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2 years ago

Which of the following are factors of x^2+5x+4

Mathematics

1 answer:

soldier1979 [14.2K]2 years ago

3 0

Answer:

(x + 4) and (x + 1)

Step-by-step explanation:

x² + 5x + 4

Consider the factors of the constant term (+ 4) which sum to give the coefficient of the x- term (+ 5)

The factors are 4 and 1 , since

4 × 1 = 4 and 4 + 1 = 5 , then

x² + 5x + 4 = (x + 4)(x + 1) ← in factored form

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A cone-shaped paper cup can hold 35 cubic inches of food. If the radius of the cone is 2.4 inches, what is the height of the con

SVETLANKA909090 [29]

$\bf \textit{volume of a cone}\\\\
V=\cfrac{\pi r^2 h}{3}~~
\begin{cases}
r=radius\\
h=height\\
-----\\
r=2.4\\
V=35
\end{cases}\implies 35=\cfrac{\pi (2.4)^2 h}{3}\implies 105=5.76\pi h
\\\\\\
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7 0

3 years ago

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A fair die is rolled repeatedly. find the expected number of rolls until all 6 faces appear.

Makovka662 [10]

Each face has a chance of 1/6
So you beed 6 rolls

8 0

3 years ago

Perimeter of the triangle below ?

Paha777 [63]

Answer:

31x^2-13x

Step-by-step explanation:

to find the perimeter of a triangle, add all sides.

P=a+b+c

P=(5x^2+x)+(8x^2-3x)+(18x^2-11x)

combine like terms

5x^2+8x^2-18x^2= 31x^2

x-3x-11x= -13x

31x^2-13x

5 0

3 years ago

A ball is thrown directly up in the air from a height of 5 feet with an initial velocity of 60 ft/s. Ignoring air resistance, ho

Mice21 [21]

Answer:

3.8 seconds

Step-by-step explanation:

Given equation

$h= -16t^2 + 60t + 5$

When the ball hits the ground then height is 0

So we replace h with 0 and solve for t

$0= -16t^2 + 60t + 5$

a= -16 , b= 60 and c= 5

Apply quadratic formula to solve for t

$t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

= $\frac{-60+\sqrt{60^2-4\left(-16\right)\cdot \:5}}{2\left(-16\right)}[/tex[tex]=\frac{-60+-\sqrt{3920}}{-32}$

$=\frac{-60+-28\sqrt{5}}{-32}$

$=\frac{4(-15+-7\sqrt{5})}{-32}$

$=\frac{(-15+-7\sqrt{5})}{-8}$

Now make two fractions and solve for x

t= $-\frac{7\sqrt{5}-15}{8}$ =-0.0815

t= $\frac{7\sqrt{5}+15}{8}$ =3.83

So answer is 3.8 seconds

4 0

2 years ago

When a scientist conducted a genetics experiments with peas, one sample of offspring consisted of 943 peas, with 717 of them hav

pshichka [43]

Using the normal approximation to the binomial distribution, it is found that:

a) 0.242 = 24.2% probability of getting 717 or more peas with red flowers.

b) Since Z < 2, 717 peas with red flowers is not significantly high.

c) Since 717 peas with red flowers is not a significantly high result, we cannot conclude that the scientist's assumption is wrong.

For each pea, there are only two possible outcomes. Either they have a red flower, or they do not. The probability of a pea having a red flower is independent of any other pea, which means that the binomial distribution is used to solve this question.

Binomial distribution:

Probability of x successes on n trials, with p probability.

Normal distribution:

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

It measures how many standard deviations the measure is from the mean.
After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

If Z > 2, the result is considered <u>significantly high</u>.

If $np \geq 10$ and $n(1-p) \geq 10$ , the binomial distribution can be approximated to the normal with:

$\mu = np$

$\sigma = \sqrt{np(1-p)}$

In this problem:

943 peas, thus, $n = 943$
3/4 probability of being red, thus $p = \frac{3}{4} = 0.75$ .

Applying the approximation:

$\mu = np = 943(0.75) = 707.25$

$\sigma = \sqrt{np(1-p)} = \sqrt{943(0.75)(0.25)} = 13.297$

Item a:

Using continuity correction, this probability is $P(X \geq 717 - 0.5) = P(X \geq 716.5)$ , which is <u>1 subtracted by the p-value of Z when X = 716.5</u>.

Then:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{716.5 - 707.25}{13.297}$

$Z = 0.7$

$Z = 0.7$ has a p-value of 0.758.

1 - 0.758 = 0.242

0.242 = 24.2% probability of getting 717 or more peas with red flowers.

Item b:

Since Z < 2, 717 peas with red flowers is not significantly high.

Item c:

Since 717 peas with red flowers is not a significantly high result, we cannot conclude that the scientist's assumption is wrong.

A similar problem is given at brainly.com/question/25212369

6 0

2 years ago