Why the given linear function f(x) = x is called Identity Function? Justify.

Answer:

Step-by-step explanation 43 453 645

[tex]\displaystyle \lim_{x\to 0}~\cfrac{1-cos^2(7x)}{8x^2(~~1-sin^2(7x)~~)}~\hfill \boxed{u=7x\implies \cfrac{u}{7}=x\implies \cfrac{u^2}{49}=x^2} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1-cos^2(u)}{8\left(\frac{u^2}{49} \right)(~~1-sin^2(u)~~)}\implies \cfrac{1-cos^2(u)}{ ~~ \frac{8u^2(~~1-sin^2(u)~~)}{49} ~~ }\implies \cfrac{[1-cos^2(u)]49}{8u^2(~~1-sin^2(u)~~)} \\\\\\ \cfrac{[1-cos(u)][1-cos(u)]49}{8u^2(~~1-sin^2(u)~~)}\implies \cfrac{1-cos(u)}{u}\cdot \cfrac{49[1-cos(u)]}{8u[1-sin^2(u)]} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\displaystyle \lim_{x\to 0}~\cfrac{1-cos(u)}{u}\cdot \cfrac{49[1-cos(u)]}{8u[1-sin^2(u)]}\implies \lim_{x\to 0}~\cfrac{1-cos(u)}{u}\cdot \lim_{x\to 0}~\cfrac{49[1-cos(u)]}{8u[1-sin^2(u)]} \\\\\\ \displaystyle \lim_{x\to 0}~\cfrac{1-cos(7x)}{7x}\cdot \lim_{x\to 0}~\cfrac{49[1-cos(7x)]}{8(7x)[1-sin^2(7x)]} \\\\\\ \displaystyle \text{\LARGE 0}\cdot \lim_{x\to 0}~\cfrac{49[1-cos(7x)]}{8(7x)[1-sin^2(7x)]}\implies \text{\LARGE 0}[/tex]

x>-8

look at the image below for the graph answer.

Answer:

9/64

Step-by-step explanation:

it is just 3/8 x 3/8

In the fractions given 2/3 + 7/3 * -9/4 and (4/5 - 2) * (3/4 - 2/3) the results of the expressions are -55/12 and -1/10 respectively

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator. The numerator defines the number of equal parts taken, whereas the denominator defines the total number of equal parts in a whole.

In the first expression;

2/3 + 7/3 * -9/4

Applying PEDMAS

2/3 + 7/3 * -9/4 = -55/12

In the second expression;

(4/5 - 2) * (3/4 - 2/3) = - 1/10

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The cups of giardia-laced lemonade that Wiyot will have sold by the time his parents get a call from county health officials on day 8 is 75 cups.

From the information, Wiyot sells 33 lemonades on the first day, and 6 additional lemonades each day as the summer heats up.

This is an arithmetic sequence and will be expressed as:

= a + (n - 1)d

a = first term = 33

d = common difference = 6

n = 8

This will be:

= a + (n - 1)d

= 33 + (8 - 1)6

= 33 + (7 × 6)

= 33 + 42

= 75

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The number of rotations will be the ratio of the total distance traveled to the distance traveled in one rotation thus the total rotation to cover 20 feet will be 7.64.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

The longest line which can be drawn inside the circle will be the diameter.

The number of rotations will be the ratio of the total distance traveled to the distance traveled in one rotation.

Distance traveled in one rotation = Perimeter of the wheel.

⇒ 2π(5) = 31.42 inches

The number of rotations = (20×12)/31.42 = 7.63

Hence "The number of rotations will be the ratio of the total distance traveled to the distance traveled in one rotation thus the total rotation to cover 20 feet will be 7.64".

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The required compound inequality is given as 5 < x < 25.

Given that,
To determine a compound inequality to represent a budget to spend between $5 and $25 at Starbucks in a month.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Let x be the amount to be spend at Starbucks in a month,
According to the question,
X should not be less than 5 and should not be greater than 25,
So X > 5 and x < 25
Compounding the above inequalities,
5 < x < 25

Thus, the required compound inequality is given as 5 < x < 25.

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Answer:

The area of one face of the cube is 25 square inches.

Step-by-step explana

Answer:

8 bracelets can be made from given beads.

Step-by-step explanation:

To make similar bracelets using all the beads, we have to find the highest common factor of no of beads

Factors of 72 => 1, 2, 3, 4, 6, 8 , 9, 12, 18, 24, 36, 72

Factors of 32=> 1 , 2, 4 , 8 , 16 , 32

Observing this data, HCF of 72and 32 will be 8.

Therefore, total 8 bracelets can be made from given beads.

Answer:

[tex]\large\begin{array}{c|c|c|}\cline{2-3}&x&y\\\cline{2-3}\phantom{\dfrac12}&0&\boxed{9}\\\cline{2-3}\phantom{\dfrac12}&\boxed{2}&0\\\cline{2-3}\phantom{\dfrac12}&4&\boxed{-9}\\\cline{2-3}\end{array}[/tex]

Step-by-step explanation:

Given equation:

[tex]9x+2y=18[/tex]

Substitute x = 0 into the given equation and solve for y:

[tex]\begin{aligned}x=0 \implies 9(0)+2y&=18\\2y&=18\\\dfrac{2y}{2}&=\dfrac{18}{2}\\y&=9\end{aligned}[/tex]

Substitute y = 0 into the given equation and solve for x:

[tex]\begin{aligned}y=0 \implies 9x+2(0)&=18\\9x&=18\\\dfrac{9x}{9}&=\dfrac{18}{9}\\x&=2\end{aligned}[/tex]

Substitute x = 4 into the given equation and solve for y:

[tex]\begin{aligned}x=4 \implies 9(4)+2y&=18\\36+2y&=18\\36+2y-36&=18-36\\2y&=-18\\\dfrac{2y}{2}&=\dfrac{-18}{2}\\y&=-9\end{aligned}[/tex]

Therefore:

[tex]\large\begin{array}{c|c|c|}\cline{2-3}&x&y\\\cline{2-3}\phantom{\dfrac12}&0&\boxed{9}\\\cline{2-3}\phantom{\dfrac12}&\boxed{2}&0\\\cline{2-3}\phantom{\dfrac12}&4&\boxed{-9}\\\cline{2-3}\end{array}[/tex]

Answer:

b. 0.64 and 64/100

Step-by-step explanation:

hope this helps!!

Answer: B.) 0.64 and 64/100

Step-by-step explanation:

A percentage is x/100

For example, 4% = 4/100.

So 64% = 64/100

64/100 = 0.64

Step-by-step explanation:

the expression is

45 × 12 + 45 × 32

this is the same as

45 × (12 + 32)

you can extract a common factor from a sum and make it the central factor for the sum.

it is the opposite operation of simplifying this central multiplication, where you have to multiply every part of the left factor with every part of the right factor and sin things up according to the resulting signs.

so, the 4th answer is correct.

Answer:

Step-by-step explanation:

We are told that P(dark) = 5/12 and Nd = 25. Plugging these numbers in we get:

5/12 = 25 / (25 + Nw)

Solving this equation for Nw yields Nw = 35.

Therefore, there must be 35 milk chocolates in the bag.

Answer:

Step-by-step explanation:

Answer:

[tex]x= 3+\sqrt{2}, \quad x= 3 -\sqrt{2}[/tex]

Step-by-step explanation:

Given quadratic equation:

[tex]y = x^2 - 6x+7[/tex]

To complete the square, begin by adding and subtracting the square of half the coefficient of the term in x:

[tex]\implies y = x^2 - 6x+\left(\dfrac{-6}{2}\right)^2-\left(\dfrac{-6}{2}\right)^2+7[/tex]

[tex]\implies y = x^2 - 6x+\left(-3\right)^2-\left(-3\right)^2+7[/tex]

[tex]\implies y = x^2 - 6x+9-9+7[/tex]

Factor the perfect square trinomial:

[tex]\implies y=(x-3)^2-9+7[/tex]

[tex]\implies y=(x-3)^2-2[/tex]

To solve the quadratic, set it to zero and solve for x:

[tex]\implies (x-3)^2-2=0[/tex]

[tex]\implies (x-3)^2-2+2=0+2[/tex]

[tex]\implies (x-3)^2=2[/tex]

[tex]\implies \sqrt{(x-3)^2}=\sqrt{2}[/tex]

[tex]\implies x-3= \pm\sqrt{2}[/tex]

[tex]\implies x-3+3= 3\pm\sqrt{2}[/tex]

[tex]\implies x= 3\pm\sqrt{2}[/tex]

Therefore, the solution to the given quadratic equation is:

[tex]x= 3+\sqrt{2}, \quad x= 3 -\sqrt{2}[/tex]

Number of people in a room  is the discreate data .

Data that only accepts specific values is referred to as discrete data or discrete values. This type of data, which can be counted and has a finite number of values, is frequently expressed as whole numbers or integers.

Information that only has a limited range of values is said to be discrete. These values don't have to be whole numbers (a child's shoe size might be 3.5 or a company's profit might be £3456.25), but they must be fixed values; a child's shoe size cannot be 3.72!

Discrete means "made up of individual, separate units" (not to be confused with "discreet," a completely different word that just so happens to sound similar). Discrete entities, such as logical statements and (obviously) integers, are the focus of discrete mathematics.

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The probability for the given case is 5/23.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

Given that,

Total number of students is 29.

The students who play instrument are 23.

Those who play a sport are 9.

And, those who play both are 5.

Given problem is the case of conditional probability which can be solved by Bayes's theorem as,

P(A|B) = P(A ∩ B) / P(B)

Suppose, A be the event the students play instrument.

B be the event the students play a sport.

And, A ∩ B is the event they play th both.

Then A|B implies the event when a student play instrument given he plays sport.

Apply the rule of probability in the equation for Bayes's theorem to get,

P(A|B) = (5/29) / (23/29)

          = 5/23

Hence, the probability that a student plays an instrument given that they play a sport is 5/23.

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The two ways of forming isosceles triangle by bending the metal strip using length by length by base are

A triangle that have the two sides equal is referred to as an isosceles triangle.

Using a strip of 20 inches long to construct an isosceles triangle means that the perimeter of the triangle is 20 inches

the perimeter is equal to base + length + length

bending 6 inches already means one of the dimensions is gotten then fo the other is based on if

if the 6 is base then minus the 6 from 20 and divide the rest for the length

20 - 6 = 14

the two lengths is 14 one length is 7. so we have 6 + 7 + 7 = 20

If the 6 is length then get another 6 and the rest is base

20 - 6 = 14

14 - 6 = 8

therefore we have 6 + 6 +8 = 20 inches

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1.    in this exercise you  must substitute the value of  of x = 12  in the equation of the parable given, if the result is 10 then the ball pass through the hoop

2.    Y = (-.125)(12)^2+ (1.84)(12)+6 = -18+22.08+6 = 10.06≅10 , of  this form it is demonstrated, that the ball pass through the  hoop

The equation of the line in slope - intercept form is [tex]y=\frac{-7}{4}x-5[/tex]


Explain what the slope-intercept form is?

Simply put, the slope-intercept form is the way to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible. This expression is sometimes referred to as y = mx + b form

Given: x = -4 , y = 2 and b = -5

y = mx + b

2 = m (-4) + (-5)

m = [tex]\frac{-7}{4}[/tex]
By putting the value of m we get equation of line
[tex]y=\frac{-7}{4}x-5[/tex]

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Answer:

82 miles

Step-by-step explanation:

75-29.50 = 45.50

45.50/0.55 = 82.7272727273

82 x 0.55 = 45.10

45.10+29.50 = 74.60

Answer:

12.5 72

Step-by-step explanation:

Because shows that the basketball player wear size 11.5 73 inches tall so basically the answer would be 12.5 72

The equation of the regression line is y = 0.77x + 61.95. The residual is 2.2 inches. The residual means that the gap between the estimated and anticipated values is 2.2 inches.

A regression line shows a linear connection between the y-dependent axis's variables and the x-independent axis's variables. The connection is determined by examining the data pattern created by the variables.

From the table, the points are given as follows:

(7, 64.5), (10, 70), (12.5, 72), (8.5, 71), (9, 69), (10, 70), (11, 75), (12.5, 69), (13, 71), (10.5, 68).

Inserting these points into the linear regression calculator, the equation is given as follows:

y = 0.77x + 61.95 ...(i)

For a shoe size of 11.5 inches, the predicted height is given as below:

y = 0.77(11.5) + 61.95 = 70.8 inches.

The residual is the gap between the estimated and anticipated values, hence:

Residual = 73 inches - 70.8 inches = 2.2 inches.

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The solution to the questions are:

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

Length = 350 - 2x

Width = x

The area of a rectangle is the product of its dimensions

So, we have

Area = Length x Width

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

A = (350 - 2x) * x

Evaluate

A = 350x - 2x²

Differentiate and set to 0

350 - 4x = 0

So, we have

4x = 350

Divide by 4

x = 87.5

Recall that

Length = 350 - 2x

So, we have

Length = 350 - 2 x 87.5

Evaluate

Length = 175

The area is then calculated as

Area = Length x Width

So, we have

Area = 175 x 87.5

Evaluate

Area = 15312.5 square meters

Hence, the area is 15312.5 square meters

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1.

2.

A dilation occurs when each of the side lengths of an image are multiplied by a constant, which is called scale factor.

For item a, the scale factor is of:

12/4 = 3.

The scale factor is greater than 1, hence it represents an enlargement, and the missing values are found multiplying the equivalent sides by 3, hence:

For item b, the scale factor is of:

5/12 = 0.4167.

The scale factor is less than 1, hence it is a reduction, and the missing value is of:

x = 6 x 0.4167 = 2.5.

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The opposite of |3| = - |3|

What is Modulus Function?

Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.

It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:

Given data ,

Let the number be x

x = |3|

Now , the opposite of the number x = -x

So ,

The opposite of |x| = -|x|

And ,

The opposite of |3| = - |3|

Hence , The opposite of |3| = - |3|

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The equation of line h that passes through (2,6) and is parallel to a line passing through (-3, 4) and (1, 1) is 4y + 3x = 30

Slope is the ratio of the change in the y-coordinates to the change in the x-coordintes of any two given points.

It is a measure of the steepness of a line.

Slope may be positive or negative

slope of the line joining the the points (-3,4) and (1,1)

slope = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

[tex]x_{1}[/tex] = -3, [tex]x_{2}[/tex] = 1, [tex]y_{1}[/tex] = 4, [tex]y_{2}[/tex] = 1

slope = 1-4 / 1 - -3

slope = -3/4

since the two lines are parallel their slopes are equal.

equation of first line

y = mx + c

where y = 6, x = 2, m = -3/4

6 = -3/4(2) + c

6 = -3/2 + c

c = 6 + 3/2

c = 15/2

Equation, y = -3/4x + 15/2

multiply through by 4

2y = -3x +30

2y + 3x = 30

In conclusion the equation of the line passing through the given point is 2y + 3x = 30

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The area of the rectangle can be expressed as [tex](\frac{6x}{5})^2[/tex].

What is the area of the rectangle?

If the length of the rectangle is 'l' and the breadth of the rectangle is 'b', then the area of the rectangle can be computed as

                   Area = l * b

Given data:

        The width of the rectangle is 3x/5 cm.

   And its length is four times its width so length = 4 * 3x/5

                                                                                 = 12x/5 cm.

Then the area will be

              Area = length * breadth

                       = 12x/5 * 3x/5

                       = 36x²/25

                       [tex]=(\frac{6x}{5})^2[/tex]

Hence, the area of the rectangle can be expressed as [tex](\frac{6x}{5})^2[/tex].

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Consumidores secundarios are organisms in an ecosystem that feed on primary consumers, which in turn feed on producers.

They occupy the second trophic level in a food chain or food web.

The inequality that compares the given numbers -4;-1 is -4 < -1.

Inequalities are created through the connection of two expressions.

It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this case, it should be noted -4 is less than -1. Therefore, the inequality will be -4 < -1.

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