Ask question

Ask question

All categories

3 years ago

14

Which equation can be used to find the unknown length, b, in this triangle?

2 answers:

KIM [24]3 years ago

5 0

Answer:

4²+b² = 5²

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem to find the length of the missing side.

The Pythagorean theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse. Algebraically, this is represented as

a²+b² = c²

We have the measure of one leg, 4 in. We also have the measure of the hypotenuse, 5 in. This gives us

4²+b² = 5²

Romashka-Z-Leto [24]3 years ago

3 0

The equation for finding the hypotneus of a right triangle is
${a }^{2} + {b}^{2} = c {}^{2}$
so we know that 4²+b²=5²
so that would simplify as 16+b=25
so x=25-16
which is 9
so therefore we can conclude that
$b = 9inches$

You might be interested in

Round to the nearest tenth place it is repeating decimal 4/6

Scilla [17]

Answer:

0.7

Step-by-step explanation:

I divided 4 by 6

0.6666666666666...

Simplify to 0.7

8 0

3 years ago

Learning Task 3

ASHA 777 [7]

Answer:

1. The sides are: 38.5, 39.5, 40.5 and 41.5

2. Presently, Inzo is 15 years old and Miz is 10 years old

3. $Distance = 3682km$

4. Possible pairs are: (12, 14), (16, 18) and (20, 24)

5. $L < 38m$

Step-by-step explanation:

The question has lots of missing details. See the comment section for complete question

Solving (a):

Given

Shape: Quadrilateral

Sides: Consecutive

$Perimeter = 160$

Let one of the sides be x. The other sides will be x + 1, x + 2 and x + 3.

So, the perimeter is:

$Perimeter = x + x + 1 + x + 2 + x + 3$

This gives:

$160 = x + x + 1 + x + 2 + x + 3$

Collect Like Terms

$160 -1-2-3= x+x+x+x$

$154= 4x$

Divide both sides by 4

$38.5 = x$

$x =38.5$

<em>So, the sides are: 38.5, 39.5, 40.5 and 41.5</em>

<em></em>

Solving (b):

Given

Presently: $Inzo = 10 + Miz$

Five years ago: $Miz - 5= \frac{1}{3} * (Inzo-5)$ --- (Missing from the question)

Required: Determine their present ages

Substitute $10 + Miz$ for Inzo in the second equation

$Miz - 5 = \frac{1}{3} * (10 + Miz - 5)$

$Miz - 5 = \frac{1}{3} * (Miz + 5)$

Multiply both sides by 3

$3Miz - 15 = Miz + 5$

Collect Like Terms

$3Miz -Miz = 15 + 5$

$2Miz= 20$

Divide both sides by 2

$Miz = 10$

Substitute 10 for Miz in $Inzo = 10 + Miz$

$Inzo = 10 + 5$

$Inzo = 15$

<em>So presently, Inzo is 15 years old and Miz is 10 years old</em>

Solving (3):

Given

Express Train:

$Speed = 100kph$

$Time = t$

Local Train:

$Speed = 45kph$

$Time = t + 45$

Required: Determine the distance between A and B

Distance is calculated as:

$Distance = Speed * Time$

For the express train:

$Distance = 100 * t$

For the local train

$Distance = 45 * (45 + t)$

Distance between both stations are equal; So,

$100 * t = 45 * (45 + t)$

$100 t = 2025 + 45t$

Collect Like Terms

$100 t -45t= 2025$

$55t= 2025$

Divide by 55

$t = 36.82$

Substitute 36.82 for t in $Distance = 100 * t$

$Distance = 100 * 36.82$

$Distance = 3682km$

Solving (4):

Let the even numbers be: n and n + 2.

Sum greater than 24: $n + n + 2 > 24$

Sum less than 60: $n + n + 2 < 60$

So, we have:

$n + n + 2 > 24$

$2n + 2 > 24$

Collect Like Terms

$2n > 24-2$

$2n > 22$

$n > 11$

$n + n + 2 < 60$

$2n + 2< 60$

Collect Like Terms

$2n < 60-2$

$2n < 58$

Divide by 2

$n$

So, we have:

$n > 11$ and $n < 29$

So, possible pairs are: (12, 14), (16, 18) and (20, 24)

Solving (5):

Given

$Perimeter < 152m$

Required: Find the possible lengths

Let the length be L.

Perimeter is calculated as:

$Perimeter =4 * L$

$Perimeter =4 L$

So, we have:

$4L < 152m$

Divide through by 4

$L < 38m$

Hence, length is less than 38m (e.g. 37m)

5 0

2 years ago

olga nikolaevna [1]

Answer:

Fraction of the original board left = $\frac{2}{15}$

Step-by-step explanation:

Let the length of the board is = l feet

Marty saws off $\frac{1}{5}$ of a wooden board.

Length of the board left = l - $(\frac{1}{5})l$

= $(\frac{4}{5})l$ feet

He saws off $\frac{3}{4}th$ of the remaining board,

Board left = $(\frac{4}{5})l-[(\frac{4}{5})l\times (\frac{3}{4})]$

= $\frac{4}{5}l-\frac{3}{5}l$

= $\frac{1}{5}l$ feet

He finally saws off $\frac{1}{3}$ rd of the remaining board.

Board left = $\frac{1}{5}l-[\frac{1}{5}\times \frac{1}{3}]l$

= $(\frac{1}{5}-\frac{1}{15})l$

= $\frac{2}{15}l$ feet

Fraction of the original board left = $\frac{\frac{2}{15}l}{l}$

= $\frac{2}{15}$

6 0

3 years ago

Which of the following lists the angles from smallest to largest

Tomtit [17]

I don’t understand the question

3 0

3 years ago

Read 2 more answers

The girl went to the store at 10:45 and lasted 1 hour and 30 minutes . At what time did she come out of the store

mars1129 [50]

She left at 12:15. 10:45 plus 1 hour= 11:45 + 15 min +12 +15= 12:15

4 0

4 years ago