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The x-coordinates where the line y = 2x + 3 intersects the circle is equal to -2 and -4.

Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²  

Where:

From the information provided, we have the following system of equations:

(x - 3)² + (y + 6)² = 50      ......equation 1.

y = 2x + 3              .............equation 2.

In order to determine the x-coordinates at the point of intersection, we would substitute the equation 2 into equation 1:

(x - 3)² + (2x + 3 + 6)² = 50

(x - 3)² + (2x + 9)² = 50

x² - 6x + 9 + 4x² + 36x + 81 - 50 = 0

5x² + 30x + 40 = 0

x² + 6x + 8 = 0

x² + 6x + 9 = 1

(x + 3)² = 1

Taking the square of both sides of the equation, we have;

x + 3 = ±1

x = ±1 - 3

x = -2 and -4

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Answer:

0.63 kg

Step-by-step explanation:

KE = 1/2mv²

solve for m:

m = 2(KE)/v²

m = 2(140J) / (21m/s)²

m = 280J / 441 = 0.63 kg

The amount needed to be deposited in an account in order to have $5000 in 27 month is $4997.74.

Simple interest is based on the principal amount of a loan or the first deposit in a savings account.

To calculate the amount that needed to be deposited, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the amount needed to be deposited is $4997.74.

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The interest rate, to the nearest hundredth of a percent, which would be required in order for Grace to end up with $190 is 2.38%.

Mathematically, compound interest can be calculated by using this formula:

A(t) = P(1 + r)^{t}

Where:

Substituting the given parameters into the compound interest formula, we have;

190 = 140(1 + r)^{13}

190/140 = (1 + r)^{13}

1.3571 = (1 + r)^{13}

Taking the 13th root of both sides of the equation, we have:

[tex]\sqrt[13]{1.3571} = \sqrt[13]{(1 + r )^{13} }[/tex]

1.0238 = 1 + r

r = 1.02378 - 1

Interest rate, r = 0.0238

Interest rate, r = 2.38%

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Answer:

C. The solution to the system is (-4,3) where the 2 lines MEET

Step-by-step explanation:

D. The system has no solution only if the lines are PARALLEL

A. The system has infinite solutions only if both equations give ONE and the same line

minute math

Here, in the given equation it is true because two different sign, and the result is negative.

To multiply or divide signed integers, always multiply or divide the absolute values and use these rules to determine the sign of the answer.

When multiply two integers with the same signs, the result is always positive. Just multiply the absolute values and make the answer positive.

When multiply two integers with the different signs, the result is negative.

Here in this equation,

20 ÷ (-5)

= - 4

So, it is true.

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The region bounded by the equations has a precise area of 21.33 units.

A boundary or some set of constraints are imposed on a bounded region. To put it another way, the size of a bounded shape cannot be infinite. Anything that is bound must be able to be contained within certain parameters.

x2 = 4y2 from equation (1), y3 = 4y2 y3 - 4y2 = 0 y2(y - 4) = 0 y2 = 0 or y-4 = 0 or y = 4 These will be our integration bounds. We have given that x2 = y3 --------- (1) and x = 2y --------- (2).

Therefore, we will express area as A = [- 4]04 = [- 4 - 0] = 64 - 85.33 A = -21.33, or A = 21.33. This indicates that the area of the bounded region is 21.33 units.

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The rate of change (slope) of the distance in feet below sea level with respect to time that the submarine traveled is 11 feet .

Slope and rate of change are the same thing. The difference is just semantics of the situation.

Typically we use the word “slope” when we are referring to a graph, and we use the phrase “rate of change” when we are referring to a table or a situation in real life.

But that’s not absolute. We can count the slope on a graph, but there’s also a “slope formula” for use when you have two coordinate points or two data points — even though you are not creating a graph.

It is the derivative of of the slope, or the second derivative of the original function.

For example, if you plot position verses time, the slope between two points(change in position per change in time) is the velocity. This is the first derivative.

Take any two points ( 0 , 380 ) and ( 15 , 545 )

slope m = 545 - 380 / 15 - 0

= 165 / 15

= 33 / 3

= 11 / 1

= 11 feet

Hence the slope m is 11 feet .

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So, the maximum volume of the cone is approximately 1047.19 cubic inches.

The volume of a cone is given by the formula V = (1/3) * pi * r^2 * h, where r is the radius of the base and h is the height of the cone. In this case, the height of the cone is the radius of the circle, which is 10 inches, and the radius of the base is half the length of the circumference of the sector, which is (theta/360) * 2 * pi * 10 inches.

We want to find the value of theta that maximizes the volume of the cone. We can do this by taking the derivative of the volume formula with respect to theta, setting it equal to 0, and solving for theta.

V = (1/3) * pi * r^2 * h

= (1/3) * pi * ((theta/360) * 2 * pi * 10)^2 * 10

= (1/3) * pi * (theta/36)^2 * 100

dV/dtheta = (2/3) * pi * (theta/36) * (100/36)

= (2/3) * pi * theta/36

Setting dV/dtheta = 0 and solving for theta, we get theta = 0.

Since the magnitude of theta must be positive, the maximum volume occurs when theta = 0, which means that the entire circle is used to form the cone. The maximum volume of the cone is then

V = (1/3) * pi * r^2 * h

= (1/3) * pi * (10)^2 * 10

= (1/3) * pi * 100 * 10

= (1/3) * pi * 1000

= approximately 1047.19 cubic inches

So, the maximum volume of the cone is approximately 1047.19 cubic inches.

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We want to find the value of theta that maximizes the volume of the cone. We can do this by taking the derivative of the volume formula with respect to theta, setting it equal to 0, and solving for theta.

V = (1/3) * pi * r^2 * h

= (1/3) * pi * ((theta/360) * 2 * pi * 10)^2 * 10

= (1/3) * pi * (theta/36)^2 * 100

dV/dtheta = (2/3) * pi * (theta/36) * (100/36)

= (2/3) * pi * theta/36

Setting dV/dtheta = 0 and solving for theta, we get theta = 0.

Since the magnitude of theta must be positive, the maximum volume occurs when theta = 0, which means that the entire circle is used to form the cone. The maximum volume of the cone is then

V = (1/3) * pi * r^2 * h

= (1/3) * pi * (10)^2 * 10

= (1/3) * pi * 100 * 10

= (1/3) * pi * 1000

= approximately 1047.19 cubic inches

So, the maximum volume of the cone is approximately 1047.19 cubic inches.

Answer: 10 pieces

Step-by-step explanation:

Answer:

10 ropes

Step-by-step explanation:

5 divided by 1/2 is 10

TU with endpoints T(1,2) and U(4,6) and its images after the composition are T' = (-1, -1) and U' = (2,3) and T'' = (-3, 7) and U'' = (0,11).

Tradition holds that the reflection of point P across the line, denoted by the word P', is the "image" of point P. (pronounced "P prime").

Given, line TU with endpoints T(1,2) and U(4,6).

To find the translation:

In 1:

Translate TU 2 units left and 3 units down.

That means,

T' = (-1, -1) and U' = (2,3)

In 2:

Translate TU 4 units left and 5 units up.

That means,

T'' = (-3, 7) and U'' = (0,11)

Therefore, the image points are T' = (-1, -1) and U' = (2,3) and T'' = (-3, 7) and U'' = (0,11)

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Yes, in a group of 2,000 people, at least 5 must have the same birthday.

This is due to the Pigeonhole Principle, which states that if there are more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon.

In this case, there are 2,000 people (the pigeons) and 365 possible birthdays (the pigeonholes). This means that, since 2,000 is greater than 365, at least 5 people must share the same birthday.

The Pigeonhole Principle states that if you have more items than boxes, then at least one box must contain more than one item. It can also be used to prove that certain problems have no solution.

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Complete Question:

In a group of 2,000 people, must at least 5 have the same birthday? Why?  Let X be the set of 2000 people (the pigeons) and Y the set of all possible birthdays (the pigeonholes). Define a function B: X - Y by specifying th B(x) = x's birthday. Now 2,000 > 4.366 = 1,464, and so by the generalized pigeonhole principle, there must be some birthday y such that B-1(y) has --Select- 4 + 1 = 5 elements. Hence at -Select- 5 people must share the same birthday.

Answer:

  117.79 m

Step-by-step explanation:

You have an observer 337 m from a skyscraper who measures the angle of elevation from a point 1.75 m above the ground to be 19°. You want to know the height of the skyscraper.

The tangent relation tells you ...

  Tan = Opposite/Adjacent

Solving for the side opposite the angle, we get ...

  Opposite = Adjacent · Tan

In this scenario, the height of the building above the eye height is ...

  height above eyes = (337 m)(tan 19°) = 116.038 m

Then the height of the building is ...

  skyscraper height = eye height + height above eyes

  skyscraper height = 1.75 m + 116.038 m = 117.788 m

The height of the skyscraper is about 117.79 meters.

The statement is true. Functions that are concave upward are always increasing.

What is Concave Upward Function?

Where the derivative f′ is growing, a function f is concave up (or upwards). This is equivalent to the derivative of f′, which is represented by the notation f′′f, start superscript, prime, end superscript, positive.

Explanation:

If a function is concave upward on an interval, it must be increasing on the interval. Given statement is true. Functions that are concave upward are always increasing.

A function is said to be concave upward on an interval if f″(x) > 0 at each point in the interval and concave downward on an interval if f″(x) < 0 at each point in the interval.

At interval if function is increasing then functions that are concave upward are always increasing.

Hence, The statement is true. Functions that are concave upward are always increasing.

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Answer:

  (c)  y = -1

Step-by-step explanation:

You want the equation of the horizontal line through (0, -1).

A horizontal line has the same y-value for every x-value. Its equation is ...

   y = constant

If you want the line to go through a point with a y-coordinate of -1, then the constant must be -1.

  y = -1 . . . . . . . horizontal line through (0, -1)

The solution to the system of equations, y = 4x - 9 and y = x - 3, is: (2, -1)

The coordinates of the ordered pair that will make both equations true is the solution to the system.

Given the linear equations as:

y = 4x - 9 --> equation 1

y = x - 3 --> equation 2

Make both linear equations equal to each other and find the value of x. Thus:

4x - 9 = x - 3

Combine like terms

4x - x = 9 - 3

3x = 6

Divide both sides by 3

3x/3 = 6/3

x = 2

To find the value of y, substitute x = 2 into equation 1:

y = 4(2) - 9

y = 8 - 9

y = -1

The solution is, (2, -1).

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Answer:

37.237%

Step-by-step explanation:

Use the Formula I = P x R x T

P = Principal amount (the beginning balance).

R = Interest rate (usually per year, expressed as a decimal).

T = Number of time periods (generally one-year time periods).

Plug in the values

I = 5305 x R x 20

Solve for R by dividing 20 by 5305

I=5305 x R x 20

20 / 5305 = 0.0037

Answer: 10.56 or 10.6 %

Step-by-step explanation:

5305 x x^20 = 39534

39534/5305 = x^20

20√39534/5305 = x

x = 1.1056

1.1056 x 100 = 110.56

110.56 - 100 = 10.56 or 10.6

Answer:

Step-by-step explanation:

You want to solve the given system of equations by eliminating the y-term. You also want to know what constants are used in the process.

The y-term can be eliminated from these equations by combining them in such a way as to may the coefficient of y be zero. This can be done an infinite number of ways.

One way that works reasonably well is to identify the coefficients of y, and multiply each equation by the y-coefficient in the other equation. The resulting equations can be subtracted one from the other to eliminate the y-terms, which now have identical coefficients. You can choose the equation with the smaller x-coefficient to subtract from the other one.

The y-term coefficients are 2 and 3.

Multiply the first equation by 3, and the second by 2.

  3 × (2x +2y) = 3 × 7   ⇒   6x +6y = 21

  2 × (6x +3y) = 2 × (-2)   ⇒   12x +6y = -4

The x-coefficients are 6 and 12. We choose to subtract the first equation (with x-coefficient 6) from the second equation:

  (12x +6y) -(6x +6y) = (-4) -(21)

  6x = -25 . . . . . . . . simplified

  x = -25/6 = -4 1/6 . . . . . divide by 6

Substituting for x in the first equation, we have ...

  2(-25/6) +2y = 7

  2y = 7 +25/3 . . . . . add 25/3

  2y = 46/3 . . . . . . . .combine terms

  y = 23/3 = 7 2/3 . . . . divide by 2

The solution to the equations is (x, y) = (-4 1/6, 7 2/3).

Since these numbers are not integers, we choose to check them in the original equations. We used the first equation to find y, so we'll use the second equation for checking.

   6(-4 1/6) +3(7 2/3) = -25 +23 = -2 . . . . . . as required

__

Additional comment

If you solve these by addition, rather than subtraction, you want to choose multipliers that result in opposite coefficients, so they add to zero. Essentially, you use the opposite coefficients, as described above, but you negate one of them.

Above, we chose the subtraction in a way that resulted in the x-coefficient being positive. If you arbitrarily choose the signs of the multipliers (always negating the second one, for example), the combined equations may make the x-coefficient negative. That works, too, but may require more mental effort to deal with the minus sign.

Of course, you can use the x-coefficients and eliminate the x-terms.

Or, you can use a single multiplier that corresponds to the ratio of the coefficients. For example the ratio of the 2nd y-coefficient to the first one is 3/2. Multiplying the first equation by this will give the y-term a coefficient of 3, matching the y-coefficient in the 2nd equation. Then the subtraction can proceed as already described.

  (6x +3y) -3/2(2x +2y) = (-2) -3/2(7)

  3x = -25/2 . . . . . simplified; y is gone.

Based on the definition of the angles of a straight line, the measure of the smallest angle is: are: 40°.

The sum of all the angles on a straight line is equal to 180 degrees.

To find the size of the smallest angle, find the value of a by creating the equation below:

(2a + 62) + (54 - a) + (5a - 20) = 180

Open the parentheses:

2a + 62 + 54 - a + 5a - 20 = 180

Combine like terms

6a + 96 = 180

6a = 180 - 96

6a = 84

6a/6 = 84/6

a = 14

Find the measure of each angles:

2a + 62 = 2(14) + 62 = 90°

54 - a = 54 - 14 = 40°

5a - 20 = 5(14) - 20 = 50°

The size of the smallest angle is 40°.

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Answer:

91.4%

Step-by-step explanation:

First do: 32,000/35,000 = X/100

Then multiply 32,000 by 100 which is 3,200,000

Then divide 3,200,000 by 35,000

You will get 91.42857142857143

The fraction 1¹/₂ + ⁵/₇ = 2³/₁₄

Fractions are numbers written in the form a/b where a and b are integers and b ≠ 0.

Since we have the fractions 1¹/₂ and  ⁵/₇ and we want to compute the sum

1¹/₂ + ⁵/₇, we re-write the first fraction as an improper fraction.

So, 1¹/₂ = ³/₂

Now, re-writting the equation, we have

³/₂ + ⁵/₇

To find the sum, wetake the L.C.M of both numbers which 2 × 7 = 14.

So, we make both denominators equal to the L.C.M.

So,  

³/₂ × ⁷/₇ + ⁵/₇ × ²/₂ = ²¹/₁₄ + ¹⁰/₁₄

= (21 + 10)/14

= 31/14

= (28 + 3)/14

= 28/14 + 3/14

= 2 + 3/14

= 2³/₁₄

So, 1¹/₂ + ⁵/₇ = 2³/₁₄

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Reagan will grow 1/2 inch than her brother if Reagan grew 9/10 of an inch and her brother grew 2/5 of an inch by using ratio and proportion concept,

When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. Two ratios are set to be equal in an equation called a proportion. For instance, if there is 1 boy and 3 girls, the ratio would be written as 1: 3 (there are 3 girls for every boy), meaning that there are 1 in 4 boys and 3 in 4 girls.

A: b a/b is the ratio formula, which may be used to calculate any two values. A:b::c:da:b::c:da, on the other hand, is how the percentage formula is written.

Given,

The height grown by Reagan=9/10 inch

The height grown by Reagan brother=2/5 inch

(9/10)-(2/5)

=1/2 inch

Therefore, Reagan will grow 1/2 inch than her brother.

Therefore,

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Answer:

4/15

Step-by-step explanation:

1/3 x 5/5 = 5/15, 2/5 x3/3 = 6/15

5/15+6/15= 11/15

15/15- 11/15= 4/15

so 4/15 people don't have neither blue nor brown eyes.

Answer:

x is equal to 87

Step-by-step explanation:

42 +51=93

93-180=x

x=87

Answer:

0.27563735723563.

Step-by-step explanation:

74 is an acute angle since it is less than 90° cos (74) = 0.27563735723563. Write cos (74) in terms of sin Since 74° is less than 90, we can express this in terms of a cofunction.

The Option that can be proven is:

Definitions, assertions, and methods are linked in a proper fashion to get the desired outcome in mathematical proof.

This procedure helps pupils understand the rationale behind the statement. This is also true of counterexamples and their important significance in mathematics.

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Answer:

x = -0.8.

Step-by-step explanation:

To solve for x in the equation g(x) = 10, we need to find the value of x that makes g(x) equal to 10. Since we are given that g(x) = 2/x+1, we can substitute this expression for g(x) in the equation g(x) = 10 to get:

2/x+1 = 10

Next, we can multiply both sides of the equation by x+1 to get rid of the fraction on the left side:

2 = 10 * (x+1)

This simplifies to 2 = 10x + 10, which we can rearrange to get 2 - 10 = 10x. Subtracting 10 from both sides gives us -8 = 10x. Finally, dividing both sides by 10 gives us the solution: x = -0.8.

Therefore, the value of x that makes g(x) equal to 10 is x = -0.8.

Answer:

Below

Step-by-step explanation:

Primes under 25      2 3 5 7 11 13 17 19 23

   5 7 13

    7  7   11    ( can we use numbers twice?)

         you can look for more....but that may be it ....