Starting from the same place, Miranda walks due west and Blake walks due east. On the number line, 0 represents their starting point; negative values represent the distance in feet, traveled west; and positive values represent the distance in feet, traveled east. How many feet apart are Miranda and Blake on the number line? Enter your answer in the box.
Answer:
360 feet
Explanation:
There are 10 hash marks between 0 and 300; this means that each hash mark is 300/10 = 30 feet.
Miranda's location is 5 hash marks below 0; this puts her at 5(30) = 150 feet below 0, or -150.
Blake's location is 7 hash marks above 0; this puts him at 7(30) = 210 feet above 0, or 210.
This means they are 210--150 = 210+150 = 360 feet.
To find the distance between Miranda and Blake on a number line, you sum the absolute values of the distances each has traveled from the starting point O, regardless of direction.
Explanation:
If Miranda walks due west and Blake walks due east from the same starting point O (represented as 0 on the number line), then the distance between Miranda and Blake is the sum of their absolute distances from the starting point. For example, if Miranda walks 2 feet west and Blake walks 3 feet east, the distance between them on the number line would be 2 (west) + 3 (east) = 5 feet.
Here, we're using the concept of absolute value where negative values represent westbound distances, and positive values represent eastbound distances. Unlike calculating displacement, where direction mattered, calculating the distance between two points doesn't require you to consider direction. The magnitude of distance traveled in opposite directions from the same starting point is simply added together.
So, applying these principles of number lines and absolute values, to get the distance between Miranda and Blake, you add the distance each has traveled from the starting point O, regardless of their directions.
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Which expression is equivalent to (3a5 + b4)2
Answer:
The expression [tex]9a^{10}+6a^2b^4+b^8[/tex] is equivalent to the given expression.
Step-by-step explanation:
The given expression is
[tex](3a^5+b^4)^2[/tex]
Use algebraic formula:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
[tex](3a^5+b^4)^2=(3a^5)^2+2(3a^5)(b^4)+(b^4)^2[/tex]
[tex](3a^5+b^4)^2=3^2(a^5)^2+6a^5b^4+(b^4)^2[/tex]
Use exponent property:
[tex](a^m)^n=a^{mn}[/tex]
[tex](3a^5+b^4)^2=9a^{10}+6a^5b^4+b^8[/tex]
Therefore expression [tex]9a^{10}+6a^5b^4+b^8[/tex] is equivalent to the given expression.
Find two numbers if their difference is 16 and their ratio is 5:7.
Answer:
40,56
(btw if ur here for rsm write it as 40,56 not 56,40)
which of these nonterminating decimals can be converted into a rational number? A 0.48907542... b 0.02020202... C 0.92589542... D 0.10203040...
Paul is painting a square wall with an area of 115 square feet. To the nearest foot, what is the length of the wall? Hint: A = s2.
11 **
29
42
58
Decimals B, C, and D can be converted into rational numbers as they have repeating patterns.
Explanation:A nonterminating decimal can be converted into a rational number if it is a repeating decimal. Among the given options, decimals B, C, and D can be converted into rational numbers because they have repeating patterns.
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The cost for a business to make greeting cards can be divided into one-time costs, and repeated costs, suppose the total to make 300 cards is $900.00, and the total to make 650 is 1,600.00. What is the total cost to make 1,000 cards? Round your answer to the nearest dollar
A) 2,100.00
B) 2,300.00
C)2,500.00
D)3,000.00
In 1924 the temperature in Fairfield Montana drop 63° to -21° in 12 hours. What was the average hourly change in temperature
The table shows the ingredients used in a medicine. If all the decimals were rounded to the nearest whole percent, would this table be helpful in comparing the amount of each ingredient? Explain. Ingredient Percent Substance A 19.6% Substance B 19.9% Substance C 19.5% Substance D 14.5% A. Yes; substance B would still be the largest part of the medicine. B. No; three of the percentages would round to 19%. C. No; three of the percentages would round to 20%. D. No; two of the percentages would round to 20%.
Selena babysit on the weekends. The equation is Y equals 13x represents the amount of money she earns. What is the constant of proportionality
Yousef typed a 36-word paragraph in 2/3 minute. What is his typing speed, in words per minute? Enter your answer in the box.
we know that
Yousef typed a [tex]36[/tex]-word paragraph in [tex]2/3[/tex] minute
so
by proportion
Find the number of words typed in one minute
[tex]\frac{36}{(2/3)} \frac{words}{minutes} =\frac{x}{1} \frac{words}{minute}\\ \\x=36*\frac{3}{2}\\ \\x= 54\ words[/tex]
therefore
the answer is
Yousef typing speed, in words per minute is equal to
[tex]54\frac{words}{minute}[/tex]
The typing speed of Yousuf in words per minutes is [tex]54\;\rm words\;per\;minute[/tex].
Yousuf typed 36 words in [tex]\dfrac{2}{3}\;\rm minutes[/tex].
By Unitary method, calculate the speed of typing by Yousuf as-
[tex]\dfrac{2}{3} \;\rm minutes \rightarrow 36\;\rm words\\1\;\rm minute \rightarrow \dfrac{36}{(\frac{2}{3})}\;\rm words\\1\;\rm minute \rightarrow \dfrac{36\times 3}{2}\;\rm words\\1\;\rm minute \rightarrow 54\;\rm words[/tex]
Hence, the typing speed of Yousuf in words per minutes is [tex]54\;\rm words\;per\;minute[/tex].
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Kelly has 3/4 of a pie left. She wants to slip the pie with 3 of her friends.How much pie will each person get?
Raul is solving -6x=72.Find his mistake and correct it.
Nora took 8 bottles of water to a picnic. Of those bottles of water, she and her friends opened a certain number of bottles. b. What expression can be used to determine the number of unopened bottles at the end of the picnic?
A. 8+b
B. B+8
C.8-b
D.b-8
Final answer:
To calculate the number of unopened bottles after some have been opened, subtract the number of opened bottles (b) from the total number brought to the picnic (8), resulting in the expression 8 - b.
Explanation:
The expression to determine the number of unopened bottles of water at the end of the picnic, when Nora took 8 bottles and a certain number of bottles were opened, would be 8 - b. Here, the variable b represents the number of bottles that were opened, and since we start with 8 bottles, we subtract the number that were opened (b) from the total number of bottles (8) to get the number that remain unopened.
the solution to -5 m = -20 is negative true or false
There are 32 female performers in a dance recital. The ratio of men to women is 3;8. How may men are in the dance recital?
Find the slope. Is it positive,negative,zero or undefined? Show your work. Y=-1/8x+12
The diameter of Virus A is 2.6 • 10^-7 millimeters. If Virus B has a diameter that is 15 times larger than Virus A, find the diameter of Virus B.
The diameter of Virus B, which is 15 times larger than Virus A, is 3.9 • 10^-6 millimeters.
Explanation:Virus A possesses a minute diameter, measuring at 2.6 x 10^(-7) millimeters. When comparing it to Virus B, which is 15 times larger, you simply multiply Virus A's diameter by 15. Therefore, Virus B boasts a diameter of (2.6 x 10^(-7) mm) x 15, resulting in 3.9 x 10^(-6) millimeters. This means that Virus B is significantly larger than Virus A. This mathematical relationship highlights the scale and size differences between these two viruses, emphasizing the substantial increase in diameter when transitioning from Virus A to Virus B, due to the multiplication factor of 15.
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Find the percent of each number 350% of 96
What is the value of the underlined digit 28?
Mixed numbers between 5 and 7 with an interval of 1/3
What is the solution to the inequality 2(x + 3) ≥ –10 – 4x? solve step by step, please.
Jada has picked 1 cup of strawberries for a cake, which is enough for ¾ of the cake. How many cups does she need for the whole cake?
Answer:
she needs 1 [tex]\frac{1}{3}[/tex] cup of strawberries
Step-by-step explanation:
To find the number of cups needed, we will simply solve using proportion
From the question, Jade picked 1 cup of strawberries for 3/4 of a cake
and we are asked to find the number of cups needed for a whole cake
Let x be the number of cups needed for the whole cake
[tex]\frac{3}{4} cake[/tex] = 1 cup of strawberries
1 cake = x
Cross multiply
[tex]\frac{3}{4}[/tex] × x = 1 × 1
[tex]\frac{3x}{4}[/tex] = 1
cross multiply
3x =4
To get the value of x, we simply divide both-side of the equation by 3
[tex]\frac{3x}{3}[/tex] = [tex]\frac{4}{3}[/tex]
(On the left-hand side of the equation, 3 will cancel out 3 leaving us with x and on the right-hand side of the equation 4 will be divided by 3 which will give us 1 [tex]\frac{1}{3}[/tex] )
x = 1 [tex]\frac{1}{3}[/tex]
Therefore 1 [tex]\frac{1}{3}[/tex] cup of strawberries is needed for the whole cake.
The area of a square is 49 cm. What is the length of one side
What is the equation of this line
Y=1/4x
Y=4x
Y=-1/4x
Y= -4x
if two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplemantary are the lines parallel?
When two lines in a plane are cut by a transversal and a pair of consecutive interior angles is supplementary, the lines are parallel.
Explanation:When two lines in a plane are cut by a transversal and a pair of consecutive interior angles is supplementary, the lines are parallel.
We know that consecutive interior angles are located on the same side of the transversal and are inside the two lines.
Since the consecutive interior angles are supplementary, they add up to 180 degrees. This indicates that the lines are parallel.
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What is 9 divided by 261
the length of a rectangle is 2cm more than 5 times the width ,the perimeter is 196 cm,what is the width & length?
What is the slope of this line?
Enter your answer in the box.
Simplify.
x + (7 + 14x)
i need some help with solving inequalitys 9x-9 greater thab or equal to 2(8x-15)
The Burmese pythons can be anywhere from 16 to 23 feet long. What is the difference in length inches between the longest and shortest Burmese python?
Answer: There is a difference of 84 inches.
Step-by-step explanation:
Since we have given that
Longest length of python = 23 feet
Shortest length of python = 16 feet
As we know that
1 feet = 12 inches
23 feet = 23×12=276 inches
16 feet = 16×12=192 inches
Difference between them is
276-192=84 inches
Hence, there is a difference of 84 inches.