Answer:
he walked 1 mile
Step-by-step explanation:
we find the common denominator which is 10. 3/5=6/10
6/10+4/10=10/10 or 1 mile
Answer: △DEF is congruent to △D'E'F' because you can map △DEF to △D'E'F' using a reflection across the x-axis, which is a rigid motion.
Explanation:
1) Reflections, rotations and translations are rigid transformations, because they do not modify the lengths of the segments nor the angles, so the images and the preimages are congruents.
2) Let's see what transformation map △DEF is to △D'E'F' by analyzing the vertices of preimage and image:
Preimage Image
D (-3, -1) D' (-3, 1)
E (2, -4) E' (2, 4)
F (4, -4) F' (4, 4)
As you see when the image is formed, the coordinate x of the image is kept, and the coordinate y is negated. This rule is (x, y) → (x, - y), which is the rigid transformation reflection across the x-axis.
Answer:-3
Step-by-step explanation:
40-7=33
33/-11=-3
He spent 12 dollars on each oou day
Answer:
(e) csc x − cot x − ln(1 + cos x) + C
(c) 0
Step-by-step explanation:
(e) ∫ (1 + sin x) / (1 + cos x) dx
Split the integral.
∫ 1 / (1 + cos x) dx + ∫ sin x / (1 + cos x) dx
Multiply top and bottom of first integral by the conjugate, 1 − cos x.
∫ (1 − cos x) / (1 − cos²x) dx + ∫ sin x / (1 + cos x) dx
Pythagorean identity.
∫ (1 − cos x) / (sin²x) dx + ∫ sin x / (1 + cos x) dx
Divide.
∫ (csc²x − cot x csc x) dx + ∫ sin x / (1 + cos x) dx
Integrate.
csc x − cot x − ln(1 + cos x) + C
(c) ∫₋₇⁷ erf(x) dx
= ∫₋₇⁰ erf(x) dx + ∫₀⁷ erf(x) dx
The error function is odd (erf(-x) = -erf(x)), so:
= -∫₀⁷ erf(x) dx + ∫₀⁷ erf(x) dx
= 0