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zvonat [6]
2 years ago
14

What is 75% as a fraction in simplest form

Mathematics
1 answer:
ludmilkaskok [199]2 years ago
7 0
75% = 75/100÷ 5= 15/20 ÷5= ¾. does this help? hope it does
hope it helps :)
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Find x so that the points (x,x+1), (x+2,x+3) and (x+3,2x+4) form a right-angled triangle.
azamat

Let <em>a</em>, <em>b</em>, and <em>c</em> be vectors each starting at the origin and terminating at the points (<em>x</em>, <em>x</em> + 1), (<em>x</em> + 2, <em>x</em> + 3), and (<em>x</em> + 3, 2<em>x</em> + 4), respectively.

Then the vectors <em>a</em> - <em>b</em>, <em>a</em> - <em>c</em>, and <em>b</em> - <em>c</em> are vectors that point in directions parallel to each of the legs formed by the triangle with these points as its vertices.

If this triangle is to contain a right angle, then exactly one of these pairs of vectors must be orthogonal. In other words, one of the following must be true:

(<em>a</em> - <em>b</em>) • (<em>a</em> - <em>c</em>) = 0

<em>or</em>

(<em>a</em> - <em>b</em>) • (<em>b</em> - <em>c</em>) = 0

<em>or</em>

(<em>a</em> - <em>c</em>) • (<em>b</em> - <em>c</em>) = 0

We have

<em>a</em> - <em>b</em> = (<em>x</em>, <em>x</em> + 1) - (<em>x</em> + 2, <em>x</em> + 3) = (-2, -2)

<em>a</em> - <em>c</em> = (<em>x</em>, <em>x</em> + 1) - (<em>x</em> + 3, 2<em>x</em> + 4) = (-3, -<em>x</em> - 3)

<em>b</em> - <em>c</em> = (<em>x</em> + 2, <em>x</em> + 3) - (<em>x</em> + 3, 2<em>x</em> + 4) = (-1, -<em>x</em> - 1)

Case 1: If (<em>a</em> - <em>b</em>) • (<em>a</em> - <em>c</em>) = 0, then

(-2, -2) • (-3, -<em>x</em> - 3) = (-2)×(-3) + (-2)×(-<em>x</em> - 3) = 2<em>x</em> + 12 = 0   ==>   <em>x</em> = -6

which would make <em>a</em> - <em>c</em> = (-3, 3) and <em>b</em> - <em>c</em> = (-1, 5), and their dot product is not zero. Then the triangles vertices are at the points (-6, -5), (-4, -3), and (-3, -8).

Case 2: If (<em>a</em> - <em>b</em>) • (<em>b</em> - <em>c</em>) = 0, then

(-2, -2) • (-1, -<em>x</em> - 1) = (-2)×(-1) + (-2)×(-<em>x</em> - 1) = 2<em>x</em> + 4 = 0   ==>   <em>x</em> = -2

which would make <em>a</em> - <em>c</em> = (-3, -1) and <em>b</em> = (-1, 1), and their dot product is also not zero. The vertices are the points (-2, -1), (0, 1), and (1, 0).

Case 3: If (<em>a</em> - <em>c</em>) • (<em>b</em> - <em>c</em>) = 0, then

(-3, -<em>x</em> - 3) • (-1, -<em>x</em> - 1) = (-3)×(-1) + (-<em>x</em> - 3)×(-<em>x</em> - 1) = <em>x</em> ² + 4<em>x</em> + 6 = 0

but the solutions to <em>x</em> here are non-real, so we throw out this case.

So there are two possible values of <em>x</em> that make a right triangle, <em>x</em> = -6 and <em>x</em> = -2.

3 0
3 years ago
write 700/200 as a terminating decimal. then describe two methods for converting a mixed number to a decimal
zhuklara [117]
\frac{700}{200}=\frac{7}{2}\\\\\#1\\\frac{7}{2}=3\frac{1}{2}=3\frac{5}{10}=3.5\\\\\#2\\\frac{7}{2}=\frac{6+1}{2}=\frac{6}{2}+\frac{1}{2}=3+\frac{1}{2}=3+0.5=3.5\\\\\underline{0.5}\\1:2\\\underline{0}\\10\\\underline{10}\\R=0

5 0
2 years ago
Jan has a job selling magazine subscriptions by phone. She makes a base salary of $9.60 per hour plus a 5% commission on
blagie [28]

Answer:

$597.50

Step-by-step explanation:

(9.60x35)+(5230x.05)

336+261.50

8 0
3 years ago
It is in the picture
Fed [463]

Answer:

a 5/2; b. 2.5; c 0.9; d. 90%

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
A doctor's office schedules 15 minutes for each patient and a half hour for the doctor's lunch at 11:30 a.m. If the doctor start
Ierofanga [76]

9514 1404 393

Answer:

  24

Step-by-step explanation:

If we reschedule the doctor's half-hour break so that s/he quits work at 3:00 pm, s/he will have worked 6 straight hours from 9 am to 3 pm. Seeing 4 patients each hour, the doctor will have seen ...

  (6 h) × (4 pt/h) = 24 pt

The doctor saw 24 patients by 3:30 pm.

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3 years ago
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