(2+3i)+2i(2+3i) = 1(2+3i) + 2i(2+3i) = (1+2i)(2+3i)
Taking point <em>Z </em> as the origin, the coordinates of the points on ΔBAD are
given by changing the sign of the coordinates of points in ΔDCB.
- The angle that is congruent to ∠DBA is; <u>D. ∠BDC</u>
Reasons:
The given parameters are;
Triangle ΔBAD is the image of ΔDCB following a rotation of 180°.
Required:
The angle congruent to ∠DBA.
Solution:
Given that the rotation of triangle DCB is 180°, we have that the
coordinates of a point (x, y) in ΔDCB is (-x, -y) in ΔDBA.
Therefore, side DC is parallel to side AB
Which gives;
∠DBA is congruent to ∠BDC by alternate interior angles theorem.
∠DBA ≅ ∠BDC
The angle that is congruent to ∠DBA is; option <u>D. ∠BDC</u>
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Learn more about rotation transformation here:
brainly.com/question/4738741
Answer:
40 yards
Step-by-step explanation:
Data:
The hyperbola equation is expressed as follows:
Dividing each term by 250 000 gives:
thus:
a² = 40
Therefore, the houses will be 20 yards apart.
Answer:
He will save $1.995 if he purchases it in the neighboring county
Step-by-step explanation:
Don's county:
Sales tax of 7.75%.
So he pays
399 + 0.0775*399 = $429.9225
Neighboring county:
Sales tax of 7.25%.
So he pays
399 + 0.0725*399 = $427.9275
Savings:
429.9225 - 427.9275 = 1.995
He will save $1.995 if he purchases it in the neighboring county
Answer:
Step-by-step explanation:
f(x) = y = 3x/(8 + x) (I am assuming that the 8 + x is the denominator. Please use parentheses in the future if you forgot this. If there are no parentheses, then my solution will not work for you.)
Exchange x and y; that is, replace x by y and y by x simultaneously:
x = 3y/(8 + y).
Then use algebra to solve for y in terms of x:
(8 + y)x = 3y (multiply both sides by the denominator to clear the fraction)
8x + xy = 3y (distribute)
xy − 3y = −8x (rearrange terms with all y's on the left side of the equation)
y(x − 3) = −8x (factor out y as a common factor)
y = −8x/(x − 3) (divide by x − 3)
Finally, replace y by f-1(x):
f-1(x) = −8x/(x − 3).
This is the inverse of f(x). It can be checked by finding f(f-1(x)) and f-1(f(x)), and verifying that both equal x after simplifying.
