How would you solve it?

Regis leans a 10-foot ladder against a wall. The base of the ladder makes a 65 angle with the ground.

hammer [34]

The distance, In feet, from the base of the ladder to the base of the wall is 4.2 ft.

He needs to move the ladder 0.1 ft closer to the base of the building.

The situation forms a right angle triangle.

<h3>Right angle triangle</h3>

Right angle triangle has one of its angles as 90 degrees. The sides and angle can be found using trigonometric ratios.

The length of the ladder is the hypotenuse of the triangle formed. Therefore, the distance, In feet, from the base of the ladder to the base of the wall can be calculated as follows;

cos 65° = adjacent / hypotenuse

cos 65° = d / 10

d = 10 × 0.42261826174

d = 4.22618261741

d = 4.2 ft

She needs to move the ladder so it reached a window 9.6 feet above the ground. Therefore, the distance from the base of the ladder and the wall is as follows;

cos 65 = d / 9.6

d = 9.6 × 0.42261826174

d = 4.05696

d = 4.1

Therefore, he needs to move the ladder 0.1 ft closer to the building.

learn more on right angle triangle here: brainly.com/question/14988069

8 0

2 years ago

Find the equation of an exponential function in the form y = ab^x, given the points (0, 3) and (2, 108/25). Please simplify your

lilavasa [31]

We have the equation:

$y=a\cdot b^x$

We know two points and we will use them to calculate the parameters a and b.

The point (0,3) will let us know a, as b^0=1.

$\begin{gathered} y=a\cdot b^x \\ 3=a\cdot b^0=a \\ a=3 \end{gathered}$

Now, we use the point (2, 108/25) to calcualte b:

$\begin{gathered} y=3\cdot b^x \\ \frac{108}{25}=3\cdot b^2 \\ 3\cdot b^2=\frac{108}{25} \\ b^2=\frac{108}{25\cdot3}=\frac{108}{3}\cdot\frac{1}{25}=\frac{36}{25} \\ b=\sqrt[]{\frac{36}{25}} \\ b=\frac{\sqrt[]{36}}{\sqrt[]{25}} \\ b=\frac{6}{5} \end{gathered}$

Then, we can write the equation as:

$y=3\cdot(\frac{6}{5})^x$

5 0

1 year ago

For Amy's cell phone plan, she pays $30 per month and $0.05 per text message. She wants to keep her bill under $60 per month. Wh

S_A_V [24]

Answer:

.05x + 30 < 60

Step-by-step explanation:

.05x + 30 < 60

.05 is the cost per text. Since we don't know how many text messages she sends, we have to use x to represent it. We know she pays $30 every month no matter what so, we can write .05x + 30. < means it has to be LESS than $60 NOT EQUAL TO, but less than.

I hope this helps you out!

3 0

2 years ago

Which of these triangles appears not to be congruent to any others shown

Wittaler [7]

Answer:

B, C, F

Step-by-step explanation:

B- has different lengths for each side and different angles

C-has different lengths for each side and different angles

F-has different lengths for each side and different angles

Non congruent triangles means if shape is reflected or rotated they would not look the same. Congruent triangles have same equal length and angles are equal in measure.

3 0

3 years ago

Which of the following is a solution to the following system of inequalities?

iren2701 [21]

Option D: $(0,3)$ is the solution to the inequalities.