Describe the relationship between the circumference and the diameter of a circle.
a. Pi times half the diameter equals the circumference.
b. Pi times the diameter equals the circumference.
c. The circumference divided by half the radius equals Pi.
d. The circumference times the diameter equals Pi .​

Answer:

140

Step-by-step explanation:

this is because of alternate suplementry lines

Answer:

5x^2 - 13x + 6

Step-by-step explanation:

(8x^2 - 6x + 2) - (3x^2 + 7x - 4) =

First, drop the first set of parentheses because they are unnecessary.

= 8x^2 - 6x + 2 - (3x^2 + 7x - 4)

Now, distribute the minus sign to the left of the set of parentheses. Think of that negative sign as -1 multiplied by the parentheses. You change every sign inside the parentheses.

= 8x^2 - 6x + 2 - 3x^2 - 7x + 4

Next, group like terms together.

= 8x^2 - 3x^2 - 6x - 7x + 2 + 4

Finally, combine like terms.

= 5x^2 - 13x + 6

Answer:

-0.8 and 0.75.

Step-by-step explanation:

20x^4 + x^3 + 8x^2 + x – 12 = 0

by the rational roots theorem:-

The leading coefficient is 20 with factors +/-  1,2,4,5,10,20

and the constant is -12 with factors  +/- 1,2,3,4,6,12

so there are many possible roots like -1, 2, 3/4 3/5 , -4/5 .....

Drawing a graph would be the quickest way to do this,  either manually, using graphical software or a graphical calculator.

I used the latter and got 2 rational roots -0.8 and 0.75.

The rational roots of the polynomial f(x) = 20[tex]x^4[/tex] + [tex]x^3[/tex] + 8[tex]x^2[/tex] + x – 12 is -0.8 and 0.75 and this can be determined by sketching the graph of the given polynomial.

Given :

f(x) = 20[tex]x^4[/tex] + [tex]x^3[/tex] + 8[tex]x^2[/tex] + x – 12

The following steps can be used in order to determine the rational roots of the given polynomial:

Step 1 - Write the polynomial equation.

f(x) = 20[tex]x^4[/tex] + [tex]x^3[/tex] + 8[tex]x^2[/tex] + x – 12

Step 2 - Draw the graph of the above polynomial equation.

Step 3 - The coefficient of [tex]x^4[/tex] is 20 with factors +/-  1,2,4,5,10,20

Step 4 - The constant term of the given polynomial is -12 with factors  +/- 1,2,3,4,6,12.

Step 5 - So, from the polynomial equation, the two rational roots are -0.8 and 0.75.

For more information, refer to the link given below:

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Answer: 140 degree

Step-by-step explanation: The line LMU is basically 180, so what you'll do is 90 degree KLM plus 50 degree LMK which will give you 140 degree. A whole triangle is a supplementary angle so it's 180 degree. To find KMU, you do (180 - 140) - (180 - 40) = 140. So the answer for angle KMU is 140.

Answer:    B

Step-by-step explanation:

Answer a is incorrect because only the seniors were questioned and answer c is incorrect because nothing was mentioned in the question about only testing males.

Your answer is B

Answer:

b

Step-by-step explanation:

was on khan academy <3

Answer:

Step-by-step explanation:

Vertex of y = |x| have the coordinates (0, 0).

f(x) + n - shift the graph n units up

f(x) - n - shift the graph n units down

f(x + n) - shift the graph n units to the left

f(x - n) - shift the graph n units to the right

nf(x) - stretches/shrinks vertically

f(nx) - stretches/shrinks horizontally

We have

f(x) = |8x + 8| - 3 = |8(x + 1)| - 3 = |8| · |x+1| - 3 = 8|x + 1| - 3

g(x) = |x| → f(x) = 8g(x + 1) - 3

vertically streched by 8      (0, 8 · 0) → (0, 0)

shifted 1 unit to the left    (0 - 1, 0) → (-1, 0)

shifted 3 units down       (-1, 0 - 3) → (-1, -3)

Answer: 6x^7+ 12x^6+ 3x^5

Hope that helped

Answer:

x = 0.417 or x = -0.917

Step-by-step explanation:

We are given the following expression and we are to solve it for the variable x:

[tex] x ^2 + \frac { 1 } { 2 } x + \frac { 1 } { 1 6 } = \frac { 4 } { 9 } [/tex]

We will find the least common multiple of 2. 6 and 9:

[tex]x^2 \times 144 +\frac{1}{2}x \times 144 +\frac{1}{16} \times 144 = \frac{4}{9} \times 144[/tex]

Simplifying it to get:

[tex]144x^2+72x+9=64[/tex]

[tex]144x^2+72x+9-64=0[/tex]

[tex]144x^2+72x-55=0[/tex]

Using the quadratic formula to solve for x:

[tex]x=\frac{-b \pm\sqrt{b^2-4ac} }{2a}[/tex]

[tex]x=\frac{-72 \pm\sqrt{72^2-4(144)(-55)} }{2a}[/tex]

[tex]x=\frac{5}{12}[/tex] or [tex]0.417[/tex]

[tex]x=-\frac{11}{12}[/tex] or [tex]-0.917[/tex]

The answer is:

The speed of the wind is 150mph.

To calculate the speed of the wind, we need to write two equations using the given information about the speed when the airplane was traveling with the wind and against the wind, considering that it travel the same length of time.

So, writing the equations, we have:

Traveling with the wind:

We know that the speed of the airplane is 325 mph and it travels 1360 miles with the wind, so, for the equation, we have:

[tex]distance=(AirplaneSpeed+WindSpeed)*t[/tex]

[tex]1360miles=(325mph+WindSpeed)*t[/tex]

[tex]t=\frac{1360miles}{325mph+WindSpeed}[/tex]

Traveling against the wind:

We know that the speed of the airplane is 325 mph and it travels 1240 miles with the wind, so, for the equation, we have:

[tex]distance=(AirplaneSpeed-WindSpeed)*t[/tex]

[tex]1240miles=(325mph-WindSpeed)*t[/tex]

[tex]t=\frac{1240miles}{325mph-WindSpeed}[/tex]

Then, making making equal the time, we have:

[tex]\frac{1360miles}{325mph+WindSpeed}=\frac{1240miles}{325mph-WindSpeed}[/tex]

[tex]\frac{1360miles}{325mph+WindSpeed}=\frac{1240miles}{325mph-WindSpeed}\\\\(1360miles)*(325mph-WindSpeed)=(1240miles)*(325mph+WindSpeed)\\\\442000miles.mph-1360miles*WindSpeed=403000miles.mph+1240miles*WindSpeed\\\\442000miles.mph-403000miles.mph=1240miles*WindSpeed+1360miles*WindSpeed\\\\39000miles.mph=2600miles*Windspeed\\\\WindSpeed=\frac{39000miles.mph}{2600miles}=150mph[/tex]

Hence, we have that the speed of the wind is 150mph.

Have a nice day!

Answer:

B

Step-by-step explanation:

Given

[tex]\left[\begin{array}{ccc}-2&3&0\\-4&2&6\\6&-5&6\end{array}\right][/tex]

The product of 3x2 will be six.. We have a scalar which has to be multiplied by the matrix. The method of multiplying a scalar with a matrix is to multiply each element of the matrix by the scalar.  

After multiplication the matrix will be:

[tex]\left[\begin{array}{ccc}-12&18&0\\-24&12&36\\36&-30&36\end{array}\right][/tex]

So, B is the correct answer..

To solve this question, you need to perform a scalar multiplication of the matrix by 3*2. Scalar multiplication involves multiplying every element of the matrix by the scalar value.
First, let's find the scalar value:
3 * 2 = 6
Now, let's multiply every element in the matrix by the scalar value 6:
Original matrix:
[ -2,  3,  0 ]
[ -4,  2,  6 ]
[  6, -5,  6 ]
After scalar multiplication by 6:
[ -2*6,  3*6,  0*6 ]
[ -4*6,  2*6,  6*6 ]
[  6*6, -5*6,  6*6 ]
Performing the multiplication for each element gives us:
[ -12,  18,   0 ]
[ -24,  12,  36 ]
[  36, -30,  36 ]
The resulting matrix after multiplying by the scalar value of 6 is:
[ -12,  18,   0 ]
[ -24,  12,  36 ]
[  36, -30,  36 ]
So the correct answer to the given matrix question is the matrix displayed above.

Answer:

[tex]{x}^{3} - 4x - 12[/tex]

Step-by-step explanation:

[tex] {x}^{3} + 6 \times 2 - 4x - 24[/tex]

[tex] = {x}^{3} + 12 - 4x - 24[/tex]

[tex] = {x}^{3} - 4x + 12 - 24[/tex]

[tex] = {x}^{3} - 4x - 12[/tex]

Answer: x= -7/11

Step-by-step explanation:

13x+17+5x=7x+10

collect the like terms by adding their coefficients

18x+17=7x+10

move variable to the left side and change its sign

18x-7x+17=10

move constant to the right side and change its sign

18x-7x=10-17

collect the like terms

11x=10-17

calculate the difference

11x= -7

divide both sides by 11

x= -7/11

The solution to this equation 3x +17 + 5x = 7x + 10 is x = -7

The solution to this equation 3x +17 + 5x = 7x + 10

Given equation is:

3x +17 + 5x = 7x + 10

To find the value of x, combine the like terms by adding or subtraction.

3x + 5x - 7x = 10 - 17

x = - 7

Therefore, x = -7 is the solution to this equation 3x +17 + 5x = 7x + 10

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Answer:

the equation of circle is x²  + y² + 6x - 24y + 128 = 0

Step-by-step explanation:

To find the general form of the equation of the circle with center A (-3, 12) and radius r=5,  we simply use this formula;

General Equation of a circle is   (x - a)²  +  (y-b)² = r²

(a,b) are the two point at the center of the circle which are (-3, 12)

which implies a = -3 and b = 12

r is the radius of the circle which is given as 5 from the above diagram

to get r², we simply square 5 and so r²  = 25

We can now plug in the values of our variables into the equation

(x - a)²  +  (y-b)² = r²

(x - [-3])²   +   ( y  -  12)²  =   5²

(x +3)²   +   ( y  -  12)²  =   5²

we will expand all the brackets

x² +  6x +  9  + y² -24y + 144 = 25

x² +6x + y² -24y + 153 = 25

Take 25 to the left hand side of the equation

x² +6x + y² -24y + 153  -  25 = 0

x² +6x + y² -24y + 128 = 0

Rearranging the equation to give us a standard form of the equation of the circle, we have;

x² + y² + 6x - 24y  + 128 =0

{Note:  (x + 3)²  =  (x+3)(x+3) = x² + 6x + 9 and  

(y - 12)²  = (y -12)(y-12) = y² - 24y + 144}

Therefore the general form of the equation  of a circle with center(-3, 12) and radius 5 is x² + y² + 6x - 24y  + 128 =0

Answer:

y = 2x - 5

Step-by-step explanation:

The equation has to have the same slope -- in this case, it is 2 -- to be parallel to 2x - y = 4.

Now we have y = 2x - k.

Then, we plug in the coordinates to our new equation to solve for k.

-1 = 2(2)-k

-1 = 4-k

k = 5

So the final equation would be y = 2x - 5

Answer: 1110 grams

Step-by-step explanation: see the paper attached. (:

Answer:

The sample space is SG,GG,SS,GS. I know this because the sample space is the set of all possible outcomes of an experiment.

Hope this helped!

The sample space when the spinner that's divided into two sections is spun twice is; {SG, GG, SS, GS}

We are given that the sections are labeled STOP and GO.

Now the spinner is divided into two equally sized sections as S and G.

Now, if the spinner is spun twice, we could get the following results;

SG, SS, GS, GG.

Thus, the sample space is given by the total possible outcome of the spin which is;

{SG, SS, GS, GG}

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Answer:

8

Step-by-step explanation:

Answer:

the second step in solving a system of nonlinear equations by substitution is usually:

solve one equation for either variable of the given equation

Answer:

substituting a value in place of one of the variables to find the remaining variable.

Step-by-step explanation:

The key to solve this problem is using ratios and proportions.

Ratio is the relationship between two numbers, defined as the quotient of one number for the other. So:  The ratio between two numbers a and b is the fraction a/b and it is read a to b. This reason can also be written a : b.

Given two reasons a/b and c/d we say that they are in proportion if a/b = c/d. The terms a and d are called extremes while b and c are the means.  In every proportion the product of the extremes is equal to the product of the means: a.d = b.c

A student uses the ratio of 4 oranges to 6 fluid ounces of juice to find the numbers of oranges needed to make 24 fluid ounces of juice.

The ratio of 4 oranges to 6 fluid ounces of juice is 4/6.

The ratio of x oranges to 24 fluid ounces of juice is x/24

Writing the proportion

4/6 = x/24

Clear x to obtain the oranges needed

x = (4)(24)/6 = 96/6 = 16

Then, the proportion is:

[tex]\frac{4}{6} = \frac{16}{24}[/tex]

The error in the student's work was that they reversed the reason, 24/16 instead of 16/24.

The student's error is in setting up the proportion and not cross multiplying correctly. The correct proportion is 4/6 = x/24. By cross multiplying and solving for x, we find that 16 oranges are needed to make 24 fluid ounces of juice.

The error in the student's work is in setting up the proportion. The correct proportion should be:

4/6 = x/24

To find the number of oranges needed to make 24 fluid ounces of juice, we can cross multiply and solve for x.

Cross Multiplying: 4 * 24 = 6 * x

Simplifying the equation: 96 = 6x

Dividing both sides by 6, we find x = 16.

Therefore, the correct answer is that 16 oranges are needed to make 24 fluid ounces of juice.

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Answer:

D

Step-by-step explanation:

g(x) = √(x - 2) - 3

The range is all the possible values of g(x).  Since we can't take the square root of a negative number, the lowest that g(x) can be is:

g(x) = √0 - 3

g(x) = -3

The highest that g(x) can be is:

g(x) = √∞ - 3

g(x) = ∞

So the range is:

[-3, ∞)

Answer:

To find the mean absolute deviation of the data, start by finding the mean of the data set. Find the sum of the data values, and divide the sum by the number of data values. ... Divide the sum of the absolute values of the differences by the number of data values.

Sample Answer: First, find the mean of the data set by averaging. Next, find the absolute deviations for each data point. That is, find the distance each point is from the mean. Then find the mean of the absolute deviations.

Answer:

If (x+k) is a factor of f(x), then -k is a root (or solution) of f(x).

Step-by-step explanation:

Where are the answer choices?  Please share them.

If (x+k) is a factor of f(x), then -k is a root (or solution) of f(x).

If (x+k) is a factor of f(x), then f(-k) = 0

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

(x + k) is a factor of f(x)

If (x+k) is a factor of f(x), then f(-k) = 0. This is known as the factor theorem.

It states that if a polynomial f(x) has a factor of (x-a), then f(a) = 0.

In this case, since (x+k) is a factor of f(x), we can substitute -k for x in the factor theorem to get f(-k) = 0.

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Answer:

Step-by-step explanation:

X = number of Yan's marbles.  x-3 = number of Geraldo's marbles

annswer: x + (x - 3) = 21

hopes this helps :)

Answer:

Yan has 12 marbles and Geraldo has 9

Step-by-step explanation:

Because 12 + 9 =21 and 9 is 3 less than 12.

Answer:

The desired equation is y = x + 8.

Step-by-step explanation:

As we move right from (-2,6) to (4,12), x increases by 6 and y also increases by 6.  Thus, the slope, m, m = rise / run, is m = 6/6, or just m = 1.

Start with the slope intercept form y = mx + b.  Since m = 1, we now have y = x + b.  Subbing 4 for x, 12 for y, we can find b:  12 = 4 + b.  Thus, b = 8.

The desired equation is y = x + 8.

Answer:

The answer to your question is y=1x+8

Step-by-step explanation: We already know that the slope formula is:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

Substitute the values to find the slope

m= 12-6/4-(-2)

m= 6/4+2

m= 6/6

m=1, so, therefore, the slope is 1

And the y-intercept would be 8

Hope this helps and Please mark my answer as the brainliest

Answer:

11.4 mixture:26 and 2/3

7.8 mixture: 53 and 1/3

Step-by-step explanation: Sorry if this is hard to underestand. This is my first answer. This is a RSM question that has been checked.

11.4+7.8=9

 x+80-x=80

Multiply

11.4x+624-7.8x=720

3.6x=96

1.2=32

0.6x=16

6x=160

x=26 2/3

80-26 2/3= 53 1.3

Answer:

53 1/3 for $7.80, and 26 2/3 for $11.40

Step-by-step explanation:

x*11.4=11.4x

(80-x)*7.8=624-7.8

9*80=720

Those three steps are because he wants to make 80 pounds out of $9, $11.40 for a pound, and then a pound for $7.80. Since the total is 80 pounds, it could be 11.4 for x pounds and 7.8 for 80-x pounds. Then the equation is:

11.4x+624-7.8x=720

Simplify:

3.6x=96

Times both times by 10:

36x=960

x=26 2/3

80-x=53 1/3

ANSWER

The correct answer is C

EXPLANATION

We want to find the quotient:

[tex] - \frac{10}{19} \div ( - \frac{5}{7} )[/tex]

We multiply by the reciprocal of the second fraction:

[tex]- \frac{10}{19} \times ( - \frac{7}{5} )[/tex]

We cancel out the common factors to obtain:

[tex]- \frac{2}{19} \times ( - \frac{7}{1} )[/tex]

We multiply to get

[tex]\frac{ - 2 \times - 7}{19 \times 1} [/tex]

This simplifies to :

[tex] \frac{14}{19} [/tex]

The correct answer is C

The answer is:

Option C.

[tex]\frac{14}{19}[/tex]

To perform fraction division, we need to follow the convert the expression and multiply the first fraction (numerator) by the inverse of the second fraction (denominator).

For example:

[tex]\frac{\frac{a}{b} }{\frac{c}{d} }=\frac{a}{b}*\frac{d}{c}[/tex]

So, we are given the following expression:

[tex]-\frac{10}{19}\div (-\frac{5}{7})[/tex]

Which is equal to:

[tex]\frac{-10}{19}\div (\frac{-5}{7})[/tex]

Then, calculating we have:

[tex]\frac{-10}{19}\div (\frac{-5}{7})=\frac{10}{19}*\frac{7}{5}\\\\\frac{10}{19}*\frac{7}{5}=\frac{10*7}{19*5}=\frac{70}{95}\\\\\frac{70}{95}=\frac{5*14}{5*19}=\frac{14}{19}[/tex]

Hence, we have that the correct option is:

Option C.

[tex]\frac{14}{19}[/tex]

Have a nice day!

the answer to this question is 110°

Answer:

Step-by-step explanation:

[tex]x^2-8x-20=0\\\\x^2+2x-10x-20=0\\\\x(x+2)-10(x+2)=0\\\\(x+2)(x-10)=0\iff x+2=0\ \vee\ x-10=0\\\\x+2=0\qquad\text{subtract 2 from both sides}\\\boxed{x=-2}\\\\x-10=0\qquad\text{add 10 to both sides}\\\boxed{x=10}[/tex]

Answer:

a) exactly one triangle

Step-by-step explanation:

two sides and a non included angle is given

The table that best shows the impacts resulting from human activity is:

Impact of Human Activities

Human Activity Impact

Forest area cleared to construct an airport Increase in sound pollution

Vegetation cleared to construct a power plant Contamination of water

Hence the correct option is 2.

In the table illustrating the impacts resulting from human activities, the most fitting combination is the one stating that clearing forest areas to construct an airport leads to an increase in pollution, while the vegetation cleared for a power plant results in the contamination of water.

This pairing accurately reflects the environmental consequences associated with these specific human actions. When forests are cleared for airport construction, it often involves disrupting ecosystems, releasing pollutants, and contributing to air pollution.

On the other hand, clearing vegetation for a power plant can lead to water contamination, potentially through the release of pollutants into nearby water sources. This representation effectively highlights the diverse environmental impacts of human activities on both air and water quality, emphasizing the importance of responsible practices to mitigate these detrimental effects. Hence the correct option is 2.

Option 2 is correct. It directly links human activities to negative environmental consequences like sound pollution from airport construction and water contamination from power plant development.

Forest area cleared to construct an airport leading to an increase in sound pollution: This illustrates a direct impact of human activity on the environment. Clearing forests for infrastructure development like airports often leads to increased noise pollution due to aircraft operations and associated activities.

Vegetation cleared to construct a power plant leading to contamination of water: Again, this demonstrates a direct consequence of human activity. The clearance of vegetation for industrial purposes such as power plants can result in soil erosion and runoff, which may contaminate nearby water sources with sediments, chemicals, or pollutants.

Both of these impacts highlight tangible and negative consequences of human activities on the environment, emphasizing the importance of considering the environmental impacts of development and infrastructure projects. Therefore, option 2 effectively portrays the impacts resulting from human activities.

Complete Question:

Which table best shows the impacts resulting from human activity?

1) Impact of Human Activities:

Human Activity ; Impact

Forest area cleared to construct an airport  ; Increase in oxygen level

Vegetation cleared to construct an oil mine  ;  Increase in pollution

2) Impact of Human Activities:

Human Activity  ;    Impact

Forest area cleared to construct an airport  ;  Increase in sound pollution

Vegetation cleared to construct a power plant  ;  Contamination of water

3) Impact of Human Activities:

Human Activity  ;  Impact

Beehives cleared from urban areas  ;  Increase in vegetation

Dams constructed on a river    ;    Increase in fish population

4) Impact of Human Activities

Human Activity   ;  Impact

Beehives cleared from urban areas   ;  Increase in bird population

Dams constructed on a river    ;   Better quality of water