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3 years ago

How can one fourthx − 3 = one halfx + 8 be set up as a system of equations?

1 answer:

7 0

First, set each half of the equation equal to zero:

1/4x - 3 = 0
1/2x +8 = 0

Notice how I stacked the equations, lining up "like terms."

Multiply both equations by "4" to eliminate the fractions:

(4) 1/4x -3 = 0 --> x - 12 = 0
(4) 1/2x+8 = 0 --> 2x + 32 = 0

Add the equations equal: 3x + 20 = 0
Subtract 20 from both side - 20 -20
Simplify 3x = -20
Divide both sides by 3 3 3
Final answer: x = -20/3

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What can Range can also be called

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Range. Range is the difference between the largest and smallest number in a set of numbers.

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3 years ago

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5(4x - 1.5x) + 12 = 4x - 2

MAXImum [283]

Answer:

-1.647058824

Step-by-step explanation:

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3 years ago

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A researcher wants to investigate the effect of weather on college students' study habits. On a sunny day, the researcher sits i

LekaFEV [45]

The investigation that was carried out by the researcher illustrates a one-shot case study.

<h3>What is a one-shot case study?</h3>

It should be noted that a one-shot case study simply means a research design where a single group is observed after experiencing some treatment on a single occasion.

Since the researcher sits in the quad and records the number of minutes each student puts into studying, it's a one-shot case study.

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3 years ago

Suppose you want to place a shelf that is 30 1/3 inches long in the center of a wall that is 45 3/4 inches wide. About how fare

mrs_skeptik [129]

Answer:

7.71 inches far from each edge of the wall you should place the shelf.

Step-by-step explanation:

Given:

$\textrm{size of a shelf}=30\frac{1}{3} =\frac{91}{3}=30.33\ inches\\\textrm{size of a wall}=45\frac{3}{4} =\frac{183}{4}=45.75\ inches\\$

Let,

AB = distance between the edges or distance of wall.

ED = size of the shelf.

C is the centre of the wall.

To Find:

Distance from the edge of the wall to the shelf, when the shell is placed at the center of the wall.

AE = DB = ?

Solution:

As we need to place the shelf exactly in the center.

First we will calculate the distance from the center of the wall to the edge.

So the distance from the centre of the wall to the edge will be exactly half of the size of the wall.

$CB = \frac{1}{2}\times AB\\ =\frac{1}{2}\times 45.75\\\therefore CB=22.875\ inches$

now the distance from the centre to the end of the shelf will be exactly half of the size of the shelf.

$CE = \frac{1}{2}\times DE\\ =\frac{1}{2}\times 30.33\\\therefore CB=15.165\ inches$

Now we want to calculate the distance from the edge of the wall to the shelf,that is the distance from the end of the shelf to the edge of the wall.

$AE=BD= BC-CD\\=22.875-15.165\\=7.71\ inches\\\therefore AE = BD = 7.71\ inches$

Therefore, 7.71 inches far from each edge of the wall you should place the shelf.

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3 years ago

Find a rational number between -1/3 and 1/2

noname [10]

Answer:

1/6

Step-by-step explanation:

Rational numbers between two rational numbers:

First find the Least Common Denominator for 2 and 3
Then find equivalent fractions with the LCD.

LCD of 2 and 3 = 6

$\sf \dfrac{-1}{3}=\dfrac{-1*2}{3*2}=\dfrac{-2}{6}\\\\\dfrac{1}{2}=\dfrac{1*3}{2*3}=\dfrac{3}{6}$

$\sf Rational \ number \ between \ \dfrac{-2}{6} \ and \ \dfrac{3}{6} \ is \ \bf \dfrac{1}{6}$

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2 years ago