A parachutist's rate during a free fall reaches 189 kilometers per hour. What is this rate in meters per second? At this rate, how many meters will the parachutist fall during 5 seconds of free fall? Do not round your answers.

Answer:

The correct option for the provided problem is D. A selection or listing of objects in which the order of the objects is not important.

Step-by-step explanation:

Consider the provided information.

Selecting all the parts of a set of objects without considering its order in which the objects are selecting is known as combination.

Now consider the provided options:

Options A, B, and C are not valid as the description does not fits accurately.

Thus, the correct option for the provided problem is D. A selection or listing of objects in which the order of the objects is not important.

Answer:

A selection or listing of objects in which the order of the objects is not important

Step-by-step explanation:

Answer:

  3

Step-by-step explanation:

The diagram shows the answer: 3 pictures will fit vertically.

You can solve this algebraically as well. For n pictures, there will be n-1 spaces, so the total height of the page must satisfy ...

  1 + 3n + 1/2(n -1) + 1 ≤ 12

  3.5n + 1.5 ≤ 12 . . . . . . . . . . . simplify

  3.5n ≤ 10.5 . . . . . . . . . . . . . .subtract 1.5

  n ≤ 3 . . . . . . . . . . . . . . . . . . . divide by 3.5

Up to 3 pictures will fit in a column.

Answer:

Step-by-step explanation:

We know that the function is measured in terms of time. And the constant distance traveled in 50 miles. The inverse of the function is supposing say t(d) which measures the function in terms of distance traveled. The inverse of the function is obtained by dividing the distance by 50 as in the original function then the function is multiplied by 50. So the inverse of function obtained is: t(d) = d/50

Steps: d(t) = 50t

          t = d/50

          t(d) = d/50

I hope this helps!

Answer:

Proofs are in the explanation.

Step-by-step explanation:

b)  My first thought is to divide top and bottom on the left hand side by [tex]\cos(\alpha)[/tex].

I see this would give me 1 on top and where that sine is, it would give me tangent since sine/cosine=tangent.

Let's do it and see:

[tex]\frac{\cos(\alpha)}{\cos(\alpha)-\sin(\alpha)} \cdot \frac{\frac{1}{\cos(\alpha)}}{\frac{1}{\cos(\alpha)}}[/tex]

[tex]=\frac{\frac{\cos(\alpha)}{\cos(\alpha)}}{\frac{\cos(\alpha)}{\cos(\alpha)}-\frac{\sin(\alpha)}{\cos(\alpha)}}[/tex]

[tex]=\frac{1}{1-\tan(\alpha)}[/tex]

c) My first idea here is to expand the cos(x+y) using the sum identity for cosine.

So let's do that:

[tex]\frac{\cos(x)\cos(y)-\sin(x)\sin(y)}{\cos(x)\sin(y)}[/tex]

Separating the fraction:

[tex]\frac{\cos(x)\cos(y)}{\cos(x)\sin(y)}-\frac{\sin(x)\sin(y)}{\cos(x)\sin(y)}[/tex]

The cos(x) cancel's in the first fraction and the sin(y) cancels in the second fraction:

[tex]\frac{\cos(y)}{\sin(y)}-\frac{\sin(x)}{\cos(x)}[/tex]

[tex]\cot(y)-\tan(x)[/tex]

d) This one makes me think it is definitely essential that we use properties of logarithms.

The left hand side can be condense into one logarithm using the product law:

[tex]\ln|(1+\cos(\theta))(1-\cos(\theta))|[/tex]

We are multiplying conjugates inside that natural log so we only need to multiply the first and the last:

[tex]\ln|1-\cos^2(\theta)|[/tex]

I can rewrite [tex]1-\cos^2(\theta)[/tex] using the Pythagorean Identity:

[tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex]:

[tex]\ln|\sin^2(\theta)|[/tex]

Now by power rule for logarithms:

[tex]2\ln|\sin(\theta)|[/tex]

Answer:

  3x ≥ -6

Step-by-step explanation:

"No less than" means "greater than or equal to". An appropriate translation of the problem statement is ...

  3x ≥ -6

Answer:

3x ≥ -6

Step-by-step explanation:

The the inequality that could be used to solve three times a number is no less than negative six is 3x ≥ -6.

Answer:

Question 1: the slope is -6

Question 2: the first choice is the one you want

Step-by-step explanation:

For the first one, I can't tell what fraction is on the left side with the y, but it doesn't matter.  To me it looks like 1/2, but like I said, it won't change or affect our answer regarding the slope.  That number has nothing to do with the slope.  

In order to determine the slope of that line that is currently in point-slope form, we need to change it to slope-intercept form.  Another expression for slope-intercept form is to solve it for y.  Doing that:

[tex]y - \frac{1}{2}=-6x-42[/tex]

Now we can add 1/2 to both sides.  That gives us the slope-intercept form of the line:

[tex]y=-6x- \frac{83}{2}[/tex]

The form is y = mx + b, where the number in the "m" place is the slope.  Our slope is -6.

For the second one, we will sub in the x coordinate in a pair for x in the equation of the line and do the same for y to see if the left side equals the right side.  The answer is [tex](\frac{2}{9},-7)[/tex] and I'll show you why.  I will also show you how another point DOESN'T work in the equation.  Filling in 2/9 for x and -7 for y:

[tex]-7+7=-3( \frac{2}{9} -\frac{2}{9})[/tex] which simplifies to

0 = -3(0) so

0 = 0 and this is true.

The other point I am going to use in exactly the same process is (-3, -7) since it doesn't have fractions in it.  First I'm going to distribute the -3 into the parenthesis to get:

[tex]y+7= -3 x + \frac{6}{9}[/tex]

Subbing in -3 for x and -7 for y:

[tex]-7+7=-3( -3) +\frac{6}{9}[/tex]

As you can see, the left side equals 0 but the right side does not.  If the lft side doesn't equal the right side, then the expression is not true, so the point is not on the line.

Answer:

  see below

Step-by-step explanation:

The vertex order has been reversed, so a reflection is involved. The direction of the short side has been changed by 90°, so a rotation is potentially involved. Depending on the precise rotation and/or reflections, translation may be involved.

One potential set of transformations is ...

Another potential set of transformations (shown below) is ...

Answer: We can expect about 40.13% of bottles to have a volume less than 32 oz.

Step-by-step explanation:

Given : The volumes of soda in quart soda bottles can be described by a Normal model with

[tex]\mu=\text{32.3 oz}\\\\\sigma=\text{1.2 oz}[/tex]

Let X be the random variable that represents the volume of a randomly selected bottle.

z-score :[tex]\dfrac{x-\mu}{\sigma}[/tex]

For x = 32 oz

[tex]z=\dfrac{32-32.3}{1.2}=-0.25[/tex]

The probability of bottles have a volume less than 32 oz is given by :-

[tex]P(X<32)=P(z<-0.25)=0.4012937[/tex]           [Using standard normal table]

In percent, [tex]0.4012937\times100=40.12937\%\approx40.13\%[/tex]

Hence, we can expect about 40.13% of bottles to have a volume less than 32 oz.

Answer:

The measure of arc BC = 124°

Step-by-step explanation:

From the figure we can write,

measure of arc AB + measure of arc BC + measure of arc AC = 360

measure of arc AB   = 146°

measure of arc BC = 90°

Therefore measure arc BC = 360 - (146 + 90)

 = 360 - 236

 = 124°

The measure of arc BC = 124°

Answer: 124 degrees

Step-by-step explanation: There is a 90 degree angle in the top right of the circle. There is a 146 degree angle. Add these two angles.

90 + 146 = 236

These two angles combined are 236 degrees. We are trying to find BC, which is the rest of the circle. There are 360 degrees in a circle. Subtract 360 from 236.

360 - 236 = 124

BC = 124 degrees.

Answer:

  233 cartons of food; 467 cartons of clothing

Step-by-step explanation:

This linear programming problem can be formulated as two inequalities (in addition to the usual constraints that the variables be non-negative). One of these expresses the constraint on weight. Let f and c represent numbers of food and clothing containers, respectively.

  40f +25c ≤ 21000

The other expresses the limit on volume.

  20f + 5c ≤ 7000

_____

Feasible Region vertex

We can subtract the boundary line equation of the first inequality from that of 5 times the second to find f:

  5(20f +5c) -(40f +25c) = 5(7000) -21000

  60f = 14000

  f = 233 1/3

The second boundary line equation can be rearranged to find c:

  c = 1400 -4f = 466 2/3

The nearest integer numbers to these values are ...

  (f, c) = (233, 467)

The other vertices of the feasible region are associated with one or the other variable being zero: (f, c) = (0, 840) or (350, 0).

Check of Integer Solution

Trying these in the constraint inequalities gives ...

Selection of the Answer

The answer to the question will be the feasible region vertex that maximizes the number of people helped. That is, we want to maximize ...

  p = 13f + 6c

The values of p at the vertices are ...

  p = 13·233 + 6·467 = 5831

  p = 13·0 + 6·840 = 5040

  p = 13·350 + 6·0 = 2100

The most people are helped when the plane is filled with 233 food cartons and 467 clothing cartons.

This is a linear programming problem. We create two constraints based on weight and volume, and create an equation to maximize the number of people helped. The exact solution depends on solving this using a suitable tool.

This problem can be approached as a linear programming problem where the goal is to maximize the number of people helped. Total weight cannot exceed 21000 pounds, and total volume must not exceed 7000 cubic feet.

Let X be the number of cartons of food, and Y be the number of cartons of clothing.

So, we have two constraints: 40X + 25Y ≤ 21000 (weight constraint) and 20X + 5Y ≤ 7000 (volume constraint). We want to maximize the number of people helped (Z), represented by 13X + 6Y (since each food carton helps 13 people and each clothing carton helps 6 people).

The exact number of food and clothing cartons will depend on how we solve this linear programming problem. This is typically done using tools like a graphing calculator or software, which can give us the number of X and Y which maximizes Z.

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Answer:  [tex]\dfrac{20}{3}\text{ hours}[/tex]

Step-by-step explanation:

Let x be the speed of slower pump and 1.5x be the speed of faster pump to fill the swimming pool .

Then , According to the given question, we have the following equation:-

[tex]x+1.5x=\dfrac{1}{4}\\\\\rightarrow\ 2.5x=\dfrac{1}{4}\\\\\Rightarrow\ x=\dfrac{1}{10}=[/tex]

Now, the time taken by faster pump to fill the pool is given by :-

[tex]t=\dfrac{1}{1.5x}=\dfrac{10}{1.5}=\dfrac{20}{3}\text{ hours}[/tex]

Hence, the faster pump would take [tex]\dfrac{20}{3}\text{ hours}[/tex]  to fill the pool if it had worked alone at its constant rate.

Answer:

Option A (Exterior)

Step-by-step explanation:

To understand this question, it is important to understand the concept of the exterior angle. An exterior angle is an angle which is made by two intersecting lines outside of the shape. Basically, one of the two lines is extended outside the shape. The angle between the extended line and the other line which is not extended is the exterior angle. It is outside the shape. The interior angle is the angle which is made by the same two lines but inside the shape.

The sum of the interior angle and the exterior angle is 180 degrees. It is also interesting to note that the sum of the angles in the triangle is 180 degrees.

Suppose that the angles in the triangles are A, B, and C, and the associated exterior angle with the angle A is angle D. By the argument, A+B+C=180 degrees and A+D=180 degrees. Since 180 degrees = 180 degrees, therefore A+B+C = A+D. Angle A cancels on both sides and reduces to B+C=D. This proves that the exterior angle of a triangle is equal to the sum of the two remote interior angles!!!

Answer:

Please provide the polynomial to answer this question

Step-by-step explanation:

An expression will be said a polynomial if it contains variables like x, p , q, t etc etc.

They can be of any degree. like [tex]x^2[/tex] , [tex]y^3[/tex] , [tex]t^4[/tex] etc

The degree of a polynomial is the highest  exponent of the variable we have in the polynomial

Example : Degree of polynomial [tex]x^3-1 = 3[/tex]

If it do not have any variable , it is not called a polynomial because it basically gives us a constant

The given function violates both conditions for a polynomial, the correct answer is B. This is not a polynomial function because the variable powers are not all non-negative integers, and the coefficients are not constants.

To determine if the given function is a polynomial, we need to check two things:

The variable powers should be non-negative integers (whole numbers).

The coefficients of each term should be constants.

Let's analyze the function f(x)=√x+1 · (x+2)

Variable powers: The variable powers in the function are 1/2 and 1. The power 1/2 (square root) is not a non-negative integer, and thus violates the first condition for a polynomial.

Coefficients: The coefficients in the function are (1/2) and 1, which are not constants, but rather they involve variables. This also violates the second condition for a polynomial.

Since the given function violates both conditions for a polynomial, the correct answer is:

B. This is not a polynomial function because the variable powers are not all non-negative integers, and the coefficients are not constants.

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The complete question is:

Determine if the function is a polynomial function. If the function is a polynomial function, state the degree and the leading coefficient. If the function is not a polynomial, state why.

f(x)=√x+1 · (x+2)

A.This is not a polynomial function because there is no leading coefficient.

B. This is not a polynomial function because the variable powers are not all non-negative integers.

C. This is not a polynomial function because the factors are not all linear.

D. This is not a polynomial function because it is not written in the form f(x) = axⁿ + bxⁿ⁻¹ + ..... + rx² + sx + t.

Answer:

C(x)= 41x + 680

Step-by-step explanation:

If the fixed cost is 680, that will apply regardless of how many jackets the company makes for you. The number of jackets is unknown.  However, we know that the cost of producing a single jacket is 41, so we can represent that expression as 41x.  Putting those things together gives us a function of the cost:

C(x) = 41x + 680

The equation to determine the total cost encountered by Marty's Tee Shirt & Jacket Company in producing x jackets is C(x) = 680 + 41x.

To determine the total cost, C(x), encountered by Marty's Tee Shirt & Jacket Company in producing x jackets, we need to consider both the fixed costs and the variable costs. The fixed costs, which are $680, are incurred regardless of the number of jackets produced. The variable costs, which are $41 per jacket, increase with each additional jacket produced. So the equation to calculate the total cost is:

C(x) = fixed costs + (variable costs per jacket) * x

Substituting the given values, the equation becomes:

C(x) = 680 + 41x

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Based on the properties of a parallelogram, the missing angle measures are:

The opposite angles of a parallelogram are defined as congruent angles, while the adjacent angles in a parallelogram are supplementary.

Thus:

m∠U = m∠S = 70°

m∠R = 180 - 70 = 110°

m∠T = m∠R =110°

Therefore, based on the properties of a parallelogram, the missing angle measures are:

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The missing angle measures are:

A parallelogram's opposing angles are known as congruent angles, whilst its adjacent angles are known as supplementary angles.

So, by the property of parallelogram

m∠U = m∠S = 70°

m∠R = 180 - 70

m∠R = 110°

and, m∠T = m∠R =110°

Thus, by the properties of a parallelogram, the angle are:

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Answer: Option C

No; Jamie could not have won 11 games because [tex]2x - 5 \neq 30[/tex]

Step-by-step explanation:

Let's call x the number of games that Jamie has won

Let's call y the number of games that Imani has won

We know that Imani has won 5 more games than Jamie.

Then we can say that:

[tex]y= x - 5[/tex]

We know that the total number of games that Jamie and Imani have won together is 30.

So

[tex]x + y = 30[/tex]

We want to know if it is possible that [tex]x = 11[/tex].

Then we substitute the first equation in the second and get the following:

[tex]x + x - 5 =30\\2x - 5 = 30[/tex]

Now replace [tex]x = 11[/tex] in the equation and check if equality is met.

[tex]2 (11) - 5 = 30\\22 - 5 = 30\\17 \neq 30[/tex]

Equality is not met, then the correct answer is option C

Answer: is c (no Jamie could not have won 11 games because 2x-5=/30

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

Graphically: the graphs of a function and its inverse are symmetric with respect to the line y = x.

Algebraically: If functions f(x) and g(x) are inverses of each other, then the composition of f and g must equal x, and the composition of g and f must also equal x.

Two functions are inverse of each other:

An inverse function is defined as a function, which can reverse into another function.

For example,

[tex]f(x) = 3x - 2\\\\g(x) = \frac{x+2}{3}[/tex]

Checking if g(x) and f(x) are inverse of each other.

fog(x) = [tex]3(\frac{x+2}{3} )- 2 = x + 2 - 2 = x[/tex]

gof(x) = [tex]\frac{3x-2+2}{3} = x[/tex]

Since, fog(x) = gof(x) = x, it is algebraically verified that f(x) and g(x) are inverse of each other.

To prove that graphically, we plot the two functions.

As can be observed the two functions are symmetric to each other across the line y = x, thus, they are inverse of each other. (To check if the two functions are symmetric of each other, pick the graph of one function, for every point, interchange the x and y coordinates and plot them. The new graph will be of the inverse function.)

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Answer:

D x=1

Step-by-step explanation:

6^(3-x)=6^2

Since the bases are the same, the exponents have to be the same

3-x = 2

Subtract 3 from each side

3-x-3 = 2-3

-x = -1

Multiply each side by -1

x = 1

Answer: Option D

[tex]x=1[/tex]

Step-by-step explanation:

We have the following exponential equation

[tex]6^{3-x}=6^2[/tex]

We must solve the equation for the variable x

Note that the exponential expressions [tex]6^{3-x}[/tex] and [tex]6 ^ 2[/tex] have the same base: 6

So if [tex]6^{3-x}=6^2[/tex] this means that [tex]3-x = 2[/tex]

Then we have that:

[tex]3-x = 2[/tex]

[tex]x = 3-2\\x=1[/tex]

Answer:

  y = -x +5

Step-by-step explanation:

The 2-point form of the equation of a line is useful for this.

  y = (y2 -y1)/(x2 -x1)(x -x1) + y1 . . . 2-point form of equation for a line

  y = (-2 -6)/(7 -(-1))/(x -(-1)) +6 . . . . substitute the give points

  y = -8/8(x +1) +6 . . . . . . . . . . . . . . simplify a bit; next, simplify more

  y = -x +5

The equation of the line passing through the point s (-1, 6) and (7, -2) is y = -x + 5

The formula for calculating the equation of a line is expressed as y = mx + b where;

m is the slope of the line

b is the y-intercept

Given the coordinate points  (-1,6) and (7, -2)

Get the slope:

Slope = -2-6/7-(-1)

Slope = -8/8

Slope = - 1

Get the y-intercept:

-2 = -1(7) + b

-2 = -7 + b

b = -2 + 7

b = 5

Get the required equation:

Recall that y = mx + b

Substituting m = -1 and b = 5 into the equation:

y = -x + 5

Hence the equation of the line passing through the point s (-1, 6) and (7, -2) is y = -x + 5

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Answer:

  D)  Amplitude: 2; period: π; midline: y = 1

Step-by-step explanation:

The question is much more easily answered from the graph than from the description of the graph.

The amplitude is the extent of the peak above the midline (2), or half the peak-to-peak value (4/2=2). The midline is the line halfway between the peaks (1). The period is the horizontal distance between peaks of the same polarity (π).

Answer:

  4 m

Step-by-step explanation:

Use the formula for the area of a triangle. Fill in the given numbers and solve for the unknown.

  A = (1/2)bh

  48 m² = (1/2)(24 m)h . . . . . put in the given numbers

  (48 m²)/(12 m) = h = 4 m . . . . divide by the coefficient of h

The height of the triangle is 4 meters.

Answer:

Step-by-step explanation:

The given side is opposite the given acute angle in this right triangle, so the applicable relation is ...

  Sin(25°) = CB/AB

Solving for AB, we get ...

  AB = CB/sin(25°) ≈ 37.859

__

The relation involving the other leg of the triangle is ...

  Tan(25°) = CB/AC

Solving for AC, we get ...

  AC = CB/tan(25°) ≈ 34.312

__

Of course, the missing angle is the complement of angle A, so is 90-25 = 65 degrees.

Answer:

Surface area of the right prism =  156 square units

Step-by-step explanation:

Surface area of prism = area of 2 triangle + area of three rectangles

To find the area of triangles

Here base b = 4 units and height h = 3 units

Area of triangle = bh/2

 = (4 * 3)/2 = 6  square units

Area of 2 rectangles = 2 * 6 = 12 units

To find the area of rectangles

length of rectangle = 12 units,

Here 3 rectangles with 3 different width

width1 = √(4² + 3²) = 5 units

width2 = 4 units and width3 = 3 units

Area1 = Length * width1

 = 12 * 5 = 60 square units

Area1 = Length * width2

 = 12 * 4 = 48square units

Area1 = Length * width3

 = 12 * 3 = 36 square units

Total area of three rectangles = 60 + 48 + 36 = 144

To find the surface area of prism

Surface area = Area of triangles + area of rectangles

 = 12 + 144 = 156 square units

Answer:

Step-by-step explanation:

1. -2y+7 < 1

Add 2y-1:

  6 < 2y

Divide by 2:

  3 < y

__

2. 4y +3 < -5

Subtract 3:

  4y < -8

Divide by 4:

  y < -2

_____

These are graphed on the number line with open circles because y=-2 and y=3 are not part of the solution set.

Answer:

Step-by-step explanation:

[tex](1)\\\\-2y+7<1\qquad\text{subtract 7 from both sides}\\-2y+7-7<1-7\\-2y<-6\qquad\text{change the signs}\\2y>6\qquad\text{divide both sides by 2}\\\boxed{y>3}\\\\(2)\\\\4y+3<-5\qquad\text{subtract 3 from both sides}\\4y+3-3<-5-3\\4y<-8\qquad\text{divide both sides by 4}\\\boxed{y<-2}\\\\\text{From (1) and (2) we have:}\ y<-2\ or\ y>3[/tex]

[tex]<,\ >-\text{op}\text{en circle}\\\leq,\ \geq-\text{closed circle}[/tex]

Answer:

Option B After 14 years the car is worth $0

Step-by-step explanation:

we have

[tex]V=-1,385n+18,790[/tex]

where

V is the value of the cars

n is the number of years

Determine the n-intercept of the graph

we know that

The n-intercept is the value of n (number of years) when the value of V (value of the car) is equal to 0

so

For V=0

substitute and solve for n

[tex]0=-1,385n+18,790[/tex]

[tex]1,385n=18,790[/tex]

[tex]n=18,790/1,385[/tex]

[tex]n=14\ years[/tex]

That means

After 14 years the car is worth $0

Answer:

B

Step-by-step explanation:

Answer:

P: 20pi A: 400-100pi

[tex]\frac{3}{4} = log_{2}(\sqrt[4]{8} )\\-4 = log_{3} \frac{1}{81} \\-6= -3log_{5} 25\\\frac{1}{3} = log_{6} (\sqrt[3]{6} )[/tex]

Here's how you solve it!

[tex]log_{2} \sqrt[4]{8}[/tex]

Write it in exponential form

[tex]log_{2} (2 \frac{3}{4} )[/tex]

Then simplify

[tex]\frac{3}{4}[/tex]

[tex]log_{3} \frac{1}{81}[/tex]

Write in exponential form

[tex]log_{3} (3^{-4} )[/tex]

Simplify

-4

[tex]-3log_{5} 25[/tex]

Write in exponential form

[tex]-3log_{5} (5^{2} )[/tex]

Simplify

-3 * 2 = -6

-6

[tex]log_{6} \sqrt[3]{6}[/tex]

Write in exponential form

[tex]log_{6} (6\frac{1}{3} )[/tex]

Simplify

[tex]\frac{1}{3}[/tex]

Hope this helps! :3

The problem involves simplifying mathematical expressions, through steps as prescribed by BIDMAS/PEDMAS rules. Start by addressing anything within parentheses, follow through with multiplication or division, and finally handle addition or subtraction.

This question involves the process of mathematical simplification of expressions. To solve this, you will first need to perform any calculations within the parentheses, then handle any multiplication or division from left to right, lastly address any addition or subtraction, also from left to right (also known as the order of operations or BIDMAS/PEDMAS). For example, if you have an expression like '2(3+4)': First, process the operation within the parentheses, in this case, it's a sum so you have '2*7', resulting in '14'. This is considered the simplified version of your expression.

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Answer:

The radius is: 1

Step-by-step explanation:

The equation of a circle in center-radius form is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

Where the center is at the point (h, k) and the radius is "r".

Given the equation of the circle:

[tex]x^2+y^2=1[/tex]

You can identify that:

[tex]r^2=1[/tex]

Then, solving for "r", you get that the radius of the circle is:

[tex]r=\sqrt{1}\\\\r=1[/tex]

Answer:

Radius = 1

Step-by-step explanation:

It is given that equation of a circle is x² + y² = 1

Points to remember

Equation of a circle with center(h, k) and radius r is given by,

(x - h)²  + (y - k)² = r²

To find the radius of circle

Compare the two equations

x² + y² = 1  and (x - h)²  + (y - k)² = r²

we get the center is (0, 0)

therefore we can write

r² = 1

r = 1

Therefore radius r = 1

Answer:

(x − 3)² + (y − 4)² = 5

Step-by-step explanation:

The equation of a circle is:

(x − h)² + (y − k)² = r²

where (h, k) is the center and r is the radius.

First use the distance formula to find the radius:

d² = (x₂ − x₁)² + (y₂ − y₁)²

r² = (2 − 3)² + (6 − 4)²

r² = 1 + 4

r² = 5

Given that (h, k) = (3, 4):

(x − 3)² + (y − 4)² = 5

Answer:

Step-by-step explanation:

Inserting the coordinates of the center (3, 4) into the standard equation of a circle with center at (h, k) and radius r, we get:

(x - 3)^2 + (y - 4)^2 = r^2

Next, we substitute 2 for x, 6 for y and solve the resulting equation for r^2:

(2 - 3)^2 + (6 - 4)^2 = r^2, or

      1      +       4       =  r^2.

Thus, the radius is √5.  Subbing this result into the equation found above, (x - 3)^2 + (y - 4)^2 = r^2, we get:

(x - 3)^2 + (y - 4)^2 = (√5)^2 = 5, which matches the last of the four possible answer choices.

Answer:

The vertex is the point (-6,-34)

Step-by-step explanation:

we know that

The equation of a vertical parabola into 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]y=x^{2}+12x+2[/tex]

Convert in vertex form

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

[tex]y-2=x^{2}+12x[/tex]

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

[tex]y-2+36=x^{2}+12x+36[/tex]

[tex]y+34=x^{2}+12x+36[/tex]

Rewrite as perfect squares

[tex]y+34=(x+6)^{2}[/tex]

[tex]y=(x+6)^{2}-34[/tex]

The vertex is the point (-6,-34)