m∠BAC = 27°
Solution:
ABCD is a quadrilateral.
AB and CD are parallel lines.
Given m∠BCD = 54°
AC bisect ∠BCD.
m∠DCA + m∠CAB = m∠BCD
m∠DCA + m∠DCA = 54° (since ∠ACB = ∠DCA)
2 m∠DCA = 54°
Divide by 2 on both sides, we get
m∠DCA = 27°
AB and CD are parallel lines and AC is the transversal.
<em>If two parallel lines cut by a transversal, then the alternate interior angles are equal.</em>
m∠BAC = m∠DCA
m∠BAC = 27°
Hence m∠BAC = 27°.
ANSWER
Phase shift: 2 units right.
EXPLANATION
The given sine function is

In mathematics, a horizontal shift may also be referred to as the phase shift.
This function is shifted to the right 2 units.
Answer:
1 : 4
Step-by-step explanation:
Remember, your units have to match, so
3 in : 1 ft
doesn't look right, change 1 ft to 12 in.
3 in : 12 in
reduce by 3
1 : 4
Answer:
y= 3/2x- 4
Step-by-step explanation:
3/2 = mx
b= -4
y=mx+b
Answer:
2.4 hours
Step-by-step explanation:
Let total work = X
Rate of work done = X ÷ time
Rate of A = X/4
Rate of B = X/6
If they work together, rate is the sum of their individual rates, i.e.
X/4 + X/6
= (3X + 2X)/12 (taking LCM)
=5X/12
Rate = X/time
5X/12 = X/time
time = X÷(5X/12)
time = X × 12/(5X)
time = 2.4 hours
Shortcut:
Product of individual times/sum of individual times
= (4×6)/(4+6)
=24/10
=2.4 hours