a circle has a circumference of 12. it has an arc of length 11. what is the central angle of the arc, in degrees?

Answer:

Part A) The function written in vertex form is [tex]f(x)=15(x+2)^{2}-79[/tex]

Part B) The vertex of the function is the point [tex](-2,-79)[/tex]

Step-by-step explanation:

Part A) Write the function in vertex form

we know that

The equation of a vertical parabola in vertex form is equal to

[tex]y=a(x-h)^{2}+k[/tex]

where

(h,k) is the vertex of the parabola

In this problem we have

[tex]f(x)=15x^{2}+60x-19[/tex]

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]f(x)+19=15x^{2}+60x[/tex]

Factor the leading coefficient

[tex]f(x)+19=15(x^{2}+4x)[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side

[tex]f(x)+19+60=15(x^{2}+4x+4)[/tex]

[tex]f(x)+79=15(x^{2}+4x+4)[/tex]

Rewrite as perfect squares

[tex]f(x)+79=15(x+2)^{2}[/tex]

[tex]f(x)=15(x+2)^{2}-79[/tex] -----> function in vertex form

Part B) Name the vertex for the function

we have

[tex]f(x)=15(x+2)^{2}-79[/tex]

The vertex of the function is the point [tex](-2,-79)[/tex]

The parabola open upward, so the vertex is a minimum

see the attached figure to better understand the problem

Answer:

65°

Step-by-step explanation:

<3 + <6 = 180  because they are same side interior angles

115 + <6 = 180

Subtract 115 from each side

115-115 +<6 = 180 -115

<6 = 65

Answer:

6-12j

Step-by-step explanation:

Best regards

The algebraic expression is: 12j - 6

Shade in 9 boxes

12÷4= 3 (This is 1 fourth)

3×3=9 (This is 3 fourths)

From the said figure, 9 out of the 12 pieces of the figure are shaded

The figure is cut into 12 equal pieces, and 3/4 of the figure is shaded. To find out how many pieces are shaded, we need to calculate 3/4 of 12.

To do this, we can multiply 3/4 by 12:

3/4 * 12 = 36/4 = 9.

So, 9 out of the 12 pieces are shaded.

To visualize this, imagine a circle divided into 12 equal slices. If you shade 3/4 of the circle, you will shade 9 out of the 12 slices.

Therefore, 9 out of the 12 pieces of the figure are shaded

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Answer:

x = -3

Step-by-step explanation:

Substitute the values m = 1 and from the points into the slope formula. Then solve for x.

[tex]m = \frac{y_2-y_1}{x_2-x_1}\\\\1 = \frac{1--6}{4-x}\\\\1 = \frac{7}{4-x}\\\\4-x = 7\\\\-3 = x[/tex]

Answer:

The area of the octagon is [tex]173.8\ in^{2}[/tex]

Step-by-step explanation:

we know that

The area of a regular octagon is equal to the area of eight isosceles triangle

The base of each isosceles triangle is equal to the length side of the regular octagon

The vertex angle of each isosceles triangle is equal to

[tex]360\°/8=45\°[/tex]

The area of each isosceles triangle is equal to

[tex]A=\frac{1}{2}bh[/tex]

where

b is the length side of the regular octagon

h is the height of each isosceles triangle

Find the length side of the regular octagon b

The perimeter of a octagon is equal to

[tex]P=8b[/tex]

[tex]P=48\ in[/tex]

so

[tex]48=8b[/tex]

[tex]b=6\ in[/tex]

Find the height of each isosceles triangle h

[tex]tan(45\°/2)=(b/2)/h[/tex]

[tex]h=(b/2)/tan(45\°/2)[/tex]

substitute the values

[tex]h=(6/2)/tan(22.5\°)=7.24\ in[/tex]

Find the area of the octagon

[tex]A=8[\frac{1}{2}bh][/tex]

[tex]A=8[\frac{1}{2}(6)(7.24)]=173.8\ in^{2}[/tex]

Answer:

use the formula A = 1/2ab(sin C)

Step-by-step explanation:

the domain, is the values for "x", namely the values used up over the x-axis.

the arrowheads on the lines, indicate the graph continues, upwards and to the sides, so it keeps on going to infinity.

however, let's notice that the values between -3 and 5, are not used up, those are not part of the graph, and therefore, are not part of the domain, however -3 and 5 ARE part of it, whilst all numbers between them are not.

using interval notation

( -∞ , -3 ]  ∪ [ 5 , +∞ )

it's notable that the ∞ signs have a parentheses, reason being, is a number we never touch because we don't know what the last number is :).

ans 4th. ∆dcj =∆yam

Answer:

See attached picture.

Step-by-step explanation:

If you graph the system, you will find a region of solutions which are shaded. The point must be within the darkest shaded portion where each equation overlaps. This means it is a solution to both. Choose a point form your list in this region.

See attached picture.

Answer: ITS (0,5)

Step-by-step explanation:

i just did the algebra nation!!!

adequate notice of leave

Answer:

at least a 2 week notice

Step-by-step explanation:

Answer: Normally C/C++

Step-by-step explanation:

The Arduino platform uses a language that is based on the C++ programming language. Despite some simplifications and extensions to better interact with Arduino hardware, those who are familiar with C++ will find similarities in Arduino.

The Arduino language is based on the C++ programming language. Although the materials provided mention Python, Scheme, and Modula-3, none of these are directly related to the Arduino language. The Arduino language includes many functions and libraries common in C++, which means that if you are familiar with C++, you will find it easier to understand and use Arduino.

However, note that Arduino is also slightly different from standard C++ as it includes some simplifications and extensions to make it easier to work with the Arduino hardware.

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Answer: 4 inches x 7 inches

Step-by-step explanation: Knowing that the formula for the area is length times width, 4 x 7 = 28 square inches. The perimeter of the rectangle with 2 sides that are 4 inches and 2 sides that are 7 inches is 22 inches. (2 x 4) + (2x7) = 8 + 14 = 22 inches.

The dimensions of the note card are length = 4 inches and width = 7 inches or length = 7 inches and width = 4 inches.

Let l be the length of the rectangular note card and w be its width.

Since the area of the rectangular note card is 28 square inches, we have that

lw = 28 (1)(the area of a rectangle).

Also, the perimeter of the rectangular note card is 22 inches. We have that

2(l + w) = 22 (2) (perimeter of a rectangle)

So, l + w = 11 (3)

From (3), l = 11 - w.

Substituting l into (1), we have

(11 - w)w = 28

11w - w² = 28

re-arranging, we have

w² - 11w + 28 = 0

Factorizing, we have

w² - 7w - 4w + 28 = 0

w(w - 7)- 4(w - 7) = 0

(w - 7)(w - 4) = 0

w - 7 = 0 or w - 4 = 0

w = 7 or w = 4

Since l = 11 - w,

substituting w = 7 into l, we have

l = 11 - 7 = 4 inches

substituting w = 4 into l, we have

l = 11 - 4 = 7 inches.

So, we have l = 4 and w =  7 or l = 7 and w = 4

So, the dimensions of the note card are length = 4 inches and width = 7 inches or length = 7 inches and width = 4 inches.

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Answer:10/16 (can simplify I think)

Step-by-step explanation: First you do 10+6 to find out the total of all the marbles which is 16. There are 10 blacks so you do 10/16 AS you wanna find out the probability of getting the black.

Answer:

62.5%

Step-by-step explanation:

First you add up all the marbles and then divide 100 into the sum of all of the marbles and then you times it by the black marbles to find the percent

100/(6+10)*10=%

X is 7 and y is 7 square root of 3.

Answer:

x = 7 and y = 7√3

Step-by-step explanation:

Let's review, and then apply, the definition of "cosine."

cos Ф = adjacent side / hypotenuse.

Here, x is the adjacent side, Ф is the angle and is 60°, and 14 represents the length of the hypotenuse.  cos Ф = adjacent side / hypotenuse becomes:

adjacent side = hypotenuse * cos Ф.

Here, Ф = 60° and cos Ф = cos 60° = 1/2.  Therefore,

in this case, x = 14(1/2), or 7.

Applying the definition of sine:

sin Ф = opp / hyp.  In this case, sin Ф = sin 60° = y/14, so that

y = 14 sin 60°, or y = 14(√3 / 2) = 7√3.

In summary, x = 7 and y = 7√3.

I would use the pythagorean theorem to find the lengths of each side. a² + b² = c².

Side AB is one we're looking for. If you make other right triangle with that same side you can see that one length is 4 and the other is 3. So, 4² + 3² = c² → 25 = c² → 5 = c. Side AB is length 5.

Side AC is another. Do the same with that side and you get that one length is 4 and the other is 3. (This is the same one as above) so side AC is length 5.

Side BC is the last one. One of the lengths is 1 and the other is 1 → 1² + 1² = c² → 2 = c² → 1.414213562 = c so side BC is approximately length 1.41.

Add each length up and you get a perimeter of roughly 11.4

Answer:

[tex]x=2[/tex]

Step-by-step explanation:

Given: [tex]4x-6=2x-2[/tex]

To solve for x, we need to isolate the x values on one side of the equation. Let's start by subtracting 2x from both sides.

[tex]2x-6=-2[/tex]

To further isolate x on one side of the variable, we should add 6 to both sides.

[tex]2x=4[/tex]

Finally, we need to take the coefficient of 2 off of the x to solve for x. To do this, divide both sides by the coefficient, 2.

[tex]\frac{2x}{2} = \frac{4}{2}[/tex]

[tex]x=2[/tex]

Answer: x=2

Step-by-step explanation:

* Hopfully the helps:) Mark me the brainliest:)!!

Answer:

0, 2 and - 6

Step-by-step explanation:

To find the zeros of f(x), equate f(x) to zero, that is

x(x - 2)(x + 6) = 0

Equate each factor to zero and solve for x

x = 0

x - 2 = 0 ⇒ x = 2

x + 6 = 0 ⇒ x = - 6

Answer:

b.

Step-by-step explanation:

x=0,−2+√17,−2−√17

Decimal Form:

x=0,2.12310562…,−6.12310562

Answer:

its 5

Step-by-step explanation:

what you do is put then like this 33346678 then you add them and you get 40

then see how meny there are so here we have 8 so we devid by 8 and get 5

Mean is the average of the data set

Work:

Total: 3 + 3 + 3 + 4 + 6 + 6 + 7 + 8 = 40

Mean = 40/8 = 5

Explanation:

To find the mean of a data set, add all the values together and divide by the number of values in the set.

So

First, count the number values in your data set.

Next, sum up all values in your data set, it means you need to add all together

Last, to find mean(average) = sum of all values / total number

Answer:

14

Step-by-step explanation:

1,4,9,16,25,36,49,64,81,100,121,144,169,196

Well according to my calculations its 110.

4p + 7 = 3 + 4 + 4p

subtract 4p on both sides

7=7

since the equation equals it is infinite many solutions or...

all real numbers

Answer:

Infinite solutions!!

Step-by-step explanation:

4p + 7 = 3 + 4 + 4p

7 = 3 + 4

7 = 7

Let the soup can be represented by = s

Let the tuna can be represented by = t

Let the error of the scale in grams be represented by = e

4 cans of soup and 3 cans of tuna are placed on a correct scale and reads 80 ounces.

A can of soup and a can of tuna are placed on this scale, and it reads 24 ounces.

Two cans of tuna weigh 18 ounces on the bad scale.

Now equations becomes:

[tex]4s+3t=80[/tex]   ....(1)

[tex]s+t+e=24[/tex]    .... (2)

[tex]2t+e=18[/tex]     ..... (3)

From equation 3 we get

[tex]e=18-2t[/tex]

Putting this in equation 2

[tex]s+t+18-2t=24[/tex] = [tex]s-t=6[/tex]   ..... (4)  

Now we will solve equations 1 and 4.

Multiplying equation (4) by '4' we get, [tex]4s-4t=24[/tex]

Now subtracting this from equation 1, we get

[tex]7t=56[/tex]

[tex]t=8[/tex]

Now 4s+3t=80 ,

[tex]4s+24=80[/tex]

[tex]4s=56[/tex]

s = 14

And s+t+e = 24

14+8+e = 24

e = 2

Hence, a can of tuna weighs 8 ounces, a can of soup weighs 14 ounces and the amount of error is 2 ounces.

To find the amount of error in the scale and the correct weight of each type of can, set up a system of equations. Solve the equations to find that the amount of error in the scale is 0 ounces and the correct weight of each can is 15 ounces for soup and 9 ounces for tuna.

To find the amount of error in the scale and the correct weight of each type of can, we need to set up a system of equations.

Let's assume the weight of a can of soup is 's' and the weight of a can of tuna is 't'. From the given information, we can write the following equations:

1. s + t = 24   (equation 1)

2. 4s + 3t = 80  (equation 2)

We also know that two cans of tuna weigh 18 ounces on the bad scale. Therefore, we can write:

3. 2t = 18

From equation 3, we can solve for t: t = 18/2 = 9 ounces.

Substitute the value of t in equation 1 to find s: s + 9 = 24. Solving for s gives s = 15 ounces.

So, the amount of error in the scale is 24 - (15 + 9) = 24 - 24 = 0 ounces. The correct weight of each type of can is 15 ounces for soup and 9 ounces for tuna.

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Final answer:

John can afford a maximum of 13 help sessions with his $170 budget for the year, after accounting for the $25.50 annual fee and the $10.50 per session charge.

Explanation:

To find the maximum number of help sessions John can use within his budget, we need to set up a simple algebraic equation. The total cost for the online help service consists of an annual fee plus the charge per help session. The equation to represent this situation will be:

Total Cost = Annual Fee + (Charge per Session × Number of Sessions)

We know the Annual Fee is $25.50, the Charge per Session is $10.50, and John's budget, or the Total Cost, is $170.

Let's denote the Number of Sessions as 'x'. The equation therefore becomes:

$170 = $25.50 + ($10.50 × x)

Subtracting the annual fee from both sides gives us:

$170 - $25.50 = $10.50 × x

$144.50 = $10.50 × x

Dividing both sides by $10.50 gives us the number of sessions John can afford:

x = $144.50 / $10.50

x = 13.7619...

Since John can't have a fraction of a session, we round down to the nearest whole number. John can afford a maximum of 13 help sessions within his budget of $170 for the year.

ANSWER

1. k=13

2. x=-10

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} + 3x - 10[/tex]

To find f(x+5), plug in (x+5) wherever you see x.

This implies that:

[tex]f(x) = {(x + 5)}^{2} + 3(x + 5) - 10[/tex]

Expand:

[tex]f(x) = {x}^{2} + 10x + 25+ 3x + 15- 10[/tex]

Simplify to obtain

[tex]f(x) = {x}^{2} + 13x + 30[/tex]

We now compare with,

[tex]f(x) = {x}^{2} + kx + 30[/tex]

This implies that:

[tex]k = 13[/tex]

To find the smallest zero of f(x+5), we equate the function to zero and solve for x.

[tex]{x}^{2} + 13x + 30 = 0[/tex]

[tex] {x}^{2} + 10x + 3x + 30 = 0[/tex]

[tex]x(x + 10) + 3(x + 10) = 0[/tex]

[tex](x + 3)(x + 10) = 0[/tex]

[tex]x = - 10 \: or \: x = - 3[/tex]

The smallest zero is -10.

Answer:

k=13 while x =-10 :)

Step-by-step explanation:

Final answer:

The two positive integers in question are 8 and 3, as they satisfy both conditions: one integer is 5 less than the other and their product equals 24.

Explanation:

The problem asks us to find two positive integers where one is 5 less than the other and their product equals 24. Let's denote the larger integer as 'x'. Then, the other integer would be 'x - 5'. We can set up the equation:

x(x - 5) = 24

Which simplifies to:

x² - 5x - 24 = 0

By factoring this quadratic equation, we end up with:

(x - 8)(x + 3) = 0

We are given the numbers are positive integers, so we take the positive root which is:

x = 8

Subsequently, the smaller integer would be:

8 - 5 = 3

So the two integers are 8 and 3.

Answer: option c

Step-by-step explanation:

By definition, if you have:

[tex]\sqrt[n]{x}[/tex]

you can rewrite it has following:

[tex]x^{\frac{1}{n}}[/tex]

Therefore, keeping the above on mind, you can rewrite the expression given in the problem, as you can see below:

[tex]15x^{\frac{1}{3}}y^{\frac{1}{5}}=(15\sqrt[3]{x})(\sqrt[5]{y})[/tex]

Both terms are multiples of 15, then take the 15th root of both and multiply the exponents by 15. Therefore you obtain:

[tex]15\sqrt[15]{x^5y^3}[/tex]

The answer is:

c. [tex]15\sqrt[15]{x^{5}y^{3}}[/tex]

To express the expression using a radical we must remember that:

Transforming radical to exponential form:

[tex]\sqrt[n]{x}=x^{\frac{1}{n}}\\\sqrt{x}=x^{\frac{1}{2} }[/tex]

So, the given expression is:

[tex]15x^{\frac{1}{3}}y^{\frac{1}{5}}[/tex]

Its radical form will be:

[tex]15\sqrt[3]{x}\sqrt[5]{y}[/tex]

Then, the expression could be also equivalent to:

[tex]15\sqrt[3]{x}\sqrt[5]{y}=15\sqrt[15]{x^{5}}\sqrt[15]{y^{3}}\\\\15\sqrt[15]{x^{5}}\sqrt[15]{y^{3}}=15\sqrt[15]{x^{5}y^{3}}[/tex]

Have a nice day!

Answer:  option B.

Step-by-step explanation:

You can apply the elimination method:

- Multiply the first equation by -7 and the second equation by 3.

- Add both equations to cancel out the variable y.

- Solve for x

[tex]\left \{ {{(-7)9x+3y=(-39)(-7)} \atop {(3)(4x+7y)=(-57)(3)}} \right.\\\\\left \{ {{-63x-21y=273} \atop {12x+21y=-171}} \right.\\-------\\-51x=102\\x=-2[/tex]

- Substitute x=-2 into any of the original equations ans solve for y. Then:

[tex]9(-2)+3y=-39\\-18+3y=-39\\3y=-21\\y=-7[/tex]

The answer is:

B.

[tex]x=-2\\y=-7[/tex]

Solving the system of equations by elimination, we have:

[tex]\left \{ {{9x+3y=-39} \atop {4x+7y=-57}} \right.[/tex]

Then, multiplying the second equation by [tex]-\frac{9}{4}[/tex]

So,

[tex]\left \{ {{9x+3y=-39} \atop {4x*(-\frac{9}{4}) +7y*(-\frac{9}{4}) =-57*(-\frac{9}{4})}} \right\\\\\left \{ {{9x+3y=-39} \atop {-9x-\frac{63}{4}y=\frac{513}{4} }} \right\\\\-\frac{51}{4}y=\frac{357}{4}\\\\y=\frac{357}{4}*(-\frac{4}{51})=-\frac{1428}{204}=-7[/tex]

Then, substituting y=-7 into the first equation (also, we could substitute it into the first equation) we have:

[tex]9x+3(-7)=-39\\9x-21=-39\\9x=-39+21\\9x=-18\\x=\frac{-18}{9}=-2[/tex]

So, the solutions for the system of equations are:

[tex]x=-2\\y=-7[/tex]

Have a nice day!

Answer:

8,if it broke some tiny thing from that it will fail but if it not broke it will be heavy then the broke one. the one that do not broke is the heavy one.

Step-by-step explanation: