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Morgarella [4.7K]
3 years ago
7

How to solve two step inequalities

Mathematics
1 answer:
DENIUS [597]3 years ago
4 0

Answer:

Solving two step inequalities

Solving Two Step Linear Inequalities. To solve a two-step inequality, undo the addition or subtraction first, using inverse operations , and then undo the multiplication or division. The inverse operation of addition is subtraction and vice versa.

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Having some trouble with these questions, how do I work them out?
matrenka [14]

5.

Let x be the age of the father and y be the age of the son. As of today, he's 3 times older, so we have x=3y

10 years ago their ages were, respectively, x-10 and y-10, and the father was 5 times older: x-10 = 5(y-10)

So, we have the system

\begin{cases} x=3y\\x-10=5(y-10)\end{cases}

Using the first equation, we can substitute every occurrence of "x" with "3y" in the second equation:

3y-10=5(y-10) \iff 3y-10=5y-50 \iff 2y = 40 \iff y=20

So, the son is 20 years old, which means that the father is 60 years old.

Indeed, 10 years ago they were 10 and 50 years old, so the father was 5 times older.

6.

Let x be the age of the grandfather and y the age of the granddaughter. We know that the grandfather is 10 times older: x=10y

He also is 54 years older: x=y+54

Again, if we substitute x=10y in the second equation we have

10y=y+54 \iff 9y=54 \iff y=6

7 0
3 years ago
A two-factor research study has 2 levels of factor A and three 3 of factor B with n = 8 participants in each treatment condition
Oksanka [162]

Answer:

a.​5

Step-by-step explanation:

The computation of the value for df^{between treatments} is shown below:

According to the question, the data provided is as follows

Two levels of factor A

And, there are three of factor B

So, the total number of treatment conditions is

= 2 × 3

= 6

Now the value for df^{between treatments} is

= 6  - 1

= 5

Hence, the correct option is a.5

4 0
3 years ago
Debbie had $100.00 to spend on shoes and shirts. She bought 1 pair of shoes for $53.84, including sales tax. Each shirt costs $8
nexus9112 [7]

she can buy 5 shirts maximum

100-53.84=46.16 that is how much she has left to spend on shirts. 46.16÷8.19=5.63 but you can't have 0.63 shirts so in the end she can buy 5 shirts

7 0
3 years ago
How do I solve x/8+15=20
bogdanovich [222]

Answer:

x = 40

Step-by-step explanation:

1/8x + 15 = 20

         -15    -15

1/8x = 5

x8      x8

x = 40  

3 0
3 years ago
Read 2 more answers
Complete the equation of the line through ( 4 , -8 ) and ( 8 , 5 )
irinina [24]

Answer:

Therefore the equation of the line through ( 4 , -8 ) and ( 8 , 5 ) is

13x - 4y = 84.

Step-by-step explanation:

Given:

Let,

point A( x₁ , y₁) ≡ ( 4 ,-8)

point B( x₂ , y₂) ≡ (8 , 5)

To Find:

Equation of Line AB =?

Solution:

Equation of a line passing through Two points A( x₁ , y₁) and B( x₂ , y₂)is given by the formula

(y - y_{1} )=(\frac{y_{2}-y_{1} }{x_{2}-x_{1} })\times(x-x_{1}) \\

Substituting the given values in a above equation we get

(y-(-8))=(\frac{5-(8)}{8-4})\times (x-4)\\ \\(y+8)=\frac{13}{4}(x-4)\\\\4(y+8)=13(x-4)\\4y+32=13x-52\\13x-4y=84...............\textrm{which is the required equation of the line AB}

Therefore the equation of the line through ( 4 , -8 ) and ( 8 , 5 ) is

13x - 4y = 84.

4 0
3 years ago
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