Problem 2 Charlie estimates the height of a building to be 924 feet. Charlie's father tells him that his estimate has a 20% error. Explain why this is not enough information for Charlie to find the actual height of the building. Based on this information, what are the two possible values for the actual height of this building?​

Answer: x = 22

Step-by-step explanation:

       We will use the exterior angle theorem to solve. First, we will write an equation, then we will solve by combing like terms are using inverse operations.

(6x - 7) = (2x) + (103 - x)

6x - 7 = 2x + 103 - x

6x - 7 = x + 103

5x = 110

x = 22

7/3 in notation one can be written as 7 : 3 and 7/3 in notation two can be written as 0.7 and 0.3.

The ratio is a comparison between two similar quantities in the simplest fraction form. We can write ratios in fractions and in decimals also.

We know we can write a : b as a/b in fraction form and a/(a+b) and b/(a+b) in decimal form.

∴ 7/3 in decimal form can be written as 7 : 3 and 7/3 can also be written as 7/(7+3) = 7/10 = 0.7 and 3/(7+3) = 3/10 = 0.3.

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For the given function f(x), x-intercepts are 1,2 and 6 and the y-intercept is -12

Given :

[tex]f(x) = x^{3} -9x^{2} +20x -12 \\[/tex]

One of the factors of f(x) is (x-6)

Dividing f(x) by (x-6), we get :
[tex]\frac{x^{3} -9x^{2} +20x -12 \\}{x-6} = x^{2} -3x +2[/tex]

Now expanding, [tex]x^{2} -3x +2[/tex]

[tex]x^{2} -3x +2 = x^{2} -2x -x +2 =x(x-2) -(x-2) = (x-2)(x-1)[/tex]

Hence, [tex]x^{3} -9x^{2} +20x -12 = (x-6)(x-1)(x-2)[/tex]

For x-intercept, f(x) = 0 . Then

(x-6)(x-1)(x-2) =0

x = 1,2 and 6

For y-intercept, x=0 in f(x)

f(0) = -12

Hence, the x-intercepts are 1,2, and 6 and the y-intercept is -12.

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Answer:

15

Step-by-step explanation:

16c+4(-5)=220

16c-20=220

16c=240

C=15

The union of two sets contains all the elements contained in either set (or both sets). The intersection of two sets contains only the elements that are in both sets

Therefore the answer is B.

The solution for the given binomial multiplication is 6x³ + 10x² - 17x - 7

Given,

The binomials; (2x² + 4x - 7) (3x - 1)

We can use FOIL method to solve this;

FOIL method;

Binomials are multiplied using the FOIL Method. An acronym is FOIL FOIL. First, Outside, Inside, and Last are the letters that stand for the order of multiplying terms. To get your answer, multiply the first term, then the outside term, then the inside term, then the last term, and then combine terms that are similar.

Here,

(2x² + 4x - 7) (3x - 1)

= (3x × 2x²) + (3x × 4x) - (3x × 7) - 2x² + 4x - 7

= 6x³ + 12x² - 21x - 2x² + 4x - 7

= 6x³ + 10x² - 17x - 7

That is,

The solution for the given binomial multiplication is 6x³ + 10x² - 17x - 7

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area of triangle with vertices (x1,y1) ; (x2,y2) and (x3,y3) is

(x1 (y2 - y3 ) + x2 ( y3 - y1 )+ x3 ( y1 - y2))/2

hence, substituting the points (x1, y1)= (-2, 1);

( x2, y2)= (0,3) ; and (x3, y3)= (4,-4) in the area formula ,we get

area of triangle =

( -2(3-(-4)) + 0( -4 - 1) + 4(1-3))/2

(-14+0-8)\2

22\2

11 sq unit

If the university invest in a one year CD at 5.12% interest compounded continuously, the interest it will earn is determined by calculating as: Interest = Future value – Present value which would be $2.54 million

Continuously compounded interest means that a principal amount is constantly earning interest with infinite compounding periods for a certain time period. There are no increment compounding periods as with monthly or annually compounding.

The continuously compounding formula:

FV = PV* e^rt

Where FV is the future amount, PV is the initial amount, e is a mathematical constant (2.7183), r is the rate and t is the time period.

Hence,

FV = 49* 2.7183^(0.0512*1) =51.57

Interest earned= 51.57-49=2.54

Hence, the university will earn an interest of $2.54 million.

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Answer:

2000 pounds is 1 ton

6 tons is 12,000

7 tons is 14,000

16,000 pounds is 8 tons

The solution of x for the equation [tex]\sqrt{3x - 4} = 2\sqrt{x-5}[/tex] is x = 16.

Given,

The equation; [tex]\sqrt{3x-4} =2\sqrt{x-5}[/tex]

We have to solve this equation to get the value of x.

That is,

[tex]\sqrt{3x-4} =2\sqrt{x-5}[/tex]

Square both sides to remove square root.

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

We get,

3x - 4 = 4 (x - 5)

That is,

3x - 4 = 4x - 20

Here,

20 - 4 = 4x - 3x

Then,

x = 16

That is,

The solution of x for the equation [tex]\sqrt{3x - 4} = 2\sqrt{x-5}[/tex] is x = 16.

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The most appropriate choice for matrix and multiplicative inverse of matrix will be given by

B is the multiplicative inverse of A

What is a matrix and multiplicative inverse of matrix?

Matrix is a rectangular representation of numbers or symbols arranged in the form of rows and column. Matrix is a very important tool in mathematics.

To learn about multiplicative inverse, it is important to know about identity matrix

[tex]\begin{bmatrix} 1 & 0 \\ 0 & 1\end{bmatrix}[/tex] is a 2 x 2 identity matrix denoted by I.

Let A and B be two matrices

A is said to be a multiplicative inverse of B if AB = BA = I

Here,

A=   [tex]\begin{bmatrix} 2& 1\\1 & 1\end{bmatrix}[/tex] B = [tex]\begin{bmatrix} 1& -1\\-1 & 2\end{bmatrix}[/tex]

AB =

[tex]\begin{bmatrix} 2& 1\\1 & 1\end{bmatrix}\begin{bmatrix} 1& -1\\-1 & 2\end{bmatrix}[/tex]

[tex]\begin{bmatrix} 2\times 1 + 1 \times -1& 2 \times -1 + 1\times 2\\1 \times 1+1\times-1 & 1 \times -1 + 1 \times 2\end{bmatrix}\\\begin{bmatrix} 1& 0\\0&1\end{bmatrix}\\[/tex]

BA =

[tex]\begin{bmatrix} 1& -1\\-1 & 2\end{bmatrix}\begin{bmatrix} 2& 1\\1 & 1\end{bmatrix}[/tex]

[tex]\begin{bmatrix} 1\times 2 + -1 \times 1& 1 \times 1 + -1\times 1\\-1 \times 2+2\times 1 & -1 \times 1+ 2 \times 1\end{bmatrix}\\\begin{bmatrix} 1& 0\\0&1\end{bmatrix}\\[/tex]

AB = BA = [tex]\begin{bmatrix} 1& 0\\0&1\end{bmatrix}\\[/tex]

So B is the multiplicative inverse of A

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a)I WILL USE THE THEOREM OF PYTHAGORAS IN TRIANGLE BCD

[tex] {y}^{2} = {(5.3)}^{2} - {(4.4)}^{2} \\ {y}^{2} = 28.9 - 19.36 \\ {y}^{2} = 9.54 \\ y = \sqrt{9.54} \\ y = 3.09[/tex]

y=3.90cm

b)

[tex] \sin(x) = \frac{cb}{ac} \\ \sin(x) = \frac{5.3}{8.2} \\ x = sin^{ - 1} ( \frac{5.3}{8.2} ) \\ x =40.27[/tex]

x=40,27 cm

GOODLUCK.

Answer:

QPR SAS

Step-by-step explanation:

As you can see. Hope it can help

Using BODMAS we can conclude, Yes, both will give same result.

The rule used to solve mathematical expressions is known as the BODMAS rule. The order of operations for mathematical formulas requiring several operations is known as BODMAS. B. Brackets, O. Order of powers, D. Division, M. Multiplication, A. Addition, and S. Subtraction make up the acronym.

−9×(−9)−9

⇒ - 9 × 81

⇒ -729

⇒ [−9×(−9)]−9​

⇒ [81] -9

⇒ -729

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Answer:

119º and 61º

Step-by-step explanation:

2x-15 and 3x+5 are supplementary because the angles corresponding to 2x-15 is supplementary with 3x+5

2x-15+3x+5=180

5x-10=180

5x=190

x=38

fill in x

2(38)-15

=76-15

=61

angle is 61

fill in x for angle 2

3(38)+5

=114+5

=119

angle 2 is 119

Answer

The polynomial is

P(x) = 2x⁴ - 5x³ + 3x²

Explanation

We are told to write a polynomial of degree 4 with zeros (roots)

x = 1

x = (3/2) = 1.5

x = 0

x = 0 (multiplicity of 2 means it appears twice)

So, we can piece together the polynomial

P(x) = (x - 1) (x - 1.5) (x) (x)

We can write this as

P(x) = x² (x - 1) (x - 1.5)

= (x³ - x²) (x - 1.5)

We can multiply through by 2 to turn the 1.5 into a whole number

P(x) = (x³ - x²) (2x - 3)

= x³ (2x - 3) - x² (2x - 3)

= 2x⁴ - 3³ - 2³ + 3x²

= 2x⁴ - 5x³ + 3x²

Hope this Helps!!!

Answer:

First, 24 divided by 8 equals 3. this means you divide 12 by 3. you get 4. 4 cups of sugar will be used when 8 cups of flour are used.

Using a linear function, it is found that her taxi ride was of 5 miles.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which the coefficients are described as follows:

For the cost function, we have that:

Thus the cost for a ride of x miles is of:

C(x) = 3.75x + 1.10.

Her total fee was of $19.85, hence the mileage is found as follows:

19.85 = 3.75x + 1.10

x = (19.85 - 1.10)/3.75

x = 5 miles.

Which was the length of her taxi ride.

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Answer:

h = 6.36619772 cm

Step-by-step explanation:

h = (3 * v) / (πr2)

Answer:

h = 20 cm

Step-by-step explanation:

the volume (V) of a cone is calculated as

V = [tex]\frac{1}{3}[/tex] πr²h ( where r is the radius )

given r = 9 and V = 540π , then

[tex]\frac{1}{3}[/tex] π × 9² × h = 540π

[tex]\frac{1}{3}[/tex] × π × 81h = 540π

27πh = 540π ( divide both sides by 27π )

h = [tex]\frac{540\pi }{27\pi }[/tex] = 20 cm

Each person will get a 5/24 portion of the available cake with Paige

Cake available with Paige = 5/6

Number of people = 4 people

Fractions: A numerical value that designates a portion of a whole is used to represent fractions. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

Fraction of cake each person gets:

Cake available with Paige/Number of people with whom the cake is to share equally

= (5/6)/(4)

= (5/6)*(1/4)

= 5/24

The fraction of cake each person will get is 5/24

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Answer:

3(c) + 25

Step-by-step explanation:

Write an expression that represents the total owed for 3 months of cable at a price of c dollars for each month, plus a one-time equipment fee of $25?

2(25) + c

25c + 3

3(c) + 25

3(c + 25)

89 squares will be present.

Given that the rectangle has the following dimensions: length = 96 cm, breadth = 84 cm, and

its total area is 8064 square centimeters, we may deduce that the maximum square area

[tex]\sqrt[2]{8064}[/tex]

that can be removed from the rectangle with its total area of 8064 square centimeters is equal to 89.8 square centimeters.

In order to determine the total number of squares, divide 8064 by 89.8 to arrive at 89.

Taking an integer's square root is the opposite of squaring an integer. A number's square value is obtained by multiplying it by itself, whereas the square root value is obtained by finding a number that, when squared, produces the original value of the number.

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Answer: x^2-9x+20

Step-by-step explanation: you have to distribute (x-5) (x-4)

which would be x^2-4x -5x +20 when you simplify that you get x^2-9x+20

1. Based on the proportional relationship table created, 4.8 gallons of water will be in the fish tank after 3 mins.

2. 25 minutes.

3. The Constant of proportionality is: 1.6.

In a proportional relationship between variables x and y, the Constant of proportionality, k, is determined using any pair of values from the table as:

k = y/x.

The relationship is modelled as y = kx.

Constant of proportionality = k = y/x = 0.8/0.5

Constant of proportionality = k = 1.6

The equation for the relationship would be: y = 1.6x. Use the equation to complete the table:

For x = 1:

y = 1.6(1) = 1

For x = 3:

y = 1.6(3) = 4.8

For y = 40:

40 = 1.6x

40/1.6 = x

x = 25

The complete table is:

x             y              

0.5        0.8

1            1.6

3           4.8

25        40

1. Using the proportional relationship table, we can conclude that, 4.8 gallons of water will be in the fish tank after 3 mins.

2. Using the proportional relationship table, the time it would take to fill the tank with 40 gallons of water is: 25 mins.

3. Constant of proportionality = k = 1.6.

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The new length of the building will be 110 feet.

Volume of Cuboid:

                              Volume of cuboid is

                        V =  length x breadth x height cubic unit

Given,

The building was going to be 100 feet long, 75 feet deep, and 30 feet high.

Therefore, the volume will be:

               = 75 × 100 × 30 ft³

               = 225000 ft³

Now owner decided increase the volume of the building by 10% without changing the dimensions of the depth and the height.

There was an increase by 10%,

New volume will be,

V' = 225000 + (10% × 225000)

  = 247500 ft³

Therefore, the new length will be:

as,

        Volume =  length x breadth x height

        length  =  Volume/ (breadth x height)

New length will be

                      = 247500/(30 × 75)

= 110 feet

Thus the new length of the building will be 110 feet.

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For the gold worth $1323.80 per ounce ,the nugget containing 0.82 ounce of gold is worth of $1085.516.

As given in the question,

On a tour of a gold mine,

Ounce of gold contained by nuggets found in the mine = 0.82 ounce

Worth of gold per ounce = $1323.80 per ounce

Worth of nuggets containing 0.82 ounce of gold

Worth of 1 ounce of gold = $1323.80

⇒ Worth of nuggets containing 0.82 ounce of gold =$( 1323.80 ×0.82 )

                                                                                      = $1085.516

Therefore, for the gold worth $1323.80 per ounce ,the nugget containing 0.82 ounce of gold is worth of $1085.516.

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Answer:

D

Step-by-step explanation: