MATHEMATICS MIDDLE SCHOOL

if (ax+2)(bx+7) = 15xsquared + cx +14 for all values of x, and a+b =8, what are the two possible values for c?

Answers

Answer 1

Answer:

The two possible values for c are 31 and 41

Step-by-step explanation:

Given Expression:

$(a x+2)(b x+7)=15 x^(2)+c x+14$

a + b = 8

To expand,

Multiply a x with (b x + 7) = $a b x^(2)+7 a x$

Multiply 2 with (b x + 7) = 2 b x +14

Now, combining the above, we get

$a b x^(2)+7 a x+2 b x+14=15 x^(2)+c x+14$

$a b x^(2)+x(7 a+2 b)+14=a b x^(2)$

When comparing both sides, we get

a b = 15, 7 a + 2 b = c

$a=(15)/(b) \text { or } b=(a)/(15)$

Now, substitute above value in a + b = 8. So,

$(15)/(b)+b=8$

$15+b^(2)=8 b$

$b^(2)-8 b+15=0$

Factorising above, we get the equation as

$b^(2)-3 b-5 b+15=0$

(b - 3) (b - 5) = 0

b = 3 and 5

If b = 3, then

$a=(15)/(b)=(15)/(3)=5$

If b = 5, then

$a=(15)/(5)=3$

If a = 3, b = 5

c =7 a + 2 b = 7 (3) + 2 (5) = 21 + 10 = 31

If a = 5, b = 3

c =7 (5) +2 (3) = 35 + 6 = 41

Therefore, the values of ‘c’ are 31 and 41.

Related Questions

Use the magic penny parable to determine how much money you would have after 8 days.
9x–2(x+8) = 5x–11(2–x)Find out X
Forty is what percent of 125?A. 32% B. 65% C. 100% D. 313%
My number has 8 tens the digit in the ones place is greater than the digit in the tens place
Janet has 17 quarters and $13 in bills. How much total money does she have?

Harvey bought a. Frame in which he put his family picture in what is the area of the frame not covered by the picture

Answers

Answer:

Area of the frame not covered with photo is equal to 129 square inches

Step-by-step explanation:

Given: Image of a frame

To find: Area of the frame not covered by the picture

Solution:

Area of rectangle = length of the rectangle × breadth of rectangle

Area of the frame = length of frame × breadth of frame = 23 × 15 = 345 square inches

Area of the frame covered with photo = 18 × 12 = 216 square inches

Area of the frame not covered with photo = Area of the frame - Area of the frame covered with photo = 345 - 216 = 129 square inches

Can someone explain INTERQUARTILE RANGE for me, and please give an example. Thank you!

Answers

The IQR describes the middle 50% of values when ordered from lowest to highest. To find the interquartile range (IQR), first find the median (middle value) of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.

Madison is making party favors.She wants to make enough favors so each guest gets the same number of party favors.She knows there will be 6 or 8 at the party. What is the least number of party favors Madison should make?

Answers

The correct answer is: 24

Explanation:
To find the least number of party favors, we have to consider the number of guests.

In this case, there are two possibilities—6 or 8.

For 6: 6, 12, 18, 24 (Add 6 to each number)
For 8: 8, 16, 24 (Add 8 to each number)

Now in both series, the least number (that is in common) is 24. Hence, Madison should make at least 24 party favors.

A:24
6:6,12,18,24<--
8:8,16,24<--

What is the surface area of 10cm 15cm and 10

Answers

The surface area of 10cm, 15cm, and 10cm is found by splitting the dimensions to many different equations.
1st equation: 10 times 15
2nd equation: 10 times 10
3rd equation: 10 times 10
4th equation: 10 times 15
5th equations: 10 times 15
6th equation: 10 times 15
You would then add all the solutions up to get the final solution.
The answer is...
800

popcorn kernels are sold in one-pound bags.If four ounces of kernels make two quarts if popped popcorn,how many bags of kernels will i need to make ten gallons of popped popcorn?

Answers

popcorn kernels in 1 lb bags.
4 ounces of kernels make two quartz of popped popcorn

Number of bag of kernels to fill ten gallons of popped popcorn.

1 pound = 16 ounces
16 ounces / 4 ounces = 4
4 * 2 quarts = 8 quarts
8 quarts / 4 quarts per gallon = 2 gallons

1 pound bag of popcorn kernel produces 2 gallons worth of popped popcorn.

To make 10 gallons worth of popped popcorn, you need 5 1-pound bags of popcorn kernels.

What is 2/9 as a decimal ?

Answers

0.22222 so on

.22222 so on

this ur answer

to find the decimal of 2/9 , u have to do 2 divided by 9 which equals 0.22222222222

Other Questions

What is 65% of 60??? PLZZZZZZZZZZ HELP thanks! :)

Help me please with this problem.

Someone drove 20 miles in 24 minutes at this rate how many miles did they drive in 6 minutes

If m∠ABC = 72°, what is m∠DAB?A) 72° B) 108° C) 144° D) 216°