7. The real solutions of 3^2 −+2=0 area. 1 and -2/3b. -1 and 2/3c. There are no real solutionsd. 1 is the only real solutione. -2/3 is the only real solution

The exact length of the arc formed by a central angle measuring 120° in a circle with a radius of 12.3 cm is 8.2π cm.

To calculate the exact length of an arc formed by a central angle measuring 120° in a circle with a radius of 12.3 cm, we can use the formula:

Arc Length = (Central Angle / 360°) * Circumference

First, let's calculate the circumference of the circle:

Circumference = 2 * π * radius

Substituting the given radius value into the formula, we get:

Circumference = 2 * π * 12.3 cm

Circumference = 24.6π cm

Now, let's calculate the arc length using the central angle of 120°:

Arc Length = (120° / 360°) * 24.6π cm

Arc Length = (1/3) * 24.6π cm

Arc Length = 8.2π cm

Therefore, the exact length of the arc formed by a central angle measuring 120° in a circle with a radius of 12.3 cm is 8.2π cm.

It's important to note that in this case, since the central angle is given in degrees, the result is expressed in terms of π. If you need a decimal approximation, you can calculate the numerical value using an appropriate approximation for π.

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Answer:

X = 920

Step-by-step explanation:

To start off, we have to find how many times 34% can go into 100%. It can go in precisely 2.94117647059 times. Then, we take that number and multiply it by 312.8, since 312.8 is 34% of 100%. We get 920 from that, which is the answer.

Hope this helped!

A percentage is a way to describe a part of a whole. The value of x rounded to the nearest whole number is 920.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given that the number 312.8 is 34% of x. Therefore, we can write,

34% of x = 312.8

(34/100) × x = 312.8

Multiply both the sides of the equation by 100,

(34/100) × x × 100 = 312.8 × 100

Divide both the sides of the equation by 34,

[(34/100) × x × 100] ÷ 34 = (312.8 × 100) ÷ 38

x = (312.8 × 100)/34

x = 920

Hence, the value of x rounded to the nearest whole number is 920.

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The number of complex zeroes that the polynomial has in the graph is 1.

Given a graph of a polynomial.

We have to find the complex zeroes of the polynomial.

Complex zeroes of a polynomial are the zeroes of the polynomial which are complex numbers.

The zeroes of a polynomial functions are the x intercepts of the graph of the function.

x intercepts are the points which touches the X axis.

Here the graph touches the X axis at x = -4, x = -2, x = 1 and x = 4.

So there are 4 real roots.

The degree of the polynomial is the number of times that the direction of the graph changes.

Here degree = 5

Number of real roots = 4

Number of imaginary roots = 1

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9514 1404 393

Answer:

  see attached

Step-by-step explanation:

a) A table and graph are attached.

__

b) The relationship is NOT PROPORTIONAL. The line does not go through the origin (0, 0).

Answer: Choice A

A translation 4 units to the left followed by a dilation by 2

=============================================================

Explanation:

The following transformations will make the pre-image and image congruent to one another:

If you apply any of those transformations mentioned above, then the image is an identical copy of the pre-image. Nothing about the figure has changed other than it has been shifted, rotated, or reflected in some way. The figure retains its original size and shape. These transformations are called isometries.

A dilation on the other hand does not preserve the size. "Dilation by 2" means the scale factor is 2, so the image will be twice as large compared to the pre-image, in terms of linear dimension. This means there is no way the image is congruent to the pre-image if a dilation has occurred.

Based on all this, choice A is the answer. Choices B, C, and D only involve the three isometries mentioned earlier and no dilation at all, so they can be ruled out.

Answer:

so first put a dot on -5 on the y axis then go up 4 and to the right 1 and put a second dot and connect them

Answer:

Answer and steps in picture.

Answer:

not sure but i think its 9

Step-by-step explanation:

Answer:

3 x 3 x 3= 18  so 27cm squared

Step-by-step explanation:

Hope this helps! :D

Answer:

145

Step-by-step explanation:

Answer:

Resolver la ecuación para xx hallando aa, bb y cc de la ecuación cuadrática y aplicando la fórmula cuadrática.

x=3,−4x=3,-4

Hi there!  

»»————-　★　————-««

I believe your answer is:  

\(k = -0.4\)

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

\(2k+9=7-3k\\\rule{150}{0.5}\\\rightarrow 2k + 9 = 7-3k\\\\\rightarrow 2k + 3k + 9 = 7 - 3k + 3k\\\\\rightarrow 5k + 9 = 7\\\\\rightarrow5k + 9 - 9 = 7 - 9\\\\\rightarrow 5k = -2\\\\\rightarrow \frac{5k=-2}{5}\\\\\rightarrow \boxed{k = -\frac{2}{5} = -0.4}\)

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

a. 2, because it is the coefficient of the highest degree.

b. 4

c. 5 terms.

d. -10

e. 3, as it is the coefficient of x^2.

If you need more help don't hesitate to ask :)

Time taken by both April and Bob to complete the work is 2 days.

Given that, April can complete a project in 3 days and Bob can complete the same project in 6 days.

The basic concept of Time and Work is similar to that across all Arithmetic topics, i.e. the concept of Proportionality. Efficiency is inversely proportional to the Time taken when the amount of work done is constant.

Here,

Work done by April in 3 days = 1/3

Work done by Bob in 6 days = 1/6

Time take by both to complete work = 1/3 + 1/6

= 2/6 + 1/6

= 3/6

= 1/2

Therefore, time taken by both April and Bob to complete the work is 2 days.

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If you start at (0,-4) and you move left 1 unit and right 4 units, you end at (3, -4)

From the question, we have the following parameters that can be used in our computation:

Start = (0, -4)

Also, we have

You move left 1 unit and right 4 units

Mathematically, this can be expressed as

(x, y) = (x - 1 + 4, y)

Substitute the known values in the above equation, so, we have the following representation

Endpoint = (0 - 1 + 4, -4)

Evaluate the expression

Endpoint = (3, -4)

Hence, the endpoint is (3, -4)

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(a) The annual interest rate is approximately 14.79%.

(b) It would take approximately 6.24 years for the investment to be worth at least $40,000.

(a) To find the value of r, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

A = Final amount

P = Principal amount (initial investment)

r = Annual interest rate (in decimal form)

n = Number of times interest is compounded per year

t = Number of years

In this case, the principal amount P is $6000, the final amount A is $16000, the number of years t is 10, and the interest is compounded annually (n = 1). We need to solve for r.

16000 = 6000(1 + r/1)^(1*10)

Dividing both sides by 6000:

16000/6000 = (1 + r)^10

Simplifying the left side:

2.6667 = (1 + r)^10

Taking the 10th root of both sides:

(1 + r) = (2.6667)^(1/10)

(1 + r) ≈ 1.1479

Subtracting 1 from both sides:

r ≈ 1.1479 - 1

r ≈ 0.1479

Therefore, the annual interest rate is approximately 14.79%.

(b) To find the time taken for the investment to be worth at least $40,000, we can again use the compound interest formula and solve for t:

40000 = 6000(1 + 0.1479/1)^(1*t)

Dividing both sides by 6000:

40000/6000 = (1 + 0.1479)^t

6.6667 = (1.1479)^t

Taking the logarithm (base 1.1479) of both sides:

log base 1.1479 (6.6667) = t

t ≈ 6.24

Therefore, it would take approximately 6.24 years for the investment to be worth at least $40,000.

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Answer:

80.54

Step-by-step explanation:

height- 30

base- 5

tan-1(30/5)

tan-1(6)

= 80.54

why are there two of these?
Answer:

53.9

Step-by-step explanation:

89% of all houses have garages and 48% have garages and pools. We try to find houses with a pool that have a garage. Let's assume that there are 100 houses in her neighborhood. then 89 of them have garages and 48 of them have garages and pools. 48 / 89 = about 0.5393. Conver this to percent and we get 53.9

Answer:

Maximum= (-2,15)

Minimum= (2,-15)

Answer: 0.00923521

Step-by-step explanation:

Given : The probability U.S households play video or computer games=69%=0.69

here, the probability of each U.S household play video or computer games is fixed as 0.69

Then, the probability of each U.S household not play video or computer games= 1-0.69=0.31

For independent events the probability of their intersection is product of probability of each event.

Now, the probability that none play video/computer games will be :-

\((0.31)^4=0.00923521\)

The volume of cone is 175 m³

Firstly,

Volume of Pyramid.

The volume (V) of a pyramid is  

V = ⅓Ah

Data:

V = 175m³

Calculation:

175 = ⅓× A× h

Ah = 175*3

Ah = 525m³

Secondly,

The volume (V) of a cone is

V = ⅓Ah

Data:

Ah = 525 m³

Calculation:

V = ⅓ A× h

V = 175 m³

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Answer:

  144

Step-by-step explanation:

For a bitstring of length n, there are Fibonacci(n+2) strings containing no two consecutive zeros. This can be seen by constructing the strings starting with n=1.

1-bit strings: 1, 0 -- 2 strings not containing consecutive 0s

2-bit strings: 11, 10, 01 -- 3 strings not containing consecutive 0s

Note that we have added 1 to all the 1-bit strings, and added 0 only to the string ending in 1.

3-bit strings: 111, 110, 101, 011, 010 -- 5 strings not containing consecutive 0s

Note that these 5 strings consist of all (3) of the 2-bit strings with 1 appended, and all (1) of the 2-bit strings ending in 1 with 0 appended. The number that now end in 0 is the number previously ending in 1.

__

If (x, y) represents the numbers of n-bit strings ending in (0, 1), then the number of (n+1)-bit strings ending in (0, 1) is (y, x+y). That is, the recursive relation is ...

  \((x_1,y_1)=(1,1)\\(x_n,y_n)=(y_{n-1},\,x_{n-1}+y_{n-1})\\b_n=x_n+y_n\quad\text{number of n-bit strings without consecutive 0s}\)

For n=1 to n=10, these pairs are ...

  (1, 1), (1, 2), (2, 3), (3, 5), (5, 8), (8, 13), (13, 21), (21, 34), (34, 55), (55, 89)

The sequence of b[n] values is ...

  2, 3, 5, 8, 13, 21, 34, 55, 89, 144

which are the n=3 to n=12 numbers from the Fibonacci sequence.

That is, there will be Fibonacci(12) = 144 10-bit strings with no consecutive 0s.

Answer:

2.05 secs

Step-by-step explanation:

we will use quadratic formula to work out the time t.

t = ((-b ± √(b² - 4ac)) ÷ 2a)

where a is the value of the first coefficient, b is value of the second and c is value of the constant.

h = -9t² + 15t + 7

we need water level, so h = 0.

-9t² + 15t  + 7 = 0

a = -9, b = 15, c = 7.

t = ((-b ± √(b² - 4ac)) ÷ 2a)

= ((-(15) ± √((15)² - 4(-9)(7))) ÷ 2(-9))

= ((-15 ± √(225 - -252)) ÷ -18)

= ((-15 ± √(225 + 252)) ÷ -18)

= ((-15 ± √(477)) ÷ -18)

= -0.380 or 2.05

t is time, so it has to be positive.

t = 2.05 seconds to nearest one hundredth

The probability that Jessica picks a yellow pencil is 80%.

What exactly is probability?

Probability is a measure of an event's possibility or chance of occurring. It is stated as a number ranging from 0 to 1, or as a percentage ranging from 0% to 100%, where 0 indicates an impossible occurrence and 1 (or 100%) represents a certain event.

Now,

The probability of picking a yellow pencil =  the number of yellow pencils / total number of pencils:

Probability of picking a yellow pencil = Number of yellow pencils / Total number of pencils

In this case, there are 8 yellow pencils out of a total of 10 pencils:

Probability of picking a yellow pencil = 8 / 10

Simplifying the fraction by dividing both the numerator and denominator by 2, we get:

Probability of picking a yellow pencil = 4 / 5

Probability of picking a yellow pencil = 4 / 5 x 100%

Probability of picking a yellow pencil = 80%

Therefore, the probability that Jessica picks a yellow pencil is 80%.

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Answer:

it is a commutative property

Answer:

The probability that the selected number is an odd number or a multiple of 3 is 6/9, or 2/3. This is because there are 6 numbers that meet the criteria out of the 9 numbers in the set: 1, 3, 5, 7, 9, and 3.

The acceleration of the collar at point A is 5 ft/s^2.

A) To determine the normal force on the collar at point A, we need to consider the forces acting on the collar. The only force acting on the collar in the vertical direction is the weight of the collar (5 lb), which is balanced by the normal force exerted by the rod. Therefore, we can write:

N - 5 = 0

where N is the normal force. Solving for N, we get:

N = 5 lb

B) To determine the acceleration of the collar at point A, we need to use Newton's second law, which states that the net force acting on an object is equal to its mass times its acceleration. The net force on the collar is given by the force exerted by the spring, which is equal to the spring constant times the displacement of the collar from its unstretched length. At point A, the displacement of the collar is:

x = L - y = 3 - 0 = 3 ft

where L is the length of the rod and y is the position of the collar on the rod. Therefore, the force exerted by the spring is:

F = kx = 10 lb/ft × 3 ft = 30 lb

The weight of the collar is:

W = mg = 5 lb

where g is the acceleration due to gravity. The net force on the collar is therefore:

Fnet = F - W = 30 - 5 = 25 lb

Using Newton's second law, we can write:

Fnet = ma

where a is the acceleration of the collar. Solving for a, we get:

a = Fnet / m = 25 lb / 5 lb = 5 ft/s^2

Therefore, the acceleration of the collar at point A is 5 ft/s^2.

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Answer:

AA and SAS

Step-by-step explanation:

AA theorem happens If triangles have two of the same angles, then the triangles are similar. SAS happens If triangles have two pairs of proportional sides and equal included angles, then the triangles are similar.

Answer:

57

Step-by-step explanation:

this is the boybfiend