A prism, with the base below, has a height of 12 units. What is the volume of the prism?

A candle shop sells scented candles for $16 each and unscented candles for $10 each. The shop sells 28 candles today and makes $

Rudiy27

<h3>The system of linear equations that represents the situation is:</h3>

a + b = 28

16a + 10b = 400

<h3>20 scented candles and 8 unscented candles were sold</h3>

Solution:

Let "a" be the number of scented candles sold

Let "b" be the number of unscented candles sold

From given,

Cost of 1 scented candles = $ 16

Cost of 1 unscented candles = $ 10

The shop sells 28 candles today

Therefore,

a + b = 28

b = 28 - a ------- eqn 1

The shop sells 28 candles today and makes $400

Therefore,

number of scented candles sold x Cost of 1 scented candle + number of unscented candles sold x Cost of 1 unscented candles = 400

$a \times 16 + b \times 10 = 400$

16a + 10b = 400 ------ eqn 2

Substitute eqn 1 in eqn 2

16a + 10(28 - a) = 400

16a + 280 - 10a = 400

6a = 400 - 280

6a = 120

a = 20

Substitute a = 20 in eqn 1

b = 28 - 20

b = 8

Thus 20 scented candles and 8 unscented candles were sold

7 0

3 years ago

Luke earns $11.00 per hour. He works 32 1/2 hours per week. What is his weekly wage

skad [1K]

Luke’s weekly wage would be $357.5 because you multiply the 11 dollars an hour times the hours a week

6 0

3 years ago

Read 2 more answers

Please help 100 points and brainlest for all the answers

masha68 [24]

Answer:

See explanation

Step-by-step explanation:

Q1. The graph of given data is attached.

The relationship is directly proportional as the line connecting all points is straight line passing through the origin.

For every 1 unit change in x, the change of y is 16.

Therefore, the equation that represents this line is

$y=16x$

If $x=10,$ then $y=16\cdot 10=160$ square feet.

Q2. Yes, the relationship shows the direct proportionality as the line connecting all points is straight line passing through the origin (see second attached graph).

For every 1 unit change in x, the change of y is 0.45.

Therefore, the equation of the line is

$y=0.45x$

Q3. Yes, the relationship shows the direct proportionality as the line connecting all points is straight line passing through the origin.

Find the constant of proportionality:

If x = 2, y = 25, then

when x = 1, y = 12.5

so k = 12.5

and the equation of the line is

$y=12.5x$

When $x=14,$ then $y=12.5\cdot 14=175$

Hence, the cost of 14 tickets is $175

Q4. This table does not show the direct variation because

if x = 500 and y = 40, then

for x = 100, y is $40\div 5=8$

and for x = 700, y must be $7\cdot 8=56$ not 50.

Hence, this relationship does not show the direct proportionality between x and y.

Q5. This elationship shows the direct proportionality as the line connecting all points is straight line passing through the origin.

The constant of proportionality is $k=1.75$

The equation of proportionality is $y=1.75x$

When $y=28,$ then

$28=1.75x\\ \\x=\dfrac{28}{1.75}\\ \\x=16$

This means for $28 you could buy 16 ice cream scoops.

Q6. The line passes through the point (2,61), so the constant of proportionality is

$k=\dfrac{61}{2}=30.5$

The equation of proportional relationship is

$y=30.5x$

When $y=274.50,$ then

$274.50=30.5x\\ \\x=\dfrac{274.5}{30.5}\\ \\x=9$

This means you could buy 9 tickets for $274.50

Q7. The equation which represent proportional relationship should have the equation of the form

$y=kx$

Circle all equations in this form:

$y=5x\\ \\p=0.5m\\ \\y=\dfrac{1}{2}x\\ \\M=3n\\ \\y=2x$

Q8. A relationship between two variables in which one is a constant multiple of the other. In particular, when one variable changes the other changes in proportion to the first. If y is directly proportional to x, the equation is of the form y = kx (where k is a constant).

This means that the graph of direct variation is always a straight line passing through the origin (because x = 0 and y = 0 satisfy the equation for all k).

Not all lines represent the proportional relationship. Only those, which pass through the origin.

4 0

3 years ago

Read 2 more answers

5x- 4y +2z when x= 8,y =3 and z =3

vova2212 [387]

34

Step-by-step explanation:

=5x-4y+2z

=5×8-4×3+2×3

=40-12+6

=46-12

=34

4 0

2 years ago

If I turned 9 on November 9th, 2015, exactly how old am I now? (Oct 16th, 2021)

inysia [295]

The answer to this is quite simple my friend.

So if you were 9, purely turning on November 9th of 2015 at a undisclosed time, you would've been born in November of 2006. Currently, now of October 16, 2021, you would be:

Add:

4 + 10 + 1 = 15

So you would be 15 years old.

Hope this helps, currently it's 10/17/2021 for me and 1:56 am (EST).

Have a nice morning, night, dusk etc.

-ROR

8 0

3 years ago