A plan for a baseball diamond is drawn in a coordinate plane. The baseball diamond is in the shape of a square with vertices at approximately (0, 64), (64, 0), (0, -64), and (-64, 0). One unit in the coordinate plane represents 1 ft. What is the approximate area of the baseball diamond?

The total surface area of the square pyramid (SA) = 144 yd².

A square pyramid is a solid shape that has a square base and four rectangular lateral faces.

The total surface area of a square pyramid is the sum of the area of its square base and four rectangular lateral faces. To find the total surface area, the following formula is used:

Total surface area of a square pyramid (SA) = A + 1/2(Pl), where:

Given the following:

Area of base (A) = 8² = 64 yd²

Perimeter of base (P) = 4(8) = 32 yds

Slant height of pyramid (l) = 5 yds

Plug in the values

Total surface area of a square pyramid (SA) = 64 + 1/2(32)(5)

Total surface area of a square pyramid (SA) = 64 + 80

Total surface area of a square pyramid (SA) = 144 yd².

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The measure of the angle x or the value of the x is 53.13 degrees if an interior designer is sketching a rough outline of a corner room of an office building.

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

It is given that:

The area of triangle A = 1728 square feet

The base length of the triangle b = 72 feet

Let h be the height of the triangle

Area = (1/2)b×h

1728 = (1/2)72×h

h = 48 feet

Half of the 72 is 72/2 = 36

As we know,

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

Applying trigonometric ratio:

tan(x) = 48/36

tan(x) = 1.333

x = 53.13 degrees

Thus, the measure of the angle x or the value of the x is 53.13 degrees if an interior designer is sketching a rough outline of a corner room of an office building.

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Answer: 8/33

Step-by-step explanation:

So the probability of picking a purple marble is 8/12, after that there are 11 marbles left in the box

Now the probability of picking a green marble without placing the first marble back is 4/11

So the probability of doing both is 8/12 x 4/11 = 8/33

Answer:

no

Step-by-step explanation:

So you can express a polynomial in factored form as such: [tex]a(x)*b(x)*c(x)...[/tex] where a(x), b(x), and c(x), each represent a polynomial which are each factors of the equation. It's important to note that each factor is being multiplied by each other, meaning if any of the factors output 0, the entire thing is 0, no matter the value of the other factors, since 0 * some value = 0. For this reason, if we plug in the value that makes (x+1) 0, into the polynomial, and the polynomials value is 0, that means it is a factor.

x + 1 = 0

x = -1

The value that makes the factor 0, is -1. This means that if it is a factor of the polynomial, then plugging in -1 as x into the polynomial should make the value 0.

Original Equation:

[tex]12x+5x+3x^2-5[/tex]

Plug in -1 as x

[tex]12(-1)+5(-1)+3(-1)^2-5[/tex]

Multiply values

[tex]-12-5+3(1)-5[/tex]

Simplify:

[tex]-17+3-5\\-14-5\\-19[/tex]

Since the value of the polynomial is not 0, this means x+1 is not a factor

You can also solve this use the Remainder Theorem and Factor Theorem which essentially uses the same logic

Remainder Theorem:

   If a polynomial P(x) is divided by x-a, the remainder is P(a)

Using the remainder theorem, if x-a is indeed a factor, then that means the remainder should be 0, just as 11 is a factor of 77, and 77/11 has a remainder of 0. This is what the factor theorem essentially states

Factor Theorem:

   The expression "x-a" is a factor of P(x) if and only if P(a) = 0

Answer:

C

Step-by-step explanation:

y is greater or equal to 0

x is also greater or equal to 0

you can see that only one answer choice can be the answer

the line is x-y = 2

the upper side is x-y <= 2

proves that c is the answer

x-y ≤ 2

y ≥ 0

x ≥ 0 satisfies this graph. Thus option C is correct.

A schematic or visual presentation that organizes the depiction of data or quantities is known as a graph. The relationships connecting two or more objects are frequently represented by the spots on a graph. They are employed to arrange data in order to highlight correlations and patterns. This data is presented as a pattern on a graph.

When y is bigger than 0 and x is also.

The equation is 2x-y.

x-y ≤ 2 on the upper side of the graph is represented in this same way.

x-y ≤ 2; y ≥ 0 and x ≥ 0 will be the correct represented points in the graph. Therefore, option C is the correct option.

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An error exists in the distinction between the exact length of an object and its measured length.

The closest to the percent error for Diego's measurement exists at 4.3%.

An error exists in the distinction between the exact length of an object and its measured length.

Error = Actual length - Measured length

= 23cm - 22cm

= 1 cm

Percent error = Error/ Actual length × 100

= 1 /23 × 10

= 4.35%

Therefore, the closest to the percent error for Diego's measurement exists at 4.3%.

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(a) The solution to the given system of equations is x = 1, y = 2, z = -3

(b) The solutions to the system of equations are (3.4142, -9.2426) and (0.5858, -0.7574)

From the question, we are to solve the given system of equations

The given system of equation is

x + y + z = 0      ----------- (1)

2x + z = -1         ----------- (2)

x - y - z = 2       ----------- (3)

Add equations (1) and (3)

x + y + z = 0      ----------- (1)

x - y - z = 2       ----------- (3)

__________

2x = 2

x = 2/2

x = 1

Substitute the value of x into equation (2) to find z

2x + z = -1        

2(1) + z = -1

2 + z = -1

z = -1 -2

z = -3

Substitute the values of x and z into equation (1) to determine the value of y

x + y + z = 0    

1 + y + -3 = 0

1 + y - 3 = 0

y = 3 -1

y = 2

Hence, the solution to the given system of equations is x = 1, y = 2, z = -3

b.

The given system of equations is

3x + y = 1                       --------- (1)

6x² - y² - 2y -3 = 0        --------- (2)

From equation (1)

3x + y = 1

y = 1 - 3x -------- (3)

Substitute into equation (2)

6x² - y² - 2y -3 = 0

6x² - (1 -3x)² -2(1 -3x) -3 = 0

6x² - (1 -3x)(1 -3x) -2 + 6x -3 = 0

6x² - (1 -3x -3x +9x²) -2 +6x -3 = 0

6x² - (1 -6x + 9x²) +6x -5 = 0

6x² -1 +6x -9x² +6x -5 = 0

-3x² +12x -6 = 0

3x² -12x +6 = 0

x² -4x + 2 = 0

Solve the quadratic equation by the formula method,

x = [-b±√(b²-4ac)]/2a

a = 1, b = -4 and c = 2

Thus,

x = [-(-4)±√((-4)²-4(1)(2))]/2(1)

x = [4±√(16-8)]/2

x = (4±√8)/2

x = (4+√8)/2 OR (4 - √8)/2

x = 3.4142 OR x = 0.5858

Substitute the values of x into equation (3)

y = 1 - 3x

When x = 3.4142

y = 1 - 3(3.4142)

y = -9.2426

When x = 0.5858

y = 1 - 3(0.5858)

y = -0.7574

Hence, the solutions to the system of equations are (3.4142, -9.2426) and (0.5858, -0.7574)

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To estimate the value for g(10), that means that you have to substitute 10 in every x of g(x), then [tex]$g(x) =x^2-10[/tex] exists g(10) = 90.

The value of g(10), we have to substitute in every x of f(x), the

[tex]f(x) = 2x + 1[/tex] exists f(90) = 181

Therefore, the value of f[g(10)] exists 181.

To estimate the value for g(10), that means that you have to substitute 10 in every x of g(x), then

[tex]$g(x) =x^2-10[/tex]

substitute the value of x = 10

[tex]$g(10) = (10)^2-10[/tex]

simplifying the equation, we get

g(10) = 100 - 10

g(10) = 90

We have the value of g(10), we have to substitute in every x of f(x), then

f(x) = 2x + 1

substitute the value of x = 90

f(90) = 2(90) + 1

simplifying the equation, we get

f(90) = 180 + 1

f(90) = 181

The value of f[g(10)] exists 181.

Therefore, the correct answer is option b) 181.

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Answer:

x = 75

Step-by-step explanation:

Given information from the question:

x - 3y = 30

y = 15

We can substitute y = 15 into the equation to find x.

x - 3(15) = 30

x - 45 = 30

x - 45 + 45 = 30 + 45

x = 75

Answer:

75

Step-by-step explanation:

x-3y=30

x-3×15=30

x-45=30

x=30+45

x=75

For the given function f(x) = 5x² + 2x - 3,

Part A: The x-intercepts of the graph f(x) are: (-1, 0) and (3/5, 0).

Part B: The vertex of the graph of f(X) is going to be a minimum and its coordinates are (-0.2, -3.2).

Part C: The values obtained in the part A and Part B are used for graphing the given function. Since the vertex is minimum, the parabola opens upwards.

The x-intercepts of a function or equation are obtained at y = 0.

Then, on substituting y = 0 in the function gives the x-coordinate i.e., the x-intercept.

To calculate the x coordinate of vertex(h, k), use the formula mentioned below:

h = -b/2a

When the function is in the form of ax² + bx + c.

Then, to calculate the y-coordinate of the vertex, substitute obtained h value in the place of x in the function.

Thus, the required coordinates of the vertex are obtained as (h, k).

It is given that,

f(x) = 5x² + 2x - 3

Part A: Finding the x-intercepts:

Substituting y = 0 i.e., f(x) = 0;

⇒ 5x² + 2x - 3 = 0

On simplifying/factorizing,

⇒ 5x² + 5x - 3x - 3 = 0

⇒ 5x(x + 1) - 3(x +1) = 0

⇒ (5x - 3)(x + 1) =0

∴ x = 3/5 or x = -1

Thus, the x-intercepts are (3/5, 0) and (-1, 0).

Part B: Finding the vertex of the given function:

We have h = -b/2a

From the given function 5x² + 2x - 3; a = 5, b = 2 and c = -3

So, h = -2/2(5) = -1/5 = -0.2

Then, on substituting h = x = -0.2 in the function we get

k = 5(-0.2)² + 2(-0.2) - 3

k = -3.2

Thus, the coordinates of the vertex are (h, k) = (-0.2, -3.2).

Since a > 0 i.e., 5 > 0, the vertex of the graph is going to be minimum and the graph of f(x) opens upwards.

Part C: Steps to graph f(X):

Step 1: Plot the x-intercepts in the coordinate plane

Step 2: Plot the vertex of the function

Step 3: draw a curve line passing through them, opening towards up.

Thus, the graph of the given function is plotted as shown below.

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Answer:

1) 0.10

2) 0.15

3) 0.100

4) No

[tex]a = \frac{\pi.r {}^{2} }{4} = \frac{3.14 \times 10 {}^{2} }{4} = \frac{3.14 \times 100}{4} [/tex]

[tex]a = 78.5[/tex]

Answer:

Each number is increasing by [tex]\frac{1}{4}[/tex].  The next number would be 1 [tex]\frac{1}{4}[/tex] or [tex]\frac{5}{4}[/tex]

Step-by-step explanation:

I am not sure what the question is.  I am wondering if they are asking how is the list growing or what would be the next number.

Each number is increasing by 1/4

[tex]\frac{1}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{2}{4}[/tex] or [tex]\frac{1}{2}[/tex]

[tex]\frac{1}{2}[/tex] + [tex]\frac{1}{4}[/tex] is the same as [tex]\frac{2}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{4}[/tex] To change [tex]\frac{1}{2}[/tex] to [tex]\frac{2}{4}[/tex]  you multiple the top and the bottom of [tex]\frac{1}{2}[/tex] by2 to get [tex]\frac{2}{4}[/tex]

[tex]\frac{3}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{4}{4}[/tex] or 1

The percentage form of given fraction is 60% and the hundredths form is 0.60

According to the statement

we have given that the a fraction and we have to find the percentage of that fraction and write in the form hundredths.

So, For this purpose,

The given fraction is 12/20.

Then the definition of the percentage is that

The Percentage, a relative value indicating hundredth parts of any quantity.

so, the percentage of given fraction is :

Percentage fraction = 12/20 * 100

After solving it, The percentage fraction will become:

Percentage fraction = 60%

and Now convert into the hundredths form then

In the hundredths form it will become

from 60% to 0.60.

So, The percentage form of given fraction is 60% and the hundredths form is 0.60

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Answer:

9/41

Step-by-step explanation:

Cosine represents adjacent / hypotenuse.

When A is the reference angle, AB is the adjacent side (9) and AC is the hypotenuse (41).

9/41 is already simplified.

Answer: [tex]\Large\boxed{y-1=\frac{4}{5} (x+2)}[/tex]

Step-by-step explanation:

Given the requirement for function

Point-slope form : y - y₁ = m (x - x₁)

Given information

m = 4/5

Point = (x₁, y₁) = (-2, 1)

Substitute values into the function form

y - y₁ = m (x - x₁)

y - (1) = (4/5) (x - (-2))

Simplify the function

[tex]\Large\boxed{y-1=\frac{4}{5} (x+2)}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Hello,

[tex]3x + 4 = 8[/tex]

[tex]3x + 4 - 4 = 8 - 4[/tex]

[tex]3x = 4[/tex]

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

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

Answer:

Step-by-step explanation:

To graph by hand I would first convert both equations into y=mx+b.

We start with:

[tex]\left \{ {{2x-2y=4} \atop {x+2y=8}} \right.[/tex]

Solve for y for 2x-2y=4

[tex]2x+2y=4\\2y=4-2x\\y=2-x[/tex]

Solve for y for x+2y=8

[tex]x+2y=8\\2y=8-x\\y=4-\frac{x}{2}[/tex]

Giving the new but equal system of equations:

[tex]\left \{ {{y=2x-x} \atop {y=4-\frac{x}{2} }} \right.[/tex]

From this point on you can graph the two functions to find where the two lines intersect, thats your solution.

I've gone ahead and graphed it on desmos for you

Answer:

18.0  cm to 1 decimal point.

Step-by-step explanation:

First  work out the unknown side (s) of the right triangle using the Pythagoras theorem:

s^2  = 13^2 - 5^2

       = 169 - 25 = 144

s = sqrt 144 = 12 cm.

Now consider the other triangle:

s = 12

The missing angle = 180 - 65 - 40 = 75 degrees.

By the Sine Rule:

x / sin 75 = 12 / sin40

x = 12 sin 75 / sin 40

  = 18.03

    -

The distance from the center to where the foci are located exists 8 units.

The formula associated with the focus of an ellipse exists given as;

c² = a² − b²

Where c exists the distance from the focus to the center.

a exists the distance from the center to a vertex,

the major axis exists 10 units.

b exists the distance from the center to a co-vertex, the minor axis exists 6 units

c² = a² − b²

c² = 10² - 6²

c² = 100 - 36

c² = 64

[tex]c = \sqrt{64}[/tex]

c = 8

Therefore, the distance from the center to where the foci are located exists 8 units.

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The characteristics of a linear function that has a slope of 0 is a horizontal line that passes through the y-axis at y= b

A linear equation is given as:

y = mx + b

Where m represents the slope of the linear equation.

When the value of  is 0

i.e. m = 0, the equation becomes

y = 0 *x + b

Evaluate

y= b

The above equation is a horizontal line that passes through the y-axis at y= b

Hence, the characteristics of a linear function that has a slope of 0 is a horizontal line that passes through the y-axis at y= b

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Answer:

86.

Step-by-step explanation:

His total score is 99 + 85 + x where x is score on third test,

99 + 85 + x = 3 *90   (as his average must be 90, so:

184 + x = 270

x = 270 - 184

  =   86.

Answer:

86

Step-by-step explanation:

Let x be the required score for Lamar's third test in order to get an average of 90 or higher.

Start with the initial equation:

[tex]\frac{99+85+x}{3}\geq 90[/tex]

Simplify the numerator in the fraction:

[tex]\frac{184+x}{3}\geq90[/tex]

Multiply both sides by 3 to cancel out division on left side of equation:

[tex]184+x\geq 270[/tex]

Subtract 184 from both sides to isolate the x variable:

[tex]x\geq86[/tex]

Leaving us with x must be greater than or equal to 86.

Let the mass of the object exists at 60 N and the height exists at 3m then work

exists in 1764.

What is work?

The work done by a force exists determined to be the product of a component of the force in the direction of the displacement and the magnitude of this displacement.

Work can be estimated by multiplying Force and Distance in the direction of force as follows.

W = F × d. Unit.

Given data:

m = mass of the object = 60 N

h = height = 3 m

Work = Fh = mgh

g = gravity = 9.8 m/s²

work = Fh = mgh

[tex]= 60*3*9.8[/tex]

= 1764

Therefore, the work exists in 1764.

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Answer:

C

Step-by-step explanation:

For any function x, inverse will = 1/x. so the answer is C

Answer:

C. [tex]f^{-1}(x) = \frac{1}{5} x[/tex]

Step-by-step explanation:

The question is asking to find [tex]f^{-1}(x)[/tex] of f(x)=5x, which is the same as finding the inverse of the function.

To find the inverse of a function, we first need to replace f(x) with y.

The function will therefore be:

y = 5x

Now, we solve the equation for x.

So divide both sides by 5.

y = 5x

÷5  ÷5

_________

[tex]\frac{y}{5} = x[/tex]

Now, we replace x with y and y with x.

[tex]\frac{x}{5} = y[/tex]

Finally, we replace y with [tex]f^{-1}(x)[/tex].

[tex]\frac{x}{5} = f^{-1}(x)[/tex]

We can re-write this though, to make it easier to read.

We can write [tex]f^{-1}(x)[/tex] first, and rewrite [tex]\frac{x}{5}[/tex] as [tex]\frac{1}{5}x[/tex].

[tex]f^{-1}(x) = \frac{1}{5} x[/tex]

Therefore, the answer is C.

The midpoint between A and E is (0,1)

The coordinates of the cities are given as:

A(-2,3), B(2,7), C(7,8), D(6,3) and E(2,-1).

From the above, we have:

A = (-2,3)

E = (2,-1)

The midpoint between A and E is calculated using

Midpoint = 1/2 * (x1 + x2, y1 + y2)

Substitute the known values in the above equation

Midpoint = 1/2 * (-2 + 2, 3 - 1)

This gives

Midpoint = 1/2 * (0, 2)

Evaluate the product

Midpoint = (0, 1)

Hence, the midpoint between A and E is (0,1)

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The number of different integers there are for the condition described in which case, the square of the square of the integer is a two-digit integer as in the task content is 4 possible integers which includes; -2, -3, 2, 3.

According to the task content, the square of the square of such integers must be a two-digit number, that is, less than or equal to 99.

The numbers in discuss, x must satisfy;

x⁴ < 99.

The numbers in this regard are therefore, -2, -3, 2, 3.

Ultimately, the integers which satisfy the condition described in which case, the square of the square of the integer is a two-digit integer as in the task content is 4 possible integers which includes; -2, -3, 2, 3.

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Answer:

343.608 million to nearest thousand.

Step-by-step explanation:

Projected annual percent of growth = 3%  ( from the values 1.03 in the equation)

Worth is 2012 ( 12 years after 2000) is:

241(1.03)^12

= 343.608 million

The satellite makes 8 revolutions around the earth, it passes 177272 kilometers.

The orbital velocity of the satellite exists independent of its mass. The radius of the orbit exists as the only variable. If the satellite orbits near the planet at such a low height, its orbital speed must be extremely fast. If the orbital speed exists less than the required value, the satellite will be drawn to the earth's surface by gravity.

The satellite rotates around the earth to form a circle,

diameter of circle = Diameter of earth + 2(Height)

d = 6714 + 2(343)

d = 6714+ 686

d = 7057

Perimeter = πd

Perimeter = 3.14 (7057)

Perimeter = 22158.98

Total Revolution exists 8

Therefore, 8πd = 8(22158.98)

= 177272 kilometers.

Therefore, the satellite makes 8 revolutions around the earth, it passes 177272 kilometers.

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See attachment for the area model of the equation 4x^2+12x+9 = (2x+3)^2

Area models are shapes used to model or illustrate products, multiplications, divisions and quotients

The equation is given as:

4x^2+12x+9 = (2x+3)^2

Express (2x+3)^2 as the product of (2x+3) and (2x+3)

4x^2+12x+9 = (2x+3) * (2x+3)

The above means that the area model is a square.

So, the side lengths of the model must be equal, where the side lengths are 2x + 3 and the area of the square is 4x^2+12x+9

See attachment for the area model of the equation 4x^2+12x+9 = (2x+3)^2

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