HELP ASAP WITH EXPLANATION: If f(x) + f(2 − x) = 4 for all x, find f(y − 2) + f(4 − y)

[tex]{ \red{ \bold{cos \: y \: }}}[/tex]

Step-by-step explanation:

[tex]{ \green{ \tt{ \frac{1 \: + \: \cos \: y \: }{1 \: + \: \sec \: y \: }}}} \: → {eq}^{n} (1)[/tex]

But, as you know that

[tex]{ \blue{ \tt{sec \: y \:}}} = { \green{ \tt{\frac{1}{ \ \cos \: y }}}} [/tex]

Then the equation (1) becomes

[tex]{ \green{ \tt{ \frac{1 \: + \: cos \: y }{1 \: + \: \frac{1}{cos \: y} }}}} \: [/tex]

Multiply Numerator and Denominator by [tex] \frac{cos \: y}{cos \: y} [/tex]

then,

[tex]{ \green{ \tt{( \frac{cos \: y}{cos \: y})}}} \: { \green{ \tt{ \frac{1 \: + \: cos \: y}{1 \: + \: \frac{1}{cos \: y}}}}} [/tex]

[tex] = { \green{ \tt{ \frac{cos \: y \: + \: {cos}^{2} \: y }{cos \: y \: + \: 1 }}}}[/tex]

take cos y as common, then

[tex]{ \green{ \tt{cos \: y}}} \: { \green{ \tt( \frac{1 \: + \: cos \: y}{cos \: y \: + \: 1} )}}[/tex]

Here, (1+cos y/cos y + 1) gets cancelled.

Then the remaining answer is cos y.

Answer:

389 is the answer

Hope you like it!

Answer: 55.2 in

Step-by-step explanation:

1ft = 12 in

41.4/9 = 4.6 ft

4.6 x 12 = 55.2 in

The value |x−9|≤9 is equivalent to [18,0] in interval notation.

According to the statement

We have given that the distance of 9 from the number 9. and we have to find the all value of x between it.

So, For find all x value we use absolute value inequalities.

distance of 9 from number 9.

So, when we draw the number line

we see that the number will become

The distance from x to 9 can be represented using an absolute value symbol, |x−9|.

Write the values of x that satisfy the condition as an absolute value inequality.

So, it become

|x−9|≤9

Now write two inequalities then it become

x−9≤9 and x−9≥−9

x≤18  and x≥0

So, The solution set is x≤18 and x≥0,

then the solution set is an interval including all real numbers between and including 18 and 0.

So |x−9|≤9 is equivalent to [18,0] in interval notation.

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Answer:

Step-by-step explanation:

You want to begin by making each fraction have  the same common denominator. The LCF (least common factor) is 77. So, knowing this, we can now multiply the fractions that need to have a denominator of 77.

1. 5/7*11/11=55/77

2. 9/11 * 7/7 =63/77

Now we can add

55/77 + 63/77 + 21/77 = 139/77 or 1.805194805

Answer:

c,d

Step-by-step explanation:

Answer:

8v-28/v^2-2v-24

Step-by-step explanation:

1. Find common denominator

2. Combine fractions with common denominator

3. Re-order terms so constants are on the left

Since the value 0.98 is less than 1, we can therefore say that balance in this account is decreasing.

Exponential Function can be used for increase rate and also for decay rate.  The difference between the two are the plus and minus signs. To put it in another perspective, If Y = P(M)³

If M is less than one, that means it is decaying or decreasing. And if M is greater than one, that means it is increasing.

Given that Some banks charge a fee on savings accounts that are left inactive for an extended period of time. And the equation

y = 5000(0.98)^x  represents the value, y, of one account that was left inactive for a period of x years.

According to the equation, to know if the balance in this account is increasing or decreasing, we will analyze the value 0.98.

Since the value 0.98 is less than 1, we can therefore say that balance in this account is decreasing.

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The value of x when the secants intersect is 4

A secant of a circle is a line that connects two distinct points on a curve.

The secant touches two sides of the circumference of a circle.

Therefore, using secant rule,

4(x + 2 + 4) = 5(x - 1 + 5)

Hence,

4(x + 6) = 5(x + 4)

Hence, open the brackets

4x + 24 = 5x + 20

Therefore, subtract 4x from both sides

4x - 4x + 24 = 5x - 4x + 20

24 = x + 20

subtract 20 from both sides

24 - 20 = x + 20 - 20

x = 4

Therefore, the value of x is 4.

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The material-handling cost per wall mirror under activity-based costing is $280

What is activity-based costing?

Activity-based costing involves absorbing overheads based on cost drivers which directly impact the incurrence of the overhead, in this case, material moves determine the amount of material-handling costs to be incurred, hence, material-handing overheads would be absorbed into the two products based on material moves, which is the appropriate cost driver.

There 25 materials move in both divisions (i.e. 7+18=25)

Material-handling cost per material move=Budgeted material-handling costs /total material moves

Budgeted material-handling costs =$30,000

Material-handling cost per material move=$30,000/25

Material-handling cost per material move=$1,200

Total material-handing costs for wall mirror=number of material moves for wall mirror*Material-handling cost per material move

Total material-handing costs for wall mirror=7*$120

Total material-handing costs for wall mirror=$8,400

material-handling cost per wall mirror=Total material-handing costs for wall mirror/number of wall mirrors

material-handling cost per wall mirror=$8,400/30

material-handling cost per wall mirror=$280

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Answer:

5,526

Step-by-step explanation:

Mean of scores = Total Value of Scores / Number of Values

= [tex]\frac{3820+5500+8560+4400+5350}{5} \\[/tex]

= 5,526

Answer:5526

Step-by-step explanation: Add everything up and divide by 5 because there are 5 numbers

Answer:

Now, the father is 60, and the son is 24.

Step-by-step explanation:

Now:

Father's age = f

Son's age = s

4 years ago:

Father's age = f - 4

Son's age = s - 4

In 12 years:

Father's age = f + 12

Son's age = s + 12

Now:

f = 3(s - 4)

In 12 years:

f + 12 = 2(s + 12)

We have 2 equations that we can solve in a system of equations.

f = 3(s - 4)

f + 12 = 2(s + 12)

f = 3s - 12

f + 12 = 2s + 24

f = 3s - 12

f = 2s + 12

Since above both equations are in terms of f, set the right sides equal and solve for s.

3s - 12 = 2s + 12

s = 24

f = 3(s - 4)

f = 3(24 - 4)

f = 3(20)

f = 60

Now, the father is 60, and the son is 24.

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:2x + 6 + 5x + 90 = 180[/tex]

[ by linear pair ]

[tex]\qquad❖ \: \sf \:7x + 6 = 180 - 90[/tex]

[tex]\qquad❖ \: \sf \:7x + 6 = 90[/tex]

[tex]\qquad❖ \: \sf \:7x = 90 - 6[/tex]

[tex]\qquad❖ \: \sf \:7x = 84[/tex]

[tex]\qquad❖ \: \sf \:x = 84 \div 7[/tex]

[tex]\qquad❖ \: \sf \:x = 12[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \:x = 12 \degree[/tex]

Answer:

second option

Step-by-step explanation:

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

Since the two triangles ABE and ADE are congruent, their corresponding sides and angles are equal.

After observing all the options, we can conclude that :

Only angle AED and angle AEB are angles of given triangles and are actually equal.

[tex] \qquad \large \sf {Conclusion} : [/tex]

The value of the expression 2n - 1 when n = 7 is 13.

2n - 1

when n = 7

2n - 1

= 2(7) - 1

= 14 - 1

= 13

Mathematical expression is an expression which involves the combination of numbers and variables in a valid way, in a function of addition, subtraction, multiplication, division and exponentiation

Therefore, the value of the expression 2n - 1 when n = 7 is 13.

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P( A Student participates in Both sports and Drama) =0.07

The probability of an occurrence can be determined using the probability formula by simply dividing the favorable number of possibilities by the entire number of possible outcomes.

To find the probability that a student participates in both sports and drama:

Let

A =Student  participate in Sport

B = Student  participate in Drama

Thus we have:

P(A) = 0.42

P(B) = 0.25

and

P(Ac and B or A and Bc) =0.53

P(Ac and B ) + P( A and Bc) =0.53

P(B) - P(A and B) + P(A) - P(A and B) = 0.53

0.25 - P(A and B )  +  0.42 - P(A and B) = 0.53

0.25+0.42 - 2 * P( A and B) = 0.53

0.67 - 2 * P(A and B) = 0.53

0.67 - 0.53  = 2* P(A and B)

0.14  =  2 * P(A and B)

0.14 / 2  = P( A and B)

0.07 = P( A and B)

that is:

P( A and B) = 0.07

P( A Student  participate in Both sports and Drama) =0.07.

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The probability that a student participates in both sports and drama is [tex]0.14[/tex].

If [tex]A[/tex] and [tex]B[/tex] are any two events, then the probability of the joint event [tex](A\cup B)[/tex] is given by the following formula: [tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

Given that 42% of the students participate in sports and 25% of the students participate in drama and 53% of the students participate in either sports or drama.

Suppose [tex]S[/tex] denotes that "a student participates in sports" and [tex]D[/tex] denotes that "a student participates in drama".
So, we have [tex]P(S)=\frac{42}{100}=0.42[/tex], [tex]P(D)=\frac{25}{100}=0.25[/tex], [tex]P(S\cup D)=\frac{53}{100}=0.53[/tex].

We want to find the probability that a student participates in both sports and drama i.e., we want to find [tex]P(S\cap D)[/tex].

By the above formula, we obtain:

[tex]P(S\cup D)=P(S)+P(D)-P(S\cap D)\\\Longrightarrow P(S\cap D)=P(S)+P(D)-P(S\cup D)\\\Longrightarrow P(S\cap D)=0.42+0.25-0.53\\\therefore P(S\cap D)=0.14=\frac{14}{100}[/tex]

Therefore, the probability that a student participates in both sports and drama is [tex]0.14[/tex].

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Answer:

8

Step-by-step explanation:

-32/-4 the minus takes out the second minus then we are left with 32/4which makes the answer a positive 8

Answer:

B) 9:35

Step-by-step explanation:

the travel time we get by dividing the distance by the speed

distance / distance/time = time

so,

60 / 80 = 6/8 = 3/4 = 0.75 hours or 45 minutes.

since she arrived 20 minutes late, that means at 10:20 am, she left home 45 - 20 = 25 minutes before 10:00am.

and that is 9:35 am.

Answer:

What is this?

Can't understand anything!

Answer : what is this question?

The answer to the questions of volumes are given as follows

a) [tex]v=128 \pi[/tex]

b) [tex]v=\frac{128}{3} \pi[/tex]

 c)[tex]v=\frac{1024}{5} \pi[/tex]

d)[tex]V=\frac{13568}{15} \pi[/tex]

Generally, the questions are  mathematically solved below

[tex]y=\sqrt{x}, y=4, x=0[/tex]

a) x-axis

if $y=4, x=16, x=0$

Using disk method

[tex]} v=\pi \int_{0}^{16}(\sqrt{x})^{2} d x \\[/tex]

[tex]v=\pi\left(\frac{x^{2}}{2}\right)_{0}^{16} \\[/tex]

[tex]v=\frac{\pi}{2} \times 16 \times 16 \\[/tex]

[tex]v=128 \pi[/tex]

b)  line y=4

if x=0, y=0 ;

[tex]y=\sqrt{x} \Rightarrow x=y^{2}[/tex]

Using shell method

[tex]v = \int_{0}^{4} 2 \pi(4-y) \cdot y^{2} d y \\[/tex]

[tex]v=2 \pi \int_{0}^{4}\left(4 y^{2}-y^{3}\right) d y[/tex]

[tex]v=2 \pi\left[\frac{4 y^{3}}{3}-\frac{y^{4}}{4}\right]_{0}^{4} \\[/tex]

[tex]v=\frac{2 \pi}{12}[1024-768] \\[/tex]

[tex]v=\frac{512 \pi}{12} \\[/tex]

[tex]v=\frac{128}{3} \pi[/tex]

c) y-axis

0 ≤ y ≤ 4

x=y^2

Using disk method

volume

[tex]v=\pi \int_{0}^{4} y^{4} d y$[/tex]

[tex]v=\pi\left(\frac{y 5}{5}\right)_{0}^{4} \\[/tex]

[tex]v=\frac{1024}{5} \pi[/tex]

d) line x=-1

y=√x, y=4, x=0

0 ≤ x ≤ 6

Using shell method

volume is

[tex]V=\int_{0}^{16} 2 \pi(1+x) \sqrt{x} d x$[/tex]

[tex]V=2 \pi\int_{0}^{16}(x^{1 / 2}+x^{3 / 2}\right) )d x\right. \\[/tex]

[tex]V=2 \pi\left[\frac{x^{3 / 2}}{3 / 2}+\frac{x^{5 / 2}}{5 / 2}\right]_{0}^{16} \\[/tex]

[tex]V=2 \pi\left[2 / 3 \cdot\left(4^{2}\right)^{3 / 2}+2 / 5\left(4^{2}\right)^{5 / 2}\right] \\[/tex]

[tex]V=4 \pi / 3 \cdot 4^{3}+4 \pi / 5 \cdot 4^{5} \\[/tex]

[tex]V=4 \pi\left(\frac{1}{3}+\frac{4^{2}}{5}\right)[/tex]

[tex]V=\frac{256}{15}(5+48) \pi \\[/tex]

[tex]V=\frac{256 \times 53}{15} \pi \\[/tex]

[tex]V=\frac{13568}{15} \pi[/tex]

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The value of x from the given circle is 4

The intersecting chords theorem is a statement in geometry that describes a relation of the four line segments created by two intersecting chords within a circle.

It states that the products of the lengths of the line segments on each chord are equal.

According to the theorem;

x * 3 = 2 * (4 + 2)

3x = 2(6)

3x = 12

Divide both sides by 3

3x/3 = 12/3

x =4

Hence the value of x from the given circle is 4

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The cubic equation f(x) = x³ + 2 · x² + 4 · x + 8 has one real root and two complex roots.

In this problem we have a cubic equation and the nature of their roots must be inferred according to a algebraic method.

Cubic equations are polynomials of the form y = a · x³ + b · x² + c · x + d, there is a method to infer the nature of the roots of such polynomials: The discriminant from Cardano's method, an analytical method used to solve polynomials of the form a · x³ + b · x² + c · x + d = 0.

The discriminant is described below:

Δ = 18 · a · b · c · d - 4 · b³ · d + b² · c² - 4 · a · c³ - 27 · a² · d²      (1)

Where:

If we know that a = 1, b = 2, c = 4 and d = 8, then the nature of the roots is:

Δ = 18 · 1 · 2 · 4 · 8 - 4 · 2³ · 8 + 2² · 4² - 4 · 1 · 4³ - 27 · 1² · 8²

Δ = - 1024

The cubic equation f(x) = x³ + 2 · x² + 4 · x + 8 has one real root and two complex roots.

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Answer:

mLx = 144

mLy=154

Step-by-step explanation:

180-36=144

x=144

180-62=118

36+118=154

180-154=26

180-26=154

y=154

Answer:

154 degrees

Step-by-step explanation:

you can find measure of angle y, since it is the supplement of angle a, so

measure of angle y = 180 - measure of angle a, which is 144 degrees

you can find the measure of angle x, by finding its complement.

Looking at the center triangle, we see that it is formed from angle a, the supplement of angle b, and the supplement of angle x, so the equation is 180 = 36 + 180 - 62 + supplement of angle x

so, the supplement of angle x is 26 degrees, so x is 154 degrees

The equation that can be used to find the cost of each binder n in dollars is 861=7n.

Given that the cost of 7 binders is $8.61.

We are required to form an equation that represents the total cost of each binder n in dollars.

Equation is like a relationship between all the variables that are expressed in equal to form.It may be linear equation or may be more types.

Suppose the cost of 1 binder is n dollar.

We know that the total cost is basically the product of price of 1 unit and number of quantities of units.

Total cost=Price of 1 unit* number of units

8.61=n*7

8.61=7n

Hence the equation that can be used to find the cost of each binder n in dollars is 861=7n.

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An exterior angle is equal to the sum of two non-adjacent interior angle of the triangle. Option B

The term triangle refers to a figure that has three sides. There are several types of triangles such as the;

Despite all these types of triangle, the basic geometric properties of triangles can be applied to all types of triangle that we have mentioned above.

Considering the question, an equation that could be used to represent one of the exterior angles and a logical conjecture about the exterior angles of a triangle is that; m<4 = m<1 + m<2. An exterior angle is equal to the sum of two non-adjacent interior angle of the triangle. Option B

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First, I will subtract 53 from 697.

697 - 53 = 644

Next, I will divide the total by 2.

644 / 2 = 322.

This means the cost of the garden table is 322.

I will add 53 back to the total.

322 + 53 = 375.

The cost of the bench is $375.

Answer:

(2+n)-3

That's how you write if that is what you want.

Answer:

(0, 8/3) = y-intercept

Step-by-step explanation:

I chose to find the y-intercept since it is easy to find with the given information.

The equation for a line is y = mx + b

To find the y-intercept, we must plug in the info we have and solve for b:

4 = -1/3 (-4) + b

4 = -4/3 + b

8/3 = b

To find a point on the line, you also could have added -1 to 4 and 3 to -4 since slope means rise/run or change in y/change in x:

(y - 1) / (x + 3) = (4 - 1) / (-4 + 3) = (3, -1) (flip since it's the y and x coordinate) = (-1, 3)