A design for a library has a scale of 1/3 in= 1ft. The height of the library in the drawing is 12 inches. What is the
actual height of the library?

Answer + Step-by-step explanation:

Part A :

Let M(a , b) be a point where the graphs

of the equations y = 8ˣ and y = 2ˣ⁺² intersect.

M lies on both graphs

Then

the coordinates of M verify both equations (equation of graph1 and equation of graph 2)

Then

[tex]b=8^{a}\ \text{on the other hand} \ b=2^{a+2}[/tex]

Then

[tex]8^{a}=2^{a+2}[/tex]

Therefore ‘a’ (the x-coordinates of the points M where the two graphs intersect) is a solution to the equation :

[tex]8^{x}=2^{x+2}[/tex]

Part B : check the attached table.

Part C :

Graphically, we try to spot the points of intersection of the two graphs ,the x-coordinates of those points are the solution to our equation.

In our case , obviously the two graphs intersect at only one point M(1 ,8)

Therefore 1 is the only solution to 8ˣ = 2ˣ⁺².

Also ,Check the attached graph.

Answer:on the given cushion. We want to represent cost like 30 in terms of cost. Rita. Now by the identity sector tragical toe one by scientists. Now we know that science can't theta plus Costco Arteta is equal to one. So they get signed. Tetteh is equal to plus minus quite a tough one. Minus cause squared theta. So this will be a photo one by plus minus square wrote off one minus y squared theta.

Step-by-step explanation:

Answer:

241.5 km

Step-by-step explanation:

The distance between London and Cardiff in kilometres is 241.5 km

The transformation of the equation will be f(x) = (-x)³ + 4.

Then the correct option is D.

A function is a statement, tenet, or rule that establishes a connection between two variables. Mathematics is replete with functions, which are necessary for the construction of intricate connections.

The collection of all the values that the function may input while it is defined is known as the domain. The whole set of values that the function's output can produce is referred to as the range. The set of values that might be a function's outputs is known as the co-domain.

The function's graph is provided below.

f(x) = x³

If the graph crosses the y-axis, substitute a negative value for x.

The function will then be f(x) = (-x) ³

Add 4 if the graph has been raised by 4 units.

The equation will then be transformed to f(x) = (-x)³ + 4

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Answer:hi

Step-by-step explanation:hello

Answer:

Step-by-step explanation:for the triangle GIF, angle g = 80

angle f = 42 since angle FBA = 138

so angle i = 180 - 42 - 80

                 = 58

The value of

Domain(- ∞,∞), Range(- 16, ∞), Minimum Value = -16

Function is a quadratic function. x-intercepts are -4 and 4.

The function decreasing before vertex = (-∞,0)

The function increasing after vertex = (0, ∞)

y-intercept is -16.

Function is Positive(- ∞, - 4) ∪ (4, ∞) : , Function is negative : (- 4, 4)

Interval Increasing  Domain(0,∞),

Interval Decreasing  Range(- ∞, -16)

According to the data, equation  f(x) = [tex]x^{2}[/tex] – 16

It is an upward parabola because coefficient of  is positive.

The vertex form of a parabola is

f(x) = a[tex](x - h)^{2}[/tex] . . . (2)

where, a is constant and (h , k) is vertex.

From (1) and (2), we get

a = 1, h = 0, k = - 16

So, vertex of the parabola is (0,-16).

The given function is defined for all values of x. So,

Domain : (- ∞,∞)

The value of a function which is an upward parabola cannot be less than the y-coordinate of its vertex. So

Range : (- 16, ∞)

Minimum Value = y-coordinate of vertex = -16

Function is a quadratic function.

For f(x)=0

⇒ 0  = [tex]x^{2}[/tex] - 16

⇒ 16 =  [tex]x^{2}[/tex]

⇒ x = ± 4

So, x-intercepts are -4 and 4.

The function decreasing before vertex = (-∞,0)

The function increasing after vertex = (0, ∞)

For x=0,

f(0) = [tex](0)^{2}[/tex] - 16

⇒ - 16

So, y-intercept is -16.

Function is Positive : (- ∞, - 4) ∪ (4, ∞)

Function is negative : (- 4, 4)

Interval Increasing  Domain: (0,∞)

Interval Decreasing  Range: (- ∞, -16)

Following are the key features of functions

1. Domain and Range

2. x-intercept and y-intercept

3. Positive and Negative intervals

4. Intervals of increasing, decreasing and constant behavior

5. Parent Functions

6. Maxima and Minima

Domain and Range

Domain : The domain is the set of all possible inputs or x-values. To find the domain of a function, we have to look at the x-axis of the graph.

Determining Domain :

1. Start at the origin.

2. Move along the x-axis until you find the lowest possible x-value. This is your lower bound.

3. Return to the origin.

4. Move along the x-axis until you find your highest possible x-value. This is your upper bound.

Range :The range is the set of all possible outputs or y-values. To find the range of the graph, we have to look at the y-axis of the graph.

Determining Range :

For the range, do the same thing but move along the y-axis.

x-intercepts and y-intercepts

x-intercept :

1. This is where the graph crosses the x-axis.

2. To find it algebraically, set y = 0.

3. Have many names :

x-intercept

  -Roots

  -Zeros

  -y-intercept :

1. This is where the graph crosses the y-axis.

2. To find it algebraically, set x = 0.

Positive Interval :

In the diagram below, the graph of the function is above the x-axis in the following intervals.

(-3, -1) and (2, 4)

More precisely, y is positive when x ∈ (-3, -1) and (2, 4).

So, the positive intervals for the above graph are

(-3, -1) and (2, 4)

Negative Interval :

In the diagram above, the graph of the function is below the x-axis in the following intervals.

(-∞, -3), (-1, 2) and (4, +∞)

More precisely, y is negative when x ∈ (-∞, -3), (-1, 2) and (4, +∞).

So, the negative intervals for the above graph are

(-∞, -3), (-1, 2) and (4, +∞)

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Answer: x = -10

▬▬▬▬▬▬▬▬▬▬

         [tex]4 + 8 \times x = -76[/tex]

▬▬▬▬▬▬▬▬▬▬

[tex]4+8(x)-4=-76-4\\8(x)=-80\\\frac{8(x)}{8}=\frac{-80}{8}\\= -10\\x = -10[/tex]

▬▬▬▬▬▬▬▬▬▬

Answer Explained:

Given the keywords sum(add), times(multiply), as well as a number(variable), we can make an equation out of this, which was 4 + 8 * x = -76. We subtracted the sides by 4, then divided both of the sides by the next factor, 8, to get -10.

Thus,

4 + 8 × -10 = -76

Hope this helped you. :)

Based on the amount that Ron Sample gets at the beginning of each year, the number of years, and the interest compounded annually, the amount that should be invested to award the price is $35,720.80.

The value of $8,000 is constant which makes it an annuity. However, it comes at the beginning of each year which makes it an annuity due.

The amount to be invested to gain this $8,000 every year is therefore the present value of this annuity due based on the interest rate.

Present value of annuity due = Annuity due x (Present value interest factor of annuity due, 6%, 5 years)

= 8,000 x 4.4651

= $35,720.80

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The dimensions of the original piece of cardboard are 24 inches by 12 inches

The given parameters are:

Length (l)= Width (w) + 12

Length of the square cut out = 6

Volume of box, V = 1728

The volume of the box is then calculated as

V = Length of squares * Length * Width

This gives

V = 6 * (w + 12) * w

So, we have:

6 * (w + 12) * w = 1728

Divide both sides by 6

(w + 12) * w = 288

Expand

w^2 + 12w - 288 = 0

Using a graphing calculator, we have:

w = 12

Substitute w = 12 in l = w + 12

Evaluate

l = 12 + 12

l = 24

Hence, the dimensions of the original piece of cardboard are 24 inches by 12 inches

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Complete question

Lorene plans to make a box from rectangular sheets of cardboard from which she cuts out 6 inches squares from each corner. The length of the original piece of cardboard is 12 inches more than the width. If the box is 1728 inches cubed, determine the dimensions of the original piece of cardboard.

Answer:

XY = 13 cm

Step-by-step explanation:

Area of a triangle formula:

area = base × height / 2

a = bh / 2

Plug numbers into equation:

32.5 = b × 5 / 2

Multiply both sides by 2 to isolate the variable

65 = b × 5

Divide both sides by 5 to isolate the variable

13 = b

Check your work:

32.5 = 13 × 5 / 2

32.5 = 65 / 2

32.5 = 32.5

Correct

Answer:

d none

Step-by-step explanation:

because they are sloping down

From the fig the Area model is, = 3/5(2/5 + 1/3)

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area. Now, imagine your square is made up of smaller unit squares.
Area of rectangle = l x b
given that, lets consider the fig as rectangle with one side 2/5+1/3 as breadth and another side 3/5

As we know , Area of rectangle = l x b

l=3/5

b=2/5+1/3

Area model= 3/5(2/5 + 1/3)

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Answer:

The Area model for the fig. is, = 3/5(2/5 + 1/3).

Step-by-step explanation:

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.

Rectangle area = l x b

Given that, let's imagine the fig as a rectangle with a width of 2/5+1/3 and a length of 3/5.

As we know , Area of rectangle = l x b

l=3/5

b=2/5+1/3

Area model= 3/5(2/5 + 1/3)

The multiplication of 0.34 by 0.568 will be 0.19312 and the number of significant figures is five.

In positional notation, significant figures are the digits in a number that are trustworthy and required to denote the amount of something. Significant figures are the number of digits that add to the correctness of a value, frequently a measurement.

It should be noted that significant figures are the numbers that are reliable and are usually non zero digits.

In this case, the multiplication of 0.34 by 0.568 will be 0.19312.

Therefore, the number of significant figures is five.

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Functions b(x) is not one-to-one functions as the domain of there inverse is not the range of function then you can't find an inverse function. Function d(x) doesn't include x, then you can't also find an inverse function.

What is Mathematical function ?

Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable.

Steps of Finding the inverse of a function f(x):

1. First, replace f(x) with y. This is done to make the rest of the process easier.

2. Replace every x with a y and replace every y with an x.

3. Solve the equation from Step 2 for y. This is the step where mistakes are most often made so be careful with this step.

4. Replace y with  In other words, you’ve managed to find the inverse.

5. Remember: the domain of f is the range of  and the range of f is the domain of [tex]f^{-1}(x)[/tex].

Using this algorithm, you can find the inverse of non.

for f(x) = x^2 +3

y = x^2 + 3

x = y^2 + 3

y = √x-3

[tex]f^{-1}(x)[/tex] = √x-3

The domain and the range of f'(x) :

domain : [3,∞]

Range : [3,∞]

The domain and the range of f(x) :

Domain: x ∈ R (all real number)

Range: y ≥ 3

Functions b(x) is not one-to-one functions as the domain of there inverse is not the range of function then you can't find an inverse function. Function d(x) doesn't include x, then you can't also find an inverse function.

Therefore, for both the given function we cannot find the inverse.

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The length of river Nile is 6825 KM and the length of river Congo is 4370 KM

From the question, we are to determine the lengths of the each river

From the given information,

"The longest river in Africa is the Nile it is 2455 KM longer than the Congo river"

Let the length of river Nile be N

and the length of river Conge be C

Thus,

N = C + 2455

Also,

"the sum of the lengths of these rivers is 11,195 KM"

That is ,

N + C = 11195

Substitute the first equation into the second equation

N + C = 11195

C + 2455 + C = 11195

2C + 2455 = 11195

2C = 11195 - 2455

2C = 8740

C = 8740/2

C = 4370

Substitute the value of C into the first equation

N = C + 2455

N = 4370 + 2455

N = 6825

Hence, the length of river Nile is 6825 KM and the length of river Congo is 4370 KM

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Answer:

96cm²

Step-by-step explanation:

1.) You can split the shape into 2: a rectangle and a triangle.

2.) The formula to find the area of the rectangle is:

length × width.

10 (length) × 8 (width) = 80cm²

3.) Then you can find the area of the triangle. The formula for finding the area of a triangle is:

½ × base × height.

½ × 4 (base) × 8 (height) = 16cm²

3.) Add the two answers together to give you the combined and total area of the shape.

80cm² + 16cm² = 96cm²

Answer: 4800 decimeter

Step-by-step explanation:

0.0048 km = 48 dm

4800 dm = 0.48 km

The given scenario, "A school administrator gets the alphabetical list of students and chooses every third one to survey", is Systematic Sampling.

In the question, we are asked to identify the type of sampling used in the scenario: "a school administrator gets the alphabetical list of students and chooses every third one to survey", among cluster, convenience, stratified, and systematic.

First, we will understand all these types of sampling:-

In the given scenario, the school administrator is getting the list of students in alphabetical order, similar to taking everyone in a line and counting off "1,2,3,4; 1,2,3,4; etc. And then he is choosing every third student, similar to choosing all those numbered 4.

Thus, the given scenario, "A school administrator gets the alphabetical list of students and chooses every third one to survey", is Systematic Sampling.

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Answer:

10x-11 over 4

Step-by-step explanation:

step1:find common denominator

step 2:apply the distributive property

step3: remove the parentheses for addition or subtraction

step4: reorder and gather like terms

step5: collect co-efficients of the like terms

step6: calculate the sum or difference

The x-coordinate of point R from the given coordinates is -8

The formula for calculating the midpoint of coordinates is expressed according to the formula:

M(x, y) = {(x₁+x₂)/2, (y₁+y₂)/2}

Given the coordinate points M (-3,4) and S (2, -3)

Substitute

-3 = (x₁+x₂)/2

-3 = 2+x₂/2

-6 = 2 + x₂

x₂ = -8

Similarly;

Substitute

4 = (-3+y₂)/2

4 = -3+x₂/2

8 = -3 + y₂

y₂ = 11

Hence the x-coordinate of point R from the given coordinates is -8

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Answer:

4.61x10^5

Step-by-step explanation:

You want the first number to be between 0 and 10, not equaling either. So you move the decimal place to the left. Then, you write the second half, which is that you multiply it by ten to the power of however many digits you moved to the left for, which is 5.

The equation of the line with a slope of 2/7 that passes through the point (3, -4) is:

y = (2/7)*x - 34/7

Here we know that the linear equation has a slope of 2/7, so we can start by writing it as:

y = (2/7)*x + b

Now we need to find the value of b, which is the y-intercept.

To find the value of b, we can use the values on the given point, which is (3, -4), This means that when the value of x is 3, the value of y is -4, then we can replace that in the above linear equation, so we will get:

-4 = (2/7)*3 + b

-4 - 6/7 = b

-28/7 - 6/7 = b

-34/7 = b

Then we can conclude that the linear equation is:

y = (2/7)*x - 34/7

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Hello,

[tex]4 = - 8 - \boxed{(-12)}[/tex]

Answer:

Angle 2 is 36 degrees because of Alternate Exterior Angle Theorem being that both of the angle outside and are alternate are Congruent.

The answer is X=11 because 2x+14=36, 2x=22, x=11. 2(11)+14=36

Answer:

point A and point B

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

I think it’s B. because it has negative 3 and negative 2 but for C., it is between negative 2 and negative 1 which can’t be correct since it would end at negative 2 and this is why it is b.

Answer:

I think the answer is A

Step-by-step explanation:

I'm not sure if it's correct or not but I chose the option because the atoms in substance are not chemically combined

Answer:

Step-by-step explanation:

185miles / 75mph =  2.5 hours

The amount saved by repaying the loan early is $831.25

The amount of discount received by purchasing supplies is $3,500

The net amount saved by purchasing supplies rather than repaying loan is $2,668.75

What is ordinary interest?

Ordinary interest is the interest computation that is based on 360-day a  year count rather than 365-day year count, hence, in determining the amount saved by paying $35,000 out of the amount due to Citizens Bank, we time-apportion the interest for 90 days with respect to 360 days not 365 days.

Amount saved in interest=$35,000*9.5%*90/360

Amount saved in interest=$831.25

Using the $35,000 to purchase serving supplies, 10% discount is given off the normal cost of $35,000

Amount saved with discount=10%*$35,000

Amount saved with discount=$3,500

The difference between discount on supplies and interest saved=$3,500-$831.25

The difference between discount on supplies and interest saved=$ 2,668.75

The other factors to consider before making the final decisions include, the fact the loan is more important than the supplies because the loan relates to the firm's financing rather than operational needs of supplies

Secondly, the amount saved in interest may be more if another loan of $35,000 can be borrowed elsewhere with significant lower interest rates

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Answer:

250 ounces of 40% percent copper alloy

Step-by-step explanation:

Let a be the number of ounces of 40% copper alloy.

[tex].4a + .7(500) = .6(500 + a)[/tex]

[tex].4a + 350 = 300 + .6a[/tex]

[tex].2a = 50[/tex]

[tex]2a = 500[/tex]

[tex]a = 250[/tex]

250 ounces of 40% copper alloy.