Express 4x^2-25 as a product of two binomials.

Answers

Answer 1

Answer:

An expression is defined as a set of numbers, variables, and mathematical operations. The expression 4x²-25 as a product of two binomials can be written as (2x - 5)(2x + 5).

What is an Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression 4x² - 25 as a product of two binomials can be written as,

4x² - 25

Rewriting the expression,

= (2x)² - (5)²

Using the algebraic property, a²-b²=(a+b)(a-b),

= (2x - 5)(2x + 5)

Hence, the expression 4x²-25 as a product of two binomials can be written as (2x - 5)(2x + 5).

Learn more about Expression here:

brainly.com/question/13947055

#SPJ2

Answer 2

Answer:

4x^2-25= (2x)^2-5^2=(2x-5)(2x+5)

Used: a^2-b^2=(a+b)(a-b)

Related Questions

What should be done to both sides of the equation in order to solve y + 8.5 = 17.2?
Aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a lawn, and y, the size of the lawn in acres. Two of his points are (3, 1.5) and (5, 2.5). Which statement describes the slope of the line through these two points?It takes Aaron about 1 hour to mow 2 acres.Aaron’s rate for mowing lawns is 0.5 acres per hour.The ratio of acres to time is 5 acres to 3 hours. The rate to mow a lawn is 0.6 hours per acre.
a walking path across a park is represented by the equation y=-2x-7. a new path will be built perpendicular to this path. the paths will intercect at the point (-2,-3) . identify equation that represents new path
A student has earned scores of 87, 81, and 88 on the first 3 of 4 tests. If the student wants an average (arithmetic mean) of exactly 87, what score must she earn on the fourth test?
24 less than 3 times the number itself is equals to a number.what is the number?

a box with no top is constructed from a 10 inch x 12 inch piece of cardboard by cutting out congruent squares from each corner of the cardboard and then folding the resulting tabs. We determined the volume of that box (in cubic inches) is given by V(x) = 4x³ - 44x² + 120x where x denotes the length of the side of the square which is removed from each corner (in inches), 0 < x < 5. Solve the inequality V(x)≥80 analytically and interpret your answer in the context of that example.

Answers

Answer:

$To solve the inequality $V(x) \geq 80$, we'll first set up the inequality and then find the values of $x$ that satisfy it.The inequality is $4x^3 - 44x^2 + 120x \geq 80$.Let's simplify it further:$4x^3 - 44x^2 + 120x - 80 \geq 0$.Now, we need to find the values of $x$ that make this inequality true.We can start by factoring the expression:$4(x^3 - 11x^2 + 30x - 20) \geq 0$.$

$Now, let's factor the cubic polynomial inside the parentheses:$x^3 - 11x^2 + 30x - 20 = (x - 2)(x - 5)(x - 2)$.Now, the inequality becomes:$4(x - 2)(x - 5)(x - 2) \geq 0$.To determine the intervals where this inequality is satisfied, we can use a sign chart. We'll consider the values of $x$ that make each factor and the whole expression positive or negative.$

$1. $x - 2$ is positive for $x > 2$ and negative for $x < 2$.\n2. $x - 5$ is positive for $x > 5$ and negative for $x < 5$.\n3. $x - 2$ is positive for $x > 2$ and negative for $x < 2$.Now, consider the overall sign of the expression $4(x - 2)(x - 5)(x - 2)$:- Positive when all three factors are positive (i.e., $x > 5$).- Negative when exactly one factor is negative (i.e., $2 < x < 5$).- Positive when all three factors are negative (i.e., $x < 2$).$

$So, the solution to the inequality $V(x) \geq 80$ is:\[x < 2 \text{ or } 2 < x < 5.\]$

Step-by-step explanation:

In the context of the example, this means that the side length of the square removed from each corner must be less than 2 inches or between 2 and 5 inches for the volume of the box to be greater than or equal to 80 cubic inches. This helps determine the range of valid values for

x to achieve the desired volume for the box.

Final Answer:

The solution to the inequality V(x) ≥ 80 is x ≥ 3.5 inches.

Explanation:

To solve the inequality V(x) ≥ 80, we set the equation 4x³ - 44x² + 120x ≥ 80 and simplify. This simplifies to x³ - 11x² + 30x - 20 ≥ 0, which can be factored as (x - 3.5)(x - 2)(x - 2.857) ≥ 0. Since x represents the side length of the squares removed from the corners, it cannot be negative, so we focus on the values of x that make the expression on the left side of the inequality greater than or equal to zero. This leads us to the solution x ≥ 3.5 inches.

In the context of the example, when the side length of the squares removed from each corner is 3.5 inches or larger, the resulting box has a volume greater than or equal to 80 cubic inches. This means that to achieve a box with a volume of at least 80 cubic inches, you need to remove squares with sides of at least 3.5 inches.

Learn more about inequality

brainly.com/question/32125218

#SPJ11

How do I solve this math problem you and your friend are selling magazine subscriptions for a fundraiser. After w weeks , you have sold (7w = 6) subsriptions and your friend has sold ( 9w = 2) subscriptions. Whats the diffrence written in simple expression form?

Answers

Answer:

The diffrence written in simple expression form is 40/63

Step-by-step explanation:

To solve for the difference normally you have to subtract your own subscription from that of your friends,

Let's perform this operation step wise

Now your subscription is

(7w = 6)

w=6/7

Your friends own is

( 9w = 2)

w=2/9

So the difference in simple form is

6/7-2/9

The LCM is 63 I.E 9*7=63

=54-14/63

=40/63

1.8 Graphing Ordered Pairs: Practice!Write the ordered pair for each point.
A
1. A
2. B
3. C
4. D
5. E
6. F

Answers

A(2,4)
B(-1,2)
C(-3,-2)
D(2,0)
E(0,-4)
F(5,-4)

Write an equation in standard form then solve 2q^2+22q+=-60

Answers

In standard form the equation reads 2q²+22q+60=0. In order to solve for q you have to factor the expression on the left first. Take out a factor of 2 and you have 2(q²+11q+30). Factor the inside and you have 2[(q+6)(q+5)]. Set the factors equal to 0 and solve and you finish with q=-6 or q=-5.

Fruit:sugar in 2:3 . If 8kg of sugar is used how much fruit ?

Answers

F:S = 2:3

F:8 = 2:3

F/8 = 2/3

F = 2/3 * 8

F = 16/3

Therefore F, Fruit = 16/3 kg.

Solve this inequality: 3p – 16 < 20. A. p < –12
B. p < 12
C. p < 1/3
D. p < 11/3

Answers

3p - 16 < 20
3p < 20 + 16
3p < 36
p < 12

The answer is B.

3p - 16 < 20

3p < 20 + 16

3p < 36

p < 36/3

p < 12

Option B.

Other Questions

What is the at least probability of 6

Marlene brought a pitcher filled with 10 cups of water to her volleyball game. The paper cups she brought hold Two-thirds of a cup of water each. How many paper cups can Marlene fill with water?Which math sentence represents the problem?Two-thirds divided by 10 = 20/30=1/1510 divided by two-thirds = 30/2=1510 divided by three-halves = 20/3] 6 and two-thirds1/10 divided by two-thirds = 3/20

4. A triangle with base (2x+2) and height (x-2) is cut out of a rectangular sheet of paper that is (3x+4) by (2x+3) what is the area of the paper that remains?

Four out of every five teenagers surveyed went to a movie theater in the past month. If 95 teenagers were surveyed, how many had gone to the movies in the past month?