If you vertically stretch the exponential function f(x) = 2* by a factor of 4, what
is the equation of the new function?
A. g(x) = 2.4*
OB. g(x) = 24x
OC. g(x)=1.2*
OD. g(x)=4-2*

Answer:

C

Step-by-step explanation:

9x² - 4[tex]y^{6}[/tex]

can be factored as a difference of squares , that is

(U + V)(U - V)

9x² - 4[tex]y^{6}[/tex] = (3x)² - (2y³)²

with U = 2x and V = 2y³

Answer:

U= 3x and V=2y^3

Step-by-step explanation:

9x^2= (3x)^2

4y^6 = (2y^3)^2

=(3x)^2 - (2y^3)^2

Apply this rule below

x^2 - y^2 = (x + 7) - (x - y)

(3x)^2 - (2y^3)^2 = (3x + 2y^3) + (3x - 2y^3)

= (3x + 2y^3) (3x - 2y^3)

Answer:

r is -11

Step-by-step explanation:

Move the like terms to the same side. 4r-6r is -2r

14 + 8 is 22

22/-2 is -11

[tex]\large\boxed{y=\frac{1}{4}x+2}[/tex]

The point-slope form is actually [tex]y-4=\frac{1}{4}(x-8)[/tex]; I assume there was a copy/paste issue.

Also, the correct answer is not in the answer choices given; again assuming a copy/paste issue.

Start by distributing the [tex]\frac{1}{4}[/tex] to [tex]x[/tex] and [tex]-8[/tex].

[tex]y-4=\dfrac{1}{4}x-2[/tex]

Add [tex]4[/tex] to both sides of the equation.

[tex]\begin{aligned}y-4+4&=\frac{1}{4}x-2+4\\y&=\frac{1}{4}x+2\end{aligned}[/tex]

The probability that if Air America books 15 persons, there will be enough seats available is 0.913.

First of all, we would determine the probability that if Air America books 15 persons, there won't be enough seats available by using binomial distribution:

P(x = 15) = 0.85¹⁵

P(x = 15) = 0.087.

Based on logic, the probability that if Air America books 15 persons, there will be enough seats available is given by:

P = 1 - 0.087

P = 0.913.

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Answer:

B

Step-by-step explanation:

7/20 x 1/2 x 1/6

Answer:

Step-by-step explanation:

The question is asking you to identify the domain for each of the parts of the piecewise-defined function. This means you need to identify the corresponding part on the graph, and determine its horizontal extent.

The first step in solving a problem is to look at the given information. The graph is shown as three (3) non-overlapping horizontal line segments. The open- or filled-circle end points tell you whether that x-value is part of the line segment.

The blanks in the function definition are where the domain descriptions go for the piecewise-defined function. This means you have to match the function description to the left of "if x ∈" with the set of x-values it corresponds to. The "x ∈" notation suggests you want to specify the domain in "interval notation," rather than as an inequality.

The first part of the function definition is ...

  f(x) = -4

This matches the horizontal line segment at the bottom of the graph. The closed dots at its ends mean it is defined for ...

  -6 ≤ x ≤ -2

In interval notation, a square bracket is used when the end point is included in the interval.

  f(x) = -4  if x ∈ [-6, -2]

The second part of the function definition is ...

  f(x) = -3

This matches the horizontal line segment in the middle of the graph. The open dot at the left end, and the closed dot at the right end mean it is defined for ...

  -2 < x ≤ 1

We use a round bracket (parenthesis) when an end point is not included in the interval.

  f(x) = -3  if x ∈ (-2, 1]

The third part of the function definition is ...

  f(x) = 4

This matches the horizontal line segment at the top of the graph. The open dot at the left end, and the closed dot at the right end mean it is defined for ...

  1 < x ≤ 5

In interval notation, this is ...

  f(x) = 4  if x ∈ (1, 5]

Answer:

y = 4/5x + 2

Step-by-step explanation:

Standard equation given slope and y-intercept -> y = mx + b

After substituting variables m and b, you get y = 4/5x + 2.

The height of the new photo must be 945 pixels (option B).

To calculate the height of the photograph, we must first know what proportion the sides of the previous photo have, for this we do the following operation:

According to the above, the height of the photo is equal to 75% of the width. So to find the height of the new photograph we must do the following operation:

So the height of the new photo should be 945 pixels.

Note: This question is incomplete. Here is the missing part:

Question

Jorge wants to determine the enlarged dimensions of a digital photo to be used as wallpaper on his computer screen. The original photo was 800 pixels wide by 600 pixels high. The new photo will be 1,260 pixels wide. What will the new height be?

Options

460 pixels

945 pixels

1,680 pixels

1,860 pixels

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Step-by-step explanation:

118+2×=180

180-118=62

62÷2(×)=31

×=31

Answer:

x + x + 118 = 180

Step-by-step explanation:

...........

Answer:

3, 5, 7

Step-by-step explanation:

We can assign the first number as x. Since all the numbers are odd the next number will be x+2, and the last will be x+4.

3*(x+4) = 7(x)

3x+12 = 7x

12 = 4x

x = 3

x+2 = 5

x+4 = 7

Answer:

Falde

Step-by-step explanation:

the solution is at the point of intersection of the 2 lines

the lines intersect at (- 5, 1 ) , then

the solution is (- 5, 1 )

The measure of the segment JK is 0 unit

A line is the shortest distance between two points

Given the following parameters

GJ = 70.2

JH = 26.5

GK = 70.2

Determine the measure of JK

JK = JG + GK

Since JG = -GJ then;

JK = -GJ + GK

JK = -70.2 + 70.2

JK = 0

Hence the measure of the segment JK is 0 unit

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Probability that Martin passed the exam when he attend the class daily is given by 1/3.

Probability is the possibility to occurrence of an event.

In other words, Probability is the ratio of number of favorable cases under an event to total number of cases under that event.

Let P be the event that Martin passed the exam and A be the event that he attend the class daily.

Given that,

40% of students passed tbe exam.

The probability to pass the exam is given by,

[tex]P(P)=40%=\frac{40}{100}=\frac{4}{10}[/tex]

90% students attend the class daily

probability to attend the class daily is given by,

[tex]P(A)=90%=\frac{90}{100}=\frac{9}{10}[/tex]

30% student both passed the exam and attended class

So probability to both passed the exam and attend the class is given by,

[tex]P(P\cap A)=30%=\frac{30}{100}=\frac{3}{10}[/tex]

Now conditional probability that Martin will passed the exam if he attend class daily is given by,

[tex]P(P|A)=\frac{P(P\cap A)}{P(A)}=\frac{\frac{3}{10}}{\frac{9}{10}}=\frac{3}{9}=\frac{1}{3}[/tex]

Hence the required pobability that Martin passed the exam when he attend the class daily is given by 1/3.

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Answer:

121 i.e. 11²

Step-by-step explanation:

(a+b)² = a² + 2ab + b²

x² + 2 × x × 11 + 11² = (x + 11)²

The difference betweeh the two companies' moving rates is:

(f - g)(x) =  -2x + 200

Here we have two functions:

f(x) = 3x + 400

g(x) = 5x + 200

These functions represent the moving rates for two different companies.

If we want to find the difference between the moving rates, we just need to take the difference between the functions:

(f - g)(x) = f(x) - g(x) = (3x + 400) - (5x + 200) = -2x + 200

So the difference betweeh the two companies' moving rates is:

(f - g)(x) =  -2x + 200

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Answer:

1

Step-by-step explanation:

We can find the slope using the slope formula, which is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

The order of the points doesn't matter, but the points that are farthest right (8, 8) can be our y2 and x2 and the points that are farthest left (5, 5) can be our y1 and x1.

Thus, we have [tex]\frac{8-5}{8-5}=\frac{3}{3}=1[/tex]

Answer:

x + y = w

w > x

w > y

Step-by-step explanation:

x and y are interior angles of a triangle.

w is the exterior angle ( opposite to angles x and y ) of a triangle.

There is a formula that exterior angle of a triangle is equal to sum of two interior angles of a triangle.

So,

x + y = w

If x + y = w,

Then,

w > x

w > y

Using trigonometric identities, and equality is reached, hence the equality is proved.

These three identities are used:

Hence:

[tex]\sec^4{x} = \frac{1 + \tan^2{x}}{1 - \sin^2{x}}[/tex]

[tex]\sec^4{x} = \frac{\sec^2{x}}{\cos^2{x}}[/tex]

[tex]\sec^4{x} = \sec^2{x} \times \sec^2{x}[/tex]

[tex]\sec^4{x} = \sec^4{x}[/tex]

Equality is reached, hence the equality is proved.

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Answer:

[tex]x \leq \frac{7 - x}{3}[/tex]

Step-by-step explanation:

This expression is an inequality which is a relation that makes a non-equal comparison between two numbers/expressions

we want x to be alone in one side, y + 3x ≤ 7

Subtract y from both sides,

y + - y + 3x ≤ 7 - y

3x ≤ 7 - y

divided both sides by 3 to get x alone

3x / 3 ≤ 7 - y / 3

x ≤ 7 - y / 3

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The value of f(x) when x = 3 is 4

The definition of the piecewise function is given as:

[tex]f(x) = \left[\begin{array}{cc}-x& x \le -1\\1&x = 0\\x + 1&x \ge 1\end{array}\right[/tex]

When x = 3, the domain is [tex]x \ge 1[/tex]

At [tex]x \ge 1[/tex], the function definition is

f(x) = x + 1

So, we have:

f(3) = 3 + 1

Evaluate

f(3) = 4

Hence, the value of f(x) when x = 3 is 4

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Complete question

A piecewise function is defined as shown.

[tex]f(x) = \left[\begin{array}{cc}-x& x \le -1\\1&x = 0\\x + 1&x \ge 1\end{array}\right[/tex]

What is the value of f(x) when x=3?

Answer:

4

Step-by-step explanation:

A line bisector is a straight line that divides a given line into two equal parts. Thus the following steps are required by Naomi to show that point D is equidistant from points  A and C.

BD ⊥ AC (given)

BD = 3 units, and AC = 8 units.

BD is the perpendicular bisector of segment AC (given)

Thus,

<BDA  ≅ <BDC (right angles formed by a perpendicular bisector)

AD ≅ DC (equal parts of a bisected line)

AD ≅ DC = 4 units

Thus joining points B to A, and B to C,

BA ≅ BC.

So that applying Pythagoras theorem to ΔABD, we have:

[tex]/hyp/^{2}[/tex] = [tex]Adj 1^{2}[/tex] + [tex]Adj 2^{2}[/tex]

[tex]AB^{2}[/tex] = [tex]3^{2}[/tex] + [tex]4^{2}[/tex]

       = [tex]\sqrt{25}[/tex]

 AB      = 5 units

So that,

BA ≅ BC = 5 units

Therefore, it can be concluded that point D is equidistant from points A and C.

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Answer: A

Step-by-step explanation:

The line has a positive slope.

Also, the line should be shaded below.

This leaves us with D.

Life , Health , Car are considered to be very important insurance ,  Rental Car Damage , Travel Insurance has no usage.

Insurance is safe guarding any thing which has some monetary or emotional value to it , It can be life , health , car , house , your gold etc.

Insurance protects you against something you can never predict .The life is unpredictable and Insurance is a cover to that .

As given in the question , a person can be lucky enough that he never gets to use the money that he invested in the Insurance , but not investing due to this is wrong.

This is not difference of opinion but lack of prediction of future and lack of understanding the needs of life.

Life , Health , Car , Home , Fire etc . insurance that protects the basic amenities of life are considered to be very important ,

while nowadays insurance of Rental Car Damage , Travel Insurance , these are some which has no usage beyond the fact that they cover nothing.

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The ordered pair on the inequality y < 2/3x + 2 is D. (1,2)

The inequality is given as:

y < 2/3x + 2

Next, we test the options:

A. (0,3)

3 < 2/3 * 0 + 2

3 < 2 --- false

B. (-3,1)

1 < 2/3 * -3 + 2

1 < 0 --- false

C. (3,5)

5 < 2/3 * 3 + 2

5 < 4 --- false

D. (1,2)

2 < 2/3 * 1 + 2

2 < 2.67 --- true

Hence, the ordered pair on the inequality y < 2/3x + 2 is D. (1,2)

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Answer: [tex]x\sqrt[9]{y^{2} }[/tex]

Step-by-step explanation: For all expressions in the form [tex]x^{\frac{a}{b}[/tex] , the expression is equal to [tex]\sqrt[b]{x^a}[/tex]. The denominator in a fractional exponent is the type of root it is. For example, [tex]x^\frac{1}{3}[/tex] is going to be the cubed root, or the

3rd root of x ([tex]\sqrt[3]{x}[/tex]). The numerator is what power x is raised to. For example, [tex]x^\frac{3}{2}[/tex] is going to be [tex]\sqrt{x^3}[/tex].

In fractional exponents, the square root only takes the form of the variable it is assigned to. What does that mean? Well, for [tex]xy^\frac{2}{9}[/tex], the square root only applies to the y. The x is considered a constant and can be moved out. Thus, we get [tex]x\sqrt[9]{y^2}[/tex].

Answer: The graph of g is the graph of f translated 10 units down, and [tex]g(x)=2x-10[/tex]

Step-by-step explanation:

The y-intercept of f(x) is 6, and the y-intercept of g(x) is -4, so the graph of g is the graph of f translated 10 units down.

So, the equation of g(x) is [tex]g(x)=2x-10[/tex]

Answer:

5 units right and g(x)= f(x - 5).

Answer:

Step-by-step explanation:

it should be sth like green graph

Answer: 5

Step-by-step explanation:

By the inscribed angle theorem.

[tex]\frac{9}{15}=\frac{2x-1}{3x}\\\\27x=30x-15\\\\-3x=-15\\\\x=5[/tex]

Answer:

Step-by-step explanation:

Among angles i , k , g , a  ,i and k are the exterior angles.

Given i°, k° ,g° ,a° are some angles and we have to find which angle is exterior angle.

The angle between a side of a polygon and an extended side is known as exterior angle of polygon. The sum of exterior angles of a polygon is equal to 180 degrees. We have to identify exterior angles among i° ,k° ,g° ,a°.

The angle i is an exterior angle because it is formed on a line opposite to angle d.

Angle k is also an exterior angle because it is also formed on opposite side of an angle.

Angle g is not an exterior angle.

Angle a is not an exterior angle.

Hence i and k are exterior angles among i, g, k, a.

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