Given the function f(x) = 6x2 + 3Find f(-2) -2227915

Answer

The space being considered will be able to fit 7,000 people since its maximum capcity according to our calculations is 8,000 and 7,000 is less than 8,000.

Step-by-step explanation

As event planners, we have a space that is 400 feet wide and 300 feet long and we are hoping to fit in 7000 people assuming each person takes up a space of 15 square feet of space to stand on average.

To do this, we will find out how much square feet of space is contained in the 400 feet wide and 300 feet long space that we have available.

Area of the space = Length × Width

Length = 300 feet

Width = 400 feet

Area of the space = 300 × 400 = 120,000 square feet

Let the number of persons that this space can accomodate be x

1 person = 15 square feet

We can rewrite that as

15 square feet = 1 person

120,000 square feet = x persons

A mathematical relation can be established by simply cross multiplying

We then obtain

15 × x = 120,000 × 1

15x = 120,000

Divide both sides by 15

(15x/15) = (120,000/15)

x = 8,000 persons.

Therefore, the space being considered will be able to fit 7,000 people since its maximum capcity according to our calculations is 8,000 and 7,000 is less than 8,000.

Hope this Helps!!!

Answer:

y = 4x - 6

Step-by-step explanation:

Hi there!

We are given the points (3,6) and (1, -2), and that a line passes through these 2 points

We want to find the equation of said line

There are 3 ways to write the equation of the line:

The  most common way is slope-intercept form, so let's write the equation of the line this way

First, we need to find the slope

The slope (m)  can be found using the formula \(\frac{y_2-y_1}{x_2-x_1}\), where \((x_1, y_1)\) & \((x_2, y_2)\) are points

Before we calculate, let's label the values of the points.

\(x_1=3\\y_1=6\\x_2=1\\y_2=-2\)

Now substitute into the formula

m=\(\frac{y_2-y_1}{x_2-x_1}\)

m=\(\frac{-2-6}{1-3}\)

Subtract

m=\(\frac{-8}{-2}\)

Divide

m= 4

The slope of the line is 4

Substitute 4 as m in y=mx+b:

y = 4x + b

Now to find b

Since the equation passes through both (3,6) and (1, -2), we can use either point to help solve for b.

Taking (3,6) for example:

Substitute 3 as x and 6 as y.

6 = 4(3) + b

Multiply

6 = 12 + b

Subtract 12 from both sides

-6 = b

Substitute -6 as b into the equation

y = 4x - 6

Hope this helps!

Topic: finding the equation of the line

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Answer:

3n + 7.6 = 52.6

Step-by-step explanation:

Answer:

8.9 cm

Step-by-step explanation:

We have
\(\overline {UV} = 16.8 cm\\\\\overline {WV} = 7.9 cm\\\\ Since all lines are scalars, \overline{WV} = \overline{VW}\\\textrm{We see that \overline{UW} + \overline{WV} = \overline{UV}\\\\\overline {UW} \\ = \overline {UV} - \overline {WV} = 16.9 - 7.9 = 8.9 cm}\)

Answer:

1/26

Step-by-step explanation:

'or' in the question means add

theres only 1 card that is 10 of spades

and

theres only 1 card that is four of diamonds

1/52 + 1/52 = 2/52 = 1/26

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A fair decision can be made by implementing an impartial evaluation process based on established criteria and selecting the student who best meets the requirements.

To make a fair decision about who goes to dinner when only one student per school can attend, the following process can be implemented:

Clear Criteria: Establish clear and objective criteria that will be used to evaluate the students. This could include factors such as leadership abilities, involvement in student council activities, communication skills, or any other relevant qualities.

Application or Nomination: Allow all three students, Alina, Robert, and Makayla, to submit applications or nominations stating why they believe they should be chosen to attend the dinner. This ensures that each student has an opportunity to present their case.

Evaluation Committee: Form an evaluation committee comprising individuals who are impartial and not directly involved in the student council. This committee could include teachers, administrators, or other school staff members.

Evaluation Process: The committee will review and evaluate the applications or nominations based on the established criteria. Each application should be reviewed independently, without knowledge of the other students' submissions, to avoid bias.

Decision Making: The committee will collectively discuss and consider the strengths and merits of each student. They should strive to make an informed and fair decision based solely on the established criteria. It is important to maintain confidentiality throughout the decision-making process.

Communication: Once a decision has been reached, the selected student should be notified promptly. It is essential to communicate the decision respectfully to the other students who were not chosen, emphasizing the difficulty of the decision-making process and expressing appreciation for their involvement.

By implementing these steps, the decision about who goes to dinner can be made based on objective criteria and impartial evaluation, ensuring fairness and transparency in the selection process.

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Ernesto bought the ceramic vase for $56 including 12% tax.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A ceramic vase was originally priced at $100 but went on sale for 50% off.

∴ The discounted price is (50/100)×100 = $50.

Now after Ernesto bought the ceramic vase he had to pay a tax of 12%.

∴ {(100 + 12)/100}×50.

= (112/100)×50.

= 56.

So he paid $56 including 12% tax.

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Answer:

120 m²

Step-by-step explanation:

We khow that the area of a triangle is the product of the lenght and the wight

let x be the width

so the lenght is 15

Answer:

  120 square meters

Step-by-step explanation:

The missing leg of the right triangle is found from the Pythagorean theorem:

  diagonal² = length² + width²

  length² = diagonal² -width²

  length = √(17² -8²) = √(289 -64) = √225 = 15

So, the rectangle is 8 m by 15 m and has an area that is ...

  A = LW = (15 m)(8 m) = 120 m²

Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

Answer:2.

Step-by-step explanation:

trust me on this one

Answer: 68y+106=36-y

Answer:

histogram

Step-by-step explanation:

The smallest positive debt that can be paid off using sticker trading is $7$ dollars.

To find the smallest positive debt that can be paid off using sticker trading, we need to consider the values of the stickers (in dollars) and find the smallest positive amount that can be reached through a combination of these values.

Given that a Harry Potter sticker is worth $49 and a Twilight sticker is worth $35, we can approach this problem using the concept of the greatest common divisor (GCD) of these two values.

The GCD of $49$ and $35$ is $7$. This means that any multiple of the GCD can be represented using these sticker values.

In other words, any positive multiple of $7$ dollars can be paid off using sticker trading.

Therefore, the smallest positive debt that can be paid off using sticker trading is $7$ dollars.

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Answer:

\(y=x^2+18x+79\)

\(y=(x+9)^2-2\)

Step-by-step explanation:

We want to find a function of the form:

\(y=ax^2+bx+c\)

We know that it passes through the three points: (-11, 2); (-9, -2); and (-5,14).

In other words, if we substitute -11 for x, we should get 2 for y. So:

\((2)=a(-11)^2+b(-11)+c\)

Simplify:

\(2=121a-11b+c\)

We will do it to the two other points as well. So, for (-9, -2):

\(\begin{aligned}(-2)&=a(-9)^2+b(-9)+c\\\Rightarrow-2&=81a-9b+c\end{aligned}\)

And similarly:

\(\begin{aligned}(14)&=a(-5)^2+b(-5)+c\\\Rightarrow 14&=25a-5b+c\end{aligned}\)

So, to find our function, we will need to determine the values of a, b, and c.

We essentially have a triple system of equations:

\(\begin{cases}2=121a-11b+c\\-2=81a-9b+c\\14=25a-5b+c\end{cases}\)

To approach this, we can first whittle it down only using two variables.

So, let's use the First and Second Equation. Let's remove the variable b. To do so, we can use elimination. We can multiply the First Equation by 9 and the Second Equation by -11. This will yield:

\(\begin{cases}{\begin{aligned}9(2)&=9(121a-11b+c)\\-11(-2)&=-11(81a-9b+c)\end{cases}}\)

Distribute:

\(\begin{cases}18=1089a-99b+9c\\22=-891a+99b-11c\end{cases}\)

Now, we can add the two equations together:

\((18+22)=(1089a-891a)+(-99b+99b)+(9c-11c)\)

Simplify:

\(40=198a-2c\)

Now, let's do the same using the First and Third Equations. We want to cancel the variable b. So, let's multiply the First Equation by 5 and the Third Equation by -11. So:

\(\begin{cases}{\begin{aligned}5(2)=5(121a-11b+c)\\-11(14)=-11(25a-5b+c)\end{cases}\)

Simplify:

\(\begin{cases}10=605a-55b+5c\\-154=-275a+55b-11c\end{cases}\)

Now, let's add the two equations together:

\((10-154)=(605a-275a)+(-55b+55b)+(5c-11c)\)

Simplify:

\(-144=330a-6c\)

Therefore, we now have the two equations:

\(\begin{cases}40=198a-2c\\-144=330a-6c\end\)

Let's cancel the c. So, multiply the First Equation by -3. We don't have to do anything special to the second. So:

\(-3(40)=-3(198a-2c)\)

Multiply:

\(-120=-594a+6c\)

Now, add it to the Second Equation:

\((-120+-144)=(-594a+330a)+(6c-6c)\)

Add:

\(-264=-264a\)

Divide both sides by -264. So, the value of a is:

\(a=1\)

Now, we can use either of the two equations above to obtain c. Let's use the first one. So:

\(40=198a-2c\)

Substitute 1 for a:

\(40=198(1)-2c\)

Solve for c. Subtract 198 from both sides and divide by -2:

\(\begin{aligned}40&=198-2c\\ -158&=-2c \\79 &=c \end{aligned}\)

So, the value of c is 79.

Finally, we can find b. We can use any of the three original equations. Let's use the First Equation. So:

\(2=121a-11b+c\)

Substitute 1 for a and 79 for c and determine the value of b:

\(\begin{aligned}2&=121(1)-11b+(79)\\2&=121+79-11b\\2&=200-11b\\-198&=-11b\\18&=b\end{cases}\)

Therefore, the value of b is 18.

So, our equation is:

\(y=ax^2+bx+c\)

Substitute in the values:

\(y=(1)x^2+(18)x+(79)\)

Simplify:

\(y=x^2+18x+79\)

Now, let's put this into vertex form. To do so, we will need to complete the square. First, let's group the first two terms together:

\(y=(x^2+18x)+79\)

To complete the square, we will divide the b term by 2 and then square it.

b is 18. 18/2 is 9 and 9² is 81. Therefore, we will add 81 into our parentheses:

\(y=(x^2+18x+81)+79\)

Since we added 81, we must also subtract 81. So:

\(y=(x^2+18x+81)+79-81\)

Subtract:

\(y=(x^2+18x+81)-2\)

The grouped terms are a perfect square trinomial. Factor:

\(y=(x+9)^2-2\)

And this is in vertex form.

And we are done!

Expanding the product in the vertex form of the quadratic equation we get the standard form:

y = a*x² - (2ah)*x + (k - ah²)

The vertex form of a quadratic equation whose vertex is (h, k) and leading coefficient is a, is written as follows:

y = a*(x - h)² + k

To get the standard form, just expand the product, then we will get the quadratic equation in standard form:

y = ax² - 2ahx - ah² + k

Grouping the correspondent terms we get the actual the standard form:

y = a*x² - (2ah)*x + (k - ah²)

Where the 3 coefficients are a, -2ah, and (k + ah²)

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Answer:

  (a) 15

  (b) -2

  (c) 2

Step-by-step explanation:

For each given value of x, determine the applicable function definition and use that to determine the function value.

-4 is less than -1, so the first function definition applies:

  f(-4) = -5(-4) -5 = 20 -5

  f(-4) = 15

__

-1 is equal to -1, so the second function definition applies:

  f(-1) = (-1)^2 +2(-1) -1 = 1 -2 -1

  f(-1) = -2

__

1 is greater than -1, so the second function definition applies:

  f(1) = (1)^2 +2(1) -1 = 1 + 2 -1

  f(1) = 2

The value of P(x=1) from the given discrete data is 0.5.

From the given data

Let P(x=2)=x

p+p+x=1

x=1-2p

E(x²)=∑PiXi²=P(0)²+p(1)²+(1-2p)(2)²

= 0+p+(1-2p)4

= 4-7p

E(x)=∑PiXi=P(0)+P(1)(1-2p)(2)

= 0+p+2-4p

= 2-3p

Given that, E(x²)=E(x)

4-7p=2-3p

4p=2

p=0.5

Therefore, the value of P(x=1) from the given discrete data is 0.5.

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Answer:

m ∠DGA  =  78°

Step-by-step explanation:

∠CGB and ∠DGA are vertically opposite angles formed at the intersection of the two rays AB and CD

Such angles are equal to each other

Therefore
m ∠DGA  = m ∠CGB  = 78°

Answer:2.1

Step-by-step explanation:

i added them then divided by 7

Answer:

  a.  False

  b.  True

  c.  True

  d.  True

  e.  False

Step-by-step explanation:

You want to know the truth value of various logical expressions when b = False, and x = 0.

An And (&&) expression is true if and only if all parts are true. An OR (||) expression is true if any part is true.

When 'b' is false, b&&__ will be false, and !b||__ will be true. This makes (a) and (e) false, and (d) true.

When x = 0, __||x==0 will be true, so (b) is true.

The And (&&) of expression (c) will only be true when both parts are true. For b = False and x = 0, both parts are true, so (c) is true.

   {a, b, c, d, e} = {False, True, True, True, False}

A formula without free variables is a formula that does not contain any variables that are not quantified.

Sentences are commonly referred to as formulas devoid of any unrestricted variables. These statements hold a truth value independent of the variable values, hence the reason.

Open formulas are frequently referred to as formulas with free variables. These are not actually declarations; instead, they are arrangements that can transform into declarations by allotting definite values to the independent variables.

Formulas without free variables are often easier to work with than formulas with free variables.

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Answer:

\(16-(6.25+2*2.25)\)

Step-by-step explanation:

To find the amount of money she has left, you want to subtract the price of the ticket and the price of the two snacks from the amount of money she starts with.

So we want to subtract 6.25 once and subtract 2.25 twice (because she bought two snacks) from 16

16-6.25-2*2.25

Or you can also do this by adding up the monetary value of the ticket and the snacks and subtract that from the initial amount of money that Parvati has

16-(6.25+2*2.25)

(I am assuming that the "2.2.25" is supposed to say \(2*2.25\))

It depends on the number of variables, if the inequality has one variable, then it is graphed on a number line.

The type of diagram that we need to use depends on the number of variables that we have.

That is the main reason, for example:

x > 2

Is graphed on a number line.

y > 3x + 4

is graphed on a coordinate plane.

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The vertex form of parabola y = x² + 9 · x + 8 is the quadratic equation y + 49 / 4 = (x + 9 / 2)².

Herein we find the equation of a parabola in standard form, that is, a quadratic equation of the form:

y = a · x² + b · x + c

Where:

And we are asked to transform this expression into vertex form, that is, a quadratic equation of the form:

y - k = C · (x - h)²

Where:

This can be done by means of algebra properties. First, write the quadratic equation:

y = x² + 9 · x + 8

Second, use algebra properties until a perfect square trinomial is found:

y = x² + 9 · x + 8

y + 49 / 4 = x² + 9 · x + 81 / 4

Third, factor the perfect square trinomial:

y + 49 / 4 = (x + 9 / 2)²

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Answer:

y-4=-7/4(x+4)

Step-by-step explanation:

Point Slope Form: y-y*sub*1=m(x-x*sub*1)

Parallel lines have the same slope as the line to which they are parallel.

y-4=-7/4(x+4)

Hope this helps :)

The average rate of change for the interval from x =  7 to x =  8 is 35.  

To calculate the average rate of change for the interval from x =  7 to x =  8, we need to find the difference in y- values and divide it by the difference inx-values within that interval.

Let's calculate it step by step using the given table  

For the interval from x =  7 to x =  8  x1 =  7, y1 = -37  x2 =  8, y2 = -2   Difference in y- values Δy =  y2- y1 = -2-(- 37) =  35  

Difference inx-values Δx =  x2- x1 =  8- 7 =  1  

Average rate of change =  Δy/ Δx =  35/ 1 =  35  

Thus, the average rate of change for the interval from x =  7 to x =  8 is 35.   Note: It's important to mention that the values calculated then are grounded solely on the given data. Please  insure you  corroborate the  delicacy of the  handed data and  environment before using the answer in any important or critical  operations.

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Answer:

b. g(x)=|x+3|-1

Step-by-step explanation:

The total value of the furniture sold by Joyce last week is A = $ 6,733.33

Given data ,

Let's call the value of the furniture Joyce sold "x".

She receives 10% commission on the first $1,200 of sales, which is $120:

Commission on first $1,200 = 0.1 * 1200 = 120

The remaining sales that she earns commission on is the difference between the total value of the furniture sold and the first $1,200:

Remaining sales = x - 1200

She earns 15% commission on the remaining sales, which is 0.15 times the remaining sales:

Commission on remaining sales = 0.15 * (x - 1200)

Her total earnings from commission last week was $950. So we can write an equation:

Commission on first $1,200 + Commission on remaining sales = $950

Substituting the expressions we found for the two commissions, we get:

120 + 0.15(x - 1200) = 950

120 + 0.15x - 180 = 950

On simplifying the equation , we get

0.15x - 60 = 950

0.15x = 1010

x = 6,733.33

Hence , the value of the furniture Joyce sold last week was $6,733.33

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