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2 years ago

What are the solutions to the equation 0 = x2 – x –6? Select two options

Mathematics

2 answers:

KatRina [158]2 years ago

6 0

Answer:

$x=3$ or $x=-2$

Step-by-step explanation:

This is factorable.

The leading coefficient is 1.

Since this is a quadratic all we have to do is find two numbers that multiply to be c and add up to be b to factor the expression that is to the left of the equal sign.

By the way a quadratic expression looks like $ax^2+bx+c$ .

So we want to find two numbers that multiply to be -6 and add up to be -1.

Those numbers are -3 and 2 since (-3)(2)=-6 and -3+2=-1.

So the factored form is:

$(x-3)(x+2)=0$ .

Since we have a product is zero then at least one of the factors need to be zero in order for the equation to hold.

So this means we have the following two equations to solve:

$x-3=0$ or $x+2=0$

First equation we will add 3 on both sides.

Second equation we will subtract 2 on both sides.

$x=3$ or $x=-2$

Lemur [1.5K]2 years ago

5 0

(X-3)(x+2)=0

So, X=3,X= -2
X={3,-2}

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Estimate the unit rate if 12 pairs of socks sell for $5.79.

11111nata11111 [884]

If 12 pairs of socks sell for $5.79, then the unit rate is 12 : 5.79. If we want to find a unit rate for one pair of socks, we need to divide 5.79 by 12:
5.79 / 12 = 0,4825
So the unit rate is 1 : 0.4825
Hope this was helpful, and if so, please mark as brainliest. ((: Thank you!

3 0

1 year ago

Uma urna contém 10 bolas identificadas pelas letras A, B, ..., J. Uma bola é extraída ao acaso da urna e sua letra é observada.

arlik [135]

Answer:

a) Probability that a letter of the drawn ball is vowel = (3/10) = 0.30

b) Probability that a letter of the drawn ball is consonant = (7/10) = 0.70

a) Probabilidade de uma letra da bola sacada ser vogal = (3/10) = 0.30

b) Probabilidade de uma letra da bola sacada ser consoante = (7/10) = 0,70

Step-by-step explanation:

English Translation

A ballot box contains 10 balls identified by the letters A, B, ..., J. A ball is drawn at random from the ballot box and its letter is observed. (Make the sample space and all events explicit). What is the probability that a letter of the drawn ball is: a) Vowel b) Consonant

Solution

The 10 balls are identified by A, B, C, D, E, F, G, H, I and J

Note that the probability of an event is given as the number of elements in that event divided by the number of elements in the sample space.

a) Probability of drawing a ball that has a vowel letter = P(v)

P(v) = n(v) ÷ n(S)

n(v) = Number of balls with vowel letters = 3 (that is, A, E and I)

n(S) = Total number of balls = 10

P(v) = (3/10) = 0.30

b) Probability of drawing a ball that has a consonant letter = P(c)

P(c) = n(c) ÷ n(S)

n(c) = Number of balls with consonant letters = 7 (that is, B, C, D, F, G, H and J)

n(S) = Total number of balls = 10

P(c) = (7/10) = 0.70

In Portugese/Em português

As 10 bolas são identificadas por A, B, C, D, E, F, G, H, I e J.

Observe que a probabilidade de um evento é fornecida como o número de elementos nesse evento dividido pelo número de elementos no espaço de amostra.

a) Probabilidade de desenhar uma bola com uma letra de vogal = P (v)

P (v) = n (v) ÷ n (S)

n (v) = Número de bolas com letras de vogal = 3 (ou seja, A, E e I)

n (S) = Número total de bolas = 10

P (v) = (3/10) = 0,30

b) Probabilidade de desenhar uma bola com uma letra consoante = P (c)

P (c) = n (c) ÷ n (S)

n (c) = Número de bolas com letras consoantes = 7 (ou seja, B, C, D, F, G, H e J)

n (S) = Número total de bolas = 10

P (c) = (7/10) = 0,70

Hope this Helps!!!!

Espero que isto ajude!!!!

3 0

2 years ago

State the size of angle OAB, giving a reason for your answer

Alja [10]

Answer:

Angle OAB = 90°

Reason: tangent theorem of a circle

Step-by-step explanation:

The diagram given shows a tangent line of the given circle with center O. The tangent touches the circle at point A.

The diagram also shows the radius of the circle, OA, drawn from the center to the circle to meet at the point of tangency.

Thus, according to the Tangent Theorem of a circle, the point at which the radius drawn from the center meets the point of tangency = 90°. The tangent is perdendicular to the radius drawn to meet at the point of tangency.

Therefore, angle OAB = 90°

5 0

2 years ago

Write the equation of a line that is perpendicular to y = 5 y=5y, equals, 5 and that passes through the point ( − 7 , − 5 ) (−7,

Jlenok [28]

The line of the equation perpendicular to y=5 and cuts through (-5,-7) will be given by
m(x-x1)=y-y1
where m=slope.
from y=0x+5, the slope of the perpendicular line m=0,
thus the equation will be:
0(x--5)=y--7
0=y+7
y=-7
The equation is y=-7

3 0

2 years ago

Read 2 more answers

Market-share-analysis company Net Applications monitors and reports on Internet browser usage. According to Net Applications, in

ASHA 777 [7]

Answer:

a) There is a 2.43% probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

b) There is an 80.50% probability that at least 3 of the 20 Internet browsers users use Chrome as their Internet browser.

c) The expected number of Chrome users is 4.074.

d) The variance for the number of Chrome users is 3.2441.

The standard deviation for the number of Chrome users is 1.8011.

Step-by-step explanation:

For each Internet browser user, there are only two possible outcomes. Either they use Chrome, or they do not. This means that we can solve this problem using concepts of the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

In this problem we have that:

Google Chrome has a 20.37% share of the browser market. This means that $p = 0.2037$

20 Internet users are sampled, so $n = 20$ .

a.Compute the probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

This is P(X = 8).

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

$P(X = 8) = C_{20,8}.(0.2037)^{8}.(0.7963)^{12} = 0.0243$

There is a 2.43% probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

b.Compute the probability that at least 3 of the 20 Internet browsers users use Chrome as their Internet browser.

Either there are less than 3 Chrome users, or there are three or more. The sum of the probabilities of these events is decimal 1. So:

$P(X < 3) + P(X \geq 3) = 1$

$P(X \geq 3) = 1 - P(X < 3)$

In which

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

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

$P(X = 0) = C_{20,0}.(0.2037)^{0}.(0.7963)^{20} = 0.0105$

$P(X = 1) = C_{20,1}.(0.2037)^{1}.(0.7963)^{19} = 0.0538$

$P(X = 2) = C_{20,2}.(0.2037)^{2}.(0.7963)^{18} = 0.1307$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0105 + 0.0538 + 0.1307 = 0.1950$

$P(X \geq 3) = 1 - P(X < 3) = 1 - 0.1950 = 0.8050$

There is an 80.50% probability that at least 3 of the 20 Internet browsers users use Chrome as their Internet browser.

c.For the sample of 20 Internet browser users, compute the expected number of Chrome users

We have that, for a binomial experiment:

$E(X) = np$

$E(X) = 20*0.2037 = 4.074$

The expected number of Chrome users is 4.074.

d.For the sample of 20 Internet browser users, compute the variance and standard deviation for the number of Chrome users.

We have that, for a binomial experiment, the variance is

$Var(X) = np(1-p)$

$Var(X) = 20*0.2037*(0.7963) = 3.2441$

The variance for the number of Chrome users is 3.2441.

The standard deviation is the square root of the variance. So

$\sqrt{Var(X)} = \sqrt{3.2441} = 1.8011$

The standard deviation for the number of Chrome users is 1.8011.

6 0

2 years ago