Given the equation 4x + 7 = 3(2x − 5), solve for the variable. Explain each step and justify your process.B.Sam solved a similar equation below. Is Sam's solution correct? Explain why or why not.
5x − 1 = 2(x + 4)
5x − 1 = 2x + 8
7x − 1 = 8
7x = 7
x = 1

Answers

Answer 1

Answer: Part 1: $4x + 7 = 3(2x - 5)$

$4x+7=6x-15$

$7=6x-15-4x$

$7=2x-15$

$7+15=2x$

$22=2x$

$22=2x / 2$

$x=11$

Part 2: Sam is not correct because he messed up the second step. He added 2x on both sides to get 7x, instead he should have subtracted.

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The amount $180.00 is what percent greater than $135.00? A. 33.33% B. 25% C. 133.33% D. 35%

Answers

the answer is A. 33.33%

Help answer 1/5x-2/3y=30 when y = 15

Answers

The value of the variable x at y = 15 will be 200.

What is the solution to the equation?

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

The equation is given below.

(1/5)x - (2/3)y = 30

Solve the equation for x, then we have

(1/5)x = 30 + (2/3)y

x = 150 + (10/3) y

The value of the variable x at y = 15 will be

x = 150 + (10/3) × 15

x = 150 + 50

x = 200

The value of the variable x at y = 15 will be 200.

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$\frac{1}5x-\frac{2}3y=30$

Plug in 15 for y.

$\frac{1}5x-\frac{2}3(15)=30$

2/3 of 15 is 10.

$\frac{1}5x-10=30$

Add 10 to each side.

$\frac{1}5x=40$

Divide each side by 1/5.
(dividing by a fraction is the same as multiplying by its reciprocal...flip 1/5...×5)

$\boxed{x=200}$

Simplify the following

Square root 15 / Square root 3

Answers

Answer:

The answer is √5 .

Step-by-step explanation:

Youhavetorationalizethefractioninordertogetridofsurdinthedenorminatorbymultiplying√3tobothnumeratoramddenorminator:

$( √(15) )/( √(3) )$

$= ( √(15) )/( √(3) ) * ( √(3) )/( √(3) )$

$= ( √(15) * √(3) )/( √(3) * √(3) )$

$= ( √(45) )/(3)$

$= ( √(9 * 5) )/(3)$

$= (3 √(5) )/(3)$

$= √(5)$

#1. Given the binomials (x - 2), (x - 1), (x + 2), and (x - 4), which one is a factor of f(x) = x3 + 7x2 + 14x + 8? (x - 2) (x - 1) (x + 2) (x - 4) Given the binomials (x + 1), (x + 4), (x - 5), and (x - 2), which one is a factor of f(x) = 3x3 - 12x2 - 4x - 55? (x + 1) (x + 4) (x - 5) (x - 2) #2. What is the f of x over the g of x when f(x) = 6x3 - 19x2 + 16x - 4 and g(x) = x - 2?6x2 - 7x + 2/3x2 - 9x + 8/ 6x2 - 7x + 2 - 8 over the quantity of x minus 2/3x2 - 9x + 8 - 8 over the quantity of x minus 2

#3. What is the f of x over the g of x when f(x) = 6x3 - 19x2 + 16x - 4 and g(x) = x - 2? #4.What is the quotient when -3x3 + 5x + 14 is divided by x - 2? -3x2 - 6x - 7/- 3x2 - x + 12/-3x2 + 6x - 7 + 28 over the quantity of x minus 2/
-3x2 - x + 12 + 28 over the quantity of x minus 2.

#4. What is the quotient when x3 - 5x2 + 2x + 5 is divided by x - 2?

x2 - 3x - 4/ x2 - 7x + 16/x2 - 3x - 4 - 3 over the quantity of x minus 2

x2 - 7x + 16 - 3 over the quantity of x minus 2

Answers

#1
Factoring the function:
f(x) = x3 + 7x2 + 14x + 8
f(x) = (x + 4) (x + 1) (x + 2)

From the options, (x + 2) is the factor

#2
f(x) / g(x) = (6x3 - 19x2 + 16x - 4) / (x - 2)
This can be solved by factoring the numerator, by synthetic division or using the remainder theorem.

The result is:
6x^2 - 7x + 2 or (x - 2/3)(x - 1/2)

#3 same with #2

#4
(x3 - 5x2 + 2x + 5) / (x - 2)
Again, this can be solved by a number of methods, the result is:
x2 -3x - 4 - (3/x-2)

Factoring the function:

f(x) = x3 + 7x2 + 14x + 8

f(x) = (x + 4) (x + 1) (x + 2)

From the options, (x + 2) is the factor

f(x) / g(x) = (6x3 - 19x2 + 16x - 4) / (x - 2)

This can be solved by factoring the numerator, by synthetic division or using the remainder theorem.

The result is:

6x^2 - 7x + 2 or (x - 2/3)(x - 1/2)

#3 same with #2

(x3 - 5x2 + 2x + 5) / (x - 2)

Again, this can be solved by a number of methods, the result is:

x2 -3x - 4 - (3/x-2)

Find the maximum value of x+y given thatx>=-3
y>=5x-9
3x+y<=15

Answers

x ≥ -3
y ≥ 5x - 9
3x + y ≤ 15

3(-3) + (5x - 9) ≤ 15
    -9 + (5x - 9) ≤ 15
    (-9 - 9) + 5x ≤ 15
   -18 + 5x ≤ 15
   + 18    + 18
   5x ≤ 33
      5 5
   x ≤ 6.6
     y ≤ 5(6.6) - 9
   y ≤ 33 - 9
   y ≤ 24
   (x, y) ≤ (6.6, 24)

Determine the length, to 1 decimal place, of the arc that subtends an angle of 5.4 radians at the centre of a circle with radius 7 cm.

Answers

The length, to 1 decimal place, of the arc that subtends an angle of 5.4 radians at the center of a circle with a radius of 7 cm is 37.8 cm.

What is a circle?

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

It is given that:

The arc subtends an angle of 5.4 radians at the center of a circle with a radius of 7 cm.

As we know, the relationship between radius of the circle, central angle, and arc length is:

s = rθ

r = 7 cm

θ = 5.4 radians.

When two lines or rays converge at the same point, the measurement between them is called an "Angle."

s = 7×5.4

s = 37.8 cm

Thus, the length, to 1 decimal place, of the arc that subtends an angle of 5.4 radians at the center of a circle with a radius of 7 cm is 37.8 cm.

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Answer:

37.8

Step-by-step explanation:

Length = radius * Θ

L=7*5.4

L=37.8

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Have a great day!

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