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g100num [7]
2 years ago
13

Jen ran 3/4 mile in 18 minutes at 9 am and 2 1/4 miles in 27 minutes at 6 pm. Is this proportional or non proportional?

Mathematics
1 answer:
VMariaS [17]2 years ago
7 0

Answer:

It's non-proportional

Step-by-step explanation:

You could tell every 1/4 mile is 6 minutes, so every other number should be a multiple of 6 if it is a multiple of 1/4. 27 is not a multiple of 6.

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Find the exact value of cos(a+b) if cos a=-1/3 and cos b=-1/4 if the terminal side if a lies in quadrant 3 and the terminal side
maria [59]

Answer:

cos(a + b) = \frac{1}{12}(1-2\sqrt{30})

Step-by-step explanation:

cos(a + b) = cos(a).cos(b) - sin(a).sin(b) [Identity]

cos(a) = -\frac{1}{3}

cos(b) = -\frac{1}{4}

Since, terminal side of angle 'a' lies in quadrant 3, sine of angle 'a' will be negative.

sin(a) = -\sqrt{1-(-\frac{1}{3})^2} [Since, sin(a) = \sqrt{(1-\text{cos}^2a)}]

         = -\sqrt{\frac{8}{9}}

         = -\frac{2\sqrt{2}}{3}

Similarly, terminal side of angle 'b' lies in quadrant 2, sine of angle 'b' will be  negative.

sin(b) = -\sqrt{1-(-\frac{1}{4})^2}

         = -\sqrt{\frac{15}{16}}

         = -\frac{\sqrt{15}}{4}

By substituting these values in the identity,

cos(a + b) = (-\frac{1}{3})(-\frac{1}{4})-(-\frac{2\sqrt{2}}{3})(-\frac{\sqrt{15}}{4})

                = \frac{1}{12}-\frac{\sqrt{120}}{12}

                = \frac{1}{12}(1-\sqrt{120})

                = \frac{1}{12}(1-2\sqrt{30})

Therefore, cos(a + b) = \frac{1}{12}(1-2\sqrt{30})

5 0
3 years ago
Write the standard form of the equation of each line. <br> y=1/4 x+2
sweet-ann [11.9K]

y=mx+c where m = 1/4

c=2

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Answer:

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2 years ago
Write the equation of the line that passes through points (-7,8) and (4,-5)
Alex

Answer:

y=-3/11x+67/11

Step-by-step explanation:

y-8=-5-8/4--7(x--7)

y-8=-3/11(x+7)

11y-88=-3x-21

11y=-3x-21+88

11y=-3x+67

y=-3/11x+67/11

5 0
2 years ago
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Jimmy has a window frame in his house. The window measures to have a width of 36 inches and a height of 48 inches. What is the d
Olenka [21]

Answer:

B.60 inches

Step-by-step explanation:

you know you can consider two triangles because of the diagonal cut. and the distance wound be √(36²+48²)=60 inches

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