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3 years ago

HELP!!! CORRECT ANSWER NEEDED OR ELSE I FAIL ;-; STUDY ISLAND !!

Mathematics

1 answer:

Ket [755]3 years ago

5 0

Answer:

B. Step 2 uses the associative property, and step 3 uses the commutative property.

Step-by-step explanation:

The associative property lets you group terms for addition any way you like. It appears that in Step 2, the grouping is ...

4 + (1/6 + 3) + 5/6

The commutative property lets you change the order of any pair of terms involved in addition. It appears that in Step 3, the order of the terms within the group has been swapped.

4 + (3 + 1/6) + 5/6

_____

<em>Comment on associative and commutative properties</em>

What applies to terms in addition applies to factors in multiplication.

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PLEASE HELP GIVING MANY POINTS!

NeTakaya

Answer:

69.01 m

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you ...

Tan = Opposite/Adjacent

The tangent function is useful for problems like this. Let the height of the spire be represented by h. The distance (d) across the plaza from the first surveyor satisfies the relation ...

tan(50°) = (h -1.65)/d

Rearranging to solve for d, we have ...

d = (h -1.65)/tan(50°)

The distance across the plaza from the second surveyor satisfies the relation ...

tan(30°) = (101.65 -h)/d

Rearranging this, we have ...

d = (101.65 -h)/tan(30°)

Equating these expressions for d, we can solve for h.

(h -1.65)/tan(50°) = (101.65 -h)/tan(30°)

h(1/tan(50°) +1/tan(30°)) = 101.65/tan(30°) +1.65/tan(50°)

We can divide by the coefficient of h and simplify to get ...

h = (101.65·tan(50°) +1.65·tan(30°))/(tan(30°) +tan(50°))

h ≈ 69.0148 ≈ 69.01 . . . . meters

The tip of the spire is 69.01 m above the plaza.

3 0

3 years ago

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:

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