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3 years ago

8x = 2y + 5 3x = y + 7

1 answer:

8 0

Hello there!

8x = 2y + 5
3x = y + 7
Use the substitution property
We need to solve 3x = y + 7 for y
3x = y + 7
3x - y = 7
-y = 7 - 3x
Divide both sides by -1
-y/-1 = -3x -7/-1
y = 3x - 7
Substitute 3x - 7 for y in 8x = 2y + 5
8x = 2y + 5
8x = 2(3x - 7) + 5
8x = 6x - 14 + 5
8x = 6x - 9
8x - 6x = -9
2x = -9
x= -9/2
To find y, we need to substitute -9/2 for x in y = 3x -7
y = 3x - 7
y = 3(-9/2) - 7
y = -41/2

The correct answer is option A (-9/2; -41/2)

Good luck with your studies!

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What is continuous compounding? how does the apy for continuous compounding compare to the apy for, say, daily compounding? e

aliya0001 [1]

Continuous compounding is the mathematical limit that compound interest can reach.

It is the limit of the function A(1 + 1/n) ^ n as n approaches infinity. IN theory interest is added to the initial amount A every infinitesimally small instant.
The limit of (1 + 1/n)^n is the number e ( = 2.718281828 to 9 dec places).

Say we invest $1000 at daily compounding at yearly interest of 2 %. After 1 year the $1000 will increase to:-

1000 ( 1 + 0.02/365)^365 = $1020.20

with continuous compounding this will be

1000 * e^1 = $2718.28

4 0

2 years ago

Read 2 more answers

A bag contains 170 marbles. There are red, blue and yellow marbles in a ratio of 9:3:5. How many yellow marbles does the bag con

telo118 [61]

Answer:

50 yellow marbles.

Step-by-step explanation:

Information:

170 marbles

RED : BLUE : YELLOW

9 : 3 : 5

Solving:

To find out how many yellow parts there are, we need to find out how many marbles 5 parts account to.

Altogether, 9 + 3 + 5 = 17. This means there are 17 parts.

The bag contains 170 marbles and the ratio adds up to 17 parts.

We can figure out what 1 part of the ratio accounts to by dividing 170 by 17.

$\frac{170}{17}$ = 10.

1 part = 10

Now remember yellow is 5 parts, now that we know that 1 part is 10, we need to multiply 10 by 5 to find out how many yellow marbles we have.

5 x 10 = 50.

Therefore we have 50 yellow marbles.

7 0

2 years ago

Mr zambito buys a 3 1/2 - pound bag of dog food every 3 weeks mr zambito feeds his dog the same amount of dog food each day how

Murljashka [212]

3 1/2 pound = 7/2 pounds.
We know that the dog eats 7/2 (3.5) pounds every 21 days since there are 7 days in a week and Mr.Z only buys dog food every 3 weeks.

Set up a proportion. 3.5 lb = x 
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Cross multiply and divide. 3.5 lb x 365 days = 1277.5 / 21 days = 60.83 lb

3 0

2 years ago

Indicate the equation of the line, in standard form, that passes through (2, -4) and has a slope of 3/5. Enter your answer into

yulyashka [42]

The equation of the line is $y = (3/5)x + 26/5$

Step-by-step explanation:

The line passes through the point (2,-4).
The line has the slope of 3/5.

To find the equation of the line passing through a point and given its slope, the slope-intercept form is used to find its equation.

The equation of the line when a point and slope is given :

⇒ $(y-y1) = m(x-x1)$

where,

m is the slope of the line.
(x1,y1) is the point (2.-4) in which the line passes through.

Therefore, the equation of the line can be framed by,

⇒ $(y-(-4)) = 3/5 (x-2)$

⇒ $(y+4) = 3/5(x-2)$

Take the denominator 5 to the left side of the equation.

⇒ $5(y+4) = 3(x-2)$

Now, multiply the number outside the bracket to each term inside the bracket.

⇒ $5y+20 = 3x -6$

⇒ $5y = 3x-26$

Divide by 5 on both sides of the equation,

⇒ $y = (3/5)x + 26/5$

Therefore, the equation of the line is $y = (3/5)x + 26/5$

4 0

2 years ago

Read 2 more answers

Assume that the cheetah travels an average of 40 mph to go from its resting place to a rock near a river. On the return trip to

Ronch [10]

Answer:

The return trip take 5 minutes 27 seconds

Step-by-step explanation:

Let

x -----> the time it take the cheetah travels to go from its resting place to a rock near a river in hours

y ----> the time it take the cheetah the return trip to its resting place in hours

we know that

The distance from its resting place to a rock near a river is the same that the return trip

The average speed multiplied by the time is equal to distance

The total time is 15 minutes

Convert to hours

15 min=15/60 hours

x+y=(15/60)

x+y=1/4

4x+4y=1 -----> equation A

40x=70y ----> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The solution is the point ( 0.1591,0.0909)

see the attached figure

The time it take the cheetah travels to go from its resting place to a rock near a river is 0.1591 hours

The time it take the cheetah the return trip to its resting place is 0.0909 hours

Convert to minutes and seconds

0.0909 hours=0.0909(60)=5.454 minutes

o.454 minutes=0.454(6)=27.24 seconds

therefore

The return trip take 5 minutes 27 seconds

To the river

The time it take the cheetah travels to go from its resting place to a rock near a river is 0.1591 hours

The rate is 40 mph

To find out the distance multiply the average rate by the time

Find out the distances

The distance from its resting place to a rock near a river is

$d_1=40x=40(0.1591)=6.36\ miles$

From the river

The time it take the cheetah the return trip to its resting place is 0.0909 hours

The rate is 70 mph

To find out the distance multiply the average rate by the time

Find out the distances

The distance of the return trip is

$d_2=70x=70(0.0909)=6.36\ miles$

Both distances are the same

8 0

2 years ago