Answer:
The length of BE is 27 units ⇒ 3rd answer
Step-by-step explanation:
In circle A:
∠BAE ≅ ∠DAE
Line segments A B, A E, and A D are radii
Lines are drawn from point B to point E and from point E to point D to form secants B E and E D
The length of B E is 3 x minus 24 and the length of E D is x + 10
We need to find the length of BE
∵ AB and AD are radii in circle A
∴ AB ≅ AD
In Δs EAB and EAD
∵ ∠BAE ≅ ∠DAE ⇒ given
∵ AB = AD ⇒ proved
∵ EA = EA ⇒ common side in the two triangles
- Two triangles have two corresponding sides equal and the
including angles between them are equal, then the two
triangles are congruent by SAS postulate of congruence
∴ Δ EAB ≅ Δ EAD ⇒ SAS postulate of congruence
By using the result of congruence
∴ EB ≅ ED
∵ EB = 3 x - 24
∵ ED = x + 10
- Equate the two expressions to find x
∴ 3 x - 24 = x + 10
- Add 24 to both sides
∴ 3 x = x + 34
- Subtract x from both sides
∴ 2 x = 34
- Divide both sides by 2
∴ x = 17
Substitute the value of x in the expression of the length of BE to find its length
∵ BE = 3 x - 24
∵ x = 17
∴ BE = 3(17) - 24
∴ BE = 51 - 24
∴ BE = 27
The length of BE is 27 units
Cramer's rule works as follows:
x+3y=16
3x+y=8
Then
x=Dx/D
y=Dy/D
where Dx,Dy,D are 2x2 matrices formed from of coefficients and right hand side.
D=
1 3
3 1
=1-9=-8
Dx=matrix D with first column replaced by the vector [16,8]=
16,3
8 1
=16-24
=-8
Dy=matrix D with second column replaced by the vector [16,8]=
1 16
3 8
=8-48
=-40
Therefore
x=-8/-8=1
y=--40/-8=5
Check:
x+3y=1+3(5)=16
3x+y=3(1)+5=8 ok.
Q11
Suppose the two numbers are x and y so xy = 3000
the HCF = 10
we know that product of two numbers = product of their HCF and LCM
XY = HCF * LCM
3000 = 10 * LCM
3000/10 = LCM
300 = LCM
Answer 300
Q12 : Let us say second number is x so
product of x and 160 = product of HCF and LCM of ( x and 160 )
160 x = 32 * 1760
x= 32 * 1760 / 160
x= 352
Answer : 352
Answer:
Step-by-step explanation:
The relationship between A, the area of the glacier in square kilometers, and t, the number of years the glacier has been melting, is modeled by the equation.:
We want to determine the value of t for which the area, A(t)=15 square kilometers.
Therefore, the time for which the area will be 15 sqyare kilometers is:
-20 ln(1/3) years.
$187,500 is cost of house. 20%, or $37,500 is the down payment. The loan amount would be $187,500 - $37,500 = $150,000. If we assume the annual rate of the loan is 4.65% Then the monthly rate would be 4.65%/12 = 0.3875% If the loan is $150,000, the interest is 0.3875% The interst for the first month is $150,000 * 0.3875% = $581.25. You stated that their payment is $1,575. So the amount that pays off the loan is $1,575 - $581.25 = $993.75. At the end of the month, they owe $150,000 - $993.75 = $149,006.25 For the second month, the amount of the payment that goes towards intrest is $149,006.25 * 0.3875% = $577.40. and the amount that goes towards the loan is $997.60. At the end of the second month they owe $148,008.65. Regarding realized income, we recommend a monthly loan payment not to exceed 28% of the monthly income. So if a payment of $1,575 is 28% of Gross, then the math is : $1,575 = 0.28*Gross. Gross = $5,625 monthly. About $67,500 annually. About $33.75 an hour.
