Answer:
x=23
Step-by-step explanation:
The two angles are equal so you can set 8x-77 and 3x+38 equal to each other and write it as:
8x-77=3x+38
Then you get like terms on the same sides by subtracting 3x from both sides and getting:
5x-77=38
Then you add 77 to both sides and get:
5x=115
Then you divide both sides by 5 and get x=23
Answer
B) 287.6cm²
Step-by-step explanation:
First you need the radius, since you have the diameter you have to divide it by 2 in order to get the radius (8.4 divided by 2 = 4.2) then use the formula A=2πrh and plug in the radius and your height (h) which is 10.9cm into the formula.
Answer:
3 triangles
Step-by-step explanation:
Perimeter of triangle = a + b + c
Given that :
P = 12
and a, b, c are natural numbers
Let :
Side A = a
Side B = b
Side C = 12 - (a + b)
Side A + side B > side C - - - (condition 1)
a + b > 12 - (a + b)
a + b > 12 - a - b
a + a + b + b > 12
2a + 2b > 12
2(a + b) > 12
a + b > 6
Side A - side B < side C
a - b < 12 - (a + b)
a - b + a + b < 12
2a < 12
a < 6
b < 6 (arbitrary point)
Going by the Constraint above :
The only three possibilities are :
(2, 5, 5)
(3, 4, 5)
(4, 4, 4)
Total number of triangle = 3
Equilateral triangle (all 3 sides equal) = (4, 4, 4) = 1
Isosceles triangle (only 2 sides equal) = (2, 5, 5) = 1
Answer:
f(x) = -2/3(x +11) +5
Step-by-step explanation:
The point-slope form of the equation of a line will give you the desired linear function:
y = m(x -h) +k . . . . . for slope m through point (h, k)
You are give point (x, f(x)) = (-11, 5) = (h, k), and you are given slope m = -2/3. Putting these values into the function form gives ...
f(x) = -2/3(x +11) +5
Answer:
D) In step 5, he should have multiplied both sides by 1/3
Step-by-step explanation:
Given expression,
Using distributive property,
Using additive property of equality,
Make the fraction with same denominator by taking LCM of Denominators in left side the equation,
Adding fractions,
Write 3 as a fraction,
Using multiplicative property of equality for isolating the variable in right side, multiply 1/3 in both sides,
Hence, it is clear that he did mistake in step 5 he should have multiplied both sides by 1/3.