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3 years ago

Mac's age is 3 years less than twice Joe's age. The sum of their ages is 30. Find their ages.

Mathematics

1 answer:

k0ka [10]3 years ago

4 0

Answer:

Mac is 19 years old, Joe is 11 years old

Step-by-step explanation:

2J - 3 = M

J + M = 30

M = 30 - J

2J - 3 = 30 - J

3J = 33

J = 11

M = 30 - 11

M = 19

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Step-by-step explanation:

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3 years ago

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3 years ago

Lines 3x-2y+7=0 and 6x+ay-18=0 is perpendicular. What is the value of a?

BlackZzzverrR [31]

Answer:

$\boxed{\sf a = 9 }$

Step-by-step explanation:

Two lines are given to us which are perpendicular to each other and we need to find out the value of a . The given equations are ,

$\sf\longrightarrow 3x - 2y +7=0$

$\sf\longrightarrow 6x +ay -18 = 0$

Step 1 : Convert the equations in slope intercept form of the line .

$\sf\longrightarrow y = \dfrac{3x}{2} +\dfrac{ 7 }{2}$

and ,

$\sf\longrightarrow y = -\dfrac{6x }{a}+\dfrac{18}{a}$

Step 2: Find the slope of the lines :-

Now we know that the product of slope of two perpendicular lines is -1. Therefore , from Slope Intercept Form of the line we can say that the slope of first line is ,

$\sf\longrightarrow Slope_1 = \dfrac{3}{2}$

And the slope of the second line is ,

$\sf\longrightarrow Slope_2 =\dfrac{-6}{a}$

Step 3: Multiply the slopes :-

$\sf\longrightarrow \dfrac{3}{2}\times \dfrac{-6}{a}= -1$

Multiply ,

$\sf\longrightarrow \dfrac{-9}{a}= -1$

Multiply both sides by a ,

$\sf\longrightarrow (-1)a = -9$

Divide both sides by -1 ,

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Hence the value of a is 9 .

8 0

3 years ago

Helppp can someone solve this please

Norma-Jean [14]

Answer:

$\displaystyle x=-15$

Step-by-step explanation:

Solution Of A System Of Equations

A system of linear equations is given as

$\displaystyle \left\{\begin{matrix}ax+by=c\\ dx+ey=f\end{matrix}\right.$

There are many methods to solve them. We will use the method of reduction

The given system is

$\displaystyle \left\{\begin{matrix}2x+3y=45\\ x+y=10\end{matrix}\right.$

Multiplying the second equation by -3

$\displaystyle \left\{\begin{matrix}2x+3y=45\\ -3x-3y=-30\end{matrix}\right.$

Adding the resulting equations

$\displaystyle -x=15$

$\displaystyle x=-15$

5 0

3 years ago