4. Renuka's teacher asks her to factorise completely 8x²-12x. Renuka wrote 2x (4x-6) as her answer Explain why she does not score full marks and give the correct answer.​

Answer:

2^6009 + 6^2003 / 49 ig lol

f(x) and g(x) are inverses using composition

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

To confirm the inverse relationship using composition.

For valid inverse f(g(x)) must be equal to g(f(x))

f(x) = ∛(x) + 13; g(x) = (x - 13)³:

f(g(x)) = f((x - 13)³)

f(g(x)) = ∛((x - 13)³) + 13

f(g(x)) = x - 13 + 13

f(g(x)) = x

g(f(x)) = g(∛(x) + 13)

g(f(x)) =  (∛(x) + 13 - 13)³

g(f(x)) =  (∛(x))³
g(f(x)) =  x

Since f(g(x)) = g(f(x)) then f(x) and g(x) are inverse

f(x) = x³ + 1; g(x) = ∛(x - 1):

f(x) = x³ + 1; g(x) = ∛(x - 1)

f(g(x)) = f(∛(x - 1))

f(g(x)) =  (∛(x - 1))³ + 1

f(g(x)) =  x - 1 + 1

f(g(x)) =  x

g(f(x)) = g(x³ + 1)

g(f(x)) = ∛((x³ + 1) - 1)

g(f(x)) = ∛(x³)

g(f(x)) = x

Since f(g(x)) = g(f(x)) then f(x) and g(x) are inverse

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Answer:

  see attached

Step-by-step explanation:

You want a parallelogram with angles of 20° and 160°.

The drawing will start with a line for one side. An angle of 20° can be drawn using a protractor, geometry app, or by approximating its slope.

The slope of a line 20° from the x-axis is tan(20°) ≈ 0.36397. A line with a slope of 4/11 = 0.3636... will have an angle of about 19.983° from the x-axis. For accuracy you can expect in a hand-drawn figure, this is "close enough." It is probably closer to 20° than you could draw using a protractor.

A parallelogram with the required angles is shown in the attachment. Point B is 11 units right and 4 units up from point A, so the angle at A is 20° when rounded to the nearest tenth.

__

Additional comment

Another very close approximation of tan(20°) is 9.9/27.2. A line with that slope makes an angle of 20.00002° with the x-axis.

The simplified ratio of miles to gallons is 14:1. The solution has been obtained by using the concept of ratios.

What are ratios?

A ratio is a comparison or condensed version of two identical values. The reciprocity of this relationship tells us how many times one quantity is equal to the other. To put it simply, a ratio is a number that can be used to represent one thing as a percentage of another.

We are given the distance to be 189 miles and the volume of gas 13[tex]\frac{1}{2}[/tex] gallons.

So, in order to find the ratio of miles to gallons, we need to divide 189 miles onto 13[tex]\frac{1}{2}[/tex] gallons of gas.

We get

189/13.5 = 14

Hence, the ratio of miles to gallons is 14:1.

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Answer:

CD = 15

Step-by-step explanation:

We are given two quadrilaterals: CDEF and GIJH.

We know that CD = 3x - 6, and GI = x + 8.

We want to find the length of CD.

Notice how CD and GI both have one tick mark on them.
This indicates that these two are congruent, meaning that they have the same length.

Because of that, CD = GI.

If we substitute 3x - 6 for CD and x + 8 for GI, we get:

3x - 6 = x + 8

Now, we can solve this like a regular equation.

Add 6 to both sides.

3x - 6 = x + 8

    +6       +6

_________________

3x = x + 14

Subtract x from both sides.

3x = x + 14

-x    -x

_____________-

2x = 14

Divide both sides by 2.

2x = 14

÷2    ÷2

____________

x = 7

We found the value of x.

Now, substitute 7 as x in 3x-6 (the length of CD).

CD = 3x - 6 = 3(7) - 6 = 21 - 6 = 15

Therefore, CD = 15.

The velocity of the ball when it returns to the ground is -8 m/s

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The distance of a ball thrown upward is given by:

h(t) = -2t² + 12t - 10

The ball hits ground when h(t) = 0, hence:

-2t² + 12t - 10 = 0

t = 5 or 1

The velocity (V) of the ball is:

V = dh/dt

V = (d/dt)(-2t² + 12t - 10) = -4t + 12

V = -4t + 12

The ball hits ground when t = 5 or 1 s, hence:

V(1) = -4(1) + 12 = 8 m/s

V(5) = -4(5) + 12 = -8

The velocity on the ground is -8 m/s

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The product of 12 and a number and then the product multiplied by itself 7 times is (12n)^7.

In Mathematics, an algebraic expression is a mathematical equation that can be used for showing the relationship which exist between two (2) or more variables, numerical quantities, as well as in conjunction with different mathematical operations.

Additionally, a coefficient simply refers to a constant numerical value (number or numeral) that written before the variable in any algebraic expression.

Assuming the variable n represents the unknown numerical value (number), we would translate the word problem into an algebraic expression as follows;

The product of 12 and a number = 12 × n = 12n

Since the product is multiplied by itself 7 times, we have the following algebraic expression;

Algebraic expression = (12n)^7

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The function f( x ) = |cos( π x )| is differentiable everywhere on the interval ( 0 , 5 4 ) except at x= 1/2.

The correct option is (C).

In mathematics, a function is represented as a rule that produces a distinct result for each input x.

The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

Function, f( x ) = |cos( π x )|

Now, if we plot the graph for function f( x ) = |cos( π x )|.

The graph touches the x axis at two points, x= 0.5 and x= 1.25.

We know, the function touches at point on x- axis cannot be differentiable at that point.

Hence, except x= 0.5 the function is differentiable.

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Let x = the original price of the electric wok.

r(x) = x - $5 (the price after the rebate)

p(x) = x * (1 - 0.25) (the price after the discount)

Given that x = $38, we can substitute that value in to find the final cost of the wok in each composition:

r(p(x)) = r(p(38)) = r(38 * (1 - 0.25)) = r(28.5) = 28.5 - $5 = $23.50

p(r(x)) = p(r(38)) = p(38 - $5) = p(33) = 33 * (1 - 0.25) = $24.75

So, r(p(x)) = $23.50 and p(r(x)) = $24.75

r(p(x)) will save her the most money.

F(x)=1/(x+3)(x-7) is the rational functions which is graphed.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A vertical asymptote is a value of x for which the function is not defined, that is, it is a point which is outside the domain of a function;

In a graphic, these vertical asymptotes are given by dashed vertical lines.

An example is a value of x for which the denominator of the function is 0.

In this graphic:

Dashed vertical lines at: x=-3, x=7 , thus, for x+3 and x-7 the denominator is zero.

Thus, the function graphed is:

F(x)=1/(x+3)(x-7)

Hence, F(x)=1/(x+3)(x-7) is the rational functions which is graphed.

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The value of x in this equation is found to be 8±4√7.

What is Pythagoras theorem?

The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC2 = AB2 + AC2 in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.

Here given in the question that one side of the wall 5 feet

So as it is a rectangular bedroom it can be split into 2 right-angled triangles.

So the hypotenuse of the triangle is 13 feet

Now using the Pythagoras theorem we can find out the length of the other wall

b²=h²-p²

(x-4)²+(x+6)² = (x+10)²

x²+16-8x+x²+36+12x = x²+100+20x

x²-16x-48=0

x= 8±4√7.

Hence The value of x in this equation is found to be 8±4√7.

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a. The mean stock price of Cenovus Energy is 15.437.

b. The standard deviation for the sample prices of Cenovus Energy is

3.93.

c. The median stock price for Cenovus Energy is 14

d.  The range in Cenovus Energy's stock price is 11.5.

e. The coefficient of variation for each stock are 28.071% Cenovus Energy for % and 9% for TD Bank.

f. As the coefficient of variation is more for TD Bank it is riskier to buy.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean.

a. The mean stock price of Cenovus Energy is,

= (18 + 19 + 12 + 16 + 17.50 + 12 + 7.50 + 10)/8.

= 112/8.

= 14.

b. The variance for the sample prices of Cenovus Energy is,

= [tex]\frac{1}{n}\[ \sum_{i=1}^{n}[x_i - \overline{x}]^2[/tex].

= (1/8)×[(18 - 14)² + (19 - 14)² + (14 - 12)² + (16 - 14)² +(17.50 - 14)² +(14 - 12)² +(14 - 7.50)² + (14 - 7.50)² +(14 - 10)²].

= (1/8)×[16 + 25 + 4 + 4 + 12.25 + 4 + 42.25 + 16].

= (1/8)×(123.5).

= 15.437.

Standard deviation = √(15.437).

= 3.93.

c. To find the median stock price for Cenovus Energy first we have the data set in ascending order.

7.50, 10.00, 12.00, 12.00, 16.00, 17.50, 18.00, 19.00.

So, The median of the stock price for Cenovus Energy is,

= (12 + 16)/2.

= 28/2.

= 14.

d. The range in Cenovus Energy's stock price is (19.00 - 7.50).

= 11.5.

e. The coefficient of variation for each stock is,

CV = {(Standard Deviation)/(Mean)}×100%.

CV = (3.93/14)×100%.

CV = 28.071 for Cenovus Energy.

CV = (6.30/70)×100%.

CV = 9% for TD Bank.

f. TD Bank's higher coefficient of variance makes investing riskier.

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Answer:Slope=5

Step-by-step explanation

Answer:

[tex]3x^{2}[/tex] + x + 6

Step-by-step explanation:

The last number of the first half is 3.5

A number system is defined as a system of writing to express numbers.

The set of all the 7-digit numbers that can be obtained using, for each number, all the digits 1, 2, 3,..., 7.

If you list the numbers of the set in increasing order and split the list exactly at the middle into two parts of the same size

We need to find the last number of the first half

The numbers are 7.

To split into two parts we have to divide by 2

So 7/2=3.5

Hence, the last number of the first half is 3.5

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Using sum of angles in a triangle theorem and sine law, the angle x is 20 degrees, while the length of y and z are 25.83 and 26 respectively.

Sine law is a mathematical law that states that the ratio of the lengths of two sides of a triangle to the sines of the angles opposite to them is constant. It is also known as the sine rule or the law of sines.

This is represented mathematically as;

x /sin X = y / sin Y = z / sin Z

To find angle X, we can simply use the theorem of sum of angles in a triangle.

X + Y + Z = 180°

X + 79 + 81 = 180

X = 20°

Using sine law

x / sin X = y / sin Y

9 / sin 20 = y / sin 79

y = (9 * sin 79) / sin 20

y = 25.83

Using sine rule again

z / sin Z = x / sin X

z / sin 81 = 9 / sin 20

z = (9 * sin 81) / sin 20

z = 25.99≅ 26

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The gigabytes of music  downloaded in one hour is 19.8 gb per hour

From the question, we have the following parameters that can be used in our computation:

Size =  75.24 gigabytes

Time = 3.8 hours

The rate is then calculated as

Rate = Size/Time

Substitute the known values in the above equation, so, we have the following representation

Rate = 75.24/3.8

Evaluate

Rate = 19.8

Hence, the rate is 19.8 gb per hour

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The point corresponding to the transformed function y=f(x/x)+1 is approximately (-4, 4.25), (-2, 2.5), (0, 1), (1, -0.5), (3, 1). 

we need to substitute x/x = 1 for the argument of the function f(x) and add 1 to the result.

Transformed point on point y on f(x) = f(x/x) + 1

(x, f(x)) (x, f(x/x) + 1)

(-4, 5) (-4, f(-2) + 1) ≒ (-4, 4.25)

(-2, 3) (-2, f(-1) + 1) ≈ (-2, 2.5)

(0, 0) (0, f(0) + 1)

= (0, 1)

(1, -2) (1, f(1) + 1) ≈ (1, -0.5)

(3, -4) (3, f(3/3) + 1) ≈ (3, 1)

Note that for the point (-4,5) you have to substitute x/x = -1/2 instead of x/x = 2. This gives x = -8. So the corresponding transformed point is (-4, f(-8) + 1) ≈ (-4, 2.75).

So the point corresponding to the transformed function y=f(x/x)+1 is approximately

(-4, 4.25), (-2, 2.5), (0, 1), (1, -0.5), (3, 1). 

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Answer:

  2

Step-by-step explanation:

You want the number of incorrect answers out of 8 when 8 points are given for a correct answer and 5 points are deducted for an incorrect answer, and the total score was 38.

Let x represent the number of incorrect answers. Then 8-x is the number of correct answers, and the total score is ...

  8(8 -x) -5(x) = 38

Simplifying the equation, we have ...

  64 -13x = 38

  64 -38 = 13x . . . . . . add 13x-38

  26/13 = x = 2 . . . . . . divide by 13

Lucie solved 2 problems incorrectly.

Answer:

3/2

Step-by-step explanation:

8 ratio 12 would be 2/3. but to get the right ratio sequence, we switch up the fraction to give the right answers. so 3/2 as in 12 ratio 8.

This means that, in addition to what the employee contributes, the employer will match up to 6% of an employee's total compensation to his or her 401k account.

Employee compensation is the total remuneration that an organisation pays to an employee in exchange for the work that employee performed during the accounting period, whether that payment is made in cash or in kind. Taxes less subsidies on production include those due or owed on goods or services produced as outputs as well as other taxes or subsidies on production, such as those due on labour, equipment, buildings, or other assets used in production.

Employee compensation consists of two main parts:

(a) Salary and wages paid in cash or kind;

(b) Social insurance contributions that employers are required to pay, including contributions to social security programmes, actual social contributions to other employment-related social insurance programmes, and imputed social contributions to those same programmes.

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When the triangle has a base of 3 inches and an area of 5 square inches, its height is 3.33 inches.

Since a polygon has number of sides and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to a pyramid that has vertices A, B, and C. When the three factors are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sections and three corners. The points where the three sides meet are known as the triangle's corners. The product of three triangle angles is 180 degrees.

given

triangle's surface area is equal to 1/2 * b*h

5 = 1/2 * 3 * h

10 = 3h

h = 3.33 inches.

When the triangle has a base of 3 inches and an area of 5 square inches, its height is 3.33 inches.

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The correct statements about the graph are given as follows:

The rise and the run of a graph are defined as follows:

The slope of a line is given by the change in y divided by the change in x, hence it's equation is given as follows:

Slope = Rise/Run.

For the first triangle, the rise and the run are given as follows:

Hence the slope is of:

Slope = -6/3 = -2.

For the second triangle, the rise and the run are given as follows:

Hence the slope is of:

Slope = -2/1 = -2.

As the ratios are the same, the triangles are similar, the line has a slope of -2, and the corresponding sides are proportional.

The graph is given by the image presented at the end of the answer.

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The coordinates of the endpoint P2 in the line segment are (- 4, 8).

In this problem we have the coordinates of an endpoint in a line segment and the midpoint of that segment, that is, the point in the line segment that partitions it into two parts of equal length. The formula needed to find the coordinates of the missing endpoint is:

0.5 · P1(x, y) + 0.5 · P2(x, y) = M(x, y)

Where:

If we know that P1(x, y) = (- 6, 4) and M(x, y) = (- 5, 6), then the coordinates of the other endpoint are:

0.5 · P1(x, y) + 0.5 · P2(x, y) = M(x, y)

0.5 · (- 6, 4) + 0.5 · P2(x, y) = (- 5, 6)

(- 3, 2) + 0.5 · P2(x, y) = (- 5, 6)

2 · (- 3, 2) + P2(x, y) = 2 · (- 5, 6)

(- 6, 4) + P2(x, y) = (- 10, 12)

P2(x, y) = (- 10, 12) - (- 6, 4)

P2(x, y) = (- 4, 8)

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The standard deviation of the sampling distribution of sample means will be 0.6667.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

Given information

μ= 38 and σ = 6; n = 81

The standard deviation of the sampling distribution is given as,

⇒ 6 / √81

⇒ 6 / 9

⇒ 0.6667

The standard deviation of the sampling distribution of sample means will be 0.6667.

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Answer: Let's call the present age of Emma x, the present age of Carson y, and the present age of their dad z.

From the information provided we know that:

x + y = (1/2)z + 4

We can find the value of z by isolating it:

x + y = (1/2)z + 4

x + y + 4 = (1/2)z + 4 + 4

x + y + 4 = (1/2)z + 8

2(x + y + 4) = z

We don't know the actual age of Emma, Carson and their dad, we only know the relationship between them.

Step-by-step explanation:

The values of Radius PQ if PQ = 24 and OR = 5. is 13 and The radius if PQ has length 24 and 9 units aways from center is 15 .

What is area of circle ?

Area of circle can be defined as  product of pi and square of radius.

Given,

In the chord PQ of O , point R is choosen so that OR is perpendicular to PQ.

The radius if PQ = 24 and OR = 5.

r = [tex]\sqrt{(24/2)^2 +5^2 }[/tex]

r = [tex]\sqrt{144+25}[/tex]

r = [tex]\sqrt{169}[/tex]

r = 13.

The radius if PQ has length 24 and 9 units aways from center.

radius  = [tex]\sqrt{(24/2)^2 + 9^2}[/tex]

= [tex]\sqrt{(12)^2 + 9^2}[/tex]

= [tex]\sqrt{144+81}[/tex]

= [tex]\sqrt{225}[/tex]

r = 15 .

The far from PQ from the center if it has length 16 and the circle has radius 10 is

PQ = [tex]\sqrt{10^2 - (16/2)^2}[/tex]

PQ = [tex]\sqrt{100-64}[/tex]

PQ = [tex]\sqrt{36}[/tex]

PQ = 6

The value of OR if PQ has length 6[tex]\sqrt{5}[/tex] and radius 9 .

OR = [tex]\sqrt{(9^2) - (3\sqrt{5})^2 }[/tex]

OR = [tex]\sqrt{81-45}[/tex]

OR = [tex]\sqrt{36}[/tex]

OR = 6 .

The value of OP .

OP = [tex]\sqrt{QR^2 + OR^2 }[/tex]

OP = [tex]\sqrt{(2\sqrt{3})^2 + (2\sqrt{2})^2 }[/tex]

OP = [tex]\sqrt{12+8}[/tex]

OP = 2[tex]\sqrt{5}[/tex]

Hence, the values of Radius PQ if PQ = 24 and OR = 5 is 13 and The radius if PQ has length 24 and 9 units aways from center is 15 .

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