One day, I decide to run to the park. On the way there, I run at a rate of x^2 miles per hour for 3 hours. On the way back, I take the same path and jog at a slower rate of 16 - 4x miles per hour so that it takes me 4 hours to get home. Given that x > 0, what is x? Express your answer as a common fraction.
Answer:
8/3
Step-by-step explanation:
Since we know that the distance that I traveled to the park and the distance that I traveled to get back home are the same, and that distance = rate x time, we have that
(x^2)(3)=(16-4x)(4)
3x^2=64-16x
3x^2+16x-64=0
(3x-8)(x+8)=0
Solving this equation, we get the solutions x=8/3 and x=-8. Since x must be positive, we have x=8/3.
The value of x = 8/3 and this can be determined by forming the quadratic equation using the given data and then factorizing it.
Given :
One day, I decide to run to the park. On the way there, I run at a rate of x^2 miles per hour for 3 hours.On the way back, I take the same path and jog at a slower rate of 16 - 4x miles per hour so that it takes me 4 hours to get home.x > 0The quadratic equation that represents the given situation is:
[tex](x^2)\times 3 = (16-4x)\times 4[/tex]
Simplify the above quadratic equation.
[tex]3x^2= 64-16x[/tex]
[tex]3x^2+16x - 64=0[/tex]
Now, factorize the above equation.
[tex]3x^2+24x-8x - 64=0[/tex]
3x(x+8) - 8(x + 8) = 0
(x + 8)(3x - 8) = 0
x = -8 will be rejected because x is always positive. So, the value of x = 8/3.
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One mile is equal to 5,280 feet.
How many feet are in 6 miles?
(BLANK) ft
Can you please help and explain I will give brainliest or thanks
Hiiiiiioo helpppp pleas I want to undertsand
A bag contains red and blue marbles. Given that 17/20 of the marbles are red, what percent of the marbles are blue?
Help PLZZZ
The percentage of the marbles that are blue is 15%.
What is a percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a bag contains red and blue marbles. Given that 17/20 of the marbles are red.
The percentage of red marble,
17/20 = 85%
Percent of the blue marble:
100%-85%=15%
Therefore, the percentage of the marbles that are blue is 15%.
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Explain why it works to break apart a number by place values to multiply
Answer:
We are still multiplying the sum of the addends whose result is those numbers. In other words, we are multiplying those same numbers too.
Step-by-step explanation:
Because when we break apart a number by placing values to multiply like when we do in partial products, we are still multiplying the sum of the addends whose result is those numbers. In other words, we are multiplying those same numbers too.
Check below that Partial Products example:
[tex]46*32=\\46=(40+6)\\32=(30+2)\\(40+6)(30+2)=1200+80+180+120[/tex]
Breaking a number apart by place values then multiply gives the same product as multiply the numbers directly because under multiplication condition, each digit in a number multiplies every other digit in the other value.
Using the expression as an example :
(17 × 12)
17 = 10 + 7 (tens and unit respectively)
12 = 10 + 2 (tens and unit respectively)
17 × 2 = (10 + 7)(10 + 2)
(10 + 7)(10 + 2) = (10×10) + (10×2) + (7×10) + (7×2) (10×10) + (10×2) + (7×10) + (7×2) = 100 + 20 + 70 + 14 = 204Therefore, the product will give the same result always.
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Help Please!
The equation below shows the total volume (V),in cubic units, of 2 identical boxes with each side equal to s units:
V = 2s3
If s = 3.5 units, what is the value of V?
A: 21.0 cubic units
B: 24.5 cubic units
C: 36.75 cubic units
D: 85.75 cubic units
Answer:
85.75 cubic units
Step-by-step explanation:
You got the formula [tex]V=2s^3[/tex] and you know that s = 3.5 units
The only thing you need to do is to substitute the value of s in your formula. This is
[tex]V= 2(3.5)^3[/tex]
And you need to do all the operations
[tex]V= 2(3.5)^3 = 2(42.875) = 85.75[/tex]
And your answer is D
The value of V for s = 3.5 units is,
⇒ V = 85.75 cubic units
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The equation below shows the total volume (V),in cubic units, of 2 identical boxes with each side equal to s units as,
⇒ V = 2s³
Here, We have;
s = 3.5 units
Hence, We get;
⇒ V = 2s³
⇒ V = 2 × 3.5³
⇒ V = 85.75 cubic units
Thus, The value of V for s = 3.5 units is,
⇒ V = 85.75 cubic units
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WILL GIVE BRAINLIEST!
Jake, Becky, and Max are meeting at Charley's Pizza for dinner and then plan to go to a movie. When they arrive at the pizza place, each one of them has a different coupon. They decide to use the coupon that will give them the best deal. Jake's coupon is $19.99 for a pizza and pasta meal deal; Becky's coupon is for two large one-topping pizzas--each at of the menu price; and Max's coupon is for three medium one-topping pizzas -- each at off the menu price. According to the menu, a medium one-topping pizza is $8.99, and a large one-topping pizza is $14.89. They also spend $1.25 each for sodas and $5.00 on the tip. At the movie theater, Max has a coupon that's good for off a third movie ticket when you purchase two other movie tickets at the regular price. The regular price of each movie ticket is $9.80.
Although Jake, Becky, and Max plan to split the cost of the pizza and movie, they decide that with the coupons, it's just easier if one of them pays at each place. So, the friends agree that Jake will pay for the pizza and Becky will pay for the movies. At the end of the night, they'll figure out how much Max owes both Jake and Becky.
At Charley's Pizza, they should use ________ coupon.
becky's
Jake's
max's
How to add a great answer
They should use Becky's coupon. I had the same question and I got it right. Hope this helps :)
Points A(−1.5) and B(6) are marked on a number line. Find the coordinate of point M if it is known that AM:MB=1:2. Find all possible answers.
Final answer:
By adding the distance from A to M to A's coordinate, we find that M's coordinate is 1.
Explanation:
The question asks to find the coordinate of point M on a number line where point A has a coordinate of −1.5, point B has a coordinate of 6, and the ratio of the distances AM to MB is 1:2. To solve this, we first identify that AM and MB are segments on the number line with point M somewhere between A and B. Since AM:MB = 1:2, we know that for every unit distance from A to M, there are 2 unit distances from M to B.
The total distance between A and B is 6 - (−1.5) = 7.5 units. Dividing this distance in the ratio 1:2, implies that AM takes up one-third of the total distance and MB takes up two-thirds of the total distance. Therefore, AM = ¼ * 7.5 = 2.5 units. Adding this distance to the coordinate of A gives us the coordinate for M: −1.5 + 2.5 = 1. So, the coordinate of point M is 1.
A number is divided into the ratio 5:9. If the first part is 35, find the number.
How do I round 6.44 to the nearest minute
If you place a 45-foot ladder against the top of a 36-foot building, how many feet will the bottom of the ladder be from the bottom of the building?
Answer:
27
Step-by-step explanation:
A line contains the points (-12, -60) and (60, -42).
What is the slope of the line in simplified form?
The slope of the line in simplified form is [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
The slope of a line which contains points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex]
is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
The given is:
1. Point (-12 , -60) lies on the line
2. Point (60 , -42) lies on the line
We need to find the slope of the line
∵ [tex](x_{1},y_{1})[/tex] = (-12 , -60)
∵ [tex](x_{2},y_{2})[/tex] = (60 , -42)
- Substitute these values in the rule
∴ [tex]m=\frac{-42-(-60)}{60-(-12)}[/tex]
∴ [tex]m=\frac{-42+60}{60+12}[/tex]
∴ [tex]m=\frac{18}{72}[/tex]
∴ [tex]m=\frac{1}{4}[/tex]
The slope of the line in simplified form is [tex]\frac{1}{4}[/tex]
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math question down below
Alicia plots a point at (0, 5) and (0, -2). What is the distance between the points?
It would be 7 units because when you put down the points and you draw a diaganal line between the two points and it crosses 7 intersections.
Hope you stay safe and this answer helps you.
A used electronics store pays $40 for each cell phone, spends $25 refurbishing the phone, and sells the refurbished phone to a customer for $100. Write an expression in simplest form that represents the company's earnings (in dollars) from buying, processing, and selling cell phones. Use x to represent the number of cell phones they sell.
Answer:
[tex]y=35\cdot{x}[/tex]
Step-by-step explanation:
The two expenses for the phones is $40 and $25 per phone. It is sold for $100. The amount of earnings is the sale price of the phone minus the expense for the phone. Let x be the number of phones they sell and y be the earnings. The expression is:
[tex]y=100x-(40+25)\cdot{x}[/tex]
[tex]y=35\cdot{x}[/tex]
While shopping, Kyla found a dress that she would like to purchase, but it costs $52.25 more than she has. Kyla charges $5.50 an hour for babysitting. She wants to figure out how many hours she must babysit to earn $52.25 to buy the dress. Use a double number line to support your answer.
Kyla has to babysit for 9.55 hours to earn $52.50 so that she can buy the dress.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
The dress costs $52.50 more that Kyla has, so she has to earn that much money by babysitting so that she can have the full amount of that dress.
Kyla charges $5.50 for an hour.
So, for $52.50 she has to work for 52.50 divided by 5.50;
52.50/5.50 hours
= 9.55 hours
Therefore, Kyla has to babysit for 9.55 hours to earn $52.50 so that she can buy the dress.
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Members of the BladeRunner Skating Club collected $950 from fundraising activities. They want to buy Ultrablade skates which are $48 a pair. How many pairs of skates can they buy? What does the remainder represent?
(-3/4+4/3)+a=0
What value of a will make the equation a true statement
The value of A that will satisfy the equation (-3/4 + 4/3) + A = 0 is -7/12 after finding a common denominator and simplifying the fractions.
Explanation:To find the value of a that will make the equation (-3/4 + 4/3) + a = 0 a true statement, we need to first simplify the fraction part of the equation.
Let's find a common denominator for the fractions, which is 12. Converting both fractions, we get:
-3/4 = -9/124/3 = 16/12Now, adding these two fractions we have:
-9/12 + 16/12 = 7/12
So, the equation now is:
7/12 + a = 0
To solve for a, we need to isolate a on one side of the equation:
a = -7/12
Therefore, the value of a that makes the equation true is -7/12.
What is a cause of mechanical weathering?
A. sunlight
B. natural acids
C. physical forces
D.rainwater
Answer:
Physical force is ur answer mate
Hope it helps.
If n=50 find the value of 6n
three times some number decreased by five is no less than 16
The problem involves mathematical inequalities. We translate the sentence into the inequality 3x - 5 ≥ 16 and solve for 'x', resulting in 'x ≥ 7'. Thus, the number must be 7 or any number above 7.
Explanation:The student's question involves mathematical inequalities. To solve it, let's use 'x' to represent the unknown number in the problem. The question can therefore be translated into the following inequality: 3x - 5 ≥ 16. To find 'x', follow these steps:
Add 5 to both sides of the inequality to undo the subtraction: 3x ≥ 21.Divide both sides of the inequality by 3, to isolate on 'x': x ≥ 7.So, the original sentence 'three times some number decreased by five is no less than 16' is equivalent to the inequality 'x ≥ 7'. Hence, the number must be 7 or any number greater than 7.
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Stephanie planted a home garden. She planted 2 rows of tomatoes with 5 tomato plants in each row. She also planted squash in rows of 7 plants each.
If x represents the number of rows of squash she planted, which of the following equations can be used to find the total number of plants Stephanie planted in her home garden?
A.
y = 7x + 10
B.
y = 7x + 7
C.
y = 8x + 7
D.
y = 15x + 7
Answer:
A. y = 7x + 10Step-by-step explanation:
The expression we have to find must include the total number of plants.
According to the problem, Stephanie has 2 rows of tomatoes with 5 tomatoes each, that means she has 10 tomato plants, so the expression must have 10 as a term.
You can see already that the only option that has 10 as a term is option A. Therefore, that's the right answer.
In addition, the other plant is represents by 7x, because the problem states that she planted squash in rows of 7 plants, where x expresses rows.
What is 7√11√ in simplest radical form? Enter your answer in the box.
Answer:
[tex]\sqrt{\frac{7}{11} }[/tex]
Step-by-step explanation:
The right expression of the question is
[tex]\frac{\sqrt{7} }{\sqrt{11} }[/tex]
The simplest radical form of this expression is obtained by applying the right property, which is about the quotient between radicals. According to this property, the quotient of radical is equal to the radical of the quotient, that is
[tex]\frac{\sqrt{7} }{\sqrt{11} }=\sqrt{\frac{7}{11} }[/tex]
Ashley is riding her bicycle. She rides at a speed of
9
kilometers per hour for
14.4
kilometers. For how many hours does she ride
Use factor trees to find the GCF of 32, 24, and 40.
before the rain began,the water in a lake was 268 inches deep.the rain began and after four hours of rain,the lake was 274 inches deep.the rain continued for one more hour at the same intensity.what was the depth of the lake when the rain stopped?
If before the rain began, the water in a lake was 268 inches deep. the rain began and after four hours of rain, the lake was 274 inches deep. the rain continued for one more hour at the same intensity, then the depth of the lake will be 275 inches.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Before the rain began, the water in a lake was 268 inches deep.
Rain began and after four hours of rain, the lake was 274 inches deep
Let us find the amount of increase of water for 4 fours.
274-268=4 inches.
In four hours, 4 inches of water increased.
At the same rate, in one hour the water is increased by 1 inch.
So, the depth of the lake when the rain stopped is 275 inches.
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Zahra compares two wireless data plans. Which equation gives the correct value of n, the number of GB, for which Plans A and B cost the same? (GB means “gigabytes of data.”)
Answer:
5n = 30 + 3(n - 4)
Step-by-step explanation:
Round 8.876 to the nearest whole number.
Answer:
Step-by-step explanation: