 in order from lightest to heaviest
Multiply and answer on scientific notation : (3.8 x 10^8) (6.9 x 10^5)
If a rock weighs 12.64 on Jupiter how much does it weigh on earth? What is an equation that represents the situation is y=
How to divide 19 divided by 789 step by step?
To divide 19 by 789, we perform long division, considering decimal places and significant figures. A calculator can provide the decimal result, but users should adjust for the correct number of significant figures, especially when working with scientific notation where exponents are subtracted and coefficients are divided.
Explanation:Dividing 19 by 789 step by step is essentially the process of long division. To divide 19 by 789, we would write 19 as the dividend and 789 as the divisor. Since 19 is smaller than 789, we inherently work with a number less than 1. Therefore, we can apply division by powers of 10 to make the problem more manageable.
We start by considering decimal places and significant figures. For example, if we have 1.9436 and we want to divide it by 1000, we simply move the decimal point three places to the left, resulting in 0.0019436. When we convert ratios to whole numbers, we divide both sides by the smaller amount to simplify the division.
For instance, when calculating 337/217 using a calculator, we obtain a long decimal answer, but we must take into account the significant figures to report the answer accurately. In scientific notation, we subtract exponents during division but divide the coefficients normally.
Ron is tiling a countertop. He needs to place 54 square tiles on each of 8 rows to cover the counter. He wants to randomly place 8 groups of 4 blue tiles each and have the rest of the tiles be white. how many white tiles wwill Ron need ?
Answer: There are 400 white tiles which Ron will need.
Step-by-step explanation:
Since we have given that
Number of rows to cover the counter = 8
Number of tiles to cover each 8 rows = 54 square tiles
So, total number of tiles to cover 8 rows is given by
[tex]8\times 54=432[/tex]
Number of groups on which 4 blue tiles are placed = 8
Total number of blue tiles on 8 groups is given by
[tex]8\times 4=32[/tex]
Remaining are the white tiles so, it is given by
[tex]432-32=400[/tex]
So, there are 400 white tiles which Ron will need.
Adding and Subtracting Fractions. Solve each problem.Write your answer as a mixed number if possible.
1. 4 2/7 - 2 1/5
2.5 7/8 + 11/4
3.5/8 - 7/3
4.16/5 + 2 1/2
The answers to the four mixed number problems are 2 3/35, 16 7/8, -1 17/24, and 5 7/10, respectively.
Explanation:These problems involve adding and subtracting fractions and writing the answer as a mixed number, if possible. Let's go through each one step-by-step.
1. 4 2/7 - 2 1/5: First, convert these mixed numbers into improper fractions (4 2/7 = 30/7 and 2 1/5 = 11/5). The common denominator is 35. Rewrite the fractions as 150/35 and 77/35, subtract to get 73/35 which simplifies to '2 3/35'.
2. 5 7/8 + 11/4: Convert these mixed numbers into improper fractions (5 7/8 = 47/8 and 11/4 = 44/4). The common denominator is 8. Rewrite the fractions as 47/8 and 88/8, add to get 135/8 which simplifies to '16 7/8'.
3. 5/8 - 7/3: The common denominator is 24. Rewrite the fractions as 15/24 and 56/24. Subtract to get -41/24 which simplifies to '-1 17/24'.
4. 16/5 + 2 1/2: Convert the mixed number into an improper fraction (2 1/2 = 5/2). The common denominator is 10. Rewrite the fractions as 32/10 and 25/10. Add to get 57/10 which simplifies to '5 7/10'.
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Write a real world situation that could be modeled by the equation 100-6x=160-10x.
Answer:
Suppose you have $100 and you spent 6 dollar each day, and your friend has $160 and he/she spent $10 each day. After x days you both have equal amount, find the number of days.
Step-by-step explanation:
Consider the provided information.
We need to write a real world situation that could be modeled by the equation 100-6x=160-10x.
You can use any situation to represents this equation.
The left side of the equation consists of a constant and a variable also the right side of the equation consists of a constant and a variable.
Suppose you have $100 and you spent 6 dollar each day, and your friend has $160 and he/she spent $10 each day. After x days you both have equal amount, find the number of days.
Miguel's grandparents love 159 miles from his house. if it takes 3 hours to drive to his grandparents house, what is the average speed?
Final answer:
To find Miguel's average speed, divide the distance to his grandparents' house, 159 miles, by the time it takes, 3 hours, which gives us an average speed of 53 mph.
Explanation:
To calculate Miguel's average speed when driving to his grandparents' house, we use the formula for average speed, which is the distance traveled divided by the time taken to travel that distance. In this case, if Miguel's grandparents live 159 miles away and it takes 3 hours to get there, we divide the distance by the time to find the average speed:
Average speed = Distance ÷ Time
Average speed = 159 miles ÷ 3 hours
Average speed = 53 miles per hour (mph)
Therefore, Miguel's average speed to his grandparents' house is 53 mph.
1 kg of sand has a volume of 400 cm*. What is its densityin g/cm*.
( * is cubed)
Nick's iPod has 360 songs 15% are top-forty hits 40% are house music and the rest are Justin Bieber songs how many songs are top-forty hits, how many songs are house music, and how many songs are by Justin Bieber
Answer:
JUSTIN BIEBER
Step-by-step explanation:
360 ÷ 10 = 36 = 10%
36 ÷ 2 = 18 = 5%
36 + 18 = 54 = 15% = Top-Forty Hits
-
36 × 4 = 144 = 40% = House Music
-
144 + 54 = 198
360 - 198 = 162 = Justin Bieber
But just saying I ❤️ Justin Bieber
Sharon is 54 inches tall. A tree in her backyard 5 times as tall as she is. The floor of her tree houses at a height that is twice as tall as she is. What is the difference, and inches, between the top of the tree in the floor of the treehouse
Find the slope of the line.
Answer: [tex]m = \frac{1}{6}[/tex]
Step-by-step explanation:
(-5,-4) = (x1, y1)
(1,-3) = (x2, y2)
Slope = [tex]\frac{y2-y1}{x2-x1}[/tex]
= [tex]\frac{-3-(-4)}{1-(-5)}[/tex]
= [tex]\frac{-3+4}{1+5}[/tex]
= [tex]\frac{1}{1+5}[/tex]
= [tex]\frac{1}{6}[/tex]
What is 11.875 as a fraction
11.875 can be expressed as the fraction 11 7/8.
To express 11.875 as a fraction, we can start by recognizing that the decimal can be written as a mixed number with a whole number and a fraction component. The whole number is 11, and the fraction component is 0.875. To convert the fraction component to a fraction, we observe that 0.875 is equivalent to 875/1000 because there are 875 parts out of 1000 in the decimal representation. We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 125.
Dividing 875 by 125 results in 7, and dividing 1000 by 125 results in 8. Therefore, 0.875 can be simplified to 7/8.
Combining the whole number and the fraction component, we can write 11.875 as the mixed number 11 7/8.
Thus, 11.875 can be expressed as the fraction 11 7/8.
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What is the slope of the line on the graph?
A Web music store offers two versions of a popular song. The size of the standard version is 2.1 megabytes (MB). The size of the high-quality version is
4.8 MB. Yesterday, there were 1010 downloads of the song, for a total download size of 3039 MB. How many downloads of the high-quality version were there?
The average distance in kilometers (km) from the sun to the planet Mercury is about 58,000,000 km. Write this distance in scientific notation. .
Connie and Chris are saving money to go to a concert. Connie has $9 and saves $6 per week.
Connie wrote an equation to determine how much she saves in a given week.
y=6x+9
Chris has $27 and saves $3 per week.
Chris made a graph to show how much he saves in a given week.
How many weeks will it take Connie and Chris to save the same amount of money?