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3 years ago

9

On Monday, Deborah ran 3 2− 5miles and on Tuesday she ran 4 1− 5miles. How many miles did she run on these two days together?

1 answer:

notsponge [240]3 years ago

6 0

Mixed fraction:

3 2/5 = 17/5

4 4/5 = 24/5

Miles she ran:

17/5 + 24/5

= 41/5 miles or 8.2 miles

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Can someone help me with number 3 please??!!

ipn [44]

There are 2 way to solve this.

one using Pythagoras theorem and 2nd using trigonometry

so lets solve it by both

using Pythagoras theorem we know

base^2 + perpendicular^2 = hypotanes^2

6^2 + x^2 = 12^2

36 + x^2 = 144

x^2 = 144- 36 = 108

x = √(108) = √( 2×2×3×3×3)

= (2×3) √ (3) = 6 √3

so answer is option 2

bow lets use trigonometry

we know
sin theta = perpendicular / hypotanes
sin 60 = x /12
x = 12 × sin 60
we kNow sin 60 = √3/ 2
so
x = 12×√3 /2 = 6√3

7 0

3 years ago

Three lines of crops in a garden form a triangular shape. Strawberries are planted in a 10 ft line and green beans are planted i

Marat540 [252]

Answer:

$p = 19.18$

Step-by-step explanation:

This question is illustrated using the attachment and will be solved using cosine formula

$a^2 = b^2 + c^2 - 2bcCosA$

<em>Let the strawberry side be s, the Green beans be b and the pumpkins be p.</em>

<em />

The cosine formula in this case is:

$g^2 = s^2 + p^2 - 2spCosG$

Where

$s = 10$

$g = 18$

The equation becomes

$18^2 = 10^2 + p^2 - 2 * 10 * p * Cos\ 68$

$324 = 100 + p^2 - 20 * p * 0.375$

$324 = 100 + p^2 - 7.5p$

Collect Like Terms

$p^2 - 7.5p + 100 - 324 = 0$

$p^2 - 7.5p - 224 = 0$

Using quadratic formula:

$p = \frac{-b\±\sqrt{b^2-4ac}}{2a}$

Where

$a = 1$

$b = -7.5$

$c = -224$

$p = \frac{-(-7.5)\±\sqrt{(-7.5)^2-4*1*-224}}{2*1}$

$p = \frac{7.5\±\sqrt{56.25+896}}{2}$

$p = \frac{7.5\±\sqrt{952.25}}{2}$

$p = \frac{7.5\± 30.86}{2}$

$p = \frac{7.5 + 30.86}{2}$ or $p = \frac{7.5 - 30.86}{2}$

$p = \frac{38.36}{2}$ or $p = \frac{-23.36}{2}$

$p = 19.18$ or $p = -11.68$

But length can not be negative.

So:

$p = 19.18$

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