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3 years ago

(x + 2)(x + 3)(x + 4) can be written in the form x + ax² + bx + c

Mathematics

1 answer:

ELEN [110]3 years ago

5 0

Answer:

$a=9, b=26, c=24$

Step-by-step explanation:

Let's expand the expression bit by bit.

$(x+2)(x+3)=(x)(x)+(x)(3)+(2)(x)+(2)(3)=x^2+5x+6$ by FOIL.

We have that $(x^2+5x+6)(x+4)=x(x^2+5x+6)+4(x^2+5x+6)=x^3+5x^2+6x+4x^2+20x+24=x^3+9x^2+26x+24$ .

So, the answer is $\boxed{a=9, b=26, c=24}$

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If log x+y/5 = 1/2(log x + log y) the find the value of x/y + y/x ?

V125BC [204]

Given that

log (x+y)/5 =( 1/2) {log x+logy}

We know that

log a+ log b = log ab

⇛log (x+y)/5 =( 1/2) log(xy)

We know that log a^m = m log a

⇛log (x+y)/5 = log (xy)^1/2

⇛log (x+y)/5 = log√(xy)

⇛(x+y)/5 = √(xy)

On squaring both sides then

⇛{ (x+y)/5}^2 = {√(xy)}^2

⇛(x+y)^2/5^2 = xy

⇛(x^2+y^2+2xy)/25 = xy

⇛x^2+y^2+2xy = 25xy

⇛x^2+y^2 = 25xy-2xy

⇛x^2+y^2 = 23xy

⇛( x^2+y^2)/xy = 23

⇛(x^2/xy) +(y^2/xy) = 23

⇛{(x×x)/xy} +{(y×y)/xy} = 23

⇛(x/y)+(y/x) = 23

Therefore, (x/y)+(y/x) = 23

Hence, the value of (x/y)+(y/x) is 23.

4 0

2 years ago

A sequence can be generated by using an = an-1 + 4, where a1 = 6 and n is a whole number greater than 1. What are the first four

Firlakuza [10]

Answer:

The first four terms are 4,8,12,16

Step-by-Step Explanation:

The given relation between the nth term and it's previous term is given by:

$\boxed{an = an - 1 + 4}$

GiveN:

a1 = 4

Now finding the other three terms of the AP with the given relation.

$a2 = a1 + 4$

Putting a1 = 4,

$a2 = 4 + 4 = 8$

Now, Third term:

$a3 = a2 + 4$

Putting a2 = 8,

$a3 = 8 + 4 = 12$

Now, Fourth term:

$a4 = a3 + 4$

Putting a3 = 12,

$a4 = 12 + 4 = 16$

Hence, The first four terms of the AP is 4, 8, 12 & 16.

7 0

2 years ago

Which of the following sets of numbers could not represent the three sides of a

sweet-ann [11.9K]

I think the answer is d hope this helps

4 0

3 years ago

Read 2 more answers

The average gasoline price of one of the major oil companies in Europe has been $1.25 per liter. Recently, the company has under

Ann [662]

Answer:

$t=\frac{1.20-1.25}{\frac{0.14}{\sqrt{49}}}=-2.50$

Step-by-step explanation:

Data given and notation

$\bar X=1.20$ represent the sample mean given

$\sigma = 0.14$ represent the population standard deviation

$n=49$ sample size

$\mu_o =1.25$ represent the value that we want to test

t would represent the statistic (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean for the gasoline prices is lower than 1.25, the system of hypothesis would be:

Null hypothesis: $\mu \geq 1.25$

Alternative hypothesis: $\mu < 1.25$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{1.20-1.25}{\frac{0.14}{\sqrt{49}}}=-2.50$

5 0

3 years ago

A basketball player makes 70% of his free throws the random numbers below represent 20 trials for a simulation let the numbers 0

Nesterboy [21]

Answer:

40%

Step-by-step explanation:

Given the result of the simulation below:

(5,5) (0,6) (9,6) (7,4) (9,1) (7,3) (0,4) (9,3) (2,9) (1,4)

(6,8) (5,3) (1,7) (1,7) (1,8) (3,5) (7,2) (2,1) (0,6) (1,8)

n(S)=20

The numbers 0 to 6 represent a made free throw .
The numbers 7 to 9 represent a missed free throw.
Therefore, any result containing 7 to 9 does not satisfy our requirement that the player makes both throws.

Let Event A be the event that the player made both throws

The pairs in which the player made both throws are:

(5,5) (0,6) (0,4) (1,4) (5,3) (3,5) (2,1) (0,6)

n(A)=8

Therefore:

$P(A)=\frac{n(A)}{n(S)}=\frac{8}{20}=0.4\\$

The probability that the player made both throws is 40%.

6 0

3 years ago

Read 2 more answers