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3 years ago

Type the integer that makes the following addition sentence true Blank + (-8) = -2

Mathematics

1 answer:

kati45 [8]3 years ago

3 0

The answer would be 6. This be because 6 + -8 = -2.

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Isaac invested $77,000 in an account paying an interest rate of 4.6% compounded continuously. Assuming no deposits or withdrawal

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Answer:

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2 years ago

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goldenfox [79]

Answer: $\frac{8}{17}$ or 8:17

Step-by-step explanation:

For any angle x (other than right angle) in a right triangle ,the trigonometric ratio of sin x is given by :-

$\sin x=\frac{\text{side opposite to x}}{\text{Hypotenuse}}$

Given: A right triangle with hypotenuse = 68 units

The side adjacent to S = 60

Let h be the side opposite to S, then using Pythagoras in the given right triangle, we get

$(68)^2=60^2+h^2\\\\\Rightarrow\ h^2=68^2-60^2\\\\\Rightarrow\ h^2=1024\\\\\Rightarrow\ h=\sqrt{1024}=32$

Thus, the side opposite to S = 32 units

Now, the trigonometric ratio for sin S is given by :-

$\sin S=\frac{\text{side opposite to S}}{\text{Hypotenuse}}\\\\\Rightarrow\sin S=\frac{32}{68}=\frac{8}{17}$

Hence, the trigonometric ratio for sin S = $\frac{8}{17}$ or 8:17

5 0

3 years ago

find the gradient of the line joining (3,7) and (6,9). Hence, find the acute angle it makes with the positive x-y axis

stiv31 [10]

Answer:

33.7 degrees

Step-by-step explanation:

As we go from (3,7) to (6,9), x increases by 3 and y increases by 2. Thus, the gradient (slope) of the line connecting these two points is

m = rise / run = 2/3. Using the slope-intercept formula y = mx + b, we obtain

7 = (2/3)(3) + b, or 7 = 2 + b, so we see that b = 5 and y = (2/3)x + 5. The y-intercept is (0, 5).

Next we find the x-intercept. We set y = (2/3)x + 5 = to 0 and solve for x:

(2/3)x = -5, or (3/2)(2/3)x = -5(3/2), or x = -15/2, so that the x-intercept is

(-15/2, 0). This line intersects the x-axis at (-15/2, 0).

Now look at the segment of this line connecting (-15/2, 0) and (0, 5). Here x increases by 15/2 and y increases by 5, and so the tangent of the acute angle in question is

tan Ф = 5 / (15/2) = 10 / 15 = 2/3.

Using the inverse tangent function, we get Ф = arctan 2/3, or approx.

33.7 degrees.

I believe you meant "the acute angle it makes with the positive x-axis."

3 0

3 years ago