Answer:
Step-by-step explanation:
Start by finding how many integers there are from 10-30...
30-10+1=20+1=21
Note we have to add 1 since it is inclusive.
Now, let's find how many multiples of 4 or 5 there are from 10-30...
4*3=12
4*4=16
4*5=20
4*6=24
4*7=28
5*2=10
5*3=15
5*4=20
5*5=25
5*6=30
5+5-1=9
Note we have to subtract 1 since 20 is counted twice.
The probability would be...
Answer:
the answer is 6
Step-by-step explanation:
6............................
Answer:
- <u><em>A dilation by a scale factor of 4 and then a reflection across the x-axis </em></u>
Explanation:
<u>1. Vertices of triangle FGH:</u>
- F: (-2,1)
- G: (-3,3)
- H: (0,1)
<u>2. Vertices of triangle F'G'H':</u>
- F': (-8,-4)
- G': (-12,-12)
- H': (0, -4)
<u>3. Solution:</u>
Look at the coordinates of the point H and H': to transform (0,1) to (0,-4) you can muliply each coordinate by 4 and then change the y-coordinate from 4 to -4. That is<em> a dilation by a scale factor of 4 and a reflection across the x-axis.</em> This is the proof:
- Rule for a dilation by a scale factor of 4: (x,y) → 4(x,y)
(0,1) → 4(0,1) = (0,4)
- Rule for a reflection across the x-axis:{ (x,y) → (x, -y)
(0,4) → (0,-4)
Verfiy the transformations of the other vertices with the same rule:
- Dilation by a scale factor of 4: multiply each coordinate by 4
4(-2,1) → (-8,4)
4(-3,3) → (-12,12)
- Relfection across the x-axis: keep the x-coordinate and negate the y-coordinate
(-8,4) → (-8,-4) ⇒ F'
(-12,12) → (-12,-12) ⇒ G'
Therefore, the three points follow the rules for <em>a dilation by a scale factor of 4 and then a reflection across the x-axis.</em>
Answer:
-24+12(d-3)+22=-24+34(d-3)
10(d-3)
10d=-30
d=-30/10
d=3
Minor Arc AC = 110 degrees (given)
As indicated in the hints,
OA=OC => OAC=OCA=(180-110)/2 = 35
Similarly,
OAB=OBA=(48-35)=13
=>
OBC=OCB=(180-35-35-13-13)/2=(180-96)/2=84/2=42
=>
Angle B = 13+42 = 55 degrees
Check:
55+55+35+35+13+13 = 180 degrees (angles of a triangle) ok.
