There are a total of 126 people in a group. One person in seven has a cat for a pet. How many people do not have a cat?

Without sketching the graph, find the x-intercepts and y-intercepts of the graph of the equation y=x²-x-6 What is/are the x-inte

oksian1 [2.3K]

Given the equation:

$y=x^2-x-6$

Let's find the x-intercepts and the y-intercepts of the graph.

• x-intercept:

The x-intercept are the points where the parabola crosses the x-axis. At x-intercept the y-value is zero.

To find the x-intercepts, substitute 0 for y and solve for x.

We have:

$0=x^2-x-6$

Rewrite the equation:

$x^2-x-6=0$

Factor the left hand side of the equation:

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

Equate each factor to zero:

x - 3 = 0

Add 3 to both sides:

x - 3 + 3 = 0 + 3

x = 3

x + 2 = 0

Subtract 2 from both sides:

x + 2 - 2 = 0 - 2

x = -2

Therefore, the x-intercepts are:

3, -2

• y-intercept:

The y-intercept is the point where the parabola crosses the y-axis. The x-value at the y-intercept is zero.

To find the y-intercept, substitute 0 for x and solve:

$\begin{gathered} y=0^2-0-6 \\ \\ y=-6 \end{gathered}$

Therefore, the y-intercept is -6.

In point form:

x-intercept: (3, 0), (-2, 0)

y-intercept: (0, -6)

ANSWER:

A. The x-intercepts are (3, 0), (-2, 0)

A. The y-intercept is (0, -6)

5 0

2 years ago

What does x equal in the equation 4x + (−3) = 5x + 3?

fgiga [73]

Answer:

x = -6

Step-by-step explanation:

First write the equation.

4x + -3 = 5x + 3

The isolate x in the equation. Add -4x to both sides.

4x + -3 + -4x = 5x + 3 + -4x

-3 = x + 3

Then add -3 to both sides.

-3 + -3 = x + 3 + -3

-6 = x

Now you have the value of x = -6.

Cheers.

3 0

4 years ago

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As Sales Manager for ISeeYou Productions, you are planning to review the prices you charge clients for television advertisement

aksik [14]

The development fee p can be modeled by the equation p=-400q+9600 where p is the price the company charges and q is the number of contracts they get. The total revenue R ISeeYou obtains by signing q contracts is found by using the function: $R(q)=-400q^{2}+9600q$ . The cost ISeeYou Productions can be found by using the following function: C(q)=800q+16000. The monthlhy profit of Express ISeeYou Productions if found with the next function: $P(q)=-400p^{2}+8800q-16000$ . ISeeYou should sign 2 or 20 contracts to break even.

a) In order to solve part a of the problem, we will suppose the price will have a linear relation with the amount of contracts they signed, so we need to find two points to build this function.

We know that when signing 6 contracts, the company charges $7,200, so our first point will be:

(6, 7200)

we also know that the company signs 14 contracts when they charge $4,000. So our second point is:

(14, 4000)

so we can use these points to find the slope of the line by using the

slope formula:

$m=\frac{p_{2}-p_{1}}{q_{2}-q_{1}}$

$m=\frac{4000-7200}{14-6}$

so the slope is:

m=-400

We can now use one of those points and the slope to find the function for the price, so we get:

$y-y_{1}=m(x-x_{1})$

$p-p_{1}=m(q-q_{1})$

if we used the point: (6, 7200) we get:

$p-7200=-400(q-6)$

which can now be simplified:

p=-400q+2400+7200

so the price function is:

p=-400q+9600

b) In order to find the revenue equation we need to multiply the price equation by the amount of contracts they signed in a month, so we get:

R(q)=pq

$R(q)=(-400q+9600)q$

$R(q)=-400q^{2}+9600q$

c) The cost can be found by adding the fixed cost and the variable cost, so we get:

C(q)=800q+16000

d) The profit is found by subtracting the montly cost from the monthly revenue, so we get:

P(q)=R(q)-C(q)

so

$P(q)=-400q^{2}+9600q-(800q+16000)$

so we can now simplify our function to get:

$P(q)=-400q^{2}+9600q-800q-16000$

$P(q)=-400q^{2}+8800q-16000$

e) In order to find the number of contracts for the company to break even, we need to find the q contracts that will give a profit of $0 so we set the function of the previous part of the problem equal to zero so we get:

$P(q)=-400q^{2}+8800q-16000$

$-400q^{2}+8800q-16000=0$

we can start by factoring a -400 from the left side so we get:

$-400(q^{2}-22q+40)=0$

we can divide both sides of the equation into -400 to simplify the equation so we get:

$q^{2}-22q+40=0$

and now we can factor the left side of the equation to get:

(q-20)(q-2)=0

we can now split this into two equations to get:

q-2=0 and q-20=0

so our two answers are:

q=2 and q=20

the company will break even when signing 2 and 20 contracts.

In the attached picture you will be able to see the break even points on the graph of revenue and cost.

For more information on how to solve this type of problems, you can go to the next link.

brainly.com/question/23407629?referrer=searchResults

6 0

3 years ago

The sum of the squares of 3 consecutive positive integers is 116. What are the numbers?

irina [24]

1st number = n
2nd number = n+1
3rd number = n+2

sum of the squares of 3 consecutive numbers is 116

n² + (n+1)² + (n+2)² = 116
n² + (n+1)(n+1) + (n+2)(n+2) = 116
n² + [n(n+1)+1(n+1)] + [n(n+2)+2(n+2)] = 116
n² + n² + n + n + 1 + n² + 2n + 2n + 4 = 116
n² + n² + n² + n + n + 2n + 2n + 1 + 4 = 116
3n² + 6n + 5 = 116 Last option.

5 0

3 years ago

10ac-x/11=-3 solve for a

Masja [62]

1) You'll have to get raid of the fraction by multiplying 10ac by 11, x/11 by 11 which the 11's cancels out and -3 multiplied by 11 .
2)Now you have 10ac -x = -33. Add x on both sides of the equal sign you get 10ac = -33 + x
3) Divide both sides by 10c to get "a" by itself, so "a" = -33+x divided by 10c

4 0

4 years ago

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