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]
1 year 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]1 year 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
1) Omar has scored 85, 71, and 77 on the first three exams in his math class. If the standard 70,80,90 scale is used for grades
Rus_ich [418]

Answer:

a. 47

b. 87

c. 127

Step-by-step explanation:

Assume a total of 4 exams ( first 3 plus a final)

Let final score be X,

Hence,  average score = (85 + 71 + 77 + x) / 4 = (233 + x) / 4

a) to get a C, the average score must be 70

70 = (233 + x) / 4

(233 + x) = 70 (4) = 280

x = 280 - 233 = 47 (Ans)

b) to get a B, the average score must be 80

80 = (233 + x) / 4

(233 + x) = 80 (4) = 320

x = 320 - 233 = 87 (Ans)

c) to get a A, the average score must be 90

90 = (233 + x) / 4

(233 + x) = 90 (4) = 360

x = 360 - 233 =  127 (Ans)

6 0
2 years ago
For which sample size (n) and sample proportion (p) can a normal curve be
Nonamiya [84]

Answer:

Option c.

Step-by-step explanation:

Using the normal curve to approximate a sampling distribution:

For a sample size n and a proportion n, the normal curve can be used if:

np \geq 10 and n(1-p) \geq 10

Option a:

np = 35*0.8 = 28 > 10

n(1-p) = 35*0.2 = 7 < 10

So option a cannot be used.

Option b:

np = 65*0.9 = 58.5 > 10

n(1-p) = 65*0.1 = 6.5 < 10

So option b cannot be used.

Option c:

np = 65*0.8 = 52 > 10

n(1-p) = 65*0.2 = 13 > 10

So option c can be used, and is the answer

Option d:

np = 35*0.9 = 31.5 > 10

n(1-p) = 35*0.1 = 3.5 < 10

So option d cannot be used.

The answer is given by option c.

7 0
3 years ago
Select the possible dimensions of a rectangular prism with volume of 48 in.
xenn [34]

Answer:

6 in * 4 in * 2 in

Step-by-step explanation:

Given the following data;

Volume of rectangular prism = 48 in³

To find its possible dimensions;

Volume of rectangular prism = length * breadth * height

48 = length * breadth * height

From the given options, option B is most likely to be its dimensions.

Where;

Length = 6 in

Breadth = 4 in

Height = 2 in

Substituting into the formula, we have;

48 in = 6 * 4 * 2

48 in = 48 in

8 0
3 years ago
3x +12 =90 what is x
castortr0y [4]

Answer:

x=26

Step-by-step explanation:

3x +12 =90

subtract 12 from each side

3x=78

divide 3 from each side

x=26

3 0
2 years ago
Read 2 more answers
What is the exact volume of a sphere with a diameter of 18 cm?<br><br><br> <img src="https://tex.z-dn.net/?f=%20%5Cpi%20" id="Te
Vesna [10]
Sphere Volume =  <span>( <span>π <span>•diameter^3) / 6
</span></span></span>
Sphere Volume =  3.14159 * 18^3 / 6

Sphere Volume =  3.14159 * <span> <span> <span> 5,832 </span> / 6

</span></span>Sphere Volume =  3.14159 * 972

Sphere Volume =  <span> <span> <span> 3,053.63 </span> </span> </span>
6 0
3 years ago
Other questions:
  • In the American Heart Association journal Hypertension, researchers report that individuals who practice Transcendental Meditati
    8·1 answer
  • Francis is making cookies. The recipe for chocolate chip cookies calls for 2 2/3 cups of flour, the recipe for peanut butter cal
    10·1 answer
  • Write a proportion to solve this
    12·1 answer
  • What is 1342.5414 rounded to the nearest thousandth?
    9·1 answer
  • Xander rolls two 6-sided number cubes. What is the theoretical probability of rolling an even number on the first cube and a num
    9·1 answer
  • Help a homie out please
    8·2 answers
  • 2(x + 2) + 1= 5(-x + 8)
    6·1 answer
  • Respuesta para 8×-2=-9+7×
    11·1 answer
  • A playground slide has a price of $770. With sales tax, it will cost $847. What is the sales tax percentage?
    11·1 answer
  • Write the equation of the line in standard form passing through (2,-4) with a slope of -7​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!