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3 years ago

The triangles below are congruent which if the following statements must be true ?

Mathematics

1 answer:

ira [324]3 years ago

5 0

Answer:

The correct answer is BC = DF. Hope this helps! Have a good day!

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What is the intermediate step in the form (x+a)2 = b as a result of completing the square for the following

skelet666 [1.2K]

For this case we have the following expression:

$x ^ 2-4x + 10 = 4x + 10$

We follow the steps below:

We subtract 4x on both sides of the equation:

$x ^ 2-4x + 10-4x = 4x + 10-4x\\x ^ 2-8x + 10 = 10$

We subtract 10 from both sides of the equation:

$x ^ 2-8x + 10-10 = 10-10\\x ^ 2-8x = 0$

Now, we must complete squares.

When we have an equation of the form:

$ax ^ 2 + bx + c = 0$ , if we want to complete squares we must subtract c on both sides of the equation obtaining:

$ax ^ 2 + bx + c-c = -c\\ax ^ 2 + bx = -c$

The square is completed by adding to both sides of the equation: $(\frac{b}{2})^{2}$

So, we have left:

$ax^2+bx + (\frac {b} {2})^{2} = - c + (\frac {b} {2}) ^ {2}$

In the given expression we have:

$a = 1\\b = -8\\c = 0$

And to complete the square we have:

$(\frac {b} {2}) ^ {2} = (\frac {-8} {2}) ^ {2} = 16$

Rewriting we have:

$x ^ 2-8x + 16 = 16$

We factor the left side of the equation, that is, we look for two numbers that when added together result in -8 and when multiplied as a result 16. We have:

$-4-4 = -8\\-4 * -4 = 16$

So, we have:

$(x-4) (x-4) = 16\\(x-4) ^ 2 = 16$

Answer:

The intermediate step is to complete squares

$(x-4) ^ 2 = 16$

7 0

3 years ago

1. Which point is located at (-2,-6)

andriy [413]

1 k
2 n j f
3 (-3,1)
that what i think they are

7 0

3 years ago

Read 2 more answers

A skateboarder went a kilometer in 3 minutes with the wind, and returned in four minutes against the wind.

inn [45]

Step-by-step answer:

Answer to problems of this kind is the reciprocal of the harmonic mean of the time required.

We need to find the average of the speeds, not the average of the time.

The respective speeds are 1/3 and 1/4.

The average of the speeds is therefore (1/3+1/4)/2 = 7/24 (harmonic mean of the time taken).

The time required is therefore the reciprocal of the unit speed,

T = 1/(7/24) = 24/7 = 3 3/7 minutes, or approximately 3.43 minutes.

8 0

3 years ago

A bag holds 13 marbles. 6 are blue, 2 are green, and 5 are red. you select a marble from the bag. what is the probability that t

navik [9.2K]

Answer:

$\boxed {\boxed {\sf B. \ \frac{8}{13} }}$

Step-by-step explanation:

Probability is found by dividing the number of favorable outcomes by the total number of outcomes.

$P= \frac{favorable \ outcomes}{total \ outcomes}$

For this problem, the favorable outcome is selecting a blue or green marble. There are 8 outcomes for this because there are 6 outcomes for blue and 2 fr green.

The total outcomes are all the marbles. Each marble could be an outcome, so there are 13 outcomes (1 for each marble).

$P(blue \ or \ green) = \frac{8}{13}$

This fraction cannot be reduced, so the probability of selecting a blue or green marble is 8/13.

7 0

3 years ago

Solve for x. 6 - 4x = -22

Kitty [74]

Answer:

x = 7

Step-by-step explanation:

6 - 4x = -22

-6 - 6

-4x = -28

x = -28/-4

x = 7

8 0

3 years ago