Answer: b
Step-by-step explanation:
9514 1404 393
Answer:
10
Step-by-step explanation:
The distance formula is useful.
d = √((x2 -x1)^2 +(y2 -y1)^2)
d = √((7 -1)^2 +(12 -4)^2) = √(6^2 +8^2) = √(36 +64) = √100
d = 10
The distance between P and Q is 10.
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<em>Additional comment</em>
You may recognize the run : rise ratio of 6 : 8 = 3 : 4. This suggests a 3-4-5 right triangle with a scale factor of 2. If you're familiar with that Pythagorean triple, you can write down the answer as soon as you see the rise and run numbers.
Answer: D x>_ 0
Step-by-step explanation: Because the circle is shaded and the x can only get bigger (ex: Can’t be -1 or -3)
Answer:
1. x = 15, y = 8
2. m∠MSN = 90°
3. x = 20
4. y = 9
5. x = 8, m∠PQS = 24, m∠SQR = 66
6. y = 15, m∠RPT = 55, m∠TPW = 35
Step-by-step explanation:
1. to solve for y
9y + 18 = 90
9y + 18 - 18 = 90 - 18
9y = 72
9y/9 = 72/9
y = 8
to solve for x
5x + x = 90
6x = 90
6x/6 = 90/6
x = 15
2. m∠MSN = 90°, because ∠MSN is a right angle, which is equal to 90
3. To find x
3x + 10 + x = 90
3x + x = 4x
4x + 10 = 90
4x + 10 - 10 = 90 - 10
4x = 80
4x/4 = 80/4
x = 20
4. To find y
7y - 3 + 3y + 3 = 90
7y + 3y = 10
-3 + 3 = 0
10y = 90
10y/10 = 90/10
y = 9
5. To find x
3x + 8x + 2 = 90
3x + 8x = 11x
11x + 2 = 90
11x + 2 - 2 = 90 -2
11x = 88
11x/11 = 88/11
x = 8
To find ∠PQS
∠PQS = 3x
x = 8
so 3(x) = 3(8)
3(8) = 24
so ∠PQS = 24
To find ∠SQR
∠SQR = 8x + 2
x = 8
so ∠SQR = 8(x) + 2 = 8(8) + 2
8(8) + 2
= 64 + 2
= 66
6. To find y
4y - 5 + 2y + 5 = 90
4y + 2y = 6y
-5 + 5 = 0
6y = 90
6y/6 = 90/6
y = 15
To find ∠RPT
∠RPT = 4y - 5
y = 15
so ∠RPT = 4y - 5 = 4(15) - 5
4(15) - 5
= 60 - 5
= 55
To find ∠TPW
∠TPW = 2y + 5
y = 15
so ∠TPW = 2y + 5 = 2(15) + 5
2(15) + 5
= 30 + 5
= 35
Pythagoras theorem only works for right triangle (90 degree)
Trigonometry (sin, cos, tan) works everywhere!
Hopefully I answered your question!
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