3,284,361 is even or odd number

Gabby received change worth $2.10. She received 3 more dimes than nickels and 4 less quarters than nickels. How many of each kin

xz_007 [3.2K]

Answer:

Gabby received

7 nickels

10 dimes

3 quarters

Step-by-step explanation:

Let

x----> the number of dimes

y----> the number of nickels

z---> the number of quarters

Remember that

1 dime=$0.10

1 nickel=$0.05

1 quarter=$0.25

we know that

0.10x+0.05y+0.25z=2.10 ------> equation A

x=y+3-----> equation B

z=y-4 -----> equation C

substitute equation B and equation C in equation A and solve for y

0.10(y+3)+0.05y+0.25(y-4)=2.10

0.10y+0.30+0.05y+0.25y-1=2.10

0.40y=2.10-0.30+1

0.40y=2.80

y=7 nickels

<em>Find the value of x</em>

x=y+3 -----> x=7+3=10 dimes

<em>Find the value of z</em>

z=y-4 -----> z=7-4=3 quarters

therefore

Gabby received

7 nickels

10 dimes

3 quarters

6 0

3 years ago

Write an equation of the line passing through the point (5, 1) that is perpendicular to the line 5x+3y=15. An equation of the li

pochemuha

Answer:

$\displaystyle y = \frac{3}{5}\, x + (-2)$ .

Step-by-step explanation:

The slope of a line in a plane would be $m$ if the equation of that line could be written in the slope-intercept form $y = m\, x + b$ for some constant $b$ .

Find the slope of the given line by rearranging its equation into the slope-intercept form.

$3\, y = (-5)\, x + 15$ .

$\displaystyle y = \frac{(-5)}{3} \, x + 5$ .

Thus, the slope of the given line would be $(-5) / 3$ .

Two lines in a plane are perpendicular to one another if and only if the product of their slopes is $(-1)$ .

Let $m_{1}$ and $m_{2}$ denote the slope of the given line and the slope of the line in question, respectively.

Since the two lines are perpendicular to each other, $m_{1}\, m_{2} = (-1)$ . Apply the fact that the slope of the given line is $m_{1} = (-5) / 3$ and solve for $m_{2}$ , the slope of the line in question.

$\begin{aligned}m_{2} &= \frac{(-1)}{m_{1}} \\ &= \frac{(-1)}{(-5) / 3} = \frac{3}{5}\end{aligned}$ .

In other words, the slope of the line perpendicular to $5\, x + 3\, y = 15$ would be $(3 / 5)$ .

If the slope of a line in a plane is $m$ , and that line goes through the point $(x_{0},\, y_{0})$ , the equation of that line in point-slope form would be:

$(y - y_{0}) = m\, (x - x_{0})$ .

Since the slope of the line in question is $(3 / 5)$ and that line goes through the point $(5,\, 1)$ , the equation of that line in point-slope form would be: