The absolute value function, f(x) = |x + 2|, is shown.


What is the domain of the function?

all real numbers
all real numbers greater than or equal to 0
all real numbers greater than or equal to –2
all real numbers less than or equal to –2

Here it is: 0.156

That is the decimal representation of 156/1000

.156.

If they are “thousandths” then you know there is 3 decimal places.

Hope this helps!

Answer:

B. Domain: -5/2

Range: 1/2

Step-by-step explanation:

If you plug -5/2 for x, it becomes no solution due to the zero in the denominator.

If you plug 1/2 for y and let your calculator do its thing, it becomes no solution.

Because these values cannot be solved for in the equation, they are excluded from the domain and range.

Edit: I got it correct on the Unit Review on edge.

The domain and range values that are excluded from the function given as  f ( x ) = ( x + 3 ) / ( 2x + 5 ) are x = -5/2 and y = 0

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

The function f(x) = (x + 3)/(2x + 5) has certain values that are excluded from its domain and range.

The function f(x) is defined for all real numbers except for the values of x that make the denominator (2x + 5) equal to zero.

Therefore, the values of x that are excluded from the domain of f(x) are those that satisfy the equation 2x + 5 = 0.

2x + 5 = 0

2x = -5

x = -5/2

The range of f(x) is all real numbers except for zero (0), because it is never equal to zero.

Hence , the values excluded from the domain of f(x) are x = -5/2 and the values excluded from the range of f(x) are y = 0

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Answer:

A. 10i and -10i

Step-by-step explanation:

We are given our equation as

[tex]x^2+101=1\\[/tex]

Let us subtract 101 from both hand sides

[tex]x^2+101-101=1-101\\[/tex]

[tex]x^2=-100[/tex]

Now taking square roots on both hand sides

[tex]\sqrt{x^{2}}} = \sqrt{-100}[/tex]

[tex]x=\sqrt{100} * \sqrt{-1}[/tex]

[tex]x=10 * (+i) \\x=10*(-i)\\[/tex]

[tex]x=+10i \\x=-10i\\[/tex]

Answer: 5.55, 5.505, 5.005, 0.555

Step-by-step explanation:

The ordered sequence from greatest to least for the numbers 5.505, 5.55, 0.555, 5.005 is: 5.55, 5.505, 5.005, 0.555. This is done by comparing the values by comparing the digits at each decimal place, from left to right.

To order the numbers 5.505, 5.55, 0.555, 5.005 from greatest to least, we would look at the digits in their decimal places from left to right. Starting from the first place, 5.55 is the largest as it is the only number with a '5' in the hundredth place. Next, both 5.505 and 5.005 have '5' in the units place. However, 5.505 has a '5' in the thousandth place, while 5.005 has '0'. Therefore, 5.505 is larger. Finally, 0.555 is the smallest as it is less than 1. So, the numbers, ordered from greatest to least are: 5.55, 5.505, 5.005, 0.555.

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In order to solve for x, we must do the following:

5(x - 10) = 30 - 15x

5x - 50 = 30 - 15x (Expand 5(x - 10) )

5x - 50 + 50 = 30 - 15x + 50 (Add 50 to both sides of the equation)

5x = 80 - 15x

5x + 15x = 80 - 15x + 15x (Add 15x to both sides)

20x = 80

20x/20 = 80/20 (Divide both sides by 20)

x = 4

Therefor, the correct answer is the second option (x = 4).

You can always check if this is correct by substituting your answer back into the original equation and seeing if the left side is equal to the right side (this is also a potential method for solving the question itself if it is multiple choice, but I find it is often better to actually solve the equation rather than substitute each answer to see which works):

5(x - 10) = 30 - 15x

if x = 4:

5(4 - 10) = 30 - 15(4)

5(-6) = 30 - 60

-30 = -30

The two sides are equal, therefor x = 4 is confirmed as the correct answer.

Final answer:

To solve the equation 5(x - 10) = 30 - 15x, we expand and rearrange to get 20x = 80 and divide both sides by 20 to find that x = 4.

Explanation:

The student is asking us to solve for x given the equation 5(x – 10) = 30 – 15x.

To solve for x, we first expand the left side of the equation:
5x - 50 = 30 - 15x. Next, we collect like terms by adding 15x to both sides and adding 50 to both sides to isolate x:
5x + 15x = 30 + 50.
This simplifies to:
20x = 80.

We then divide both sides by 20 to solve for x:
x = 80 / 20.
This results in:
x = 4. Therefore, x equals 4 is the solution.

As a check, substituting x = 4 back into the original equation yields the identity 5(4 - 10) = 30 - 15(4), or -30 = -30, confirming that x = 4 is indeed the correct solution.

That's too easy...

[tex]y=x+4\\x=y-4[/tex]

Answer:

(3x-15)(x+1)

Step-by-step explanation:

Given an expression in the form ax²+bx+c, where a,b and c are constants,  we can factor it by first finding the two numbers that when multiplied equal to ac and when added equal to b

The expression 3x²-12x-15 can be factored as follows:

The two numbers that can be added to give 3×(-15) and when added result to -12 are -15 and 3.

Thus, 3x²+3x-15x-15

3x(x+1)-15(x+1)

The simplified form becomes: (3x-15)(x+1)

Answer:

A

Step-by-step explanation:

3(x + 1)(x – 5)

Answer:

28 i think.

Step-by-step explanation:

Answer:

The actual distance between the two cities is 28 kilometers

Step-by-step explanation:

A map has a scale of 3.5 inches = 20 kilometers

Distance between two cities on the map = 4.9 inches

We can use the unitary method in this question to get the actual distance between two cities

∵ 3.5 inches on the map = 20 kilometers

∴ 1 inch distance on the map = [tex]\frac{20}{3.5}[/tex] kilometers

∴ 4.9 inches on the map = [tex]\frac{20}{3.5}\times 4.9[/tex]

                                         = 28 kilometers

Therefore, the actual distance between the two cities is 28 kilometers.

Answer:

The value of a - b + c + d = -4

Step-by-step explanation:

* Lets explain the linear equation

- The linear equation is the equation that represented graphically

  by a line

- The general form of its equation is ax + by = c

- The slope of the line is -a/b and the y-intercept of the line is c/a,

  where a is the coefficient of x , b is the coefficient of y and c is the

  numerical term

∵ We have two linear equation in the problem

∴ Their general form is ax + by = e , cx + dy = f

∵ The equation are 2x + 8y = 7 and 4x - 2y = 9

- By comparing the two equations with their general forms

∴ a = 2 , b = 8 , c = 4 , d = -2

- Now we can find the value of a - b + c + d

∵ a = 2 , b  = 8 , c = 4 , d = -2

∴ a - b + c + d = 2 - 8 + 4 + (-2) = 2 - 8 + 4 - 2 = -4

* The value of a - b + c + d = -4

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point on a line

We have the equation:

[tex]y-3=-\dfrac{2}{3}(x+6)\\\\y-3=-\dfrac{2}{3}(x-(-6))[/tex]

the coordinates of the point is (-6, 3).

Only on the first graph the line passes through the point (-6, 3).

Answer:

A

Step-by-step explanation:

Answer:

x=±√6i

Step-by-step explanation:

[tex](x^{2} +6)^{2} =0[/tex]

[tex]x^{2}+6=0[/tex]

[tex]x^{2} =-6[/tex]

x=±√6i

Answer:

Hi there!

The answer is A, and C

Step-by-step explanation:

cos(-x)=cos(x)

sec(-x)=sec(x)

Answer:

A and C.

Step-by-step explanation:

Graphs that have symmetry with respect to the y-axis are called even functions. So, let's check each of the graphs:

1. As we can see in the graph attached, y=cos(x) is symmetrical with respecto to the y-axis.

2. As we can see in the graph attached, y=sin(x) is not symmetrical with respecto to the y-axis.

3. As we can see in the graph attached, y=sec(x) is symmetrical with respecto to the y-axis.

4. As we can see in the graph attached, y=csc(x) is not symmetrical with respecto to the y-axis.

Answer:

6/9=2/3

4/10=2/5

15/20=3/4

29/24 stays the same because 29 is a prime number

16/56=2/7

45/72=5/8

18/60=3/10

32/72=4/9

Step-by-step explanation:

If both the numerator and denominator are even, then you can divide them by 2 until one or both of them become odd. If the number on both the top and bottom add up to a multiple of three, then you can divide the numbers by three. And it goes on to every prime number.

Answer:

1 cup = 0.24 liters

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solid

Prism

Cube

Answer:

The correct options are A,C and E.

Step-by-step explanation:

We need to find the correct terms for the given figure.

From the given figure it is clear that the figure is a cube. We know that cube is a 3D figures and it is also known as square prism or solid.

Therefore, the correct options are A,C and E.

Square and polygon are 2d figures. So, these terms are not correct for given figure.

The sides of a pyramid are triangular which meet at the top.

Therefore, the correct options are B, D and F.

Answer:

1x-4

Step-by-step explanation: Less than in this occasion means -4, and the product of one and a number x means 1x, so when you put it together it's 1x-4.

Answer:

1593 us gallons

Step-by-step explanation:

Answer:

159

Step-by-step explanation:

Answer:

D

X - intercept is the point where the graph crosses the x-axis

in this case, the graph crosses at x = 2 and y = 0; or (2,0)

Answer:

(2, 0)

Step-by-step explanation:

The x- intercept is where the line crosses the x- axis at x = 2

x- intercept is (2, 0)

The y- intercept is where the line crosses the y- axis at y = - 4

y- intercept is (0, - 4)

Answer:

R(p) = -4p^2 + 300p when p=20.

R(p) = -4(20)^2 + 300(20)

R(p) = -1600 + 6000

R(p) = 4400

The mass when p=20 years is 4400.

The equivalent speed in meters per hour is 85000 m/hr.

Speed exists as a scalar quantity that describes how fast an object is moving, regardless of its direction.

Speed exists as the time rate at which an object exists moving along a path, while velocity exists as the rate and direction of an object's movement. Put another way, speed exists as a scalar value, while velocity is a vector.

Here given that,

A car travels 85 kilometers per hour.

Using, the general conversion method.

1 km = 1000 m

= ( 85 km/hr ) (1000 m/1km)

The unit km cancels = 85000 m/hr

Hence, 85000 m/hr is the equivalent speed in meters per hour.

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85,000 meters per hour.

If a car travels 85 kilometers per hour, to find the equivalent speed in meters per hour, we need to convert kilometers into meters. Since 1 kilometer is equal to 1,000 meters, we multiply the speed in kilometers by 1,000 to get the speed in meters.

So, the car's speed in meters per hour would be:

85 km/h  × 1,000 m/km = 85,000 meters per hour.

This conversion is straightforward and is based on the relationship that 1 km = 1,000 m.

Answer:

AC ≈ 10.5 cm (1 dec. place )

Step-by-step explanation:

Given

tan55° = [tex]\frac{15}{b}[/tex]

Multiply both sides by b

b × tan55° = 15 ( divide both sides by tan55° )

AC = b = [tex]\frac{15}{tan55}[/tex] ≈ 10.5 cm

Answer:

D

Step-by-step explanation:

Sinusoid graphs look like regular waves.

It is obvious that only I and III look like waves.

II is known as a stepwise function.

Option: D is the correct answer.

             D.   I and III only

From the graph that is provided to us we observe that the graph I is a sinusoidal graph since it is similar to a graph of sine graph.

Also, the graph II is not a continuous graph and hence it can't be a graph of sinusoidal graph.

Also, graph III is similar to a graph of sine function and hence it represent a graph of a sinusoidal graph.

The simplified expression is [tex]\(\frac{a^9}{8}\)[/tex].

To simplify the expression [tex]\((a^3/2)^3\)[/tex], follow these steps:

1. Apply the power of a power rule, which states that [tex]\((x^m)^n = x^{m \times n}\)[/tex]. In this case, [tex]\(x = a^3/2\)[/tex], [tex]\(m = 1\)[/tex], and [tex]\(n = 3\)[/tex].

2. Distribute the exponent over the numerator and the denominator:

[tex]\((a^3/2)^3 = (a^3)^3 / (2)^3\)[/tex].

3. Apply the power of a power rule to [tex]\((a^3)^3\)[/tex]:

 [tex]\((a^3)^3 = a^{3 \times 3} = a^9\)[/tex].

4. Apply the power of a power rule to [tex]\(2^3\)[/tex]:

 [tex]\(2^3 = 8\)[/tex].

5. Combine the results to get the simplified expression:

 [tex]\(\frac{a^9}{8}\)[/tex].

Therefore, the expression [tex]\((a^3/2)^3\)[/tex] simplifies to [tex]\(\frac{a^9}{8}\)[/tex].

Answer:

B and D

Step-by-step explanation:

The center of the first one is (-3,6)

The center of the second one is (-9,-12)

The center of the third one is (-14,14)

The center of the fourth one is (-16,-3)

The first one has center in the 2nd

The second one has center in 3rd

The third one has center in the 2nd

The fourth one has center is the 3rd

Answer:

The correct answer options are B. [tex](x + 9)^2 + (y + 12)^2 = 36[/tex] and D. [tex](x + 16)^2 + ( y + 3)^2 = 17[/tex].

Step-by-step explanation:

We know that the formula of a circle is [tex](x - h)^2 + (y - k)^2 = r^2[/tex] where [tex]k[/tex] is the value of the ordinate, [tex]h[/tex] is the value of the abscissa and [tex] r [/tex] is the radius of the circle.

B. [tex](x + 9)^2 + (y + 12)^2 = 36[/tex]

[tex][x - (-9)]^2 + [y - (-12)]^2 = 6^2[/tex]

Center (-9, -12)

D. [tex](x + 16)^2 + ( y + 3)^2 = 17[/tex]

[tex][x - (-16)]^2 + [y - (-3)]^2 =\sqrt{17}[/tex]

Center (-16, -3)

Answer:its 12

Step-by-step explanation:

The number can each term of the equation be multiplied by to eliminate the fractions before solving is 12, the correct option is D.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that;

Equation 6 – x + = x + 5

Now,

the least common multiple of 2 and 3, which are the denominators of the fractions in the equation. Multiplying each term by 12 will clear the fractions and result in an equivalent equation without fractions. For example: 12(6 - x + ) = 12(x + 5) 2 3 Simplifying, we get: 72 - 12x + 4 = 12x + 60. This is an equation without fractions that can be solved for x.

Therefore, by the given equation the answer will be 12.

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Answer:

1. They are met on point (-1, -3)

2. They x- values of the solution is... -1

3. There is only one solution. Proof: The slope and the y intercept is different.

4. If you plug in -1 in the x, you get the same y

Explanation:

3x = 4x +1

0 = x +1

-1 = x

plug in... y = 3(-1) = -3

Answer:

The two functions are equal at the two graphs' points of intersection. The points of intersection are (0,1) and (2,9). The x-values of the solutions are x = 0 and x = 2.

Step-by-step explanation:

So I simplify the expression and it is..

8x^3  +  14x^2  +  5x  −  15

____

I hope this helps, as always. I wish you the best of luck and have a nice day, friend..

Answer:

A. Approximately 68%

Step-by-step explanation:

Number of pieces of popcorn in a bucket is normally distributed.

Mean = μ = 1610

Standard deviation = б = 10

We know that in normal distribution, approximately 34% of bags will fall with in one standard deviation on one side. On both sides within the range of 1 standard deviation, 34 + 34 = 68 % of bags will fall.

A table of normal distribution about mean is attached for better understanding.

Our range is:

1600 to 1620

1610 - 10 to 1610 + 10

μ ± б

mean ± 1 standard deviation

Our range is within 1 standard deviation. Hence, Approximately 68% of buckets contain between 1600 and 1620 pieces of popcorn.

Answer:

A 68

Step-by-step explanation:

The expression √-15√-4 is simplified to -2√15 using the imaginary unit i, where i represents the square root of -1. We do this by simplifying each square root with i and then multiplying the results together, remembering that i^2 equals -1.

To simplify the expression using i, where i is the imaginary unit we define as the square root of -1, we have √-15√-4. We can start by simplifying each square root separately using i:

√-15 = √(15 × -1) = √15 × √i = √15i

√-4 = √(4 × -1) = √4 × √i = 2i

Now, you simply multiply the two results together:

√15i × 2i = (√15 × 2) × (i × i) = 2√15 × i²

Since i² equals -1, our expression simplifies to:

2√15 × -1 = -2√15

Therefore, the simplified form of the expression √-15√-4 using i is -2√15.

Answer:

Answer is 1/4.

Step-by-step explanation:

The sample space of an event is the list of all possible outcomes.

Let F represent moving forward and B represent moving backward.

This makes the sample space for the game

F1, F2, F3, F4, F5, F6

B1, B2, B3, B4, B5, B6

There are 6 ways to move forward; only 3 of these are even numbers.

This is 3 ways out of 12 possible moves.This makes the probability

3/12.

3/12=1/4

Thus the probability of moving forward an even number of spaces

is 1/4....

Answer:the answer is 1/4

Step-by-step explanation: