Near the beginning of Lesson 5.3, a strategy for factoring trinomials of the form x^2+ bx+c was
developed by exploring the product of the binomials (x+p) and (x+q).
Explain how the development of this factoring strategy is an example of working backwards
to solve a problem.

Answers

Answer 1

Answer:

Step-by-step explanation:

there are function that "invert" each other..

subtraction inverts addition...

3+2 = 5 ... 5-2 = 3

division inverts multiplication

5*2 = 10 ... 10/2 = 5

Using that concept, "factoring" is basically the inverse of multiplication

3x^2 + 9x can be factored to 3x(x+3)

if you multiply that out it reverts back to the original equation

so  x^2 + 5x + 6 factors to (x+3)(x+2)

if you multiply that out (foil it)

you get x^2 + 5x + 6


Related Questions

Which is the sum of the sequence {5*1, 5*8, 5*27, 5*64, 5*125, 5*216}?

Answers

Answer:

2160

Step-by-step explanation:

I find that it is easier to split the sequence into smaller, more manageable sections. For numbers beyond 13, the simplest way is to split it up into place values.

Note: * is a multiplication symbol

5*1 = 5

5*8 = 40

5*27 = (5*20) + (5*7) = 100+35 = 135

5*64 = (5*60) + (5*4) = 300+20 = 320

5*125 = (5*100) + (5*20) + (5*5) = 500+100+25 = 625

5*216 = (5*200) + (5*10) + (5*6) = 1000+50+30=1080

Now you can add all of the totals up!

135+320+625+1080 = 2160

LET R equal the rental fee for one locker write an equation that represents the situation

Answers

Answer:

R x 1= price of 1 locker

Step-by-step explanation:

it would continue the same way. Just multiply R and the number of lockers.

Is there a certain situation it was asking about?

Find the measure of the missing angles.

Answers

Answer:

e = 41 , f = 139 and d = 90

Step-by-step explanation:

?

We know that vertically opposite angles are equal.

So, e = 41° [Vertically opposite angles]

We know that linear pair of angles are supplementary (180°).

So, f + 41° = 180° [Linear pair of angles]

=> f = 180° - 41°

=> f = 139°

and d + 90° = 180° [Linear pair of angles]

=> d = 180° - 90°

=> d = 90°

Gant Accounting performs two types of services, Audit and Tax. Gant’s overhead costs consist of computer support, $267000; and legal support, $133500. Information on the two services is:
(See screenshot)

Answers

Answer:

$240,300

Step-by-step explanation:

Given :

Overhead cost :

Computer support = $267000

legal support = $133500

Overheads applied to audit services = (Number of CPU minutes used by Audit services * activity rate per CPU minute)

+

(number of legal hours used by Audit services * activity rate per legal hour)

The overhead applied to audit is thus :

40,000 * (267,000 / (40,000 + 10,000)) +

200 * (133500 / (200 + 800)

(40000 * 5.34) + (200 * 133.5)

= $240,300

The graph shown below expresses a radical function that can be written in
17
the form f(x) = a(x + k)!
C. What does the graph tell you about the
value of k in this function

Answers

Answer:

C. [tex]k[/tex] is greater than zero.

Step-by-step explanation:

We know that graph is obtained from the function of the form [tex]f(x) = a\cdot (x+k)^{1/n} + c[/tex]. According to the graph and if [tex]x + k = 0[/tex], we find that:

[tex]x = -k[/tex] (1)

[tex]x < 0[/tex] (2)

By (1) and (2):

[tex]-k < 0[/tex]

[tex]k > 0[/tex]

Hence, correct answer is C.

rút gọn :
(x+2)^2+(3-x)^2= ?

Answers

Step-by-step explanation:

=x^2+2x+4+9-6x+x^2

=2x^2-4x+13

Which side is the “adjacent” side to θ?

Answers

Answer:

third answer "a"

Step-by-step explanation:

Option 3rd A is the side adjacent

Molly and Lynn both set aside money weekly for their savings. Molly already has $650 set aside and adds $35 each week. Lynn already has $825 set aside but adds only $15 each week. Which inequality could they use to determine how many weeks, w, it will take for Molly’s savings to exceed Lynn’s savings?

Answers

FINAL ANSWER: D

Given : Molly and Lynn both set aside money weekly for their savings.

Molly already has $650 set aside and adds $35 each week.

Lynn already has $825 set aside but adds only $15 each week.

To Find :  inequality   to determine how many weeks, w, it will take for Molly’s savings to exceed Lynn’s savings

Solution:

Molly already has $650

adds $35 each week.

=> added in w  weeks  = 35w

After w weeks  = 650 + 35w

Lynn already has $825

adds $15 each week.

added in w  weeks  = 15w

After w weeks  = 825 + 15w

Molly’s savings to exceed Lynn’s savings

⇒ 650 + 35w >  825 + 15w

⇒  20w  >  175

⇒   4w >  35

⇒  w  >  35 /4

At least 9 weeks

Answer:

D

Step-by-step explanation:

First, to eliminate some answers you can figure out which way the sign should go. The question wants to know when Molly's savings will be larger so the sign should open towards her side of the equation. Since her savings are represented on the left the sign should be a greater than, >.

Then, figure out where the variables belong. The variable represents the number of weeks that have passed, so they should be multiplied by the number that is affected by the passing of weeks. This is the amount each person saves, aka the independent variable. So the "w" variable should be next to the 35 and 15.

A manufacturer of industrial solvent guarantees its customers that each drum of solvent they ship out contains at least 100 lbs of solvent. Suppose the amount of solvent in each drum is normally distributed with a mean of 101.8 pounds and a standard deviation of 3.76 pounds.

Required:
a. What is the probability that a drum meets the guarantee? Give your answer to four decimal places.
b. What would the standard deviation need to be so that the probability a drum meets the guarantee is 0.99?

Answers

Answer:

The answer is "0.6368 and 0.773".

Step-by-step explanation:

The manufacturer of organic compounds guarantees that its clients have at least 100 lbs. of solvent in every fluid drum they deliver. [tex]X\ is\ N(101.8, 3.76)\\\\P(X>100) =P(Z> \frac{100-101.8}{3.76}=P(Z>-0.47))[/tex]

For point a:

Therefore the Probability =0.6368  

For point b:

[tex]P(Z\geq \frac{100-101.8}{\sigma})=0.99\\\\P(Z\geq \frac{-1.8}{\sigma})=0.99\\\\1-P(Z< \frac{-1.8}{\sigma})=0.99\\\\P(Z< \frac{-1.8}{\sigma})=0.01\\\\z-value =0.01\\\\area=-2.33\\\\ \frac{-1.8}{\sigma}=-2.33\\\\ \sigma= \frac{-1.8}{-2.33}=0.773[/tex]

find the derivative of y=(x³-5)⁴(x⁴+3)⁵ ​

Answers

Answer:

[tex]12x^{2} (x^{3}-5)^{3} (x^{4}+3)^{5} +20x^{3} (x^{3}-5)^{4} (x^{4}+3)^{4}[/tex]

Step-by-step explanation:

What is the correct way to read 43.106

Answers

Step-by-step explanation:

Forty three thousand one hundred and six

Answer:

Forty three AND one hundred six thousandths

Step-by-step explanation:

If there is a comma ( , ) between the two numbers, you are correct.  

If there is a period / dot ( . ) between them, and you need to read the place values, you must read the numbers to the right of the . as decimals.  Those are the "th" numbers.  1 is in the tenths place, 0 in the hundredths place and the 6 in the thousandths place.  

If you are simply reading out the digit names, without assigning their value, you might say "forty three POINT one hundred six"  or "forty three DOT one hundred six" or "forty three DECIMAL one hundred six".


This semester, the tuition fee increased to $5,871. If this represents an increase by 14%, what was the original fee?

Answers

use a calculator its easy

ty
This graph shows a portion of an even function.
Use the graph to complete the table of values.
6
f(x)
-1
4
-3
-5
-6
2
DONE
2
4.
6

Answers

Answers:

first box = 1second box = 1third box = 3fourth box = 3

Refer to the graph below.

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

Explanation:

If f(x) is an even function, then f(-x) = f(x) for all x in the domain.

What this means is that we have symmetry about the y axis. We can reflect that given curve over the y axis to generate the missing left side.

The graph shows that (1,1) is on the orange curve. It reflects over to (-1,1). This means 1 goes in the first box.

Use the rule [tex](x,y) \to (-x,y)[/tex] to apply a y axis reflection. We simply just change the sign of the x coordinate from positive to negative, while keeping the y coordinate the same.

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

We can also see that (3,1) is also on the orange curve. It reflects over to (-3, 1) using that rule mentioned earlier.

1 goes in the second box

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

The graph your teacher gave you shows that if we plugged in x = 5, then we get y = 3. In other words, the point (5,3) is on the orange graph.

It reflects over to (-5, 3) to show that x = -5 leads to the output y = 3

3 goes in the third box

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

Lastly, the point (6,3) reflects to (-6,3) when reflecting over the y axis.

3 goes in the fourth box.

See the graph below.

(-5/2) divide 13/7 x 9/7
Help :(

Answers

Answer:

-45/26

Step-by-step explanation:

(-5/2)÷(13/7)×(9/7)

(-5/2)×(7/13)×(9/7)

-45/26

Answered by Gauthmath must click thanks and mark brainliest

hawkville's population is 2500 people. next year the town clerk expects the population to grow by 1.2%, how many new residents will hawkville have next year?​

Answers

Answer:

30 new residents

Step-by-step explanation:

Find how many new residents they will have by finding 1.2% of the current population.

2500(0.012)

= 30

So, Hawkville will have 30 new residents

necesito la respuesta, entre a b c o d

Answers

Answer:

a)a^4 + 19a^2 -12ab - 3b^4 +6b...

Find the sum of the arithmetic series given ai = 45, an = 85, and n = 5.

Answers

Answer:

C. 325.

Step-by-step explanation:

The last term a5 = 85

a1 = 45

Sum of n terms = n/2 (a1 + l)

So here we have n = 5, a1 = 45 and the last term l = 85

= (5/2)(45 + 85)

= 5/2 * 130

= 325.

The required sum of the arithmetic series is 325.

Arithmetic series is defined as a sequence of numbers arranged in a particular pattern.

The sum of the nth term of an arithmetic sequence is expressed as:

[tex]S_n = \frac{n}{2}[a+l]\\[/tex] where:

n is the number of terms

a is the first term

l is the last term

Given the following

a = 45

n = 5

an = l = 85

Substitute the given values in the formula above:

[tex]S_5= \frac{5}{2}(45+85)\\ S_5=\frac{5}{2}(130)\\ S_5=5 \times 65\\S_5=325[/tex]

Hence the sum of the arithmetic series is 325

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The dotplot below displays the difference in scores for 18 games between a high school soccer team and its opponent.

A dotplot titled difference in Score. A number line going from negative 2 to 4 is labeled Team score minus opponent score. Negative 2, 1; negative 1, 2; 0, 2; 1, 3; 2, 6; 3, 3; 4, 1.

Which of the following is the best explanation for the dots at –1?

In one game, the team beat the opponent by 1 goal.
In two games, the team beat the opponent by 1 goal.
In one game, the team lost to the opponent by 1 goal.
In two games, the team lost to the opponent by 1 goal.

Answers

Answer: Choice D

In two games, the team lost to the opponent by 1 goal.

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

Explanation:

Negative scores indicate the team lost, and the absolute value of those values represent how much of a loss.

So a difference of -1 means the team lost by 1 point.

We have 2 dots over this value, so there are 2 occasions where the team lost  to the opponent by 1 goal.

An example would be that say the team scored 3 goals and the opponent scored 4 goals. So we have a differential of 3-4 = -1. The order is important because we would not say 4-3 = 1.

Answer:

d

Step-by-step explanation:

took the test

The graph represents two complex numbers, z1 and z2, as solid line vectors. Which points represent their complex conjugates?

Answers

Point A represents the complex conjugate z₁ and point L represents the complex conjugate of z₂ respectively

The reason the above values of the points of the complex conjugate are correct is as follows:

Definition:

The complex conjugate of a complex number is a complex number that

having equal magnitude in the real and imaginary part as the complex

number to which it is a conjugate, but the imaginary part of the complex

conjugate has an opposite sign to the original complex number

Graphically, the complex conjugate is a reflection of the

original complex number across the x-axis because the transformation for

a reflection of the point (x, y) across the x-axis is given as follows;

Preimage (x, y) reflected across the x-axis give the image (x, -y)

In a complex number, x + y·i. we have;

x = The real part

y = The imaginary part

The reflection of z₁(1, -2) across the x-axis gives the point A(1, 2), while the

reflection of z₂(6, -7) across the x-axis gives the point L(6, 7)

To summarize;

Point A(1, 2) is the reflection and therefore represents the complex

conjugate of z₁(1, -2) and point L(6, 7) is the reflection and therefore

represents the complex conjugate of z₂(6, -7)

Learn more about complex numbers here;

https://brainly.com/question/20365080

Let T:R²->R² be a linear transformation ,and assume that T (1,2)=(-1,1) and T(1,-1)=(2,3)


compute T(3,3) pls help me

Answers

Answer:

(-4,-1)

Step-by-step explanation:

We are given T(1,2)=(-1,1) and T(1,-1)=(2,3) and T is a linear transformation.

This implies for scalars a and b that

T(a(1,2)+b(-1,1))=aT(1,2)+bT(-1,1)

T((a,2a)+(-b,b))=a(-1,1)+b(2,3)

T((a-b,2a+b))=(-a,a)+(2b,3b)

T((a-b,2a+b))=(-a+2b,a+3b)

This means we should be able to solve the system below to find a and b for T(3,3):

a-b=3 and 2a+b=3

Add equations to eliminate b and solve for a:

3a=6

Divide 3 on both sides:

a=2

If a-b=3 and a=2, then b=-1.

Plug in a=2, b=-1:

T((a-b,2a+b))=(-a+2b,a+3b)

T((2--1,2×2+-1)=(-2+2×-1,2+3×-1)

T(3,3)=(-4,-1).

What is the largest value of x for which the following equation has a real solution (x,y)?

Answers

Answer:

x = 9/2

Step-by-step explanation:

x^2+7x+y^2+4y=191/4

Complete the square: (x+7/2)^2-(49/4)+(y+2)^2-4 = 191/4

Simplify: (x+7/2)^2+(y+2)^2=191/4+49/4+4

(x+7/2)^2 + (y+2)^2 = 64

(x+7/2)^2 + (y+2)^2 = (8)^2

Center of circle -> (-7/2, -2)

Radius -> 8

-7/2 + 8 = 9/2

x = 9/2

Find the equation of the line using the point-slope formula. Write the final equation using the slope-intercept form.
perpendicular to
7y = x − 4
and passes through the point
(−2, 1)

Answers

Answer:

[tex]y = -7x -13[/tex]

Step-by-step explanation:

Given

Perpendicular to

[tex]7y = x -4[/tex]

Passes through

[tex](-2,1)[/tex]

Required

The equation

First, we calculate the slope of:

[tex]7y = x -4[/tex]

Divide through by 7

[tex]y = \frac{1}{7}x - \frac{4}{7}[/tex]

A linear function is:

[tex]y=mx + c[/tex]

Where;

[tex]m \to slope[/tex]

So:

[tex]m = \frac{1}{7}[/tex]

For the perpendicular line; the slope is:

[tex]m_2 = -\frac{1}{m}[/tex]

So, we have:

[tex]m_2 = -\frac{1}{1/7}[/tex]

[tex]m_2 = -7[/tex]

The equation is:

[tex]y = m(x - x_1) + y_1[/tex]

So, we have:

[tex]y = -7(x - -2) + 1[/tex]

[tex]y = -7(x +2) + 1[/tex]

Open bracket

[tex]y = -7x -14 + 1[/tex]

[tex]y = -7x -13[/tex]

HELP! PLEASE!!
Simplify the expression.

Answers

9514 1404 393

Answer:

  D

Step-by-step explanation:

Regrouping the factors, we have ...

 

What is the domain of the function Y = In
-X+3
2
0x62
O x32
O X<3
O
X> 3
ASAP

Answers

Answer:

i think 1/58 is correct

i hope its help you

which is more 1 ton or 2,884 pounds?

Answers

1 ton i think! i hope this helps
2,884 pounds 1 ton is only 2,000 pounds

At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are often bundled in clothes that restrict their movement? Data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experiments between 1988 and 1991. Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of 4 feet within 1 minute. The resulting data were grouped by month of birth: January, May, and September:

Answers

Answer:

Babies learn to crawl between age of 6 to 10 months.

Step-by-step explanation:

It may take longer for babies to crawl in winter season since the climate restricts the babies movement due to extra clothes. The babies who are born in summer will learn crawling earlier than those who are born in winter season.

I really need the help please and thank you

Answers

BBBBB BBBBBBBBBBBBBBBBBBBBBBBBBBBB

Express 80 inches in standard notation using feet and inches.

Answers

80 inches in standard notation using feet and inches would be expressed as 6 ft 8 inches by converting inches into feet and inches.

The solution to the given problem is to use some standard conversion units that are:

1 foot = 12 inches1 inch = 0.8333 feet

Solution:

As mentioned above that one inch is equal to 0.8333 foot therefore

1 foot = 12 inches

then,

80 inches would be equal to

= [tex]\frac{80}{12}[/tex] ft

= [tex]\frac{20}{3}[/tex] ft

= 6ft 8 inches

= 6' 8"

Thus, 80 inches in standard notation using feet and inches would be expressed as 6 ft 8 inches by converting inches into feet and inches.

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Theta Company has the following variances at the end of February:

Material Price Variance $40 Unfavorable
Material Usage Variance $225 Unfavorable
Labor Rate Variance $110 Unfavorable
Labor Efficiency Variance $335 Unfavorable

What is the journal entry to be passed by Theta Company at the end of the month of February to close the variances?

Answers

Answer:

Debit Cost of Goods Sold $710

Credit Material Price Variance $40

Credit Material Usage Variance $225

Credit Labor Rate Variance $110

Credit Labor Efficiency Variance $335

Step-by-step explanation:

Preparation of the journal entry to be passed by Theta Company at the end of the month of February to close the variances

Debit Cost of Goods Sold $710

($40+$225+$110+$335)

Credit Material Price Variance $40

Credit Material Usage Variance $225

Credit Labor Rate Variance $110

Credit Labor Efficiency Variance $335

(To close the variances)

1.2 Write the ratio 1:2 in the simplest form.​

Answers

1:2 is the simplest form
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