Abby takes a 75-centimeter by 40-centimeter rectangle of fabric and cuts from one corner of
the piece of fabric to the diagonally opposite corner. Now Abby has two equally sized triangles of fabric. What is the perimeter of each triangle centimeters

The angle of depression of the airplane is 39.8°, length of the runway is 45794 ft, and approximate height of the tower is 321 m.

The angle of depression of the airplane is given as follows:

Let the angle of depression be A.

[tex]A= {tan}^{ - 1} ( \frac{15000}{8000} ) = {39.8}^{o} [/tex]

Angle of depression is 39.8°.

If the angle of elevation is 6.8°, the length of the runway l is calculated thus:

horizontal distance of airplane from end of runway = d

length of runway, L = d - 80000 ft

[tex]d = \frac{15000}{tan 6.8°} = 125794 ft[/tex]

L = 125794 - 80000

L = 45794 ft

The length of the runway is 45794 ft

2. Let the height of the tower be H

[tex]H = \tan(69.8) \times 118 = 321m[/tex]

The approximate height of the tower is 321 m

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Answer:

2

Step-by-step explanation:

the same as...

(2) is the answer

If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be the same as that when the population is not highly skewed.

The central limit theorem states in probability theory that, in many instances, when independent random variables are added together, their correctly normalized sum tends toward a normal distribution, even if the original variables are not normally distributed.

If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be the same as that when the population is not highly skewed.

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The fact that Dean Field places random numbers in the general ledger system to make it balance and leaves the office to catch his flight is wrong.

It should be noted that a ledger simply means a record of the balance of each of the accounts of a business.

In this case, when he realizes the company’s trial balance is a mess and it does not balance, he should have waited and ensured that he re calculated it and made it balance.

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Answer:

140

Step-by-step explanation:

Angles in a triangle add up 180 :

180 = 107 + 33 + y

y = 180 - (107+33)

y = 180 - 140

y = 40

Angles on a straight line add up to 180 so :

180 = x + y

180 = x + 40

x= 180 - 40

x = 140

Hope this helped and have a good day

Answer:

x = 140°

Step-by-step explanation:

Concepts

The Exterior Angle Theorem states that the two remote angles in a triangle is equal to the exterior angle.

Application

In this case, the two remotes angles are 107 and 33°, and the exterior angle is x. Now, all we have to do is just add 107 and 33 to get our answer.

Solution

Answer:

5.6

Step-by-step explanation:

If you add all the numbers together then divide it by 15 you would get 5.6

Answer:

variable, In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).

Answer:

variable, In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).

Step-by-step explanation:

In Maths, a variable is an alphabet or term that represents an unknown number or unknown value or unknown quantity. The variables are specially used in the case of algebraic expression or algebra. For example, x+9=4 is a linear equation where x is a variable, where 9 and 4 are constants.

Answer:

35,000

Step-by-step explanation:

^4 means 4 zeros

10^4 = 10,000

3.5 times 10,000 =

35,000

The height and the base area of both the design must be equal. Then the correct option is A.

A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.

A manufacturer of kitchen utensils and gadgets is considering changing the design of their salt and pepper shakers.

Their current design is a standard cylinder, while the new design they are considering is an oblique cylinder.

The figure shows both designs.

The volume of the cylinder will be given as

V = πr² h

If the volume of the oblique cylinder and right cylinder is the same.

Then the height of both the designs must be equal and the base area of both the design must be equal.

Then the correct option is A.

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Answer:

D

Step-by-step explanation:

did the test on edmentum

Hi Student!

Let's go through each of the options that were provided to the question stating what part of the circle was highlighted in red and talk about what they mean.

First off, radius is the distance from the outer line to the middle which perfectly incapsulates what the red line is.  Therefore, the correct answer would be option A, Radius.

However, if you want to understand the rest of the definitions you can follow with the bullets provided.

Step-by-step explanation:

12 . The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations..

The rationalization the denominator of the fraction  (6)/(4+\sqrt(5)) is [tex]\dfrac{6(4-\sqrt(5))}{11}[/tex].

Suppose the given fraction is [tex]\dfrac{a}{b+c}[/tex]

Then the conjugate of the denominator is given by b - c

Thus, rationalizing the fraction will give us

[tex]\dfrac{a}{b+c} \times \dfrac{b-c}{b-c} = \dfrac{a(b-c)}{b^2 - c^2}[/tex]

The given expression is

[tex]\dfrac{6}{4+\sqrt(5)}\\\\[/tex]

By rationalizing the denominator of the fraction

[tex]\dfrac{6}{4+\sqrt(5)}\times \dfrac{4-\sqrt(5)}{4-\sqrt(5)} \\\\\\\dfrac{6(4-\sqrt(5))}{4^2-(5)}\\\\\\\dfrac{6(4-\sqrt(5))}{11}[/tex]

Thus, the rationalization the denominator of the fraction  (6)/(4+\sqrt(5)) is [tex]\dfrac{6(4-\sqrt(5))}{11}[/tex].

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The equation that best models the data is (a) y = 186 - 6.2x

The data is not provided; so I would give a general guide on how to model a linear equation.

Assume the points on the line are:

(0,186) and (1,179.8)

Start by calculating the slope of the line using:

[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]

This gives

[tex]m = \frac{179.8 - 186}{1 - 0}[/tex]

Evaluate

m = -6.2

The equation is then calculated using:

[tex]y = m(x - x_1) + y_1[/tex]

This gives

y = -6.2(x - 0) + 186

Evaluate

y = -6.2x + 186

Rewrite as:

y = 186 - 6.2x

Hence, the equation that best models the data is (a) y = 186 - 6.2x

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Considering the given function, the ordered pair (5,8) means that the signed up for 5 weeks of yoga classes and 8 weeks of kickboxing classes.

The function that represents the relationship between the number x of yoga classes that Donovan signs up for and the number y of kickboxing classes is given by:

8x + 12y = 136.

Hence the ordered pair (5,8) means that the signed up for 5 weeks of yoga classes and 8 weeks of kickboxing classes.

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Answer:

52 x 7= 50 x 7 + 2 x 7

Step-by-step explanation:

Answer:

[tex]log_2(10)[/tex]

Simplify the equation using logarithms.

[tex]2^3x=10[/tex]

[tex]log_1_0(2^3x)=log_1_0(10)[/tex]

log rule ⇩

[tex]log_a(x^y)=y*log_a(x)[/tex]

move exponent out of log.

[tex]x*log_1_0(2)=log_1_0(10)[/tex]

isolate variable further

[tex]x*log_1_0(2)=log_1_0(10)[/tex]

[tex]x=\frac{log_{10}(10)}{log_{10}(2)}[/tex]

formula for combining logs. ⇩

[tex]\frac {log_b(x)}{log_b(a)}=log_a(x)[/tex]

the result ⇩

[tex]x=log_2(10)[/tex]

Step-by-step explanation:

Because probability is always one(1).

Probability =

[tex]1 - \frac{2}{10} [/tex]

[tex] \frac{8}{10} [/tex]

[tex] \frac{4}{5} [/tex]

Is the probability of not choosing a red marble.

The table in which y varies directly with x is table C.

When a variable varies directly with another variable, it means that as one variable increases, the other variable also increases.

The equation that is used to represent direct variation is:

y = kx

Where y is the constant of proportionality

In table c, k is equal to 26

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To hold 1,000,000 inflated balloons,

38 classrooms are needed.

In three-dimensional space,

the amount of space taken by an object is the volume of that object.

The volume of the cubic,

= length x width x height

Given:

The dimensions of the normal classroom are 15 ft × 50 ft × 35 ft.

The volume of the classroom,

= 15 ft by 50 ft by 35 ft.

= 26250 cubic feet.

The number of classrooms,

= 1,000,000 / 26250

Simplifying the fraction,

we get,

= 38.09

≈ 38 to the nearest whole number.

Therefore, 38 classrooms are required.

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Answer:

  7.2 cm

Step-by-step explanation:

The height of the trapezium can be found by making use of the area formula with known values filled in.

__

The area of a trapezium is given by ...

  A = 1/2(b1 +b2)h . . . . b1, b2 are the parallel sides, h is the height

Using the given values, we have ...

  90 cm² = 1/2(6 cm +19 cm)h . . . . . . use the known values

  (90 cm²)/(12.5 cm) = h = 7.2 cm . . . . divide by the coefficient of h

The height of the trapezium is 7.2 cm.

Answer:

4 and 7/12

Step-by-step explanation:

This is addition with fractions.

We must convert to the same denominator.

1/3 and 1/4 becomes 4/12 and 3/12

This makes 7/12

1 add 3 add 7/12 is 4 and 7/12

The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.

Quadratic functions are polynomials of grade 2 of the form y = a · t² + b · t + c, where t and y are the time and the height of the ball, in seconds and feet, respectively. To determine the value of the three coefficients we need to know three different points of the form (t, y).

If we know that (t₁, y₁) = (0 s, 0 ft), (t₂, y₂) = (1 s, 16 ft) and (t₃, y₃) = (3 s, 0 ft), then the quadratic function is:

a · 0² + b · 0 + c = 0     (1)

a · 1² + b · 1 + c = 16      (2)

a · 3² + b · 3 + c = 0      (3)

The solution to this system is a = - 8, b = 24, c = 0.

The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.

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Answer:

Divide 12 by -6

Answer:

6x² + 7x-20

A. (3x-4)(2x + 5)

The formula for calculating the mark up percentage is as follows:

sticker price - invoice price/invoice price • 100 = percent mark up

Percentage mark up can be described as follows:

percentage mark up = selling price per unit - cost price per unit / cost price per unit × 100

Therefore,

Mark up is the difference between a product's selling price and cost as a percentage of the cost.

Therefore, the formula for calculating the mark up percentage is as follows:

sticker price - invoice price/invoice price • 100 = percent mark up

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Answer:

I guess, A is the wanted answer, but

A and D together are the really correct answer.

Step-by-step explanation:

if I understand this correctly, then

g(x) = sqrt(x - 3)

the domain of a function is the definition of all valid x (input) values.

the range of a function is the definition of all valid y (result) values.

well, the content (the arguments) of a square root cannot be negative (at least not while dealing with real numbers).

so, the answer options B and D are automatically out, because the domain contains values that would make the arguments of the square root negative.

I guess your teacher wants to focus only on the positive results of the square root, so A is the correct number.

BUT formally, without designated restrictions, a square root has always 2 solutions : a positive and a negative one.

because (-x)² = (x)² = x².

so, I would have to say that the really correct answer is

A + D, because the range contains both, the positive and the negative numbers.

Answer:

Multiply:

[tex](x+y)by (x+y)[/tex]

[tex] : \implies(x + y)(x + y)[/tex]

[tex] : \implies \: x(x + y) + y(x + y)[/tex]

[tex] : \implies {x}^{2} + xy + xy + {y}^{2} [/tex]

[tex] : \implies{x}^{2} + 2xy + {y}^{2} [/tex]

Multiply:

[tex]a+b \: by \: a^2-b^2[/tex]

[tex]: \implies( {a}^{2} + {b}^{2} ) \times (a + b)[/tex]

[tex]: \implies \: {a}^{2} (a + b) - {b}^{2} (a + b)[/tex]

[tex]: \implies \: {a}^{3} + {a}^{2} b - {ab}^{2} - {b}^{3} [/tex]

Multiply:

[tex](a+5) by (a^2-2a-3)[/tex]

[tex]: \implies{(a + 5) \times ( {a}^{2} - 2a - 3) }[/tex]

[tex]: \implies \: a({a}^{2} - 2a - 3) + 5( {a}^{2} - 2a - 3)[/tex]

[tex]: \implies(a \times {a}^{2} - a \times 2a - a \times 3) + (5 \times {a}^{2} - 5 \times 2a - 5 \times 3)[/tex]

[tex]: \implies{a}^{3} - {2a}^{2} - 3a + 5 {a}^{2} - 10a - 15 [/tex]

[tex]: \implies{ {a}^{3} + {3a}^{2} - 13a - 15}[/tex]

Multiply:

[tex](a^2-ab+b^3) by (a+b)[/tex]

[tex]: \implies{(a + b) \times ( {a}^{2} - ab + {b}^{3} )}[/tex]

[tex]: \implies \: a( {a}^{2} - ab + {b}^{3}) + b( {a}^{2} - ab + {b}^{3} ) [/tex]

[tex]: \implies {a}^{3} - {a}^{2} b + a {b}^{3} + {a^2b} - {ab}^{2} + {b}^{4} [/tex]

[tex]: \implies{ {a}^{3}+ab^3 - ab^2+ {b}^{4} }[/tex]

Step-by-step explanation:

[tex] \blue{ \frak{Seolle_{aph.rodite}}}[/tex]