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3 years ago

A line that contains the point (2,-3) and has a slope of 8

Mathematics

2 answers:

yKpoI14uk [10]3 years ago

6 0

Y=mx+b
Sub in what you know and solve
-3=8(2)+b
-3=16+b
-3-16=b
-19=b
The equation is y=8x-19
Hope this helps!

NeTakaya3 years ago

3 0

Y+3=8(x-3)
y=8x-27
hope this helps!

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A cash box contains $74 made up of quarters, half-dollars, and one-dollar

Strike441 [17]

Answer:

25 one-dollar coins, 16 half-dollar coins, and 164 quarters

Step-by-step explanation:

First, set up equations based on the information given:

$0.25q+0.50h+1.00d=74$

$\displaystyle{h=\frac{3}{5}d+1}$

$q=4(d+h)$

Then, substitute q in the first equation with the expression from the third equation:

$0.25[4(d+h)]+0.50h+1.00d=74\\1d+1h+0.50h+1.00d=74\\2d+1.5h=74$

Next, substitute h in that equation with the expression from the second equation:

$\displaystyle{2d+1.5(\frac{3}{5}d+1)=74}$

$2d+0.9d+1.5=74\\2.9d+1.5=74$

Solve for d, the number of one-dollar coins:

$2.9d+1.5=74\\2.9d=72.5\\d=25$

Substitute 25 for d in the second equation to find h, the number of half-dollar coins:

$\displaystyle{h=\frac{3}{5}d+1}$

$\displaystyle{h=\frac{3}{5}(25)+1}$

$h=15+1\\h=16$

Substitute 25 for d and 16 for h in the third equation to find q, the number of quarters:

$q=4(d+h)\\q=4(25+16)\\q=4(41)\\q=164$

Then, verify that the coins total $74:

$0.25(164)+0.50(16)+1.00(25)=74\\41+8+25=74\\74=74\\\text{Check.}$

Next, verify that the number of half-dollar coins is one more than three-fifths of the number of one-dollar coins:

$\displaystyle{h=\frac{3}{5}d+1}$

$\displaystyle{16=\frac{3}{5}(25)+1}$

$16 = 15 + 1\\16 = 16\\\text{Check.}$

Finally, verify that the number of quarters is four times the number one-dollar and half-dollar coins together:

$q=4(d+h)\\164=4(25+16)\\164=4(41)\\164=164\\\text{Check.}$

6 0

3 years ago

Can someone plz help me

Illusion [34]

First rectangle:
Has 3 cubes in each 5 layers, and imagine it, so we have all dimension needed which is:
l=3 unit
w=1 unit
h=5 unit.
V=l×w×h
V=3×1×5
V=15 cubic inches.

Second rectangular:
Doing the same like that to get:
l=5 unit
w=1 unit
h=3 unit
V=15 cubic inches. As a result, there are no prism that are greater to each other, which mean that they have the same volume of 15 cubic inches. Hope it help!

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3 years ago