Determine the input value for which the statement f(x) = g(x) is true. From the graph, the input value is approximately_______ .
f(x) = 3 and g(x) = x – 2 3 = x – 2 5 = x The x-value at which the two functions’ values are equal is______ .
2 answers:
For this inquiry, we are presented with a graph, and we're tasked with determining the x-coordinate of where the two lines intersect.
An examination of the graph indicates that the input value is around 3.3.
In the graph,
To derive g(x), we need the slope and y-intercept.
The slope represents the ratio of vertical change to horizontal change.
In this case, the rise is 3 units and the run is 2 units. The line intersects the y-axis at -2.
Thus, the equation for g(x) becomes
Next, we will perform
Substituting the values of both functions will yield
By adding 2 to both sides, we have
We will apply cross multiplication
Thus, the approximate input value is 3.3.
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Answer:
(1) The necessary proportion of spirit to varnish stands at 1:3.
(2) A total of 80 ml of mineral spirit is required.
(3) The ratio of the heights to the widths of the tapestries is 3:2.
Step-by-step explanation:
(1) To achieve a mixture containing 25% mineral spirit, the blend consists of 25% spirit and 75% varnish.
Therefore,
Consequently, the proportion of spirit to varnish is 1:3.
(2) Using 240ml of varnish indicates this is 75% of the entire solution, which means the ratio of varnish to the total solution is 3:4.
Let the total solution quantity be .
Thus, .
⇒
⇒
⇒
⇒
This means the total solution amounts to 320 ml.
Now, calculating Spirit = Total solution - Varnish
⇒Spirit = 320ml-240ml
⇒Spirit = 80ml
Therefore, when using 240 ml of varnish, you will require 80 ml of mineral spirit.
(3) The dimensions of Robison's tapestries are uniform at 1.5m in length and 1m in width. Initially, to obtain whole numbers, we multiply these dimensions by 10.
Thus, the dimensions become 15m long and 10m wide.
Now, the proportion of Height to Width is 15:10
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⇒
Thus, the proportion of the heights of the tapestries to their widths is 3:2.
Begin by disregarding the inequality symbol and substituting it with an '=' sign. After that, determine the x- and y-intercepts.
15x + 10y = 1,100
x-intercept:
15x + 0 = 1,100
x = 1,100/15 = 73.33
y-intercept:
0 + 10y = 1,100
y = 1,100/10 = 110
Now, plot the points (73.33,0) and (0,110). Given that the inequality symbol is ≥, representing equality, connect these points using a solid line.
Next, let's identify a point on the graph, for instance, the origin (0,0). Use this point in the equation.
15x + 10y ≥ 1,100
15(0) + 10(0)? 1,100
0? 1,100
0 < 1,100
This makes the ≥ statement false. As a result, the alternate area defined by the line is the solution. Consequently, shade that region. The resulting graph is displayed in the attached image.
