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Answer:
The equation of the line would be y = -2x + 3
Step-by-step explanation:
In order to find the equation of the line, start by using point-slope form with the known information.
y - y1 = m(x -x1)
y - 1 = -2(x - 1)
Now that we have this, solve for y.
y - 1 = -2x + 2
y = -2x + 3
Answer:
24
Step-by-step explanation:
Direct variation (with constant of proportionality) has the form:
Where,
- A & B are the 2 variables being compared
is the constant of proportionality
Using cookies, 
, and sugar, 
, we can write:
Substituting 
and 
, and solving for , we have:
Thus, constant of proportionality is 24
Answer:
x = 1/2 and 3/2
Step-by-step explanation:
The given equation is logₓ (8x-3) - logₓ 4 = 2
Then we have to determine the value of x.
logₓ ![[\frac{(8x-3)}{4}]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B%288x-3%29%7D%7B4%7D%5D)
= 2 [ since log a - log b = log 
]
Now 
[if 
b = c then 
= b]
4x² = 8x -3
4x² - 8x + 3 = 0
(2x)² - 2(4x) + (4-4) + 3 = 0
[(2x)² - 2 (4x) + 4 ] - 1 = 0
(2x - 2)² = 1
(2x - 2)² = ± 1 ⇒
2x - 2 = 1 and 2x - 2 = -1
x = 3/2 2x = 1
x = 1/2
Therefore, x = 1/2 and 3/2 are the answers.
9514 1404 393
Answer:
E
Step-by-step explanation:
A. The ⊥ symbol means "is perpendicular to". The two lines l1 and l2 are parallel, not perpendicular.
B. Angles g and f are vertical angles. They are congruent. If both are 45°, then they are complementary, but we cannot assume that is the case. They are shown as obtuse angles.
C. Angles e and h are vertical angles. They are congruent. If both are 45°, then they are complementary, but we cannot assume that is the case. They are shown as acute angles, but with no particular angle measure.
D. Angle d is shown as an acute angle. In general, we cannot assume its measure based on its appearance in the diagram.
E. Angles d and g are shown as, respectively, an acute angle and an obtuse angle. Where a transversal crosses parallel lines, all acute angles are supplementary to all obtuse angles. Hence the sum of angles d and g will be 180 degrees. This statement is true.
F. Angles c and f are congruent angles, shown as obtuse. Their sum will be 270° if and only if their measures are each 135°. There is no indication in the diagram that the angles have any particular measure, so we cannot assume their sum is 270°.
