Answer:
The measure of angle ABC is 36° ⇒ 1st answer
Step-by-step explanation:
Let us revise some important facts in the circle
- The measure of the center angle is equal to the measure of its subtended arc
- The measure of the inscribed angle is equal to half the measure of the central angle subtended by the same arc
- The vertex of a central angle is the center of the circle and its sides are radii in the circle
- The vertex of an inscribed angle is a point on the circle, and its sides are chords in the circle
In circle D
∵ D is the center of the circle
∵ A and C lie on the circle
- DA and DC are radii
∴ ∠ADC is a central angle subtended by arc AC
∴ m∠ADC = m of arc AC
∵ m∠ADC = (7x + 2)°
∵ m of arc AC = (8x - 8)°
- Equate them to find x
∴ 8x - 8 = 7x + 2
- subtract 7x from both sides
∴ x - 8 = 2
- Add 8 to both sides
∴ x = 10
Substitute the value of x in the measure of ∠ADC
∵ m∠ADC = 7(10) + 2 = 70 + 2
∴ m∠ADC = 72°
∵ AB and BC are two chords in circle D
∴ ∠ABC is an inscribed angle subtended by arc AC
∵ ∠ADC is a central angle subtended by arc AC
- By using the 2nd fact above
∴ m∠ABC =
m∠ADC
∴ m∠ABC =
× 72
∴ m∠ABC = 36°
Answer:
1. 10 degrees
2. x=35
3. x=20
Step-by-step explanation:
1. 90-80=10
a complementary angle is 90 degrees
2. 70/2=35
vertical angles are congruent
3. 90-30=60/3=20
it's a 90 degree angle
Answer: 162
Step-by-step explanation:
So you will need to find the Markup. The original cost is $120.
- Divide the number by 100 is 1.2. $1.2 is 1% of the $120.
- Now times the number by 35. $1.2 x 35 is $42.
- Finally, add the number. 120 + 42 = 162.
I hope this is the answer you are looking for.
Answer:
Speed of boat in still water is 14 km/hr and speed of current is 8 km/hr
Step-by-step explanation:
Average speed of down stream = 22 km/h
Average speed of up stream = 6 km/hr
Consider the speed of boat in still water be x km/hr and speed of current be y km/hr
As such speed of down stream would be x + y km/hr and speed of down stream would be x - y km/hr. i.e
x+y = 22
x-y = 6
by solving these two equation, we get
2x=28
x=14 km/hr
y=16-13
y=8 km/hr
Hence, the speed of boat in still water is 14 km/hr and speed of current is 8 km/hr
Answer:
is closest to the total surface area of the box
Step-by-step explanation:
we know that
The surface area of the box is equal to
![SA=2B+PH](https://tex.z-dn.net/?f=SA%3D2B%2BPH)
where
B is the area of the base
P is the perimeter of the base
H is the height of the box
we have
![L=7\frac{3}{4}\ in=\frac{7*4+3}{4}=\frac{31}{4}\ in](https://tex.z-dn.net/?f=L%3D7%5Cfrac%7B3%7D%7B4%7D%5C%20in%3D%5Cfrac%7B7%2A4%2B3%7D%7B4%7D%3D%5Cfrac%7B31%7D%7B4%7D%5C%20in)
![W=3\frac{1}{4}\ in=\frac{3*4+1}{4}=\frac{13}{4}\ in](https://tex.z-dn.net/?f=W%3D3%5Cfrac%7B1%7D%7B4%7D%5C%20in%3D%5Cfrac%7B3%2A4%2B1%7D%7B4%7D%3D%5Cfrac%7B13%7D%7B4%7D%5C%20in)
![H=3\frac{7}{8}\ in=\frac{3*8+7}{8}=\frac{31}{8}\ in](https://tex.z-dn.net/?f=H%3D3%5Cfrac%7B7%7D%7B8%7D%5C%20in%3D%5Cfrac%7B3%2A8%2B7%7D%7B8%7D%3D%5Cfrac%7B31%7D%7B8%7D%5C%20in)
<em>Find the area of the base B</em>
![B=LW](https://tex.z-dn.net/?f=B%3DLW)
![B=(\frac{31}{4})(\frac{13}{4})=\frac{403}{16}\ in^{2}](https://tex.z-dn.net/?f=B%3D%28%5Cfrac%7B31%7D%7B4%7D%29%28%5Cfrac%7B13%7D%7B4%7D%29%3D%5Cfrac%7B403%7D%7B16%7D%5C%20in%5E%7B2%7D)
<em>Find the perimeter of the base P</em>
![P=2(L+W)](https://tex.z-dn.net/?f=P%3D2%28L%2BW%29)
![P=2(\frac{31}{4}+\frac{13}{4}))](https://tex.z-dn.net/?f=P%3D2%28%5Cfrac%7B31%7D%7B4%7D%2B%5Cfrac%7B13%7D%7B4%7D%29%29)
![P=2(\frac{44}{4})=22\ in](https://tex.z-dn.net/?f=P%3D2%28%5Cfrac%7B44%7D%7B4%7D%29%3D22%5C%20in)
<em>Find the surface area</em>
![SA=2(\frac{403}{16})+22(\frac{31}{8})](https://tex.z-dn.net/?f=SA%3D2%28%5Cfrac%7B403%7D%7B16%7D%29%2B22%28%5Cfrac%7B31%7D%7B8%7D%29)
![SA=(\frac{403}{8})+(\frac{682}{8})](https://tex.z-dn.net/?f=SA%3D%28%5Cfrac%7B403%7D%7B8%7D%29%2B%28%5Cfrac%7B682%7D%7B8%7D%29)
![SA=\frac{1,085}{8}=135.625\ in^{2}](https://tex.z-dn.net/?f=SA%3D%5Cfrac%7B1%2C085%7D%7B8%7D%3D135.625%5C%20in%5E%7B2%7D)