MATHEMATICS MIDDLE SCHOOL

Sally's cat is stuck in a tree 18 ft off the ground. The base of a ladder is placed 6 feet away from the base of the tree. What is the minimum length ladder needed to reach the cat (rounded to the nearest foot)?

Answers

Answer 1

Answer:

Answer: 19 ft

Step-by-step explanation:

Hi, we have to apply the Pythagorean Theorem, since the tree and the ladder form a right triangle. (see attachment)

Hypotenuse squared = side squared + side squared.

Hypotenuse of a right triangle is the longest side.

Replacing with the values given:

x^2 = 18^2 + 6 ^2

Where x is the length of the ladder.( because is the longest side)

Solving for x:

√(18^2 + 6 ^2)= x

19 ft

Answer 2

Answer: around 12 feet of minimum latter needed. :)

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(99 POINTS!) What are some challenges that Hypatia, the first woman mathematician, faced in her lifetime.

Answers

In Hypatia's young years, she had no troubles at all. Her father was an instructor who educated her in almost business she needed to know. Literature, philosophy, science, arts, and even environmental action which comprised of swimming, horseback riding, and rowing. Hypatia was basically a cheat sheet. She aided other minors with her ability and was treated to be an orator, or national lecturer. Her dialogues mostly embodied of consultation on Diophantus (the father of algebra). Explanation to his undetermined dilemmas, and the metaphor he arranged was talked about. People came from country to country to hear this girl lecture.

People always made fun of Hypatia for her scintillating grasp. She went to a school of Greek. The Greeks logic was that whose beliefs were adverse of the commanding Christian religion at the time. Each and everybody who accepted thought was considered a skeptic from the interruption that was created among the two contrasting beliefs. Ever since Cyril became the elder of Egypt, people thought that it would be better if the annihilation of Hypatia would bring back truce to Alexandria. While on her way to the academy, she was captured by an association of population who trusted Cyril. They deprived her of her attire and down to her exposed skin while dragging her torso to the church where they slaughtered her into bits. The last thing they did was ignite her body.

Cyril and Orestes became bitter political rivals as church and state fought for control

(-3,2) and ( 2,-13) slope intercept equation

Answers

Given:

The points are (-3, 2) and (2, -13).

To find:

Slope-intercept form of the equation.

Solution:

Here $x_1=-3, y_1=2, x_2=2, y_2=-13$ .

Slope of the line:

$$m=(y_2-y_1)/(x_2-x_1)$

$$m=(-13-2)/(2-(-3))$

$$m=(-15)/(5)$

m = -3

Using point-slope formula:

$y-y_1=m(x-x_1)$

$y-2=-3(x-(-3))$

$y-2=-3(x+3)$

$y-2=-3x-9$

Add 2 on both sides.

$y-2+2=-3x-9+2$

$y=-3x-7$

Slope-intercept form of the equation is y = -3x - 7.

Jon's weight loss for each week of the month is 4 lbs., 3.5 lbs. and 2 lbs. He gained 4.5 lbs. the last week. If Jon originally weighted 153 lbs., how much does he weigh now?

Answers

Answer:

148 lbs

Step-by-step explanation:

Given: Jon's weight loss for each week of the month is 4 lbs., 3.5 lbs. and 2 lbs. He gained 4.5 lbs. the last week.

To Find: If Jon originally weighted 153 lbs., how much does he weigh now

Solution:

Jon's original weight $=153$ $\text{lbs}$

Jon's weight loss in three successive weeks are $= 4$ $\text{lbs}$

$= 3.5$ $\text{lbs}$

$= 2$ $\text{lbs}$

Total weight loss in three weeks is $=4+3.5+2$ $\text{lbs}$

$=9.5$ $\text{lbs}$

Jon's weight after three weeks $=153-\text{weigth loss}$

$=153-9.5$

$143.5$ $\text{lbs}$

Gain in Jon's weight $= 4.5$ $\text{lbs}$

Jon's weight after 4 weeks $=143.5+\text{weight gain}$

$143.5+4.5$

$148$ $\text{lbs}$

Jon weighs $148$ $\text{lbs}$ now.

You have to add the weight he loss then subtract it from 153

Even numbers from 20 to 32

Answers

even numbers are divisible by 2 and end with numbers that are divisible by 2 (except 0) such as 2,4,6,8,0

so
20,22,24,26,28,30,32

Nova was flying a drone that she got for her birthday. Nova is 36 yards lower than the drone. The distance from Nova to the drone is 200 yards. What is the angle of elevation?

Answers

For the right triangle NDO (look at the image) $\sin \angle OND= (OD)/(ND) = (36)/(200) = (9)/(50)$ .
Then $\angle OND=\sin^(-1) (9)/(50)$ .

What does algebra mean in math

Answers

algebra is solving for the unknown so
if you have 10 apples and you give 5 to your friend, how many apples would you have so that is also 10-5=x solve for x

or it could be more complicated like (x-2)/6+4x-3=17

algebra is a question that uses any letter of the alphabet to replace a missing box, example:
4y equals 20 because 4 x 5 is 20

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