An x-method chart shows the product a c at the top of x and b at the bottom of x. Above the chart is the expression a x squared + b x + c. Consider the trinomial 6x2 + 13x + 6. The value of ac is . The value of b is . The two numbers that have a product of ac and a sum of b are 4 and .

Answers

Answer 1

Answer:

1. ac = 36

2. b = 13

3. 4 and 9

Step-by-step explanation:

Given

6x² + 13x + 6

Required

Fill in the gaps

Solving (1): The value of AC

The general form of an equation is:

ax² + bx + c

By comparison:

a = 6

b = 13

c = 6

So,

ac = a * c

ac = 6 * 6

ac = 36

Solving (2): The value of b

In (1) above, we showed that

b = 13

Solving (3): Two numbers that satisfy product ac and sum b

We have that.

ac = 36

If one of the numbers is 4, then the other number is

Other number = 36/4

Other number = 9

Alternatively, we have that.

b = 13

If one of the numbers is 4, then the other number would be:

Other number = 13 - 4

Other number = 9

Answer 2

Answer:

ac = 36

b = 13

The two numbers that have a product of ac and a sum of b are 4 and 9

Step-by-step explanation:


Related Questions

Skittles come in many different colors in my bag of 40 Skittles I had 12 green ones what percent of the bag was Green?​

Answers

Answer:

4.8

Step-by-step explanation:

Plz Help The function shown models the total number of insects in a colony x months after a small number of the insects are brought into a region.

What was the total number of insects in the colony when they were first brought into the region ? Enter your answer in the box​

Answers

Answer:

I think it's 25? If I can edit I'll come back with answer..(if it's not 25.)

Step-by-step explanation:

Savannah and Reagan both work in a grocery store. They each stocked the same number of shelves last Saturday, but it took Reagan less time. They've been told that they'll spend their entire 4-hour shifts next Saturday stocking shelves. If their average speeds are consistent, who will likely stock more shelves next Saturday?

HELP!

Answers

Answer:

Reagan

Explanation:

Since Reagan is able to stock the same number of shelves as Savannah while spending less time to do so, it means that Reagan is able to stock shelves faster than Savannah, thus Reagan is able to stock more shelves than Savannah given that their average speeds are constant and that they both work under 4-hour shifts.

Hope this helps :)

A bag of coins contains only quarters and dimes.
• The number of dimes in the bag can be represented by x.
• The number of quarters is 6 more than twice the number of dimes.
• There are a total of 276 coins in the bag.
What is x, the number of dimes in the bag?

helpp pls​

Answers

Answer:

Number of dimes in the bag = 90

Number of quarters in the bag = 186

Step-by-step explanation:

Let

x = Number of dimes in the bag

y = Number of quarters in the bag

= 2x + 6

Total = 276

276 = x + 2x + 6

276 = 3x + 6

276 - 6 = 3x

270 = 3x

x = 270/3

= 90

x = 90

Number of dimes in the bag = 90

Number of quarters in the bag = 2x + 6

= 2(90) + 6

=180 + 6

= 186

Total = Number of dimes in the bag + Number of quarters

= 90 + 186

= 276

Nicholas is buying shirts for his baseball team. He will pay $9.50 for each shirt plus a one-time fee of $22.50 for the design. Which equation can be used to find y, the total cost to buy x shirts?
(I mark Brainlist)

A. y = 9.5x + 22.5
B. y =22.5 + 9.5
C. y = 9.5x - 22.5
D. y = 22.5x - 9.5

Answers

Answer:

C or A

Step-by-step explanation:

I think that it is most likely C but you could try A to

An ammonia and water mixture fills a five-gallon container. Eighty percent of the mixture is ammonia, but some of the mixture will be drained and replaced with pure water. If a five-gallon mixture of fifty percent ammonia is desired, how many quarts of the mixture need to be drained before the water is added, given that 4 quarts equals a gallon

Answers

Answer:

The volume of the 80% ammonia that is to be drained before water is added is 7.5 quartz

Step-by-step explanation:

The volume of the ammonia and water mixture = 5 gallons

The percentage of ammonia in the mixture = 80%

The volume of ammonia desired = 5 gallons

The percentage concentration of ammonia desired = 50%

The diluting solution = Pure water

The measure of 4 quarts = 1 gallon

Therefore, we have, by equivalence solutions;

80% × x gallon = 50% × 5 gallons

x gallon = 50% × 5 gallons/(80%) = 3.125 gallons

x = 3.125 gallons

The volume of the 80% ammonia that is to be drained = 5 gallons - 3.125 gallons = 1.875 gallons

4 quarts = 1 gallon

1 gallon = 4 quarts

∴ 1.875 gallons = 4 × 1.875 quartz = 7.5 quartz

The volume of the 80% ammonia that is to be drained before water is added = 7.5 quartz

Answer:

7.5

Step-by-step explanation:

A shoe store is having a clearance sale on their summer shoes. All summer shoes are marked 55% off. A sign states you can take an additional 10% off the clearance sale prices. Kelly is deciding between two pairs of sandals shown in the table.
Shoes Original Price
Blue Sandals $75
Tan Sandals $68

If she buys the blue sandals, what is the final price Kelly will pay? Round to the nearest cent.

Answers

Answer:

$30.38

Step-by-step explanation:

Final Price = Original Price - Discount

Final Price = 75 - 41.25

Final Price = $33.75

Then its the additional 10%

So now you make your original cost $33.75 to make it easier so

Final Price = Original Price - Discount

Final Price = 33.75 - 3.375

Final Price = $30.38

Final Answer: $30.38

The final price Kelly will pay round to the nearest cent is $30 38¢

What is percent?

In mathematics, a percent is a number or ratio expressed as a fraction of 100. It is often denoted using percentage sign "%".

Now it is given that,

Discount = 55%

Additional discount = 10%

Original Price of Blue Sandals = $75

Original Price of Tan Sandals =  $68

Since Kelly bought blue sandels,

So, discount on Blue Sandals = 55% of $75

discount on Blue Sandals = 0.55 * $75 = $41.25

So, Cost of Blue Sandals = $75 - $41.25

⇒ Cost of Blue Sandals = $33.75

Now there is additional discount of 10%

Additional discount = 10% of $33.75

Additional discount = 0.10% * $33.75

Additional discount = $3.375

Thus, Final Cost of Blue Sandals = $33.75 - $3.375

⇒ Final Cost of Blue Sandals = $30.375

Round to the nearest cent final cost of Blue Sandals = $30 38¢

Thus, the final price Kelly will pay round to the nearest cent is $30 38¢

To learn more about Percentage visit :

brainly.com/question/24304697

#SPJ2

Help me find the area please!

Answers

Answer:

787.5

Step-by-step explanation:

Givens

The bottom part of the figure is a trapezoid. Solve it first

a = 15 cm

b = 34 cm

h = 19 cm

Formula

Area = 1/2 (a + b)*h

Solution Trapezoid

area = 1/2 (15 + 34)*19

Area = 1/2 * 49 * 19

Area = 465.5

Remark

The top half of the figure is a parallelogram.

Formula

Area = base * height

Givens

base = 23

height = 14

Solution

Area = 23 * 14

Area = 322

Total Area

Total Area = 322 + 465.5

Total Area = 787.5

the green shape is a dilation of the black shape.what is the scale factor of the dilation? ​

Answers

Answer:  5

Step-by-step explanation:

Scale factor = [tex]\dfrac{\text{ side length of image}}{\text{Side-length of original figure}}[/tex]

Given: Black triangle ( original) having perpendicular with length 4 units.  [2 blocks above and 2 boxes below the x-axis ]

Green triangle ( image) having corresponding side as 20 units  [10 blocks above and 10 boxes below the x-axis ].

Scale factor of dilation = [tex]\dfrac{20}{4}=5[/tex]

Hence, the scale factor of the dilation = 5

Neeeeeed help?!?!!!!!!!

Answers

Step-by-step explanation:

number of minutes I guess

y + 12.5 = 21.7, y =

Answers

Answer:

y = 9.2

Step-by-step explanation:

21.7 - 12.5 = 9.2

Answer:

y = 9.2

Step-by-step explanation:

what is 7.0893 as a decimal but in word form.​

Answers

Answer:

seven and eight hundred ninety-three ten-thousandths

Step-by-step explanation:

Seven and eight hundred ninety-three ten- thousand or seven point zero eight nine three

3r²-6-3r=0 i have to use quadratic formula but i dont get how to imput it

Answers

Answer:

r = 2

r = -1

Step-by-step explanation:

So first, we need to get this is order of: ax^2 + bx + c

3r^2 - 6 - 3r

3^2 - 3r - 6

the formula is: -b ± √b^2 -4ac/2a

"ax^2 + bx + c" = "3^2 - 3r - 6"

a = 3

b = -3

c = -6

-b ± √b^2 -4ac/2a

-(-3) ± √(-3)^2 -4(3)(-6)/2(3)

3 ± √9 + (-12)(-6)/6

3 ± √9 + (72)/6

3 ± √9 + 72/6

3 ± √81/6

3 ± 9/6

3 - 9/6

-6/6

-1 = r

3 + 9/6

12/6

2 = r

Formula down below --

                                      |

                                     V

Peter is calculating the interest earned on a
deposit of $275 in an account that earns 8%
simple interest after 12 years.

Answers

Answer:

a) He substituted 0.8 instead of 0.08.

b) $264

Step-by-step explanation:

The full question is: a. What did Peter do incorrectly? b. What is the correct amount of interest?

Using the equation [tex]I=prt[/tex], we can substitute the given values.I = 275 x 0.08 x 12I = 264

At Samantha's Hats, there are 12 baseball caps and 4 other hats. What percentage of the hats are baseball caps?

Answers

75% are baseball caps

how to find radius of the base examples​

Answers

Answer:

r=[tex]\frac{c}{2\pi }[/tex]

Step-by-step explanation:

what is 3/5 divided by 1/2 as a reduced fraction

Answers

6/5 or 1 1/5
Hope this helps

HELP WILL MARK BRAINLIEST

Answers

Answer:

The answer is D: y = -2x + 6

Step-by-step explanation:

the y-intercept is 6, and the slope goes down 2 and right 1. -2/1 is the same as -2.

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

9. In the diagram below of rectangle RSTU, diagonals RT and SU intersect
at O. If RT = 6x + 4 and SO = 7x - 6, what is the length of US?

Answers

Your Answer should be 16

Hence, option (2) is correct i.e., the length of the [tex]US[/tex] is [tex]2cm[/tex].

What is the diagonal?

A polygon is defined as a flat or plane, two-dimensional closed shape bounded with straight sides.

A diagonal is a line segment connecting the opposite vertices (or corners) of a polygon. In other words, a diagonal is a line segment connecting two non-adjacent vertices of a polygon.

Here given that,

In the diagram below of rectangle [tex]RSTU[/tex], diagonals [tex]RT[/tex] and [tex]SU[/tex] intersect

at [tex]O[/tex]. If [tex]RT = 6x + 4[/tex] and [tex]SO = 7x - 6[/tex],

[tex]US=SO(2)\\\\US=7x-6(2)\\\\US=14x-12[/tex]

So,

[tex]6x+4=14x-12\\\\4+12=14x-6x\\\\16=8x\\\\x=\frac{!6}{8}\\\\x=2[/tex]

Hence, option (2) is correct i.e., the length of the [tex]US[/tex] is [tex]2cm[/tex].

To know more about the diagonals

https://brainly.com/question/28592115

#SPJ2

Find the slope of the line that passes through (8,6) and (4,15)

Answers

Is the line positive or negative

PLEASE HELP FAST!! WILL MARK AS BRAINLIEST IF GIVEN GOID ANSWER....​

Answers

Answer:

x = 36

y = 37.95

Step-by-step explanation:

By geometric mean property:

[tex] {12}^{2} = 4 \times x \\ \\ 144 = 4 \times x \\ \\ x = \frac{144}{4} \\ \\ x = 36 \\ \\ [/tex]

By Pythagoras Theorem:

[tex] {y}^{2} = {12}^{2} + {x}^{2} \\ \\ {y}^{2} = {12}^{2} + {36}^{2} \\ \\ {y}^{2} = 144 + 1296 \\ \\ {y}^{2} = 1440 \\ \\ y = \sqrt{1440} \\ \\ y = 37.95[/tex]

please help me answer this ASAP if u view it then u'll see the question properly
[tex] \frac{1 + \sqrt{3} }{ \sqrt{12} } [/tex]
i will give brainliest answer if it the correct answers ​

Answers

Answer:

1/6 sqrt(3) + 1/2

Step-by-step explanation:

(1 + sqrt(3))

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

sqrt(12)

Multiply the top and bottom by sqrt(12)

(1 + sqrt(3)) * sqrt(12)

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

sqrt(12)*sqrt(12)

sqrt(12) + sqrt(3) * sqrt(12)

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

12

Simplify

sqrt(4)sqrt(3) + 6

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

12

2 sqrt(3) +6

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

12

1/6 sqrt(3) + 1/2

a car dealer so 32 cars their first month The next month they sell 54 cars What is the percentage of change in the number of sold cars​

Answers

Answer:

68.75%

Step-by-step explanation:

First you do 54 - 32 to get 22.

Then you divide 22 by 32 to get the decimal 0.6875

Finally, you multiply 0.6875 by 100 to get 68.75% :D

Answer:

68.73% more cars were sold

Step-by-step explanation:

from 32 cars that represented 100% went to 54 so is a diference of 54-32=22

Now what percentage  of 32 is 22?

32 is 100%

22 is x%

x=(22*100)/32=2200/32=68.73%

plz help me asap i need help plz i will mark you as brainlist

Answers

Answer:

the third one

There are 82 chairs at a birthday party. The chairs need to be lined up in equal-sized rows. How many possible ways can the chairs be lined up

Answers

Answer:

2 rows of 41

Step-by-step explanation:

i had the same question

The number of possible ways can the chairs be lined up is 2 rows of 41.

Given that,

There are 82 chairs at a birthday party. The chairs need to be lined up in equal-sized rows.

Based on the above information, the calculation is as follows:

[tex]= 2 \times 41[/tex]

= 82 chairs

Here 2 denotes the rows.

Therefore we can conclude that the number of possible ways can the chairs be lined up is 2 rows of 41.

Learn more: brainly.com/question/13549064

Can someone help with this I’ll mark u as brainlist

Answers

Answer:i don’t really k ow but i need points to ask questions

Step-by-step explanation:

how many times does 35 go into 78?​

Answers

Answer:

It goes in 2 times

Step-by-step explanation:

Can i have branliest, so i can go up a rank?

Answer:

35 goes into 78 two whole times but, it goes into it 2.22857143 times, or rounded to 2.23 times. the answer you put down depends on the directions.

Please help me on this

Answers

Answer:

PAGE 1

8.) d

9.) b

PAGE 2

6.) b

7.) d

PAGE 3

4.) c

5.) a

PAGE 4

1.) c

2.) c

3.) a

PAGE 5

10.) b

11.) d

Step-by-step explanation:

PAGE 1

8.) x - 20 + x + 10 = 180 (collect like terms)

2x - 10 = 180 (add 10 on both sides)

2x = 190 (divide by 2 on both sides)

x = 95

9.) 2y + y = 180 (collect like terms)

3y = 180 (divide by 3 on both sides)

y = 60

x = y ----> x = 60

PAGE 2

6.)  16x - 6 = 90 (add 6 on both sides)

16x = 96 (divide by 16 on both sides)

x = 6

7.) 5x + 30 = 7x (subtract 5x on both sides)

30 = 2x (divide by 2 on both sides)

15 = x

PAGE 3

4.) <8 and <16 are corresponding angles

5.) 180 - 130 = 50

PAGE 4

1.)  HD and GE are skew lines

2.) AC, EG, and BD are parallel to FH

3.) EF, GH, and BF are perpendicular to FH

PAGE 5

10.) | and || only are the only ones correct

11.) l || m, by the Converse of the Consecutive Interior Angles Theorem.

b/c the two angles equal 180 together and one angle is on line l and the other is on line m. This shows they're parallel.

Hope this helps ya!!


In this question, all lengths are in centimetres.
Given
AB: AC = 1:2
AB= 3x-4
AC= 2x + 12
show that
AC: BC = 2:3
BС= 7X-2

Answers

Answer:

Step-by-step explanation:

AB/AC =1/2

(3x-4)/(2x+12)=1/2

2(3x-4) = 1(2x+12)

6x-8=2x+12

4x=20

X=5

AC/BC =3x-4/7x-2=22/33=2/3

AB/AC=3x-4/7x-2=22/33=2/3

AB/AC=3x-4/2x+12

6x-8=2x+12

You would get 4/5 still trying to work out the last mark

Step-by-step explanation:

First find x:

AB:AC=1:2

2(3x-4)=2x+12

6x-8=2x+12

4x-8=12

4x=20

x=5

Substitute:

AC=2x+12

=(2x5)+12

=10+12

=22

BC=7x-2

=(7x5)-2

=35-2

=33

22/33=2/3

Therefore AC:BC = 2:3

If 7 pounds cost $5.46, find the cost of 3 pounds. ​

Answers

Answer:

$2.19

Step-by-step explanation:

7 divided by 3 is 2.5

5.46 divided by 2.5 is 2.184

round it and get 2.19

Other Questions
Which of the following is an example of a total war practice carried out during World War ? O A. Submarine warfare O B. The use of bombs Rationing D. Extermination camps Compr 18 cuadernos, 24 carpetas y 17 lapiceras. El precio de las carpetas excede al de los cuadernos en un 40%, mientras que el precio de las lapiceras es el 20% del precio de los cuadernos. Si el importe de la compra fue de $11.825, calcular el precio unitario de cada artculo Two of your friends go bowling. One friend rents a pair of bowling shoes for $3 and bowls 3 games. The other friend brings his own bowling shoes, bowls 4 games and buys a soda for $0.50. Both friends spend the same amount of money. Show how you can write and solve an equation to find the cost of one game. 1. How does risk play a role in innovation?2. Imagine trying to develop a new product or invention. Which of these risks would be the hardest for you to take?a. Getting criticized for trying something new and differentb. Gathering the funds and materials to start your productc. Losing all your profits and savings if your product flopsd. Being remembered as a failure Why did people move to the frontier? A.They were running away. B.They were poor. C.The land had been settled. D.They wanted more freedoms. What is the value of f(-1)?O f(-1) = -3Of(-1) = -1O f(- 1) = 0Of(-1) = 6 6. Which graph best represents the solution set of y>3 x-4? Energy conversion within a plant cell would be limited most severely by removal of the cell's - A mitochondria B chloroplasts C ribosomes D endoplasmic reticulum By what percent is 16 greater than 12. True or False. Exponential Functions will create a straight line on a graph In 1992, Jason bought a gallon of gas for $1.15. Yesterday, he bought a gallon of gas for $2.12. What is the percentage increase of the price of a gallon of gas from 1992 to yesterday? If necessary, round to the nearest tenth of a percent. A. 84.3% B. 45.8% C. 54.2% D. 15.7% Youve learned to identify whether a function is even or odd both graphically and algebraically. How does the notation for reflections over the x-axis and over the y-axis relate to the notation for even and odd functions? Remember that if f(-x) = f(x), a function is even, and if f(-x) = -f(x), then the function is odd. what is the function of brushes in D.C motor BRAINLIESTTTTTTTTTTTT DUEEEEEEWhich European country shown in the diagram has the LEAST free economy?Group of answer choicesA. CubaB. RussiaC. GermanyD. United Kingdom PLZ HELP MEEEEEEE,;-; Again||||||||||||||||||||||||||| jason sees that 2 out of every 5 cars that passes by his house has the windshield wipers on. What is the probability that that of the next 4 cars that pass his house, 2 will have their windshield wipers on? I need help please I am having hard time doing this please help thanks in advance also best answer get's brainlest Cotton grows well in sandy soils. True or false?