Answer:
The measure of segment AC is 36 units
Step-by-step explanation:
- The mid-point divides the segment into two equal parts in length
- B is the mid point of segment AC
- That means B divides segment AC into two equal parts in length
∴ AB = BC
∵ AC = 5x - 9
∵ AB = 2x
- The two parts AB and BC are equal in length
∴ BC = 2x
∵ AC = AB + BC
- Substitute the values of AB and BC in the expression of AC
∴ AC = 2x + 2x
∴ AC = 4x
∵ AC = 5x - 9
- Equate the two values of AC
∴ 5x - 9 = 4x
- Add 9 to both sides
∴ 5x = 4x + 9
- Subtract 4x from both sides
∴ x = 9
- Substitute the value of x in any expression of AC
∵ AC = 4x
∵ x = 9
∴ AC = 4(9) = 36
* The measure of segment AC is 36 units
Answer:
About 41.5%
Step-by-step explanation:
<em>Given:</em>
<em>A bowl has 8 green grapes and 15 red grapes. Henry randomly chooses a grape, eats it, and then chooses another grape.</em>
<em>To Find:</em>
<em>What is the probability that both grapes are red?</em>
<em>Answer choices:</em>
<em>about 39.7%</em>
<em>about 41.5%</em>
<em>about 42.5%</em>
<em>about 44.5%</em>
<em>Solution:</em>
<em>Since, there are 8 green grapes and 15 red grapes, the total number of grapes is 23 .</em>
<em>As the red grapes are 15..</em>
<em>Thus,</em>
<em>The probability of choosing a red grape the first time is 15/23.</em>
<em>Because out of the total 23 grapes only 15 were red grape.</em>
<em>The probability of choosing the red grape the second time will be 14/22. Because the number of red grapes has already decreased by one and so is the total number of grapes after first choice</em>
<em>Hence, the probability of choosing or eating two red grapes will be :</em>
<em>15/23×14/22</em>
<em>=105/253</em>
<em>=0.415</em>
<em>= 41.5%</em>
<em>Therefore, the probability that both grapes are red is about 41.5%</em>
Answer:
Vertical shift is 2 units top and horizontal shift is 
units to the right
Step-by-step explanation:
Consider the function f(x) = a cos(bx + c) + d.
In this graph, the horizontal shift is -c/b and the vertical shift is d.
Let's compare our graph, f(x) = -3 cos(2x - π) + 2 with this graph.
Here, a = -3, b = 2, c = -π and d = 2.
So, vertical shift = d = 2 units top and
horizontal shift = 
units to the right.
Last year He was 7 years old.
His father is 4 times the age 7 x 4 = 28
Last year his dad was 28, so this year he is 29.
Combined age this year = 29 + 8 = 37
51 - 37 = 14 years
14/ 2 people = 7 years
8 + 7 = 15
29 + 7 = 36
15 + 36 = 51
It will take 7 years.
