Triangle ABC is an isosceles triangle.
Solution:
Given data:
∠ABC = 70° and ∠ACD = 55°
<em>If two parallel lines are cut by a transversal, then alternate interior angles are congruent.</em>
m∠BAC = m∠ACD
m∠BAC = 55°
<em>Sum of the angles in a straight line add up to 180°.</em>
m∠ACD + m∠ACB + m∠ABC = 180°
55° + m∠ACB + 70° = 180°
m∠ACB + 125° = 180°
Subtract 125° from both sides, we get
m∠ACB = 55°
In triangle ABC,
∠BAC = 55° and ∠ACB = 55°
∠BAC = ∠ACB
Two angles in the triangle are equal.
Therefor triangle ABC is an isosceles triangle.
Answer:
(-16a)-72b+56
Step-by-step explanation:
Multiply 8 to each number
Hope this helped :)
Answer:
5.16
Step-by-step explanation:
Since after x=3, value of y starts decreasing for increasing values of x, let's choose. Also we need to find f(x) for x=3.4
x=3,4,5 and f(x)=7,3,1 to find lagrange polynomial
P(x)= ((x-x2)(x-x3)y1)/((x1-x2)(x1-x3) + ((x-x1)(x-x3)y2)/((x2-x1)(x2-x3) + ((x-x1)(x-x2)y3)/((x3-x1)(x3-x2)
P(x)= ((x-4)(x-5)7)/((3-4)(3-5)) + ((x-3)(x-5)3)/((4-3)(4-5)) + ((x-3)(x-4)1)/((5-3)(5-4))
P(x)= x² -11x+31
P(3.4)= 5.16
Answer:
Step-by-step explanation:
percentage of graduates with loan = 62%
total sample = 50
Number of student in the sample with student loan
= (percentage of graduates with loan) x (total sample)
= 62% x 50
= 31
Proportion of student in the sample with student loan =
Answer: number of years that it will take for the balance to reach $120,000 is 42 years
Step-by-step explanation:
Initial amount deposited into the account is $4000. This means that the principal is $4000
P = 4000
It was compounded annually. This means that it was compounded once in a year. So
n = 1
The rate at which the principal was compounded is 8.4%. So
r = 8.4/100 = 0.084
Let the number of years that it will take for the balance to reach $120,000. It means that it was compounded for a total of t years.
Amount, A at the end of t years is $120,000
The formula for compound interest is
A = P(1+r/n)^nt
120000 = 4000(1 + 0.084/1)^1×t
120000/4000 = 1.084^t
30 = 1.084^t
t = 42 years
