what ac is equal to

Answer: 27

Step-by-step explanation:

Mean = Sum of data/Number of data = (2 + 7 + x)/3 = 12

(x+9)/3 = 12

x+9 = 36

x = 27

The distance between the two stations is 360km.

Speed is the rate of change of distance.

Rate is a measure of one quantity against another in this case distance and time.

Analysis:

time at station A = 12:24

time at station B = 14:12

time spent = 14:12 - 12:24 = 1 hour 48 minutes = convert 48 minutes to hour

we divide 48 by 60 = 0.8

Total time = 1.8 hours

Distance = speed x time = 200 x 1.8 = 360 km

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The formula is [tex]\frac{n(n+1)(2n+1)}{6}[/tex]

What are series?

In mathematics, we can describe a series as adding infinitely many numbers or quantities to a given starting number or amount.

We will find the formula as shown as below:

Let [tex]S=1+2^2+3^2+4^2+................+n^2[/tex]

We know [tex](n+1)^3=n^3+3n^2+3n+1[/tex]

[tex](1+1)^3=1^3+3(1)^2+3(1)+1[/tex]

[tex](2+1)^3=2^3+3(2)^2+3(2)+1[/tex]

[tex](3+1)^3=3^3+3(3)^2+3(3)+1[/tex]

.

.

[tex](n+1)^3=n^3+3(n)^2+3(n)+1[/tex]

On adding

[tex]2^3+3^3+4^3......(n+1)^3=(1^3+2^3+3^3+.....+n^3)+3(1^2+2^2+.....+n^2)+3(1+2+3....n)+(1+1+1+....+1)[/tex]

[tex]2^3+3^3+4^3......(n+1)^3-(1^3+2^3+3^3+.....+n^3)=3S+\frac{3n(n+1)}{2}+(1+1+1+....+1)[/tex]

[tex](n+1)^3-1^3=3S+\frac{3n(n+1)}{2} +n[/tex]

[tex]n^3+3(n)^2+3(n)+1-1=3S+\frac{3n(n+1)}{2} +n[/tex]

[tex]2n^3+6n^2+6n=6S+3n^2+3n+2n[/tex]

[tex]6S=2n^3+3n^2+n[/tex]

[tex]6S=2n^2(n+1)+n(n+1)[/tex]

[tex]6S=(n+1)(2n^2+n)[/tex]

[tex]6S=n(n+1)(2n+1)[/tex]

[tex]S=\frac{n(n+1)(2n+1)}{6}[/tex]

Hence, the formula is [tex]\frac{n(n+1)(2n+1)}{6}[/tex]

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The two possible solutions to the given equation ( 6x^2-35 = -11x ) are x = 5/3 and x = -7/2

Given the equation; 6x² - 35 = -11x

The quadratic formula is expressed as;

x = [ -b±√( b² - 4(ac)  ]/2a

First, we re-arrange our equation in the form of ax² + bx + c = 0

6x² + 11x - 35 = 0

We substitute into the formula.

x = [ -b±√( b² - 4(ac)  ]/2a

x = [ -11±√( 11² - 4( 6 × -35 )  ]/2×6

x = [ -11±√( 121 + 840 ]/12

x = [ -11±√961 ]/12

x = [ -11 ± 31 ]/12

x = (-11 + 31)/12,  (-11 + 31 )/12

x = 20/12,  -42/12

x = 5/3, -7/2

Therefore, the two possible solutions to the given equation ( 6x^2-35 = -11x ) are x = 5/3 and x = -7/2

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Answer:

B

Step-by-step explanation:

the value of the x should be the same if we want to verify whether x+2 is a factor of f(x)

so if x=-2 ,f(-2) = 29

x+2=0 f(0) = 1

f(0) [tex]\neq[/tex] f(-2) ,so x+2 is not a factor

what it actually means it that if we move the graphic of f(x) to left along to x axis 2 units, the graphic of new one cannot coincide with the original one.

The permutations is computed below.

1. Evaluate 9P4

9P4 = 9!/(9 - 4)

= 9!/5!

= (9 × 8 × 7 × 6)

= 3024

2. How many ways can 5 students sit on a row of 15 chairs for a photograph?

= 15!(15 - 5)

= 15!/10!

= (15 × 14 × 13 × 12 × 11)

= 360360

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Quadratic expressions are mathematical expressions that have the power of one of its alphabets being equal to and not more than two. The given expression in the question can be simplified as 81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex]  - 45[tex]x^{2}[/tex] - 54x - 112

Algebraic expressions are mathematical expressions that consist of given number(s) and alphabet(s). When the power (exponential) of one of the alphabets is given as two, then the expression can be classified as a quadratic expression.

Thus the given expansion of the quadratic expression can be simplified as follows:

([tex]9x^{2}[/tex] + 9x - 4)([tex]9x^{2}[/tex] + 9x - 10) - 72

But,

([tex]9x^{2}[/tex] + 9x - 4)([tex]9x^{2}[/tex] + 9x - 10) = [tex]9x^{2}[/tex]([tex]9x^{2}[/tex] + 9x - 10) + 9x([tex]9x^{2}[/tex] + 9x - 10) - 4([tex]9x^{2}[/tex] + 9x - 10)

               = 81[tex]x^{4}[/tex] + 81[tex]x^{3}[/tex] - 90[tex]x^{2}[/tex] + 81[tex]x^{3}[/tex] + 81 [tex]x^{2}[/tex] - 90x - 36 [tex]x^{2}[/tex] + 36x - 40

               = 81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex]  - 45[tex]x^{2}[/tex] - 54x - 40

So that we have;

(81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex]  - 45[tex]x^{2}[/tex] - 54x - 40) - 72  = 81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex]  - 45[tex]x^{2}[/tex] - 54x - 40 -72

                  = 81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex]  - 45[tex]x^{2}[/tex] - 54x - 112

Thus the simplification of the given expression is 81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex]  - 45[tex]x^{2}[/tex] - 54x - 112

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Answer:  Choice C

Reason:

The curve is below the x axis on the interval [tex]-\infty < \text{x} < 3[/tex] which shortens down to the interval notation [tex](-\infty, 3)[/tex], so this is when f(x) < 0.

The number of individuals who participated in the entire experiment was 80.

In the question, we are informed that an Independent group experiment or between-subjects experiment comparing four treatment conditions produces 20 scores in each treatment condition.

We are asked to find the number of individuals who participated in the entire experiment.

The number of treatment conditions in the experiment is given to be 4.

The scores in each treatment condition for the experiment is given to be 20.

The total number of individuals who participated in the experiment will be the product of the number of treatment conditions in the experiment and the scores in each treatment condition for the experiment.

Thus, the number of individuals who participated in the entire experiment = 4*20 = 80.

Thus, the number of individuals who participated in the entire experiment was 80.

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The Polynomial Roots are given as follows:
 

x₁=−1.2085

x₂=0.2709+1.2576i

x₃=0.2709−1.2576i

It is to be noted that the Polynomial 3x³+ 2x2 + 3x + 6 has no real rational roots that can be found using the rational root text. Hence, this was solved using the Qubic Formulas.

The roots (also known as zeroes or solutions) of a polynomial P (x) P(x) P(x) are the x values for which P (x) P(x) P(x) equals zero.

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​

Answer: 12

Step-by-step explanation:

I got it right

Prediction of the value of the dependent variable outside the experimental region is called extrapolation.

According to the question,

Prediction of the value of the dependent variable outside the experimental region is called extrapolation.

Extrapolation is the statistical method beamed at understanding the unknown data from the known data.

Hence, prediction of the value of the dependent variable outside the experimental region is called extrapolation.

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Step-by-step explanation:

Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

You need to add the amount Shawna & Ryan ate together, then subtract it from 1 to find the amount of pizza that was left for Dominic to eat.

[tex]\frac{1}{3}[/tex] + [tex]\frac{1}{2}[/tex] = ?

Make all the denominators the same to add fractions.

[tex]\frac{1}{3}[/tex]  is [tex]\frac{2}{6}[/tex]

[tex]\frac{1}{2}[/tex]  is [tex]\frac{3}{6}[/tex]

[tex]\frac{2}{6}[/tex] +  [tex]\frac{3}{6}[/tex] = [tex]\frac{5}{6}[/tex]

1 -  [tex]\frac{5}{6}[/tex] = [tex]\frac{1}{6}[/tex]

The points which represents the vertices of the given equation are; (15, −2) and (−1, −2).

The complete question gives the equation of the ellipse as; (x-7)²/64+(y+2)²/9=1.

Since, It follows from convention that general equation of ellipse with centre as (h, k) takes the form;

(x-h)²/a² +(y-k)²/b² = 1.

Consequently, it follows from observation that the value of a and b in the given equation in the task content is; √64 = 8 and √9 = 3 respectively.

Since, 8 > 3, The vertices of the ellipse are given by; (h±a, k).

The vertices in this scenario are therefore;

(7+8, -2) and (7-8, -2).

= (15, -2) and (-1, -2).

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The solution of the inequality, |x + 6| ≥ 5 is given as follows,

(A) x > -1

(B) It follows that x either belongs to the interval (-∞, -11) or to the interval (-1,∞) for the given absolute inequality.

(A) Solving the Given Inequality:

|x + 6| ≥ 5

x+6 ≥ 5 or x+6 ≤ (-5)

x+6-6 ≥ 5-6 or x+6-6 ≤ (-5)-6

x ≥ -1 or x ≤ -11

Hence the solution of the given inequality is given as,

x ∈ (-∞, -11] or x ∈ [-1, ∞)

(B) Description of the Solution

From the given absolute inequality, it can be concluded that x either belongs to the interval (-∞, -11] or to the interval [-1, ∞). Hence, on the number line, the solution of the inequality will be shown as a shaded region from -∞ to -11 and from -1 to ∞. The area between -1 and -11 will remain unshaded.

In the deduced solution, the interval is either open or closed on both sides. Open interval means the extreme value is not includes. On the other hand, closed interval indicates inclusion of the extreme point in the solution of the inequality.

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Answer:

circle

Step-by-step explanation:

any point on the circumference of a circle is equidistant from the centre.

The shortest possible time to perform the tasks is 30 minutes, these activities would be performed in this time by the couple made up of you and your aunt 1.

To calculate the shortest time to complete the wedding tasks, we must carefully observe the information in the table and identify the time that each person takes to complete the tasks. Subsequently, we must identify the people who take the shortest time, in this case it is you and your aunt 1 as shown below:

You

aunt 1

Additionally, we must subtract the two values, to know how long it will take in total for both people to perform the three required activities.

According to the above, the most efficient couple is your aunt 1 and you because you will take 30 minutes to complete the activities.

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Answer:

Answer:The chocolate are 0.0042 lighter than the stated on the label

Answer:

L' (-1, 1)

M' (1, 2)

N' (1, -1)

Answer:

[tex]\textsf{2.} \quad y=\dfrac{35}{x}[/tex]

[tex]\textsf{3.} \quad y=-\dfrac{90}{x}[/tex]

[tex]\textsf{4.} \quad y=\dfrac{63}{x}[/tex]

[tex]\textsf{5.} \quad y=-\dfrac{112}{x}[/tex]

Step-by-step explanation:

If y is inversely proportional to x, then:

[tex]y \propto\dfrac{1}{x} \implies y=\dfrac{k}{x} \quad \textsf{(for some constant }k)[/tex]

Question 2

Substitute one of the given ordered pairs into the inverse variation equation and solve for k:

[tex]\implies 7=\dfrac{k}{5}[/tex]

[tex]\implies 7 \cdot 5=\dfrac{k}{5} \cdot 5[/tex]

[tex]\implies k=35[/tex]

Substitute the found value of k into the formula to create the inverse variation equation for the given ordered pairs:

[tex]\implies y=\dfrac{35}{x}[/tex]

Question 3

Substitute y = -15 and x = 6 into the formula and solve for k:

[tex]\implies -15=\dfrac{k}{6}[/tex]

[tex]\implies -15 \cdot 6=\dfrac{k}{6} \cdot 6[/tex]

[tex]\implies k=-90[/tex]

Substitute the found value of k into the formula to create the inverse variation equation for the given values:

[tex]\implies y=-\dfrac{90}{x}[/tex]

Question 4

Substitute one of the given ordered pairs into the inverse variation equation and solve for k:

[tex]\implies 9=\dfrac{k}{7}[/tex]

[tex]\implies 9 \cdot 7=\dfrac{k}{7} \cdot 7[/tex]

[tex]\implies k=63[/tex]

Substitute the found value of k into the formula to create the inverse variation equation for the given ordered pairs:

[tex]\implies y=\dfrac{63}{x}[/tex]

Question 5

Substitute one of the given ordered pairs into the inverse variation equation and solve for k:

[tex]\implies -16=\dfrac{k}{7}[/tex]

[tex]\implies -16 \cdot 7=\dfrac{k}{7} \cdot 7[/tex]

[tex]\implies k=-112[/tex]

Substitute the found value of k into the formula to create the inverse variation equation for the given ordered pairs:

[tex]\implies y=-\dfrac{112}{x}[/tex]

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Answer:

its not 15 points ):

Step-by-step explanation:

Answer:

y = |x + 8|

Explanation:

Please see the table attached below.

Answer:y=|x+8|

Step-by-step explanation:

The circumference and area of the circle are 27. 0 inches and 58. 0 inches square respectively.

The formula for circumference of a circle is given as;

Circumference = 2 π r

We have diameter = 8. 6 inches

Radius = diameter/ 2

Radius = 8.6/2 = 4. 3 inches

Circumference = 2 × 3. 14 × 4. 3 = 27. 0 Inches

The formula for area of a circle = π r ^2

Area = 3. 14 × 4. 3 × 4. 3

Area = 58. 0 Inches square

Thus, the circumference and area of the circle are 27. 0 inches and 58. 0 inches square respectively.

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B because it’s a linear graph.

Answer:

No largest no could be 100

Step-by-step explanation:

Yes, the sum of the three numbers is 200, and the largest number can indeed be 75.

Let's assume the three numbers are:

Smallest number = 25

Middle number = x (unknown)

Largest number = 75

The sum of the three numbers is 200, so we can set up the equation:

25 + x + 75 = 200

Now, let's solve for x:

x = 200 - 25 - 75

x = 100

So, the middle number is 100.

Now, we can check if the largest number (75) is correct:

25 + 100 + 75 = 200

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The function for the given graph is f(x) = (x - 4)(x + 2)(x + 4).

In the given graph,

The points that lie on the x-axis are (-4, 0), (-2, 0), and (4, 0) where y-coordinate is 0 and the x coordinates are -4, -2, and 4.

On solving the given functions,

Option A:

f(x) = (x - 4)(x + 2)(x + 4)

Since y = 0 consider f(x) becomes 0

So,

(x - 4)(x + 2)(x + 4) = 0

According to the zero product rule,

x - 4 = 0, x + 2 = 0, and x + 4 = 0

⇒ x = 4, x = -2 and x = -4.

Thus, option A represents the function of the given graph.

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Disclaimer: The question given on the portal was incomplete. Here is the complete question.

Question:

Select the correct answer. which equation could represent the graphed function (given in the figure below)?

The volume of the shipping crate is 36 m per cube.

According to the statement

we have given that the

A rectangular-prism-shaped toy chest is 2 m by 1 m by 1 m. A shipping crate is packed with 18 of these toy chests.

And we have to find the volume of the crate.

So,

volume of toy = 2*1*1

Volume of toy = 2 meter per cube.

And Now,

The volume of shipping crate = Volume of one toy* total number of toys in crate

so, Substitute the values in the formula then

The volume of shipping crate = Volume of one toy* total number of toys in crate

The volume of shipping crate = 2*18

The volume of shipping crate = 36 m per cube.

So, The volume of the shipping crate is 36 m per cube.

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x = 4 would be the solution of the given problem.

I can't speak to the first part of this question, as I don't totally have context for what they're asking, but we can solve for x using one of the laws of logarithms, namely:

log.m + log.n = log.mn

Using this law, we can combine and rewrite our initial equation as

log(x^2- x) = 3

Remember that logarithms are simply another way of writing exponents. The logarithm  is just another way of writing the fact . Keeping that in mind, we can express our logarithm in terms of exponents as

log(x^2- x) = 3 --> x^2- 2x = 8

2³ = 8, so we can replace the left side of our equation with 8 to get

x^2 - 2x - 8 =0

(x-4)(x+2) = 0

Hence x = 4 0r -2. As x cannot be negative so it would be 4.

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Answer:

[tex]-\frac{61}{14}[/tex]

Step-by-step explanation:

Question: 5 - 7(z+1) = 7(-9-3z)

We multiply the number in front of the bracket first, since that is multiplication.

--> 5 -7z -7 = -63 - 21z

--> -7z -2 = -63 - 21z

Now, we move all the z and all the numbers to each side.

--> -7z +21z = -63 +2

--> 14z = -61

--> z = -61/14

This cannot be simplified further, so z is -61/14.