parallel lines r and s are cut by two transversals, parallel lines t and u

x = 50 * tan(60) = 50sqrt(3) =86.6 feet

tower is 93.6 feet tall

The surface area of the earth using the given formula is 51471.85 m².

The surface area of a solid can be defined as the area covered by its surface. There are two types of area for a solid exact and lateral.

The lateral area represents only the visible portion of the surface area while the exact area is the area of the total surface of the solid.

Given that,

The radius of earth r = 6.4 × 10⁶ m.

The area of a sphere is given as S = 4π × r².

Substitute the value of r to obtain,

S = 4π × (6.4 × 10⁶)²

  = 51471.85

Hence, the surface area of Earth is approximated as 51471.85 m².

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Answer:

d. Carrying a notebook and immediately recording all of her transactions in it.

Step-by-step explanation:

The correct answer is option D.

A bank statement is a document that is typically sent by the bank to the account holder every month, summarizing all the transactions of an account during the month.

Bank statements contain bank account information, such as account number and a detailed list of deposits and withdrawals.

Cassandra's best option would probably be carrying a notebook and immediately recording all of her transactions in it.

Since she does not like to do a lot of heavy thinking when she gets home, and tends to lose pieces of paper, this method is ideal because it would allow her to consolidate all her purchase records in one notebook, eliminating the need to carry receipts, and recording them immediately will make it so she can relax when she gets home.

Perhaps once a month, she can compile all of her notebook activity into a computer program and reconcile it to her bank statements. 

Hence, the correct option is D.

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Answer:

0.039 on gradpoint

Step-by-step explanation:

I got it right on the test

Let the length of the rectangle = x

since the perimeter is 24m then the width of rectangle is (12-x)m.

the area of rectangle is:
 A=x*(12-x)

A=-x^2+12x

x=-12/-2 =6:

Since the length is 6m the width will be: 12-6=6m

We conclude that this rectangle has the maximum area when its shape is square of side 6m.
We find the value of area for x=6m :

Area = 6^2 =36M^2

To cover 50 windows with coverings that are 15 windows long, at least 4 window coverings are needed to span all the windows.

The question asks how many window coverings are necessary to span 50 windows, given that each window covering is 15 windows long. To find out how many window coverings are required, you divide the total number of windows by the length of one window covering. So, we do 50 ÷ 15 which equals approximately 3.33. Since you can't have a fraction of a window covering, you'll need at least 4 full window coverings to span all 50 windows.

Answer: Volume of cylinder is 1152.38 m³.

Step-by-step explanation:

Since we have given that

Radius of cylinder = 10 m

Height of cylinder = 11 m

Using Cavalieri's principle , volume of an oblique cylinder is equal to volume of cone.

So, Volume of an oblique cylinder is given by

[tex]V=\frac{1}{3}\pi r^2h\\\\V=\frac{1}{3}\frac{22}{7}\times 10\times 10\times 11\\\\V=1152.38\ m^3[/tex]

Hence, Volume of cylinder is 1152.38 m³.

perimeter = 4s

56=4s

s=56/4 = 14

diagonal = sqrt (s^2 x 2)= sqrt(14^2 x 2) = sqrt(392) = 19.7989 cm

round answer as needed

Answer:

The approximate length of diagonal is:

19.796 cm.

Step-by-step explanation:

We are given the perimeter of a square as 56 cm.

Let 's' be the side of the square.

We know that the perimeter of square is given as:

[tex]Perimeter=4\times s\\\\56=4s\\\\s=\dfrac{56}{4}\\\\s=14[/tex]

Hence, the side of square is 14 cm.

Now, the length of a diagonal(D) is given as:[tex]D=\sqrt{2}s[/tex]

( Since it could be proved with the help of Pythagorean Theorem )

Hence, as s=14 cm

Hence, the length of diagonal is:

[tex]D=\sqrt{2}\times 12\\\\D=1.414\times 14\\\\D=19.796\ cm[/tex]

Hence, the approximate length of diagonal is:

19.796 cm.

The consecutive integers are 5 and 6.

Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."

Given:

The sum of the reciprocals of two consecutive integers is 11/30.

Let the integers be n and n+1.

Then,

1/n + 1/n+1 = 11/30

{n + 1 + n}/n(n+ 1) = 11/30

30(2n+1 ) = 11(n²+n)

60n + 30 = 11n² + 11n

11n² - 49n - 30 = 0

(11n +6) (n-5) = 0

Only taking,

n = 5.

So, 5 and 6.

Therefore, 5 and 6 are the integers.

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Answer:

2.[tex]16a^2-4a+4a-1[/tex]

Step-by-step explanation:

We have to find the polynomial can be simplified to a difference of squares.

1.[tex]10a^2+3a-3a-16[/tex]

Combine like terms

[tex]10a^2-16[/tex]

10 in [tex]10a^2[/tex] is not a perfect square number  because when a number end with one zero then the number is not perfect square number.

Therefore, it can not be simplified to a difference of squares.

2.[tex]16a^2-4a+4a-1[/tex]

[tex]16a^2-1[/tex]

Combine like terms

[tex](4a)^2-(1)^2[/tex]

Hence, the polynomial can be simplified as difference of squares.

3.[tex]25a^2+6a-6a+36[/tex]

Combine like terms

[tex]25a^2+36[/tex]

[tex](5a)^2+(6)^2[/tex]

Hence, the polynomial can not be simplified as  difference of squares because the polynomial can be  simplified as sum of squares.

4.[tex]24a^2-9a+9a+4[/tex]

Combine like terms

[tex]24a^2+4[/tex]

[tex]24a^2+(2)^2[/tex]

[tex]24=2\times 2\times 3\times 2[/tex]

24 is not  a perfect square number because  when factorize 24 then 2 and 3 are not paired.

Hence, the polynomial can not be simplified as difference of squares.

Answer:

35.5 mph

Step-by-step explanation:

We are given that Sally Leadfoot was pulled over on her way from Syracuse to Ithaca by an officer claiming she was speeding.

Speed limit =65 mph

Sally traveled distance  97 km in 102 minutes

We have to find the Sally's average speed in mph

Time =102 minutes

We know that 1 hour =60 minutes

[tex]102 minutes=\frac{102}{60}=1.7 [/tex]hours

We know that 1 km=0.621371

97 km=[tex]0.621371 \times 97=60.272987[/tex]miles

Average speed =[tex]\frac{60.272987}{1.7}=35.45 mph[/tex]

Average speed  of Sally's =35.5 mph

Hence, average speed of Sally is less than 65 mph .Therefore, she was not fast speeding and she deserves a ticket.

the first line in the chart has x as 0 and Y as 25

 this means the fixed amount would be $25

Answer:

$25

Step-by-step explanation:

because the first number in the chart is $25

hope this helps!

L = lemon drops

J = jelly beans

L +J = 100

L=100-J

1.90L + 1.20J=1.48*100

1.90(100-j) +1.20J =148

190-1.90J+1.20J=148

190-0.7J=148

-0.7J=-42

J = 60

L=100-60 = 40

40 pounds of Lemon Drops are needed

Final answer:

40 pounds of lemon drops are needed.

Explanation:

To find out how many pounds of lemon drops are needed to make a 100-pound mix that costs $1.48 per pound, we can set up a system of equations. Let L represent the number of pounds of lemon drops and J represent the number of pounds of jelly beans.

Since the total weight of the mix is 100 pounds:

L + J = 100

Given the cost of lemon drops is $1.90 per pound and jelly beans cost $1.20 per pound, and the entire mix should cost $1.48 per pound:

1.90L + 1.20J = 100 * 1.48

We already have that L + J = 100, so J can be expressed as 100 - L. Substituting J in the second equation we get:

1.90L + 1.20(100 - L) = 148

Solving for L:

1.90L + 120 - 1.20L = 148

0.70L = 28

L = 28 / 0.70

L = 40

Therefore, 40 pounds of lemon drops are needed for the mix.

The true statement is: The graph of [tex]\(y = \log(x) + 4\)[/tex] is the graph of y = (log(x) translated 4 units up.

Let's analyze each statement:

1. The graph of [tex]\(y - \log(x-4)\)[/tex] is the graph of [tex]\(y - \log(x)\)[/tex] translated 4 units down.

  This statement is incorrect. The function [tex]\(y - \log(x-4)\)[/tex] is the result of shifting the graph of [tex]\(y = \log(x)\) 4[/tex] units to the right, not down.

2. The graph of [tex]\(y = \log(x) - 4\)[/tex] is the graph of [tex]\(y = \log(x)\)[/tex] translated 4 units down.

  This statement is incorrect. The function [tex]\(y = \log(x) - 4\)[/tex] represents a vertical translation of 4 units down from the graph of [tex]\(y = \log(x)\)[/tex], not left.

3. The graph of [tex]\(y = \log(x) + 4\)[/tex] is the graph of [tex]\(y = \log(x)\)[/tex] translated 4 units up.

  This statement is true. Adding a constant term to a function vertically shifts the graph of the function by that amount. So, adding 4 to [tex]\(y = \log(x)\)[/tex] shifts it 4 units up.

4. The graph of [tex]\(y = \log(x+4)\)[/tex] is the graph of [tex]\(y = \log_2(x)\)[/tex] translated 4 units right.

  This statement is incorrect. The function [tex]\(y = \log(x+4)\)[/tex] represents a horizontal translation of 4 units to the left from the graph of [tex]\(y = \log(x)\).[/tex]

Therefore, the true statement is: The graph of [tex]\(y = \log(x) + 4\)[/tex] is the graph of y = (log(x) translated 4 units up.

Question

Which statement is true?

The graph of Y - log(x-4) is the graph of y-log,(x) translated 4 units down.

The graph of Y = log: (x)-4 is the graph of y = log. (x) translated 4 units left.

The graph of y = log,(x)+4 is the graph of Y=log.(x) translated 4 units up.

The graph of y = log. (x+4) is the graph of y = log2 (x) translated 4 units right.

Final answer:

A function is in simplified form when all unnecessary terms have been eliminated, subscripts are used appropriately, and it uses the most compact and standard notation possible. Always verify the reasonableness of the simplified function.

Explanation:

To determine when a function is in simplified form, several steps should be followed:

When you have eliminated all unnecessary terms and used standard conventions for simplification mentioned above, the function is considered to be in its simplest form. It is always good practice to check the answer to see if it is reasonable and does not violate any known principles or constraints.

[tex]4(x+2)=2(x+3)+2(x-1)\\\\use\ the\ distributive\ property:\ a(b\pm c)=ab\pm ac\\\\(4)(x)+(4)(2)=(2)(x)+(2)(3)+(2)(x)-(2)(1)\\\\4x+8=2x+6+2x-2\ \ \ \ |simplify\\\\4x+8=(2x+2x)+(6-2)\\\\4x+8=4x+4\ \ \ \ |-4x\\\\8=4\ FALSE!!!\\\\Answer:\ NO\ SOLUTION\ (x\in\O)[/tex]