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3 years ago

8

Insert two fractions between 3/5 and 4/7

1 answer:

user100 [1]3 years ago

4 0

The answer is (3) 10/17, 7/12

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Semicircles and quarter circles are types of arc lengths. Recall that an arc is simply part of a circle. We learned about the de

attashe74 [19]

The question is incomplete. Here is the complete question.

Semicircles and quarter circles are types of arc lengths. Recall that an arc is simply part of a circle. we learned about the degree measure of an ac, but they also have physical lengths.

a) Determine the arc length to the nearest tenth of an inch.

b) Explain why the following proportion would solve for the length of AC below: $\frac{x}{12\pi } = \frac{130}{360}$

c) Solve the proportion in (b) to find the length of AC to the nearest tenth of an inch.

Note: The image in the attachment shows the arc to solve this question.

Answer: a) 9.4 in

c) x = 13.6 in

Step-by-step explanation:

a) $\frac{arclength}{2\pi.r } = \frac{mAB}{360}$ , where:

r is the radius of the circumference

mAB is the angle of the arc

arc length = $\frac{mAB.2.\pi.r }{360}$

arc length = $\frac{90.2.3.14.6}{360}$

arc length = 9.4

The arc lenght for the image is 9.4 inches.

b) An <u>arc</u> <u>length</u> is a fraction of the circumference of a circle. To determine the arc length, the ratio of the length of an arc to the circumference is equal to the ratio of the measure of the arc to 360°. So, suppose the arc length is x, for the arc in (b):

$\frac{x}{2.6.\pi } = \frac{130}{360}$

$\frac{x}{12\pi } = \frac{130}{360}$

c) Resolving (b):

x = $\frac{130.12.3.14}{360}$

x = 13.6

The arc length for the image is 13.6 inches.

6 0

3 years ago

Use the graph below to estimate the solution to the system of equations shown.

Mila [183]

Answer: The second choice is answer.

Step-by-step explanation:

<h3>The first line (Blue One)</h3>

$y=-x-3$ (Slope is -1 and intercepts y at -3)

<h3>The second one (Red One)</h3>

$y=2x-8$ (Slope is 2, to find y-intercept. Substitute x = 0 then we get -8) (For x-intercept, it's 4. Just substitute y=0 to get x-intercept.)

Because there are choices, it's easy to notice.

The first one, x = -4 and almost -5 which is not right. (x is around 1 almost 2.)

The second one, x = 1 and almost 2 is right.

The third one, x = -1 and almost -2 is not right (The intersection isn't even at -1 or any negative number for x-axis.)

The fourth one, just like the first one... x = 4 almost 5

<h3>Or solve the equations.</h3>

$y=-x-3\\y=2x-8$

Substitute y=2x-8 in y=-x-3

$2x-8=-x-3\\2x-8+x+3=0\\3x-5=0\\3x=5\\x=\frac{5}{3}\\(x=1\frac{2}{3})$

Look at the value of x then find the answer that matches the value of x.

Now for y, substitute x = 5/3 in y = -x-3 (or in 2x-8 if you want.)

$y=-\frac{5}{3} -3\\y=-\frac{5}{3} -\frac{9}{3} \\y=-\frac{14}{3} \\(y=-4\frac{2}{3} )$

So the answer is the second choice.

6 0

3 years ago

What is the equation for this table? 30 points!!!!

Marat540 [252]

That was made up?cz I tried to solve it and I kept getting different #s

5 0

3 years ago

A number is divided by 6, and then the quotient is added to 29. The result is 41.

VashaNatasha [74]

Answer:2

Step-by-step explanation:x/6+29=41

41-29=12

12/6=2

3 0

3 years ago

For the function f(x)=ax^3+bx^2-5x+9, determine the values of a and b so that f(-1)=12 and f'(-1)=3

Alecsey [184]

If

<em>f(x)</em> = <em>ax</em> ³ + <em>bx</em> ² - 5<em>x</em> + 9

then

<em>f '(x)</em> = 3<em>ax </em>² + 2<em>bx</em> - 5

Given that <em>f</em> (-1) = 12 and <em>f</em> '(-1) = 3, we get the system of equations

-<em>a</em> + <em>b</em> + 5 + 9 = 12

3<em>a</em> - 2<em>b</em> - 5 = 3

or

-<em>a</em> + <em>b</em> = -2

3<em>a</em> - 2<em>b</em> = 8

Multiply through the first equation by 2 and add it to the second one to eliminate <em>b</em> and solve for <em>a</em> :

2(-<em>a</em> + <em>b</em>) + (3<em>a</em> - 2<em>b</em>) = 2(-2) + 8

-2<em>a</em> + 2<em>b</em> + 3<em>a</em> - 2<em>b</em> = -4 + 8

<em>a</em> = 4

Substitute this into the first equation above to solve for <em>b</em> :

-4 + <em>b</em> = -2

<em>b</em> = 2

4 0

3 years ago