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Lubov Fominskaja [6]
2 years ago
8

Abel saved 43 more nickels than dimes. After he spent 17 dimes he had twice as many nickels than dimes. How many coins did he ha

ve left?
Mathematics
1 answer:
Alborosie2 years ago
8 0

Answer:

180 coins

Explanation:

N = number of nickels (no nickels spent)

D = number of dimes initially saved

D' = number of dimes left after spending

1) N = D + 43

2) D' = D - 17

3) N = 2*D' = 2*(D - 17)

Set equations 1) and 3) equal to each other and solve for D:

D + 43 = 2*(D - 17)

D + 43 = 2*D - 34

D = 43 + 34 = 77

N = D + 43 = 77 + 43 = 120 nickels left

D' = D - 17 = 77 - 17 = 60 dimes left

Total coins left = 120 + 60 = 180 coins (I hope this is not too confusing for you)

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Write the equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x
Solnce55 [7]

Answer:

The equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x is \mathbf{y=-\frac{2}{3}x+3 }

Step-by-step explanation:

We need to Write the equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x

The equation in slope-intercept form is: y=mx+b where m is slope and b is y-intercept.

Finding Slope:

The both equations given are parallel. So, they have same slope.

Slope of given equation y= - 2/3x is m = -2/3

This equation is in slope-intercept form, comparing with general equation  y=mx+b where m is slope , we get the value of m= -2/3

So, slope of required line is: m = -2/3

Finding y-intercept

Using slope m = -2/3 and point (-3,5) we can find y-intercept

y=mx+b\\5=-\frac{2}{3}(-3)+b\\5=2+b\\ b=5-2\\b=3

So, we get b = 3

Now, the equation of required line:

having slope m = -2/3 and y-intercept b =3

y=mx+b\\y=-\frac{2}{3}x+3

The equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x is \mathbf{y=-\frac{2}{3}x+3 }

5 0
3 years ago
Read 2 more answers
5k race surveyed runners about their finishing times (f) and the number of previous races they had run (n). The organizers found
vichka [17]
I FOUND YOUR COMPLETE QUESTION IN OTHER SOURCES.
 
SEE ATTACHED IMAGE, PLEASE.
 
The first thing we must do for this case is to define variables.
 n = number of 5k races covered
 f = end time.
 We have the following equation:
 f = -1.2n + 38.1
 We note that the slope of the line is:
 m = -1.2 minutes per race
 Therefore, the time decreases 1.2 minutes when the number of races increases n.
 Answer:
 
The model predicts that for each additional race to runner has run, the finishing time decreases by about 1.2 minutes

3 0
3 years ago
1. In a triangle, if m<1 = 27° and m<2 = 90°, what is m<3?
Nesterboy [21]
The answer is c. 117 degrees
5 0
3 years ago
Can somebody tell me if I did it right I’m not sure how I’m supposed to find the distance?
Salsk061 [2.6K]

Answer:

6.4 units

Step-by-step explanation:

Use the distance formula:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

d=\sqrt{(8-3)^2+(-3-(-7))^2}

d=\sqrt{(5)^2+(4)^2}

d=\sqrt{25+16}

d=\sqrt{41}

d=6.4

Therefore, the distance between (3,-7) and (8,-3) is 6.4 units

Hopefully, this was helpful!

5 0
3 years ago
Read 2 more answers
What is the equation of the line that passes through (4,-1) and (-2,3)
vladimir1956 [14]

Answer: y-6 = 0.5 (x-8)

Step-by-step explanation:

y − y1 = m(x − x1)

The equation is useful when we know:

one point on the line: (x1,y1)

and the slope of the line: m,

and want to find other points on the line.

Have a play with it first (move the point, try different slopes):

8 0
3 years ago
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