At an elementary school there are two fenced in areas on the playground. The small play area is
1
4
the area of the large play area. The total square footage of the two areas is 2000 ft2. What is the size of the small play area?
A) 200 ft2
B) 400 ft2
C) 800 ft2
D) 1600 ft2
​

Answer:

7

Step-by-step explanation:

This is an equation of an ellipse of the form:

[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]

Where a and b are the minor and major intercepts, given a<b

In this question, a<b and a = 3 and b = 7

The distance from the center to the major intercept is b, thus the distance we are seeking for is 7

Answer:

b = 7 units.

Step-by-step explanation:

The given equation of the ellipse is

[tex]\frac{x^{2} }{9} +\frac{y^{2} }{49}=1[/tex]

As we know in an ellipse  [tex]\frac{x^{2} }{a^{2} }+ \frac{y^{2} }{b^{2}}=1[/tex]

a will be major axis and b is the minor axis when ( a > b )

In the given equation 49 > 9 ⇒ b² > a²

so major axis will be = √49

                                  = 7

Therefore, distance from center to the major intercept is b = 7 units.

Answer: GCF = x

Step-by-step explanation:

x(x^3/x + x^2/x + -6x/x)

x(x^2 + -6)

x(x - 2)(x + 3)

Answer:

x(x + 3)(x - 2)

Step-by-step explanation:

Factor out x from each term

= x(x² + x - 6)

To factor the quadratic

Consider the factors of the constant term (- 6) which sum to give the coefficient of the x - term (+ 1)

The factors are + 3 and - 2, since

+ 3 × - 2 = - 6 and + 3 - 2 = + 1, hence

x² + x - 6 = (x + 3)(x - 2)

---------------------------------------

x³ + x² - 6x = x(x + 3)(x - 2) ← in factored form

The answer is:

[tex]A(13)=107.37Km^{2}[/tex]

We can calculate the area of the lake after 13 years using the following equation:

[tex]A(t)=A(initial)(1-ShrinkingRate)^{t}[/tex]

Where,

A(t), is the area after t time (years)

A(Initial), is the initial area

Shrinking Rate, is the rafe of shrinking and it's 6% or 0.06.

t, is the time

So, substituting we have:

[tex]A(13)=240(1-0.06)^{13}=240*0.447=107.37Km^{2}[/tex]

So, the are after 13 years will be:

[tex]A(13)=107.37Km^{2}[/tex]

Have a nice day!

p(x) * r(x) = ab^x * cd^x

p(x) * r(x) = (a*c)*(b^x*d^x)

p(x)*r(x) = ac(bd)^x

For the last step, I used the rule that (ab)^x = a^x*b^x

The product of two exponential functions p(x) = ab^x and r(x) = cd^x is calculated by following the rules of exponents in mathematics, resulting in p(x) * r(x) = a * c * (bd)^x

The student is asking for the product of two exponential functions. If p(x) = ab^x and r(x) = cd^x, their product can be calculated as follows:

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Answer:

[tex](2,200\pi +8,000)\ ft^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the figure is equal to the volume of cube plus the volume of the cylinder

step 1

Find the volume of the cube

The volume of the cube is equal to

[tex]V=b^{3}[/tex]

we have

[tex]b=2(10)=20\ ft[/tex] ----> the length side of the cube is equal to the diameter of the cylinder

so

[tex]V=20^{3}=8,000\ ft^{3}[/tex]

step 2

Find the volume of the cylinder

The volume of the cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=10\ ft[/tex]

[tex]h=42-20=22\ ft[/tex]

substitute

[tex]V=\pi (10)^{2} (22)[/tex]

[tex]V=2,200\pi\ ft^{3}[/tex]

step 3

The volume of the figure is equal to

[tex](2,200\pi +8,000)\ ft^{3}[/tex]

The volume of the figure = volume of oblique cylinder + volume of cube = 2,200π + 8,000 cubic feet.

Volume of oblique cylinder = πr²h [radius of cylinder = r].

The volume of the figure = volume of oblique cylinder + volume of cube = πr²h + s³

Given the following:

Plug in the values into πr²h + s³:

The volume of the figure = π(10²)(22) + 20³

The volume of the figure = 2,200π + 8,000 cubic feet.

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Answer:

y =0

Step-by-step explanation:

From the equation;

8³ × 8⁻⁵×8^y = 8⁻²= 1/8²

From the laws of indices;

aⁿ×aⁿ = a^2n

Therefore;

8³ × 8⁻⁵×8^y = 8^(3+-5+y)

8^(-2+y) = 8^-2 ; but the bases are the same and thus the exponents are the same;

-2 + y = -2

      y = 0

Answer:

The value of y is 0

Step-by-step explanation:

8³ * 8^-5*8^y = 8^-2 or 1/8²

Taking indices of both sides

From first law of indices;

Multiplication sign change to addition; i.e. x^a * x^b = x^(a + b).

So,

8³ * 8^-5*8^y = 8^-2

Becomes

8^(3 + (-5) + y) = 8^-2

Same base of 8 can cancel one another. So, we're left with

3 + (-5) + y = -2

Open the bracket

3 - 5 + y = -2

-2 + y = -2

Make y the subject of formula

y = 2 - 2

y = 0

Hence, the value of y in the equation is 0

To find the slope of a line passing through the origin and a point, use the formula slope = (y2 - y1)/(x2 - x1). For a line passing through origin and the point (-8,-5), the slope is 5/8.

The topic at hand revolves around the concept of slope and the algebra of straight lines. The slope is calculated by finding the change in y (vertical axis) over the change in x (horizontal axis). To find the slope of a line passing through the origin and the point (-8,-5), use the formula slope = (y2 - y1)/(x2 - x1).

In this case, the origin is point (0,0) and the given point is (-8,-5). So to find the slope, we substitute these values into the slope formula: slope = (-5 - 0)/(-8 - 0) = 5/8. Therefore, the slope of the line passing through the origin and the point (-8,-5) is 5/8.

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The slope of the line is 5/8.

The slope of a line, denoted by m, represents the rate of change between the vertical and horizontal components of two points on the line.

To find the slope of a line passing through the origin and intersecting the point (-8, -5), we can use the slope formula. The slope formula is given by: m = (y2 - y1) / (x2 - x1).

Plugging in the values from the given point gives: m = (-5 - 0) / (-8 - 0)

= -5 / -8

= 5/8.

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Answer:

The answer to 4-3 is 1.

Step-by-step explanation:

The quadratic code '4 - 3' corresponds to the mathematical expression "4 minus 3," which equals 1.

The quadratic equation '4 - 3' is a simple algebraic equation that can be decoded as follows:

Start with the number 4.

Subtract 3 from it.

So, the decoded mathematical expression is:

4 - 3 = 1

The result is 1.

Therefore, the quadratic code '4 - 3' corresponds to the mathematical expression "4 minus 3," which equals 1.

This demonstrates how to decode and interpret a simple algebraic expression, showing that when you subtract 3 from 4, the result is 1.

It's a basic example of performing arithmetic operations on numbers.

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The probable question may be:

Decode the quadratic expression '4 - 3​' to reveal the mathematical expression it represents. Provide the complete mathematical expression that corresponds to the given quadratic code.

Answer:false

Step-by-step explanation: divide each side by 7 you get b ≤ -7. The red line needs to go the other way since it is less than

Answer:

False, it is incorrect

Step-by-step explanation:

7b≤ -49

Divide by 7

7b/7 ≤-49/7

b ≤-7

We have a closed circle at -7  (closed because of the equals)

b is less than so the lines goes to the left

32,000 divided by 500 = 64

Answer: 32000/500= 64 approximately

Step-by-step explanation:

64 is the answer because 31969/488= 65.51

the lesser number is 5.

Let the first number = x

Let the second number = y

set up two equations

x + y = 17

2/3 x -3 = y

sub the second equation into the first one

x + 2/3 x - 3 = 17

collect like terms (1x = 3/3 x)

5/3 x - 3 = 17

add 3 to both sides

5/3 x = 20

multiply by 3 on both sides

5x = 60

divide by 5 on both sides

x = 12

sub back in one of the equations and solve to find the other number:

x + y = 17

12 + y = 17

y= 5

•have a good day• :) ~ ♡lipika♡

The lesser number is 5.

Let us consider that first number is x .

Since, second number is 3 less than 2/3 of the other number.

So that, second number [tex]=\frac{2}{3}x-3[/tex]

The sum of both number is 17.

             [tex]x+\frac{2}{3}x-3=17\\\\\frac{5}{3}x=17+3\\\\\frac{5}{3}x=20\\\\x=20*\frac{3}{5}=12[/tex]

Lesser number is. [tex]=\frac{2}{3}x-3=\frac{2}{3}*12-3=5[/tex]

Hence, the lesser number is 5.

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2/3 is 0.6 repeating

66% is just 66%

same with 0.67

order is 0..67, 2/3, then 66%. i am the stupid.

% = decimal number

Answer:

0.67, 2/3, 66%

Step-by-step explanation:

2/3 decimal is 0.66666666667

66% decimal is 0.66

and 0.67 is 0.67

Hope this helped! Please mark as brainliest! Thanks!

Answer:

11.99 ft

Step-by-step explanation:

The formula for the volume of a cyl. of radius r and height h is V = πr²h.

Solving this immediately for h yields:

         V

h = ----------

         πr²

Inserting the known quantities results in:

         V           1356.48 ft³

h = ---------- = ----------------------      Note that r = (1/2)d, so r = (1/2)(12 ft) = 6 ft

         πr²         3.14159 (6 ft)²

   =   11.994 ft

The height of the cyl. is 11.99 ft (to the nearest hundredth foot)

Final answer:

To find the height of the cylinder with a volume of 1,356.48 cubic feet and a diameter of 12 feet, divide the volume by the area of the base (calculated with a radius of 6 feet) to get approximately 11.99 feet.

Explanation:

To calculate the height of a cylinder when the volume and diameter are given, we use the formula for the volume of a cylinder, V = πr²h, where V is the volume, r is the radius, and h is the height. In this case, we have a volume of 1,356.48 cubic feet and a diameter of 12 feet, meaning the radius is 6 feet (half of the diameter). So we can plug these values into our formula to solve for h.

First, calculate the area of the base (πr²): 3.14159 × (6 feet)² = 3.14159 × 36 = 113.0976 square feet. Then we divide the given volume by this area to find the height: 1,356.48 cubic feet / 113.0976 square feet = 11.99 feet. Therefore, the final answer for the height of the cylinder is approximately 11.99 feet.

Answer:

C

Step-by-step explanation:

In translating graphs of functions, we can follow 2 rules:

1. The graph of  [tex]f(x)+a[/tex] is the graph of  [tex]f(x)[/tex] shifted a units UP VERTICALLY and the graph of   [tex]f(x)-a[/tex] is the graph of  [tex]f(x)[/tex] shifted a units DOWN VERTICALLY.

2. The graph of  [tex]f(x+a)[/tex]  is the graph of   [tex]f(x)[/tex]  shifted a units to the LEFT HORIZONTALLY and the graph of  [tex]f(x-a)[/tex]  is the graph of  [tex]f(x)[/tex]  shifted a units RIGHT HORIZONTALLY.

If we understand the 2 rules above, we clearly know that f(x+2) will be a horizontal shift to the LEFT, of course, with respect to the function  [tex]f(x)=x^3[/tex]. Looking at the answer choices, C is right.

Answer:

2/25 is the Answer, as a decimal it is 0.08

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

x + 1/50 = 1/10

Step 2: Subtract 1/50 from both sides.

x + 1/50 - 1/50 = 1/10 - 1/50

X = 2/25

Proof that it is the answer

0.02 + 0.08 = 0.1

0.02 is 1/50

0.08 is 2/25

0.1 is 1/10

Hope this helps!

[tex]\bold{Hey\ there!} \\ \bold{\frac{1}{50}+x=\frac{1}{10}}\\ \\ \bold{You\ have\ to\ simplify\ both\ sides\ of\ your\ equation\downarrow}\\ \bold{Like:x+\frac{1}{50}=\frac{1}{10}} \\ \\ \bold{Next,\ you\ have\ to\ \underline{SUBTRACT}\ by\ \frac{1}{50}\ on\ your\ sides} \\ \bold{x+\frac{1}{50}-\frac{1}{50}=\frac{1}{10}-\frac{1}{50}}\\ \\ \bold{Cancel:\frac{1}{50}-\frac{1}{50}because\ it\ equals\ to\0!} \\ \bold{Keep:\frac{1}{10}-\frac{1}{50}\ because\ it\ helps\ us\ solve\ for\ our\ answer!}[/tex]

[tex]\bold{\frac{1}{10}-\frac{1}{50}=\frac{2}{25}} \\ \\ \\ \\ \boxed{\boxed{\bold{Answer:x=\frac{2}{25}}}}\checkmark \\ \\ \\ \bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ your\ day!} \\ \\ \\ \frak{LoveYourselfFirst:)}[/tex]

Answer:

~

Step-by-step explanation:

There isn't enough context information to solve the following problem.

Answer:

5.94x10^1

Step-by-step explanation:

In scientific notation all numbers are written in the form of m×10n (m times ten raised to the power of n), where the exponent n is an integer, and the coefficient m is any real number, called the significand or mantissa. If the number is negative then a minus sign precedes m (as in ordinary decimal notation).

Answer:

145°

Step-by-step explanation:

The angle is 90°+55°=145°

Answer: 145°

Step-by-step explanation:

The angle of straight lines is always 180°, so I took 180 and subtracted 55 from it, and then 90 to get 35. I got 90 because the x and y axis are perpendicular to each other, and the angle between perpendicular lines is always 90. 35° is the angle of the small un marked section to the left of the circles, so to get the angle of the circle-like line, I did 180-35 to get 145°.

The awnser is 20 x 3

Hope this helps!

The area of a rectangle with length 4x^3 and width 5 is expressed as the monomial 20x^3 by multiplying the length and width.

To express the area of a rectangle as a monomial when given the length and width, we simply need to multiply these two dimensions together. In this case, the rectangle has a length of 4x^3 and a width of 5. The area (A) of a rectangle is given by the formula A = length * width.

So, the area of this rectangle can be calculated as:

A = 4x^3  * 5

Now, we multiply the numerical coefficients (4 and 5) and then combine them with the variable part:

A = (4 * 5) x^3

A = 20x^3

This expression, 20x^3, represents the area of the rectangle as a monomial

Answer:

9

Step-by-step explanation:

Answer:

0.8 cup(s)

Step-by-step explanation:

2 x 0.4 = 0.8

Answer:

0.8

Step-by-step explanation:

So to get this answer you had to mulyiply the 2 cups of flour by the size you want which is 0.4 . 2(0.4)=0.8

Answer:

it is bigger by 1/5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Tracey Earns in week= $102.45

Tracy=2x-12.45

102.45=2x-12.45

2x= 102.45+12.45

2x=114.90

x= 114.90/2

x=$57.45

Kayla earns 57.45 dollars

The equation is n = (102.45 + 12.45) x 2.

And Kayla earns $229.8.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

In a week, Tracey earns $12.45 less than twice the amount Kayla earns. Tracy earns $102.45.

Let n be the amount Kayla earns.

Then,

Kayla earns,

n = (102.45 + 12.45) x 2

n = $229.8

Therefore, Kayla earns $229.8.

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Answer: [tex]f(x)=4^x[/tex]

Step-by-step explanation:

The general exponential function is given by :-

[tex]f(x)=Ab^x[/tex], where A is initial amount , b is multiplicative growth rate and x is time period.

Also, the multiplicative growth rate is the common ratio of the consecutive terms.

From the given table , [tex]b=\dfrac{256}{64}=4[/tex]

Substitute, x = 3 , f(x)=64 and b=4 , we get

[tex]64=A(4)^3\\\\\Rightarrow\ 64=A(64)\\\\\Rightarrow\ A=1[/tex]

Hence, the exponential function represents the data in the table is

[tex]f(x)=(1)(4)^x\\\\\Rightarrow\ f(x)=4^x[/tex]

Answer:

Equation: $21.50•n=c

Answer:

option C is the correct answer

Step-by-step explanation:

The trigonometric equation you are using has a general form

y = A* tan w*(x - r)

Where

A is the amplitude of the function

w is the frequency rad/s

r  is the phase shift

In your case

A = -2

The frequency is

w = (2*pi)/period

period = pi/4

w = 8

r = -pi/2

y = -2* cos 8*(x + pi/2)

Answer:

$2280

Step-by-step explanation:

I see you've already found part a, which is to find the amount of interest earned. The next part is easy, to find the balance of the account after four years, just add the interest you've found back to the principal (the original size of the account or loan). $2000 + $280 equals $2280.

The interest earned on the account is $280. The balance of the account after 4 years is $2280.

To find the interest earned on the account, we use the formula for simple interest:

I = PRT

where:

Substituting the given values:

I = $2000 * 3.5/100 * 4 = $280

To find the balance of the account, we add the interest earned to the principal:

Balance = P + I = $2000 + $280 = $2280

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X is 3

Refer to picture

Answer:15

Step-by-step explanation:h=2 A/b meaning h=2 67.5/9

Answer:

h = 15 meters

Step-by-step explanation:

The area of a triangle is determined by its height multiplied by its base.

The equation is A = 1/2*bh.

Plugging in the numbers gives us 67.5 = 1/2*9h.

Dividing by 4.5 in both sides gives us that h = 67.5/4.5 = 15 meters.

Answer:

Step-by-step explanation:

4b-1=b

3b-1=0

3b=1

b=1/3

24b=

24(1/3)=

8

Equations are expression separated by an equal sign. The value of 24b if 4b-1 = b is 8

Equations are expression separated by an equal sign

Given the expresion

4b - 1 = b

Find the value of "b"

4b - b = 1

3b = 1

b = 1/3

Determine the value of 24b

24b = 24(1/3)

24b = 8

Hence the value of 24b if 4b-1 = b is 8

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