Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. Group of answer choices 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x + 9) = –3 + 9 2(x2 + 6x) = –3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x) = 3

Answer:

\(y = 4\)

Step-by-step explanation:

Because no matter what value x is, y is always 4

Answer:

Area = 324ft²

Perimeter = 72ft

Step-by-step explanation:

Area of a square = length²

Area of a square = (18ft)² = 324ft²

Perimeter of a square = 4*length

Perimeter of a square = 4ft*18 = 72ft

Answer:

(0.9, -2.1)

Step-by-step explanation:

should be correct from what I looked up on how to find the coordinates 3/10 of the way from ordered pair A to ordered pair B

Suppose that quiz scores in a beginning statistics class have a mean of 7.1 with a standard deviation of 0.4, the range in which at least 75% of the data will reside is from 6.3 to 7.9.

Chebyshev's Theorem is a statistical tool that provides a range for how much data is likely to fall within a certain number of standard deviations from the mean.

Specifically, it tells us that, for any set of data, no matter how it is distributed, at least 1 - (1/k^2) of the data will fall within k standard deviations from the mean, where k is any positive number greater than 1.

In this case, we want to find the range in which at least 75% of the data will reside. We can use Chebyshev's Theorem to determine the minimum value of k that will give us this range. We know that at least 75% of the data should fall within two standard deviations from the mean, so we can set k = 2.

Using Chebyshev's Theorem, we can say that at least 1 - (1/2^2) = 75% of the data will fall within 2 standard deviations from the mean. The standard deviation is 0.4, so two standard deviations would be 2 * 0.4 = 0.8.

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The axis of symmetry of the function f(x) = x² - 6x-1 is equal to 3.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry, Xmin = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

By substituting the parameters, we have the following:

Axis of symmetry, Xmin = -b/2a

Axis of symmetry, Xmin = -(-6)/2(1)

Axis of symmetry, Xmin = 6/2

Axis of symmetry, Xmin = 3.

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Using the given information, Billy's grade in his Math class will be 94.85%

From the question, we are to determine what the grade of Billy should be.

From the given information,
Billy had 100% in his Math class and he got 27/34 on his midterm

Also,

The midterm is 25%

This means the exam is 75%

Billy's grade will be

100% of 75 + 27/34 of 25

= 75 + 19.85

= 94.85

Hence, Billy's grade will be 94.85%

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It is proved that \(x[n-n_1] × h[n-n_2] = y[n-n_1-n_2]\)

How to prove \(x[n-n_1] × h[n-n_2] = y[n-n_1-n_2]\)?

To prove that \(x[n-n_1] × h[n-n_2] = y[n-n_1-n_2]\) , we need to express the convolution sum of

\(x[n-n_1] \: and \: h[n-n_2]\), and then simplify it to obtain \(y[n-n_1-n_2]\)

Let's start by expressing the convolution sum of \(x[n-n_1] \: and \: h[n-n_2]\)

:\(x[n-n_1] ×h[n-n_2] = ∑ x[k-n_1] × h[n-n_2-k]\) where the summation is over all possible values of k.

Now, we can replace k with \(n - n_1 - m\), which gives:

\(x[n-n_1] × h[n-n_2] = ∑ x[n-n_1-m] × h[n-n_2-n+n_1+m]\)

Next, we can rearrange the terms inside the summation to obtain:

\(x[n-n_1] × h[n-n_2] = ∑ x[n-m] × h[n-n_1-n_2+m]\)

Notice that the expression inside the summation is identical to the definition of y[n], so we can replace it with y[n] and simplify:

\(x[n-n_1] × h[n-n_2] = ∑ x[n-m] × h[n-n_1-n_2+m] = ∑ y[n-m] \)

The last expression is the convolution sum of x[n] and h[n], which we know equals y[n]. Therefore:

\(x[n-n_1] × h[n-n_2] = y[n-n_1-n_2]\)

And we have proven that \(x[n-n_1] × h[n-n_2] = y[n-n_1-n_2]\)

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The linear function for the total cost C is:

A function is an expression, rule, or law that defines a relationship between one variable.

Example:

\(f(\text{x}) = 2\text{x} + 1\)

\(f(1) = 2 + 1 = 3\)

\(f(2) = 2 \times 2 + 1 = 4 + 1 = 5\)

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The total cost for x cubic yards.

\(\bold{C = 28 + 48x}\)

Thus, the function is C = 28 + 48x.

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The correct answer is Option C. The graph represents the function f (x) = StartFraction 1 Over x EndFraction minus 1 is On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = 0.

On a coordinate plane, the graph of a hyperbola is shown.

In quadrant 1, one curve opens up and to the right, while in quadrant 3, the other curve opens down and to the left.

The vertical asymptote is at x = -1, and the horizontal asymptote is at y = 0. This hyperbola is symmetrical across both the x and y axes.

The function f(x) = 1/x - 1 has a vertical asymptote at x = 0 because the denominator approaches zero as x approaches zero.

A fraction with a denominator of zero cannot exist.

The horizontal asymptote of this function is y = -1 because as x approaches infinity or negative infinity, f(x) approaches -1.

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Answer:

Question 1 : Pierre is right

Question 2 : 0.85 (because 1 - 0.15 = 0.85)

Question 3 : Less than 1

Step-by-step explanation:

Answer: 0.418 < p < 0.512

Step-by-step explanation: A 95% conifdence interval for a population proportion is given by:

\(p + z\sqrt{\frac{p(1-p)}{n} }\)

where:

p is the proportion

z is score in z-table

n is sample size

The proportion for people who said "yes" is

\(p=\frac{202}{434}\) = 0.465

For a 95% confidence interval, z = 1.96.

Calculating

\(0.465 + 1.96*\sqrt{\frac{0.465(0.535)}{434} }\)

\(0.465 + 1.96*\sqrt{0.00057}\)

0.465 ± 1.96*0.024

0.465 ± 0.047

Interval is between:

0.465 - 0.047 = 0.418

0.465 + 0.047 = 0.512

The interval with 95% of confidence is between 0.418 and 0.512.

Answer:

D=340

Step-by-step explanation:

D=360 - 180/9

 =360 - 20

 =340

Answer:

D = 340

Step-by-step explanation:

First, we input the value 9 in place of the variable N.

\(d = 360 - \frac{180}{n} \\ d = 360 - \frac{180}{9} \)

Next, we begin to perform the order of operations to solve the equation. The Order of Operations (or PEMDAS) dictates that, from left to right, we should start from:

Parentheses

Exponents

Multiplying and Dividing

Adding and Subtracting

So first, we'll divide 180 by 9.

\(d = 360 - \frac{180}{9} \\ d = 360 - 20\)

Finally, we'll subtract 20 from 360.

\(d = 360 - 20 \\ d = 340\)

Answer:

632.83mm²

Step-by-step explanation:

Applying Pythagorean theorem to triangle SOH

SH² = SO² + OH²

SH = \(\sqrt{(15.4)^2+(7.2)^2}=17mm\)

Since the base of the pyramid is a regular pentagon, angle OAH
is 108°/2 = 54°.

AH = 7.2/tan 54° = 5.23mm

So AB = 2AH = 10.46mm

The area of triangle SAB is:

A1 = 1/2 × SH × AB = 1/2 × 17 × 10.46 = 88.91mm²

The area of all triangles is

A2 = 5 × A1 = 5 × 88.91 = 444.55mm²

The area of the base is:

A3 = (perimeter × apothem)/2 = (5 × 10.46 × 7.2)/2 = 188.28mm²

The surface area of the pyramid is:

A2 + A3 = 444.55 + 188.28 = 632.83mm²

Step-by-step explanation:

the surface area is the sum of the base area (pentagon) and the 5 side triangles (we only need to calculate one and then multiply by 5, as they are all equal).

these side triangles are isoceles triangles (the legs are equally long).

the usual area formula for a pentagon is

1/2 × perimeter × apothem

the apothem is the minimum distance from the center of the pentagon to each of its sides.

in our case this is 7.2 mm.

how to get the perimeter or the length of an individual side of the pentagon ?

if the apothem of a pentagon is given, the side length can be calculated with the formula

side length = 2 × apothem length × tan(180/n)

where 'n' is the number of sides (5 in our case). After getting the side length, the perimeter of the pentagon can be calculated with the formula

perimeter = 5 × side length.

so, in our case

side length = 2 × 7.2 × tan(180/5) = 14.4 × tan(36) =

= 10.4622124... mm

perimeter = 5 × 10.4622124... = 52.31106202... mm

area of the pentagon = 1/2 × perimeter × apothem =

= 1/2 × 52.31106202... × 7.2 = 188.3198233... mm²

now for the side triangles.

the area of such a triangle is

1/2 × baseline × height

baseline = pentagon side length

height we get via Pythagoras from the inner pyramid height and the apothem :

height² = 7.2² + 15.4² = 51.84 + 273.16 = 289

height = 17 mm

area of one side triangle =

1/2 × 10.4622124... × 17 = 88.92880543... mm²

all 5 side triangles are then

444.6440271... mm²

and the total surface area is then

444.6440271... + 188.3198233... = 632.9638504... mm²

≈ 632.96 mm²

Answer: 14

Step-by-step explanation:

300 minus 80 = 220

220 is the budget for the shirts so we divide 220 by 15 to get 14

Hope this helps!

Answer:14 shirts

Step-by-step explanation:300- 80 = 220

220/ 15 = 14.6  round 14.6 to 14 (because you cant buy half a shirt)

you can get 14 shirts

Answer:

24.5%

Step-by-step explanation:

Given

P(Off-Campus) = 0.30

P(Part-Time Job | Off-Campus) = 0.62

P(Part-Time Job | On-Campus) = 0.65

Inferred

P(On-Campus) = 0.70

P(No Part-Time Job | Off-Campus) = 0.38

P(No Part-Time Job | On-Campus) = 0.35

Calculation

P(No Part-Time Job | On-Campus) = P(No Part-Time Job ∩ On-Campus)/P(On-Campus)

0.35 = P(No Part-Time Job ∩ On-Campus)/0.70

0.245 = P(No Part-Time Job ∩ On-Campus)

Therefore, 24.5% of students that live on campus do not have a part-time job.

Answer:

Step-by-step explanation:

all of the angles complete a circle so they must add up to 360 degrees.

230 + 38 + 52 + x = 360

320 + x = 360

x = 40 degrees

Answer:

10  miles

Step-by-step explanation:

tree points form a right triangle with sides 8, 6 and x

x is the hypotenuse of the triangle

x²=8²+6²=100

x=√100=10  miles

The equation of the cobb-Douglas production function in this case is \(Y = A \times K^{0.2} \times L^{0.8}\)

The Cobb-Douglas production function is a widely used economic model that explains how inputs such as labor and capital contribute to the production of goods and services. In this particular case, we assume that the share of capital in output is 20%, which means that 20% of the output is generated by capital and 80% by labor.

The equation of the Cobb-Douglas production function can be written as:

\(Y = A \times K^{\alpha} \times L^{\beta}\)

where Y is the output, A is a measure of the productivity of the economy, K is the amount of capital, L is the amount of labor, and α and β are the shares of capital and labor in output, respectively.

In this case, since the share of capital in output is 20%, α = 0.2 and β = 0.8. Therefore, the equation of the Cobb-Douglas production function becomes:

\(Y = A \times K^{0.2} \times L^{0.8}\)

This equation shows how changes in the amount of capital and labor affect the output of an economy. For example, an increase in the amount of capital will increase output, but the effect will be smaller than an equivalent increase in the amount of labor, due to the lower share of capital in output.

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Answer:

Last option:

\(\dfrac{4x^4y^2}{z}\)

Step-by-step explanation:

Original expression is

\(\dfrac{12x^6y^{-4}z^2}{3x^2y^{-6}z^3}\\\\\)

Let us eliminate the obvious wrong answers

\(\dfrac{12}{3} = 4\\\\\)

so the coefficient in the answer should be 4.

We can eliminate first and third choices

Now for each term with the same variable, compute the division
\(\dfrac{x^6}{x^2} = x^{6-2} = x^4\\\\\)

Second choice is out so the last choice is the correct one.

We can go further with the other terms

\(\dfrac{y^{-4}}{y^{-6}} = y^{-4 - (-6)} = y ^{-4+6} = y^2\)

\(\dfrac{z^2}{z^3} = z^{2-3} = z^{-1} = \dfrac{1}{z}\)

Multiplying all these individual terms gives
\(4 \cdot x^4 \cdot y^2 \cdot \dfrac{1}{z}\\\\= \dfrac{4x^4y^2}{z}\)

The equation given in slope-intercept form does not represent the graph because the y-intercept of the graph is equal to 4 while the y-intercept of the equation is equal to 5.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Based on the information provided regarding the equations and graphs, the y-intercept are as follows:

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The expressions that are equivalent to the expression 8x + 32y are:

4(4 ⁢x + 8y) − 2⁢(4x)

8(x + 4y)

Equivalent expressions are expressions that work the same even though they look different.

If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s).

Let's simply the options to see if they are equivalent to the expression 8x + 32y:

4(4 ⁢x + 8y) − 2⁢(4x)   = 16x + 32y - 8x

                               = 8x + 32y

8(x + 4y)  = 8x  + 32y

(2x + 12y) + (6x + 18y) = 2x + 6x + 12y + 18y

                                   = 8x + 30y

Therefore, only 4(4 ⁢x + 8y) − 2⁢(4x) and 8(x + 4y)  are equivalent to the expression below.

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Complete Question

Which of the following expressions are equivalent to the expression below?

8x + 32y

4(4 ⁢x + 8y) − 2⁢(4x)

8(x + 4y)

(2x + 12y) + (6x + 18y)

Answer:

-9/14 so the answer is B

Step-by-step explanation:

Hope this helps

Answer:

b <3

Step-by-step explanation:

edge 2021

Answer:

x=-4 is the answer to you equation

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Basically, for every 5 boys there is 3 girls. A simple way to solve this, but longer, yet the one I personally use count up, go 5*2 3*2 and find which one adds up to 64. Once you get to 64, total including the product of both, you will have the amount of boys and girls. In this case

5*8 and 3*8 = 64

3*8 = 24

5*8 = 40

There are 24 girls

Its an acute triangle by angles.

Its a NONE by sides.

Answer:

Y varies directly with x.

This can be represented below as

Substitute the value of y=24 and x=6 to find the value of k

Substitute k=4 to get the equation connecting y and x

Substitute the value of x=8 to get the value of y

Hence,

The value of y when x= 8 is

Answer:

  a) False

  b) True

Step-by-step explanation:

a) h(1) = 0/0, which is certainly undefined. There may or may not be a finite limit at that point, so the line x=1 is not necessarily a vertical asymptote.

The assertion that x=1 is necessarily a vertical asymptote is False.

__

b) h(2) = 4/0, another undefined value. However, we can be certain that the limit of h(x) as x → 2 is infinite, meaning the line x=2 will be a vertical asymptote.

The assertion that x=2 is necessarily a vertical asymptote is True.

_____

The graph shows a simple example of a function that has the given characteristics.

Answer:

there is no picture?

Step-by-step explanation: