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meriva
3 years ago
13

If AC is parallel to DF, what is the measure, in degrees, of ∠ABD

Mathematics
1 answer:
Kamila [148]3 years ago
3 0

Answer:

Yes it is parellell

Step-by-step explanation:

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A metallurgist has one alloy containing 45% copper and another containing 69% copper. How many pounds of each alloy must be use
lakkis [162]

5.25 pounds of one alloy containing 45% copper and 36.75 pounds of 69% copper is used to make 42 pounds of 66% copper

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the amount of 45% copper and y represent the amount of 66% copper needed to make 42 pounds of a third alloy containing 66% copper. Hence:

x + y = 42   (1)

Also:

0.45x + 0.69y = 42(0.66)   (2)

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x = 5.25, y = 36.75

5.25 pounds of one alloy containing 45% copper and 36.75 pounds of 69% copper is used to make 42 pounds of 66% copper

Find out more on equation at: brainly.com/question/2972832

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Find the exact value of sin2 theta given sin theta =5/13, 90°&lt;theta &lt;180°
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\bf sin(\theta )=\cfrac{\stackrel{opposite}{5}}{\stackrel{hypotenuse}{13}}\impliedby \textit{now let's find the \underline{adjacent side}}&#10;\\\\\\&#10;\textit{using the pythagorean theorem}\\\\&#10;c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a\qquad &#10;\begin{cases}&#10;c=hypotenuse\\&#10;a=adjacent\\&#10;b=opposite\\&#10;\end{cases}

\bf \pm\sqrt{13^2-5^2}=a\implies \pm\sqrt{144}=a\implies \pm 12 =a \implies \stackrel{II~quadrant}{-12=a}&#10;\\\\\\&#10;therefore \qquad cos(\theta )=\cfrac{\stackrel{adjacent}{-12}}{\stackrel{hypotenuse}{13}}&#10;\\\\&#10;-------------------------------\\\\&#10;sin(2\theta )\implies 2sin(\theta )cos(\theta )\implies 2\left(\frac{5}{13}  \right)\left( \frac{-12}{13} \right)\implies -\cfrac{120}{169}
3 0
3 years ago
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