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Alex787 [66]
3 years ago
6

Clark Kent walks 3 miles west and then 4 miles north. How far is it for Superman to fly in a straight line back to his starting

point? (It makes a right triangle.)
Question 16 options:

3 miles


5 miles


7 miles


9 miles
Mathematics
2 answers:
KonstantinChe [14]3 years ago
7 0
It would be 5 miles if the triangle was a right angle
kozerog [31]3 years ago
5 0
You can use the pythagorean theorem a² + b² = c², where a and b are perpendicular sides of a triangle and c is the hypotenuse.

For this problem, a = 3, b = 4
c = √(3² + 4²) = √5² = 5
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If x= 1/2-√3 , prove that x³-2x²-7x+5=3
prohojiy [21]
x=\frac{1}{2}-\sqrt3\\\\x^3-2x^2-7x+5=3\\\\(\frac{1}{2}-\sqrt3)^3-2(\frac{1}{2}-\sqrt3)^2-7(\frac{1}{2}-\sqrt3)+5\\\\=(\frac{1}{2})^3-3\cdot(\frac{1}{2})^2\cdto\sqrt3+3\cdot\frac{1}{2}\cdot(\sqrt3)^2-(\sqrt3)^3-...\\\\...-2[(\frac{1}{2})^2-2\cdot\frac{1}{2}\cdot\sqrt3+(\sqrt3)^2]-\frac{7}{2}+7\sqrt3+5

=\frac{1}{8}-\frac{3\sqrt3}{4}+\frac{9}{2}-3\sqrt3-2(\frac{1}{4}-\sqrt3+3)-\frac{7}{2}+7\sqrt3+5\\\\=\frac{1}{8}+\frac{9}{2}-\frac{1}{2}-6-\frac{7}{2}+5-\frac{3}{4}\sqrt3-3\sqrt3+2\sqrt3+7\sqrt3\\\\=\frac{1}{8}+\frac{1}{2}-1+5\frac{1}{4}\sqrt3=\frac{1}{8}-\frac{1}{2}+5\frac{1}{4}\sqrt3=\frac{1}{8}-\frac{4}{8}+5\frac{1}{4}\sqrt3\\\\=-\frac{3}{8}+5\frac{1}{4}\sqrt3\neq3
6 0
2 years ago
There are mangoes and oranges in a basket in the ratio 7: 11. If the total number of fruits is 720, then how many mangoes are th
lbvjy [14]

Answer:

280 mangoes

Step-by-step explanation:

sum the parts of the ratio, 7 + 11 = 18 parts

Divide the total by 18 to find the value of one part of the ratio.

720 ÷ 18 = 40 ← value of 1 part of the ratio , then

7 × 40 = 280 ← number of mangoes

8 0
2 years ago
Read 2 more answers
Original price: $50; markdown: 2.2%; retail price:
larisa86 [58]
$50x2.2%
50x0.022=1.1
$50-$1.1=$48.9
4 0
3 years ago
The number of students who chose lunch was 5 more than the number of students who chose breakfast. Write a system of linear equa
Papessa [141]

Answer:

The system of linear equations are y=5+x and  x+y=25

Step-by-step explanation:

Given : The number of students who chose lunch was 5 more than the number of students who chose breakfast. Let x represent the number of students who chose breakfast and y represent the number of students who chose lunch.

(50 students picked, 25 picked dinner the rest picked lunch and breakfast)

To find : Write a system of linear equations that represents the numbers of students who chose breakfast and lunch ?

Solution :

The number of students who chose breakfast be 'x'

The number of students who chose lunch be 'y'.

The number of students who chose lunch was 5 more than the number of students who chose breakfast.

i.e. y=5+x

Now, Total student were 50 and 25 picked dinner the rest picked lunch and breakfast i.e. 25.

So, x+y=25

Therefore, the system of linear equations are y=5+x and  x+y=25

4 0
3 years ago
WILL MARK BRAINLIEST!!! Find the fifth roots of 243(cos 240° + i sin 240°).
Snowcat [4.5K]

Answer:

<h2>3(cos 336 + i sin 336)</h2>

Step-by-step explanation:

Fifth root of 243 = 3,

Suppose r( cos Ф + i sinФ) is the fifth root of 243(cos 240 + i sin 240),

then r^5( cos  Ф  + i sin  Ф )^5 = 243(cos 240 + i sin 240).

Equating equal parts and using de Moivre's theorem:

r^5 =243  and  cos  5Ф  + i sin  5Ф = cos 240 + i sin 240

r = 3 and  5Ф = 240 +360p so Ф =  48 + 72p

So Ф = 48, 120, 192, 264, 336  for   48 ≤ Ф < 360

So there are 5 distinct solutions given by:

3(cos 48 + i sin 48),

3(cos 120 + i sin 120),

3(cos 192 + i sin 192),

3(cos 264 + i sin 264),

3(cos 336 + i sin 336)

6 0
2 years ago
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