Answer:
#7. JK = 1
Step-by-step explanation:
So all these problems are similar in the fact that you are given three pieces of information and you need to determine x. Let's look at #7.
We are to find the length JK but we are given it in terms of x. To find the length, we need to find x. Using the information we have about KL and JL, we can find this. Note, the value of JL is 5, and the value of KL is x + 8.
JK + KL = JL
( 2x + 9 ) + ( x + 8 ) = 5
3x + 17 = 5
3x = -12
x = -4
Now that we have the value of x, we can find the value of JK:
JK = 2x + 9
JK = 2(-4) + 9
JK = -8 + 9
JK = 1
Hence, the length of JK is 1.
Using this same basic idea, you can solve all of these problems.
Cheers.
Answer:
The correct solution is "4.6".
Step-by-step explanation:
Given:
Interest rate,
r = 6.2%
or,
= 0.062
Amount,
A = 100000
Principle,
P = 76000
As we know,
⇒ ![A=P(1+\frac{r}{100} )^n](https://tex.z-dn.net/?f=A%3DP%281%2B%5Cfrac%7Br%7D%7B100%7D%20%29%5En)
On substituting the values, we get
⇒ ![100000=76000(1+\frac{6.2}{100} )^n](https://tex.z-dn.net/?f=100000%3D76000%281%2B%5Cfrac%7B6.2%7D%7B100%7D%20%29%5En)
⇒ ![(1+0.062)^n=\frac{100}{76}](https://tex.z-dn.net/?f=%281%2B0.062%29%5En%3D%5Cfrac%7B100%7D%7B76%7D)
On taking log both sides, we get
⇒ ![n \ log_e(1.062)=log_e(\frac{100}{76} )](https://tex.z-dn.net/?f=n%20%5C%20log_e%281.062%29%3Dlog_e%28%5Cfrac%7B100%7D%7B76%7D%20%29)
⇒ ![n=\frac{ln(\frac{100}{76} )}{ln(1.062)}](https://tex.z-dn.net/?f=n%3D%5Cfrac%7Bln%28%5Cfrac%7B100%7D%7B76%7D%20%29%7D%7Bln%281.062%29%7D)
By putting the values of log, we get
⇒ ![=4.5622](https://tex.z-dn.net/?f=%3D4.5622)
or,
⇒
Answer:
im not fully sure but I'd say it is 9(5+0.78)
Simple interest=Principal*Rate*Time
31=420*R*2.5 years
r =2.95%
Annual rate of interest=2.95%
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°