Why is the War of 1812 known as the "Second War of Independence"? Check all that apply.

Nancy walked 516 yards in 6 minutes and then another 368 yards in 4 minutes. What was Nancy's average speed? * A. 89 yd/min B. 8

Rina8888 [55]

Average speed = (total distance covered) / (time to cover the whole distance)

Total distance = (516 + 368) = 884 yards
Total time = (6 + 4) = 10 minutes

Average speed = (884 yards) / (10 minutes)

Average speed = 88.4 yards/minute (C)

Other ways to write the same speed:

-- 4.42 feet/second
-- 265.2 feet/minute
-- 53.04 inches/second
-- 5,304 yards/hour
-- 3.014 mph (rounded)
-- 810.07 furlong/fortnight

7 0

2 years ago

Since it is given that AB ≅ AC, it must also be true that AB = AC. Assume ∠B and ∠C are not congruent. Then the measure of one a

BartSMP [9]

Answer: The required conclusion is

"if in triangle ABC, AB ≅ AC, then ∠B and ∠C must be congruent".

Step-by-step explanation: Given that in triangle ABC, AB ≅ AC, implies that AB = AC must be true. We are given to assume ∠B and ∠C are not congruent. Then the measure of one angle is greater than the other.

If m∠B > m∠C, then AC > AB because of the triangle parts relationship theorem.

For the same reason, if m∠B < m∠C, then AC < AB.

This is a contradiction to the given information.

We are to state the conclusion.

Since in the beginning, it is given that AB ≅ AC and we have assumed that ∠B and ∠C are not congruent, so

our assumption must be wrong.

That is, ∠B and ∠C must be congruent.

Thus, the required conclusion is

if in triangle ABC, AB ≅ AC, then ∠B and ∠C must be congruent.

5 0

2 years ago

Read 2 more answers

4cos^2(x)-7cos(x)+3 Please help and explain how you did it :)

dangina [55]

I assume you're asked to solve

4 cos²(x) - 7 cos(x) + 3 = 0

Factor the left side:

(4 cos(x) - 3) (cos(x) - 1) = 0

Then either

4 cos(x) - 3 = 0 or cos(x) - 1 = 0

cos(x) = 3/4 or cos(x) = 1

From the first case, we get

x = cos⁻¹(3/4) + 2nπ or x = -cos⁻¹(3/4) + 2nπ

and from the second,

x = nπ

where n is any integer.

7 0

2 years ago

Stephen & Richard share a lottery win of £2950 in the ratio 2 : 3. Stephen then shares his part between himself, his wife &a

horsena [70]

Answer:

Stephen's wife got £354 more than his son.

Step-by-step explanation:

Given:

Amount of Lottery = £2950

Now Given:

Stephen & Richard share a lottery amount in the ratio 2 : 3

Let the common factor between them be 'x'.

So we can say that;

$2x+3x=2950\\\\5x = 2950$

Dividing both side by 5 we get;

$\frac{5x}{5}=\frac{2950}{5}\\\\x = 590$

So we can say that;

Stephen share would be = $2x =2\times 590 = \£1180$

Now Given:

Stephen then shares his part between himself, his wife & their son in the ratio 3 : 5 : 2.

Let the common factor between them be 'y'.

So we can say that;

$3y+5y+2y=1180\\\\10y=1180$

Dividing both side by 10 we get;

$\frac{10y}{10}=\frac{1180}{10}\\\\y=118$

So Stephen's wife share = $5y = 5\times 118= \£590$

And Stephen's son share = $2y=2\times118 =\£236$

Now we need to find how much more her wife got then her son.

To find how much more her wife got than her son we will subtract Stephen's son share from Stephen's wife share.

framing in equation form we get;

Amount more her wife got than her son = $590-236 = \£354$

Hence Stephen's wife got £354 more than his son.

3 0

2 years ago

Solve these simultaneous equations 2x+3y=13 4x-y=-2

Neko [114]

X = 1/2 y = 4 by elimination

6 0

3 years ago

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