Answer:
y = 12x - 37
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = 12, thus
y = 12x + c ← is the partial equation
To find c substitute (3, - 1) into the partial equation
- 1 = 36 + c ⇒ c = - 1 - 36 = - 37
y = 12x - 37 ← is the equation of the line
Answer:
The angles measured between the shadow and the wall trim and the shadow and the top or bottom of the picture should be equal if the picture is level
Step-by-step explanation:
Whereby the picture is 12 inches above the wall trim and the Sun is casting a shadow on the wall, therefore, the edges of the shadow of a straight edged object is straight
If the picture is level, the shadow cast by the sun is transversal to the wall trim and the line formed by extending the bottom or top of the picture in the direction of the shadow. That is, if the picture is parallel, the shadow cast by the Sun on the wall is transversal to the picture and the wall trim if or when the shadow eventually crosses the picture
With the protractor, the angle between the shadow and the wall trim and the shadow and the top or bottom is measured
The angles measured should be the same if the picture is level.
We need 56 pints of the 55 % <em>pure fruit</em> juice and 84 pints of the 80 % <em>pure fruit</em> juice to prepare 140 pints of 70 % <em>pure fruit</em> juice.
<h3>How to use weighted averages to find the correct juice concentration</h3>
In this problem we have to use two kinds of juice with different concentrations. To get a certain concentration, we must adjust quantities of each kind and <em>weighted</em> averages offers a method that is easy to apply:
70 · 140 = 55 · x + 80 · (140 - x)
70 · 140 = 80 · 140 - 25 · x
25 · x = 10 · 140
x = 56
We need 56 pints of the 55 % <em>pure fruit</em> juice and 84 pints of the 80 % <em>pure fruit</em> juice to prepare 140 pints of 70 % <em>pure fruit</em> juice.
To learn more on weighted averages: brainly.com/question/28042295
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Answer: x = -5/2 and x = -3/2
Step-by-step explanation:
(2x + 5)2 = 4x (x + 5) +25
4x + 10 = 4x² + 20x + 25
[minus 4x on both sides.]
10 = 4x² + 16x + 25
[minus 10 on both sides.]
0 = 4x² + 16x + 15
ac = 4(15) = 60,then find the factors that add up to 16, which is 6 and 10.
0 = 4x² + 6x + 10x + 15
0 = 2x(2x + 3) + 5(2x + 3)
0 = (2x + 5)(2x + 3)
2x + 5 = 0 2x + 3 = 0
2x = -5 2x = -3
x = -5/2 x = -3/2
Answer:
361.7cm²
Step-by-step explanation:
Volume of sphere 1= 8cm³
=
Volume of sphere 2 = 647cm³
But volume of sphere = 4/3πr³
The radius of sphere 2
647 = 4/3πr³
((3*647)/4)/π= r³
5.36544 = r
Surface area = 4πr²
Surface area for the big sphere
= 4π5.36544²
= 361.7cm²
