What is the solution to the equation? 1/7g=3/14

Mathematics

1 answer:

Crazy boy [7]2 years ago

6 0

Answer:

g = 21/4

Decimal form:

g = 5.25

Mixed Number:

5 1/4

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Here’s a graph of a linear function. Write the equation that describes that function. (Zoom in if blurry)

Maru [420]

Answer: y = x/2 + 3

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m = change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

Looking at the graph,

y2 = 6

y1 = 4

x2 = 6

x1 = 2

Slope,m = (6 - 4)/(6 - 2) = 2/4 = 1/2

To determine the intercept, we would substitute x = 2, y = 4 and m= 1/2 into y = mx + c. It becomes

4 = 1/2 × 2 + c

4 = 1 + c

c = 4 - 1

c = 3

The equation becomes

y = x/2 + 3

5 0

2 years ago

How do you do this question?

mihalych1998 [28]

Answer:

C) π/6

Step-by-step explanation:

The area under the curve from x=-π/2 to x=k is 3 times the area under the curve from x=k to x=π/2.

$\int\limits^k_{-\frac{\pi }{2}} {cos\ x} \, dx = 3\int\limits^{\frac{\pi }{2}}_k {cos\ x} \, dx\\sin\ x\ |^{k}_{-\frac{\pi }{2}} = 3\ sin\ x\ |^{\frac{\pi }{2}}_k\\(sin\ k - (-1)) = 3\ (1 - sin\ k)\\sin\ k + 1 = 3 - 3\ sin\ k\\4\ sin\ k = 2\\sin\ k = \frac{1}{2}\\k = \frac{\pi}{6}$