The property that justifies the sentence 6a2 + 2a = 2a(3a + 1) is:

Answer:

b. x=2

Step-by-step explanation:

The axis of symmetry of a parabola gives us a line of symmetry where the parabola appears the same but flipped on either side. It passes through the parabola's vertex, or the minimum/maximum point of the parabola. Here, we can see that the parabola's minimum point occurs when x=2. Therefore, its axis of symmetry is x=2.

I hope this helps!

Answer:

1 kg of mushrooms costs £2.7.

Step-by-step explanation:

Step 1: Write equations.

Let a be the cost of apples per kg and m the cost of mushrooms per kg.

First equation: Ibrar buys 3 kg of apples. He also buys 0.4 kg of mushrooms. The total cost is £6.93.

\(3a + 0.4m = 6.93\)

Second equation: 1 kg of apples cost £1.95.

\(a = 1.95\)

Step 2: Solve the system of equations.

1) \(3a + 0.4m = 6.93\)

2) \(a = 1.95\)

Substitute a in the first equation with a from second.

\(3a + 0.4m = 6.93\\3(1.95) + 0.4m = 6.93\)

Solve for m.

\(5.85 + 0.4m = 6.93\\0.4m = 6.93 - 5.85 \\0.4m = 1.08\\m = \frac{1.08}{0.4}\\m = \text{\£}2.7\)

The cost of 1 kg of mushrooms is £2.7.

Two or more expressions with an Equal sign is called as Equation.

Given that Ibrar buys 3kg of apples

Ibrar buys 0.4kg of mushrooms.

The total cost is £6.93

3x+0.4y=6.93...(*)

1kg of apples cost is £1.95

x=1.95

Substitute the value of x in *

3(1.95)+0.4y=6.93

5.85+0.4y=6.93

Subtract 5.85 on both sides

0.4y=6.93-5.85

0.4y=1.08

Divide both sides by 0.4

y=2.7

Hence, the cost of 1 kg of mushrooms is £2.7.

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The number of ways in which Kristen can rank her favorite four from 8 using permutations is 1680.

The permutation is a way of finding the number of ways of selecting a set of articles from a larger set of articles, with the order of selection being significant.

If we want to choose r items from n items, where the order of selection is significant, then we can find the number of ways of doing this using the permutation as follows:

nPr = n!/{(n - r)!}.

In the question, we are asked to find the number of ways Kristen can rank her favorite four investments from the 8 potential investments that her financial advisor has given her.

Thus, using permutations, we need to select 4 items from 8 items, with order of selection being significant.

Substituting n = 8, and r = 4 in the formula, we get:

8P4 = 8!/{(8 - 4)!}

= 8!/4!

= 5 * 6 * 7 * 8

= 1680.

Thus, the number of ways in which Kristen can rank her favorite four from 8 using permutations is 1680.

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the rate of change of height at h = 15cm, 0. 0159 cm/s

What is Rate?

A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.

When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.

Beads are dropped to create a conical pile such that the ratio of its radius to the height of the pile is constant at 2:3.

Volume is increasing at a rate of 5 cm3/s.

The volume of a Cone: \(\frac{1}{3}*\pi *r^{2} *h\)

given r/h =2/3

so V =  \(\frac{1}{3}*\pi *(2/3 *h)^{2} *h\)

V = \(\frac{4}{27} * \pi *h^{3}\)

So \(\frac{dv}{dt} =\frac{4}{9} * \pi *h^{2}\) \(\frac{dh}{dt}\)

\(\frac{dh}{dt}\) = \(\frac{5}{4/9 *\pi *225}\)

\(\frac{dh}{dt} = \frac{1}{20*\pi }\)

=0. 0159 cm/s

Hence the rate of change of height at h = 15cm, 0. 0159 cm/s

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The value of the expression e⁻⁴ is 0.0183 to four decimal places.

We are given the expression:

e⁻⁴

We need to evaluate the expression to four decimal places.

Now, we know that the value of e is:

e = 2.71828182846

Now, e⁻⁴ can also be written as:

e⁻⁴ = 1 / e⁴

Substituting the value of e, we get that:

1 / e⁴ = 1 / (2.71828182846)⁴

= 1 / 54.5981500331

= 0.0183156389

Now rounding off to 4 decimal places, we get that:

= 0.0183

Therefore, the value of the expression e⁻⁴ is 0.0183.

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The integral for the area of the surface obtained by rotating the curve about the x-axis and the y-axis, are:

S = ∫[3,5] 2πxe−x√(1+(e−x−xe−x)²)dx and S = ∫[3e−3,5e−5] 2π(ln(y)/y)√(1+(1/y−ln(y)/y)²)dy respectively.

To set up the integral for the area of the surface obtained by rotating the curve about the x-axis and the y-axis, we need to use the formulas for surface area of revolution.

For rotation about the x-axis, the formula is:
S = ∫2πy√(1+(dy/dx)²)dx

For rotation about the y-axis, the formula is:
S = ∫2πx√(1+(dy/dx)²)dy

Plugging in the given curve y = xe−x and the bounds 3 ≤ x ≤ 5, we get:

For rotation about the x-axis:
S = ∫[3,5] 2πxe−x√(1+(e−x−xe−x)²)dx

For rotation about the y-axis:
S = ∫[3e−3,5e−5] 2π(ln(y)/y)√(1+(1/y−ln(y)/y)²)dy

These are the integrals that need to be evaluated to find the area of the surface obtained by rotating the curve about the x-axis and the y-axis.

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In this country, the currency is called sirktian. If a person earns 0 to 26,400 sirktians, then they have to pay 0 sirktians in tax. If they earn more than that, then they have to pay a flat tax of 27% on everything over 26,400 sirktians.

Thus, for an individual earning 28,700 sirktians, the tax they owe would be:Tax on the first 26,400

sirktians = 0 sirktians Tax on the remaining 2,300 sirktians (28,700 - 26,400) = 27% of 2,300 sirktians = (27/100) × 2,300 sirktians = 621 sirktians

Therefore, the total tax owed by the individual earning 28,700 sirktians would be 0 + 621 = 621 sirktians.The piecewise function that describes the amount of taxes paid, T, as a function of sirktians earned, x, for individuals paying personal income tax in this country is:T

(x) = {0 if 0 ≤ x ≤ 26,400; 0.27(x - 26,400) if x > 26,400}

The graph of this function is shown below:

Therefore, the correct graph is (D).

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Answer:

x = 3.86

a = 5.86

Step-by-step explanation:

From the triangles attached,

By applying cosine rule in triangle 1,

cos(50)° = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\)

cos(50)° = \(\frac{x}{6}\)

x = 6cos(50)°

x = 3.86

Now we apply sine rule in the second triangle,

sin(23)° = \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\)

sin(23)° = \(\frac{a}{15}\)

a = 15sin(23)°

a = 5.86

Answer:

C

Step-by-step explanation:

angels 5 can't be acute because 6 is acute, 3 and 5 are not congruent.

The statement which is true about angles 3 and 5 is angles 3 and 5 are supplementary angles.

Supplementary angles are those angles whose sum of the angles is 180°.

Common example of supplementary angles is the interior angles of the triangle.

A transversal is a line segment, which intersects two or more other line segments. When a transversal intersects parallel lines many angles are formed.

If two parallel lines are intersected by a transversal, the corresponding angles are congruent.

Here, there are two parallel lines cut by a transversal line.

We have that interior angles on the same side of the transversal line will be supplementary.

That is angles 3 and 5 are supplementary which is why they are congruent.

Hence the statement that angles 3 and 5 are supplementary is the true statement.

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The inequality that represents x is x ≥ 0/

The basic square rοοt οperatiοn. (οften knοwn as the "square rοοt functiοn") is a mapping that applies tο the set οf nοnnegative real numbers. The square rοοt functiοn, in geοmetric terms, cοnverts a square's area tο its side length.

The οrder οf pοsitive numbers is preserved by the square functiοn: greater numbers have larger squares. The square, then, is a mοnοtοnic functiοn οn the range [0, +]. With negative numbers, absοlute values are mοre significant than squares, making it a mοnοtοnically decreasing functiοn οn [(, 0]].

Here, The domain of the graph is domain : [0, +∞)

With this, we can clearly state that 0 < x < +∞

Thus, The inequality that represents x is x ≥ 0

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Answer:

Option A

Step-by-step explanation:

Angular velocity of an object is defined by,

Angular velocity (w) = \(\frac{\triangle \theta}{\triangle t}\)

Here, Δθ = Change in angle of rotation

Δt = Duration or time

In this question Δθ = \(\frac{7\pi }{2}\) radians and Δt = 24 seconds

Therefore, angular velocity = \(\frac{\frac{7\pi }{2} }{24}\)

                                              = \(\frac{7\pi }{48}\) radians per second

Option A is the answer.

Answer:

✔ his effect on others

✔ He was fearful.

✔ He becomes less fearful of Lemon Brown.

Answer:

his effect on others

He was fearful.

He becomes less fearful of Lemon Brown.

Step-by-step explanation:

hi

Answer:

C)

Step-by-step explanation:

one is zero and one is positive. The addition symbol indicates that you are adding a positive number

Answer:

C. Paying a cell phone bill

The coefficient of correlation can be determined using the coefficient of determination, which is given as the square of the correlation coefficient. In this case, the coefficient of determination is 0.81, indicating that 81% of the variability in the dependent variable (y) can be explained by the independent variable (x).

To find the coefficient of correlation, we take the square root of the coefficient of determination. Taking the square root of 0.81 gives us 0.9. However, the coefficient of correlation can be positive or negative, depending on the direction of the relationship between the variables.

Looking at the given regression line y^= -2.88 + 1.77x, the positive slope of 1.77 indicates a positive relationship between x and y. Therefore, the coefficient of correlation would also be positive.

Hence, the answer is (c) +0.90, indicating a positive correlation between the variables.

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Based on the given graph, the following describes the polynomial function.

The function has an odd degree. (Option B)

The function has one turning point. (Option C)

The function does not have a negative leading coefficient since its leading coefficient is positive. It also has x-intercepts at x=-6, x=-2, x=4, and x=6, so the statement "the function has zero x-intercepts" is incorrect.

A polynomial function is a mathematical function that consists of one or more terms, where each term is a constant, a variable, or a product of a constant and a variable raised to a non-negative integer power.

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Are you good at surfing? Is it similar to skateboarding?

The sequence of natural numbers that leaves a remainder of 3 when divided by 10 is:

3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, ...

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The break-even point is 20 units.

The cost and revenue at the break-even point is $4600.

The break-even point is the point at which the cost and revenue are equal. Thus, we can say:

R(x) = C(x)

230x = 220x + 200

230x - 220x = 200

10x = 200

x = 200/10

x = 20

Thus, the break-even point is 20 units

cost and revenue at the break-even point:

Put x = 20 into the C(x) and R(x) respectively

C(x) = 220x + 200

C(20) = 220(20) + 200

C(20) = $4600

R(x) = 230x

R(20) = 230 * 20

R(20) = $4600

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Answer:The value of tangent of theta when theta equals 3pi/4 is -1.

Step-by-step explanation:

Answer:  -1

Step-by-step explanation:

What is tan of theta if theta= 3pi/4?

This is the same as:

What is tan  \(\frac{3\pi }{4}\) ?

You need to look at a unit circle.

At \(\frac{3\pi }{4}\) , the point is \((\frac{-\sqrt{2} }{2} ,\frac{\sqrt{2} }{2})\)             >see image

the x in point (x, y) is cos x, so cos x = \(\frac{-\sqrt{2} }{2}\)

the y in point (x, y) is sin x, so sin x = \(\frac{\sqrt{2} }{2}\)

tanx = sinx / cosx

\(tan x = \frac{\frac{\sqrt{2} }{2}}{\frac{-\sqrt{2} }{2}}\)                                 >Use keep change flip for fractions

\(tan x = \frac{\sqrt{2} }{2}*\frac{2}{-\sqrt{2} }\)                         >simplify

tan x = -1

The sequence of arithmetic sequence be 37, 29, 21, 13 then the 52nd term exists 445.

The term "arithmetic sequence" refers to an ordered collection of numbers with a common difference between each succeeding word.

Arithmetic sequences are those that contain these patterns. The difference between successive terms in an arithmetic series is constant.

An arithmetic sequence, also known as an arithmetic progression, is a set of numbers where each term differs from the one before it. The arithmetic sequence formula makes it simple to determine a term's value and the sequence's common difference.

The AP's first period is 37.

Common difference = 37 - 29 = 29 - 21 = 8.

Let the equation of arithmetic sequence be a + ( n - 1 )d, where d is the common difference and a is the first term.

To find the 52nd term, we get

substitute the values in the above equation, we get

⇒ 37 + ( 52 - 1 )8

simplifying the above equation, we get

⇒ 37 + ( 51 )8

⇒ 37 + 408

⇒ 445

Therefore, the 52nd term of the arithmetic sequence exists 445.

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Hey there! I'm happy to help!

Since we are using graphs, we will do not need to algebraically solve this system of equations.

When you graph a system of equations, the solution is always the point at which the two lines intersect.

Here is our system of equations graphed. We see that the lines intersect at about (1 1/3, 2 1/3). Therefore, the correct answer is C. x=1 1/3, y=2 1/3

Have a wonderful day! :D

In this refinery-type problem, we are given the equation: 10x1 + 5x2 + 5x3 = 300 and 5x1 + 10x2 + 8x3 = 300

The goal is to find the values of x1, x2, and x3 that satisfy both equations simultaneously.

The given refinery-type problem consists of two equations that need to be solved simultaneously to find the values of x1, x2, and x3. To solve this problem, we can use a method called simultaneous equation solving. However, since the problem does not specify a method, I will  provide the steps to set up the equations for further solving.

The steps are explained as follows to find the values of x1, x2, and x3:
1. Choose one of the equations and solve it for one variable in terms of the other variables. Let's choose the first equation and solve it for x1:
  10x1 = 300 - 5x2 - 5x3
  Divide both sides by 10:
  x1 = (300 - 5x2 - 5x3)/10
2. Substitute the expression for x1 obtained in step 1 into the second equation:
  5((300 - 5x2 - 5x3)/10) + 10x2 + 8x3 = 300
3. Simplify the equation obtained in step 2:
  (1500 - 25x2 - 25x3 + 20x2 + 16x3)/10 = 300
  Combine like terms:
  (1500 - 5x2 - 9x3)/10 = 300
4. Multiply both sides of the equation by 10 to eliminate the fraction:
  1500 - 5x2 - 9x3 = 3000
5. Rearrange the equation to isolate the variables:
  -5x2 - 9x3 = 3000 - 1500
  -5x2 - 9x3 = 1500
Now we have a system of two equations with two variables:
x1 = (300 - 5x2 - 5x3)/10
-5x2 - 9x3 = 1500
To find the values of x2 and x3, we can use various methods such as substitution or elimination.
In summary, the given refinery-type problem consists of two equations that need to be solved simultaneously to find the values of x1, x2, and x3. The steps provided above outline how to set up the equations and begin the solving process. Further solving would require using a specific method to find the values of x2 and x3.

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To determine whether the series ∑(n=2 to ∞) 6 / (n^2 - 1) is convergent or divergent, we can express the partial sums (sn) as a telescoping sum.

The telescoping sum method involves expressing each term in the series as a difference of two terms that cancel each other out when summed, leaving only a finite number of terms.

Let's express the terms of the series as a telescoping sum:

1. Write out the general term of the series:

a_n = 6 / (n^2 - 1)

2. Split the general term into two partial fractions:

a_n = 6 / [(n - 1)(n + 1)]

3. Express the general term as the difference of two terms:

a_n = (1/(n - 1)) - (1/(n + 1))

Now, let's calculate the partial sums (sn):

s_n = ∑(k=2 to n) [(1/(k - 1)) - (1/(k + 1))]

By telescoping, we can see that most terms will cancel out:

s_n = [(1/1) - (1/3)] + [(1/2) - (1/4)] + [(1/3) - (1/5)] + ... + [(1/(n-1)) - (1/(n+1))]

As we can observe, all terms cancel out except for the first and last terms:

s_n = 1 - (1/(n+1))

Now, let's analyze the behavior of the partial sums as n approaches infinity:

lim(n→∞) s_n = lim(n→∞) [1 - (1/(n+1))]

As n approaches infinity, the term 1/(n+1) approaches zero, resulting in:

lim(n→∞) s_n = 1 - 0 = 1

Since the limit of the partial sums (s_n) is a finite value (1), the series is convergent.

Therefore, the series ∑(n=2 to ∞) 6 / (n^2 - 1) is convergent.

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Answer:

72°

Step-by-step explanation:

A line is 180° and the total angle degrees are 180°

180 - 140 = 40

68 + 40 = 108

180 - 108 = 72

Answer:

- \(\frac{5x}{7}\)

Step-by-step explanation:

Given

\(\frac{5x-10x^2}{14x-7}\) ← factor out 5x in the numerator and 7 in the denominator

= \(\frac{5x(1-2x)}{7(2x-1)}\) ← factor out - 1 on the numerator

= \(\frac{-5x(2x-1)}{7(2x-1)}\) ← cancel the common factor (2x - 1)

= - \(\frac{5x}{7}\)

The probability that the selected pencil is red is 1/5

The distribution of the pencils are given as:

Red = 3

Green = 4

Black = 2

Blue = 6

When a pencil is selected, the probability that the pencil is red is:

P(Red) = Red/Total

This gives

P(Red) = 3/(3 + 4 + 2 + 6)

Evaluate the sum

P(Red) = 3/15

Simplify the quotient

P(Red) = 1/5

Hence, the probability that the selected pencil is red is 1/5

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