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Answer:
Step-by-step explanation:
Because is being multiplied by S, we can divide
from both sides of the equation. This will give us:
÷
But, that looks a bit hectic. Instead of dividing, you can multiply by the reciprocal (which is essentially how to divide fractions). So, instead of ÷
, you get:
×
When multiplying fractions, remember you can just multiply straight across-- numerator x numerator, then denominator x denominator.
By doing that, you get the fraction
cannot be simplified any more, so S=
is your answer :)
I hope this helps
9514 1404 393
Answer:
- 13 ft
- (a) 1 second; (b) t = 0, t = 1/2
Step-by-step explanation:
<h3>1. </h3>Let w represent the length of the wire. Then the height of attachment is (w-1). The Pythagorean theorem tells us a relevant relation is ...
5² +(w -1)² = w²
w² -2w +26 = w² . . . . . . . eliminate parentheses, collect terms
26 = 2w . . . . . . . . . . . . add 2w
13 = w . . . . . . . . . . . . divide by 2
The length of the wire is 13 feet.
__
<h3>2. </h3>(a) When h = 0, the equation is ...
0 = -16t^2 +8t +8
Dividing by -8 puts this into standard form:
2t^2 -t -1 = 0
Factoring, we get ...
(2t +1)(t -1) = 0
The positive value of t that makes a factor zero is t = 1.
It will take 1 second for the gymnast to reach the ground.
__
(b) When h = 8, the equation is ...
8 = -16t^2 +8t +8
Subtract 8 and divide by 8 to get ...
0 = -2t^2 +t
0 = t(1 -2t) . . . . factor out t
Values of t that make the factors zero are ...
t = 0
t = 1/2
The gymnast will be 8 feet above the ground at the start of the dismount, and 1/2 second later.
Answer:
The equation in slope-intercept form that represents the situation is y=0.25*x + 84 where y represents the temperature in ° F and x the number of chirps per minute.
Step-by-step explanation:
A linear equation can be expressed in the form y=m*x + b. In this equation, x and y are coordinates of a point, m is the slope and b is the y coordinate of the y-intercept. Since this equation describes a line in terms of its slope and its y-intercept, this equation is said to be in its slope-intercept form.
When there are two points of a line (x1, y1) and (x2, y2), the slope is determined by the quotient between the difference of the ordinate of these two points and the difference of the abscissa of the same points. This is:
Having a point on the line, you can substitute the values of m, x and y in the equation y = mx + b and thus find b.
In this case:
- (x1, y1): (92, 107)
- (x2, y2): (116, 113)
So:
m= 0.25
substituting the values of m, x1 and y1 in the equation y = mx + b you have:
107= 0.25*92 + b
107 - 0.25*92= b
84=b
<u><em>The equation in slope-intercept form that represents the situation is y=0.25*x + 84 where y represents the temperature in ° F and x the number of chirps per minute.</em></u>