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2 years ago

Complete each trinomial such that it can be rewritten in the form a(x+b)^2 or a(x-b)^2

Mathematics

1 answer:

scoundrel [369]2 years ago

6 0

The value of the expression in the form a(x+b)^2 is 1.5(x+2)^2 - 4

<h3>Vertex Form of a quadratic expression</h3>

Given the quadratic expressions

1.5x^2+6x+......

1.5(x^2 + 4x)

Using the completing the square method

The coefficient of x = 4

Half of the coefficient = 4/2 = 2

The square of the result = 2^2 = 4

The equation is expressed as:

f(x) = 1.5(x^2+4x+ 4) - 4

f(x) = 1.5(x+2)^2 - 4

Hence the value of the expression in the form a(x+b)^2 is 1.5(x+2)^2 - 4

Learn more on completing the square method here: brainly.com/question/1596209

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Can you help me plss!

Ksivusya [100]

(1/3) × the cone's volume = The cylinder's volume.

Step-by-step explanation:

Step 1:

The volume of any cone is obtained by multiplying $\frac{1}{3}$ with π, the square of the radius ( $r^{2}$ ) and the height ( $h$ ).

So the volume of the cone, $V=\pi r^{2} \frac{h}{3}$ .

Step 2:

The cylinder's volume is nearly the same as the cone but instead by multiplying $\frac{1}{3}$ we multiply with 1.

So the cylinder's volume is determined by multiplying π with the square of the radius of the cylinder ( $r^{2}$ ) and the height of the cylinder ( $h$ ).

So the the cone's volume, $V = \pi r^{2} h$ .

Step 3:

Now we equate both the volumes to each other.

The cone's volume : The cylinder's volume = $\pi r^{2} \frac{h}{3}: \pi r^{2} h$ = $\frac{1}{3} : 1$ .

So if we multiply the cone's volume with $\frac{1}{3}$ we will get the cylinder's volume with the same dimensions.

5 0

3 years ago

What is the volume of the prism below

lesya [120]

Answer:

B. 196 units squared

Step-by-step explanation:

The formula of a prism is V = Bh

= (1/2 bh) h

=(1/2 x 7 x 14) x 4

= (3.5 x 14) x 4

=49 x 4

= 196 units squared

I haven't did these type of questions in a while, but i think my answer is correct. Hope it helps :)

5 0

3 years ago

10. A company finds that 45% of first-time visitors to its website do not buy any of its products. If there are 75 first-time vi

vekshin1

Using the binomial distribution, it is found that the probability that exactly 36 of them buy a product is of 0.044.

For each first-time visitor, there are only two possible outcomes, either they buy a product, or they do not. The probability of a first-time visitor buying a product is independent of any other first-time visitor, hence the binomial distribution is used to solve this question.

<h3>What is the binomial distribution formula?</h3>

The formula is:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

In this problem:

45% of first-time visitors to its website do not buy any of its products, hence 55% buy, that is, p = 0.55.

There are 75 first-time visitors on a given day, hence n = 75.

The probability that exactly 36 of them buy a product is P(X = 36), hence:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 36) = C_{75,36}.(0.55)^{36}.(0.45)^{39} = 0.044$

More can be learned about the binomial distribution at brainly.com/question/24863377

8 0

2 years ago

Need help with this

Alecsey [184]

$\frac{x {}^{3} - 3x {}^{2} - 10x {}^{2} + 30x + 4x - 12 }{x - 3 } \\ \frac{x {}^{2} \times (x - 3) - 10x \times (x - 3) + 4 \times (x - 3) }{x - 3} \\ \frac{(x - 3)(x {}^{2} - 10x + 4 )}{x - 3} \\ x {}^{2} - 10x + 4$

8 0

3 years ago

Answers choices<br> <1<br> <4<br> <2<br> <3

Maslowich

Answer:

B) 4

Step-by-step explanation:

1. <em>It is either 3 or 4</em>, since those are only two angles comparing the lighthouse and the boat.

2. The angle of depression is noted below the horizontal and above the actual line, and out of 3 and 4, <em>4 is the only angle that is below its corresponding horizontal</em>.

So, the angle of depression from the lighthouse to the boat is 4.

7 0

3 years ago