Use the difference of squares identity to write this polynomial expression in factored form : 9x^2-49

Answers

Answer 1

Answer:

The expression in factored form is (3x - 7)(3x + 7)

Step-by-step explanation:

Here in this question, we are interested in using the difference of two squares to factor the given expression.

Mathematically, supposed we have two squares a^2 and b^2, and we are told to factorize a^2-b^2.

By using the difference of two squares;

a^2-b^2 can thus be written as;

(a-b)(a + b)

Now, we can apply same approach to the problem at hand.

9x^2 - 49

kindly note that 9x^2 can be written as ((3x)^2 and 49 can be written as 7^2

So applying what we have said earlier about difference of two squares;

9x^2 - 49 will be ;

(3x-7)(3x + 7)

Answer 2

Answer:

The answer is (3x - 7) (3x +7)

Step-by-step explanation:

Use The Difference Of Squares Identity To Write This Polynomial Expression In Factored Form : 9x^2-49

Related Questions

Solve for x. 23x +2=15x+48x+6

Answers

Answer:

[tex]x = - \frac{1}{10} [/tex]

Step-by-step explanation:

23x +2 = 15x+48x+6

To solve for x group like terms

That's

Send the constants to the right side of the equation and those with variables to the left side

We have

23x - 15x - 48x = 6 - 2

Simplify

- 40x = 4

Divide both sides by -40

[tex] \frac{ - 40x}{ - 40} = \frac{4}{ - 40} [/tex]

We have the final answer as

[tex]x = - \frac{1}{10} [/tex]

Hope this helps you

If you simplify both sides, it shows that 23x+2=63x+6. If you cancel out the x, it shows that 2=40x+6. If you cancel out the numbers it shows that -4=40x. Divide all sides to show that -1/10=x.

 If 2x3 – 4x2 + kx + 10 is divided by (x + 2), the remainder is 4. Find the value of k using remainder theorem. Please help :)​

Answers

The polynomial remainder theorem states that the remainder of the division of a polynomial [tex]P(x)[/tex] by [tex]x-a[/tex] is equal to [tex]P(a)[/tex].

Therefore

[tex]P(-2)=4\\2\cdot(-2)^3 - 4\cdot(-2)^2 + k\cdot(-2) + 10=4\\-16-16-2k=-6\\-2k=26\\k=-13[/tex]

1. Which expression is equivalent to (-2)(a + 6)?

Answers

Answer:

please mark my answer brainliest

Step-by-step explanation:

- 2a -12

Marta esta poniendo sus libros en una estantería. Le faltan 7 libros para poder poner 12 en cada estante; sin embargo, si pone 10 libros en cada estante, se quedan 5 libros sin poner. ¿Cuantos es antes tiene la estantería?

Answers

Answer:

x = 6       la cantidad de estantes

y = 65    cantidad de libros

Step-by-step explanation:

LLamemos "x" la cantidad de estantes que tiene Marta, y llamaremos "y" la cantidad de libros.

La primera condición que se debe cumplir es que cuando Marta coloca 12 libros en cada estante entonces le faltan 7, esto lo expresamos así:

y  +  7  = 12*x        (1)

La segunda condición establece que si Marta coloca los libros en número de 10 por estante le quedan 5 sin colocar, luego esto en lenguaje matemático se expresa así:

y  -   5   = 10*x     (2)

Ahora hemos obtenido un sistema de dos ecuaciones con dos incógnitas que se resuelve por cualquiera de los métodos conocidos, usaremos el método de sustitución.

Despejamos   y en la primera ecuación y lo sustituimos en la segunda, de esa forma obtendremos el valor de x

y  =  12*x  - 7

(12*x - 7 ) - 5  = 10*x

2*x  -12 = 0

2*x = 12

x = 6       la cantidad de estantes, y

y  =  12*x -7

y  =  72  -  7

y =  65    cantidad de libros

Jonas needs a cell phone. He has a choice between two companies with the following monthly billing policies. Each company’s monthly billing policy has an initial operating fee and charge per text message. Sprint charges $29.95 monthly plus .15 cents per text, AT&T charges $4.95 monthly plus .39 cents per text. Create equations for the two cell phone plans.

Answers

Answer:

Since both companies have a different plan, two equations are created to determine which company Jonas should choose with respect to the number of messages sent.

Step-by-step explanation:

- Sprint = $ 29.95 * X (0.15)

- AT & T = $ 4.95 * X (0.39)

One dollar equals 100 cents, so 0.15 cents equals $ 0.0015 dollars.

- Sprint = $ 29.95 * X (0.0015)

- AT & T = $ 4.95 * X (0.0039)

Si Jonas envía 500 mensajes de texto el valor mensual de cada empresa sería de:

- Sprint = $ 29.95 * 500 (0.0015)  = 22.46 dollar per month.

- AT & T = $ 4.95 * 500 (0.0039)  = 9.65 dollar per month.

The company Jonas should choose is AT&T.

AT&T also charges a little more per number of text messages, but since the phone's value is so low it would take thousands of text messages to compare to Sprint's monthly value.

The price of a stock decreased by 60 cents one week, decreased 10 cents the next week, and decreased another 20 cents the following week. What is the average change in the price of the stock over the three weeks? need to know right now ASAP!! –270 cents per week –90 cents per week –87 cents per week –30 cents per week

Answers

Hi there! Hopefully this helps!

----------------------------------------------------------------------------------------------------------

It decreased by 30 cents per week.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The average rate of change is calculated as:

the ratio of the sum of the change in the three weeks divided by the number of weeks. (The number of weeks being 3)

 Rate of change = [tex]\frac{-60 -10 -20}{3}[/tex].

(-60 + -10 + -20 = -90). So, to simplify it:

[tex]\frac{-90}{3}[/tex] = -30

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Incase you are confused:

Since the average rate of change is negative, this means that the stock price has decreased.

Combine the radicals. 3√5-8√5+2√5

Answers

Answer:  [tex]-3\sqrt{5}[/tex]

-3 times the square root of 5

=============================================

Explanation:

Let [tex]x = \sqrt{5}[/tex]

Replace all the root 5 terms with x and we go from

[tex]3\sqrt{5}-8\sqrt{5}+2\sqrt{5}[/tex]

to

[tex]3x-8x+2x[/tex]

From here, combine like terms to get

[tex]3x-8x+2x = -5x+2x = -3x[/tex]

and the last thing to do is replace the x with sqrt(5)

[tex]-3x = -3\sqrt{5}[/tex]

Meaning that,

[tex]3x-8x+2x = -3x[/tex]

[tex]3\sqrt{5}-8\sqrt{5}+2\sqrt{5} = -3\sqrt{5}[/tex]

What are the lower quartile, upper quartile, and median for this box and
whisker plot?

A) LQ = 22 UQ = 10 Median = 18.5

B) LQ = 10 UQ = 22 Median = 18

C) LQ = 10 UQ = 22 Median = 18.5

D) LQ = 10 UQ = 22 Median = 19​

Answers

Answer:

C

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The lower quartile range is shown by the bottom of the box which is at 10.

The median is shown in the middle line, which is closer to 18 than 18.5.

The upper quartile range in the end of the box, which is at 22!

(You can also look at the picture attached if that helps.)

A ship travels due north for 100 miles from point C to point A. From point A the ship travels to point B at 60° east of north. From point B, the ship returns to point C heading 45° west of south. What approximate distance did the ship travel from point A to point B? How far does it travel in total?

Answers

Answer:

AandB=80miles

Total=240miles

Step-by-step explanation:

Draw the figure first indicating the figures then find the distance each degrees then find the total

The distance ship travels from A to B is 273.2 miles and total distance covered by ship is  707.82 miles.

What is laws of sines?

The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.

The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle. At least two angles and their corresponding side measurements should be used at once for the sine law to function.

Given distance from C to A = 100 miles north

From B to A ship travels 60° east of north,

and From B to C 45° west of south,

the figure for problem is attached,

from figure we can  calculate the angles of A, B and C

so ∠A makes supplementary with 60°

∠A + 60° = 180°

∠A = 120°

for ∠B we need to draw an imaginary perpendicular on the line extending from A, we get

∠B + 45° + 30° = 90° (30° is angle of imaginary right triangle)

∠B = 90 - 75 = 15°

and ∠C can be found by,

∠A + ∠B + ∠C = 180°

∠C = 180 - 15 - 120

∠C = 45°

now use sine formula for triangles,

sinA/a = sinB/b = sinC/c

where A, B and C are angles of triangle and a, b and c are length of opposite side of angle A, B and C respectively.

a = BC, b = AC, and c = AB

so

sinA/BC = sinB/AC = sinC/AB

we have AC = 100 miles

substitute the values

sinC/AB = sinB/AC

sin(45)/AB = sin(15)/100

AB = 100/(√2sin(15))

AB = 100/0.3659

AB = 273.298 miles

and sinA/BC = sinB/AC

BC = AC sinA/sinB

BC = 100(sin 120/sin15)

BC = 100(0.866/0.2588)

BC = 100 x 3.3462

BC = 334.62 miles

total distance = AB + BC + AC

total distance = 334.62 + 273.2 + 100

total distance =  707.82 miles

Hence the distance from A to B is 273.2 miles and total distance is 707.82 miles.

Learn more about  laws of sines;

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How many significant figures does each value contain? 5.6803 kg has significant figures. 0.00047 seconds has significant figures. 0.240 miles has significant figures.

Answers

Answer:

5.6803 has five significant figures.

0.00047 has two significant figures.

0.240 has three significant figures.

What are Significant Figures?

Significant figures are numbers that are necessary to express a true value.

Place the values in scientific notation.

[tex]5.6803 * 10^{0} = 5.6803\\\\4.7 * 10^{-4} = 0.00047\\\\2.4 * 10^{-1}=0.240[/tex]

Explanation

5.6803

The zero that is within 5.6803 is "trapped," meaning it is in between two nonzero digits. Therefore, all five digits are significant figures.

This answer is also already in scientific notation because 5.6803 satisfies the inequality [tex]1 < x < 10[/tex], which decides if a number is correctly written in scientific notation or not.

0.00047

The zeroes that precede the 4 and the 7 are not significant because they are dropped in scientific notation and are not trapped by other nonzero digits. Therefore, only two digits of this value are significant.

0.240

Since the zero at the end of 0.240 is a trailing zero, it is significant along with the 2 and the 4. The zero that precedes these digits and the decimal point is not significant. Therefore, only three digits of this value are significant.

Therefore:

5.6803 has five significant figures.

0.00047 has two significant figures.

0.240 has three significant figures.

Which statement best illustrates using the vertical line test to determine if the graph below is a function of x? The graph is not a function of x because the line x = 0 intersects the graph at two points. The graph is a function of x because the line x = 5 does not intersect the graph. The graph is not a function of x because the line y = 0 intersects the graph at two points. The graph is a function of x because the line y = 5 does not intersect the graph.

Answers

Answer:

The graph is not a function of x because the line x = 0 intersects the graph at two points.

Step-by-step explanation:

This graph is not a function because it fails the vertical line test, since several vertical lines would intersect the graph at 2 points.

This answer choice is correct, as the line x = 0 intersects the graph at 2 points, (0, 2) and (0, -2).

Answer:

A

Step-by-step explanation:

kinda confused buttttt anyone know this?

Answers

Answer:

Hey there!

The overlapping part is the product.

Thus, the product is 1/8.

Hope this helps :)

Which expression is equivalent to (–2)(a + 6)?
A. –2a + 6
B. 2a + 12
C. –2a – 12
D. –2a + 12

Answers

The answer is option c.

HELP HELP HELP Sally can paint a room in 4 hours. Joe can paint a room in 6 hours. How
long will it take if they paint the room together? I’m not sure if it’s 1.4

Answers

Answer:

2 hrs, 24 min

Step-by-step explanation:

Sally:  in one hour, she can paint 1/4 of the room.

Joe: in one our, he can paint 1/6 of the room

Hour one: 1/4+1/6=3/12+2/12=5/12

1÷5/12=1*12/5=12/5

12/5= 2 & 2/5 hours, or 2.4 hours, or 2 hrs 24 minutes

Answer: 2.4 hours

Step-by-step explanation:

1/4 1/6

LCM

3/12+2/12=5/12 repricical 12/5 =2.4

Please help!
Suppose that [tex]\alpha[/tex] is inversely proportional to [tex]\beta[/tex]. If [tex]\alpha=4[/tex] when [tex]\beta=9[/tex], find [tex]\alpha[/tex] when [tex]\beta=-72[/tex]

Answers

Answer:

The answer is

[tex] \alpha = - \frac{1}{2} [/tex]

Step-by-step explanation:

From the question

[tex]\alpha[/tex] is inversely proportional to [tex]\beta[/tex] is written as

[tex] \alpha = \frac{k}{ \beta } [/tex]

where k is the constant of proportionality

When

[tex]\alpha[/tex] = 4[tex]\beta[/tex] = 9

Substituting the values into the formula

we have

[tex]4 = \frac{k}{9} [/tex]

cross multiply

k = 4 × 9

k = 36

So the formula for the variation is

[tex] \alpha = \frac{36}{ \beta } [/tex]

when

[tex]\beta[/tex] = - 72

That's

[tex] \alpha = \frac{36}{ - 72} [/tex]

Simplify

We have the final answer as

[tex] \alpha = - \frac{ 1}{2} [/tex]

Hope this helps you

**Yoxelt buys 4 1/ 2 gallons of soda. One-fourth of the soda he bought was Pepsi and the rest was Sprite. How many gallons of Pepsi did Yoxelt buy? Show all work below.

Answers

Answer:

1 1/8

Step-by-step explanation:

1/4 of 4 1/2 is Pepsi.

1/4 * 4 1/2 = (1/4) * 4 + (1/4) * (1/2) = 1 1/8

Dena uses 7.4 pints of white paint and blue paint to paint her bedroom walls. 2/5 of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use yo paint her bedroom walls

Answers

Answer:

4.44 pints

Step-by-step explanation:

7.4 times 3/5

A man traveled to his country home, a distance of 150 miles and then back. His average rate of speed going was 50 miles an hour and his average return speed was 30 miles per hour. His average rate of speed for the entire trip was Need help will mark brainlist

Answers

Answer:

  37.5 mi/h

Step-by-step explanation:

  time = distance / speed

On the trip 'going', the time was (150 mi)/(50 mi/h) = 3 h.

On the return trip, the time was (150 mi)/(30 mi/h) = 5 h.

__

  speed = distance / time

The average speed for the whole trip was ...

  speed = (150 mi +150 mi)/(3 h +5 h) = (300 mi)/(8 h) = 37.5 mi/h

His average rate of speed was 37.5 miles per hour.

How to work out the medium in maths

Answers

Answer:

To find the median you cross off the first few numbers and the last few until you get to the middle then when you get the middle number that will be your median

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

It's the middle value of a list of numbers arranged in order.

For example the median of the list 1 2 3 4 5 is 3.

If there are an even number of values, the median is the mean of the middle two. For example:

1 3 4 5 7 9:

The middle 2 numbers are 4 and 5 so

the median is  (4 + 5) / 2 = 4.5

please help me you will recieve 5 stars IF RIGHT ANSWER !

Answers

Answer:

[tex]\huge\boxed{\frac{7}{8}}[/tex]

Step-by-step explanation:

[tex](\frac{49 }{64})^{1/2}[/tex]

=> [tex](\frac{7^2}{8^2} )^{1/2}[/tex]

=> [tex]\frac{7^{2*1/2}}{8^{2*1/2}}[/tex]

=> [tex]\frac{7}{8}[/tex]

Answer:

Below

Step-by-step explanation:

You should now that:

● (m/n)^(1/2) = √(m/n)

So:

● (49/64)^(1/2) = √(m/n)

You shoukd now also that:

● √(m/n) = √m / √n

So:

● √(49/64) = √49/√64

Notice that 64 = 8^2 and 49 = 7^2

● √49 / √64 = √(7^2)/√(8^2) = 7/8

So the answer is 7/8

If two of the ordered pairs was removed which two data points will cause the correlation to decrease the most? Select Two points

1) Data point A

2) Data point B

3) Data point C

4) Data point D

Answers

Answer:

1. Data point A

4. Data point D

Step-by-step explanation:

In a scatter plot, the closer the clustered data points are close to the best line of fit, the greater the correlation that would exist between the two variables.

If we are to draw a best line of fit in the scatter plot that is shown above, the closest data points amongst data points A, B, C, D, and E, that would be close to the best line of fit are data points A and D.

Therefore, removing data point A and point D would cause the correlation to decrease the most.

Musah stands at the center of a rectangular field.He takes 50 steps north,then 25 steps West and finally 50 on a bearing of 315°. Sketch Musah's movement How far west is Musah's final point from the center? How far north is Musah's final point from the center?

Answers

Answer:

The distance of  Musah's final point from the center in the west direction is   60.355 steps

The distance of  Musah's final point from the center in the north direction is   85.355 steps

Step-by-step explanation:

Given that :

Musah stands at the center of a rectangular field.

He takes 50 steps north, then 25 steps West and finally 50 on a bearing of 315°.

The sketch for Musah's movement is seen in the attached file below.

How far west is Musah's final point from the centre?

In order to determine how far west  is Musah's,

Let d be the distance of how far west;

Then d = BC + CD cos θ

In the North West direction,

cos θ = cos 45°

d = 25 + 50( cos 45°)

d = 25 + 50([tex]\dfrac{1}{\sqrt{2}}[/tex]  )

d = 25 + 50( 0.7071)

d =25 + 35.355

d = 60.355 steps

How far north is Musah's final point from the center?

Let d₁ be the distance of how far North;

Then d₁ = AB + CD sin  θ

d₁ = 50 + 50  sin  45°

d₁ = 50 + 50([tex]\dfrac{1}{\sqrt{2}}[/tex]  )

d₁ = 50 + 50( 0.7071)

d₁ = 50 + 35.355

d₁ = 85.355  steps

Is a 118 supplementary or complementary?pls ASAP!!

Answers

Answer:

[tex]\huge\boxed{Supplementary \ Angle}[/tex]

Step-by-step explanation:

118 is a supplementary angle. It is not a complementary angle because complementary angles add up to 90 and 118 is greater than 90 degrees. So, 118 is a supplementary angle and it is an angle adding up to 180 degrees with any other angle measuring 62 degrees.

Answer:Supplementary

Step-by-step explanation:You should remember that complementary refers to any number from 0-90 and supplementary refers to any number from 90 onwards..

Hereby giving the answer as ''Supplementary''

In a given set of data, if the variance is 25, what is the standard deviation? *

Answers

Answer:  5

Explanation: apply the square root to the variance to get the standard deviation

standard deviation = sqrt(variance)

variance = (standard deviation)^2

Based on the variance of the set of data and the definition of standard deviation, the standard deviation here must be 5.

Standard deviation allows us to measure how far apart variables are in a data set.

It is calculated as:

= √Variance

= √25

= 5

In conclusion, the standard deviation is 5 .

Find out more at https://brainly.com/question/14283696.

Barbara Cusumano worked 60 hours last week. Of those hours, 40 hours were paid at the regular-time rate of $12.50 an hour, 18 hours at the time-and-a-half rate, and 2 hours at the double-time rate. What was Barbara's gross pay for the week?

Answers

Answer:

  $887.50

Step-by-step explanation:

Her gross pay is the sum of the pay amounts for each of the hour amounts:

  pay = 40(12.50) +18(12.50)(1.5) +2(12.50)(2)

  = (12.50)(40 +18(1.5) +2(2)) = 12.50(40 +27 +4) = 12.50(71)

  pay = 887.50

Barbara's gross pay for the week was $887.50.

Use the measure of the sides of triangle ABC to classify the triangle by its sides A(-1,3) B(-3,5) C(3,2)

Answers

Answer:

The triangle is a scalene triangle that has all three sides having different lengths

Step-by-step explanation:

The given vertices (and their coordinates) of the triangle are;

A(-1, 3)

B(-3, 5)

C(3, 2)

The equation for finding the lengths of a segment, l, given the coordinates, x, y is presented as follows;

[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]

For segment AB, when, (x₁, y₁) = A(-1, 3) and (x₂, y₂) = B(-3, 5),  we have;

[tex]l = \sqrt{\left (5-3 \right )^{2}+\left (-3-(-1) \right )^{2}} = 2\cdot\sqrt{2}[/tex]

Length of segment AB = 2·√2

For segment AC, when, (x₁, y₁) = A(-1, 3) and (x₂, y₂) = C(3, 2),  we have;

[tex]l = \sqrt{\left (2-3 \right )^{2}+\left (3-(-1) \right )^{2}} = \sqrt{17}[/tex]

Length of segment AC = √17

For segment BC, when, (x₁, y₁) = B(-3, 5) and (x₂, y₂) = C(3, 2),  we have;

[tex]l = \sqrt{\left (2-5 \right )^{2}+\left (3-(-3) \right )^{2}} = 3 \cdot \sqrt{5}[/tex]

Length of segment AC = 3·√5

The triangle is a scalene triangle that has all three sides having different lengths.

A triangle and the coordinates of its vertices is shown in the coordinate plane below. Enter the area of this triangle in square units, rounded to the nearest tenth. square units

Answers

Answer:

22 units²

Step-by-step explanation:

1/2b*h=area

You can either count the units or use the distance formula.

[tex]d = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]

b = 4 units

h = 11 units

area = (1/2*4)*11 = 22 units²

in exponential growth functions, the base of the exponent must be greater than 1. How would the function change if the base exponent were 1? How would the function change if the base of the exponent were between 0 and 1?

Answers

Answer:

GREAT QUESTION!!

Step-by-step explanation:

Bases of exponential functions CANNOT be 1.

It the base was between 0 and 1, .25 for example, then it would be exponential decay, because as x would increase y would decrease.

Just search up exponential decay to see what it looks like, or type in y=.25^x in google search bar.

if this helped, Please give brainly, I need it! Thank you!

Answer:

If the base of the exponent were 1, the function would remain constant. The graph would be a horizontal line. If the base of the exponent were less than 1, but greater than 0, the function would be decreasing.

Step-by-step explanation:

If the base were 1, the function would be constant.

If the base were 1, the graph would be a horizontal line.

If the base were between 0 and 1, the function would be decreasing.

A trader buys tea for $1200 and sells it for $1500. Per sack of tea he makes a profit of $50. How many sacks of tea did he have?

Answers

Answer:

6 sacks

Step-by-step explanation:

Buying Price = $1200

Selling Price = $1500

Total profit = Selling price - Buying Price

= $1500 - $1200

= $300

Given that the profit on each sack of tea is $50

Number of Sacks of Tea = Total Profit ÷ profit per sack

= $300 ÷ 50

= 6 sacks

The number of sacks of tea he has is 6.

The first step is to determine the total profit earned by the trader. Profit is the selling price less the cost price.

Profit = selling price - cost price

$1500 - $1200 = $300

The second step is to divide the total profit by the profit made per sack of tea.

Number of sacks = $300 / $50 = 6

To learn more about division, please check: https://brainly.com/question/194007

10. The probability of buying pizza for dinner is 34% and the probability of buying
a new car is 15%. The probability of buying a new car given that you eat pizza for
dinner is 42%. What is the probability of eating pizza for dinner given that they
buy a new car?

Answers

Answer:

The probability of eating pizza given that a new car is bought is 0.952

Step-by-step explanation:

This kind of problem can be solved using Baye’s theorem of conditional probability.

Let A be the event of eating pizza( same as buying pizza)

while B is the event of buying a new car

P(A) = 34% = 0.34

P(B) = 15% = 15/100 = 0.15

P(B|A) = 42% = 0.42

P(B|A) = P(BnA)/P(A)

0.42 = P(BnA)/0.34

P(B n A) = 0.34 * 0.42 = 0.1428

Now, we want to calculate P(A|B)

Mathematically;

P(A|B = P(A n B)/P(B)

Kindly know that P(A n B) = P(B n A) = 0.1428

So P(A|B) = 0.1428/0.15

P(A|B) = 0.952

Other Questions
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