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3 years ago

Daniel and Sofia both solve this system of equations:

Mathematics

2 answers:

Evgesh-ka [11]3 years ago

8 0

Answer:

Sofias solution is correct.

Step-by-step explanation:

First of all you do not need two sets of the same equation.

y=-1.5x + 5.7

y = 0.5x + 0.3

If you graph the y-intercepts first then graph the slope for the equation then you will get the right answer.

1) Graph 5.7 on the y-axis. | Then graph -1.5x going down on the y-axis and then go to the right on the x-axis.

Do the same for the other equation and you will get a solution of (2.7, 1.65) since they will intersect there.

To check your answer use: https://desmos.com/calculator

FrozenT [24]3 years ago

5 0

Answer:

Step-by-step explanation: Sofia is more likely to be correct because based on her solution you use them in the equations to check your answers and they all are correct.

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House of Mohammed sells packaged lunches, where their finance department has established a

blagie [28]

The revenue function is a quadratic equation and the graph of the function

has the shape of a parabola that is concave downwards.

The correct responses are;

(a) R = -x² + 82·x

(b) $1,645

(c) The graph of R has a maximum because the leading coefficient of the quadratic function for R is negative.

(d) R = -1·(x - 41)² + 1,681

(e) 41

(f) $1,681

Reasons:

The given function that gives the weekly revenue is; R = x·(82 - x)

Where;

R = The revenue in dollars

x = The number of lunches

(a) The revenue can be written in the form R = a·x² + b·x + c by expansion of the given function as follows;

R = x·(82 - x) = 82·x - x²

Which gives;

R = -x² + 82·x

Where, the constant term, c = 0

(b) When 35 launches are sold, we have;

x = 35

Which by plugging in the value of x = 35, gives;

R = 35 × (82 - 35) = 1,645

The revenue when 35 lunches are sold, R = $1,645

Given that the leading coefficient is negative, the shape of graph of the

function R is concave downward, and therefore, the graph has only a

maximum point.

(d) The form a·(x - h)² + k is the vertex form of quadratic equation, where;

(h, k) = The vertex of the equation

a = The leading coefficient

The function, R = x·(82 - x), can be expressed in the form a·(x - h)² + k, as follows;

R = x·(82 - x) = -x² + 82·x

At the vertex, of the equation; f(x) = a·x² + b·x + c, we have;

$\displaystyle x = \mathbf{-\frac{b}{2 \cdot a}}$

Therefore, for the revenue function, the x-value of the vertex, is; $\displaystyle x = -\frac{82}{2 \times (-1)} = \mathbf{41}$

The revenue at the vertex is; $R_{max}$ = 41×(82 - 41) = 1,681

Which gives;

(h, k) = (41, 1,681)

a = -1 (The coefficient of x² in -x² + 82·x)

The revenue equation in the form, a·(x - h)² + k is; R = -1·(x - 41)² + 1,681

(e) The number of lunches that must be sold to achieve the maximum revenue is given by the x-value at the vertex, which is; x = 41

Therefore;

The number of lunches that must be sold for the maximum revenue to be achieved is 41 lunches

(f) The maximum revenue is given by the revenue at the vertex point where x = 41, which is; R = $1,681

The maximum revenue of the company is $1,681

Learn more about the quadratic function here:

brainly.com/question/2814100

6 0

3 years ago

The equation shown below involves a perfect square trinomial. 4x2 + 20x + 25 = 7 Which of the following is a step in solving thi

fomenos

4 x^2 + 20 x + 25 = 7
Divide both sides by 4:
x^2 + 5 x + 25/4 = 7/4
Write the left-hand side as a square:
(x + 5/2)^2 = 7/4
Take the square root of both sides:
x + 5/2 = sqrt(7)/2 or x + 5/2 = -sqrt(7)/2
Subtract 5/2 from both sides:
x = sqrt(7)/2 - 5/2 or x + 5/2 = -sqrt(7)/2
Subtract 5/2 from both sides:
Answer: x = sqrt(7)/2 - 5/2 or x = -5/2 - sqrt(7)/2

3 0

4 years ago

Need help with this problem please!!!!

katrin2010 [14]

Simply find perimeter for fencing, which is 16+16+8+8 which equals 48. The area is needed for finding the garden area, which is 16*8, which is 128

4 0

3 years ago

Gasoline costs $3.25 per gallon How much does it cost to drive

JulsSmile [24]

Answer:

$100.87 (to the nearest cent)

Step-by-step explanation:

1 gallon = 27 miles

⇒ number of gallons needed to drive 838 miles = 838 ÷ 27 = 31.0370370... gallons

1 gallon = $3.25

⇒ total cost to drive 838 miles = 3.25 x 838/27 = $100.87 (to the nearest cent)

7 0

2 years ago

There has been a great deal of controversy over the last several years regarding what types of surveillance are appropriate to p

alexira [117]

Answer:

Given that a person was identified as a future terrorist, there is a 2.8544% probability that he/she actually is a future terrorist.

Step-by-step explanation:

There are 1000 future terrorists in a population of 300,000,000. So the probability that a randomly selected person in this population is a terrorist is:

$P = \frac{1,000}{300,000,000} = 0.000003 = 0.0003%$

So, we have these following probabilities:

A 99.9997% probability that a randomly chosen person is not a terrorist.

A 0.0003% probability that a randomly chosen person is a terrorist.

A 98% probability that a future terrorist is correctly identified

A 99.9% chance of correctly identifying someone who is not a future terrorist. This also means that there is a 0.01% probability of someone who is not a terrorist being identified as one.

This can be formulated as the following problem:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

$P = \frac{P(B).P(A/B)}{P(A)}$

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

Here we have:

What is the probability that the person is a terrorist, given that she was identified as a terrorist.

P(B) is the probability that the person is a terrorist. So $P(B) = 0.000003$

P(A/B) is the probability that the person was identified as a terrorist, given that she is a terrorist. The problem states that the system has a 98% chance of correctly identifying a future terrorist, so $P(A/B) = 0.98$