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Amiraneli [1.4K]
3 years ago
13

Question one:

Mathematics
1 answer:
wariber [46]3 years ago
5 0
1.) The answer is 27.5 centimeters
Explanation: 5x11=55
55/2=27.5
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Find the length of the third side. If necessary, write in simplest radical form.
Mazyrski [523]

Answer:

\boxed {\boxed {\sf 8}}

Step-by-step explanation:

This triangle has a small square, which represents a right angle. Therefore, we can use the Pythagorean Theorem.

a^2+b^2=c^2

Where <em>a</em> and <em>b </em> are the legs of the triangle and <em>c</em> is the hypotenuse.

In this triangle, 7 and √15 are the legs, because these sides make up the right angle. The unknown side is the hypotenuse, because it is opposite the right angle. So, we know two values:

a= 7 \\b= \sqrt{15}

Substitute these values into the formula.

(7)^2+(\sqrt{15})^2=c^2

Solve the exponents.

  • (7)²= 7*7=49

49+ (\sqrt{15})^2=c^2

  • (√15)²=√15*√15=15

49+15=c^2

Add.

64=c^2

Since we are solving for c, we must isolate the variable. It is being squared and the inverse of a square is the square root. Take the square root of both sides.

\sqrt{64}=\sqrt{c^2} \\\sqrt{64}= c\\8=c

The third side length is <u>8.</u>

6 0
3 years ago
Read 2 more answers
Tracey wants to ride her bicycle at least 150 miles this week. She has already
dimaraw [331]

150 - 42 = 108

108 ÷ 6 = 18

therefore m = 18

hope this helps...

3 0
3 years ago
What is 321×23 <br><br> one more thing<br><br> what is 3,829÷1221
Archy [21]
321 times 23 is 7,383
3,829 divided by 1,221 is (rounded to the nearest hundredth) 3.14
(the real number was: 3.13595414)
3 0
3 years ago
Find the directional derivative of f at the given point in the direction indicated by the angle θ.
anygoal [31]

Answer:

Directional derivative = 1/√2

Step-by-step explanation:

We are given f(x, y) = y cos(xy)

Now, we know that;

∇f(x, y) = ycos xy

Thus, applying that to the question, we have;

∇f(x, y) = [-y² sin xy, cos (xy) - xy sin xy]

At coordinates (0,1),we now have;

∇f(0, 1) = [-1²•sin0, (cos 0) - 0]

∇f(0, 1) = [0, 1]

Now, unit vector indicated by the angle θ is given as; u = [cos θ, sin θ]

From the question, since θ = π/4, thus

u = [cos π/4, sin π/4]

Cos π/4 in surd form is; 1/√2

Also, sin π/4 in surd form is; 1/√2

So, u = [1/√2, 1/√2]

Directional derivative = [∇f(0, 1)] • u

= [0, 1] × [1/√2, 1/√2] = 0 + 1/√2 = 1/√2

4 0
3 years ago
Delphine has to place 64 bottles of water on a banquet table. it must have a way to fill a rectangular. what are the possible ar
tangare [24]

Answer:

Since 64= 2^6, you have the following arrangements.

Optional: 64 \times 1 (and it's mirror version 1 \times 64, if you want to consider a long strip of bottles a rectangle. Technically it is, but it's open to interpretation.

32 \times 2 and it's mirror 2 \times 32;

16 \times 4 and it's mirror 4 \times 16;

Optional: 8 \times 8. Since a square is a rectangle with extra limitations.

6 0
2 years ago
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