Hi,
to find out the answer you need to divide 89 by 10 than by 5. Add those two answers together which is 23.73. That answer is dimes so 89-23.73=65.27..:) you could round the number up. I hope it helps!!!
Answer:
D. y = 5x + 29
Step-by-step explanation:
To write an equation of a line in slope-intercept form, we need to find the slope and the y-intercept.
The equation of a line is y=mx + b.
x and y are the coordinates of any point on a line.
m is the slope.
b is the y-intercept.
Lines are parallel to each other when they have the same slope. A line parallel to y = 5x + 2 would also have the slope 5.
m = 5
Since we have a point on the line, (-6, -1) and the slope, 5, there is only one missing variable, b, the y-intercept.
Substitute the known information into the equation and isolate b.
y = mx + b
-1 = 5(-6) + b <=Simplify by solving 5 X -6
-1 = -30 + b
-1 + 30 = -30 + 30 + b <= Add 30 to both sides to isolate b
29 = b
b = 29 <= Standard formatting puts the variable on the left side
Put the m and b values into the equation of a line to solve:
y = mx + b
y = 5x + 29
Answer:
radius=6
Step-by-step explanation:
arc ACB=6xPi
Pi=3.14159
arc ACB=18.85 (rounded to 2 places)
ACB is a half circle so a full circle would be 18.85x2 or 37.7
circumference (whole circle)=2 x Pi x radius
37.7=2 x 3.14159 x radius
radius= 37.7/(2 x 3.14159)
radius=6
You only have to apply the theorem of Pythagoras here. Remember the square on the hypotenuse (the longest side) is equal to the sum of the squares on the other two sides :
1. AB is the hypotenuse, so, according to the theorem we can write :
AB² = AC² + CB²
c² = 5² + 4²
c²= 25 + 16
c² = 41
applying the square root of 41 we get :
c ≈ 6.40 rounded to the hundred
The next cases are exactly the same thing so there is no need for explanation :
2.
AB is the hypotenuse here because it is the biggest side clearl :
AB² = AC² + CB²
25² = 15² + b²
Thus
b² = 25² - 15²
we just subtracted 15² on each side of the equation
b² = 625 - 225
b² = 400
applying the square root of 400 we get
b = √400 = 20
So AC = 20
3. The longest side is clearly AB = 60
So
AB² = AC² + CB²
60² = 40² + a²
subtracting 40² on each side of the equation we get :
a² = 60² - 40²
I let you finish this using your calculator and doing exactly like the previous cases
4.
AB is the hypotenuse,
AB² = AC² + CB²
23² = b² + 14²
Subtracting 14² from each side of the equation we get
b² = 23² - 14²
5.
AB is the biggest side :
AB² = AC² + CB²
29² = 23² + a²
We subtract 23² on each sides of the equation :
a² = 29² - 23²
You can finish with your calculator
6.
AB² = AC² + BC²
78² = b² + 30²
subtraction...
b² = 78² - 30²
Good luck :)
