Choose the correct answer.
Find the interest due on $800 at 12% for 120 days.
Answers
Answer:
$32
Step-by-step explanation:
To find the interest due, you will use an interest formula.
The formula will be: Interest= P · r ·
P represents our principal amount, R is our rate of interest, and N is the number of days (out of 365 which is a year).
In this situation,
$800 will be our P amount, 12% will be our R, and 120 will be our N.
This will give us:
Interest= 800 · 0.12 ·
Before we go on, I would like to clarify 12% goes out of a hundred. To find the decimal form, you will divide 12 over 100. By doing this, you will find yourselves having 0.12 (our rate of interest).
When you solve our new formula equation, you will get a long decimal number consisting of 31.5616... Remember a decimal will be rounded if it is 5 or above, if it less than 5 it will not be rounded. In this case, we got 31.5, so we round; getting us 32.
Our answer will then be $32
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Answers
2k(7-5k)+11=6k+3(k^2-1)
with work please.
Answers
⇒ (2k)* 7 - (2k)* (5k) +11= 6k+ 3* k^2- 3*1 (distributive property)
⇒ 14k -10k^2 +11= 6k+ 3k^2 -3
⇒ (14k -14k) +(-10k^2 +10k^2)+ (11-11) = (6k-14k)+ (3k^2+10k^2)+ (-3-11)
⇒ 13k^2- 8k- 14= 0
⇒ 13 (k^2- 8/13k- 14/13)=0
⇒ (k- ((4+3*sqrt(22))/13))* ((k- ((4-3*sqrt(22))/13))= 0
⇒ k= (4+3*sqrt(22))/13 or k= (4-3*sqrt(22))/13).
Hope this helps~
Answer:
k= (4+3*sqrt(22))/13 or k= (4-3*sqrt(22))/13).
Step-by-step explanation:
2k(7-5k)+11=6k+3(k^2-1)
We move all terms to the left:
2k(7-5k)+11-(6k+3(k^2-1))=0
We add all the numbers together, and all the variables
2k(-5k+7)-(6k+3(k^2-1))+11=0
We multiply parentheses
-10k^2+14k-(6k+3(k^2-1))+11=0
We calculate terms in parentheses: -(6k+3(k^2-1)), so:
6k+3(k^2-1)
We multiply parentheses
3k^2+6k-3
Back to the equation:
-(3k^2+6k-3)
We get rid of parentheses
-10k^2-3k^2+14k-6k+3+11=0
We add all the numbers together, and all the variables
-13k^2+8k+14=0
a = -13; b = 8; c = +14;
Δ = b2-4ac
Δ = 82-4·(-13)·14
Δ = 792
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
k1=−b−Δ√2ak2=−b+Δ√2a
The end solution:
Δ−−√=792−−−√=36∗22−−−−−−√=36−−√∗22−−√=622−−√
k1=−b−Δ√2a=−(8)−622√2∗−13=−8−622√−26
k2=−b+Δ√2a=−(8)+622√2∗−13=−8+622√−26
- KL = MN
- LN = √(89)
- LH: altitude
- LM = 3
- KN = 13
Find: m∠LKN
See attached image.
Answers
Answer:
45 degrees
Step-by-step explanation:
If KL = MN, and LM =3 and KN = 13, then HN = 13 - (13-3)/2 = 8
LN = sqrt(HN^2 + LH^2) -->
LN = sqrt89 sqrt(8^2 + LH^2) -->
89 = 64 + LH ^2 -->
25 = LH^2 -->
LH = 5
Because HN = 8, HK = 13 - 8 = 5
That makes both legs equal, which makes m∠LKN = 45 degrees
The angle m∠LKN is equal to 45 degrees.
To understand more, check below explanation.
Trapezoid :
It is given that,
KL = MN, LM =3 , KN = 13 and LN
So that, HN = 13 - (13-3)/2 = 13 - 5 = 8
Since, HN = 8. So that, HK = 13 - 8 = 5
In a triangle, if two sides are equal. Then, opposite angle of both sides are also equal.
In triangle LKH, LH = HK = 5 and
So that, m∠LKN = 90/2 = 45 degree.
Hence, the angle m∠LKN is equal to 45 degrees.
Learn more about the trapezoid here:
Answers
Answer:
The relationship symbol that makes the statement true is '>'.
Step-by-step explanation:
Given,
In triangles ABC and EDF,
∠A = ∠D
Since, the sum of all interior angles of a triangle is supplementary,
⇒ ∠A + ∠B + ∠C = 180° and ∠D + ∠E + ∠F = 180°
⇒ ∠A = 180° - ∠B - ∠C and ∠D = 180° - ∠E - ∠F,
By substituting the values,
180° - ∠B - ∠C = 180° - ∠E - ∠F
- ∠B - ∠C = - ∠E - ∠F
∠B + ∠C = ∠E + ∠F
∠B + 20° = ∠E + 30° ( given ∠C = 20° and ∠F = 30° )
∠B = ∠E + 10°
⇒∠B > ∠E
Hence, the relationship symbol that makes the statement true would be '>'.