Answer:
1) 6 cm
2) 117°
Step-by-step explanation:
1) Draw a picture of the rhombus. The distance between opposite sides is the height of the rhombus. If we draw the height at the vertex, we get a right triangle. Using trigonometry:
sin 30° = h / 12
h = 12 sin 30°
h = 6 cm
2) Draw a picture of the rectangle.
∠KML is the angle the diagonal makes with the shorter side ML. This angle is 54°. ∠NKM is the angle the diagonal makes with the shorter side NK. ∠KML and ∠NKM are alternate interior angles, so m∠NKM = 54°.
The angle bisector of angle ∠NKM divides the angle into two equal parts and intersects the longer side NM at point P. So m∠PKM = 27°.
KLMN is a rectangle, so it has right angles. That means ∠KML and ∠KMN are complementary. So m∠KMN = 36°.
We now know the measures of two angles of triangle KPM. Since angles of a triangle add up to 180°, we can find the measure of the third angle:
m∠KPM + 36° + 27° = 180°
m∠KPM = 117°
A word to the wise: It's <span> f(x)=125(0.9)^x, where ^ represents exponentiation.
In this case the ave. value over the interval [11, 15] is
125(0.9)^15 - 125(0.9)^11
------------------------------------- = (125/4) [ 0.9^15 - 0.9^11)
15 - 11 = (31.25) [ 0.2059 - 0.3138 ] = a negative result
= (31.25)(-0.1079) = -3.372 (av. r. of c.
over the interval [11,15] )
Do the same thing for the time interval [1,5]. Then compare the two rates of change.</span>
Answer: 36 days
Step-by-step explanation:
that’s the lowest multiple of 9 that also is a multiple of 12. It’s the LCF aka Least Common Factor
Answer:
Let's call the first studio, yoga studio A.
Let's call the second studio, yoga studio B.
The equations:
Yoga Studio A: y=10x+55
Yoga Studio B: y=12.5x+25
So, for 12 classes:
Yoga Studio A: y=10(12)+55, y=175
Yoga Studio B: y=12.5(12)+25, y=175
These two numbers are equal, so Griffin is right.
For 10 classes:
Yoga Studio A: y=10(10)+55, y=155
Yoga Studio B: y=12.5(10)+25, y=150.
These two numbers are not equal, so Gigi is wrong.
Let me know if this helps!
Answer:
B. 37 + 7 = 44
Step-by-step explanation:
If she jumps 4 more after jumping 3 to 40, means it's 4 + 3 = 7 and it reaches 44.
