Answer:
x° = 37°
Step-by-step explanation:
* Lets revise some facts of a circle
- The secant is a line intersect the circle in two points
- If two secants intersect each other in a point outside the circle,
then the measure of the angle between them is half the difference
of the measures of their intercepted arcs
* Now lets solve the problem
- There is a circle
- Two secants of this circle intersect each other in a point outside
the circle
∴ The measure of the angle between them = 1/2 the difference of the
measures of their intercepted arcs
∵ The measure of the angle between them is x°
∵ The measures of their intercepted arcs are 26° and 100°
- Use the rule above to find x
∴ x° = 1/2 [ measure of the large arc - measure of small arc]
∵ The measure of the large arc is 100°
∵ The measure of the small arc is 26°
∴ x° = 1/2 [100 - 26] = 1/2 [74] = 37°
∴ x° = 37°
Answer:
- the number is -6.4
- 52 students were in each bus (but one)
- 1 quart
Step-by-step explanation:
1. Let the number be represented by n. Then ten times the number is 10n, and 8 more than that is 10n+8. The problem statement tells us this sum is -56:
10n +8 = -56
10n = -64 . . . . . . . subtract 8 from both sides
n = -6.4 . . . . . . . . . divide both sides by 10
The number is -6.4.
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2. First of all, you can tell there is an issue with this question because the sum of digits of 472 is 13 and the sum of those digits is 4. This tells you that dividing 472 by 9 will give a remainder of 4, not 5. One of the buses will not be filled. (This process of adding digits until you get a single digit is called "casting out nines". The remaining digit is the remainder from division by 9.)
Let b represent the number of students in each bus. Then the problem statement tells us ...
9b + 5 = 472
9b = 467 . . . . . . subtract 5
b = 467/9 = 51 8/9 . . . . almost 52
52 students rode in 8 of the buses; 51 students rode in the last bus.
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3. Let q represent the number of quarts of 6% solution. Then the total amount of Boric Acid in the mix is ...
15%×2 + 6%×q = 12%×(2+q)
Multiplying by 100 to clear the % signs, we have ...
15·2 +6q = 12(2+q)
30 +6q = 24 +12q . . . . . . eliminate parentheses
6 = 6q . . . . . . . . . . . . . . . . subtract 24+6q from both sides
1 = q . . . . . . divide by 6
1 quart of 6% solution must be used.
Answer:
D) y = 3x - 9
Step-by-step explanation:
Answer:
97,655
Step-by-step explanation:
5(5)^(n-1) = 78,125
5^n = 78,125
n = 7
=> S7 = 5(5^7 -1) / (5-1)
= 5/4 (78, 125 -1)
= 5/4 (78 124) = 97,655
Use phytagorean theorem to solve the problem
c² = a² + b²
with c as hypotenuse, a and b are the two sides which are perpendicular to each other.
Plug the numbers into the formula
c² = a² + b²
c² = (46.3)² + 39²
c² = 2,143.69 + 1,521
c² = 3,664.69
c = √3,664.69
c = 60.53668..
to the nearest hundredth
c = 60.54
The length of the hypotenuse is 60.54 m
