How to solve factor by grouping. Step by step.

Answers

Answer 1

solving factor by grouping, The final factored form of the expression is n(n + 3) - 10.

What is factor?

A factor is a number that divides into another number exactly with no remainder. For example, the factors of 8 are 1, 2, 4, and 8.

What is factor by grouping?

Factor by grouping is a method of factoring polynomials, which is used to find the common factors in an expression. The idea is to group the terms of the polynomial in such a way that the common factors can be factored out of them. In other words, it is a way to simplify an algebraic expression by finding common factors among the terms and then grouping them together. For example, the polynomial 2x^2 + 6x can be factored by grouping as (2x^2 + 6x) = 2x(x + 3). This is the most common way to factor a polynomial with four terms.

To solve the problem "factor by grouping" for the expression "n^2+3n-10", you can follow these steps:

Write the expression in the form of (n^2 + An + B) + (Cn + D)

(n^2 + 3n - 10) = (n^2 + 3n) + (-10)

Factor out the greatest common factor (GCF) of the terms in the first set of parentheses.

(n^2 + 3n) = n(n + 3)

Factor out the GCF of the terms in the second set of parentheses, if possible. In this case, there is no GCF.

Combine the factored expressions from step 2 and step 3 to get the final factored form.

n(n + 3) + (-10)

The final factored form of the expression is n(n + 3) - 10.

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Related Questions

find the area of the following

Answers

Answer:

24000 ft²

Step-by-step explanation:

Triangle PRS:

b = base = PR = 240 ft

2AS = 240 ft

[tex]\sf AS = \dfrac{240}{2}\\\\ AS = 120 \ ft[/tex]

h = height = AS = 120 ft

[tex]\sf \boxed{\bf \ Area \ of \ triangle = \dfrac{1}{2}b*h}[/tex]

[tex]\sf =\dfrac{1}{2}*240*120\\\\ = 120 * 120\\\\ = 14400 \ ft^2[/tex]

Triangle PRQ:

b = PR = 240 ft

3BQ = 240 ft

[tex]\sf BQ = \dfrac{240}{3}\\\\ BQ = 80 \ ft[/tex]

[tex]\sf Area \ of \ triangle \ PRQ = \dfrac{1}{2}*240*80[/tex]

= 120 * 80

= 9600 ft²

Area of the quadrilateral PQRS = area of ΔPRS + area of ΔPRQ

= 14400 + 9600

= 24000 ft²

A school system is reducing the amount of dumpster loads of trash removed each week. in week 5, there were 60 dumpster loads of waste removed. in week 10, there were 40 dumpster loads removed. assume that the reduction in the amount of waste each week is linear. write an equation in function form to show the amount of trash removed each week. f(x) = −4x 60 f(x) = 4x 60 f(x) = −4x 80 f(x) = 4x 80

Answers

The equation in function form is f(x)=-4x+80.

What is linear function?

A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.

We can find the equation in function form as shown below:

We have given two points (5,60) and (10,40)

Slope of line

m = (40-60)/ (10-5)

m=-20/5

m=-4

Equation in slope intercept form

(y-y1) =m(x-x1)

(y-60) =-4(x-5)

y-60=-4x+20

y=-4x+20+60

y=-4x+80

y=f(x)

f(x)=-4x+80

Hence, the equation in function form is f(x)=-4x+80.

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there are five chemistry instructors and six physics instructors at a college. if a committee of four instructors is selected,

Answers

The probability of at least one of them being a physics instructor is 120 ways to form the committee.

Probability of Independent Events: The 'At Least One' Rule?

Sometimes, simply the occurrence of the event at least once matters when computing independent events. The "At Least One" Rule is used to describe this. The complement of the probability of the event never occurring will be used to calculate the probability of the event occurring at least once.

There are five chemistry instructors and six physics instructors at a college. If a committee of four instructors is selected.

Starting with 6, choose two because we require at least two professors. Let's move on to the remaining 8 individuals (there were initially 10, but now there are just 8): and select 3.

6 select 2; 8 select 3

15×56 =840

We then chose 5 individuals from a group of 10, at least 2 of whom were lecturers.

(9) = 20 options for selecting the professors. 3

(3) = 6 options for selecting the professors.

(9) (¹) = 20 × 6 = 120 ways.

Therefore, 120 ways to form the committee.

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Complete question:

There are five chemistry instructors and six physics instructors at a college. If a committee of four instructors is selected, find the probability of at least one of them being a physics instructor?

i need help putting it in expanded form and solving it

Answers

Answer:

4x^04x^04x^04x^1 which equals 256

Step-by-step explanation:

The 4 outside of the parentheses says take what you have outside of the parentheses and multiply it by itself that may times.

x raised to the zero is 1, so you are just left with 4x4x4x4 or 256

The planner needs a clearance of 9 feet under the arch has the planner met the minimum

Answers

Yes, the planner has met the minimum height, as the minimum height was 9 feet and the maximum height of the arc is 9.6 feet

How to explain the information?

As we can see that at the mid value, for x=4, the value of f(x)=9.4

It means that the maximum height occurs at mid of the arc where it is height is 9.6 feet above the ground.

It means that the planner has met the minimum height, as the minimum height was 9 feet and the maximum height of arc is 9.6 feet

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Find the missing value so that the two points have a slope of 1/2.
(9, 1) and (3, y)

Please explain

Answers

Answer: -2

Step-by-step explanation:

Substituting into the slope formula,

[tex]\frac{y-1}{3-9}=\frac{1}{2}\\\\y-1=-3\\\\y=-2[/tex]

To prove quadrilateral WXYZ is a parallelogram, Travis begins by proving △WZY ≅ △YXW by using the SAS congruency theorem.

Quadrilateral W X Y Z is shown. A diagonal is drawn from point W to point Y. Sides W Z and X Y are parallel and congruent.

Which reasons can Travis use to prove the two triangles are congruent? Check all that apply.
∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem.
WY ≅ WY by the reflexive property.
∠ZWY ≅ ∠XWY by the corresponding ∠s theorem.
WX ≅ ZY by definition of a parallelogram.
WZ ≅ XY by the given.

Answers

The reasons Travis can use to prove both triangles are congruent by the SAS congruency theorem are:

∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem.WY ≅ WY by the reflexive property.WZ ≅ XY by the given.

What is the SAS Congruency Theorem?

The SAS congruency theorem states that two triangles are congruent when they both have two pairs of corresponding congruent sides and a pair of corresponding congruent included angles.

Given the image below, we have the following proof with the statement and reasons in bracket:

WZ ≅ XY [given]

WY ≅ WY [reflexive property]

∠ZWY ≅ ∠XYW [by the alternate interior ∠s theorem]

△WZY ≅ △YXW [by the SAS congruency theorem]

Therefore, the reasons Travis can use are:

∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem.WY ≅ WY by the reflexive property.WZ ≅ XY by the given.

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Answer:

A. ∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem;

B. WY ≅ WY by the reflexive property; & E. WZ ≅ XY by the given.

Step-by-step explanation: Trust Me! Answer is correct on Edge.

Good Luck! :)

Which reasons can Travis use to prove the two triangles are congruent? Check all that apply.

A. ∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem B. WY ≅ WY by the reflexive property E. WZ ≅ XY by the given

Please help me solve this random answers will be removed

Answers

Answer:

AB-46 cm

Step-by-step explanation:

Use law of cosines

AB^2 = 24^2 + 26^2 - 2 (24)(26)cos 134

AB= 46 cm

If a line that passes through the
points (8, 10) and (4, -6) also passes through the point (b, 2b), then find the value of b?

Answers

Gradient of line= (y2-y1)/(x2-x1)
Gradient of line= (10-(-6))/(8-4)
Gradient of line= 16/4
Gradient of line= 4

Y-intercept
Y=4x+c
When x=8, y=10
10=32+c
c= -22

Equation of line
Y=4x-22

When x=b, y=2b
Y=4x-22
2b=4b-22
22=2b
b=11

omg please help me!!!

Answers

area = pi * r^2

here, the radius is 2 as its the diameter/2.

so the area is 4pi.

circumference = 2*pi*r.

so the circumference is 4pi as well.

i need help with this page

Answers

9a). The measure of segment GH from the given information can be evaluated as one-fourth of the perimeter; 48/4 = 12 cm.

9b). The measure of <EJF is 90° as the angle EJF is a right angle made at the intersection of the rhombus diagonals.

9c). The measure of <EHG is 60° as the opposite angles in a rhombus are congruent and <EHG = 2 × <EHJ = 2 × 30 = 60°.

10a). The sides labelled in the rectangle are congruent by the rectangle diagonal congruence concept; it therefore follows that the required value of x is; 9x+ 20 = 10x +8; and x = 12.

10b). The angle measures as labelled in the rhombus are congruent as this follows from the fact that the diagonal is an angle bisector. Hence, 2x +15 = 5x +3; and x = 4.

What is congruence?

The concept of congruence describes a similarly between 2 or more geometric figures or elements.

Answers

The point (12, 190) means that the temperature after 12 hours is 190 degrees Celsius

How to make a scatter plot?

To do this, we make use of the following points

(12, 190), (14, 201), (15, 301), (16, 305), (18, 350), (20, 40), (25, 450)

Where x represents the number of hours and y represents temperature

See attachment for the scatter plot.

The description of a point

To do this, we make use of the point (12, 190)

This means that the temperature after 12 hours is 190 degrees Celsius

Answers

Answer:

c. Substitute

Step-by-step explanation:

A graph of the function on the left shows the parabola touches the x-axis at x = -8/3. That is, the vertex is on the x-axis. It crosses the y-axis at y = 64.

Show a value is a root

A given solution to an equation can be verified by substituting that value into the equation an showing the result is a true statement. Here, the value x=-8/3 is a root of the given equation because that value makes the equation true.

[tex]9\left(-\dfrac{8}{3}\right)^2+48\left(-\dfrac{8}{3}\right)+64=0\\\\9\left(\dfrac{64}{9}\right)-\left(\dfrac{48\cdot8}{3}\right)+64=0\\\\64-\dfrac{3\cdot2\cdot8\cdot8}{3}+64=0\\\\64-2\cdot64+64=0\\\\0=0\qquad\text{True}[/tex]

C = 75h + 125
The equation above gives the amount C, in dollars, an electrician charges for a job that takes h hours. Ms. Sanchez and Mr. Roland each hired this electrician. The electrician worked 2 hours longer on Ms. Sanchez's job than on Mr. Roland's job. How much more did the electrician charge Ms. Sanchez than Mr. Roland?

Answers

Ms. Sanchez paid 150 dollars more than Mr. Roland.

How much more did the electrician charge Ms. Sanchez than Mr. Roland?

Let's say that the electrician worked for x hours in Mr. Roland's home, then worked for (x + 2) hours in Ms. Sanchez home.

Then we need to find the difference between the linear equations:

C(x + 2) - C(x) = (75*(x + 2) + 125) - (75*x + 125)

If we simplify that, we get:

75*x + 75*2 + 125 - 75*x - 125

= 75*2 = 150

This means that Ms. Sanchez paid 150 dollars more than Mr. Roland.

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help me please im in a rush

Answers

Answer:

The answers are in the image

Step-by-step explanation:

The solutions are in the image

Full factor of 32a^3+ 12a^2

Answers

Answer:

4a²*(9a + 3)

Step-by-step explanation:

Factorize:

Prime factorize 32 and 12. Then find GCF.

32a³ = 2 * 2 * 2 * 2 * 2 * a³

12a² = 2 * 2 * 3 * a²

GCF = 2 * 2 * a² = 4a²

32a³ + 12a² = (4a²*9a) + (4a²*3)

=4a²*(9a + 3)

Manufacturers were subdivided into groups by volume of sales. Those with more than $100 million in sales were classified as large; those from $50 to $100 million as medium size; and those between $25 and $50 million, and so on. Samples were then selected from each of these groups. What is this type of sampling called

Answers

Stratified random sampling is used to subdivided into groups by volume of sales.

According to the statements

Manufacturers are subdivided into groups by volume of sales. and for this Stratified random sampling is used.

Stratified random sampling is the technique used divide the population can be partitioned into subpopulations.

Thus, Stratified random sampling is used to subdivided into groups by volume of sales.

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find the value in the figure

Answers

Redo this question incase I may do mistakes.

(06.04 MC)
Find the perimeter of the image below:

Answers

Answer: 39 units

Step-by-step explanation:

Using the distance formula, we get that:

[tex]PT=\sqrt{10^2 + 4^2}=\sqrt{116}\\\\TS=\sqrt{7^2 + 0^2}=7\\\\SR=\sqrt{7^2 + 1^2}=\sqrt{50}\\\\RQ=\sqrt{6^2 + 5^2}=\sqrt{61}\\\\PQ=\sqrt{2^2 + 6^2}=\sqrt{40}[/tex]

So, the perimeter is

[tex]\sqrt{116}+7+\sqrt{50}+\sqrt{61}+\sqrt{40} \approx 39[/tex]

Question 5 of 10
Suppose f(x) = x² and g(x)= (1x)
graph of g(x) with the graph of f(x)?
Which statement best compares the
A. The graph of g(x) is the graph of f(x) horizontally stretched by a
factor of 4.
B. The graph of g(x) is the graph of f(x) vertically stretched by a
factor of 4.
C. The graph of g(x) is the graph of f(x) shifted units right.
D. The graph of g(x) is the graph of f(x) horizontally compressed by a
factor of 4.

Answers

Answer: A

Step-by-step explanation:

See attached image.

You are out to dinner with 10 friends (meaning there are 11 of you). The bill total is $110. You all want to split the bill evenly. How would you write this as an improper fraction?

A 110/10
B 10/111
C 11/110
D 110/11

Answers

Answer:

110/11

Step-by-step explanation:

divide the bill by 11 people.

Answer:

D. 110/11

Step-by-step explanation:

110 Dollars

11 people to split it with

110/11 to find the total for each person

i don’t know this answer help pls

Answers

Answer:

Step-by-step explanation:

Starting price is $5.50. And for every mile it costs $1.50.

A friend asked lara to help her divide 456.3 by 100. what should lara tell her? a. move the decimal point three places to the right. b. move the decimal point two places to the right. c. move the decimal point three places to the left. d. move the decimal point two places to the left.

Answers

Answer:

Step-by-step explanation:

The correct answer is D. If we are multiplying by 10 we would move the decimal place one place to the right to show that the number is now 10 times bigger. If we multiply by one hundred. We are getting 100 times bigger, so we would move the decimal place 2 places to the right.

The opposite is true if we are dividing. Instead of moving the decimal to the right to show that the number is getting bigger, we move to the left to show that the number is getting smaller. If we are getting smaller by 10, we would move the decimal one place to the left. In this case, we are getting 100 times smaller so we move the decimal two places to the left.

A shopkeeper has $680 in the denominations of $50, $20, $10 and $5 notes. The number of notes of each denomination is equal. What is the total number of notes?

Answers

The total number of notes is 32

The number of notes

Let the number of notes be x

$50 = x

$20 = x

$10 = x

$5 = x

Total number of notes = 4x

Let's find 'x'

50x + 20x + 10x + 5x = 680

85x = 680

x = 680/ 85

x = 8

We know that;

Total number of notes = 4x = 4 × 8 = 32 notes

Thus, the total number of notes is 32

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20 PIONTSSS TO WHOEVER ANDWER THIS QUESTION !!!

Answers

Answer:

The answer would be 36cm².

Step-by-step explanation:

⇒ Two prisms are similar.

⇒ Scale factor = 3:8

⇒ The ratio of the surface area is 9:64.

⇒ So S₁ : S₂ = 9:64

⇒ S₁ : 256 = 9:64

⇒ S₁ = 36cm²

This would mean that the answer is 36 centimeters ² (squared).

The answer is 36cm2.

Pls help me on 103 :((

Answers

Answer:

J) [tex]18cm^2[/tex]

Step-by-step explanation:

a square inscribed in a circle means that the radius of the circle is the same thing as a line drawn from the center of the square to a corner.

this will give you the side measurements for a triangle (look at the attached picture). now use the Pythagorean theorem to find the hypotenuse aka the side length of the square. then multiply it by itself.

Answer: H

Step-by-step explanation:

Finding the Diameter

If we draw a line through a diagonal of the square, two triangles are formed. The angle opposite the diagonal is 90°, as all angles are 90° in a square. One of the properties of a circle state that the angle in a semicircle is always 90°, which means that the diagonal formed a semi-circle.

A semi-circle only forms when a diameter is drawn in a circle, making the diagonal a diameter. This will be useful information, as we can calculate the side length of a square using the length of its diagonal.

A diameter is just twice the length of a radius, so the diagonal of the square would be 6 cm.

[tex]2*3=6[/tex]

Finding the Length of One Side

The diagonal also splits the square into two 45-45-90 triangles. These triangles have a special property that their hypotenuse is √2 times each leg, and all legs are the same length.

Therefore, we can calculate the length of a leg by dividing the hypotenuse by √2.

[tex]\frac{6}{\sqrt{3}}[/tex]

The length of one side of the square is [tex]\frac{6}{\sqrt{3}}[/tex]

Finding the Area

As we already know the length of one side, we can just square it to get the area.

[tex](\frac{6}{\sqrt{3}})^2[/tex]

[tex]\frac{6^2}{(\sqrt{3})^2}[/tex] [Properties of Exponents]

[tex]\frac{36}{3}[/tex]

[tex]12[/tex]

Hence, the area of the square is 12 cm².

Solve for x in the equation: 8a = 2xy + b.

Answers

Step-by-step explanation:

Simplifying 8a = 2xy + b

Reorder the terms: 8a = b + 2xy

Solving 8a = b + 2xy

Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right.

Divide each side by '8'. a = 0.125b + 0.25xy

Simplifying a = 0.125b + 0.25xy

Describe how the graph of the function g(x) = -5x²-2 is related to the graph of
the function f(x) = 5x².

(A) reflection of f(x) = 5x² across the x-axis and translated left 2 units

(B) translation of f(x) = 5x² down 2 units

(C) reflection of f(x) = 5x² across the x-axis and translated down 2 units

(D) reflection of f(x) = 5x² right 2 units

Answers

Answer:

Simplify (5√3 − 2√5) the whole square

Answers

Answer:

95 - 20[tex]\sqrt{15}[/tex]

Step-by-step explanation:

(5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )²

= (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )(5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )

each term in the second factor is multiplied by each term in the first factor, that is

5[tex]\sqrt{3}[/tex] (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] ) - 2[tex]\sqrt{5}[/tex] (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] ) ← distribute parenthesis

= 75 - 10[tex]\sqrt{15}[/tex] - 10[tex]\sqrt{15}[/tex] + 20 ← collect like terms

= 95 - 20[tex]\sqrt{15}[/tex]

Answer:

95 - 20√15

Step-by-step explanation:

I assume the expression is (5√3 − 2√5)^2 (?).

(5√3 − 2√5)*(5√3 − 2√5)

25√3^2 - 20√15 + 4√5^2

25*3 - 20√15 +4*5

75 - 20√15 +20

95 - 20√15

Which of these statements is true for f(x) = 2.3*?
OA. The y-intercept is (0, 1).
OB. The domain is x > 0.
OC. The y-intercept is (0, 2).
OD. It is always decreasing.

Answers

The true statement for f(x) = 2(3)^x is the y-intercept is (0, 2).

How to determine the true statement?

The function is given as:

f(x) = 2(3)^x

Set x = 0 to determine the y-intercept

f(0) = 2(3)^0

Evaluate

f(0) = 2

This means that the y-intercept of f(x) = 2(3)^x is (0,2)