Answer: To write a linear equation to model the relationship between the height h of the candle and time t, we need to find the slope and y-intercept of the line that represents this relationship.
The slope of the line is given by the rise over the run, or the change in the y-value (the height of the candle) over the change in the x-value (the time). We can calculate the slope by taking the difference in the height of the candle after 5 hours and 3 hours, and dividing it by the difference in the time:
slope = (16.5 - 18) / (5 - 3) = (-1.5) / (2) = -0.75
The y-intercept of the line is the point at which the line crosses the y-axis. This is the height of the candle when the time is 0. We can use the height of the candle after 3 hours as the y-intercept, since this is the height when the time is 3:
y-intercept = 18
We can use these values to write a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept.
Plugging in the values we found, we get:
h(t) = -0.75t + 18
This is the linear equation that models the relationship between the height h of the candle and time t.
To predict how tall the candle will be after burning for 8 hours, we can plug in t = 8 into the equation:
h(8) = -0.75(8) + 18 = -6 + 18 = 12 inches
This means that the candle will be 12 inches tall after burning for 8 hours.
Therefore, the correct answer is (d) h(t) = 0.75t + 20.25; 14.25 inches.
To write a linear equation to model the relationship between the height of the candle and time, we can use the information given. We know that after 3 hours, the candle is 18 inches tall, and after 5 hours, it is 16.5 inches tall.
We can set up a system of linear equations to represent this information. Let's call the height of the candle h and the time t. Then we can set up the following system:
h = 18 - 3t
h = 16.5 - 5t
To solve this system, we can set the two equations equal to each other and solve for t:
18 - 3t = 16.5 - 5t
1.5 = 2t
t = 0.75
This tells us that the height of the candle decreases by 0.75 inches per hour.
Now we can use this information to predict how tall the candle will be after 8 hours. We can plug in 8 for t in the equation h = 18 - 3t to find the height of the candle:
h = 18 - 3(8)
h = 18 - 24
h = -6 inches
So the candle will be about 6 inches shorter after burning for 8 hours. This means it will be about 10.5 inches tall.
The correct option is c, h(t) = -0.75t + 15.75; 9.75 inches.
This is because we found that the height of the candle decreases by 0.75 inches per hour, which is represented by the coefficient of t in the equation. The y-intercept, 15.75, represents the initial height of the candle, which we found to be 16.5 inches.
Happy to help!
find the particular solution of the differential equation that satisfies the initial condition(s). f '(s)
Particular solution of the differential equation that satisfies the initial condition f'(s) = 10s - 4s³ , f(3) = 5 is f(s) = 5s² - s⁴ + 41.
We determine the particular solution to the differential equation. We do this by integrating the given differential equation and then applying the given initial condition. The power rule should be used for the given expression.
[tex]\int\ {x^{a} } \, dx[/tex] = [tex]\frac{x^{a+1} }{a+1} }[/tex]
we have given that,
f'(s) = 10s - 4s³
f(s) = ∫ f'(s)ds
= ∫(10s - 4s³)ds
= [tex]\frac{10s^{2} }{2} - \frac{4s^{2} }{4}+ C[/tex]
f(s) = 5s² - s⁴ + C
Now we will apply the initial condition,
f(3) = 5
⇒5(3)² - (3)⁴ + C =5
-36 + C = 5
C =41
Therefore the solution is expressed as,
f(s) = 5s² - s⁴ + 41
This is the particular solution.
Given question is incomplete. Complete question is given as:
find the particular solution of the differential equation that satisfies the initial condition(s). f '(s) = 10s - 4s³, f(3) = 5.
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a card is drawn from a deck of 52 playing cards. what is the probability that it is a king and a black card?
The probability that the card is a king and a black card is 1/26.
What is the probability?There are 4 kings in a deck of 52 playing cards, and half of the cards are black, so there is a 1/13 probability that a randomly drawn card is a king, and a 1/2 probability that it is black.
To find the probability that a card is both a king and black, you can use the formula for the probability of the intersection of two events: P(A and B) = P(A) * P(B | A), where P(A) is the probability of event A occurring, and P(B | A) is the probability of event B occurring given that event A has already occurred.
Using this formula, the probability of drawing a king and a black card is:
P(King and Black) = P(King) * P(Black | King)
= (1/13) * (1/2)
= 1/26
So the probability of drawing a king and a black card is 1/26, or about 3.8%.
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HELP ASAP!!
Angles W and X are complementary. Determine the degree measure of ZW if mZX = 29.8°
55.1°
60.2°
90°
150.2°
Answer:
(b) 60.2°
Step-by-step explanation:
You want the measure of angle W if angles W and X are complementary and X = 29.8°.
Complementary anglesComplementary angles total 90°:
X + W = 90° . . . . . . . . . complementary relation
29.8° +W = 90° . . . . . . use given value
W = 90° -29.8° . . . . . . subtract 29.8°
W = 60.2°
Write an equation of the line that passes through $\left(-1,\ 3\right)$ and is parallel to the line $y=-3x+2$ .
The equation of the line that passes through point (-1, 3) and parallel to line y = 3x + 2 is
y = 3x + 4How to find the line that passes through point point (-1, 3)As a parallel line part of the qualities include that the slopes of the lines are equal
The equation of line is y = 3x + 2
The slope intercept form of the form as
y = mx + c
where
m = slope
c = intercept
x = input variables
y = output variables
Line has slope, m = 3, a new parallel line of slope 3 passing through point (-1, 3)
(y - y₁) = m (x - x₁)
y - 3 = 3 (x - -1)
y = 3x + 1 + 3
y = 3x + 4
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how large a sample should be taken in order to estimate the proportion to within 4% with a 95.44% level of confidence?
Answer: The product of two consecutive negative integers is 600. What is the value of the lesser integer?
Step-by-step explanation:
EDGE2021
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Correct representations of the inequality -3(2x - 5) 5 are - 6x + 15 10 - 5x (2 – x)
What is Inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. [1]
The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:
The symbol a b indicates that an is smaller than b.
When a > b is used, it indicates that an is bigger than b.
A is not equivalent to b in any scenario. Since an is strictly less than or strictly greater than b, these relationships are known as stringent inequalities[1]. Equivalence is not considered.
There are two form of inequality relations that are not strict, in contrast to strict inequalities:
The indication of an or b denotes that.
According to our question-
The fourth response is shown by an open circle at 5, and a bold line that begins at 5 and points to the right (attached figure)
Detailed explanation
The difference is 5 (-3(2x - 5)). (2 - x)
First, make each side simpler.
∵ -3(2x - 5) = -3(2x) + -3(-5) (-5)
Recall that (+)=(-)
∴ -3(2x - 5) = - 6x + 15
∵ 5(2 - x) = 5(2) + 5(-x) (-x)
Recall that (+)(-) = (-)
∴ 5(2 - x) = 10 - 5x
∴ - 6x + 15 < 10 - 5x
Take 15 away from both sides.
∴ - 6x < -5 - 5x
5 times on both sides
∴ - x < - 5
Because the coefficient of x is negate, you must change the inequality's sign when you divide both sides by it.
The x coefficient is -1.
∴ Add -1 to both sides.
∴ x > 5
The appropriate answers are:
- 6x + 15 < 10 - 5x
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Will give brainliest!!
To convert the fraction 2 8/10 to a decimal, divide the numerator (8) by the denominator (10):
8/10 = 0.8Then, add the integer part (2) to the result:
2 + 0.8 = 2.8Therefore, the decimal representation of 2 8/10 is 2.8.
i need a better understanding please and thank you to whoever
The monthly payment is given as 11.95 0f the loan amount.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
The given problem can be solved by the loan formula as follows,
The expression for the loan formula is given as,
PM = A(r(1 + r)ⁿ)/((1 + r)ⁿ- 1)
Where A is the loan amount, r is the rate of interest and n is the time interval.
The corresponding values of r and n as per the question are 6% = 0.06 and 12 respectively.
Substitute these values in the above expression to get,
PM = A(0.06(1 + 0.06)ⁿ)/((1 + 0.06)ⁿ- 1)
= 0.119A
Which can be written in the form of percentage as,
PM = 0.119 × 100% of A
= 11.9% of A
Hence, the per month payment of the loan will be 11.9% of the loan amount.
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-2x+4y=17 + 3x-10y=-3
The values of x and y are -49/4 and -15/8 respectively for the given set of equations -2x + 4y = 17 and 3x - 10y = -3.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given pair of equations,
-2x + 4y = 17 (1)
3x - 10y = -3 (2)
Multiply equation (1) with 3 and equation (2) with 2
-6x + 12y = 51 (3)
6x - 20y = -6 (4)
Add equation (3) and (4),
- 8y = 15
y = -15/8
Substitute the value of y in equation (1)
-2x + 4 (-15/8) = 17
-2x - 15/2 = 17
-2x = 49/2
x = - 49/4
The values of x and y for the given equations are -49/4 and -15/8 respectively.
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For the given equation the value of x and y will be 15/4 and 17/8 respectively
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the equations are,
-2x+4y=17 -------(1)
3x-10y= -3
The value of x from equation 1 is,
-2x+4y=17
x=(17-4y)/2 -------(2)
Substitute the value of x in equation 2,
3x-10y=-3
3(17-4y)/2-10y= -3
y=17/8
The value of x is obtained as,
x=15/4
Thus, for the given equation the value of x and y will be 15/4 and 17/8 respectively
The question is incomplete the complete question is"solve the linear equation -2x+4y=17, 3x-10y=-3
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What is an equation of the line that passes through the point (-2, -6) and is
parallel to the line x + 2y = 8?
Answer:
y = -1/2x - 7
Step-by-step explanation:
First, let's get the line in slope-intercept form. This is of the form y = mx + b. This helpful because we will be able to tell what the slope is, which is important because the parallel line will have the same slope. To do this, we need to isolate y. Subtract x from both sides. This gives us [tex]2y = 8-x[/tex]. Now divide both sides by 2 to completely isolate y. This gives us [tex]y = (8-x)/2[/tex], or [tex]y = -x/2 + 4[/tex]. From this we can tell that the slope is -1/2, because that is the coefficient of x.
This is the same slope we need for the parallel line! Let's put the line in slope-intercept form. We have our slope(-1/2), so we need to solve for b, which is the y-intercept. To do this, we will plug in the point on the graph to the equation for x an y. This gives us [tex]-6 = -1/2*-2 + b[/tex], or [tex]-6 = 1 + b[/tex]. Subtracting 1 from both sides tells us that which tells us b = -7. This is the y-intercept! Now we can plug this and the slope into our equation to get our answer: y = -1/2x - 6
I hope this helps!
Box A weigh 112.04 kilograms . Box B weighs 112 kilograms. which statement is true?
Answer: A
Step-by-step explanation: Because when your weighing a box there can sometimes be decimals in the weight
1. The quotient of and three increased by 10 is 16) What is.x?
The equivalent value of the [x] that satisfy the given statement is 18.
What is equation modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.
Given is the statement -
the quotient of a number and three increased by 10 is 16
The given mathematical statement is -
the quotient of a number and three increased by 10 is 16
Assume the number to be [x]. Then, we can write -
(x/3) + 10 = 16
x/3 = 16 - 10
x/3 = 6
x = 6 x 3
x = 18
Therefore, the quotient of 18 and three increased by 10 is 16.
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A turtle is 26.2 meters from a pond when it starts crawling toward the pond. The turtle crawls straight toward the pond at a
constant rate of 3.5 meters per minute.
Which equation models the distance of the turtle from the pond? (Let q represent the turtle's distance, in meters, from the
pond and p represent the number of minutes since it started crawling toward the pond.)
A. g=26.2-3.5
B.q=26.2p+3.3
C.q=26.2p-3.5
D.q=26.2+3.5p
The equation which models the distance of the turtle from the pond is q = 26.2 + 3.5p. Option D. is the answer
How to determine which equation models the distance of the turtle from the pond?
Given that:
A turtle is 26.2 meters from a pond when it starts crawling toward the pond
The turtle crawls straight toward the pond at a constant rate of 3.5 meters per minute
q represents the turtle's distance, in meters, from the pond and p represents the number of minutes since it started crawling toward the pond
The linear equation is of the form y = mx + c
where m is the rate of change and c is the starting point or y-intercept
m = 3.5 meters per minute, c = 26.2 meters
y = q ( turtle's distance) and x = p (number of minutes)
Thus, the equation models the distance will be:
q = 26.2 + 3.5p
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can you please hellppp
The graph f(x) of y = 1/2 f(x).
How do you draw a f(x) graph?The graph demonstrates that regardless of its value, y is always positive. From the question figure, the following conclusions can be made.
Whenever x is 0, y also equals 0.
If x is 1, then y is 2.
when x is two, y is four.
Y is two when x is -1.
If x is -2, then y is 4.
It implies that the modulus function (|x|) is a function of f(x).
Here is a definition of the modulus function:
g(x)
g(x) = |x| = {x,i∫x≥0
{-x,i∫x<0
As we can see, it is twice as large as |x|, therefore the graph in the question figure
y = f(x) = 2|x |{ -2 ≤ x ≤2}
Therefore, we must create a graph y = 1/2 f(x)
y = |x | {-2 ≤ x ≤ 2}
Please see the graphic in the attachment for the graph of y = 1/2 f(x).
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Mr. Chung drove 248 miles in 4 hours. If he continues driving at the same speed, how many miles will Mr.Chung drive in 6 hours?
Answer:
Step-by-step explanation:
248miles ÷ 4hrs = 62mph
62mph × 6 hrs = 372miles
Mr. Chung will have driven 372 miles in 6 hours
Answer: Mr. Chung will have driven 372 miles in 6 hours
Step-by-step explanation:
120 thousand cars were manufactured in a country in the year 2004-OS. The production of cas
increased to 150 thousand in 2005-06. Find the percentage increase in the manufacture of cars.
Answer:
25% increase
Step-by-step explanation:
120 thousand cars were manufactured in a country in the year 2004-O5. The production of cars increased to 150 thousand in 2005-06. Find the percentage increase in the manufacture of cars.
(150 - 120) / 120 = 0.25
0.25 = 25% increase
Kenji and his theater group are putting on a play. They need to make $373.50 to cover the
costs of the props and costumes. If they charge $4.50 for each ticket, how many tickets do
they need to sell to cover their costs?
Answer: 83 on the dot
Step-by-step explanation:83x4.50=373.50
PLEASE ANSWER NOWWW!!!!!!!!
Answer:
d
Step-by-step explanation:
its 3 to the right and top and its not a negative number so we don't go left
Answer:
Graph A
Step-by-step explanation:
The equation indicates the line has a positive slope and a y-intercept of 0. The only graph that corresponds to those conditions is Graph A.
what is the period of the function h(x) = 5sin(4x-2) -3
Step-by-step explanation:
[tex]5 \sin(4(x - \frac{1}{2} ) ) - 3[/tex]
Period is b/2pi
Which is
[tex] \frac{4}{2\pi} [/tex]
[tex] \frac{2}{\pi} [/tex]
Triangle ABC has the following measures: mA = 46°, m/B = 73°, and b = 32.3. What
is the length of side c?
The length of the side c is equal to 29.54 approximately to 2 decimal place, using the sine rule.
What is the sine ruleThe sine rule is a relationship between the size of an angle in a triangle and the opposing side.
For the triangle ABC, by sine rule;
a/sinA = b/sinB = c/sinC
We first derive the angle C as follows:
46° + 73° + C = 180° {sum of interior angles of a triangle}
C = 180° - 119
C = 61°
Thus by sine rule;
c/sin61° = 32.3/sin73°
c = (32.3 × sin61°)/sin73° {cross multiplication}
c = 29.5410
Therefore, by proper application of the sine rule we have the length of the side c to be equal 29.54 approximately to 2 decimal place.
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simplify
1. 2310/35805
2. 480/720
3. 120/600
4. 315/1680
5. 126/840
6. 1848/252
Answer:
Step-by-step explanation:
1. 2310/35805 -> 3/10
2. 480/720 -> 2/3
3. 120/600 -> 1/5
4. 315/1680 -> 3/16
5. 126/840 -> 3/20
6. 1848/252 -> 22/3
Let C represent the cost in dollars and R represent the revenue in dollars. What is the break-even point? Use a table to help if necessary.
C=24x+80
R=44x
The break even point is x = 4 for cost C = 24x + 80 and Revenue R = 44x.
What is Cost and Revenue ?Cost is the amount of money spent by a business to produce or provide goods or services. It excludes the profit margin markup. Cost is the sum of money spent on making a thing or product, as seen from the seller's perspective.
Cost is defined as the total of real input costs and imputed costs associated with owner-supplied inputs.
The entire money derived from the sale of products or services pertaining to a business's core operations is referred to as revenue. Because it appears at the top of the income statement, revenue, which is also known as gross sales, is sometimes referred to as the "top line." A company's overall profits or profit are referred to as income, or net income.
The break-even threshold is reached when overall costs and total revenues are equal, leaving your small firm with no net benefit or loss. In other words, you've achieved the point in manufacturing when the income from a product matches the cost of manufacture.
At break even point cost equals revenue,
Therefore,
Cost = Revenue
⇒ 24x +80 = 44x
⇒ 20x = 80
⇒ x = 4.
The break even point is x = 4 .
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This year consumers purchased 7,234,267,990 bottles of water. Last year consumers purchased 2,000,900,999 bottles of water. Which is the best estimate of the number of bottles sold this year and last year?
9,000,000,000 is the best estimate of the number of bottles sold this year and last year
What is Number system?A number system is defined as a system of writing to express numbers.
Given,
Current year consumers purchased 7,234,267,990 bottles of water
Last year consumers purchased 2,000,900,999 bottles of water.
We need to find the best estimate of the number of bottles sold current year and last year.
The best estimate means rounding up to the nearest whole number.
The estimate of the bottles sold this year and last year from the above value is:
= 7,000,000,000 + 2,000,000,000
= 9,000,000,000
Hence, 9,000,000,000 is the best estimate of the number of bottles sold this year and last year
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what is the minimum cost in dollars for a fair to be included in the highest 3% of domestic airfares? (round your answer to the nearest integer.)
$592 is the minimum cost in dollars for a fair to be included in the highest 3% of domestic airfares. Using the concept of probability -
What is probability?Probability is a mathematical discipline that concerns with numerical figures of how probable an occurrence is to occur or how probably a statement is to be true. A number between 0 and 1 is the probability of an occurrence, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Mean – 385 per ticket
Standard Deviation - 110
Now,
P (Z > x ) = 0.03
Value of z to the cumulative probability of 0.03 from the normal distribution table is 1.88
P(x - u / (standard deviation) > x - 385/110) = 0.03
That is, (x - 385/110) = 1.88
Therefore, x = 1.88 ×( 110+385)
= 591.91 or $592
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Which transformation results in the function, I would also like a explanation on how to do this.
The transformation that is results in the given function is a horizontal shrink of scale factor 1/4.
Which transformation results in function g(x)?Remember that for a function f(x), we define a horizontal shrink of scale factor k as:
g(x) = f(x*1/k)
Here we know that:
f(x) =x^2
g(x)= f(4x) = (4x)^2
Then this is equivalent to an horizontal shrink of scale factor of 1/4
Then the scale factor is k = 1/4, and the correct option is A.
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Write the equation of the line in fully simplified slope-intercept form.
You see from the graph that when x = 0, y = 2 so the y-intercept is ( 0 , 2).
you are given points (-5 , 6) and (5 , -2). Find slope:
slope = change in y / change in x
slope = (6 - (-2)) / (-5 - 5)
slope = (6 +2) / (-5 - 5)
slope = 8/-10
slope = -4/5
slope-intercept form: y = mx + b where m = slope and b = y intercept.
y = -4/5x + 2
A person exhales about 1.25 x 10^-5 kilogram of carbon dioxide in 2 x 10^-2 minute. How many kilograms of carbon dioxide does a person
exhale each minute?
The amount of carbon dioxide does a person exhale each minute is, 0.625 x 10^-2 kilogram.
What is kilogram?
With the unit symbol kg, the kilogram serves as the International System of Units' unit of mass. The term "kilo" is frequently used in colloquial speech and is a unit of measurement that is widely used in science, engineering, and commerce worldwide. It denotes "a thousand grams."
Given:
A person exhales about 1.25 x 10^-5 kilogram of carbon dioxide in 2 x 10^-2 minute.
We have to find the amount of kilograms of carbon dioxide does a person exhale each minute.
The amount of carbon dioxide for each minute is,
[tex]\frac{1.25*10^_^5}{2*10^-^2} =\frac{1.25}{2}*10^-^5^+^3 = 0.625*10^-^2[/tex]
Hence, the amount of carbon dioxide does a person exhale each minute is, 0.625 x 10^-2 kilogram.
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A Question 7 (2 points) Retake question
Let f(x)= x + 3
The graph of f(x) is transformed into the graph of g(x) by a translation of 4 units left.
What is the equation for g(x)?
g(x) = |x-1
g(x)= |x-41 +3
g(x) = |x| +7
g(x)= x + 4 + 3
Answer:
g(x) = |x-4| + 3
Write an algebraic expreion that marhall can ue to determine the total cot of buying a watermelon that weigh w pound and ome tomatoe that weigh t pound. How much will it cot to buy a watermelon that weigh 18 1/2 and 5 pound of tomatoe
The required algebraic expression when the that total cost is $142.05.
That is $125.80 for Watermelon that weighs 185 lbs and $16.25 for 5 lbs of tomatoes.
=>Total cost = 3.25t +.68w
Given: Tomatoes cost $3.25 per lb while watermelons cost $.68 per lb.
Let w = weights of the tomatoes and watermelons.
The algebraic expression would be:
3.25t +.68w = Total cost
For 5 pounds of tomatoes and 185 lb of watermelon:
68(185) + 3.25(5)
=$125.80 + $16.25
= $142.05
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables.
Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
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You have 40 minute to exercie at the gym, and you want to burn a total of 300 hundred calorie uing both machine. How much time would you pend on both machine
You should spend 30 minutes on machine 1 and 10 minutes on machine 2.
Given,
In the question:
You have 40 minute to exercise at the gym, and you want to burn a total of 300 hundred calorie using both machine.
Now, According to the question;
300 calories in 40 minutes can be set up as a ratio to find out how many calories per hour or calories per minute you are trying for:
300 calories /40 minutes = x calories/60 minutes for calories per hour (you are aiming for 450 calories burned per hour)
300 calories / 40 minutes = 7.5 calories per minute if you want to look at it that way instead.
One version of this problem that I found online completes the setup this way:
First machine is 8 calories per minuteSecond machine is 6 calories per minuteThis allows us to set up a system of equations. The first equation will be for calories burned:
8x + 6y = 300
x is minutes on the 8 calorie per minute machine; y is minutes on the 6 calories per minute machine.
A second equation simply shows that the total minutes add up to 40:
x + y = 40
Now you can use substitution, elimination, or linear combinations to solve the system. I'll use substitution to rewrite the second equation:
x = 40 - y....(1)
Now substituting into the first equation:
8(40 - y) + 6y = 300
320 - 8y + 6y = 300
2y = 20
y = 10
Put the value of y in eq.(1)
Then, x gives the 30
Hence, You should spend 30 minutes on machine 1 and 10 minutes on machine 2.
Learn more about Linear Combination at:
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