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3 years ago

Slope intercept form? A line passes through the point (10,4) and has a slope of -1 over 2 .

Mathematics

2 answers:

Art [367]3 years ago

7 0

Hi There!

You have to find the second point.

4 - ? = -1

10 - ? = 2

4 - 5 = -1

10 - 8 = 2

Second Coordinate: (8, 5)

Y intercept is 13

Slope Intercept Form: y = -1/2x + 13

Hope This Helps :)

Law Incorporation [45]3 years ago

3 0

The slope-intercept form:

$y=mx+b$

m - slope

b - y-intercept

We have the slope $m=-\dfrac{1}{2}$ and the point (10, 4).

Substitute the value of slope and the coordinates to the equation of line:

$y=-\dfrac{1}{2}x+b\\\\4=-\dfrac{1}{2}(10)+b\\\\4=-5+b\qquad|\text{add 5 to both sides}\\\\9=b\to b=9$

Answer: $y=-\dfrac{1}{2}x+9$

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2 years ago

A box holding pennies, nickels and dimes contains thirteen coins with a total value of 83 cents. How many coins of each type are

Art [367]

Answer:

The number of pennies,nickels and dimes are (p,n,d)=(3,4,6).

Further explanation:

Given:

A box holding pennies, nickels and dimes contains thirteen coins in a box.

Total value is 83 cents.

Calculation:

Consider p,n and d be the number of pennies, nickel and dimes.

Now, total is 13 coins so $p+n+d=13$

As we know that these following are US coin.

Penny=1 cent

Nickel=5 cents

Dime=10 cents

Step 1:

The value is already given as 83 cents that is 80+3 cents.

80 cents can be possible in many combinations as follows:

(N,D)=(0,8),(2,7),(4,6),(6,5),(8,4),(10,3),(12,2),(14,1),(16,0)

It is given that the total number of cents is 13 so we choose (4,6) as (n,d) .

So the value of nickel n=4

Dimes d=6

Step 2:

The value of p is calculated as follows:

Substitute 4 for n, 6 for d in equation $p+n+d=13$ as follows:

$p+4+6=13$

$p+10=13$

$p=13-10$

p=3

Thus, the number of pennies,nickels and dimes are (p,n,d)=(3,4,6).

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