If the domain of f is all real numbers in the interval [0, 7] and
the domain of g is all real numbers in the interval [-2, 5], the
domain of f + g is all real numbers in the interval______

The solution to the functional notations would be either yes or no if the function on the left hand side and right hand side are the same. Hence we would have:

c. No:   f ( x )   ≠    f ( -x )

d. Yes:   ( - x )  = - f ( x )

Function notation is way of writing functions so that they can easily be understood in the mathematical sense. This method is applied in the question to help read the meaning in the question without much explanations.

Given data

f ( x )  =  x^3

f ( -x )  =  - x^3

c. No   f ( x )   ≠    f ( -x )

f ( x )  =  x^3   and f ( -x )  =  - x^3

f ( x ) is not equal to f ( -x )

plugging the values for the left hand side of the equation gives

x^3

and plugging the values for the right hand side of the equation gives

- x^3

since the left hand side of the equation is not equal to the right hand side of the equation it means that the both sides of the equation are not equal hence equation sated in c is not correct

f ( x )  ≠    f ( -x )  ( take note of the sign )

d. Yes   ( - x )  = - f ( x )

( - x ) is equal to - f ( x )

This represents odd functions where the negative sign persists at the left hand side and the right hand side of the equation. Odd function do appear for functions which have negative signs and have odd exponents  too.

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Answer:

please upload a picture of your question

Answer:

5x-4

Step-by-step explanation:

Product of a number, x , and 5  = 5x

   subtract 4      5x -4

16 = -4(-3) + 4 is an equation in slope-intercept form for the line passing through points (-4,16) and (3,-5)

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.  

Therefore,

m =  y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.

Be aware that tan ∅ = y/x

We also refer to this tan as the line's slope.

We have been asked to write an equation in slope-intercept form for the line passing through (-4,16) and (3,-5)

First we will find the slope(m)

We know that slope = m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

For the pairs of points (-4,16) and (3,-5)

⇒ m = [tex]\frac{-5- 16}{3 - (-4)}[/tex]

⇒ m = [tex]\frac{-21}{7}[/tex]

⇒ m = -3

We know that the equation for slope(m) and y - intercept(b) of a line is given by :

y = mx + b

Here lets take equation 16 = -4(-3) + b .Here x and y is substituted with the second two points.

⇒  16 = -4(-3) + b

⇒  16 = 12 + b

⇒  b = 16 - 12

⇒  b = 4

The equation in the slope intercept is as follows:-

16 = -4(-3) + 4

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Answer:

a question with a single correct answer: non statistical

data that consists of numbers: numerical

a question that can have a variety of answers: statistical

Step-by-step explanation:

-

The Conjecture is : "the sum of the measures of the interior angles of a triangle is 180° ".

The interior angle of any triangle is defined as the angle which is inside the triangle. In the other words if the triangle has the point within the angle it is in the interior of the angle. A triangle has three internal angles. The interior angles are always less than 180.

According to triangle Angle Sum theorem, the measurement of the sum of all interior angles of a triangle is always equals to 180°. That means, For a given triangle say ΔABC if ∠A, ∠B and ∠C are the interior angles then their sum i.e. ∠A + ∠B + ∠C = 180°.

Thus according to this we can make the conjecture about the sum of measures of the interior angles of a triangle.

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The correct location of the system of equations are;

Single solution;

y = 11 - 2•x

4•x - y = 7

x + y = 15

2•x - y = 15

No solution;

2•x + y = 7

-4•x = 2•y + 14

x = 12 - 3•y

3•x + 9•y = 24

Infinite solution;

2•x + y = 7

-6•x = 3•y - 21

The possible system of equations and their solution are presented as follows;

System of equations

Solution;

4•x - y = 7

Therefore;

11 - 2•x = 4•x - 7

6•x = 18

x = 3; Single solution;

System of equations

Solution;

2•x + y = 7 gives;

y = 7 -2•x

-4•x = 2•y + 14 gives;

y = -2•x - 7

7 -2•x = -2•x - 7

0 = 14, no solution

System of equations

Solution;

x = 12 - 3•y gives;

3•x + 9•y = 24 gives;

x = (24 - 9•y) ÷ 3 = 8 - 3•y

Which gives;

12 - 3•y = 8 - 3•y

System of equations

Solution;

2•x + y = 7 gives;

y = 7 - 2•x

-6•x = 3•y - 21 gives;

3•y = 21 - 6•x

y = 7 - 2•x

7 - 2•x = 7 - 2•x Infinitely many solutions

System of equations

Solution;

x + y = 15 gives;

y = 15 - x

2•x - y = 15 gives;

y = 2•x - 15

Which gives;

15 - x = 2•x - 15

3•x = 15 + 15 = 30

x = 30 ÷ 3 = 10 Single solution

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The measures of the sides of ΔXYZ are XY = 10.6, YZ = 11.2, XZ =  6.7 and the triangle XYZ must be an acute triangle

In this questions we have been given the the coordinates of the triangle XYZ.

X(-5, 9), Y(2, 1), Z(-8, 3)

We need to find  the measures of the sides of ΔXYZ .

We find the the measures of the sides using distance formula.

XY = √[(1 - 9)² + (2 + 5)²]

XY = √[-8² + 7²]

XY = √(64 + 49)

XY = √(113)

XY = 10.6

Now side YZ

YZ = √[(3 - 1)² + (-8 - 2)²]

YZ = √[(2)² + (-10)²]

YZ = √4 + 100

YZ = √104

YZ = 11.2

And the length of side XZ would be,

XZ = √[(3 - 9)² + (-8 + 5)²]

XZ = √(-6² + -3²)

XZ = √(36 + 9)

XZ = √45

XZ = 6.7

We find the sum of the squares of the two smaller sides, and compare the sum to the square of the largest side.

the sum of the squares of the two smaller sides is,

= 6.7² + 10.6²

= 44.89 + 115.54

= 160.43

= 12.67²

And 11.2² = 125.44

Since the sum of the squares of the two smaller sides is greater than the square of the largest side, the triangle must be an acute triangle.

Therefore, the measures of the sides of ΔXYZ are XY = 10.6, YZ = 11.2, XZ =  6.7 and the triangle XYZ must be an acute triangle

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Step-by-step explanation:

8z^3+z^2+3z-1/z-1 you can use long division to get 8z^2+(9z^2+3z-1)/(z-1). You can keep dividing this equation until you get 8z^2+9z+12+11/z-1.

By using synthetic division, you can divide it into

1 -1. 8 1 3 -1 (a.k.a their coefficients)

Then bring the 8 down three, 1 down two, and 3, down one. Take that and multiply the one by each, and put it down. 8, 1, and 2. Then, do that with -1, to get -1, -2, and 1. So, the answer is 8z^2+9z+12+11+z-1. But since it's division, and there are 4 terms on one side, and 2 terms on the other, you have to divide it so it's 8z^2+9z+12+11/z-1.

Hope this makes sense!

The equation to represent the number of people that can attend the event will be 18500 +/- 1200.

Based on the information, equation to represent the number of people that can attend the event will be 18500 +/- 1200.

The maximum number will be:

= 18500 + 1200

= 19700

The minimum number will be:

= 18500 - 1200

= 17300

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The expression 7m+3n best represents a simpler form of 4m+3(m+n).

The Simplified Algebraic Expression is defined as the expression that do not have any like terms and also it cannot be simplified further.

For Example : 2x+5y+6x , the simplified form will be 8x+5y as it cannot be simplified further.

In the given question,

=4m+3(m+n)

=4m+3m+3n    ...(multiplying 3 with m and n)

Now Combining the like terms ,

We get ;

=7m+3n

Therefore , the expression that best represents a simpler form of 4m+3(m+n)  is 7m+3n.

The correct option is (A) 7m+3n.

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explanation up top:) that's the explanation I hope you understand

The number of maximum cupcakes and cookies sold is 6 and 5 respectively.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

Alexandra sell cupcakes for 3.25 each and donuts for 1.25 each.

let x be the number of cupcakes purchased and y be the number of donuts purchased.

Now, Alexandra has 25 to spend and must buy a minimum of 11 cupcakes and donuts altogether.

So, x+ y ≥11

and, 3.25x + 1.25y ≤ 25.

Thus, x= 5.625 and y= 5.375

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The range of the average width of the index finger which is between 1.6 centimeters and 2 centimeters gives;

1. The symbols to use for the inequality are ≤ and ≥

2. The average width expressed as an inequality is; 1.6 ≤ w ≤ 2

3. The inequality for the average width in inches is 0.624 ≤ w ≤ 0.78

1. With regards to working with number ranges or intervals, the term inclusive means that the endpoints of the (closed) interval are included in the range.

The inequality symbol to be used in an inclusive interval are ≤ and ≥ (the symbols < and > are used for an exclusive measurements)

2. The minimum width = 1.6 centimeters

Maximum width = 2 centimeters

The average width in centimeters, w, written as an inequality is therefore;

3. The given conversion factor is 1 cm. = 0.39 inches.

Therefore;

1.6 cm = 1.6 × 0.39 in. = 0.624 in.

2 cm = 2 × 0.39 in. = 0.78 in.

The inequality for the average width in inches is therefore;

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The ​decreases SSwithin and increase the size of the F-ratio be the effect of changing the value of ss1 to 50 option (D) is correct.

It is described as a collection of data with the same entity that is linked to a problem. The sample is a subset of the population, yet it is still a part of it.

It is given that:

Sample Data

M1 = 10 M2 = 15

SS1 = 90 SS2 = 70​

As we know,

The F ratio:

F = S²(x)/S²(y)

From the data given we can say:

Reduce SSwithin and boost the F-magnitude. ratio's

Thus, the ​decrease SSwithin and increase the size of the F-ratio be the effect of changing the value of ss1 to 50 option (D) is correct.

The question is incomplete.

The complete question is attached in the picture.

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Range - { 1 , 0, 1 , 3 , 2 } is relation is a function.

What is domain and range ?

Definitions of domain and example?

The domain is the set of x -coordinates, {0,1,2} , and the range is the set of y -coordinates, {7,8,9,10} .

function. (1,1),(2,0),(3,1),(4,3),(0,2)

Domain - { 1,2, 3 , 4 , 0 }

Range - { 1 , 0, 1 , 3 , 2 }

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The right triangle B and c altitude length are same that is 6.

Given that,

In the given picture there are 2 right triangles.

They are B and C.

2 sides of the triangle B is 3 and [tex]3\sqrt{3}[/tex].

2 sides of the triangle C is 6 and [tex]6\sqrt{2}[/tex].

The angle for both the right triangle B and C is 90°.

We have to find the length of the altitude of right triangles B and C.

By using the Pythagorean theorem we can find the length of the altitude of the right triangle B and C.

The simplest way is to use the Pythagorean theorem if you are aware of two additional right triangle sides:

[tex]a^{2} +b^{2} =c^{2}[/tex]

Where the sides of the right triangle are a, b, and c.

First, We will find for the right triangle B.

Here, a=[tex]3\sqrt{3}[/tex] and b=3

Now, substitute in the formulae

[tex](3\sqrt{3})^{2} +3^{2}=c^{2}[/tex]

[tex]27+9=c^{2}[/tex]

[tex]36=c^{2} \\[/tex]

[tex]c^{2} =36\\[/tex]

Taking square root on both sides

[tex]\sqrt{c^{2} } =\sqrt{36}[/tex]

[tex]c=6[/tex]

Therefore, the length of the altitude of right triangle B is 6.

Now, We will find for the right triangle C.

Here, b=6 and c=[tex]6\sqrt{2}[/tex]

Now, substitute in the formulae

[tex]a^{2} +6^{2}=(6\sqrt{2}) ^{2}[/tex]

[tex]a^{2} +36=72[/tex]

[tex]a^{2}=72-36 \\[/tex]

[tex]a^{2} =36\\[/tex]

Taking square root on both sides

[tex]\sqrt{a^{2} } =\sqrt{36}[/tex]

[tex]a=6[/tex]

Therefore, the length of the altitude of right triangle B is 6.

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Step-by-step explanation:

= 16 a^6=16a divide for 16

a^6=a there are only two solutions 1 and 0 cause:

1^6=1 and 0^6=0

The expression that is equal to [tex]\frac{5x}{x^{2} -9} -\frac{4x}{x^{2} +5x+6}[/tex] is [tex]\frac{x^{2}+22x }{(x+2)(x+3)(x-3)}[/tex].

In the given question

[tex]=\frac{5x}{x^{2} -9} -\frac{4x}{x^{2} +5x+6}[/tex].....(i)

First solving the denominator of both the terms ,

=x²-9

=x²-(3)²  

=(x+3)(x-3)    ...using identity a²-b²=(a+b)(a-b)   .....(ii)

=x²+5x+6

=x²+3x+2x+6       ...by splitting the middle term

=x(x+3)+2(x+3)

=(x+2)(x+3)       ....(iii)

Substituting the value of (ii) and (iii) in   (i)

we get,

[tex]=\frac{5x}{(x+3)(x-3)} -\frac{4x}{(x+2)(x+3) }[/tex]

taking LCM as (x+2)(x+3)(x-3) we get ,

[tex]=\frac{5x(x+2)-4x(x-3)}{(x+2)(x+3)(x-3)} \\ \\ =\frac{5x^{2} +10x-4x^{2} +12x}{(x+2)(x+3)(x-3)}[/tex]

Simplifying the like terms in the numerator we get

[tex]=\frac{x^{2} +22x}{(x+2)(x+3)(x-3)}[/tex]

Therefore , the expression that equals [tex]\frac{5x}{x^{2} -9} -\frac{4x}{x^{2} +5x+6}[/tex]  is [tex]\frac{x^{2} +22x}{(x+2)(x+3)(x-3)}[/tex].

The correct option is (c).

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The property of 8(9 + 0 ) = 8(9) is the identity property of addition.

It should be noted that the identity property of addition states that the sum of 0 and any number will be equal to that number.

In this case, the property of 8(9 + 0 ) = 8(9) is the identity property of addition. This was illustrated as 9 + 0 equals to 9.

Therefore, the property is the identity property of addition.

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The property that justifies the following statement, if 12=2 x+8 and 2x+8=3y, then 12=3y is the transitive property.

Transitive property is one of the properties of equality which states that if there is an equality sign between two values or numbers and one of these numbers is equal to a third numerical value then the other number is also equal to that third numerical value.

Therefore this property can be described as,

if x = y and y = a, then x = a

The transitive property also justifies that if two values x and y are not equal, but y is equal to a, then x cannot be equal to a. That is if x ≠ y, but y = a, then x ≠ a.

So, according to the transitive property, the statement, If 12=2x+8 and 2x+8=3y, then 12=3y is valid.

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Answer: x / 7

Step-by-step explanation:

"the quotient of" represents division, or /.

"a number" represents a variable, in this case, it's x.

while "7" just means the number 7.

Hope this helps!

Based on the fact that the force needed to move object is directly proportional to the weight of the objects, the force needed to move and object that is 900 pounds is 3 newtons of force.

When things are directly proportional, it means that they increase by a given amount together and also decrease by the same amount.

If 4 Newtons are needed for 1,200 pounds, the newtons needed for 1 pound is:
= 4 / 1,200

= 1/300 newtons

If there are 900 pounds to be moved, the newtons needed are:

= 1/300 x 900

= 3 newtons of force

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Answer:

9,500

Step-by-step explanation:

first, remove the parentheses

1.2 x 10^3 + 8.3 x 10^3

Collect the like terms

take 1.2x10^3 + 8.3x10^3 and you will get 9.5 x 10^3

Evaluate the power of 10^3 = 1,000

then do 9.5x1000 = 9,500

The maximum possible length of ribbon left on the roll is 24.5 m.

Find bounds, Roll

30 → nearest half metre.

0.5 ÷ 2 = 0.25

LB = 30 – 0.25 = 29.75

GB = 30 + 0.25  = 30.25

Piece

5.8 →  nearest 10cm or 0.1m

(10÷100=0.1)

0.1÷2 = 0.05

LB = 5.8 – 0.05 = 5.75

GB = 5.8 + 0.05 = 5.85

Max length left = GB roll – LB piece

=30.25 – 5.75

=24.5m

The metric system's default unit of measurement for length. 100 centimeters equal to 1 metre. A meter is a common metric unit that is around 3 feet, 3 inches long. It measures 100 times more than a Centimetre, or 0.01 meters, in size. 1000 meters make up one kilometre.

Hence, the maximum possible length of ribbon left on the roll is 24.5 m.

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a. The formula solved for t when r is the simple interest per year is t = I/Pr

b. Using the new formula, the value of t in the table is 3 years

From the question, we are to solve the given formula for t

The given formula is

I = Prt

To solve for t, we will divide both sides of the equation by Pr

I/Pr = Prt/Pr

I/Pr = t

∴ t = I/Pr

b.

I = $75

P = $500

r = 5% = 0.05

t = 75/(500×0.05)

t = 75/25

t = 3 years

Hence, the value of t in the table is 3 years

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The area of the rectangle according to the given length and width is 107.58m².

The formula of the area of a rectangle: l × w

Now, substitute the values in the formula:

Therefore, the area of the rectangle is 107.58m².

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Step-by-step explanation:

Let's denote the length of the rectangle to be L and the width to be W.

The first sentence tells us that the length, L, is "4 less than twice the width". "4 less than" implies we subtract 4 from some quantity. What is that quantity? Well that's "twice the width." We can rewrite this sentence in terms of L and W as: L = 2W - 4.

Now we know the length of the rectangle in terms of the width.

The area of a rectangle is given by A = L x W. Using this equation, we can substitute our values for area and length:

A = L x W

96 = (2W - 4) x W

From this we can solve for W and subsequently solve for L using algebra:

96 = (2W - 4) x W

96 = 2W^2 -4W

96 = 2(W^2 - 2W)

48 = W^2 - 2W

W^2 - 2W - 48 = 0

(W - 8)(W + 6) = 0

W = 8 or W = -6

Since W is the side-length of a rectangle, we can disregard the negative solution. Therefore W = 8 ft.

If W = 8, then L = 2W - 4 = 2(8) - 4 = 12 ft.

Lastly, we know the Perimeter of a rectangle is given as P = 2L + 2W. Substituting into this equation we solve for the perimeter:

P = 2L + 2W = 2(12) + 2(8) = 40 ft.

The width of the rectangle will be 38 inches.

Let W be the rectangle's width and L its length. The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be

Perimeter of the rectangle = 2(L + W) units

If the length of a rectangle is four less than twice its width and the perimeter is 220 inches.

L = 2W - 4

Then the equation is given as,

P = 2(L + W)

220 = 2W - 4 + W

110 = 3W - 4

3W = 114

W = 38 inches

The width of the rectangle will be 38 inches.

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