Which expressions can be factored using the difference of squares identity?

Answers

Answer 1

The expression, for example, x²- 49 may be factored as (x+7)(x-7).  can be factored in using the difference of squares identity.

What is the "Difference of Squares" identity?

The difference of the square's identity is shown below:

(a+b)(a-b) = a² -b²

When an expression can be seen as the difference of two perfect squares, i.e. a² -b², we can factor it as (a+b) (a-b).

For example, x²- 49 may be factored as (x+7)(x-7).

This approach is based on the pattern (a+b)(a-b) = a² -b², which may be validated by extending the parenthesis in (a+b)(a-b).

Thus, the expression, for example, x²- 49 may be factored as (x+7)(x-7).  can be factored in using the difference of squares identity.

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Related Questions

-2
-3
S
y = -2|x|
2
X
The function is positive when
The function is negative when
The function is increasing when
The function is decreasing when

Answers

Answer: Never, All real numbers, x<0, x>0

Step-by-step explanation:

The function is positive when it is above the x-axis.

The function is negative when it is below the x-axis.

The function is increasing when the graph is going up.

The function is decreasing when the graph is going down.

what’s the inequality
17 < 9 + x

Answers

Answer:

x > 9

Step-by-step explanation:

I'm doing linear equations and one if the things says y = -x so do i plug in the x that i have already and just switch it to the opposite integer????

Answers

To solve for y we will have to simply replace the value of x and the solution we write it in the equivalent palce for y, that is:

For x = -5:

[tex]y=-(-5)\Rightarrow y=5[/tex]

For x = -2:

[tex]y=-(-2)\Rightarrow y=2[/tex]

For x = 0:

[tex]y=0[/tex]

For x = 3:

[tex]y=-3[/tex]

k (x)=6x-12 ; k(x)=15

Answers

The input value x in the function k( x ) = 6x - 12 when k( x ) = 15 is 9/2.

What is the input value (x) in the given function?

A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.

Given the data in the question;

k( x ) = 6x - 12k( x ) = 15x = ?

To determine the value of x, equate the function to 15 and solve for x.

k( x ) = 6x - 12

k( x ) = 15

15 = 6x - 12

Rearrange the equation

6x - 12 = 15

Collect like terms

6x = 15 + 12

6x = 27

Divide but sides by 6

6x/6 = 27/6

x = 27/6

x = 9/2

Therefore, the input value (x) is 9/2, this forms an ordered pair of ( 9/2, 15 ).

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The figures below are congruent. Name the corresponding sides.

Answers

Answer:

KM

KL

LM

Step-by-step explanation:

Solve each equation by factoring. Then solve the quadratic formula. (Show all work)

Answers

[tex] - {k}^{2} + 3k = 28 - 2 {k}^{2} \\ - {k}^{2} + 2 {k}^{2} + 3k - 28 = 0 \\ {k}^{2} + 3k - 28 = 0 \\ (k + 7)(k - 4) = 0 \\ \\ k + 7 = 0 \\ \\ ork - 4 = 0 \\ \\ k = - 7 \\ \\ or \\ \\ k = 4[/tex]

ATTACHED IS THE SOLUTION

I GROUPED THE LIKE TERMS TOGETHER FIRST AFTER THAT THEN FACTORISED.

Please help me please I’m begging I WILL GIVE YOU BRAINLEST

Answers

The value of x is 54.

What is the Same Side Interior Angles Theorem?

If a transversal meets two parallel lines, each pair of same-side interior angles is supplementary (their sum is 180°), according to the theorem for the "same-side interior angle theorem."

The given angles in the figure are 2x + 42° and x - 24°, which are interior angles formed on the same side of the transversal.

By Same Side Interior Angles Theorem,

2x + 42° + x - 24° = 180°

3x + 18° = 180°

3x = 180° - 18°

3x = 162°

x = 54

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A restaurant chain is measuring the levels of arsenic in chicken from its suppliers. The question is whether there is evidence that the mean level of arsenic is greater than 80 ppb, so we are testing vs , where represents the average level of arsenic in all chicken from a certain supplier. It takes money and time to test for arsenic so samples are often small. A sample of chickens from one supplier is tested, and the resulting sample mean is . Subtracting 11 from the sample data to move the mean down to the null mean of results in the following data: . 62, 78, 89, 95, 95, 137

Answers

The p-value of the test is 0.1515 which concludes that the average amount of arsenic in chicken from suppliers is 80 ppb.

The test hypothesis is as follows:

H₀: The mean amount of arsenic is 80 ppb, i.e. μ= 80.

Hₐ: The mean amount of arsenic is more significant than 80 ppb, i.e.μ > 80.

We will apply a t-test for a single mean because the population standard deviation is unknown,

It is assumed that the sample means  [tex]\bar{x}[/tex] = 91.

The adjusted sample presented is:

S = { 62, 78, 89, 95, 95, 137}

Calculate the sample standard deviation as follows:

[tex]\bar{x}[/tex] = 62 + 78 + 89  + 95 + 95 + 137 =80

[tex]s =\sqrt{\frac{1}{6-1} \times [(62-80)^2 + (78-80)^2 + (89-80)^2 + (95-80)^2 + (95-80)^2 + (137-80)^2]}[/tex]

s =28.66

[tex]t =\dfrac{\bar{x}-\mu}{s/ \sqrt{n} } = \dfrac{{91}-80}{28.6/ \sqrt{6} }=0.94[/tex]

Thus, the test statistic value is 0.94.

Compute the p-value of the test as follows:

p-value = p(tₙ₋₁ < t)

p-value = p(t₆₋₁ < t)

p-value = p(t₅ < t)

*Make use of a t-table.

As a result, the test has a p-value of 0.1515.

Rule of decision:

The null hypothesis will be rejected if the p-value of the test is less than the significance threshold, and vice versa.

p-value = 0.1515 > α = 0.05

At 5% significance, the null hypothesis will not be rejected.

As a result, we may conclude that the average amount of arsenic in chicken from suppliers is 80 ppb.

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pls help im faling geometry

Answers

Side |CB|:

Sin(60)= opposite side / hypotenuse
We know hyp=10
And opposite side =|CB|

=sin60= opp/10

So multiply both sides by 10
10sin60 = opp

|CB| = 10 (√3 ÷ 2) = 5 √3


Then we can use Pythagoras theorem to get the other side (or we can do the same thing as before using either cos60 or sin30 =|BA| /10)

a² + b² = c² where c is the hypotenuse

(5 √3)² + b² = 10²

(25)(3) + b² = 100
75+ b² = 100

-75 from both sides

b² = 25
So b = |BA| = √25 = 5

Which of the following is the best estimate of the slope of the best -fit line for the graph at the right?

Answers

The best estimate of the slope of the best-fit line for the graph at the right will be 7/4.

What is the slope?

The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope. A line that is moving up will have a positive slope, and a line that is moving down will have a negative slope if you view the line from left to right. A line's slope often indicates the steepness and direction of the line. By calculating the difference between the coordinates of the two points, (x₁,y₁) and (x₂,y₂), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.

Given Data

x coordinate = 4

y coordinate = 7

Slope = y-coordinate/ x-coordinate

Slope = 7/4

The best estimate of the slope of the best-fit line for the graph at the right will be 7/4.

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Find the slope:
(-3, 3) and (7, 6)

Answers

Answer:

slope = (3/10)

Step-by-step explanation:

(-3, 3) and (7, 6)

(x₁, y₁)        (x₂, y₂)

        y₂ - y₁         6 - 3             3              3

m = ------------ = ------------ = ------------ = ----------

        x₂ - x₁         7 - (-3)        7 + 3           10

I hope this helps!

write the equation of the line in a fully simplified slope-intercept form.

Answers

Slope Intercept Form From a Graph

Slope intercept form: [tex]y=mx+b[/tex]

m = slopeb = y-intercept

We can identify two points on the given graph and solve for the slope and the y-intercept.

Solving the Question

Two clear points on the graph are (6,0) and (0,6).

First, we can solve for the slope by using the slope equation:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] where two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

⇒ Plug in the points (6,0) and (0,6):

[tex]m=\dfrac{0-6}{6-0}\\\\m=\dfrac{-6}{6}\\\\m=-1[/tex]

Therefore. the slope of the line is -1. Plug this into [tex]y=mx+b[/tex]:

[tex]y=-x+b[/tex]

Now, we can find the y-intercept. It is the value of y when the line crosses the y-axis.

In this case, we can see on the graph that this is 6.

[tex]y=-x+6[/tex]

Answer

[tex]y=-x+6[/tex]

Find the value of p in the inequality.

three fourths times p plus 8 is greater than or equal to 3

Answers

The value of p that we get by solving the inequality given in the question is [tex]p\geq \frac{-20}{3}[/tex]

The given inequality is

[tex]\frac{3}{4}p+8\geq 3[/tex]

⇒[tex]\frac{3}{4}p\geq 3-8[/tex]                              (subtracting 8 on both sides)

⇒[tex]3p\geq -5*4[/tex]                             (multiplying both sides by 4)

⇒[tex]p\geq \frac{-20}{3}[/tex]                                  (dividing both sides by 3)

⇒[tex]p\geq -6.667[/tex]

Therefore the value of p must be greater than or equal to -20/3 or -6.667

That is, [tex]p\geq -6.667[/tex]

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Solve the equation for the given variable. (type "no solution" if the equation has no solution and type "all
real numbers" if the equation is valid for all possible x-values)
4(4x + 2) + 2(9x + 4) + 3 = 34x + 19

Answers

Answer:

all real numbers

Step-by-step explanation:

4(4x+2)+2(9x+4)+3=34x+19

16x+8+18x+8+3=34x+19

34x+19=34x+19

all real numbers

:]

What is the answer: 4(3x+2)-2

Answers

Answer:

12x + 6

Step-by-step explanation:

What is the answer:

4(3x+2)-2=

12x + 8 - 2 =

12x + 6

12x+6 because you multiply 4 times whats in the parethisss to get rid of it then simplify

Rebecca wants to prove that if the diagonals in a parallelogram are perpendicular, then it is a rhombus.

Answers

It is shown that if a parallelogram's diagonals are perpendicular, the parallelogram is a rhombus.

In mathematics, what is a parallelogram?

A parallelogram is a quadrilateral with two parallel sides (and therefore opposite angles equal).

What exactly is a rhombus?

A rhombus is a quadrilateral with all of its sides equal. Because opposite sides of a parallelogram are equal, a rhombus is a type of parallelogram in which all sides are equal.

We must demonstrate that if the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

Let ABCD be a  parallelogram .

Consider Δ AOD and Δ COD

Since, a parallelogram's diagonals bisect each other we can say that,

AO = CO

∠AOD = ∠COD = 90°

DO = OD

Δ AOD ≅ Δ COD [SAS rule]

∴ AD = CD

Because the parallelogram's adjacent sides are equal, we can conclude that all four sides are equal.

As a result, it is demonstrated that if the diagonals of a parallelogram are perpendicular, the parallelogram is a rhombus.

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Solve the system of linear equations using the substitution method.

4x + 7y = 19 and y = x + 9

A. (-4, 5)

B. (-6, 4)

C. (-1, 2)

D. (-4, 3)

Answers

Answer:D

Step-by-step explanation:

Which of these shapes are a trapezoid?

Answers

Answer: The Pink one

Step-by-step explanation: Trapezoids have 2 parallel sides and 2 non-parallel sides.

your ethics professor decides to conduct a survey in your class about whether voluntary euthanasia should be legal in the united states. for her survey, she takes all 30 students' names and assigns them each a number. then she has a computer program indiscriminately choose 15 students. we could say that her survey will be:

Answers

Hence, the survey of professor will be representative survey.

What is survey?

A survey is a technique for acquiring data from a sample of people by asking pertinent questions with the goal of comprehending populations as a whole.

Everyone involved in the information economy, from corporations to the media to the government and academia, relies on surveys as a vital source of information and insights.

The survey of professor will be representative survey.

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11. A researcher in a personal submarine begins at the surface of the ocean.
The submarine descends 20.6 meters and then ascends 57 meters. What
is the depth of the personal submarine?
A-26.3 meters
14.9 meters
B-14.9 meters
26.3 meters

Answers

The depth of the personal submarine is -14.9 meter.

What is an integer?

An integer is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.

Given that,

The submarine descends 20.6 meters and then ascends 5.7 meters. it means 20.6 is a negative number and 5.7 is a positive number.

Now,

To find the depth adding the -20.6+5.7

-20.6+5.7

-14.9

Hence, The depth of the personal submarine is -14.9 meter

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11. The price of a sweater changed from $20 to $12. By what percentage was the price of the sweater
changed?
The price of the sweater decreased by __ %

Answers

well, the change was 8 bucks.

if we take 20 to be the 100%, what is 8 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 20 & 100\\ 8& x \end{array} \implies \cfrac{20}{8}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{5}{2}=\cfrac{100}{x}\implies 5x=200\implies x=\cfrac{200}{5}\implies x=40[/tex]

Find the quotient of.(4.617 × 10 ^3 ) ÷ (5,700 ÷ 10^ 2 )

Answers

The quotient of the expression (4.617 × 10³ ) ÷ (5,700 ÷ 10² ) is 81.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that;

The expression is;

(4.617 × 10³ ) ÷ (5,700 ÷ 10² )

Now, Solve the expression by using BODMAS rule;

= (4.617 × 10³ ) ÷ (5,700 ÷ 10² )

= 4,617 ÷ 57

= 81

Thus, The quotient of the expression (4.617 × 10³ ) ÷ (5,700 ÷ 10² ) is 81.

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I need help with finding the coordinates of B, I found A but I can't seem to get the right answer for B.

Answers

The graph represents the cosine graph, the coordinates of B is (-180, -1 )

what is cosine graph?

This is a type of graph used to depict cosine values of angles. The maximum and minimum points in these type of graph is 1 and -1.

The zero points gives the maximum point on the graph, hence the graph starts at ( 0, 1 )

Point B is found by analyzing the graph.

The point is located at the minimum which is -1. this is for the output value.

The input value which is the x direction we look at the cycles covered. one full cycle is 360 degrees or -360 degrees.

Point B is in the negative and coves half cycle which is -180

Hence B ( -180, -1)

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5
8
of the staff are male. 5
12
of the staff works part time at
the aquarium. What fraction of the staff is female?

Answers

The fraction that are female in the company is 227/256

How to determine the fraction that are female?

The given parameters are

Male staff = 58

Total number of staff = 512

Start by calculating the number of female staffs

So, we have

Female staff = Total number of staff - Male staff

Substitute the known values in the above equation

So, we have

Female staff = 512 - 58

Evaluate the like terms

Female staff = 454

The fraction that are female is

Fraction = Female staff/Total number of staff

This gives

Fraction = 454/512

Simplify

Fraction = 227/256

Hence, the fraction is 227/256

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What is the value of x?

Answers

Answer:

x = 15

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

3x - 5 is an exterior angle of the triangle, then

3x - 5 = x + 25 ( subtract x from both sides )

2x - 5 = 25 ( add 5 to both sides )

2x = 30 ( divide both sides by 2 )

x = 15

Answer:

40° and 115°

Step-by-step explanation:

x+3x-5+25°=180°(angle on a straight line)

4x+20=180°

4x=180°-20

4x=160°

x=160/4

x=40°

The other angle

3x-5=3(40)-5

120-5=115°

total

40°+25°+115°=180°

the half-life of palladium-100 is 4 days. after 12 days a sample of palladium-100 has been reduced to a mass of 4 mg. what was the initial mass (in mg) of the sample? what is the mass (in mg) 7 weeks after the start? you may enter the exact value or round to 4 decimal places.

Answers

Using the half life of palladium, mass seven weeks after start was 0.7931 gm.

The half-life is the amount of time it takes for a quantity (of material) to fall to the cost. In nuclear physics, the phrase usually refers to how rapidly neutrons become radioactive atoms or how long stable atoms survive.

The term can also refer to any sort of hyperbolic (or, in rare situations, non-exponential) decay.

The  half life of palladium 100 = 4 days

after 24 days sample has reduced to a mass of 5mg

standard exponential function is

[tex]P = P_o e^{kt}[/tex]

plugging P = P₀ /2

[tex]P_o/2 = P_o e^{4k }[/tex]

[tex]1/2 = e^{4k }[/tex]

ln (1/2) = 4k

k = -0.1733

function becomes

[tex]P = P_o e^{- 0.1733 t }[/tex]

plugging P = 5 and t = 24

[tex]5 = P_o e^{( - .1733\times 24 ) }[/tex]

P₀ = 320.10

In the medical sciences, for example, the biological half of drugs and other chemicals in the human body is referred to. The flipside of half-life is doubling time in exponential growth.

For the second part of the problem:

7 weeks = 5 × 7 =49 days

plugging t = 49

[tex]P = 320.10 e^{(-.1733 * 35 ) }[/tex]

mass 7 weeks after = 0.7431 mg

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Evaluate the arithmetic series described:
a (subscript 1) = 12
a (subscript n) = 64
Find S (subscript 14)

Answers:
541
532
1082
1064
...the subscript thing isn't working for some reason

Answers

Answer:

532

Step-by-step explanation:

Sum of the first n terms of an arithmetic series:

[tex]\boxed{S_n=\dfrac{n}{2}(a_1+a_n)}[/tex]

Where:

aₙ is the nth term.a₁ is the first term.n is the position of the term.

Given terms:

[tex]a_1=12[/tex][tex]a_n=64[/tex]

Substitute the given terms into the formula to create an equation for the nth term:

[tex]\implies S_n=\dfrac{n}{2}(12+64)[/tex]

[tex]\implies S_n=\dfrac{n}{2}(76)[/tex]

[tex]\implies S_n=38n[/tex]

To find S₁₄, substitute n = 14 into the found equation:

[tex]\begin{aligned}n=14 \implies S_{14}&=38(14)\\ & = 532\end{aligned}[/tex]

I need helping finding out the answers … I’m confused.

Answers

To solve this problem, we will use the following formula for the area of a trapezoid:

[tex]A=\frac{a+b}{2}h,[/tex]

where a, and b are the lengths of the bases and h is the height.

Now, we are given that ( we will omit the units to simplify the calculations):

[tex]\begin{gathered} h=\frac{1}{4}(a+b), \\ h=2\frac{1}{2}. \end{gathered}[/tex]

Therefore:

[tex]\frac{(a+b)}{2}=2(\frac{a+b}{4})=2h=2(2+\frac{1}{2})=4+1=5.[/tex]

Substituting in the above formula, we get:

[tex]A=\frac{5}{2}\times(2\frac{1}{2}).[/tex]

Simplifying the above result, we get:

[tex]A=\frac{25}{4}ft^2.[/tex]

Answer:

[tex]\begin{gathered} A=\frac{1}{2}(2\frac{1}{2})(2\frac{1}{2}\cdot2) \\ =\frac{1}{2}(\frac{5}{2})(\frac{5}{2}\cdot2) \\ =\frac{50}{8}=\frac{25}{4}=6.25ft^2. \end{gathered}[/tex]

Last year, Lena biked 565 miles. This year, she biked k miles. Using k, write an expression for the total number of miles she biked

Answers

565+k

hope this helps!

find the values of a,b,c, and d so that h(x)=a|bx+c|+d is a translation 7 units up and 1 unit right, followed by a reflection in the y-axis of the graph of g(x)=1/3|x+3|-4

Answers

The translation shift the coordinates of the expression in the right side. And there is no change in the reflection based equation because of the absolute symbol.

What is translation and reflection?

In mathematics, the translation shift the coordinates either on the horizontal axis or on the vertical axis. It compress the expression also. Similarly, in reflection, the expression get reflected on the coordinate axis either on the upper side or downward side.

According to the question, the given expression for the translation as well as for the reflection are as follows:

h(x)=a |b(x) + c| + d

g(x)=1/3 | x + 3| - 4

And the given condition state that the translation is for 7 units and reflection is on the y-axis. Translation shift the expression and reflection reflects the expression.

Translation expression: h(x+7)=a |b(x+7) + c| + d

Reflection expression: g(-x)=1/3 | -x + 3| - 4 = 1/3 | x + 3| - 4

Therefore, the translation shift the coordinates of the expression in the right side. And there is no change in the reflection based equation because of the absolute symbol.

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Determine the equation of the circlegraphed below.-10 -9-8 -7 -6 -5 -4 -3-1109y87654321-1-2-3-4-5-6-7-8-9-1012 3 4 5 6 7 8 9 10X Which situation could NOT represent a proportional relationshipAnswerA The number gallons of water in x barrels with 42 gallons of water in each barrelB The amount an employee who makes 58.50 per hour eams in h hoursC The weight in x weeks of a puppy that gains 2 pounds per week it is starting weight is 5 poundsD The cost of purchasing p pounds of bananas for 50 55 per pound A flight from sydney to auckland takes 3 hours and 12 minutes. auckland time is 2 hours ahead of sydney's. if the flight departed at sydney 10:10am at what time did it arrive at auckland Which angle relationships are correct? Check all that apply.1 and 8 are alternate exterior angles.4 and 6 are same side interior angles.5 and 7 are vertical angles.2 and 8 are corresponding angles.3 and 6 are alternate interior angles. 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How fast was the pipe leaking in gallons per day why is Canada's system called a parliamentary democracy? Arrange events in the section in the order they occur: Mildred invites her friend over to watch White clown, The hound come sniffing around the door while Mildred are reading books, Faber gives montag hos modified seashell radio, Montag has a breakdown on public transportation due to not being able to get the sound of advertisements out of his head. HELP ME PLEASE AND HURRY :[ From a lamp post four feet away from her, Sandra looks up to the sky and sees a bird that is five feet away from her. How high up is the bird? Show all of your steps in answering the question Easton is a songwriter who collects royalties on his songs whenever they are played in a commercial or a movie. easton will earn $40 every time one of his songs is played in a commercial and he will earn $110 every time one of his songs is played in a movie. easton's songs were played on 6 more commercials than movies, and his total earnings on the royalties from all commercials and movies was $840. determine the number of commercials and the number of movies on which easton's songs were played. What is the slope y = 8x - 15 Downhill ski racing requires the racer to maintain the tuck position for over a minute while they are going extremely fast therefore the muscle fibers recruited must not fatigue easily or the scare could be severely injured which type of muscle fiber is predominantly recruited during downhill ski racing? men versus women: the average 20- to 29-year-old man is 69.9 inches tall, with a standard deviation of 3.0 inches, while the average 20- to 29-year-old woman is 64.1 inches tall, with standard deviation of 3.8 inches. a. find the z scores for a 67-inch- man and a 62-inch woman. Angelo's kayak travels 10km/h in still water. If the river's current flows at a rate of 4km/h, How long will it take to travel 35km downstream? it'll take [____] hours. ANALYZE CRAFT AND STRUCTURE REASONING AND EVIDENCEA. DIRECTIONS: Read the passage below. Then, answer the questions that follow.Our town's Shade Tree Commission is responsible for the care and maintenance oftrees growing on town property, including parks and recreational areas. The Commissionalso supposedly reviews and approves plantings around new construction and overseestree removal at building sites. Something is going wrong, though. The trees aredisappearing. Our town, once characterized by beautiful greenery, is beginning to looklike a wasteland-all for the sake of commerce.A new shopping area was just built on a wooded lot. The shade trees on the town'sright-of-way should have been preserved. Instead, all 57 trees on the lot were takendown. The Shade Tree Commission demanded that the developer be fined and newtrees be planted along the right-of-way. But perhaps the Commission should have paidattention in the first place! Our town is known for its tree-lined streets and park-likeproperties. Should we sit idly by while commerce is allowed to blight the landscape?1. What is the writer's claim in this argument?2. What is one piece of evidence supporting the writer's claim?