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3 years ago

The base of a 13 foot ladder is 5 feet away from the wall. How far up the wall does the ladder reach?

Mathematics

2 answers:

notsponge [240]3 years ago

6 0

Answer:

The ladder would be 12 feet up the wall.

Step-by-step explanation:

frez [133]3 years ago

5 0

let x be how far up the wall ladder reaches

by Pythagoras theorem

x^2+5^2=13^2

x^2 =(13^2)-(5^2)

x= square root of 144

x= 12 or x =-12(rej,x>0)

hence ladder reaches 12 foot up the wall

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Ber [7]

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2 years ago

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Is the ordered pair a solution of y ≥ 2x − 5? a. (3, 1) b. (1, −4)

Deffense [45]

Answer:

a. Yes

b. No

Step-by-step explanation:

To find if an ordered pair is a solution to the inequality, substitute its x and y values for the x and y in the inequality and solve. If the equation is true, then it is a solution. If it is not, then it is not a solution.

1) First, substitute the x and y values of (3, 1) into the inequality. So, substitute 3 for x and 1 for y:

$1 \geq 2(3)-5\\1\geq 6-5\\1\geq 1$

1 is greater than or equal to 1, so (3,1) is a solution.

2) Second, do the same with the point (1, -4). Substitute 1 for x and -4 for y:

$-4\geq 2(1)-5\\\\-4\geq 2-5\\-4\geq -3$

However, -4 is not greater than or equal to -3, thus (1, -4) is not a solution.

4 0

3 years ago

Terri has 7 pens in a box.

lora16 [44]

a) I have attached an image of a probability tree diagram.

b) 0.02332 (please round to where you need)

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Hope this helps! :)

6 0

3 years ago

A hot air balloon is flying at an altitude of 800 feet. A passenger takes a picture of the top of a tree and estimates that the

nalin [4]

The height of the tree given the depression angle to the top and the base

is given by the tangent relationship of the two given angles.

Correct response:

The height of the tree is approximately <u>79.58 feet</u>

<h3 /><h3>Methods used for the calculation of the height of the tree</h3>

Given:

Altitude of the hot air balloon = 800 feet

Angle of depression to top of tree = 43°

Angle of depression to base of tree = 46°

Required:

Height of tree

Solution:

The horizontal distance of the balloon from the tree is given as follows;

$\displaystyle tan(46^{\circ}) = \frac{Altitude \ of \ balloon}{Horizontal \ distance \ from \ tree} = \mathbf{\frac{800 \, feet}{Horizontal \ distance \ from \ tree}}$