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2 years ago

Solve for x: (5 points) negative 3 over 2, multiplied by x minus 9 equals negative 27 a −24 b −12 c 11 d 12

Mathematics

1 answer:

umka21 [38]2 years ago

4 0

Answer: b, 12

explanation: combine -3/2 * x and u get -3/2x. then isolate the variable by doing the inverse of subtraction on both sides. (add 9 on both sides). then do the inverse of multiplication on both sides. (divide by -3/2 on both sides)

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Does anyone know the answer?

Serhud [2]

Answer:

$6a {}^{2} - 2c + 2a {}^{2} - 2c {}^{2} \\ 8a {}^{2} - 2c {}^{2} - 2c$

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8 0

2 years ago

The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f(x)= 2/x^3 for x

natulia [17]

Answer:

a) 0.96

b) 0.016

c) 0.018

d) 0.982

e) x = 2

Step-by-step explanation:

We are given with the Probability density function f(x)= 2/x^3 where x > 1.

<em>Firstly we will calculate the general probability that of P(a < X < b) </em>

P(a < X < b) = $\int_{a}^{b} \frac{2}{x^{3}} dx$ = $2\int_{a}^{b} x^{-3} dx$

= $2[ \frac{x^{-3+1} }{-3+1}]^{b}_a dx$ { Because $\int_{a}^{b} x^{n} dx = [ \frac{x^{n+1} }{n+1}]^{b}_a$ }

= $2[ \frac{x^{-2} }{-2}]^{b}_a$ = $\frac{2}{-2} [ x^{-2} ]^{b}_a$

= $-1 [ b^{-2} - a^{-2} ]$ = $\frac{1}{a^{2} } - \frac{1}{b^{2} }$

a) Now P(X < 5) = P(1 < X < 5) {because x > 1 }

Comparing with general probability we get,

P(1 < X < 5) = $\frac{1}{1^{2} } - \frac{1}{5^{2} }$ = $1 - \frac{1}{25}$ = 0.96 .

b) P(X > 8) = P(8 < X < ∞) = 1/ $8^{2}$ - 1/∞ = 1/64 - 0 = 0.016

c) P(6 < X < 10) = $\frac{1}{6^{2} } - \frac{1}{10^{2} }$ = $\frac{1}{36} - \frac{1}{100 }$ = 0.018 .

d) P(x < 6 or X > 10) = P(1 < X < 6) + P(10 < X < ∞)

= $(\frac{1}{1^{2} } - \frac{1}{6^{2} })$ + (1/ $10^{2}$ - 1/∞) = 1 - 1/36 + 1/100 + 0 = 0.982

e) We have to find x such that P(X < x) = 0.75 ;

⇒ P(1 < X < x) = 0.75

⇒ $\frac{1}{1^{2} } - \frac{1}{x^{2} }$ = 0.75

⇒ $\frac{1} {x^{2} }$ = 1 - 0.75 = 0.25

⇒ $x^{2}$ = $\frac{1}{0.25}$ ⇒ $x^{2}$ = 4 ⇒ x = $2$

Therefore, value of x such that P(X < x) = 0.75 is 2.

8 0

2 years ago

Verifying Trig Functions

anzhelika [568]

Answer:

The answer to your question is below

Step-by-step explanation:

csc α - cot α = $\frac{sin \alpha }{1 + cos \alpha }$

Work with the left part

$\frac{1}{sin\alpha } - \frac{cos \alpha }{sin \alpha}$

Simplify

$\frac{1 - cos\alpha }{sin\alpha }$

Multiply by the reciprocal

$\frac{1 - cos\alpha }{sin \alpha } x \frac{1 + cos\alpha }{1 + cos\alpha }$

Simplify

$\frac{1 - cos^{2}\alpha}{sin\alpha (1 + cos\alpha)}$

Remember that

sin²α = 1 -cos²α

Substitute the previous equation

$\frac{sin^{2}\alpha }{sin\alpha(1 + cos\alpha ) }$

Simplify

$\frac{sin\alpha}{1 + cos \alpha}$

The identity i proved.

5 0

3 years ago

Someoneeee pleaseeee helpppp me outtttttt!!!!!!!

arlik [135]

Answer:

cos X = $\frac{5}{13}$

Step-by-step explanation:

simplify 15/39

3 0

2 years ago

Read 2 more answers

Divide (x4 – 11x3 – 49x2 + 899x – 2506) ÷ (x – 8).

pickupchik [31]

Okay first make sure you change negative 8 to a positive 8.
Set the problem up 8 -11 -49 899 -2506
__________________
8 -11 -49 899 -2506
-88 -1096 -1576
____________________
-11 -137 -197 -4082

Your answer will be
-11x^3 - 137x^2 - 197x - 4082

6 0

3 years ago