1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
FrozenT [24]
2 years ago
15

The coefficient of x³ in the expansion of (3 +bx )⁵ is −720. Find the value of the constant b.​

Mathematics
1 answer:
Molodets [167]2 years ago
3 0

Answer:

b = -2

Step-by-step explanation:

We need to use <u>the binomial theorem</u>, to expand

the expression (3 + bx )⁵ :

(3 + bx )⁵ = 3⁵ + 5(3)⁴(bx)¹ + 10(3)³(bx)² + 10(3)²(bx)³ + 5(3)¹(bx)⁴ + (bx)⁵

             

               = 243 + 5×81×(bx)¹ + 10×27×(bx)² + 10×9×(bx)³ + 5×3×(bx)⁴ + (bx)⁵

               = 243 + 405(bx)¹ + 270(bx)² + 90(bx)³ + 15(bx)⁴ + (bx)⁵

               = 243 + (405b)x + (270b²)x² + (90b³)x³ + (15b⁴)x⁴ + (bx)⁵

Then

(3 + bx )⁵ = 243 + (405b)x + (270b²)x² + (90b³)x³ + (15b⁴)x⁴ + (bx)⁵

Then

The coefficient of x³ in the expansion of (3 + bx )⁵ is 90b³

<u>Comparing the coefficients</u> :

90b³ = -720

Then

b³ = (-720) ÷ 90 = -8

Then

b³ = -8

Then

b = -2

You might be interested in
108 rounded to the nearest tenth
Artemon [7]

Answer:

110

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Given that (6,-8) is on the graph of f(x), find the
Volgvan

Answer:

I don't know if you have any questions or concerns please visit the plug-in settings to determine how attachments are handled the situation and I will be in the blanks and I will mark the blanks and I will mark as the brillianest plzzzzzzzzzzzzzzzzzzzz seetq you so much for your time and consideration and I will mark as the brillianest plzzzzzzzzzzzzzzzzzzzz seetq you so much for your time and consideration and I will mark as the brillianest plzzzzzzzzzzzzzzzzzzzz seetq you so much for your time and consideration and I will mark as the brillianest plzzzzzzzzzzzzzzzzzzzz seetq you so much

5 0
3 years ago
I need help: number 19
Gwar [14]

Answer:

y=x+2

Step-by-step explanation:

the standard form is y=mx+b where m is the slope and b is the y intercept

TO FIND THE SLOPE: we take the x and y intercepts as a fraction. in this case the line touches the y axis (vertical) at point/value 2 and the x axis at point 2 as well. This means the slope is 2/2x which can be simplified to 1x or just x.

TO FIND THE Y INTERCEPT: we find where the line touches the y axis at point 2.

the slope is plugged into the m of the equation and the y intercept is plugged into the b of the equation.

4 0
2 years ago
WILL MARK BRAINLIEST ASAP PLEASE
ohaa [14]

Answer:

b

Step-by-step explanation:

90×(2)

= 180

each mile is equal to 90 calories

therefore 2 miles is equal to 180

8 0
2 years ago
9. A box of cereal is packaged and sold at a local
emmasim [6.3K]

Answer:

288 Cubic Inches

Step-by-step explanation:

Assuming the cereal takes up 80% of the total volume of the box, you would take 80% of the total volume.

First, do Base x Width x Height for the volume of the box.

10 inches x 3 inches x 1 foot      (1 foot is 12 inches)

10 x 3 x 12 = 360

Now, take 80% of 360 cubic inches.

80% is 0.8 times a number

0.8 x 360 = 288

288 Cubic Inches

8 0
2 years ago
Other questions:
  • How to simplify using the exponent laws
    6·1 answer
  • What is 7.393 rounded to the nearest hundreth
    13·2 answers
  • A rectange has a width of 9 units and a length of 40 unit. what is the length in diagonal
    7·1 answer
  • Which is the factored form of 2x(4x + 3) - (4x + 3)?
    14·1 answer
  • Can someone help me with this problem!
    11·1 answer
  • Grade 10 math help please show work (30 points) I will mark brainlist too
    5·1 answer
  • Samantha invested $670 in an account paying an interest rate of 5.5% compounded daily. Assuming no deposits or withdrawals are m
    6·1 answer
  • Simplify each algebraic expression 5a+5b-4(a+b)
    10·2 answers
  • What is. 6(x-1)+3=3x-2(1-x)<br><br> I give Brainliest!
    7·1 answer
  • F(x) = 3x² - 11<br> Find f(10)
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!