Solve for x. Assume that lines which appear to be diameters are actual diameters.

In the given map, the approximate area of the Central Park is 450 blocks

Froom the question, we are to determine the approximate area of the central park.

The park is a rectangular park and the approximate area of the park can be calculated by using the formula for calculating the area of a rectangle.

If Central Park is about 50 blocks long by 9 blocks wide, we can find its approximate area by multiplying the length and width:

Area = Length x Width

Area = 50 x 9

Area = 450

Hence, the approximate area of Central Park is 450 blocks.

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Answer:

212,500

Step-by-step explanation:

One number that rounds to 213,000 when rounded to the nearest thousands is 212,500.

Step-by-step explanation:

Refer to pic..........

One way to label the tick marks on the number lines is to use whole numbers for the longer tick marks and decimals for the shorter tick marks.

For example, on the first number line, you could label the longer tick marks as 0, 1, 2, 3, 4, and 5, and the shorter tick marks as 0.1, 0.2, 0.3, etc.

This fits with the structure of the base-ten system because each whole number is ten times greater than the corresponding decimal.

Another way to label the tick marks is to use fractions for the shorter tick marks. For example, on the second number line, you could label the longer tick marks as 0, 1, 2, 3, 4, and 5, and the shorter tick marks as 1/10, 2/10, 3/10, etc.

This also fits with the structure of the base-ten system because each fraction is one-tenth of the corresponding whole number.

Both of these labeling methods are accurate and fit with the structure of the base-ten system, so either one would be an appropriate way to label the tick marks on the number lines.

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Answer:

Below

Step-by-step explanation:

Area of WHOLE rectangle = 9 x 6 = 54 units^2

 now subtract the area of the semicircle with radius 3

      whole circle is pi r^2    ( one-half of this is   1/2 pi r^2)

54 units^2 - 1/2 pi r^2

54 -  1/2 * pi * 3^2 = 39.9 units^2

The percent notation is 55%.

Percentage is the fraction of an amount that is usually expressed as a number out of hundred. Percentage is a measure of frequency. The sign that is used to represent percentage is %. In order to convert a fraction to percentage notation, multiply by 100.

Percent notation = fraction that attended the wedding x 100

= 11/20 x 100 = 55%

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If W is a subspace, then

1. Geometric description of W is a line passing through the origin with a slope of 2.

2. W is not a subspace of R ^ 2.

3. Here, W is the union of two lines passing through the origin with slopes of 1 and -1.

4. In this case, W is not a subspace of R ^ 2.

5. Geometrically, W is a line passing through the origin with a slope of 0.

6. Here, Geometrically, W is a single point at the origin.

1. W = \{x / x_{1} = 2x_{2}\} is a subspace of R^2 because it satisfies the three conditions of being a subspace: it contains the zero vector (0,0), it is closed under addition, and it is closed under scalar multiplication. Geometrically, W is a line passing through the origin with a slope of 2.

2. W = \{x / x_{1} - x_{2} = 2\} is not a subspace of R^2 because it does not contain the zero vector (0,0). Geometrically, W is a line that does not pass through the origin.

3. W=\ x / x_{1} = x_{2} or x_{1} = - x_{2} is a subspace of R^2 because it satisfies the three conditions of being a subspace. Geometrically, W is the union of two lines passing through the origin with slopes of 1 and -1.

4. W = {x: x₁ and x_{2} are rational numbers} is not a subspace of R^2 because it is not closed under scalar multiplication. For example, if we multiply the vector (1/2, 1/3) by the scalar √2, we get the vector (√2/2, √2/3), which is not in W. Geometrically, W is the set of all points with rational coordinates.

5. W = \{x / x_{1} = 0\} is a subspace of R^2 because it satisfies the three conditions of being a subspace. Geometrically, W is a line passing through the origin with a slope of 0 (the x-axis).

6. W = \{x / |x_{1}| + |x_{2}| = 0\} is a subspace of R^2 because it contains only the zero vector (0,0), which satisfies the three conditions of being a subspace. Geometrically, W is a single point at the origin.

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Answer:

To find the height of the plane, we need to use trigonometry. Let's call the height of the plane "h". We can use the given angle of 57° and the opposite side (height) to the angle to find the adjacent side (distance traveled east) using the tangent function:

tan(57°) = h / distance traveled east

We can rearrange this equation to solve for h:

h = distance traveled east x tan(57°)

To find the distance traveled east, we need to use the given distance of 322 miles and the direction traveled. Since the plane is traveling at a 57° angle northeast, we can split this into two right triangles, one facing northeast and the other facing southeast, as shown below:

N

|

|

|\ 57°

|

\

The distance traveled east is the adjacent side of the southeast-facing right triangle, which can be found using the cosine function:

cos(57°) = distance traveled east / 322

We can rearrange this equation to solve for the distance traveled east:

distance traveled east = 322 x cos(57°)

Now we can plug in this value for the distance traveled east into the equation for the height of the plane:

h = distance traveled east x tan(57°)

h = (322 x cos(57°)) x tan(57°)

Using a calculator, we can evaluate this expression to find:

h ≈ 389.4 miles

Therefore, the height of the plane to the nearest mile is 389 miles.

After using the properties of logarithms to rewrite and simplify the logarithmic expression  ln((e⁸)/7) simplifies to 1.

What are natural logarithms?

Natural logarithms are a type of logarithm that uses the number e as its base. The natural logarithm of a positive number x (written as ln(x)) is the exponent to which e must be raised to get x. In other words, ln(x) represents the power to which e must be raised to obtain x.

The number e is a mathematical constant that is approximately equal to 2.71828. It is a special number that appears in many areas of mathematics, science, and engineering. Natural logarithms have a variety of applications in fields such as calculus, probability theory, and statistics.

Some properties of natural logarithms include:

ln(1) = 0

ln(e) = 1

ln(xy) = ln(x) + ln(y) for any positive numbers x and y

ln(x/y) = ln(x) - ln(y) for any positive numbers x and y

ln(xᵃ) = a ln(x) for any positive number x and any real number a

Natural logarithms can be evaluated using a calculator or by using the properties of logarithms to simplify expressions. They are commonly used in mathematical and scientific calculations that involve exponential growth or decay.

We can use the property of logarithms that states: log(aᵇ) = b log(a) for any base a and any real number b.

Using this property, we can rewrite ln((e⁸)/7) as:

ln((e⁸)/(e⁷))

[tex]= ln(e^{(8-7)})[/tex]

= ln(e)

= 1

Therefore, ln((e⁸)/7) simplifies to 1.

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The polynomial equation 2x^(5)+6x^(4)-3x^(3)+x^(2)-9x-1=0 has 5 roots. This is because the degree of the equation is 5, and the number of roots of a polynomial equation is equal to its degree. Therefore, this equation has 5 roots. To find the roots of the equation, you can use the Rational Root Theorem, synthetic division, or other methods. However, finding the exact roots of a fifth-degree polynomial equation can be difficult and may require the use of a graphing calculator or computer software.

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The scale factor of dilation is 0.075 and the coordinates of F" are (0.9, 0.375)

The label of the triangle is added as an attachment

From the complete question, we have

DE = 12 units

Then, we have

D"E" = 0.9 units

Using the above as a guide, we have the following:

Scale factor = D"E"/DE

Scale factor = 0.9/12

Scale factor = 0.075

So, the scale factor of dilation is 0.075

This is calculated as

F = Scale factor * F

So, we have

F = 0.075 * (12, 5)

F = (0.9, 0.375)

The sine, cosine and tangent are calculated as

sin(D") = EF/DF

cos(D") = DE/DF

tan(D") = EF/DE

So, we have

sin(D") = 0.375/1 = 0.375

cos(D") = 0.9/1 = 0.9

tan(D") = 0.375/0.9 = 0.416

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Missing information in the question

Triangle DEF has coordinates D(0,0) E(12,0) F(12,5) and pictured is triangle D”E”F”.

DE = 0.9, EF = 0.375 and DF = 0.9

The values between[tex]7 * 10^-6[/tex] and [tex]6 * 10^-5 = 5.3 * 10^-5[/tex]

The result of subtracting one number from another. How much one number differs from another.

Example: The difference between 8 and 3 is 5.Another example is the difference between 100 and 50= 100-50 = 50

The difference simply means subtracting a number from another

Similarly the difference between [tex]7 * 10^-6 and 6 * 10^-5 = 6 * 10^-5 - 7 * 10^-6[/tex]

changing [tex]7 *10^-6 0.7 * 10^-5[/tex]= [tex](6 * 10^-5) - (0.7 * 10^-5)= 5.3 * 10^-5[/tex]

Therefore the values between [tex]7 * 10^-6[/tex] and [tex]6 * 10^-5[/tex] is [tex]5.3 * 10^-5[/tex]

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Podemos concluir que solo los números pares tienen cuadrados pares, ya que cualquier número par elevado al cuadrado es divisible por 2 y, por lo tanto, es par.

Los números pares tienen la forma 2n, donde n es un número entero. Si elevamos al cuadrado un número par, obtenemos:

(2n)² = 4n²

Y podemos ver que 4n² es un número par, ya que se puede escribir como 2 x 2n².

Por otro lado, los números impares tienen la forma 2n+1, donde n es un número entero. Si elevamos al cuadrado un número impar, obtenemos:

(2n+1)² = 4n² + 4n + 1

Y podemos ver que 4n² + 4n es un número par, ya que se puede escribir como 2 x (2n² + 2n), mientras que 4n² + 4n + 1 es un número impar.

Por lo tanto, podemos concluir que solo los números pares tienen cuadrados pares, mientras que los números impares tienen cuadrados impares.

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Answer:

Step-by-step explanation:

Angles in a quadrilateral add to 360°. So

[tex]60+80+120+x=360[/tex]   (where [tex]x[/tex] is the fourth angle)

[tex]260+x=360[/tex]  

[tex]x=100[/tex]°    (after subtracted 260 from both sides of equation)

The basis of the subspace of R4 defined by the equation3x1​−9x2​+2x3​−3x4​=0 is  {(3, 1, 0, 0), (-2/3, 0, 1, 0), (1, 0, 0, 1)}

A basis of the subspace of R4 defined by the equation 3x1​−9x2​+2x3​−3x4​=0 can be found by solving the equation for one of the variables in terms of the others and then writing the general solution as a linear combination of vectors.

First, solve the equation for x1 in terms of the other variables:

3x1 = 9x2 - 2x3 + 3x4

x1 = 3x2 - (2/3)x3 + x4

Next, write the general solution as a linear combination of vectors:

(x1, x2, x3, x4) = (3x2 - (2/3)x3 + x4, x2, x3, x4)

= x2(3, 1, 0, 0) + x3(-2/3, 0, 1, 0) + x4(1, 0, 0, 1)

Finally, the basis of the subspace is the set of vectors that make up the linear combination:

{(3, 1, 0, 0), (-2/3, 0, 1, 0), (1, 0, 0, 1)}

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The toothpicks she will use to make 90 squares in a straight line are 271. Squares can Kyra make if she has a box of 1,000 toothpicks are 333.

A total of 4 toothpicks are needed.

A total of 9 toothpicks are needed for further 3 squares.

So, the number of toothpicks needed to make 87 squares = [tex]\frac{87*9}{3}[/tex]

                                                                                                  = 261

Hence, the number of toothpicks needed to make 90 squares = [tex]261+10[/tex]

                                                                                                        = 271

The number of squares formed by 261 toothpicks = 87

So, the number of squares formed by 1000 toothpicks = [tex]\frac{996*87}{261} + 1[/tex]

                                                                                            = 333

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The amount of interest earned on Jenna's loan of $8000 for 15 years is $7200

The given variables and their values from the question are listed as follows:

Principal = 8000

Rate = 6%

Time = 15 years

The general formula to calculate simple interest is:

Simple interest = Principal * Rate * Time

By replacing the given values into the equation mentioned above, we obtain the subsequent expression

Simple interest = 8000 * 6% * 15

Evaluate the products in the expression

Simple interest = 7200

Hence, the amount of interest is $7200

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Complete question

Jenna borrows 8,000 for college at a yearly simple interest rate of 6 she takes 15 years

Determine the amount of interest

Answer:

f(-4) = 15

Step-by-step explanation:

A function is notated as f(x), because the x is the value you are putting in. For example. In f(x) = x + 5, the value you are putting in is x, and the output would be x + 5.

So in this case, we have f(x) = -7x-13. We are to figure out f(-4), so we can simply put in -4 as the x-value;

-7(-4) - 13

28 - 13

15

And so the value of f(-4) = 15

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Answer:

9

Step-by-step explanation:

f times 9 = 7x - 13 = 9 pls make me brianlist

Answer:

a) When we say "like terms", we mean terms that have the same variables and/or exponents.

b) When we say "combining like terms", we mean adding or subtracting terms with the same variables, so that the two terms become one term.

c) An example of combining like terms is: 6x + 3x = 9x.

Answer: The class average is 88, and Joey did better than 5 points more than the class average. Therefore, Joey's math test score is greater than 88 + 5 = 93.

So, the number sentence that represents Joey's math test score is:

D. 88 + 5 > J

Step-by-step explanation:

Answer:

Step-by-step explanation:

Ok, I hate point-slope form but I can help!

I'm going to answer slope-intercept first, then point slope.

2. y = 1/4x - 1 ; y+2 = 1/4(x+4)

3. y = -3/2x + 1 ; y+2 = -3/2(x-2)

4. y = x - 2 ; y-1 = 1(x-3)

Hope this helps!

Answer:

9x+30

Step-by-step explanation:

because form rule of like and unlike term

The value of fy(1,1) is 5.5 with one decimal digit on the right side of the decimal point.

To find the value of fy(1,1), we need to first find the partial derivative of f(x,y) with respect to y. This is done by treating x as a constant and taking the derivative with respect to y.

The partial derivative of f(x,y) with respect to y is:
fy(x,y) = (1/2)(4x2 - 2y + 7x4y5)-1/2 (-2 + 35x4y4)

Now we can plug in the values of x=1 and y=1 into the partial derivative to find the value of fy(1,1):
fy(1,1) = (1/2)(4(1)2 - 2(1) + 7(1)4(1)5)-1/2 (-2 + 35(1)4(1)4)
fy(1,1) = (1/2)(4 - 2 + 7)-1/2 (-2 + 35)
fy(1,1) = (1/2)(9)-1/2 (33)
fy(1,1) = (1/2)(1/3)(33)
fy(1,1) = 5.5

Therefore, the value of fy(1,1) is 5.5 with one decimal digit on the right side of the decimal point.

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Applying the right trigonometry ratio, each value of x is:

13. x ≈ 28.1°

14. x ≈ 13.5

15. x ≈ 219.9

16. x ≈ 59.0°

Trigonometry ratios are mathematical relationships between the angles and sides of a right triangle. The three primary trigonometry ratios are:

13. Apply the cosine ratio:

cos x = 15/17

x = cos^(-1)(15/17)

x ≈ 28.1°

14. Apply the sine ratio:

sin 75 = 13/x

x = 13/sin 75

x ≈ 13.5

15. Apply the tangent ratio:

tan 83 = x/27

x = 27 * tan 83

x ≈ 219.9

16. Apply the tangent ratio:

sin x = 12/14

x = sin^(-1)(12/14)

x ≈ 59.0°

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Answer:

23.4 ft tall

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given: Distance from the flagpole = 14 ft

Angle of elevation θ = 74.4°

To find: Length of the flagpole

Answer:

tan(74.4°) = [tex]\frac{L}{14}[/tex]

L = 14 tan(74.4°) = 50.142 ft

So the length of the pole is 50.142 ft.

By answering the above question, we may state that This expression's equation evaluation results in: r = 8.5 ft

A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A formal statement that proves the equality of two calculations is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two phrases that are inscribed on opposite sides of a letter. Frequently, the logo and indeed the particular software are identical. like in 2x - 4 = 2, for example.

The following is the formula for a circle's circumference:

C = 2πr

where is a mathematical constant that is roughly equivalent to 3.14159, C is the circumference, r is the radius, and.

The circle's circumference is stated to be 17 feet. In order to find r, we may put this equal to the circumference formula as follows:

17π = 2πr

When we divide both sides by 2, we obtain:

r = 17π / (2π)

Units cancel out, leaving:

r = 17 / 2

This expression's evaluation results in:

r = 8.5 ft

As a result, the circle's radius is 8.5 feet.

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Answer:

A. y = 52x

Step-by-step explanation:

The equation is set up in slope-intercept form y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (0,0) (4, 208)

We see the y increase by 208 and the x increase by 4, so the slope is

m = 208/4 = 52

Y-intercept is located at (0,0)

So, our equation is y = 52x

The answer is option A

In the first production method, the company produces approximately 4,996 books.

Let's represent the number of books produced as x.

Total cost of method 1 = One-time fixed cost + Variable cost * Number of books produced

= $82,363 + $9.25x

Total cost of method 2 = One-time fixed cost + Variable cost * Number of books produced

= $21,162 + $21.50x

Setting the two equations equal to each other, we get:

$82,363 + $9.25x = $21,162 + $21.50x

Simplifying this equation, we get:

$61,201 = $12.25x

Dividing both sides by $12.25, we get:

x = 4,995.92

This means that the costs from the two methods will be the same when the company produces approximately 4,996 books.

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The simplified answer is (5x)/(x^(2)-49)-(6)/(x+7) = -(x - 42)/((x + 7)(x - 7)).

To subtract and simplify the given expression, we need to find a common denominator and combine the numerators. The common denominator in this case will be (x^2 - 49), which can be factored into (x + 7)(x - 7).

So, the expression becomes:

(5x)/((x + 7)(x - 7)) - (6)/(x + 7)

To get a common denominator, we need to multiply the second term by (x - 7)/(x - 7):

(5x)/((x + 7)(x - 7)) - (6(x - 7))/((x + 7)(x - 7))

Now we can combine the numerators:

(5x - 6(x - 7))/((x + 7)(x - 7))

Simplifying the numerator gives us:

(-x + 42)/((x + 7)(x - 7))

And finally, we can simplify the expression by factoring out a -1 from the numerator:

-1(x - 42)/((x + 7)(x - 7))

So the final answer is:

-(x - 42)/((x + 7)(x - 7))

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