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If to find the height of a very tall pine tree, you place a mirror on the ground and stand where you can see the top of the pine tree. The height of  the tree is 72 feet.

Given data;

6 ft

2 ft 24 ft

Hence,

Angle of incidence = Angle of reflection

Hence,

m ∠ ACD = m ∠ ECD

Two triangle will only be the same if their corresponding angles are congruent
So,

Sine m ∠ ACD = m ∠ ECD

m Δ ABC  = Δ EDC

The corresponding of similar triangles are proportional

Hence,

BC / DC = AB / ED

= 2 / 24 = 6 / ED

2ED = 24 × 6

2ED = 144

Divide both side by 2

ED = 144 / 2

ED = 72 feet

Therefore we can conclude that the tree height is measure at 72 feet.

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Explanation:

Imagine a rectangle that is 12 by 26. Multiplying the length and width will get us the area.

We can break the 12 into 10+2

Also, break the 26 into 20+6

Check out the diagram below. We have 4 smaller rectangles. Finding the product of those sub-areas will then get us the partial products needed.

In the bottom right corner we have a 2 by 6 rectangle, so it has area 2*6 = 12 square units. This is one of the four partial products. The other partial products are found the same way.

Once you determine the four partial products, we then add them up

12+60+40+200 = 12+100+200 = 12+300 = 312

Therefore, 12*26 = 312 which we can use a calculator to confirm.

The measure of angle B in triangle ABC is 158°.

A triangle is a 2-dimensional closed shape with three sides, three angles, and three vertices. A triangle would be a category of polygon.

For the given angles of the triangle ABC.

∠BAC = 78° , ∠CAD = 46° and ∠ADB = 110°.

Now,

∠BAC = ∠BAD + ∠DAC

Put the values;

78° = ∠BAD + 46°

∠BAD = 78° - 46°

∠BAD = 32°

Now, in a triangle; the sum of all three angles is 180°.

In triangle ADB

∠ABD + ∠BAD + ∠BDA = 180°

Put the values;

∠ABD +  32° +  110°  =  180°

∠ABD = 180°  -  142°

∠ABD = 158°

Thus, the measure of angle B is 158°.

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We need to find which expression represents the situation given, in this case we have two values a distance (80 ft) and the elapsed time (40 s). The time is the input of the equation, it will be placed on the "x" variable and the distance is the output of the equation, it will be placed on the "y" variable. We need to find the expression that outputs "80" when we input 40. Let's check them one by one:

A.

This outputs 20 ft when we input 40 s, therefore it is not this one.

B.

This one outputs 160 ft when we input 40 s, therefore it is not this one.

C.

This one outputs 80 ft when we input 40 s, therefore this is the correct expression.

We now need to use this expression to calculate the distance the person will travel in 10 seconds, so we will make x equal to 10 s.

The person will walk 20 ft.

The correct option is "C".

We get 700,000 after rounding off to the place value of the underlined digit in the number 698,072.

According to the question,

We have the following number with 6 as the underlined digit:

698,072

When rounding off the number, please note that the digits to the right of the underlined digit would be zero. However, we need to be careful where we need to scale up the underlined number or it would remain the same.

For this, we need to check the number to the right of the underlined digit. If the number right next to the underlined digit is greater than 5 then the underlined digit has to be scaled up. And if it is less than 5 then the underlined digit remains the same.

So, after rounding off we will get:

700,000

Hence, the number after rounding off to 6 in 698,072 is 700,000.

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Polynomials are algebraic expressions that consist of the variables and coefficients. Six complex number system, polynomial 3x6x³-4x²+3x+52 = 0 have.

Polynomials are algebraic expressions that consist of the variables and coefficients. Variables are also sometimes called the indeterminates. We can perform the arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable.

We have following polynomial for this situation.

We observe that polynomial graph only intersects the vertical axis once.

There are no additional x-axis cutoff points in graph.

As a result, polynomial:

6 difficult solutions

No actual solution

So, we can 6 difficult solutions.

We have following polynomial for this situation.

We observe that polynomial graph only intersects the vertical axis once.

There are no additional x-axis cutoff points in graph.

As a result, polynomial:

6 difficult solutions

No actual solution

So, 6 complex solutions can be said to exist.

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The 90% confidence interval for the mean score, μ, of all students taking the test is; CI = (28.36, 30.64)

The formula for confidence interval is;

CI = x' ± z(s/√n)

where;

CI = Confidence Interval

x' is sample mean

z is critical value at confidence level

s is standard deviation

n is sample size

We are given;

n = 59

x' = 29.5

s = 5.2

z at CL 0f 90% = 1.645

Thus;

CI = 29.5 ± 1.645(5.2/√59)

CI = 29.5 ± 1.136

CI = (28.36, 30.64)

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Answer:

[tex]y=x^2-4x-2[/tex]

Step-by-step explanation:

Standard Form of Quadratic:

[tex]y=ax^2+bx+c[/tex]

Vertex Form of Quadratic:

[tex]y=a(x-h)^2+k[/tex]

h = vertex x

k = vertex y

Think of h and k as the ordered pair (h,k).

Match this ordered pair to the vertex ordered pair.

(h,k) = (2, -6)

Plug in (h,k) into vertex form:

[tex]y = a(x-2)^2-6[/tex]

Use other point to solve for a.

[tex]3 = a(5-2)^2-6[/tex]

[tex]3=a(3)^2-6[/tex]

[tex]3=9a-6[/tex]

[tex]9=9a[/tex]

[tex]a=1[/tex]

Plug a back into vertex form and expand the expression into standard form:

[tex]y=(x-2)^2-6[/tex]

[tex]y=(x-2)(x-2)-6[/tex]

Use F.O.I.L. method to expand (x-2)(x-2).

F(first):  [tex]x*x=x^2[/tex]

O(outer):  [tex]x*-2=-2x[/tex]

I(inner): [tex]-2*x =-2x[/tex]

L(last): [tex]-2*-2=4[/tex]

[tex]y=x^2-2x-2x+4-6[/tex]

Combine like terms:

[tex]y=x^2-4x-2[/tex]

Let's begin solving the problem by illustrating the problem using a diagram:

Let the height of building B be x

Re-drawing the triangles to show the unknown side:

Using trigonometric ratios and sine rule

Hence:

The height of the building B is 79 ft

The cosine of the angle given is negative.

Cosine is negative in the second and third quadrant

In the second quadrant,

In the third quadrant,

Therefore, the values that satisfy the equation are 99.6 and 260.4 degrees.

The distance between the point is 5.

The formula to find the distance between two points (x1, y1) and (x2, y2)

distance = [tex]\sqrt{(x2-x1)^{2} + (\\ y2-y1)^{2} }[/tex]

Substituting points A(2,9) and B(-2,6), we get

distance = [tex]\sqrt{(-2-2)^{2} + ( 6-9)^{2} }[/tex]

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

              = [tex]\sqrt{16 + 9}[/tex]

              =[tex]\sqrt{25}[/tex]

             = 5

Therefore the distance between the two points is 5.

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The statement quantity 8 minus one third times the square root of 9 end quantity squared plus the quantity 1 minus 5 end quantity squared is simplified to 65

Fractions are defined as parts of a whole element, set or number.

There are various types of fractions, which includes;

Based on the information provided, we have;

Now, substitute the values

(8 - 1/3(√9))² +  (1 - 5)²

Find the square root

(8 - 1/3(3))²+ (-4)²

Find the square

(8 - 1)² + 16

7² + 16

49 + 16

Add the values

65

Hence, the value of the expression is 65

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A triangle that has two sides of 10 and 6 with an area of 12 units will have the third side length of 4.

The triangle can be described as the the figure that has threes sides which can be equal or varies base on the type of the triangle it is, and the area of the triangle is given, we can use the formula for the are of triangle which i s (1/2  * b * h )

Then the Area of a triangle = (1/2  * b * h)

we were given the two sides already with the area , then we can input the values as :

12 =( 1/2 * 6 * x)

where x is the third sides that is needed

x = 4

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In order to convert a percent to a decimal number we need to move the decimal point two units to the left

The graph of the polynomial function x³ - 3x² - 4x = 0 is shown if figure.

What is Polynomial function?

A mathematical expression of algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power.

Given that;

The degree of the polynomial function f(x) is 3.

And, The roots of the equation f(x) = 0 are -1, 0, and 4.

Now, The polynomial function are calculated as;

f (x) = 0

(x + 1) (x - 0) (x - 4) = 0

x (x + 1) (x - 4) = 0

x (x² - 4x + x - 4) = 0

x (x² - 3x - 4) = 0

x³ - 3x² - 4x = 0

Thus, The polynomial function is;

x³ - 3x² - 4x = 0

Therefore, The graph of the polynomial function x³ - 3x² - 4x = 0 is shown if figure.

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viven

t = time

function

what is the probability that the machine will not need repairs within 12

rocedure

The probability would be 0.0016

Answer:

y= vw/ux

Step-by-step explanation:

hope this help

The simplified representation of the complex number expression is

23 + 37i

a + bi, where a and b are real numbers, can be used to represent any complex number.

The complex number expression is (6-4i)(1+5i)-(3-i)

now let us simplify,

or, (6-4i)(1+5i)-(3-i)

or, 6 + 30i - 4i -20i² -3 + i

or, 6 + 36i + 20 - 3 + i (we know that i² = -1)

or, 23 + 37i

Therefore the simplified complex expression is 23 + 37i

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The solution to the given equation (2(-2) - 4 = 12) is -20 and its graphical solution is shown in the image attached below.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

Next, we would solve the given equation as follows:

2(-2) - 4 = 12

Let us introduce a variable x into the equation as follows:

x = 2(-2) - 4 - 12

x = -4 - 4 - 12

x = -20

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Answer:

The line is parallel to y + x =3

=> y = -x+3

the slope = -1

passes (-12, 0)

the equation would be :

y-0 = -1(x+12)

y = -x -12 Y=-x+12

Turn into mx+b form.

Y=-x+3

Plug in (-12,0)

0=-12+b

b=12

y=-x+12

It is negative X, because the slope has to be the same since it is paralle

Step-by-step explanation:

Long division gives the answer of 24 when 72 is divided by 3.

Long division in mathematics is a strategy for breaking down complicated division problems into a series of simpler steps. It is the approach that division-based issues are typically solved using. The dividend, the quotient, the remainder, and the divisor can all be seen in the following long division.

So as we know:

Start by arranging it so that the dividend 72 is on the right side and the divisor 3 is on the left:

 3 ⟌ 7 2  

Start by arranging it so that the dividend 72 is on the right side and the divisor 3 is on the left:

    2    

   3 ⟌ 7 2  

Write the result (3 x 2 = 6) underneath the dividend after multiplying the divisor by the outcome from the previous step.

     2    

   3 ⟌ 7 2  

       6    

Write the solution below after subtracting the result from the previous step from the dividend's first digit (7 - 6 = 1).

Reduce the dividend's second digit (2) as follows:

    2    

   3 ⟌ 7 2  

     - 6    

       1 2  

The bottom number (12) is multiplied by the divisor (3) four times (s). Put 4 thus on top

Subtract the result of the previous step (3 x 4) from the divisor to get the solution (12), which you should write at the bottom:

  2 4  

   3 ⟌ 7 2  

     - 6    

       1 2  

      1 2  

Take the number above it and deduct the outcome from the preceding calculation. Write the response at the bottom after calculating (12 - 12 = 0).

The top number is the solution, and the remaining value is the bottom one.

Therefore, the result of 72 divided by 3 using long division is 24.

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Answer:

The correct number is -27.

Step-by-step explanation:

-81 ÷ 3 = -27

The number line 5 ≤ 8-3x  shows the solution to the inequality as x cannot be more than 1.

A inequality compares two values and indicates whether one is smaller, larger, or simply not equal to the other.

a  ≠ b is the information that a and b are not equal.

If a  > b, a is greater than b. (these two are defined as strict inequality)

a ≤ b proves that a is less than or equal to b

a ≥ b proves that a is greater than or equal to b

The number line 5 ≤ 8-3x  shows the solution to the inequality as x cannot be more than 1.

If x is more than 1, lets say 2

Then the inequality as follows

5 ≤ 8-3(2) ≤ 14

5 ≤ 8-6 ≤ 14

5 ≤ 2 ≤ 14  this statement becomes false

Therefore x, must be lower than 1

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From the right triangle, and using the definitions of the tangent and the cosine functions, we have:

From the problem, we identify:

Finally, using these values, we can find b and c.

Using (1):

Using (2):

In the PEMDAS method of solving , it goes to the five basic operations

1.Parenthesis 2. Exponents 3. Multiplication 4. Addition 5.Substraction

In this exercise there are NOT parenthesis, so then the first operation is Exponentiation and 2nd operation is Multiplication

So the answer is Multiply, the first option.

The base of Triangle B is 1 inches.

Given,

Triangle A has a height of 8 inches

and base of Triangle is 2 inches

Let's Find the Area of Triangle A

We know that the formula of Area of Triangle

Area of Triangle = [tex]\frac{1}{2}[/tex] × b × h

where, b is the base and h is the height of triangle.

Plug the values of base and height in above formula.

Area of Triangle A  = [tex]\frac{1}{2}[/tex] × 2 × 8

Hence, Area of Triangle A is 8 sq. inches

In this question, Some part is missing that is:

Triangle A is similar to Triangle B

Now, For Triangle B is given:

Triangle B has a height of 16 inches

and, to find the base of the triangle.

We know, Area of Triangle A is 8 sq. inches.

Area of Triangle B =  [tex]\frac{1}{2}[/tex] × b × h

8 =  [tex]\frac{1}{2}[/tex] × b × 16

8 = 8b

b = 1 inches

Hence, The base of Triangle B is 1 inches.

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Answer:

Slower

Step-by-step explanation

The scooter travels 60 feet in 4 seconds, so it is going faster than the skateboard, which travels 55 feet in 4 seconds. A cargo ship traveled 150 nautical miles in 6 hours at a constant speed. How far did the cargo ship travel in one hour?

The simplified form of the expression 29 - ( 11 - 2³ ) + 6² ÷ 4 is 35

Given the expression in the question;

29 - ( 11 - 2³ ) + 6² ÷ 4

To simply, replace 2 raised to the power of 3 with 8 and 6 raised to the power of 2 by 36

29 - ( 11 - 2³ ) + 6² ÷ 4

29 - ( 11 - 8 ) + 36 ÷ 4

Now, remove the parenthesis by performing the operation inside the parenthesis.

29 - ( 11 - 8 ) + 36 ÷ 4

29 - 3 + 36 ÷ 4

Now, divide 36 by 4

29 - 3 + 36 ÷ 4

29 - 3 + 9

Next, add -3 and 9

29 + 6

Add 29 and 6

35

Therefore, 35 is the simplified form of the expression.

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