Math Topic: Sum, Difference, and Product of two functions

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The correct graph of the following condition. {(x, y) : x - y6} is depicted in the graph attached.

A graph is a diagram showing the relation between variable quantities each measured along one of a pair of axes at right angles.

In this case, the correct graph of the following condition. {(x, y) : x - y6} is depicted in the graph attached.

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Answer:

Answer:

please see photo for detailed analysis.

log was used calculate big numbers before calculators

log is a re-arranged way to show a number with an exponent

example

log₂ 16 = 4 means 2^4 = 16

logx(Z) = y means x^y=Z

log(x-6)/log(2) + log(x)/log(2) = 4

(log(x-6)+ log(x))/log(2) = 4

(log(x-6)+ log(x)) = 4log(2)

(log(x-6)x) = log(16)

x=8

Solving a quadratic equation, the age of the man with a blood pressure of 125 mmHg is of 27 years old.

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

The solutions are:

In which:

[tex]\Delta = b^2 - 4ac[/tex]

The pressure is given by:

P = 0.006A² - 0.02A + 120.

When the pressure is of 125 mmHg, we have that:

0.006A² - 0.02A + 120 = 125.

0.006A² - 0.02A - 5 = 0.

Hence the coefficients are a = 0.006, b = -0.02, c = -5, and the solutions, applying the formula are:

A = -30 and A = 27.

Age has to be positive, hence the man is 27 years old.

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The different councils consisting of 5 freshmen and 7 sophomores are possible 9216.

We have given that,

A pool of possible candidates for a student council consists of 14 freshmen and 8 software.

We have to determine the how many different councils consisting of 5 freshmen and 7 sophomores are possible

[tex]_n C_r=\frac{n !}{r ! (n-r) !}_n C_r = number of combinations\\\n = total number of objects in the set\\\r = number of choosing objects from the set[/tex]

The total number of the council is

[tex]_{10} C_5\times _9 C_7[/tex]

=252(36)

=9216

The different councils consisting of 5 freshmen and 7 sophomores are possible 9216.

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Answer:

212520 different committees

Step-by-step explanation:

Candidates

For a President: 23

For a Vice President: 22

For a Secretary: 21

For a Treasurer: 20

Number of ways: (23)(22)(21)(20) = 212520

Hope this helps

Answer:

To whom it may concern the answer to this problem would be 212,520.

Step-by-step explanation:

Many people think this problem to be a combination problem, but it is actually a permutation. Since there must be some specific semblance to the order of the equation. Now, to begin with, the work for this problem is...

[tex]_{n}_P_{r}=\frac{n!}{(n-r)!} \\_{23} _P_{4}=\frac{23!}{(23-4)!} \\_{23}_P_{4}=\frac{23!}{19!} \\_{23}_P_{4}=\frac{23*22*21*20*19!}{19!} \\_{23}_P_{4}=\frac{212,520}{1} \\_{23}_P_{4}=212,520[/tex]

Remember that the 19! cancel each other out. Hope this helps!

A function assigns the values. The correct option is D.

A function assigns the value of each element of one set to the other specific element of another set.

The complete question is:

Which pair of statements describe the end behavior of the graph of the function f(x) = x³ + 2x² − 5x − 6?

A.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity.

B.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches negative infinity.

C.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches negative infinity.

D.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches infinity.

If we draw the graph of the given function f(x) = x³ + 2x² − 5x − 6, then it can be observed that as x approaches -∞, f(x) approaches -∞. As x approaches ∞, f(x) approaches infinity.

Hence, the correct option is D.

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Use the definitions of expectation and variance.

[tex]E(X) = \displaystyle \int_{-\infty}^\infty x f_X(x) \, dx = \frac14 \int_0^\infty x e^{-x/4} \, dx[/tex]

Integrate by parts,

[tex]\displaystyle \int_a^b u \, dv = uv \bigg|_a^b - \int_a^b v \, du[/tex]

with

[tex]u = x \implies du = dx \\\\ dv = e^{-x/4} \, dx \implies v = -4 e^{-x/4}[/tex]

Then

[tex]E(X) = \displaystyle \frac14 \left(\left(-4x e^{-x/4}\right)\bigg|_0^\infty + 4 \int_0^\infty e^{-x/4} \, dx\right)[/tex]

[tex]E(X) = \displaystyle \int_0^\infty e^{-x/4} \, dx = \boxed{4}[/tex]

(since the integral of the PDF is 1, and this integral is 4 times that)

[tex]V(X) = E\bigg((X - E(X))^2\bigg) = E(X^2) - E(X)^2[/tex]

Compute the so-called second moment.

[tex]E(X^2) = \displaystyle \int_{-\infty}^\infty x^2 f_X(x)\, dx = \frac14 \int_0^\infty x^2 e^{-x/4} \, dx[/tex]

Integrate by parts, with

[tex]u = x^2 \implies du = 2x \, dx \\\\ dv = e^{-x/4} \, dx \implies v = -4 e^{-x/4}[/tex]

Then

[tex]E(X^2) = \displaystyle \frac14 \left(\left(-4x^2 e^{-x/4}\right)\bigg|_0^\infty + 8 \int_0^\infty x e^{-x/4} \, dx\right)[/tex]

[tex]E(X^2) = 8 E(X) = 32[/tex]

and the variance is

[tex]V(X) = 32 - 4^2 = \boxed{16}[/tex]

Answer:

A.4

Step-by-step explanation:

Using the sine rule

sin(α)/A equals sin(β)/B

From the question & inserting values,

sin(90°)/8 equals sin(30°)/x

∴x equals[tex]\frac{sin(30)}{sin(90)}[/tex]×8

∴x equals 4

You can learn more on the sine rule in case you get confused.

Answer:

A

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin30° = [tex]\frac{1}{2}[/tex] , then

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{8}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2x = 8 ( divide both sides by 2 )

x = 4

Answer:

[tex]\fbox {all real numbers}[/tex]

Step-by-step explanation:

7x + 8 = 1/6 (42x + 48)

7x + 8 = 7x + 8

x = all real numbers

Answer:

6x + 7y = 14

7x + 8y = 27

6 7. x = 14

7 8. y = 27

option B

Answer:

The answer is 5

Because 200÷10 =20.

So I'm this case, 4x=20. Divide both sides by 4 and the answer is 5. So X=5

5

Answer:

Step-by-step explanation:

if 200÷10=4×u then u=?​

200 : 10 = 4u

20 = 4u

u = 20 : 4

u = 5

---------------------------

check

200 : 10 = 4 * 5

20 = 20

the answer is good

Answer:

[tex]-6.5x+11[/tex]

Step-by-step explanation:

Expand The Brackets:

[tex]x-1+12-7.5x[/tex]

[tex]=x+(-1)+12+(-7.5x)[/tex]

Combine Like Terms:

[tex]=x+(-1)+12+(-7.5x)[/tex]

[tex]=(x+-7.5x)+(-1+12)[/tex]

Answer:

[tex]-6.5x+11[/tex]

I Hope This Helps  

Answer:

The answer will be J

Step-by-step explanation:

Since you see, that the 67,896 will need to be rounded. It rounds up to 70,000 so you can elinmate M & N. 22% can be converted as a decimal to 0.2, also equals to 0.20. So elinmate L. Now you have J and K. You always times with these kinds of percentage.

Therefore the Answer Will Be J: 70,000 timed by 0.20.

Expert-Certifieder of Cousin.

Answer:  (5/1, -3)

Hope this helps :)

Answer:

Look at the attachment.

Step-by-step explanation:

Look at the attachment.

Answer:

2

Step-by-step explanation:

In asin(bx - c) + d, a is the amplitude. In this case, it's 2.

Brainliest, please :)

The graph of all the inequalities are given below.

Inequality is defined as an equation that does not contain an equal sign.

This part of the question is for simplifying your work: Make a graph and shadow the interested regions of the inequalities in the given picture.

y ≥ x, the region is left to the line.

y < -(3/7)x – 7, the region is left to the line.

y ≤ (5/3)x – 8, the region is right to the line.

y ≥ 14 – (11/12)x, the region is right to the line.

y = -(3/2)x + 5, this is the equation of line.

All the graphs are shown below.

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The conclusion is a=c statement

A modus ponens argument has the same structure as a syllogism, with two premises and a conclusion:

If P, then Q.

P occurs.

Consequently, Q occurs.

The Modus Ponens rule of inference or rule of logic requires a single premise and its logical consequences. A conditional statement states that if event 1 occurs, event 2 will also occur and that event 2 will be inferred as the outcome if event 1 occurs. For instance, if A implies B and A is assumed to be true, then it follows that B must also be true according to the Modus Ponens rule.

Hence, By modus Ponens

a=b∧b=c ⇒ a=c

So, given a=b∧b=c Then

⇒a=c.

Hence the conclusion is a=c statement .

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Answer: 110 degrees

Step-by-step explanation:

By the exterior angle theorem.

[tex]10x-10=100-2x+2x+10\\\\10x-10=110\\\\\therefore \angle ABC=110^{\circ}[/tex]

A tessellation that uses only one type of regular polygon.

The definition of a polygon is given as a closed two-dimensional figure with three or more straight lines.

When we cover a surface with a pattern of a flat geometric shapes such that there should have no overlaps or gaps, then the surface is called a tessellation.

A regular tessellation is tessellation made up by using only one type of regular polygon. These are made up of entirely congruent regular polygons all that joining vertex to vertex.

Hence, A is the correct option.

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Answer:

I believe that it should be Y; Height of an emperor penguin on Antarctica

Answer:

Z = "results of flipping two coins"

Step-by-step explanation:

A discrete variable is one which can take only certain values and usually represents values that are counted. The result of flipping two coins can only take a certain number of values of heads or tails (1 head and 1 tail, two heads, or two tails); therefore it is a discrete variable.

A continuous variable is one which can take any value, and usually represents values that are measured. The rest of the options provided (W, X, and Y) are all measurements, and are therefore continuous, not discrete.

Also, among the options presented, option Z is the only one which is "random".

Answer:

The standard deviation is about 2.915

Step-by-step explanation:

Answer:

=  2.9154759474227

Step-by-step explanation:

According to the function transformations, the value of h is -2

The complete question is in the attachment

The functions are given as:

[tex]f(x) = (2.5)^x[/tex]

[tex]g(x) = (2.5)^{x-h[/tex]

From the question, we understand that the function f(x) is translated to the left to get g(x)

From the attached graph, we can see that the function h(x) is 2 units to the left of f(x).

This transformation is represented by:

(x, y) => (x + 2, y)

So, we have:

x - h = x + 2

Evaluate the like terms

h = -2

Hence, the value of h is -2

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Answer:H=-2

Step-by-step explanation:

Answer:

  (a)  5440.42 g

Step-by-step explanation:

The amount remaining (Q) is given in terms of the initial amount (Q₀) by the exponential decay formula ...

  Q = Q₀(1/2)^(t/330) . . . . . where t is in days

__

The amount after 540 days is ...

  1750 g = Q₀(1/2)^(540/330) = 0.321666Q₀

  Q₀ = (1750 g)/(0.321666) ≈ 5440.42 g

The initial quantity was about 5440.42 grams.

The solution of the system of linear equation by substitution method is (3,1).

The method of substitution is the method for solving the linear equation where the value of one variable of one equation is placed in the place of that variable in another equation.

Given here the linear equations are

Equation 1: 6x+2y=20

Equation 2: 2x-3y=3

in equation 1 the value of y will be

6x+2y=20

⇒2y=20-6x

⇒y=(20-6x)/2

⇒y=10-3x

substituting the value of y in the equation 2, we will get

2x-3y=3

⇒2x-3(10-3x)=3

⇒2x-30+9x=3

⇒11x-30=3

⇒11x=30+3

⇒11x=33

⇒x=33/11

⇒x=3

putting the value of x in value of y in equation 1

y=10-3x

⇒y=10-3(3)

⇒y=10-9

⇒y=1

The solution of the system of linear equation by substitution method is (3,1).

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Answer:

area:3116  perimeter:240

Step-by-step explanation:

Hii!

__________________________________________________________

[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer:}\circ\leftharpoonup}}[/tex]

Pelet'rimeter =

Area = 3116 cm^2

[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation:}\circ\leftharpoonup}}[/tex]

[tex]\bullet[/tex] Let's work out the perimeter

[tex]\twoheadrightarrow\sf P=2(a+b)[/tex]. a=length & b=width

[tex]\bullet[/tex] Stick in the values

[tex]\twoheadrightarrow\sf P=2(82+38)[/tex]

[tex]\bullet[/tex] Perform the addition operation

[tex]\twoheadrightarrow\sf P=2\cdot120[/tex]

[tex]\bullet[/tex] Multiply and obtain the perimeter

[tex]\twoheadrightarrow\sf P=240cm[/tex]

[tex]\bullet[/tex] Now let's find the area

[tex]\twoheadrightarrow\sf A=lw[/tex] l=length w=width

[tex]\bullet[/tex] Stick in the values

[tex]\twoheadrightarrow\sf A=82\cdot38[/tex]

[tex]\bullet[/tex] Multiply and obtain the area

[tex]\twoheadrightarrow\sf A=3116cm^2[/tex]

--

Hope that this helped! Best wishes.

[tex]\stackrel\star{\textsl{Reach far. Aim high. Dream big.}}[/tex]

--

Based on the required width and height of the tent, the length of the cloth would have to be 14.4 ft.

The opening of the tent would be an isosceles triangle but if it is divided in two from the top, a right-angled triangle will be formed and the hypotenuse will be the length of the cloth on one side.

That length - according to the Pythagoras theorem - would be:

= √(6² + (8 /2)²)

= √(36 + 16)

= 7.2 ft

As this is the length of one side of the cloth, the length of the entire cloth is:

= 7.2 x 2

= 14.4 ft

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