Convert the given polar
coordinates into rectangular
coordinates.
(4,4)=([?],[√

Eliminate x by adding the two equations, yielding [tex]y = 6[/tex]. Then, substitute y into either equation to solve for x, obtaining [tex]x = -3[/tex]. The solution is [tex](-3,6)[/tex].

An equation is a mathematical statement that uses symbols, numbers, and variables to show that two expressions are equal, typically with an equal sign between them.

A variable is a quantity or symbol that can take on different values in a mathematical expression, equation, or formula, typically represented by a letter.

To eliminate a variable in a system of equations, we want to find a way to add or subtract the two equations so that one of the variables is eliminated.

In this case, we can eliminate the variable x by adding the two equations

[tex]x- 7y = -45[/tex]

[tex](-x +8y = 51)[/tex]

[tex]y = 6[/tex]

Now that we have found the value of y, we can substitute it into either of the original equations to solve for x. Let's use the first equation

[tex]x-7y = -45\\x- 7(6) = -45\\x = -45+42\\x = -3[/tex]

Therefore the solution to the system of equations is [tex]x= -3[/tex] and[tex]y= 6[/tex]

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the solution to the system of equations is (x, y) = (-3, 6).

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

To eliminate the variable x, we can add the two equations together. This will result in the x variable being eliminated, leaving us with an equation in terms of y:

(x - 7y) + (-x + 8y) = -45 + 51

Simplifying and solving for y, we get:

y = 6

Now that we know the value of y, we can substitute it into one of the original equations to solve for x. Using the first equation:

x - 7(6) = -45

Simplifying and solving for x, we get:

x = -3

Therefore, the solution to the system of equations is (x, y) = (-3, 6).

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The line(s) or plane(s) that contain point N and appear to fit the description are as follows;

Line perpendicular to QR is NR.

Line parallel to QR is PN.

Line(s) skew to JN.

Plane parallel to plane LMQ is JNP.

All the pairs of angles have been identified below.

The values of x and y are shown below.

In this exercise, all of the various pairs of angles should be identified as follows;

Consecutive interior = ∠3 and ∠5.

Consecutive interior = ∠4 and ∠6.

Alternate interior = ∠3 and ∠6.

Alternate interior = ∠4 and ∠5.

Alternate exterior = ∠1 and ∠8.

Alternate exterior = ∠2 and ∠7.

Corresponding = ∠1 and ∠5.

Corresponding = ∠2 and ∠6.

Corresponding = ∠3 and ∠7.

Corresponding = ∠4 and ∠8.

Next, we would determine the values of x and y as follows;

x + 35 = 180 (sum of angles on a line)

x = 180 - 35

x = 145°

y = 35 (corresponding angles theorem).

y + 48 = 180

y = 180 - 48

y = 132°

5x - 17 = 48 (vertical angles theorem).

5x = 65

x = 13°.

2x + 58 = 180 (sum of angles on a line)

2x = 238

x = 119°.

2y = 58 (corresponding angles theorem).

y = 29°.

5y - 21 = (180 - 116)

5y = 21 + 64

y = 85/5

y = 17

6x + 32 = 116

6x = 116 - 32

x = 84/6

x = 14

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The population size of the fish species after 5 years is approximately 99.

The population size of the fish species after t years is given by the exponential function P(t)=510(0.72)^t. To find the population size, we simply need to substitute the given value of t in the equation.

For example, if we want to find the population size after 5 years, we substitute t=5 in the equation:

P(5) = 510(0.72)^5

P(5) = 510*0.1934917632

P(5) = 98.680799232

P(5) ≈ 99.

Therefore, the population size of the fish species after 5 years is approximately 99.

We can determine whether the population is growing or decaying by examining the value of the base of the exponential function, which is 0.72 in this case. Since the base is less than 1, we know that the exponential function represents exponential decay. This means that the population of the fish species in the lake is decreasing over time, and the rate of decrease is determined by the value of the base. In this case, the population is decreasing by a factor of 0.72 each year.

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Answer:

C.0.75

Step-by-step explanation:

the number of occurrence is 15 and the number of simulations is 20 so

P= 15/20

.75

Answer:

First image.

Step-by-step explanation:

Second image.

The volume of solid B is about 7π cubic meters, which is approximately 21.99 cubic meters when rounded to the nearest thousandth.

The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. Since solids A and B are similar, they have the same shape, but different sizes.

Let V₁ be the volume of solid A, and V₂ be the volume of solid B. The scale factor k from solid A to solid B is 1/4, which means that the dimensions of solid B are 1/4 of the dimensions of solid A.

We can find the radius and height of solid B by multiplying the radius and height of solid A by 1/4. Therefore, we have:

V₂ = π(r/4)²(h/4) = (π/16)rh²

We are given that V₁ = 112π cubic meters, so we can solve for rh²:

112π = πr²h

rh² = 112

Substituting into the formula for V₂, we get:

V₂ = (π/16)rh² = (π/16)(112) = 7π

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The value of the expression is 17/8.

Given is an expression, 7/8 - (-2+3/4) = ( ____+____) + 7/8, we need to solve it,

7/8-(-2+3/4)

= 7/8-(-8+3)/4

= 7/8 + 5/4

= 7+10 /8

= 17/8

Hence, the value of the expression is 17/8.

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Answer:

H = 45 ½ ÷ 6 ½

Step-by-step explanation:

The formula  for the area of the base of the box is L * W.

The formula for the volume of the box is L * W * H

Therefore dividing 45 ½ (volume of box) by 6 ½ (area of base) will give you the height of the box

The binary representation of the number 77 ten is 1001101 two . This can be found by repeatedly dividing 77 by 2 and writing down the remainders in reverse order.

Binary representation is a system of representing numbers using only two digits, usually 0 and 1. It is used extensively in digital electronics and computer programming.

The remainder is the amount left over after dividing one number by another. It represents the part of the dividend that could not be evenly divided by the divisor.

According to the given information:

To convert the number 77 ten to base two, we need to find the binary representation of this number.

One way to do this is to repeatedly divide the number by 2 and keep track of the remainders. We continue dividing until the quotient is 0. Then, we read the remainders in reverse order to get the binary representation.

Here's how the calculation works:

Reading the remainders in reverse order gives us 1001101, which is the binary representation of 77 ten. Therefore, 77 ten = 1001101 two .

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Craig should make approximately 36 shirts to maximize his earnings for the week.

The maximum value of x for a quadratic equation, ax² + bx + c is given by the formula:

x (max) = -b/2a

Since the weekly income can be modeled by the function p(x)= −2x² + 145x.

In this case a = -2 and b = 145. Thus,
x (max) = -145/2(-2)

           =  145/4

           =  36.25

Thus, Craig should make approximately 36 shirts to maximize his earnings for the week

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Answer: x = 2 and x = -2.

Step-by-step explanation:

The solutions to the equation 9x^2 = 36 can be found by first dividing both sides by 9, giving x^2 = 4. Then, taking the square root of both sides gives x = ±2. Therefore, the solutions are x = 2 and x = -2.

Answer:

Step-by-step explanation:

9x^2 = 36 | :9

x^2 = 4

x=+-2

Answer:

(x-3)^2+(y-2)^2=16

Step-by-step explanation:

The equation of a circle in standard form is (x-h)^2+(y-k)^2=r^2

So, the center is (3,2), so you have to input the opposite value.

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

simplify:
(x-3)^2+(y-2)^2=16

Answer:

2(5)(5) + 4(5)(10) = 50 + 200 =

250 square centimeters

The approximate volume of the cooking pot will be;  2009.6 cubic inches.

Since volume of the cylinder is the product of the height, pie, and square of the radius.

The volume of the cylinder = [tex]\pi r^{2} h[/tex]

We know that the volume of the cylinder is  [tex]\pi r^{2} h[/tex]

Here we are given that Trevor is making soup in a cylindrical cooking pot that has a diameter of 10 inches and a height of 8 inches.

h=10 in, and r= 8 in, so

[tex]\begin{gathered} V=(3.14)(10 in)(8 in)^2 \\ V= 2009.6 in^3 \end{gathered}[/tex]

Then, the pot can hold 2009.6 cubic inches

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The retailer would pay $1,339.20 for 30 dozen work gloves.

One dozen is equal to 12, so 30 dozen would be equal to 360 gloves.

The wholesaler's list price for one dozen gloves is $62.

The discount given by the wholesaler is 28%

The retailer pays 100% - 28% = 72% of the list price.

The price the retailer pays for one dozen gloves is:

$62 x 0.72 = $44.64

Therefore, the price the retailer pays for 30 dozen gloves is:

$44.64 x 30 = $1,339.20

So the retailer would pay $1,339.20 for 30 dozen work gloves.

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The solution of Circle and angle problem is the area of the Pac-Man, to the nearest tenth mm" is 131.8 mm²

A circle is a geometric shape that is defined as the set of all points in a plane that are equidistant from a fixed point called the center.

An angle is a measure of the amount of turn between two lines that share a common endpoint, called the vertex of the angle.

To find the area of the Pac-Man, we need to find the area of the sector that represents its mouth and subtract the area of the triangle formed by the two radii and the chord of the sector.

First, we need to find the length of the arc that represents the mouth of Pac-Man. The formula for the length of an arc is:

L = (θ/360) x 2πr

Where L is the length of the arc, θ is the central angle in degrees, r is the radius of the circle, and π is approximately 3.14.

Plugging in the values we have:

L = (60/360) x 2π(13)

L = 4.29 mm

Next, we can find the area of the sector that represents the mouth of Pac-Man. The formula for the area of a sector is:

A = (θ/360) x πr²

Where A is the area of the sector, θ is the central angle in degrees, and r is the radius of the circle.

Plugging in the values we have:

A = (60/360) x π(13)²

A = 141.37 mm^2

Finally, we need to find the area of the triangle formed by the two radii and the chord of the sector. We can use the formula for the area of a triangle:

A = (1/2) x base x height

The base of the triangle is the chord of the sector, which is equal to twice the radius multiplied by sin(θ/2):

base = 2r x sin(θ/2)

base = 2(13) x sin(30)

base = 13 mm

The height of the triangle is equal to half the length of the chord times cos(θ/2):

height = (1/2) x (L/2) x cos(θ/2)

height = (1/2) x (4.29/2) x cos(30)

height = 1.47 mm

Plugging in the values we have:

A = (1/2) x 13 x 1.47

A = 9.53 mm²

Therefore, the area of the Pac-Man (sector minus triangle) is approximately:

A = 141.37 - 9.53

A = 131.84 mm²

Rounded to the nearest tenth, the area of the Pac-Man is 131.8 mm²

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By z-test the test static is 1.25.

What is z-test?

It is a statistical test to determine whether two population means are different at the time when the variances are known and the sample size is large. Also it is a hypothesis test in which the z-statistic maintains a normal distribution.

A random sample of 100 people was taken. Eighty-five of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 80%.

So from the given information we have,

sample size (n)= 100

sample proportion ( p₁) = 0.85 [ 85 of the people in the sample favored  candidate A]

So, the null hypothesis ,

H₀ : p = 0.80

The alternative hypothesis ,

Hₐ : p > 0.80

Now the test static can be determined by the formula of z-test

[tex]z= \frac{p_{1} - p }{\sqrt{\frac{p(1-p)}{n} } }[/tex]

[tex]z= \frac{0.85 - 0.80 }{\sqrt{\frac{0.80(1-0.80)}{100} } }[/tex]

[tex]z= \frac{0.05}{\sqrt{\frac{0.16}{100} } }[/tex]

z = (0.05× 10)/0.4

z= 1.25

Hence , by z-test the test static is 1.25.

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The unit price for a piece of cheese is $0.11 per pound.

To find the unit price, we need to divide the total cost by the total weight. In this case, we have 1.24 pounds of cheese that costs $11.25.

So, we can set up a proportion

1.24 pounds / $11.25 = x pounds / $1

To solve for x, we can cross-multiply

1.24 pounds * $1 = $11.25 * x pounds

1.24 = $11.25 * x

x = 1.24 / $11.25

x = 0.11

So, the unit price is $0.11 per pound.

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Answer:

1/200×60/360=1/6÷200

Answer:

Step-by-step explanation:

You want the measures of x and ∠ECB in rectangle ABCD with center point E and AE=3x+6, BD=5x+19, ∠EBA=25°.

The diagonals of a rectangle are congruent and cross at their midponts. This means the triangles they form are all isosceles.

The value of x can be found by relating the length of a half-diagonal to the length of the whole diagonal.

  2·AE = BD

  2(3x +6) = 5x +19 . . . . . . . substitute given lengths

  6x +12 = 5x +19 . . . . . eliminate parentheses

  x = 7 . . . . . . . . . . . subtract 5x+12

The value of x is 7.

Angle EBC is the complement of angle EBA, so its measure is ...

  ∠EBC = 90° -∠EBA

  ∠EBC = 90° -25° = 65°

Angle ECB is the other base angle of isosceles triangle BCE, so has the same measure as ∠EBC.

  ∠ECB = 65°

__

Additional comment

You know the corner angles of a rectangle are 90°, which is what makes angles EBA and EBC complementary.

With x = 7, AE = 27 and BD = 54. The full diagonal is double the length of the half-diagonal, as you expect.

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The probability of drawing a green marble for Carter increased from 0.357 to 0.385 after Ginny drew her two red marbles.

The probability of drawing a green marble for Carter did change after Ginny drew her two red marbles. This is because the total number of marbles left in the bag has decreased, which affects the probability of drawing a green marble.

Before Ginny drew her marbles, the probability of drawing a green marble for Carter was

P(Carter draws green) = 10/(18+10)

= 10/28

Divide the numbers

= 0.357

After Ginny drew her two red marbles, there are now 16 red marbles and 10 green marbles left in the bag. So the probability of drawing a green marble for Carter on his turn is

P(Carter draws green) = 10/(16+10) = 10/26 = 0.385

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The statement is true: If x and y are linearly independent, and if z is in Span {x, y}, then {x, y, z} is linearly dependent.

The statement is true.
Let's first understand the terms used:
Linearly independent:

A set of vectors is linearly independent if none of them can be expressed as a linear combination of the other vectors. In other words, no vector in the set can be written as a sum of scalar multiples of the other vectors.
Span:

The span of a set of vectors is the set of all linear combinations of those vectors.

In this case, Span[tex]{x, y}[/tex] is the set of all vectors that can be formed by adding scalar multiples of x and y.
Now, let's consider the given statement:
If x and y are linearly independent, it means that neither x nor y can be expressed as a linear combination of the other. However, it is given that z is in the Span[tex]{x, y}.[/tex]

This means that z can be expressed as a linear combination of x and y:
[tex]z = ax + by[/tex], where a and b are scalar constants.
Let's analyze the set[tex]{x, y, z}[/tex]. We know that z can be expressed as a linear combination of x and y, as shown above. This implies that the set [tex]{x, y, z}[/tex]is linearly dependent, because one vector (z) can be expressed as a linear combination of the others [tex](x and y)[/tex].

Thus, the statement is true: If x and y are linearly independent, and if z is in Span[tex]{x, y}[/tex], then[tex]{x, y, z}[/tex] is linearly dependent.

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Step-by-step explanation:

I don't know if so what we do this question but I kind of wish I can be with triangle don't ever stop and never ever disturb you

The lengths of all four sides of parallelogram ABCD:

AB = 15 cm, BC = 33 cm, CD = 15 cm and AD = 33 cm

Consider a parallelogram ABCD

Let's assume that x represents the length of sides AD and BC

y be the length of sides AB and CD

We know that the formula for the perimeter of parallelogram is

P = 2(length + width)

Here,  AD is 3 cm more than twice AB

So we get an expression,

AD = 3 + 2(AB)

AD = 3 + 2y

x  = 3 + 2y

USing above formula of perimeter, the perimeter of parallelogram ABCD would be,

P = 2(x + y)

96 = 2(3 + 2y + y)

48 = 3 + 3y

45 = 3y

y = 15 cm

And x = 3 + 2(15)

x = 33 cm

Therefore, the lengths of sides AD and BC =  33 cm and the lengths of sides AB and CD = 15 cm

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a) Function f(x) = 2^x is an exponential growth function because a = 2 is greater than 0 and b = 2 is greater than 1. The graph of the function starts at (0,1) and increases rapidly as x increases.

b) Function f(x) = (1/2)^x is an exponential decay function because a = 1/2 is greater than 0 and b = 1/2 is between 0 and 1. The graph of the function starts at (0,1) and decreases rapidly as x increases.

Key features of both graphs:

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We can construct a shape of area 4 square meters using the four shapes square, rectangle, triangle and parallelogram.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

The area of a plane figure is the area that its perimeter encloses. The amount of units in a figure determines its area. Area is measured in square units like cm² and m². Area of a shape is a two dimensional quantity.

Area of a square =  side² (a²)

Area of a triangle = 1/2 × base length × height (1/2×b×h)

Area of a rectangle = length × breadth ( l×b )

Area of a parallelogram = base length × height ( b×h)

Consider the square of side 1 m

Area = 1 × 1 = 1 m²

Now consider the triangle of base length , b = 1/2 m and height, h = 2 m

∴ Area = 1/2×1/2×2 = 1/2 m²

Once more , area of the parallelogram of side 1 m and height 2 m is given by

Area = 1×2= 2 m²

For the rectangle of length 1/2 m and breadth 1 m

Area = l × b = 1/2 × 1 = 1/2 m²

∴ Total area = 1 + 1/2 + 2 + 1/2 = 4 square meter.

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Therefore , the solution of the given problem of equation comes out to be the value of an is 12 when b is 147. Therefore, 12 is the right response.

In intricate algorithms, variable words are typically employed to demonstrate consistency between two opposing arguments. Equations are academic phrases that are used to demonstrate the equality of different academic figures. Consider the specifics of the above x + 7 suggestions. improving in this case provides b + 7 while constructing y + 7 before integrating.

Here,

The following values can be used to put up a proportion if the relationship between variables a and b is proportional:

=>  a / b = 4 / 49

The value of a when b is 147 can therefore be calculated using this ratio:

=>  a / 147 = 4 / 49

By cross-multiplying, we can isolate a:

=>  a = (4 / 49) * 147

Now that we know the value of a, we can:

=> a = 12

Therefore, the value of an is 12 when b is 147. Therefore, 12 is the right response.

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since the formula for the area of a circle squares the radius, the area of the larger circle is always 4 or 22 multiple the tiny square