An arc subtends a central angle measuring \dfrac{3\pi}{5}
5
3π
​
start fraction, 3, pi, divided by, 5, end fraction radians.


What fraction of the circumference is this arc?

[tex]f(x) = x^2 +x (2a+2b) +4ab-x\\\\f'(x) = 2x+x \cdot 0 + 2a+2b + 0 -1\\\\~~~~~~~~=2x+0+2a+2b-1\\\\~~~~~~~~=2x+2a+2b-1[/tex]

From the definition of the derivative,

[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{f(x+h) - f(x)}h[/tex]

We have

[tex]f(x) = x^2 + x(2a+2b) + 4ab - x = x^2 + (2a+2b-1)x + 4ab[/tex]

and so

[tex]\displaystyle f'(x) = \lim_{h\to0} \frac{\left((x+h)^2 + (2a+2b-1)(x+h) + 4ab\right) - \left(x^2 + (2a+2b-1)x + 4ab\right)}h[/tex]

[tex]\displaystyle f'(x) = \lim_{h\to0} \frac{x^2 + 2xh + h^2 + (2a+2b-1)x + (2a+2b-1)h + 4ab - x^2 - (2a+2b-1)x - 4ab}h[/tex]

[tex]\displaystyle f'(x) = \lim_{h\to0} \frac{2xh + h^2 + (2a+2b-1)h}h[/tex]

[tex]\displaystyle f'(x) = \lim_{h\to0} (2x + h + 2a+2b-1)[/tex]

[tex]\displaystyle f'(x) = \boxed{2x + 2a + 2b - 1}[/tex]

Answer:

64:125

Step-by-step explanation:

When you go from a length ratio to an area ratio you need to square the numbers involved: [tex]4^{2} :5^{2}[/tex] = 16 : 25

By the same logic, if you want to go from length to volume you need to cube the numbers involved: [tex]4^{3} :5^{3}[/tex] = 64 : 125

Answer:

  10 units

Step-by-step explanation:

Compare the given equation to the standard-form equation for a circle to identify the relevant dimension.

The equation of a circle is written in standard form as ...

  (x -h)² +(y -k)² = r² . . . . . . . centered at (h, k) with radius r

__

Comparing this to what you are given, you see that ...

  h = -25/4

  k = 0

  r² = 25

The radius is ...

  r = √25 = 5

The diameter is twice the radius, so is ...

  d = 2r = 2(5)

  d = 10

The diameter of the circle is 10 units.

Answer:

1 more.

Step-by-step explanation:

A regular octagon has 4 pairs.

A regular hexagon has 3 pairs.

Hope this helped.    :)

Answer:

Parent function:
[tex]x^2+y^2=r^2[/tex]
General equation:
[tex](x-h)^2+(x-k)^2=r^2[/tex]
Transformations:
Its a circle with a center of (100,60) and a radius of 15

Answer:

Question 3: D, 90°

Question 2: D, 84°

Step-by-step explanation:

Answer:

    2. d. 84°

    3. d. 90°

Step-by-step explanation:

Q2

Q3

Answer:

3

Step-by-step explanation:

1/2 = 0.5

1/4 = 0.25

1/2 + 1/4

= 0.5 + 0.25

= 0.75

= 75/100

= 3/4

Quarter is 1/4.

3/4 can be written as 3 x 1/4

Hence,

1/2 + 1/4 is 3 times 1/4

1/2 + 1/4 = 3 quarters.

Answer:

3/4

Step-by-step explanation:

1*(1/2)= (2/2)*(1/2)= (2*1)/(2*2)=2/4

1/2+1/4=2/4+1/4=3/4

The equivalent to the length of the string in meters is 14 / 5 meters

The length of the string is expressed in a mixed fraction form.

length of the string = 2 16 / 20

let's express it in a simplified form. This is usually in an improper fraction form.

Therefore,

2 16 / 20 = 56 / 20

Hence,

56 / 20 = 14 / 5 meters

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Answer:

57   mean

Step-by-step explanation:

x = mean

(x - 49 )  = 2 ( 61 -x)

x = 57

Answer: The date tree is 3 times as tall as the lemon tree

Step-by-step explanation:

There are two trees.

Date tree = unknown height

Lemon tree = 8 feet

Equation

? = 3 x 8

We can assume that the 8 in the equation is the height of the lemon tree since it was already given. The equation's purpose is to find the height of the date tree resulting in 3 times 8 which is 24.

If we compare their heights, we can say that the date tree is 3 times taller than the lemon tree since 24 is 3 times greater than 8.

If Lacey starts baking her cookies right away, then the time is taken for her to have made as many cookies as Clay will be 1.5 hours.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Clay and his friend Lacey are making cookies for the school dance.

Clay started early and has already made 3 dozen cookies.

He can make an additional 2 dozen cookies an hour.

Lacey has not started making cookies yet, but she has a bigger oven and can make 4 dozen cookies an hour.

Let y be the number of the cookies (in dozen) and x be the number of the hours.

Then the equations will be

y = 2x + 3 ...1

y = 4x       ...2

If Lacey starts baking her cookies right away, then the time taken for her to have made as many cookies as Clay will be

From equations 1 and 2, we have

2x + 3 = 4x

     2x = 3

       x = 1.5

Then the number of hours will be 1.5 hours.

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Answer:

It is 15 m long.

Step-by-step explanation:

Given

width (b) = 20 m

Area of the floor (A) = 300 m^2

Length (L) = ?

we know

A = L * b

300 = L * 20

L = 15 m

Hope it will help :)

Answer:

The zeros are x = -2, x = 0, x = 4.

Step-by-step explanation:

The zeros describe where the function crosses the x-axis, or where the y-value is zero. In this case, the zeros are x = -2, x = 0, x = 4.

The expression that shows the granola bars Todd bought is 12g.

The algebraic expression stands for the mixture of variables, coefficient, constant, or all three in a mathematical form where both sides are set equivalent to each other.

Given: Todd bought g boxes of granola bars.

There are 12 granola bars in each box.

Let g be the boxes of granola bars.

Therefore, the expression that shows the granola bars Todd bought is 12g.

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The correlation coefficient is 0.92

A correlation coefficient is a number between -1 and 1 that tells you the strength and direction of a relationship between variables.

In other words, it reflects how similar the measurements of two or more variables are across a dataset.

When one variable changes, the other variables change in the same direction or opposite direction.

Perfect positive correlation :When one variable changes, the other variables change in the same direction.

Perfect negative correlation :When one variable changes, the other variables change in the opposite direction.

[tex]\rm r = \dfrac{\sum (x_{i}-x')(y_{i}-y')}{\sqrt {\sum (x_{i}-x')^{2} \sum (y_{i}-y')^{2}}}[/tex]

After calculation we get

r = 0.92

Therefore it is a Perfect positive correlation

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Answer:

This is incorrect because 1 meter is 100 centimeters. But then when you keep going and when you get to 4 meters, you would get 400.

For example:

1 meter - 100 centimeters

2 meters - 200 centimeters

3 meters - 300 centimeters

4 meters - 400 centimeters

Hope this helps!

1. x=9

2. x=1

3. s=2

4. s= 2.5

5. s=6

6. T=5/6

7. x=1

8. y=2

9. x=120

10. x=16/13

11. x=-4

12. s=7

13. x=2

14. x=2

15. t=97/5

16. x=5/2

17. x=-70/3

Answer:

The value of 4x-x + 5 when x + 3 is 14

Step-by-step explanation:

4(3)= 12 - 3= 9 + 5= 14

The value of 4x - x + 5 when x = 3 is 14.

To find the value of 4x - x + 5 when x = 3, we substitute the value of x into the expression and simplify.

Plugging in x = 3, we have:

4(3) - 3 + 5

Now let's simplify each term:

4(3) = 12

-3 = -3

Now we can substitute the simplified terms back into the expression:

12 - 3 + 5

Next, we perform the addition and subtraction in order from left to right:

12 - 3 = 9

9 + 5 = 14

Therefore, the value of 4x - x + 5 when x = 3 is 14.

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Answer:

x = 9

y = 116

Step-by-step explanation:

116 and y are vertically opposite angles.

Vertically opposite angles are equal.

So,

y = 116

116 and ( 13x - 53 ) are linear pair angles.

Sum of linear pair angles is 180,

13x - 53 + 116 = 180

13x + 63 = 180

Subtract 63 on both sides,

13x = 180 - 63

13x = 117

Divide 13 on both the sides,

x = 117 / 13

x = 9

Answer:

x < & = -23/2

Step-by-step explanation:

Let a number be x.

Twice a number = 2x

2x - 3 = -26 and 2x - 3 < -26

2x = -23 and 2x < -23

x = -23/2 and x < -23/2

Using the t-distribution, it is found that the 90% confidence interval is (48.3, 48.7), hence 48.8 is not within the interval.

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 225 - 1 = 224 df, is t = 1.6517.

The other parameters are given as follows:

[tex]\overline{x} = 48.5, s = 1.8, n = 225[/tex].

Hence the bounds of the interval are given by:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 48.5 - 1.6517\frac{1.8}{\sqrt{225}} = 48.3[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 48.5 + 1.6517\frac{1.8}{\sqrt{225}} = 48.7[/tex]

The 90% confidence interval is (48.3, 48.7), hence 48.8 is not within the interval.

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Let's see

3x is one factor

#2

Mass of 1000 protons

Answer:

22.  (3)  x - 3

23.  (4)  [tex]1.67 \times 10^{-21}\: \sf g[/tex]

Step-by-step explanation:

Given expression:

[tex]3x^2-9x[/tex]

Factor out common term [tex]3x[/tex]:

[tex]\implies 3x \cdot x - 3 \cdot 3x[/tex]

[tex]\implies 3x(x-3)[/tex]

Therefore, the two factors are  [tex]3x[/tex]  and  [tex]x-3[/tex]

[tex]\textsf{Mass of 1 proton}=1.67 \times 10^{-24}\: \sf g[/tex]

[tex]1000=10 \times 10 \times 10=10^3[/tex]

[tex]\begin{aligned}\implies \textsf{Mass of 1000 protons} & = \textsf{mass of 1 proton} \times 1000\\& =(1.67 \times 10^{-24}) \times 1000\\& =1.67 \times 10^{-24}\times 10^3\\ & =1.67 \times 10^{-24+3}\\ & = 1.67 \times 10^{-21}\: \sf g\end{aligned}[/tex]

Answer:

292,968

Step-by-step explanation:

Answer:

hope this help you

Step-by-step explanation:

[tex] \cos(y) = \frac{b}{h} \\ \cos(y) = \frac{8}{12} \\ y = \cos {}^{ - 1} ( { 0.6666}^{ } ) \\ y = 48.19[/tex]

Answer: B. ((5-x))/(x^(2)+3x-4)-:((x^(2)-2x-15))/(x^(2)+5x+4)

exclusions: x≠1, x≠-1, x≠-3, x≠-4, x≠5

Step-by-step explanation:

Answer:

x = 40°

Step-by-step explanation:

using the cofunction identity

cos(90 - x) = sin x , so

90 - x = 50 , then

x = 40

that is sin40° = cos50°

We will see that there are 156,000 different combinations, so the correct option is C.

First, we need to find the selections, here we have:

Now we need to find the number of options for each of these selections.

We assumed that the number can be any integer from 0 to 9.

The total number of possibilities is equal to the product between the numbers of options, we will have:

P = 26*25*24*10 = 156,000

So, the correct option is C.

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