The second step in the process for factoring the trinomial x2-5x-36 is to

Final Answer:

The height of the shorter cliff is 70 feet and the height of the taller cliff is 118 feet.

Explanation:

To find the height of each cliff, we will use trigonometry. Specifically, we will use the tangent function, which is the ratio of the opposite side to the adjacent side of a right-angled triangle.

First, let's consider the shorter cliff (point A). We know the angle of depression from A to the bottom of the river is 38 degrees. If we imagine a horizontal line at the height of point A, we can create a right-angled triangle with one angle at the bottom of the river, the vertical side as the height of the cliff, the horizontal side as the width of the river, and the angle of depression at point A.

Using the tangent of the angle of depression, we can set up the following equation to find the height of the shorter cliff (which we will call hA):
tan(38 degrees) = height_shorter_cliff / width_river

Solving for the height of the shorter cliff, we get:
height_shorter_cliff = width_river * tan(38 degrees)

Using a calculator or trigonometry tables, we find that the height of the shorter cliff is approximately 70 feet.

Next, let's consider the taller cliff (point B). The angle of elevation from A to B is given as 28 degrees. Now we can imagine another right-angled triangle, this time with one angle at point A, the vertical side as the difference in height between cliffs A and B, the horizontal side as the width of the river, and the angle of elevation at point A.

Using the tangent of the angle of elevation, we can set up an equation to find the height difference between cliffs A and B (which we will call hB - hA):
tan(28 degrees) = (height_taller_cliff - height_shorter_cliff) / width_river

We can rearrange this to solve for the height of the taller cliff:
height_taller_cliff = width_river * tan(28 degrees) + height_shorter_cliff

Now, using our previous result for the height of the shorter cliff (70 feet), we plug it into our equation:
height_taller_cliff = 90 * tan(28 degrees) + 70

Using a calculator or trigonometry tables to evaluate tan(28 degrees), we find that the height of the taller cliff is approximately 118 feet.

Therefore, to the nearest foot, the height of the shorter cliff is 70 feet and the height of the taller cliff is 118 feet.

Answer with explanation:

Take a thread of length x cm.Convert it into circle of radius r cm.

If you divide the Length of circle by value equal to 2 π, you will obtain radius of the circle.The value 2π is a constant Quantity is an Irrational number.

[tex]\rightarrow \frac{\text{Length of thread}}{2 \pi}=r\\\\ \rightarrow \frac{x}{2 \pi}=r\\\\ \rightarrow x=2 \pi r[/tex]

Diameter of Circle =8 cm

Circumference of a circle with a diameter of 8 cm has radius equal to 4 cm because radius is half of diameter

           =2 × 3.14 × 4 cm

          = 25.12 cm

⇒So, Actual Length of thread =25.12 cm

Irrational Quantity=2 π=2×3.14=6.28 cm

So Radius

       [tex]=\frac{25.12}{6.28}\\\\=4 cm[/tex]

Diameter =Radius × 2

            =4 cm × 2

          = 8 cm

The answer of the following mathematical expressions are,

1. True

2. False

3. C. 5

4. A. 17.5 in

5. B. x = 13

Let's go through each of the expression ,

Is -7 + 9 = -9 + 7 true, false, or open?

It is option A. True

Both sides of the equation simplify to 2, so the equation is true.

Is 4x - 3 = 19 true, false, or open?

It is option B. False

When you solve for x, you get 4x = 22, and then x = 5.5. Therefore, the equation is false.

Which of the following is a solution to the equation 16 = 4x - 4?

The value of x is option C. 5

When you solve for x, you get 4x = 20, and then x = 5. So, x = 5 is a solution to the equation.

An art student wants to make a model of the classroom. The length of the classroom is 2.4 times its width. The length of the student's model is 42 inches. What should the width of the model be?

The width is equal to option A. 17.5 inches

If the length is 2.4 times the width, then the width should be 42 inches / 2.4 = 17.5 inches.

Use mental math to determine the solution to x - 3 = 10.

the value of x is option B. x = 13

Adding 3 to both sides of the equation gives x = 10 + 3, which is x = 13.

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Answer:

B. 2√10 + 2√29 units

Divide the given inequality 6x > -24 by 6 to isolate x, resulting in x > -4, which in interval notation is (-4, ∞). The correct choice is D. ( -4, ∞) ].

To solve the inequality 6x > -24, we will divide both sides of the inequality by 6 to isolate x, keeping in mind that since 6 is positive, the direction of the inequality will remain the same.

Step-by-step solution:

Start with the inequality 6x > -24.

Divide both sides by 6, which gives us x > -4.

In interval notation, this translates to (-4, ∞).

The correct choice is D. ( -4, ∞) ]

An asymptote is a line that approaches a curve indefinitely without intersecting it at any finite point. Examples include the line y = 0 for the function y = 1/x, whereas a non-example would be the intersecting line y = x with a parabola y = x^2.

An asymptote is a line that a curve approaches as it heads towards infinity, but never actually reaches.

There are several characteristics of an asymptote that are notable. First, the distance between the curve and the asymptote approaches zero as one moves along the curve towards infinity. However, the curve will never intersect the asymptote at any finite point. There are two main types of asymptotes: vertical and horizontal.

An example of an asymptote is the line y = 0, which is a horizontal asymptote for the function y = 1/x as x approaches infinity.

A common non-example of an asymptote is any line or curve that intersects a graph at a finite number of points, such as the line y = x when compared with a parabola y = x2.

The simplified product is 7x² + 28x.

Option B is the correct answer.

We have,

To simplify the product 7 x (x + 4), we need to distribute the 7x to both terms inside the parentheses.

The distributive property states that for any numbers a, b, and c,

a x (b + c) = a x b + a x c.

Applying this property to the given expression, we have:

(7x) x (x) + (7x) x 4

Multiplying 7x by x gives us 7x², and multiplying 7x by 4 gives us 28x.

So the simplified expression becomes:

7x² + 28x

Therefore,

The simplified product is 7x² + 28x.

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To find the length of the longest side of the triangle, use the Pythagorean theorem to solve for x and determine the side lengths of the triangle.

To find the length of the longest side of the triangle, we need to determine which side is the hypotenuse. In a right triangle, the hypotenuse is the side opposite the right angle. Using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides, we can find the length of the hypotenuse.

Let's denote the three sides of the triangle as A, B, and C. The left side is 2x + 12, the bottom side is 6x - 2, and the right side is 5x - 9. Since we can't determine which side is which based on the given information, we can use the variables.

By applying the Pythagorean theorem, we can set up the equation (2x + 12)^2 + (6x - 2)^2 = (5x - 9)^2. Expanding and simplifying this equation will allow us to solve for x and find the lengths of the sides of the triangle. Once we have the side lengths, we can determine which side is the longest.

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Answer:

The lowest fraction equivalent to 0.6 is [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

Given : The decimal number is 0.6

To find : An equivalent fraction for the decimal number in the lowest terms.

Solution : The decimal number 0.6 is written in fraction by removing decimal.

Step 1 - Write the decimal number

[tex]0.6[/tex]

Step 2- Remove the decimal

[tex]0.6 = \frac{6}{10}[/tex]

Step 3 - Reduced the fraction by dividing Nr. and Dr. by 2

[tex]0.6 = \frac{6}{10}=\frac{3}{5}[/tex]

Therefore, The lowest fraction equivalent to 0.6 is [tex]\frac{3}{5}[/tex]

Numerator is [tex]a_0=3[/tex] and Denominator is [tex]a_1=5[/tex]