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2 years ago

Find the length of the hypotenuse. Use Pythagoras' theorem c2 = a2 + b2

Mathematics

2 answers:

spayn [35]2 years ago

5 0

Answer:

Hypotenuse = 26

Step-by-step explanation:

Given,

Base = 24,
Perpendicular = 10
Hypotenuse = ?

Solution:

We know that,

Pythagoras theorem = (Base)²+(Perpendicular)² = (Hypotenuse)²(which is c²)

Substituting the values:

(24)² + (10)² = c²

Solving for hypotenuse,

576 + 100 = c²
676 = c²
√(676) = c
√(26*26) = c
26 = Hypotenuse

Therefore, Hypotenuse is 26.

melisa1 [442]2 years ago

4 0

Answer: 26

Step-by-Step Explanation:

a = 10
b = 24
c = ?

Using Pythagoras Theorem,
c^2 = a^2 + b^2
c^2 = 10^2 + 24^2
c^2 = 100 + 576
c^2 = 676
=> c = √676 = 26

Hence, c = 26

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Lines ℓ and m are intersected by transversal t. ℓ ∥ m. Lines l and m are horizontal with l above m and intersected by transveral

artcher [175]

Answer:

<5 = 105 degrees

Step-by-step explanation:

From the description given, since line l is parallel to m then <4 is alternate to <5 and two alternate angles are equal, if thst is the case

<4 = <5 (alternate angle)

Since <4 = 105 degrees, hence m<5 = 105 degrees

7 0

3 years ago

A motorboat takes 5 hours to travel 150 miles going upstream. The return trip takes 3 hours going downstream. What is the rate o

lys-0071 [83]

Answer:

The rate of the boat in still water is 40 miles per hour

The rate of the current is 10 miles per hour

Step-by-step explanation:

we know that

The speed or rate is equal to divide the distance by the time

Let

x ----> the rate of the current (miles per hour)

y ----> the rate of the boat in still water (miles per hour)

we have that

going upstream

$y-x=\frac{150}{5}$

$y-x=30$ ----> equation A

going downstream

$y+x=\frac{150}{3}$

$y+x=50$ ----> equation B

Solve the system of equations by elimination

Adds equation A and equation B

$y-x=30\\y+x=50\\------\\y+y=30+50\\2y=80\\y=40$

Find the value of x

$y+x=50$

$40+x=50$

$x=10$

therefore

The rate of the boat in still water is 40 miles per hour

The rate of the current is 10 miles per hour

8 0

3 years ago

- 2x + 12 = 2(x + 6)

Crank

Answer:

x=0

Step-by-step expla

4 0

3 years ago

Consider the arithmetic sequence:

Leona [35]

Answer:

If n is an integer, the function that generate the sequence 10, 12, 14, 16, ... is $\mathbf{d(n)=8+2n\:for\:n>1}$

Option D is correct option

Step-by-step explanation:

We are given the arithmetic sequence:

10, 12, 14, 16, ...

If n is an integer, which of these functions generate the sequence?

We need to find the nth term for the given sequence

The nth term for arithmetic sequence will be: $a_n=a_1+(n-1)d$

where aₙ is nth term, a₁ is first term and d is common difference

Looking at the sequence a₁ = 10 and d = 2

So, nth term will be:

$a_n=a_1+(n-1)d\\a_n=10+(n-1)2\\a_n=10+2n-2\\a_n=8+2n$

So, nth term is: $a_n=8+2n$

In the options below, the only correct answer is option D. so, we can write nth term as: $d(n) = 8 + 2n\: for\: n > 1$

So, If n is an integer, the function that generate the sequence 10, 12, 14, 16, ... is $\mathbf{d(n)=8+2n\:for\:n>1}$

Option D is correct option

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3 years ago

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Xelga [282]

Answer:7/2

Step-by-step explanation:

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3 years ago