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4 years ago

10

Francis missed 3 questions on his science test. Paige missed 1 more than twice as many questions as Francis. How many questions

did Paige miss?

1 answer:

lesya692 [45]4 years ago

8 0

The equation rx3+1 can be used to solve the problem,and your answer ends up being 7.

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Ludmilka [50]

I’m pretty sure the answer is 3

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3 years ago

Soruyu cevaplayabilirseniz çok teşekkür ederim.

sleet_krkn [62]

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5 0

3 years ago

HELP!!! PLEASE!!!!

Makovka662 [10]

Answer:

y = 2x² - 5x + 7

Step-by-step explanation:

For this problem, imagine the standard form, which is:

f(x) = ax² + bx + c = y

Using the table, and adding that y at the end, we can plug in and write out the following equations. (<em>Writing it out is important</em>):

f(-1) = a(-1)² + b(-1) + c = 14

f(0) = a(0)² + b(0) + c = 7

f(1) = a(1)² + b(1) + c = 4

f(2) = a(2)² + b(2) + c = 5

Now if this doesn't look familiar, it's actually a <u>systems of equations</u> using the a, b, and c elements as your three variables! If you simplify the equations:

f(-1) = a - b + c = 14

f(0) = c = 7

f(1) = a + b + c = 4

f(2) = 4a + 2b + c = 5

Something unique just happened. We have already defined what ' c ' is!

<u><em>c = 7</em></u>

Setting that aside, if you remove the f(x) portion of the equations, you're left with:

a - b + c = 14

a + b + c = 4

4a + 2b + c = 5

Using the two upper equations, if we add them together (you can do that as it doesn't change the values of the variables) you get:

2a + 2c = 18

Note: the ' b ' variables cancelled out in the addition [ b + (-b) ]

If you further simplify the equation:

a + c = 9

Awesome. Now we already know that <u>c = 7</u>, so if you plug that into the equation:

a + 7 = 9

Solve for a. So then a = 2

Now that we know the following:

a = 2

c = 7

We can then use the equation:

a + b + c = 4

And solve for b!

2 + b + 7 = 4

Simplify.

b + 9 = 4

Simplify.

b = -5

Now at this point, since you know what a, b and c are, you can write the equation!

f(x) = 2x² - 5x + 7

You can confirm your work by putting any of the x values in the table through!

4 0

3 years ago

Read 2 more answers

Margaret’s favorite restaurant has 3 specials every day. There are 2 choices of vegetable and 3 choices of dessert. How many dif

VMariaS [17]

Answer:

b

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Suppose an airline policy states that all baggage must be box shaped with a sum of length, width, and height not exceeding 174 i

Leya [2.2K]

Answer:

The square-based box with the greatest volume under the condition that the sum of length, width, and heigth does not exceed 174 in is a cube with each edge of 58 in and a volume of $195112 in^{3}$

Step-by-step explanation:

For this problem we have two constraints, that are as follows:

1) Sum of length, width, and heigth not exceeding 174 in

2) Lenght and width have the same measure (square-based box)

We know that volume is equal to the product of all three edges, and with the two conditions into account we have the next function:

$V=(w^{2})(174-2w)\\V=174w^{2}-2w^{3}$

The interval of interest of the objective function is [0, 87]

This problem requieres that we maximize the function that defines the volume. We start calculating the derivative of the function, wich is:

$V'=348w-6w^{2} \\V'=(348-6w)(w)$

We need to remember that the derivative of a function represents the slope of said function at a given point. The maximum value of the function will have a slope equal to zero.

So we find the value in wich the derivative equals zero:

$0=(348-6w)(w)\\w_1=0\\w_2=348/6=58$

The first value ( $w=0$ ) will leave us with a 'height-only box', so the answer must be $w=58 in$

The value is between the interval of interest.

And, once we solve for the constraints, we have that:

Lenght = Width = Heigth = 58 in

Volume = $195112 in^{2}$

8 0

3 years ago