MATHEMATICS HIGH SCHOOL

a flag pole that is 10 m talk casts a shadow that is 6 m long. what is the distance from the top of the pole to the end of the shadow

Answers

Answer 1
Answer:

Answer:

11.66 meters

Step-by-step explanation:

First draw a diagram. See attachment.

We notice that if we draw everything out, we get a right triangle.

The flag pole and its shadow are the two legs, with lengths 10 and 6 meters. We want to find the distance from the top of the pole to the end of the shadow, so we need to use the Pythagorean Theorem, which states that for a right triangle with legs a and b and hypotenuse c:

a² + b² = c²

Here, a = 10 and b = 6, and we want to find c:

a² + b² = c²

10² + 6² = c²

100 + 36 = c²

136 = c²

c = √136 = 2√34 ≈ 11.66 meters

~ an aesthetics lover
Answer 2
Answer:

Answer:

11.7

Step-by-step explanation:

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PLEASE HELP Describe the graph of the function f(x) = x3 − 18x2 + 107x − 210. Include the y-intercept, x-intercepts, and the shape of the graph.

Answers

f(x) = x³ - 18x² + 107x - 210

X - Intercept: f(x) = x³ - 18x² + 107x - 210
                         0 = x³ - 18x³ + 107x - 210
                         0 = x³ - 7x² - 11x² + 77x + 30x - 210
                         0 = x²(x) - x²(7) - 11x(x) + 11x(7) + 30(x) - 30(7)
                         0 = x²(x - 7) - 11x(x - 7) + 30(x - 7)
                         0 = (x² - 11x + 30)(x - 7)
                         0 = (x² - 6x - 5x + 30)(x - 7)
                         0 = (x(x) - x(6) - 5(x) + 5(6))(x - 7)
                         0 = (x(x - 6) - 5(x - 6))(x - 7)
                         0 = (x - 5)(x - 6)(x - 7)
                         0 = x - 5     or     0 = x - 6     or     0 = x - 7
                      + 5      + 5          + 6      + 6          + 7      + 7
                         5 = x        or       6 = x        or       7 = x
Solution Set: {5, 6, 7}

Y - Intercept: f(x) = x³ - 18x² + 107x - 210
                      f(x) = (0)³ - 18(0)² + 108(0) - 210)
                      f(x) = 0 - 18(0) + 0 - 210
                      f(x) = 0 - 0 - 210
                      f(x) = 0 - 210
                      f(x) = -210

Shape of the Graph: Odd Degree Polynomials With a Positive Leading Coefficient
 

Answer:

X - Intercept: f(x) = x³ - 18x² + 107x - 210

0 = x³ - 18x³ + 107x - 210

0 = x³ - 7x² - 11x² + 77x + 30x - 210

0 = x²(x) - x²(7) - 11x(x) + 11x(7) + 30(x) - 30(7)

0 = x²(x - 7) - 11x(x - 7) + 30(x - 7)

0 = (x² - 11x + 30)(x - 7)

0 = (x² - 6x - 5x + 30)(x - 7)

0 = (x(x) - x(6) - 5(x) + 5(6))(x - 7)

0 = (x(x - 6) - 5(x - 6))(x - 7)

0 = (x - 5)(x - 6)(x - 7)

0 = x - 5 or 0 = x - 6 or 0 = x - 7

+ 5 + 5 + 6 + 6 + 7 + 7

5 = x or 6 = x or 7 = x

Solution Set: {5, 6, 7}

Y - Intercept: f(x) = x³ - 18x² + 107x - 210

f(x) = (0)³ - 18(0)² + 108(0) - 210)

f(x) = 0 - 18(0) + 0 - 210

f(x) = 0 - 0 - 210

f(x) = 0 - 210

f(x) = -210

Work out (25/9) to the power of -3/2

Answers

To work out (25/9) to the power of -3/2, we can use the property of exponentiation. The negative exponent signifies taking the reciprocal of the base raised to the positive exponent. Additionally, the fractional exponent indicates taking the square root of the base raised to the numerator and then taking the reciprocal of the result raised to the denominator. Let's calculate it step by step.

2 less than 4 times a number is -18

Answers

Step-by-step explanation:

4x -2 = -18

to solve for x

4x = -16

x = -4

Which of these conditions might be true if polygons ABCD and KLMN are similar? A. The measures of corresponding angles of ABCD and KLMN are equal, but the lengths of corresponding sides of ABCD are half those of KLMN.B. The measures of corresponding angles of ABCD and KLMN are in the ratio 1 : 2, but the lengths of corresponding sides of ABCD and KLMN are not proportional.
C. The lengths of corresponding sides of ABCD and KLMN are equal, but the measures of corresponding angles of ABCD and KLMN are not equal.
D. The lengths of corresponding sides of ABCD and KLMN are proportional, but the measures of corresponding angles of ABCD and KLMN are not equal.
E.The measures of corresponding angles of ABCD and KLMN are not proportional, but the lengths of corresponding sides of ABCD and KLMN are proportional.

Answers

The correct answer is:


A) The measures of corresponding angles of ABCD and KLMN are equal, but the lengths of corresponding sides of ABCD are half those of KLMN.


Explanation:


The definition of similar polygons is two polygons whose corresponding angles are congruent and whose corresponding sides are proportional.


If the lengths of the corresponding sides of ABCD are half of those of KLMN, this is the proportion 1:2.


Combined with the fact that the measures of the corresponding angles are congruent, this makes ABCD and KLMN similar polygons.
The question ask to choose among the following choices that state the truth about the condition if polygon ABCD and KLMN are similar and the answer would be letter  A. The measures of corresponding angles of ABCD and KLMN are equal, but the lengths of corresponding sides of ABCD are half those of KLMN.

If m > n, which inequalities must be true? Check all that apply. m + 2.1 > n + 2.1 m - (-4) > n -(-4) m + 3 > n-3 16.5 + m > 16.5 + n 1 m > n + 2 9 + m > 6 + 1

Answers

Let's begin by listing out the information given to us:

m > n

We will proceed to solve the inequalities given as shown below:

\begin{gathered} If\colon m>n \n \n m+2.1>n+2.1 \n \text{Subtract ''2.1'' from both sides, we have:} \n m>n \n m+2.1>n+2.1\Rightarrow m>n \n \therefore m+2.1>n+2.1(TRUE) \n \n m-(-4)>n-\mleft(-4\mright) \n \Rightarrow m+4>n+4 \n \text{Subtract ''4'' from both sides, we have:} \n m>n \n m+4>n+4\Rightarrow m>n \n \therefore m+4>n+4(TRUE) \n \n m+3>n-3 \n \text{Subtract '3'' from both sides, we have:} \n m>n-3-3\Rightarrow m>n-6 \n m>n-6\ne m>n \n \therefore m+3>n-3(FALSE) \n \n \end{gathered}

The last three choices are below:

\begin{gathered} 16.5+m>16.5+n \n \text{Subtract ''16.5'' from both sides, we have:} \n m>n \n 16.5+m>16.5+n\Rightarrow m>n \n \therefore16.5+m>16.5+n(TRUE) \n \n m>n+2​ \n m>n+2​\ne m>n \n \therefore m>n+2​(FALSE) \n \n \n \end{gathered}

The inequalities marked as TRUE are the inequalities that apply

Help please I need it asap

Answers

Answer:

<2 ~= < 4 - Vertical Angles Theorem

<2 ~= <8 - Alternate Exterior Angles

<4 ~= <8 - Corresponding Angles Theorem

line I || line m - Transitive Property
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