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Simplify the following expression: -7(3e-2f+4)+6e-2

tankabanditka [31]

Answer:

-15e+14f-30

Step-by-step explanation:

First using distributive property to expand the first term:

-21e+14f-28+6e-2

Combining like terms:

-15e+14f-30

3 0

3 years ago

Let f(x)=x^2+3x−4 .

Oxana [17]

I haven't done this kind of work in a bit, but I believe it's 8.

4 0

3 years ago

Read 2 more answers

9. A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

SSSSS [86.1K]

Answer:

Part 4) $r=84\ units$

Part 9) $sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) $sin(\theta)=-\frac{9\sqrt{202}}{202}$

Step-by-step explanation:

Part 4) A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

we know that

The circumference of a circle subtends a central angle of 360 degrees

The circumference is equal to

$C=2\pi r$

using proportion

$\frac{2\pi r}{360^o}=\frac{56\pi}{120^o}$

simplify

$\frac{r}{180^o}=\frac{56}{120^o}$

solve for r

$r=\frac{56}{120^o}(180^o)$

$r=84\ units$

Part 9) Given cos(∅)=-2/3 and ∅ lies in Quadrant III. Find the exact value of sin(∅) in simplified form

Remember the trigonometric identity

$cos^2(\theta)+sin^2(\theta)=1$

we have

$cos(\theta)=-\frac{2}{3}$

substitute the given value

$(-\frac{2}{3})^2+sin^2(\theta)=1$

$\frac{4}{9}+sin^2(\theta)=1$

$sin^2(\theta)=1-\frac{4}{9}$

$sin^2(\theta)=\frac{5}{9}$

square root both sides

$sin(\theta)=\pm\frac{\sqrt{5}}{3}$

we know that

If ∅ lies in Quadrant III

then

The value of sin(∅) is negative

$sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) The terminal side of ∅ passes through the point (11,-9). What is the exact value of sin(∅) in simplified form?

see the attached figure to better understand the problem

In the right triangle ABC of the figure

$sin(\theta)=\frac{BC}{AC}$

Find the length side AC applying the Pythagorean Theorem

$AC^2=AB^2+BC^2$

substitute the given values

$AC^2=11^2+9^2$

$AC^2=202$

$AC=\sqrt{202}\ units$

so

$sin(\theta)=\frac{9}{\sqrt{202}}$

simplify

$sin(\theta)=\frac{9\sqrt{202}}{202}$

Remember that

The point (11,-9) lies in Quadrant IV

then

The value of sin(∅) is negative

therefore

$sin(\theta)=-\frac{9\sqrt{202}}{202}$

5 0

3 years ago

Here's another Math one worth 10.

tia_tia [17]

<span>In a 30-60-90 triangle the side opposite the 30 degree angle is half the length of the hypotenuse.
The short leg is </span>the side opposite the 30 degree angle. If the short leg =x, then the hypotenuse = 2x

The ratio of the short leg to the hypotenuse in the given triangle is cos(60°)

$
cos(60^o) = \frac{adjacent \ side}{hypotenuse } = \frac{x}{2x} = \frac{1}{2}$

Answer is C. 1:2

7 0

3 years ago

Does (5, 6) satisfy the inequality 2x - 3y> 6?

butalik [34]

Answer:

yes

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers