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3 years ago

Find the shortest distance from A to C in the diagram below.

Mathematics

1 answer:

Lapatulllka [165]3 years ago

8 0

Answer:

The shortest distance from A to C is $AC=5\sqrt{13}\ units$

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The shortest distance from A to C is the hypotenuse of the right triangle AYC

Applying the Pythagoras Theorem

$AC^{2}=AY^{2} +YC^{2}$

step 1

Find the length YC (hypotenuse of the right triangle YBC)

Applying the Pythagoras Theorem

$YC^{2}=YB^{2} +BC^{2}$

substitute the given values

$YC^{2}=6^{2} +15^{2}$

$YC^{2}=261$

$YC=\sqrt{261}\ units$

step 2

Find the shortest distance from A to C

$AC^{2}=AY^{2} +YC^{2}$

substitute the given values

$AC^{2}=8^{2} +\sqrt{261}^{2}$

$AC^{2}=325$

$AC=\sqrt{325}\ units$

$AC=5\sqrt{13}\ units$

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Afina-wow [57]

Answer:

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Step-by-step explanation:

To write an equation in standard form, you want to arrange the terms from increasing to decreasing powers/exponents.

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First, lets arrange like terms together. Put the terms with the same exponent together.

2x³ - 5x³ + 4x² - 6x⁶ + 12 + 4x⁴

Now combine the terms with the same exponent by subtracting 5x³ from 2x³.

-3x³ + 4x² - 6x⁶ + 12 + 4x⁴

Now let's arrange the terms from increasing to decreasing powers/exponents.

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Hope this helps!

3 0

3 years ago

Please match the proof

leva [86]

Answer:

Δ ABC $\sim$ Δ DEF

Step-by-step explanation:

Given:

$\frac{AB}{DE} = \frac{AC}{DF}= \frac{BC}{EF}$

W need to Prove Δ ABC $\sim$ Δ DEF

Solution:

Statement: Reason

$\frac{AB}{DE} = \frac{AC}{DF}= \frac{BC}{EF}$ a) Given

"While Constructing both the triangle the lines were made parallel."

DE ║ AB c) Construction of Δ DEF on to Δ ABC

" When the Lines are parallel then their corresponding angles are equal in measure."

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Now By AA similarity theorem which states that;

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3 years ago

98% of 50 is what number

Andrew [12]

<h3>To get the solution, we are looking for, we need to point out what we know.</h3>

1. We assume, that the number 50 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 50 is 100%, so we can write it down as 50=100%.

4. We know, that x is 98% of the output value, so we can write it down as x=98%.

5. Now we have two simple equations:

1) 50=100%

2) x=98%

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

50/x=100%/98%

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for what is 98% of 50

50/x=100/98

(50/x)*x=(100/98)*x - we multiply both sides of the equation by x

50=1.02040816327*x - we divide both sides of the equation by (1.02040816327) to get x

50/1.02040816327=x

49=x

x=49

now we have:

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4 years ago

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