construct a rectangle so that the diagonal is 6 cm and angle between them is 30 degree​

The approximate distance between Khloe and school is given by 18.78 miles.

Representing Khloe's movements on a coordinate plane.

Let us assume that Khloe's starting point (her school) is at the origin (0,0).

She walks 20 miles due west,

which means she moves 20 units to the left on the x-axis. Her new position is (-20,0).

She then walks 8 miles due north,

which means she moves 8 units up on the y-axis.

Her new position is (-20,8).

Finally, she walks 3 miles due east,

which means she moves 3 units to the right on the x-axis.

Her new position is (-17,8).

Distance between Khloe's final position and her starting point (the school),

Use the Pythagorean theorem,

Distance = √((change in x)^2 + (change in y)^2)

⇒Distance = √((-17-0)^2 + (8-0)^2)

⇒Distance = √(289 + 64)

⇒Distance = √353

⇒Distance ≈ 18.78 miles

Therefore, Khloe is approximately 18.78 miles away from her school.

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Answer: 30, 30%, 8181

Step-by-step explanation:

Step 1: I looked at the question and saw that it was asking which of the given options had the same value as 30%30 and 81 8181.

Step 2: I looked at the list of options and saw that 30, 30%, and 8181 all had the same value as the given numbers.

Step 3: I chose those three options as my answer.

Answer:6x-2y=8

Step-by-step explanation:

[tex]\left \{ {{3x-y=4} \atop {Ax-By=8}} \right. \\\frac{3x}{Ax} =\frac{y}{By} =\frac{4}{8}=\frac{1}{2}\\\frac{3}{A} =\frac{1}{2}\\A=6\\\frac{1}{B} =\frac{1}{2}\\B=2\\so, 6x-2y=8[/tex]

Answer:

6x - 2y = 8                            

Step-by-step explanation:

If:

3x - y = 4

⇒ 4* 2 = 8

then:

3*2 = 6

-1 * 2 = -2

The answer is:

6x - 2y = 8

Answer: 75%

Step-by-step explanation: 12 of 16 is expressed as 12/16. 12/16 is equal to .75 and a percent requires you to move the decimal place 2 to the right.

Answer:

Mohsin could be first, Yousuf could be second and luke could be third it doesn't matter really wich way roun it could be that yousuf is first or luke thirst.

Step-by-step explanation:

Classes studied for,      Classes he did not study for       Total

Classes Passed,   23                     4                                             27

Classes Failed,       3                      2                                             5

Total,                     26,                     6                                            32

Please find attached the two way frequency table formatted on Excel spreadsheet

the details provided are;

32 classes were taken by Romain in total during his high school years.

Three of the classes he attempted but failed to pass

27 out of the total classes Romain took and passed

26 classes were studied for by Romain.

Therefore;

26 - 3 = 23 is the number of classes Romain took, passed, and studied for.

32 - 27 = 5 is the total number of classes Romain failed.

Total classes Romain passed without paying attention: 27 - (26 - 3) = 4.

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To complete the table of inputs and outputs for the function g(x) = -4x - 1:

x   | g(x)

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

-3   | 11

-2/3   | 1/3

0   | -1

1/2   | -3

2   | -9

The perimeter of Felicia's playhouse is 60ft, and its area is 144ft².

In order to determine the perimeter and area of Felicia's playhouse, we must first analyze the provided diagram:

There are two rectangles and a triangle, therefore we must calculate the area of each shape, and then add the areas together to get the total area.

Area of Rectangle A = lw = 8ft x 10ft = 80ft²

Area of Rectangle B = lw = 4ft x 10ft = 40ft²

Area of Triangle C = (1/2)bh = (1/2)(8ft)(6ft) = 24ft²

Total Area = Area of Rectangle A + Area of Rectangle B + Area of Triangle C = 80ft² + 40ft² + 24ft² = 144ft²

To determine the perimeter, we must add up the lengths of all four sides of the rectangle and the three sides of the triangle.

P = 2l + 2w + a + b + c

P = 2(10ft) + 2(8ft) + 6ft + 10ft + 8ft

P = 20ft + 16ft + 6ft + 10ft + 8ft

P = 60ft

Therefore, the perimeter of Felicia's playhouse is 60ft, and its area is 144ft².

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Question

Felicia created a floor plan for a playhouse, as shown below. 2 ft 23 ft 7 ft 8 ft 844 What will be the perimeter and area of Felicia's playhouse?

If the number b is 90% less than 47 and the number a is 110% greater than b, then the value of a is 9.87.

If the number b is 90% less than 47, that means b is equal to 10% of 47, which can be calculated as:

b = 0.1 x 47

b = 4.7

If the number a is 110% greater than b, that means a is equal to 100% (or 1) plus 110% (or 1.1) of b, which can be calculated as:

a = (1 + 1.1) x b

a = 2.1 x 4.7

a = 9.87

Therefore, the value of a is 9.87.

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If the cube and sphere both have volume as 512 cubic units, then the solid that has a greater surface area is Cube.

we first find the side length of the cube and the radius of the sphere.

The volume of the cube is 512 cubic units,

We have,

⇒ side³ = 512,

⇒ side = 8

So, the side length of the cube is 8 units.

Volume of sphere is also 512 cubic units,

We have,

⇒ (4/3)πr³ = 512,

On Simplifying,

We get,

⇒ r = 4.96 units.

So, radius of sphere is = 4.96 units.

Next we can find the surface area of each solid.

The surface-area of cube is = 6×(side)²,

⇒ 6(side²) = 6(8²) = 384 square units,

The surface area of the sphere is = 4πr²,

⇒ 4π(r²) = 4π(4.96²) ≈ 309 square units.

Therefore, the Cube has a greater surface area than the sphere.

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Answer:

x=0 or x=-5

Step-by-step explanation:

the step by step explanation is uo above in the image. it will help you understand it

Answer:

Step-by-step explanation:

8x^2+40x=0. 8x(x+5)=0. 8x=0. Or x+5=0. So. X=0.x=_5

The values of x where the function f(x) is not continuous are x = 2, and the discontinuity at x = 2 is a jump discontinuity.

The function f(x) is defined as:

f(x) = {1/2x+5, x<=2

{x+3, x>2

To find the values of x where f(x) is not continuous, we need to check for three types of discontinuities: removable, jump, and infinite.

Removable discontinuity: This occurs when a function has a hole at a certain point, but can be made continuous by defining or redefining the value of the function at that point. In order for a discontinuity to be removable, the limit of the function as x approaches that point must exist.

To check for removable discontinuity, we need to check if the limit of the function as x approaches a certain point exists, but the function value is different from the limit. In this case, we only need to check the function at x = 2.

lim x->2- f(x) = lim x->2- 1/2x+5 = 6

lim x->2+ f(x) = lim x->2+ x+3 = 5

Since the limits from both sides are not equal, there is a removable discontinuity at x = 2. We can redefine the value of f(x) at x = 2 as 6 to remove the discontinuity.

Jump discontinuity: This occurs when the function has two distinct finite limits from both sides of a point, but the limits are not equal.

To check for jump discontinuity, we need to check if the limit of the function as x approaches a certain point exists from both sides, but they are not equal. In this case, we only need to check the function at x = 2.

lim x->2- f(x) = lim x->2- 1/2x+5 = 6

lim x->2+ f(x) = lim x->2+ x+3 = 5

Since the limits from both sides are not equal, there is a jump discontinuity at x = 2.

Infinite discontinuity: This occurs when the function approaches infinity or negative infinity as x approaches a certain point.

To check for infinite discontinuity, we need to check if the limit of the function as x approaches a certain point approaches infinity or negative infinity. In this case, there is no such point where f(x) approaches infinity or negative infinity.

Therefore, the values of x where the function f(x) is not continuous are x = 2, and the discontinuity at x = 2 is a jump discontinuity.

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The probability that in a random sample of 190 Americans aged 14 or older, more than 27 are single is approximately 0.9975

To solve this problem, we can use the normal approximation to the binomial distribution.

First, we need to calculate the mean and standard deviation of the number of singles in a sample of 190 Americans aged 14 or older.

Mean

μ = n × p = 190 × 0.22 = 41.8

Standard deviation

σ = sqrt(n ×p × (1 - p)) = sqrt(190 × 0.22 × (1 - 0.22)) = 5.27

Now, we can use the standard normal distribution to calculate the probability that more than 27 people in the sample are single. We convert the binomial distribution to a normal distribution by using the following formula

z = (x - μ) / σ

where x is the number of singles in the sample.

z = (27 - 41.8) / 5.27 = -2.80

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of -2.80 or lower is approximately 0.0025.

However, we want to find the probability of getting more than 27 singles, so we need to find the area to the right of z = -2.80. This is equivalent to subtracting the probability of getting a z-score of -2.80 or lower from 1:

P(Z > -2.80) = 1 - 0.0025 = 0.9975

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The probability that a randomly selected quartz timepiece will have a replacement time less than 11.9 years is 0.0007 or 0.07%.

The given information is that a company XYZ knows that the replacement times for the quartz timepieces it produces are normally distributed with a mean of 16 years and a standard deviation of 1.4 years. We need to calculate the probability that a randomly selected quartz timepiece will have a replacement time of less than 11.9 years. Let us solve this problem using the standard normal distribution.
The standard normal distribution has a mean of 0 and a standard deviation of 1. We can convert the given distribution into the standard normal distribution using the formula:
z = (x - μ)/σ
Where x is the replacement time, μ is the mean and σ is the standard deviation.

Putting the given values, we get:
z = (11.9 - 16)/1.4
z = -3.21
We need to find the probability that the replacement time is less than 11.9 years. This can be calculated as the area under the standard normal distribution curve to the left of z = -3.21.

Using the standard normal distribution table, we find that the area to the left of

z = -3.21 is 0.0007.
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Answer:

0.5

Step-by-step explanation:

trust me

Answer:In a standard deck of 52 cards, there are 12 face cards (4 jacks, 4 queens, and 4 kings) and 40 non-face cards. To find the number of five card hands consisting of no face cards, we need to count the number of hands that include only non-face cards.

The number of ways to choose 5 non-face cards out of the 40 available non-face cards is:

C(40, 5) = (40!)/(5!35!) = 658,008

Therefore, there are 658,008 five card hands consisting of no face cards at all.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

0+5+0= idc

Equatiοns such as f(x) = x² - 4x + 3, f(x) = -2x² + 4x - 1, and f(x) = 0.5x² + 2x - 1 are examples.

A mathematical entity knοwn as a functiοn cοnverts an input frοm οne set (knοwn as the dοmain) tο a singular οutput frοm anοther set (called the range). A functiοn, then, is a rule that designates precisely οne οutput fοr each input in the dοmain. The nοtatiοn f(x), where f is the functiοn's name and x is the input value, is frequently used tο denοte a functiοn. Fοr instance, the functiοn f(x) = 2x + 1 takes any input x, dοubles it, adds 1, and returns the οutcοme.

Cοntinuοus Functiοn

Functiοn: If c is a cοnstant, f(x) = c

All real numbers dοmain

Range: {c}

Examples οf equatiοns are f(x) = 2, f(x) = -5, and f(x) = 0.

Linear Prοcess:

m is the slοpe and b is the y-intercept in the equatiοn f(x) = mx + b.

All real numbers dοmain

the entire real number range

Examples οf equatiοns include: f(x) = 2x + 1, f(x) = -3x + 5, and f(x) = 0.5x - 2.

Functiοn: where a, b, and c are cοnstants and a 0; f(x) = ax² + bx + c

All real numbers dοmain

Range: If a > 0 οr if a 0, then y | y h, where h is the vertex's y-cοοrdinate

Equatiοns such as f(x) = x² - 4x + 3, f(x) = -2x²+ 4x - 1, and f(x) = 0.5x² + 2x - 1 are examples.

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Answer:

The angles are supplementary.

There are 252 flower seeds in the 14 packets that Mr. Doyle bought, which is option B.

What is Multiplication?

Multiplication is a mathematical operation that involves combining or adding a number to itself a certain number of times, resulting in a product that represents the total value of those added numbers. It is often represented using the "×" symbol or the asterisk symbol "*".

To find out how many flower seeds are in the 14 packets that Mr. Doyle bought, we can multiply the number of seeds in one packet by the number of packets he bought:

Number of seeds = 18 seeds/packet x 14 packets

Number of seeds = 252 seeds

Therefore, there are 252 flower seeds in the 14 packets that Mr. Doyle bought, which is option B.

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The equation of the parabola that passes through (-4, 0) and (-2, 0) and has a touch point at (-3, -1) is: y = 4x² + 24x + 32.

What is an equation?

Since the parabola is symmetric with respect to the vertical line passing through the vertex (which is in the second quadrant), its axis of symmetry is the line x = -3.

Let's first find the vertex of the parabola. The x-coordinate of the vertex is simply the average of the x-coordinates of the two given points on the x-axis:

x = (-4 + (-2))/2 = -3

To find the y-coordinate of the vertex, we can use the fact that the vertex lies on the axis of symmetry. Therefore, it must also be the midpoint of the distance between the touch point (-3, -1) and the y-axis.

The distance between (-3, -1) and the y-axis is 3 units. Therefore, the y-coordinate of the vertex is:

y = -1 - 3 = -4

So the vertex of the parabola is V(-3, -4).

Since the parabola is open in the second quadrant and its vertex is in the second quadrant, its equation has the form:

y = a(x + 3)²- 4

where a is a positive constant that determines the "steepness" of the parabola.

To find the value of a, we can use one of the given points on the x-axis. Let's use (-2, 0):

0 = a(-2 + 3)² - 4

4 = a

Therefore, the equation of the parabola is:

y = 4(x + 3)² - 4

or

y = 4x² + 24x + 32

So the equation of the parabola that passes through (-4, 0) and (-2, 0) and has a touch point at (-3, -1) is:

y = 4x² + 24x + 32.

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Complete question is: The equation of the given parabola is: y = 4x^2 + 24x + 32.

A sample space is a collection or a set of possible outcomes of a random experiment and using it we know that Tamara should assume that the sum of the two dice is 5 x 20.

A sample space is a collection or a set of possible outcomes of a random experiment.

The sample space is represented using the symbol, “S”.

The subset of possible outcomes of an experiment is called events.

A sample space may contain a number of outcomes that depends on the experiment.

So, Let X = a number of times the sum of the two numbers on two cubes is 5.

Two numbered cubes are rolled n = 180 times.

The event of getting a sum of 5 in independent of the other results.

The random variable X follows a Binomial distribution with parameters n = 180 and n = 1/9.

Then,

E(X) = np

Calculate how many times Tamara expects the two dice to sum to 5 as follows:

= E(X) = np

= 180 * 1/9

= 20

Therefore, a sample space is a collection or a set of possible outcomes of a random experiment, and using it we know that Tamara should assume that the sum of the two dice is 5 x 20.

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Complete question:

Tamara finds the sum of two number cubes rolled at the same time. The chart below shows all possible sums from the 36 possible combinations when rolling two number cubes. How many times should Tamara expect the sum of the two cubes to be equal to 5 if she rolls the two number cubes 180 times?

a)System of inequalities of the graph is

y-x-2≤0

y-x+3≥0

b)System of inequalities of the graph is

y-x≥0

y+x≥0

c)System of inequalities of the graph is

y-1≤0

y-x-1≤0

In mathematics, an inequality is a statement that two quantities or expressions are not equal. Specifically, an inequality describes a relationship between two values, indicating whether one value is greater than, less than, or equal to another value.

First line coordinates

X y

-2 0

0 2

slope=2-0/0+2=1

Equation of line is y=x+2

Second line coordinates

X y

3 0

0 -3

slope=-3-0/0-3=1

Equation of line is y=x-3

System of inequalities of the graph is

y-x-2≤0

y-x+3≥0

First line coordinates

X y

0 0

-1 -1

slope=-1-0/-1-0=1

Equation of line is y=x

Second line coordinates

X y

0 0

1 -1

slope=-1-0/1-0=-1

Equation of line is y=-x

System of inequalities of the graph is

y-x>0

y+x≥0

First line coordinates

y=1

Second line coordinates

X y

0 1

-1 0

slope=0-1/-1-0=1

Equation of line is y=x+1

System of inequalities of the graph is

y-1≤0

y-x-1≤0

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Answer:

There are two statements that may not be true:

B. If two lines intersect, both lines are in one plane.

F. There is exactly one line through any two points.

Statement B is not true because if two lines intersect at an angle, they are not in the same plane. This is known as skew lines.

Statement F is not true in non-Euclidean geometries, such as spherical or hyperbolic geometry. In these geometries, there can be multiple lines that pass through two points. However, in Euclidean geometry (which is what is typically taught in high school), there is exactly one line that passes through any two points.

Step-by-step explanation:

Answer: B. If two lines intersect, both lines are in one plane.

F. There is exactly one line through any two points

Step-by-step explanation:

The rest are true because I remember learning those in Geometry but B and F aren’t true because they just don’t make sense and aren’t true in general.

Answer:

The missing length is 45

Step-by-step explanation:

CD || AB

[tex]\mathrm{\cfrac{EC}{AC} =\cfrac{ED}{BD} }[/tex]

[tex]\mathrm{\cfrac{20}{8} =\cfrac{?}{18} }[/tex]

[tex]\mathrm{\cfrac{?}{18}=\cfrac{20}{8}}[/tex]

Cancel the common factor, which is 4:-

[tex]\mathrm{\cfrac{?}{18}=\cfrac{5}{2}}[/tex]

Multiply both sides by 18:-

[tex]\mathrm{?=45^o}[/tex]

Therefore, the missing length is 45.

________________________

Hope this helps!

The derivative of f(x) of (2√x+1){(2-x)/(x^2+3x)}, is f'(x) = (-x^3+5x+6)/[x(x+3)^2√x].

To find the derivative of the function f(x) = (2√x+1){(2-x)/(x^2+3x)}, we can use the product rule and the quotient rule.

First, let's find the derivative of (2-x)/(x^2+3x):

f1(x) = (2-x)/(x^2+3x)

f1'(x) = [(-1)(x^2+3x)-(2-x)(2x+3)]/(x^2+3x)^2

  = (-x^2-3x-4x+6)/(x^2+3x)^2

  = (-x^2-x+6)/(x^2+3x)^2

Next, let's find the derivative of 2√x+1:

f2(x) = 2√x+1

f2'(x) = 2(1/2√x) = 1/√x

Using the product rule, we get:

f'(x) = f1(x)f2'(x) + f2(x)f1'(x)

 = [(2-x)/(x^2+3x)](1/√x) + (2√x+1)(-x^2-x+6)/(x^2+3x)^2

 = (2-x)/(x^2√x+3x√x) - (x^2+4x-6)/(x^2+3x)^2√x

 = (2-x)/(x(x+3)√x) - (x^2+4x-6)/(x^2+3x)^2√x

Simplifying the expression, we get:

f'(x) = [(2-x)(x^2+3x) - (x^2+4x-6)x]/[x(x+3)^2√x]

 = (-x^3+5x+6)/[x(x+3)^2√x]

Therefore, the derivative of f(x) is:

f'(x) = (-x^3+5x+6)/[x(x+3)^2√x]

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Answer:

1/6

16.667%

well in simple terms 16.6

Step-by-step explanation:

Answer:

Even

Step-by-step explanation:

Its even because a parabola as the equation of x^2, that is an even graph!

:)

Answer:

even

(sorry if it's wrong but I'm pretty sure it's even.)

Answer:

94

Step-by-step explanation:

∠JKL and ∠JML are supplementary( they add to 180°).

Set their values equal to 180 to find the value of x.

15x - 19 + 13x + 3 = 180

Combine like terms

28x - 16 = 180

Add 16 to both sides to isolate the x

28x = 196

Divide both sides by 28

x = 7

Substitute the value of x into the expression for ∠JML

13(7) + 3 = ∠JML

91 + 3 = ∠JML

94° = ∠JML

To check our answer we can substitute the value of x into the expression for ∠JKL and if they add up to 180 we are correct

15(7) - 19 =∠JKL

105 -19 =∠JKL

86 =∠JKL

94° + 86° = 180°

Therefore we are correct