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kap26 [50]
3 years ago
9

3. Find the missing side lengths. Leave your answers as radicals in simplest form. Show your work to support

Mathematics
1 answer:
7nadin3 [17]3 years ago
3 0

Answer: b=2(square root of 2) and a=4

Step-by-step explanation:

Since this is a 45-45-90 triangle we know that side b is equal to b=2\sqrt{2}.

In a 45-45-90 triangle, the hypotenuse is equal to x\sqrt{2} this means in order to find missing side length a, we have to multiply (2\sqrt{2})(\sqrt{2}) this will give us 4

so the missing side lengths are, b=2\sqrt{2} and a=4

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find the area of triangle qpm. round the answer to the nearest tenth. a. 5.2 square units b. 6.3 square units c. 6.5 square unit
viva [34]
Pls. see attachment. 

We need to solve for the angles of the smaller triangle in order to solve for the angle of the larger triangle which would help us solve the missing measurement of a side.

Given:

51 degrees.

Cut the triangle into two equal sides and it forms a right triangle. All interior angles of a triangle sums up to 180 degrees.

180 – 51 – 90 = 39 degrees

39 degrees * 2 = 78 degrees.

Angle Q is 78 degrees.

In the bigger triangle, 4.3 is the hypotenuse. We need to solve for the measurement of the long leg which is the opposite of the 78 degree angle.

We will use the formula:

Sine theta = opposite / hypotenuse

Sin(78 deg) = opposite / 4.3

Sin(78 deg) * 4.3 = opposite

4.21 = opposite. This is also the height of the triangle.

 

Area of a triangle = ½ * base * height

A = ½ * 3units * 4.21units

A = 6.315 square units.

7 0
3 years ago
Find the<br>simple interest:<br>Princpd $6000<br>Interest Rate 5%<br>Time: 6 months<br>Start​
sattari [20]

Answer: The interest is: $150.00

The formula we'll use for this is the simple interest formula, or:

Where:

   P is the principal amount, $6000.00.

   r is the interest rate, 5% per year, or in decimal form, 5/100=0.05.

   t is the time involved, 6....month(s) time periods.

   Since your interest rate is "per year" and you gave your time interval in "month(s)" we need to convert your time interval into "year" as well.

       Do this by dividing your time, 6- month(s), by 12, since there's 12 months in 1 year.

   So, t is 0.5....year time periods.

To find the simple interest, we multiply 6000 × 0.05 × 0.5 to get that:

The interest is: $150.00

8 0
3 years ago
A triangle with constant base b and height h is changing with time where h(t)=3t +1. What is the rate of change of the area of t
Keith_Richards [23]

The rate of change of the area of the triangle when t=1 is also equal to 3.

<h3>Rate of change</h3>

Given the function of height of a triangle expressed as:

  • h(t) = 3t + 1

The rate of change is expressed as

  • dh/dt = 3

The rate of change of the area of the triangle when t=1 is also equal to 3.

Learn more on rate of change here: brainly.com/question/8728504

5 0
2 years ago
30% of a number is x. What is 100% of the number? Assume x&gt;0.<br> 100% of the number is
STatiana [176]

Answer:

10x/3

Step-by-step explanation:

30% is to x as 100% is to y

We are looking for y in terms of x.

30/x = 100/y

30y = 100x

y = 100x/30

y = 10x/3

6 0
3 years ago
Carson is selling lemonade. The number of cups of lemonade he sells
Sloan [31]

Answer:

none

Step-by-step explanation:

i dont know

5 0
3 years ago
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