Find the center and radius for the circle defined by the equation x^2 + y^2 + 5x -y + 2

To rewrite 64 using 2 as the base, the exponent is 6.

To rewrite 64 using 2 as the base, we need to find the exponent that represents the power of 2 that equals 64. In other words, we need to solve the equation 2 to the power of x equals 64. We can do this by finding the logarithm with base 2 of 64. Using a calculator, we find that log base 2 of 64 is 6. Therefore, the exponent is 6.

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The radius of the circle whose center is the origin and that passes through the point (5 12) is 13 units.

explanation;

taking from origin,

let 5 units equat to x - axixs

 and y = 12 units

so using pythagoras theorm radius = square root of (12)² + (5)²

                                                              = [tex]\sqrt{169}[/tex]

                                                                 =13 answer.

The radius of a circle is the length of the line section from the middle to some extent at the circumference of the circle. it is commonly abbreviated as 'r'. There can be countless radii drawn in a circle and the duration of all those radii can be the identical. it is half of the diameter of the circle.

Radius of a circle from region: in case you know the place A , the radius is r = √(A / π) . Radius of a circle from circumference: if you understand the circumference c , the radius is r = c / (2 * π) . Radius of a circle from diameter: if you understand the diameter d , the radius is r = d / 2

A line phase extending from the middle of a circle or sphere to the circumference or bounding surface. 2a = the bone at the thumb side of the human forearm also : a corresponding a part of vertebrates above fishes. b=the 1/3 and commonly biggest vein of an insect's wing.

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The length and width of the rectangle are [tex]13[/tex] cm and [tex]9[/tex] cm respectively whose area is [tex]117 cm^2[/tex].

Let the width of the rectangle be [tex]x[/tex].

Then the length of the rectangle is [tex]x+4[/tex].

Area of a rectangle [tex]=[/tex] length [tex]\times[/tex] width

Area [tex]= 117 cm^2[/tex]

[tex](x+4) \times x = 117[/tex]

[tex]x^2+4x=117[/tex]

[tex]x^2+4x-117=0[/tex]

[tex]x^2+13x-9x-117=0[/tex]

[tex]x(x+13)-9(x+13)=0[/tex]

[tex](x+13)(x-9)=0[/tex]

[tex]x+13=0, x-9=0[/tex]

[tex]x=-13, x=9[/tex]

Since, length cannot be negative. So, [tex]x=-13[/tex] is not possible.

So, [tex]x=9[/tex].

And [tex]x+4=13[/tex]

So, length [tex]= 13[/tex] cm and width [tex]= 9[/tex] cm.

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Answer:

Step-by-step explanation:

the answer is 9

Answer:

She should have multiplied by 2 instead of dividing by 2.

Step-by-step explanation:

Note: The given equation is incorrect and second equation is missing.

Consider the given equation is

[tex]k=\dfrac{1}{2}mv^2[/tex]         ...(i)

The formula find by Lashandra is

[tex]m=\dfrac{k}{2v^2}[/tex]

We need to find the Lashandra’s error.

Multiply both sides by 2 in equation (i).

[tex]2k=mv^2[/tex]

Divide both sides by [tex]v^2[/tex].

[tex]\dfrac{2k}{v^2}=m[/tex]

It means, the formula find by Lashandra is incorrect. She should have multiplied by 2 instead of dividing by 2.

Answer:

a

Step-by-step explanation:

2021 edg

Final answer:

The probability that a randomly selected golf ball will be red from a basket of 18 balls, with 9 red, is 1/2 or 50%.

Explanation:

The question is asking about the probability of selecting a red golf ball from a basket that contains 18 golf balls, with 9 of them being red. To find this probability, we divide the number of red golf balls by the total number of golf balls.

Here is the calculation:

Number of red golf balls: 9

Total number of golf balls: 18

Probability (P) of selecting a red golf ball: P = Number of red golf balls / Total number of golf balls

P = 9 / 18

P = 1/2 or 0.5 or 50%

Therefore, the probability that a randomly selected golf ball will be red is 1/2, which can also be expressed as 0.5 or 50%.

Answer:

a reflection of the line segment across the line y = –x

Step-by-step explanation:

Reflecting across the line y = -x switches the x- and y-coordinates and negates both.  This will map

(-1, 4)→(4, -1)→(-4, 1) and

(4, 1)→(1, 4)→(-1, -4)

The reflection that produces an image with endpoints at (–4, 1) and (–1, –4) is a reflection of the line segment across the line y = -x.

Option D is the correct answer.

There are two ways of translation.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

The reflection of a point over the x-axis involves changing the sign of its

y-coordinate while leaving the x-coordinate unchanged.

The reflection of a point over the y-axis involves changing the sign of its

x-coordinate, while leaving the y-coordinate unchanged.

The reflection of a point over the line y = x involves swapping its x and y-coordinates.

The reflection of a point over the line y = -x involves swapping the sign of its x and y-coordinates.

To find the reflection that produces an image with endpoints at (–4, 1) and (–1, –4), we need to reflect the original line segment across a line that produces an image with the same length and orientation as the given endpoints.

One way to do this is to plot the points and draw the line segment, then draw the candidate lines of reflection and see which one produces the desired image.

Another way is to compute the midpoint of the original line segment and see which reflection takes that midpoint to the midpoint of the desired image.

Using the second method, the midpoint of the original line segment is:

= ((–1 + 4) / 2, (4 + 1) / 2)

= (1.5, 2.5)

The midpoint of the desired image is:

= ((–4 + –1) / 2, (1 + –4) / 2)

= (-2.5, -1.5)

To find the reflection that takes (1.5, 2.5) to (-2.5, -1.5), we can see that this is the reflection across the line y = -x.

Therefore,

The reflection that produces an image with endpoints at (–4, 1) and (–1, –4) is a reflection of the line segment across the line y = -x.

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Answer:

Step-by-step explanation:

Slope-intercept form of the equation is y = mx + c

Where m = slope of the line

c = y- intercept

a). 3x + 4y - 12 = 0 [Standard form of the equation of a line]

4y + 3x = 12

4y = 12 - 3x

[tex]y=\frac{1}{4}(-3x+12)[/tex]

[tex]y=-\frac{3x}{4}+\frac{12}{4}[/tex]

[tex]y=-\frac{3x}{4}+3[/tex]

Here slope of the line is [tex]-\frac{3}{4}[/tex] and y-intercept is 3.

b). 2x + y = 1

y = -2x + 1

Slope of the line is -2 and y intercept is 1

Answer:the answer is 20

Step-by-step explanation:

y = 4x+4

 give x a number that is on the X axis line to make it a little easier

 so lets say x = 2

replace x in the equation with 2

y = 4(2) +4

so y = 8+4 =12

 s0 put a dot where x is 4 and y is 12

 do the same thing with another number then draw a straight line through both those points

The value of y when x is 3 in the equation "y = 4x + 4" is 16. This linear relationship reflects a consistent rate of change, with each unit increase in x corresponding to a 4-unit increase in y.

In the equation "y = 4x + 4," to find the value of y when x is 3, we substitute x with 3:

y = 4(3) + 4

y = 12 + 4

y = 16

Therefore, when x is 3, y is 16. This means the point on the graph is (3, 16). The equation represents a linear relationship where y depends on x with a constant rate of change of 4. For every 1-unit increase in x, y increases by 4 units due to the coefficient of x.

In summary, for the given equation "y = 4x + 4," when x is 3, y is 16. This relationship indicates a straight line with a slope of 4 and a y-intercept of 4.

The question probable may be;

Given the equation y = 4x + 4 find the value of y when x = 3.

The model which represents the total amount in terms of pennies, quarters, dimes and nickel is 0.25q + 0.10d + 0.05n + 0.60

To create a mathematical model of the total amount :

Therefore, the model which represents the total amount is 0.25q + 0.10d + 0.05n + 0.60

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The number of like terms in the given expression are:

                                           3

                ( 14x , -x and 2x)

Like terms--

The like terms are the terms which have the same variables with the same power.The coefficients of such terms may vary.

The expression is given by:

        14x-14y+7-x+z+2x

There are total 6 terms in given expression.

The number of terms with variable x are: 3  i.e.   14x , -x and 2x

The number of terms with the variable y is: 1 i.e. -14y

The number of terms with variable z is: 1 i.e.  z

and the number of constant term is: 1 i.e. 7

Hence, the number of like terms are: 3

The answer Y=1

:) hope this helps

If Mrs. smith's reading class can read a mean of 175 words per minute with a standard deviation of 20 words per minute. The top 3% of the class is to receive a special award. The minimum number of words per minute a student would have to read in order to get the award will be: 213 words per minute

Using this formula

Minimum number of words =(z score× standard deviation)  + means

Where:

z score=(100%-3%=97%)

z score= 97%=1.881

Standard deviation=175

Mean=20

Let plug in the formula

Minimum number of words =(1.881×20) + 175

Minimum number of words =37.62+175

Minimum number of words =212.62

Minimum number of words =213 (Approximately)

Inconclusion if Mrs. smith's reading class can read a mean of 175 words per minute with a standard deviation of 20 words per minute. The top 3% of the class is to receive a special award. The minimum number of words per minute a student would have to read in order to get the award will be: 213 words per minute

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Answer:

The correct answer is (19).

Step-by-step explanation:

A repeating decimal, also called a recurring decimal, is a number whose decimal representation eventually becomes periodic (i.e., the same sequence of digits repeats indefinitely). The repeating portion of a decimal expansion is conventionally denoted with a vinculum so, for example,

The minimum number of digits that repeats in such a number is known as the decimal period.

Repeating decimal notation was implemented in versions of the Wolfram Language prior to 6 as PeriodicForm[RealDigits[r]] after loading the add-on package NumberTheory`ContinuedFractions`.

All rational numbers have either finite decimal expansions (i.e., are regular numbers; e.g., ) or repeating decimals (e.g., ). However, irrational numbers, such as neither terminate nor become periodic.

Numbers such as 0.5 are sometimes regarded as repeating decimals since.