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Sonbull [250]
3 years ago
5

The sum of two numbers is 110. The larger number is 2 less than 7 times the smaller. Find the larger number.

Mathematics
1 answer:
kumpel [21]3 years ago
5 0
We call two numbers a and b, notice a>b
<span>The sum of two numbers is 110: a+b=110
</span><span>The larger number is 2 less than 7 times the smaller: a=7b-2
And by replacing a=7b-2 we have an equation: 7b-2+b=110
or 8b=110+2, and 8b=112, that means b=112:8= 14

We have two numbers: 14 and 96</span>
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Good evening,

Answer:

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Step-by-step explanation:

Visualize as if the inequality symbols are equal signs and then solve it as you would for a normal equation, note if you divide by two negative numbers at all you then switch the sign.

On a number line, an inequality sign without the “equal to” is plotted with an open circe.

An inequality sign, with the “equal to” is plotted with a closed circle.

3x - 7> 8

Add seven on both sides, we do this because we want to eliminate the 7 from one side.

3x > 15

Divide both sides by 3, we do this because you want to get rid of the 3 from x.

x > 5

As for the second inequality.

Divide both sides by -3, as I mentioned earlier switch the side since we are dividing by two negative numbers.

x ≤ 12

For the greater than inequality x > 5, plot a open circle on 5 and draw the line going to the right.

For the less than or equal to inequality x ≤ 12, plot a closed cirlce on 12 and draw the line going to the left.

A unique trick is to graph the line based on the direction (right or left) the inequality symbol is pointing to.

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Step-by-step explanation:

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<img src="https://tex.z-dn.net/?f=%20%5Chuge%7B%5Cgreen%7D%5Cfcolorbox%7Bblue%7D%7Bcyan%7D%7B%5Cbf%7B%5Cunderline%7B%5Cred%7B%5C
MariettaO [177]

\qquad\qquad\huge\underline{{\sf Answer}}

Let's find out the gradient (Slope " m ") of line q ;

\qquad \sf  \dashrightarrow \:m = \dfrac{y_2 - y_1}{x_2 - x_1}

\qquad \sf  \dashrightarrow \:m = \dfrac{4 - 0}{0 - 1}

\qquad \sf  \dashrightarrow  \:m =  - 4

Now, since we already know the gradient let's find of the equation of line by using its Slope and one of the points using point slope form of line :

\qquad \sf  \dashrightarrow \:y - 4 = m(x - 0)

\qquad \sf  \dashrightarrow \:y = mx + 4

Now, plug in the value of gradient ~

\qquad \sf  \dashrightarrow \:y =  - 4x + 4

here we can clearly observe that, the Area under the curve can easily be represented as :

\qquad \sf  \dashrightarrow \:y <  - 4x + 4

Since, all the values of y that lies in the shaded region is smaller than the actual value of y for the corresponding values of x in the equation of line q

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