What are the domain and range of g of x equals 3 times the square root of the quantity x plus 4?

D: [3, ∞) and R: [0, ∞)
D: [4, ∞) and R: (–∞, 0)
D: [–4, ∞) and R: [0, ∞)
D: (3, ∞) and R: (–∞, 0)

Answers

Answer 1

The domain and range of this square root function are: D: [–4, ∞) and R: [0, ∞).

What is a domain?

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function or relation is defined. This ultimately implies that, a domain is the set of all possible input values (x-values) for a function while a range is the set of all possible output values (y-values) of a function.

Based on the information provided, the function is represented as follows:

g(x) = √(x + 4)

Since a square root function doesn't exist for all negative values, the domain of this function is given by:

x + 4 ≥ 0

x ≥ -4

Domain = [-4, ∞]

Since we do not have a vertical translation, the range of this square root function is given by:

x ≥ 0

Range = [0, ∞]

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Answer 2

Answer:

[–4, ∞) and R: [0, ∞)

Step-by-step explanation:

I got it right on the test.


Related Questions

27.5 percent of what is 13.75

Answers

Answer:

50

Step-by-step explanation:

27.5 percent of what is 13.75

13.75 : 27.5 * 100 =

(13.75 * 100) : 27.5 =

1375 : 27.5 = 50

What property describes the number sentence of 6 0 6?

Answers

The property that defines the number sentence 6 + 0 = 6 is Additive Identity Property.

Given,

6 + 0 = 6

We have to find the property that defines the number sentence;

Additive Identity Property;

Additive identity property says that if zero is added to any real number, the resultant would be the same real number.

Here,

6 + 0 = 6

In this instance, we have added 0 to a real number (6) and have received back the same real number (6).

That is,

Additive Identity Property is the property that defines the number sentence 6 + 0 = 6

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What is a graph answer?

Answers

Answer:

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.

                                   Hope this helps!

s=ut+1 / 2 at²
u=10 a=-2 t=1/2
Work out the value of s.

Answers

The value of s in the formula

[tex]s = ut + \frac{1}{2}at^2[/tex] is [tex]\frac{19}{4}[/tex]

What is subject of a formula?

At first, it is important to know about formula

Formula is an equation which consists of variables and numbers and they are connected by mathematical operations.

In a formula, there are many variables present.

Subject of a formula is that variable which can be expressed in terms of other variables present in the formula.

Here, s is the subject of the formula

[tex]s = ut + \frac{1}{2}at^2[/tex]

u = 10, a = -2, t = [tex]\frac{1}{2}[/tex]

s = [tex]10 \times \frac{1}{2} + \frac{1}{2}\times (-2) \times (-\frac{1}{2})^2\\[/tex]

s = [tex]5 - \frac{1}{4}[/tex]

s = [tex]\frac{20 - 1}{4}\\[/tex]

s = [tex]\frac{19}{4}[/tex]

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PLSSSSSSS HELPPPPPPPPP

Answers

Answer:

undefined

Step-by-step explanation:

since all the x are zero it’s undefined and when all y is zero it’s 0

Hopes this helps please mark brainliest

what is the measure of the base in the triangle below question 7 options 11 45 25 30

Answers

The measure of the base BC in the given triangle is (C) 25 units.

What is a triangle?

A polygon with three edges and three vertices is called a triangle.

It is one of the fundamental geometric shapes.

The letter ABC stands for a triangle having the vertices A, B, and C.

In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

If all of the geometry is in the Euclidean plane, then all triangles are encompassed in a single plane, however, in higher-dimensional Euclidean spaces, this is no longer the case.

This article concerns triangles in Euclidean geometry, specifically the Euclidean plane unless otherwise stated.

So, the given triangle is an isosceles triangle with AB = AC.

Then get the value of x as follows:

AB = AC

4x + 1 = 2x + 23

4x - 2x = 23 - 1

2x = 22

x = 22/2

x = 11

Now, substitute x = 11 in 3x - 8 that is BC.

3x - 8

3(11) - 8

33 - 8

25

Therefore, the measure of the base BC in the given triangle is (C) 25 units.

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Correct question:
What is the measure of the base in the triangle below?

a. 11

b. 45

c. 25

d. 30

What are 5 types of inequalities?

Answers

The five inequality symbols are greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), and not equal to symbol ().

What are some examples of inequality?"A relation is called an inequality if two real numbers or algebraic expressions are related by the symbols ">," "," "," or ""." As an illustration, x>3 (x should be greater than 3) Open Sentence: If there is just one variable in the inequality, it is said to be an open sentence.In mathematics, an inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions. It is most commonly used to compare two numbers on the number line based on their size. In mathematics, the five inequality symbols are greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), and not equal to symbol (). When solving an inequality, you can: • add the same amount to each side; • subtract the same amount from each side; and • multiply or divide each side by the same positive quantity. If you multiply or divide each side by a negative number, the inequality symbol must be reversed.

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What are the 2 characteristics of a regular polygon?

Answers

Any polygon that is equilateral and equiangular is a regular polygon. In other words, the sides or edges and interior angles of a regular polygon are both congruent.

Given that,

We have to find what are the 2 characteristics of a regular polygon.

We know that,

What are the characters of a regular polygon?

Any polygon that is equilateral and equiangular is a regular polygon. In other words, the sides or edges and interior angles of a regular polygon are both congruent.

Regular triangles and quadrilaterals are given unique names, such as squares and equilateral triangles.

Therefore, Any polygon that is equilateral and equiangular is a regular polygon. In other words, the sides or edges and interior angles of a regular polygon are both congruent.

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(100)2 in decimal system is written as

Answers

The binary number (100[tex])_2[/tex] in decimal system is written as [tex]4_{10}[/tex].

Given:

Binary number = [tex](100)_2[/tex]

Converting Binary to decimal system:

Binary:

In computer applications, where binary numbers are represented by only two symbols or digits, i.e. 0 (zero) and 1(one).

Decimal:

Decimals are the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point.

[tex]100_2 = 1*2^2 + 0*2^1+0*2^0[/tex]

we know that,

[tex]2^0 = 1[/tex]

[tex]2^1 = 2\\2^2 =4[/tex]

substitute these values

[tex]100_2 = 1*4 + 0*2 + 0*1[/tex]

= 4 + 0 + 0

= 4 + 0

= [tex]4_{10}[/tex]

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What is the quadrant axis of 6 8?

Answers

The I quadrant will contain the point (6, 8). The number is in the I quadrant as a result.

What is Quadrant?

A quadrant is any one of the four divisions of the coordinate plane. Additionally, we refer to the sections as they are divided by the coordinate axes when we talk about the sections. The y-axis is situated on this up-down axis, and the x-axis is situated here. As you can see, it divides the coordinate space into four parts.

A point can be mathematically expressed as:

A(x, y )

The intersection of the coordinate axes divides the cartesian plane into four quadrants (x and y-axis).

                        (x, y )

In the first quadrant, the x and y coordinates are both positive.

              (x, y)

Y is positive while x is negative in the second quadrant.

                      (-x, y)

The point will be located in the third quadrant if both x and y are equally negative.

                      (-x, -y)

The point will be located in the fourth quadrant if both x and y are positive.

                       (x, -y)

pointed out; A(6, 8)

The y-coordinate in the highlighted position is positive at (8), while the x-coordinate is negative at (6).

Remember that if the x-coordinate is negative and the y-coordinate is positive, the point is in the I quadrant.

As a result, the provided point (6, 8) is said to be in the I quadrant.

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NO LINKS!! Express the statement as an inequality. Part 5​

Answers

Answer:

[tex]\textsf{(d)} \quad \sf \dfrac{1}{5} < c < \dfrac{1}{3}[/tex]

(e)    p ≤ -5

(f)     -m ≥ -9

Step-by-step explanation:

Symbol notation

< means "less than".> means "greater than".≤ means "less than or equal to".≥ means "greater than or equal to".= means "equals".

A negative real number is any real number that is less than zero.

A positive real number is any real number that is greater than zero.

Zero is neither positive nor negative.

Part (d)

[tex]\textsf{c is between $\dfrac{1}{5}$ and $\dfrac{1}{3}$}.[/tex]

If c is between 1/5 and 1/3, it is greater than 1/5 and less than 1/3 (as 1/5 < 1/3), but not equal to either number:

[tex]\sf \dfrac{1}{5} < c < \dfrac{1}{3}[/tex]

Part (e)

If p is not greater than -5, then it is less than or equal to -5:

p ≤ -5

Part (f)

If the negative of m is not less than -9, then it is greater than or equal to -9:

-m ≥ -9

Which function represents a function with direct variation?

Answers

Functions of the form  f(x)=kx represents direct variation.

The table of values that appears a constant proportion between two variables speaks to a direct variation function. In the event that there's at slightest one pair of values that features a different proportion, at that point the function isn't a direct proportion.  the equation applies to each corresponding value between the two variables. Functions of form f(x)=kx, where k is the constant, are as they were functions that can speak to a direct variation. Typically since direct proportion is spoken to by the direct variation formula that's given by. Functions of the form, there may be a constant, are the as it were functions that can speak to a direct variety. Typically since coordinate proportion is spoken to by the coordinate variation formula that's given by y=kx.

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How do you know △ ABC ≅ △ DEF explain?

Answers

We know that  △ ABC ≅ △ DEF are congruent because AB corresponds to DE of another triangle, BC corresponds to EF and AC corresponds to DF.

According to the question,

We have the following information:

△ ABC ≅ △ DEF

Now, we know that this sign is used to show that the two triangles are congruent.

Now, we also know that in these two triangles, their corresponding sides will be equal. So, all the three sides of one triangle will be corresponding to the same sides in another triangle.

Hence, we know that  △ ABC ≅ △ DEF are congruent because AB corresponds to DE of another triangle, BC corresponds to EF and AC corresponds to DF.

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Find the volume of the silo if the radius of the hemispherical top is 20 feet. Use 3.14
for pi. The volume of the silo, rounded to the nearest thousand, is about ____ feet.

Answers

Answer:

Step-by-step explanation:

V = 16755.1608 m3

Find the equation of the line that satisfies the conditions given in each of the following: 1. Through (3, 2) and (5, 7) 2. Through (-3, 4), m = 2 3. m = -3, b = 5 4. x-intercept = 3, y-intercept

Answers

The equations of the line are listed according to slope and intercept below:

y = - (5 / 2) · x - 11 / 2 y = 2 · x + 10 y = - 3 · x + 5 y = 0

How to derive the equation of line for each case

According to Euclidean geometry, a line can be constructed by knowing the location of two different points set on Cartesian plane. From analytical geometry we find that lines are represented by an equation of the form:

y = m · x + b

Where:

m - Slopex - Independent variable.y - Dependent variable.b - Intercept

The slope can be found by secant line formula:

m = Δy / Δx

Now we proceed to find the equation of the line for each case:

Case 1 - (x₁, y₁) = (3, 2), (x₂, y₂) = (5, 7)

m = (7 - 2) / (5 - 3)

m = 5 / 2

b = y - m · x

b = 2 - (5 / 2) · 3

b = 2 - 15 / 2

b = - 11 / 2

y = - (5 / 2) · x - 11 / 2

Case 2 - (x, y) = (- 3, 4), m = 2

b = y - m · x

b = 4 - 2 · (- 3)

b = 4 + 6

b = 10

y = 2 · x + 10

Case 3 - m = - 3, b = 5

y = - 3 · x + 5

Case 4 - x-intercept: 3, y-intercept: 0

m · 3 + b = 0

3 · m = - b

m · 0 + b = 0

b = 0

m = 0

y = 0

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Find the volume of a right cone that has height of 13.8m and a base with a circumference of 15.8m.

Answers

The volume of the cone is 91.05[tex]m^{3}[/tex]

What is a cone?

A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the centre of base) called the apex or vertex. We can also define the cone as a pyramid which has a circular cross-section, unlike pyramid which has a triangular cross-section.

circumference of the base of a cone is same as circumference of a circle which is 2[tex]\pi[/tex]r

15.8 = 2[tex]\pi[/tex]r

make r subject of equation

r = [tex]\frac{15.8}{2\pi }[/tex]

r = 2.51m

Volume of a cone = 1/3 x [tex]\pi[/tex][tex]r^{2}h[/tex], but h =13.8m

volume = 1/3 x 3.142 x [tex](2.51)^{2}[/tex] x 13.8 which is 91.05[tex]m^{3}[/tex]

In conclusion the volume of the cone is 91.05[tex]m^{3}[/tex]

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A water line enters a house 2.0m below ground. A smaller diameter pipe carries water to a faucet in the house. Water flows at 2.0m in the main line and 7.0m out of the second-floor faucet. Take the density of water to be 1.0 ×10^-3 ^3 If the pressure in the line is 2.00 × 10^5 and the pressure at the faucet is 1.40 × 10^5 , how far above ground is the faucet?

Answers

The difference in pressure between the main line and the second floor is 91,100 Pa.

How to calculate difference in pressure between main line and second floor ?

Bernoulli's theorem states that a drop in fluid pressure is connected with an increase in fluid velocity if the fluid flows horizontally so that there is no change in gravitational potential energy.

On the basis of the idea of energy conservation, Bernoulli's principle is explained. According to this law, the total amount of mechanical energy in a fluid travelling along a streamline will be the same at every point along that streamline in a steady flow.

Given ,

The settings provided;

The main line's water speed is 2.0 m/s,

The second floor's water speed is 7.0 m/s,

The water's density is 1.0 x 103 kg/m3.

The following formula can be used to compute the pressure difference between the main line and the second level using Bernoulli's equation:

[tex]p_1+1/2pv2/1+pgh1+ = p2+1/2pv2/2+pgh_2[/tex]

[tex]p1- p2 = 1/2pv2/2 - 1/2pv2/1 + pgh2 - pgh1[/tex]

[tex]p1 - p2 = 1/2p(v2/2 - v 2/1) + pg (h2- h1)[/tex]

p1 - p2 = 1/2(1000)(7² - 2²) + (1000 ×9.8)(5 - (-2))

p1 -  p2  = 91100 pa

Thus, the difference in pressure between the main line and the second floor is 91,100 Pa.

The complete question is : A water line enters a house 2.0 m below ground. A smaller diameter pipe carries water to a faucet 5.0 m above ground, on the second floor. Water flows at 2.0 m/s in the main line and at 7.0 m/s on the second floor. Take the density of water to be 1.0 × 103 kg/m 3 . The difference in pressure between the main line and the second floor is _______.

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if the diagonals of a parallelogram bisect each other then it must be a rhombus

Answers

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

What is rhombus?Due to the fact that it is a quadrilateral with two pairs of parallel sides, a rhombus can be considered a particular parallelogram.A rhombus also has equal sides on all four sides, exactly like a square. Because of this, it is often referred to as a tilted square.

To comprehend the relationship between the rhombus shape, parallelogram, and square, look at the graphic below.

All parallelograms are parallelograms, however not all parallelograms are rhombuses or rhombi.All squares are rhombuses, but not all rhombuses are squares.

There are three additional names for a rhombus:

DiamondLozengeRhomb

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In a clothing store, a shirt that sells for $15 is marked “10% off.” What is the discount? What is the sale price of the shirt?

Answers

Answer:

$13.50

Step-by-step explanation:

If the shirt is 10% off, that means the shirt is 90% of the original cost, which is $15.

If the shirt is 90% of the original cost which is 15, that means that we must turn the percentage into a decimal (0.9) and multiply it by 15.

0.9*15 = 13.5

The sale price of the shirt is $13.50

if y varies jointly with x and z and y=-60 when x=-5 and z=4, find y when x=4 and z=-3

Answers

The value y is -36.

What is proportionality?

Proportionality is the property of two variables being in a multiplicative relation to a constant.

Given that, y varies jointly with x and z and y=-60 when x=-5 and z=4,

y ∝ xz

Let k be the Proportionality constant,

y = kxz

-60 = k*4*-5

k = 3

When x = 4 and z = -3

y = 3*4*-3

y = -36

Hence, The value y is -36.

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Rewrite as equivalent rational expressions with denominator (5u+5)(u−9)(u+5): 9/5u^2−40u−45,2u/5u^2+30u+25

Answers

The equivalent rational expression of the given expression, 9/5u² - 40u - 45, is 9/(5u + 5)(u - 9)

The equivalent rational expression of the given expression, 2u/5u² + 30u + 25 , is 2u/(5u + 5)(u + 5)

Writing equivalent expressions

From the question, we are to rewrite the given expressions as equivalent rational expressions.

The given expressions are:

9/5u² - 40u - 45 and 2u/5u² + 30u + 25

Writing an equivalent expression for 9/5u² - 40u - 45

Factorize the denominator

5u² - 40u - 45

5u² - 45u + 5u - 45

5u(u - 9) + 5(u - 9)

(5u + 5)(u - 9)

Thus,

The equivalent expression is 9/(5u + 5)(u - 9)

Writing an equivalent expression for 2u/5u² +30u + 25

Factorize the denominator

5u² +30u + 25

5u² +25u + 5u + 25

5u(u + 5) + 5(u + 5)

(5u + 5)(u + 5)

Thus,

The equivalent expression is 2u/(5u + 5)(u + 5)

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The graph of F is shown below evaluate each integral by interpreting it in terms of area

Answers

The answer to this question is after solving definite integration 0,1,-4,-10

What is Definite integration?

It is just basically Simple Integration with limits. In other words it is completely same as area under curve

Solution:

We will proceed by finding area under curve

Here we have to consider the area above x axis as positive and area under x axis as negative area

In First part +ve area and -ve area cancels each other hence answer is 0

In second part after cancellation only 1 square block above x axis remains whose area is 1  hence answer is 1

remaining 2 parts graph is completely below x axis hene area is negative therefore definite integeration will be negative

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A person drives 120 kilometers in 2 hours. The distance traveled is proportional to the time taken. If the distance driven, in kilometers, is represented by d and the time taken, in hours, is represented by t, which equation could represent the relationship between d and t?

Answers

The equation that could represent the relationship between [d] and [t] is d = 60t.

What is the general equation of a Straight line?

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have a person drives 120 kilometers in 2 hours. The distance traveled is proportional to the time taken.

We can write the equation that could represent the relationship between [d] and [t] with the help of the equation of a straight line.

y = mx + c

for c = 0

y = mx

m = 120/2

m = 60

So -

y = 60t

or

d = 60t

Therefore, the equation that could represent the relationship between [d] and [t] is d = 60t.

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How do you find the equidistant point of a triangle?

Answers

The equidistant point of  the triangle is point O , which is shown below.

In the question ,

we have to find the equidistant point in the triangle ,

We know that the equidistant point from the vertices of the triangle is the circumcenter ,

let the circumcenter be point O .

The perpendicular bisectors of the given triangle ABC are AC and BC that intersect at point O .

We have to prove that point O lies on the perpendicular bisector of AB and it is equidistant from A , B and C .

So ,we draw OA ,OB and OC .

we know that any point on perpendicular bisector of a segment is equidistant from endpoints of the segment.

that means , OA = OC and OC = OB .

which means OA = OB .

we also know that any point that is equidistant from end points of a segment lies on its perpendicular bisector.

So, we can say that point O is on the perpendicular bisector of AB .

and

Since OA = OB = OC , the point O is equidistant from A , B and C .

Therefore , the equidistant point of the triangle is the circumcenter (point O) .

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GREETINGS NEED HELP ASAP!

Think about wether the diagram shown represents a function. then use the drop down menus to complete the statement about the diagram.
This_____represent a function because the_____ has two different _____
choices for first blank- does or does not
choices for second- x value 7, 11, -5, 2
choices for third- x values or y values ​

Answers

It is not a function because it has one-to-many function when it also has one-to-one and many-to-one.

Given that,

In the picture we have a diagram

We have to find if the diagram is a function or not.

We know that,

What is a function?

Mathematical calculus' core component is functions. The unique types of relationships are the functions. When it comes to math, a function is represented as a rule that produces a different result for each input x.

Function is satisfy one-to-one and many-to-one.

So,

In the picture we can see

Input -2 to output 7 it is one-to-one

Input 7 to output 8 and 2 it is one-to-many

Input 11 and 2 1/3  to output 5 it is many-to-one

Therefore, It is not a function because it has one-to-many function when it also has one-to-one and many-to-one.

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What is the length of 1 ton AC?

Answers

The length of 1 on AC is 54.6 cm.

Given:

Let x be the length

we know that,

AC dimensions = 54.6 * 175.7 * 85.6 cm

It is the volume = l * b * h

Volume :

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

Length :

Length is defined as the measurement or extent of something from end to end.

Breadth :

The breadth of something is the distance between its two sides.

On comparing both

Length l = 54.6 cm

Breadth b = 175.7 cm

Height h = 85.6 cm

Therefore the length of 1 on AC is 54.6 cm.

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Is centroid and Circumcentre same?

Answers

No, the centroid and Circumcentre are not same but it is same in equilateral triangle.

The intersection of a triangle's perpendicular bisectors is called the circumcenter.A triangle's circumcenter is a location that is equally spaced from each of its vertices.The centroid of a triangle is the location where its medians connect.

Triangle's centroid is always within it. The centroid of a triangle is its center of gravity in physical terms. If the triangle is evenly distributed around the plane's surface and you want to balance it by supporting it at only one point, you must do it near the center of gravity.Are the circumcenter and centroid at the same location? In the case of an equilateral triangle, they will both be.

Therefore, the centroid and Circumcentre are not same but it is same in equilateral triangle.

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What is the volume of the following rectangular prism? 4/3units 23/4units2 Volume ==equals units^3 3 cubed

Answers

The volume of the rectangular prism with length of 5 units, width of 4 units and height of 3 units is 60 unit³

What is an equation?

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

Volume is the amount of space occupied by a three dimensional side or object.

Let us assume that the rectangle prism have length of 5 units, width of 4 units and height of 3 units. Hence:

Volume of prism = length * width * height

Volume = 5 units * 4 units * 3 units = 60 unit³

The volume is 60 unit³

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Represent the following statement on a number line: I have anywhere from $5 to $8 in my pocket.

Answers

The statement "I have anywhere from $5 to $8 in my pocket." has been represented on the number line shown in the image attached below.

What is a number line?

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

Translating the statement, we have the following inequality:

Let the variable x represent the amount of money in pocket.

From $5 to $8 in my pocket = 5 ≤ x ≤ 8.

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Write the function for the graph of
g(x)
g(x)=[2x]
g(x)= [x]+2
g(x)= [x-2]
g(x)=[x]-2

Answers

The function of the graph is g(x) = [x]+2

What is linear function?

A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of terms

y = output variable

x = input variable

m = slope

c = y intercept

The c from the graph is +2

m for points (1, 3) and (-3, -1)

= (-1 - 3) / (-3 - 1)

= -4/-4

= 1

substituting to the equation  y = mx + c

y = x + 2

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