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3 years ago

Solve the following equations if x=4.

Mathematics

1 answer:

Anastaziya [24]3 years ago

4 0

Answer:

Without a [roblem to go along with x=4, this would be underfined

Step-by-step explanation:

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30 POINTS! Please answer and show work for both!

monitta

The recommended approach for such equations is to eliminate fractions first, by multiplying by the LCM of the denominators. You can simply simplify, then work them as a 2-step linear equation, doing your arithmetic with the fractions as they are.

a) (5x-1)/7 + (4x-3)/2 -(3-2x)/2 = 6 . . . . . given

... 2(5x -1) +7(4x -3) -7(3 -2x) = 84 . . . . . multiply by 14

... 10x -2 +28x -21 -21 +14x = 84 . . . . . . eliminate parentheses

... 52x -44 = 84 . . . . . . . . . . . . . . . . . . . . collect terms

... 52x = 128 . . . . . . . . . . . . . . . . . . . . . . . add 44

... x = 32/13 . . . . . . . . . . . . . . . . . . . . . . . . divide by 52 and simplify

b) (4x−3)/2 − (5−2x)/3 − (3x−4)/3 = 5 . . . given

... 2x -3/2 -5/3 +(2/3)x -x +4/3 = 5 . . . . . . .eliminate parentheses

... (5/3)x -11/6 = 5 . . . . . . . . . . . . . . . . . . . . simplify

... (5/3)x = 41/6 . . . . . . . . . . . . . . . . . . . . . . add 11/6

... x = (41/6)/(5/3) = 41/10 . . . . . . . . . . . . . .divide by the coefficient of x

_____

Using the first method, you're dealing with integers and you can do a lot of the math in your head. Using the second method, you're dealing with fractions and mixed numbers. A calculator can be helpful, especially if it handles arithmetic with fractions nicely, as many graphing calculators do.

6 0

3 years ago

Write an expression for the area of the shaded region in its simplest form. Show all of your steps.

netineya [11]

The area of the shaded region is going to be the area of the rectangle minus the area of the square.

Area of a rectangle is L * W.
A = L * W
A = (x + 10)(2x + 5)
A = x(2x + 5) + 10(2x + 5)
A = 2x^2 + 5x + 20x + 50
A = 2x^2 + 25x + 50 .....this is the area of the rectangle

area of a square is : A = a^2...where a is one side
A = (x + 1)^2
A = (x + 1)(x + 1)
A = x(x + 1) + 1(x + 1)
A = x^2 + x + x + 1
A = x^2 + 2x + 1

now we subtract the area of the square from the area of the rectangle to get the area of the shaded region.

2x^2 + 25x + 50 - (x^2 + 2x + 1) =
2x^2 + 25x + 50 - x^2 - 2x - 1 =
x^2 + 23x + 49 <== the area of the shaded region

6 0

3 years ago

HELP PLEASE !!! 4th time asking this :(( i really need help PLEASE !

harina [27]

Answer:

A: (-5,4)

B: (7,-2)

Step-by-step explanation:

It has to be in order start with the x-axis then the y-axis

4 0

3 years ago

NewPop produces their brand of soda drinks in a factory where they claim that the

Citrus2011 [14]

Answer:

a) 14960 bottles

b) 502 bottles

Step-by-step explanation:

Given that:

Mean (μ) = 24 ounces, standard deviation (σ) = 0.14 ounces

a) From empirical rule (68−95−99.7%) , 68% of the population fall within 1 standard deviation of the mean (μ ± 1σ).

Therefore 68% fall within 0.14 ounces of the mean

the number of bottle = 22,000*68% = 14960 bottles

b) To solve this we are going to use the z score equation given as:

$z=\frac{x-\mu}{\sigma}$ where x is the raw score = 23.72

$z=\frac{x-\mu}{\sigma}=\frac{23.72-24}{0.14} =-2$

From the normal probability distribution table: P(X < 23.72) = P (Z < -2) = 0.0228

The number of rejected bottles = 22000 × 0.0228 = 502 bottles

8 0

3 years ago

Find the sum of 9x² - 6x + 7, 5-4 x<br>and 6-3x²

puteri [66]

Answer:

6x² - 10x + 11

Step-by-step explanation:

Step 1: Write expression

(9x² - 6x) + (5 - 4x) + (6 - 3x²)

Step 2: Combine like terms

6x² - 10x + 11

3 0

4 years ago