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oksian1 [2.3K]
3 years ago
14

What is the factorization of the polynomial below? -3x^3+15x^2+42x

Mathematics
1 answer:
kherson [118]3 years ago
7 0
Factoring out x

x(-3x^2+15x+42)  now factor parenthetical expression

x(-3x^2+21x-6x+42)

x(-3x(x-7)-6(x-7))

x(-3x-6)(x-7)  we can factor out -3 from first parentheses

-3x(x+2)(x-7)
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What is the solution of 3+ x-2/x-3 less than or equal to 0
bagirrra123 [75]

Answer:

The solution set consists of all the real numbers smaller than or equal to 11/4:

x\leq \frac{11}{4}

Step-by-step explanation:

We need to solve for x (that means isolate x on one side of the inequality symbol) in the following inequality:

3+\frac{x-2}{x-3} \leq 0\\\frac{x-2}{x-3} \leq -3\\x-2\leq -3\,(x-3)\\x-2\leq -3x+9\\x+3x\leq 9+2\\4x\leq 11\\x\leq \frac{11}{4}

4 0
2 years ago
The blood platelet counts of a group of women have a boll-shaped distribution with a mean of 261.1 and a standard deviation of 6
alexandr402 [8]

The variable is

X: blood platelet count of a woman

This variable has a bell shaped distribution (Normal)

With mean μ=261.1 and standard deviation σ=64.3

a.

The platelet count within 3 standard deviations of the mean can be calculated as

μ±3σ

You can symbolize it as

μ-3σ ≤ X ≤ μ+3σ

According to the empirical rule of the normal distribution you know that under any bell shaped distribution:

Between μ ± σ you'll find the 68% of the distribution

Between μ ± 2σ you'll find the 95% of the distribution

Between μ ± 3σ you'll find the 99% of the distribution

So following this rule you'll find 99% of the women with platelet count within 3 standard deviations of the mean.

b.

3% of the population is found between a vertain interval, the rest 97% is separated in equal tails around this interval.

Divide 0.97 by 2

0.97/2= 0.485

Each tail contains 0.485 of the distribtuion.

a and b represent the values within you'll find 3% of the population.

Until a you'll find 0.485 of the population and until b you'll find 0.485+0.03=0.515

To calculate both unknown values you have to use the standard normal distribution. This distribution is centered in zero, the left tail is negative and the right tail is positive.

a and b are at a equal distance from the mean but with different sign, so you only have to calculate on and then you invert the sign to get the other one.

I'll calculate the positive value:

Z= (X- μ )/σ~N(0,1)

P(Z≤ b)=0.515

Look in the body of the Z-table, rigth or positive entry and reach the margins for the value:

b= 0.038

Then using the values of the mean and the standard deviation you can calculate the corresponding valueof platelet count:

b= (X- μ )/σ

0.038= (X- 261.1 )/64.3

0.038*64.3=X-261.1

2.4434+261.1=X

X=263.5434=263.5

a=-b=-0.038

a= (X- μ )/σ

-0.038= (X- 261.1 )/64.3

-0.038*64.3=X-261.1

-2.4434+261.1=X

X=258.6566= 258.7

3% of the populations platelet count is between 258.7 and 263.5.

3 0
9 months ago
You deposit $900
kakasveta [241]

Answer:40 years

Step-by-step explanation:

First you get 1% which is 9$ then you times it by 5 and get 45 multiply it by 20 you get 900 but since you want to double it then double the answer which is 40

8 0
3 years ago
Solve please!!<br> equation is in the directions!!
patriot [66]
14. The equation would be -16t^2+60t+7 To find the maximum point plug in values into the equation -b/2a to find the axis of symmetry, and plug that number in for t.
b=60, a=-16
-60/-32=t=1.875
-16(1.875)^2+60(1.875)+7=63.25
Maximum point: (1.875,63.25)
The ball will land after about 3.86 seconds
7 0
2 years ago
The sum of three consecutive numbers is equal to 123. What are the numbers?
Zina [86]

Answer:

40, 41, 42

Step-by-step explanation:

x +x+1+x+2=123

3x+3=123

3x=123-3

3x=120

x=120:3

x=40(the first number

40+1=41 (the second number

40+2=42 (the third number

4 0
3 years ago
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