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cricket20 [7]
3 years ago
15

Use the three steps to solve the problem. maple syrup worth $6.00 a gallon and corn syrup worth .80 cents a gallon are used to m

ake a mixture worth $2.36 a gallon. how many gallons of each kind of syrup are need to make 50 gallons of the mixture? {maple syrup: a0 gallons, corn syrup: a1gallons}
Mathematics
1 answer:
Ksenya-84 [330]3 years ago
3 0
<span>Cost of maple syrup = $6.00 a Gallon Cost of corn syrup = 0.80 cents a Gallon Cost of the syrup mixture = $2.36 a Gallon There is mixture of 50 Gallons Lets maple syrup be x gallons, so corn syrup be 50-x gallons Hence, 6*x + 0.80(50-x) = 2.36*50 6x + 40 - 0.8x = 118 5.2x = 78 => x = 78/5.2 => x = 15 So Maple will be syrup be 15 gallons. Corn syrup will be 35 gallons.</span>
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(a) Derive an equation of the line passing through the points A(0, 545) and B(4, 726). (Let t be the independent variable and y
a_sh-v [17]

Answer:

The equation of the line is y=45.25t+545

Step-by-step explanation:

The general for of a line is:

y=mt+n       (1)

where:

m is the slope of the line and m is the intercept with the axis of the dependent variable, y in this case.

In order to obtain the value of the slope (m) we can use the corresponding slope formula:

m=\frac{y_{2}-y_1 }{t_2-t_1}         (2)

where t_1, t_2, y_1 and y_2 are the corresponding coordinates of the given points. In this case:

t_1=0\\t_2=4\\y_1=545\\y_2=726\\

Substituting these values in equation (2) we obtain:

m=\frac{726-545}{4-0}=\frac{181}{4}=45.25\\m=45.25

Hence, the line equation is now:

y=45.25t+n     (3)

Now to obtain the value of n you can follow two options:

  1. You can substitute one of your points, A or B, in equation (3). In this way, you will obtain an equation where the variable is n

Note that for this question, it is easier to select point A because of having the independent variable equals to zero t=0. Hence, substituting point A in equation (3):

45.25*0+n=545\\n=545

Therefore, the line equation is: y=45.25t+545

The second option to find n is to think of the meaning of the <em>intercept</em>. The <em>intercept </em>of a line is defined as the point in which the line crosses the axis of the dependent variable, which also means that the value of the independent variable for this point is zero. From this, we could have automatically said that n is equal to 545.

See the attachment for a plot of the line.

7 0
3 years ago
① 5J+2S =12.20 ② 5J+ 10S =15.80 elimination method
hram777 [196]

Answer:

<h2>S = 9/20</h2><h2>J = 113/50</h2>

Step-by-step explanation:

5J +2S =12.20 ........(1)\\5J+10S=15.80......(2)\\Multiply \:equation \:(1)\:by\:the\:coefficient\:of\:x\:in equation\:(2)\\\\Multiply\:equation(2)\: by\: the\: coefficient\:of \:x\: in \:equation (1)\\\\5J +2S =12.20 ........(1) \times 5\\5J+10S=15.80......(2)\times 5\\\\25J+10S=61......(3)\\25J+50S = 79......(4)\\Subtract\:equation\:(4)\:from\: equation\: (3)\\-40S =-18\\\frac{-40S}{-40}=\frac{-18}{-40}\\  S = 9/20\\

Substitute \:9/20\:for \:x \:in\:equation\:(1)\:or \:equation\:(2)\\5J+2S = 12.20\\5J +2(9/20) =12.20\\5J +9/10=12.20\\5J=12.20-9/10\\5J=113/10\\Cross-Multiply\\50J = 113\\J = 113/50

4 0
3 years ago
The answer is there pls just show your work on how to do it
Vikentia [17]

Answer:

Y=2x+0

Step-by-step explanation:

First you have to find the slope of the graph or the rise over run, which in this case is 2

Then you have to find the y intercept, which is zeroSo the rule for thos graph is y=2x+0.

To double check our work take a random point on x axis. I chose the point 1,2

fill in the formula and you should get 2(1)+0=2 and therefore this Formula is correct

6 0
3 years ago
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What is 7.5% of 180 dollars? please provide step by step answer
Aliun [14]

Answer:

13.5

Step-by-step explanation:

7.5 percent *180=

(7.5:100)*180=

(7.5*180):100=

1350:100= 13.5

5 0
3 years ago
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What types of angles are &lt;4 and &lt;5?
alexandr1967 [171]

Answer:  Alternate interior angles

Step-by-step explanation:

7 0
2 years ago
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