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Gnesinka [82]
3 years ago
11

A 28ft ladder leans against a wall so that the base of the ladder is 5ft away from the base of the wall. How far up the wall doe

s the ladder reach?
Round to the nearest tenth.
Mathematics
1 answer:
valentinak56 [21]3 years ago
4 0

Answer:

the top of the ladder is 27.5ft above the ground.

Step-by-step explanation:

The ladder makes an angle, θ with the ground thus forming a right angle triangle with the wall of the house.

The length of the ladder represents the hypotenuse of the right angle triangle.

The ground distance from the base of the wall to the foot of the ladder represents the adjacent side of the right angle triangle.

Therefore, to determine how high up is the top of the ladder on the wall, x, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

28² = x² + 5²

784 = x² + 25

x² = 784 - 25 = 759

x = √759 = 27.5ft

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Which of the following shows the polynomial below written in descending order ?
Igoryamba

Answer:

A. 4x¹¹ + x⁷ + 3x³ - 5x + 9

Step-by-step explanation:

order the exponents from largest to smallest. variables always come first; therefore, -5x before 9

4 0
3 years ago
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Let A, B, C and D be sets. Prove that A \ B and C \ D are disjoint if and only if A ∩ C ⊆ B ∪ D
ANEK [815]

Step-by-step explanation:

We have to prove both implications of the affirmation.

1) Let's assume that A \ B and C \ D are disjoint, we have to prove that A ∩ C ⊆ B ∪ D.

We'll prove it by reducing to absurd.

Let's suppose that A ∩ C ⊄ B ∪ D. That means that there is an element x that belongs to A ∩ C but not to B ∪ D.

As x belongs to A ∩ C, x ∈ A and x ∈ C.

As x doesn't belong to B ∪ D, x ∉ B and x ∉ D.

With this, we can say that x ∈ A \ B and x ∈ C \ D.

Therefore, x ∈ (A \ B) ∩ (C \ D), absurd!

It's absurd because we were assuming that A \ B and C \ D were disjoint, therefore their intersection must be empty.

The absurd came from assuming that A ∩ C ⊄ B ∪ D.

That proves that A ∩ C ⊆ B ∪ D.

2) Let's assume that A ∩ C ⊆ B ∪ D, we have to prove that A \ B and C \ D are disjoint (i.e.  A \ B ∩ C \ D is empty)

We'll prove it again by reducing to absurd.

Let's suppose that  A \ B ∩ C \ D is not empty. That means there is an element x that belongs to  A \ B ∩ C \ D. Therefore, x ∈ A \ B and x ∈ C \ D.

As x ∈ A \ B, x belongs to A but x doesn't belong to B.  

As x ∈ C \ D, x belongs to C but x doesn't belong to D.

With this, we can say that x ∈ A ∩ C and x ∉ B ∪ D.

So, there is an element that belongs to A ∩ C but not to B∪D, absurd!

It's absurd because we were assuming that A ∩ C ⊆ B ∪ D, therefore every element of A ∩ C must belong to B ∪ D.

The absurd came from assuming that A \ B ∩ C \ D is not empty.

That proves that A \ B ∩ C \ D is empty, i.e. A \ B and C \ D are disjoint.

7 0
3 years ago
PLEASE HELP ME IT'S DUE TODAY AND IT COULD HELP MY GRADE A LOT
ElenaW [278]

Answer:

c = 13

m∡A = 60°

m∡B = 30°

Step-by-step explanation:

This is a 5-12-13 triangle. However, to make sure, I will put the steps.

Allow for each sides to be denoted as a-b-c, in which c is the hypotenuse (longest side). Set the equation:

a² + b² = c²

Plug in the corresponding numbers to the corresponding variables:

5² + 12² = c²

Simplify. First, solve the exponents, and then add:

(5²) = 5 * 5 = 25

(12²) = 12 * 12 = 144

25 + 144 = c²

c² = 169

Note the equal sign, what you do to one side, you do to the other. Isolate the variable, c, by rooting both sides:

√c² = √169

c = √169 = √(13 * 13) = 13

c = 13

13 is your answer for c.

Note the measurements of the angles. We know that this is a 30-60-90 triangle, and so it will be easy to figure it out. Note that the corresponding angles will depend on that of the opposite side's measurement lengths. The hypotenuse will always be on the opposite side of the largest angle (as given), as c, the longest side, is opposite of ∡C, which is the largest angle (90°). Based on this information, it means that ∡A would be 60° (as it is opposite of the middle number, 12), and ∡B would be 30° (opposite of the smallest number, 5).

8 0
2 years ago
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Radda [10]

Answer:

131 is the answer

3 0
3 years ago
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