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navik [9.2K]
3 years ago
10

Show that (x+1)(x+3)(x+5) can be written in the form ax3+bx2+cx+d where a b c and d are all positive intergers

Mathematics
1 answer:
Sophie [7]3 years ago
7 0

Answer:

Step-by-step explanation:

(x+1)(x+3)(x+5), multiply first two parenthesis

(x² +3x +x +3)(x+5), combine like terms

(x² +4x +3) (x+5), multiply the parenthesis

(x³ +5x² +4x² +20x +3x +15), combine like terms

x³ +9x² +23x +15 is in the form ax³ +bx² +cx +d

a=1, b=9, c=23, d=15 are all positive integers

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What is the product of 2.5 × 10−15 and 3.9 × 1026? 6.4 × 101 9.75 × 1011 6.4 × 1041 9.75 × 1041
Doss [256]

(2.5*10^{-15})(3.9*10^{26}). We begin by multiplying the "regular" numbers first. 2.5 × 3.9 = 9.75. That's good; it's already in the proper format for scientific notation. Now we multiply the bases of 10 with their exponents. Since the bases are both 10, they are like. When we multiply like bases, we add their exponents. 10^{-15+26}=10^{11}. Our answer then is 9.75*10^{11}. There you go!

5 0
3 years ago
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Which expression represents the fourth term in the binomial expansion of (e + 2f)10?
yan [13]

The fourth term of the binomial expansion (e+2f)^{10} can be calculated using the formula for (i+1)-th term of the binomial expansion:

T_{i+1}=C_{10}^i\cdot e^{10-i}\cdot (2f)^i.

In order to find term T_4, determine that

i+1=4\Rightarrow i=3.

Now

T_4=C_{10}^3\cdot e^{10-3}\cdot (2f)^3=C_{10}^3\cdot e^7\cdot (2f)^3.

Answer: correct choice is A

6 0
3 years ago
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Darius is putting tiles on the roof of his house. After working for 3 1/3 hours, he has completed 4/5 of the roof. Can Darius pu
tangare [24]

Answer:

No.

Step-by-step explanation:

It is given that Darius is putting tiles on the roof of his house.

Darius had completed = $\frac{4}{5}$ th of the work

He takes time = $3 \frac{1}{3}$ hours to complete $\frac{4}{5}$ th of the work

The remaining work = $1 -\frac{4}{5}$

                                 $=\frac{5-4}{5}$

                                 $=\frac{1}{5}$

∴  Darius completes $\frac{4}{5}$ th of the work in = $\frac{10}{3}$ hours

                           So, $\frac{1}{5}$ th of the work in = $\frac{10}{3} \times \frac{5}{4} \times \frac{1}{5}$ hours

                                                                 $=\frac{10}{12}$ hours

Therefore total time taken to complete the work $=\frac{10}{3}+\frac{10}{12}$ hours

                                                                                  $=\frac{40+10}{12}$ hours

                                                                                  $=\frac{50}{12}$ hours

                                                                                  $=4\frac{2}{12}$ hours

                                                                                  $=4\frac{1}{6}$ hours

Thus, Darius continues to work at the same rate will not be able to complete the work in 4 hours.  

                                                                                 

8 0
3 years ago
8thgrade 9^2 plus 3^2
eduard

Answer:

90

Step-by-step explanation:

9^2 = 81 and 3^2 = 9

81 + 9 = 90

5 0
3 years ago
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A measuring wheel is used to calculate the length of a path. The diameter of the wheel is 8 inches. If the wheel rotates 15 time
Oksi-84 [34.3K]
To fint the length first one must find circumference to do that we use the formula D*Pi (diameter times Pi. Diameter = 8 Pi is the constant of 3.1415
so. 8*3.1415 = appox 25.1327. cow that we have  circumference we should multiply by the amount of times the wheel rotates (15)
so. 15*251327 = appox 376.9911in now convert to feet. 12 in = 1 foot so divide by 12
so 376.9911 / 12 = about 31.4
round down to 31 feet
8 0
3 years ago
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