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2 years ago

What is the slope of the line represented by the equation y = - 글 x + 끝?

Mathematics

1 answer:

AveGali [126]2 years ago

7 0

Given:

Consider the given equation is:

$y=-\dfrac{7}{2}x+\dfrac{11}{3}$

To find:

The slope of the line that is represented by the given equation.

Solution:

The slope intercept form of a line is:

$y=mx+b$ ...(i)

Where, m is the slope and b is y-intercept.

We have,

$y=-\dfrac{7}{2}x+\dfrac{11}{3}$ ...(ii)

On comparing (i) and (ii), we get

$m=-\dfrac{7}{2}$

Therefore, the slope of the given equation is $-\dfrac{7}{2}$ .

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Which is the value of the expression (StartFraction (10 Superscript 4 Baseline) (5 squared) Over (10 cubed) (5 cubed)) cubed?

Flura [38]

Answer:

The value to the given expression is 8

Therefore $\left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3=8$

Step-by-step explanation:

Given expression is (StartFraction (10 Superscript 4 Baseline) (5 squared) Over (10 cubed) (5 cubed)) cubed

Given expression can be written as below

$\left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3$

To find the value of the given expression:

$\left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3=\frac{((10^4)(5^2))^3}{((10^3)(5^3))^3}$

( By using the property ( $(\frac{a}{b})^m=\frac{a^m}{b^m}$ )

$=\frac{(10^4)^3(5^2)^3}{(10^3)^3(5^3)^3}$

( By using the property $(ab)^m=a^mb^m$ )

$=\frac{(10^{12})(5^6)}{(10^9)(5^9)}$

( By using the property $(a^m)^n=a^{mn}$ )

$=(10^{12})(5^6)(10^{-9})(5^{-9})$

( By using the property $\frac{1}{a^m}=a^{-m}$ )

$=(10^{12-9})(5^{6-9})$ (By using the property $a^m.b^n=a^{m+n}$ )

$=(10^3)(5^{-3})$

$=\frac{10^3}{5^3}$ ( By using the property $a^{-m}=\frac{1}{a^m}$ )

$=\frac{1000}{125}$

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Therefore $\left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3=8$

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3 years ago

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Proportional relationships, please answer all of the parts! Thank you!

Natalka [10]

Answer:

a. No (see below)

b. (see below)

c. Johnny

d. Johnny = $12.50 / hour Doug = $9.16... / hour

e. Doug: extend the table to show how much he gets paid for 1 hour of work (the unit rate)

Johnny: already on the graph

Step-by-step explanation:

a. No. This is because a proportional relationship would have a certain ratio between payment and the amount of time spent working, which would not change. However, if Doug's neighbour pays him $55 for 6 hours, it's likely that this is not a proportional relationship, or we would be able to divide $55 by the 6 hours Doug spent working.

b. Even though above I said that it's probably not a proportional relationship, if it were, we would have to divide everything equally. I'm guessing the table should look like this:

Doug

Time (hr) Earnings ($)

4 $36.66...

5 $45.8333...

6 $55

7 $64.4666....

8 $73.333...

To work out how much Doug would get for working 4 hours:

4/6 x $55 = 2/3 x $55 = $36.66... (so definitely not a proportional relationship)

To work out how much Doug would get for working 5 hours:

5/6 x $55 = $45.8333.... (more evidence that this is not a proportional relationship)

To work out how much Doug would get for working 7 hours (we already got 6 hours):

7/6 x $55 = $64.4666...

To work out how much Doug would get for working 8 hours:

8/6 x $55 = $73.33... (we could double the 4 hour payment, but this is probably more accurate)

c. Johnny is getting paid more. If we look at how much Doug gets for 6 hours, it's $55. If we look out at how much Johnny gets for 6 hours, it's $75. (If we do the same with the other amounts of time, it's the same.

4 hours: D = $36.67 vs J = $50

5 hours: D = $45.83 VS J = $60

etc...

d. Johnny gets $75 per 6 hours --> 75/6 = $12.50 per hour

Doug gets $55 per 6 hours --> 55/6 = $9.1666... per hour

e. Carry on the table for Doug all the way to 1, so you can see the how much Doug gets paid for 1 hour of work (i.e. the minimum).

The unit rate is already on the graph for Johnny.

HOPE THIS HELPED :)

P.S. Mate cld you please give me Brainliest? That table took so much dam work

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Anna11 [10]

3/5 ÷ 1 1/4 = 0.48

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2 years ago