Based on problems 1-3, what can you conclude about
triangle ABC's orthocenter if x is less than 90°?

What happens to the orthocenter as x increases towards 90°?

What happens to the orthocenter as x reaches 90°?

What happens to the orthocenter as x increases to larger than 90°?

Line AD and line EG are parallel line, Transversal CH < ABC and EFH  are same side exterior angles

The presence of two parallel lines and a transversal line leads to some important theorem used in geometry

Some of the theorems include

The exterior angles refers to angles above line AD and below line EG, which are the parallel lines. These angles according to the figure are 4 and they include

The exterior angles to the left of the transversal line forms a pair of same side exterior, similarly, to the right of the transversal line forms another pair of same side exterior angles.

The question is asking  of same side exterior angles to < ABC, which is to the left of the transversal line. The pair that are same side exterior angles to the left of the transversal line are

Hence < EFH and < ABC are same side exterior angles

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Answer:B

Step-by-step explanation:

Becauee it already says the first night how many tickets were sold also on the second and the third night. And if someone read the equation they would have known that the play went in for three nights.

The rectangular equation for the plane curve defined by the parametric equation x = t + 4, y = t² is; y = x² - 8x + 16

We are given the parametric equations as;

x = t + 4

y = t²

Now, for us to convert parametric equations to a rectangular equation (cartesian equation) means that we are solving for t in terms of x and then plugging it back into the y equation.  Therefore, we have;

x = t + 4

t = x - 4

Thus;

y = (x - 4)²

Expanding this gives;

y = x² -4x - 4x + 16

y = x² - 8x + 16

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D after three rotations: 3 × 36° = 108°

F after five rotations: 5 × 36° = 180°

H after seven rotations: 7 × 36° = 252°

I after eight  rotations: 8 × 36° = 288°

Given,

In the question:

ABCDEFGHIJ is a regular decagon. It rotates clockwise about its center to form the polygon A'B'C'D'E'F G'HIJ.

To find the each angle of rotation to the point A' coincides with after that rotation.

Now, According to the question:

let's know about Decagon:

A decagon is a ten-sided polygon or 10-gon. The total sum of the interior angles of a simple decagon is 1440°. A self-intersecting regular decagon is known as a decagram.

Every regular polygon with n sides can be divided into n  congruent triangles. The angle with vertex the center of the polygon will measure

360 : n degrees.  We are given a regular decagon, therefore:

n = 10

α = 360 : n = 36°

We consider that, if the decagon is not rotated, A' coincides with A and the rotation is towards the next letter of the alphabet. This means that after one rotation of 36° A' will coincide with B, after two rotations A' will coincide with C and so on.

A' will coincide with D after three rotations: 3 × 36° = 108°

A' will coincide with F after five rotations: 5 × 36° = 180°

A' will coincide with H after seven rotations: 7 × 36° = 252°

A' will coincide with I after eight  rotations: 8 × 36° = 288°

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The value of c for the expression, -0.65(c-7) = 1.95, is 4.

According to the question,

We have the following expression:

-0.65(c-7) = 1.95

Now, 0.65 is in multiplication on the left hand side. So, it will be in the division on the right hand side. Note that the negative sign can also be moved to the right hand side.

c-7 = -1.95/0.65

c-7 = -3

Moving 7 from the left hand side will result in the change of the sign from minus to plus:

c = -3+7

c = 4

Hence, the value of c is 4 for the given expression.

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Answer:

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

Periods are the rows that span the periodic table. Families or groups are the columns that go from Page 2 up.

The maximal energy level of the electrons serves as a marker for the period (or row) in the periodic table that an atom belongs to (1 through 7). The table has 7 periods, hence there are 7 energy levels. The first period's atoms have electrons in the first energy level. The second period's atoms have electrons in two different energy states. The third period's atoms have electrons in three different energy levels. The fourth period's atoms have electrons in four different energy levels. Typically, the number of the period itself is the same as the number of energy levels in each period. The first period's atoms have electrons in the first energy level.

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The slope of given line is 43

The slope of the line is the rate of change of y with respect to xSlope of a line gives the steepness of line.

The formula of finding the slope of line with two given points is as follows,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Thewith[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]TheThe[tex]Hdb\pi[/tex]TheThelinem=y2-yy2-y1/xw-xq
x2-x1
x2-x1
x2-x1

It can be seen from the given image thatthat the line moves 3unit in x direct and 4unit in y direction.So the slope will be
be m=43

Hence,the slope of the give line is 43

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Answer:

(1,3)

(4,-3)

Step-by-step explanation:

To find y, replace x with 1 in the equation and solve for y

6x + 3y = 15

6(1) + 3y = 15

6 + 3y = 15  Subtract 6 from both sides

3y = 9  Divide both sides by 3

y = 3

(1,3)

To find x, replace y with -3 in the equation and solve for x

6x + 3y = 15

6x + 3(-3) = 15

6x - 9 = 15  Add 9 to both sides

6x = 24  Divide both sides by 6

x = 4

(4, -3)

Answer:

- 18

Step-by-step explanation:

let the number be n then double the number is 2n and

2n + 32 = [tex]\frac{2}{9}[/tex] n

multiply through by 9 to clear the fraction

18n + 288 = 2n ( subtract 2n from both sides )

16n + 288 = 0 ( subtract 188 from both sides )

16n = - 288 ( divide both sides by 16 )

n = - 18

the original number is - 18

Answer: Integers less than 4 will make the inequality true.

Step-by-step explanation:

1) subtract both sides by 4 to isolate 2x so we are now left with 8 > 2x.

2) divide both sides by 2 so we are left with just x, leaving us now with 4 > x.

Integers must be less than 4 because if you substitute x as 4, we have 12 > 12, which is not true. But, if we substitute x as 3, we are left with 12 > 10, which makes the inequality true.

The value of g(x) is √2x.

What is a composite function?

A function whose values are obtained from two given functions by first applying one to an independent variable and then using the result to apply the second, and whose domain is made up of those independent variable values for which the first function's result falls within the second function's domain.

Here, we have

g(f(x)) =x√6.

f(x) = 3x²

By applying a composite function

g(f(x)) =√6x

g(3x²) = x√6

g(x) must be √(2x)

because if we  substitute  x = 3x² in this we get

= (√2(3x^2))

= √2√3√(x²)

= √6 x

Hence, the value of g(x) is √2x.

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If there are no restrictions on the numbers then the possible number of combinations is 1,185,921.

What is a combination?

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.

Here,

There are 4 numbers needed for the combination and one can pick between 0 and 32.

This means that there are 33 numbers that can be used for the lock including 0.

The number of possible combinations is:

= Number that can be used with no restrictions on the number combination lock limit

= 33 ⁴

= 1,185,921 combinations

Hence, If there are no restrictions on the numbers then the possible number of combinations is 1,185,921.

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The number of pounds of 29% alloy and 51% alloy required to make the third alloy containing 50% aluminum is 45.82 pounds and 2.18 pounds respectively.

Let

x + y = 48

29x + 51y = 50*48

x + y = 48

29x + 51y = 2400

Solve simultaneously

From (1)

x = 48 - y

Substitute into (2)

29x + 51y = 2400

29(48 - y) + 51y = 2400

1392 - 29y + 51y = 2400

- 29y + 51y = 2400 - 1392

22y = 1008

y = 1008/22

y = 45.82 pounds

Substitute y = 45.82 pounds into (1)

x + y = 48

x + 45.82 = 48

x = 48 - 45.82

x = 2.18 pounds

So therefore, the number of pounds of 29% alloy and 51% alloy is 45.82 pounds and 2.18 pounds respectively.

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Probability of drawing a card below a 6 (count an ace as high) is 4/13

Total number of outcome : n(S) = 52

(a) In a deck number of card below a 6 (counting ace as high) is {5 , 4 , 3, 2}

so , n(E) = 4 × 4 = 16

The probability of drawing a card below a 6 (count an ace as high) = P(E)

[tex]P(E) =\frac{n(E)}{n(s)}[/tex] =16/52

P(E) = 4/13

(b) Probability of drawing a card below a 6 (count an ace as high) is 4/13

Hence , the odds of drawing a card below a 6 (count an ace as high). is 0.308

(c) we should expect to draw a card below a 6 about four times out of every 13 attempts .Also, we should expect to draw a card below or 6 four times for every nine times we draw a 6 or above is the law of large number to interpret both the probability and odds of drawing a card below 6

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The phrase that represents the algebraic expression n - 4 is option b four less than a number.

Given,

The algebraic expression; n - 4

We have to find the phrase that represents the given algebraic expression.

Algebraic expression;

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

An algebraic expression can be categorized into different categories depending on how many terms it contains: polynomial, quadrinomial, trinomial, monomial, and binomial.

So,

n - 4

That is,

4 is less than from a number

Therefore,

The phrase that represents the algebraic expression n - 4 is option b four less than a number.

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Answer:

the answer is b

Step-by-step explanation:

The ratio of the volume of the triangular prism to the volume of

 the cuboid is 3: 20

What do you mean by prism?

The base of the triangular prime is a right triangle with legs 5 cm, 4 cm

∴ b = 5 cm and h = 4 cm

∵ Its height is 9 cm

∴ H = 9 cm

→ Substitute them in the rule of the prism above

∵ V =  1/2 * (5)(4) × 9

∴ V = 90 cm³

∵ The dimensions of the base of the cuboid are 6 cm and 5 cm

∴ L = 6 cm and W = 5 cm

∵ Its height is 20 cm

∴ H = 20 cm

→ Substitute them in the rule of the cuboid above

∵ V = 6 × 5 × 20

∴ V = 600 cm³

→ Find the ratio between them

∵ V: V = 90: 600

→ Divide each term of the ratio by 30 to simplify them

∴ V: V = 3: 20

∴ The ratio of the volume of the triangular prism to the volume of

 the cuboid is 3: 20

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Answer:

$66

Explanation:

Sam earns a 5.5% commission on everything he sells. He sells a television for $1200. What is 5.5% of $1200?

Convert 5.5% to decimal form: 0.055. Now, multiply 1200 by 0.055.

Sam will earn $66 because 5.5% of 1200 is 66.

The function that represents the graph f(x) = -3|x| is f(x) = -3|x| - 5

How to find the function of the graph ?

To ascertain whether a graph accurately depicts a function, use the vertical line test. The graph is a function if a vertical line drawn across it is moved and hits it only once at any given time. If there are multiple points where the vertical line intersects the graph, the graph is not a function.

As it is already given in the question that the function

f(x) = -3|x|

We will use transformation rules to solve the given question

f(x)→f(x-a) ⇒ Graph shifted to right by a units

f(x)→f(x+a) ⇒ Graph shifted to left by a units

f(x)→f(x) - a ⇒ Graph shifted downwards by a units

f(x)→f(x) + a ⇒ Graph shifted upwards by a units

When it is translated 5 units down

Then we subtract 5 outside of the given function

∴ f(x) = -3 |x| - 5

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The expected mean for a sample of 150 women is 168.5 pounds.

Expected mean can be defined as the mean weight of a number . Based on the given data we were told that the mean weight of the us women was 168.5 pounds which implies that the expected mean is 168.5 pounds.

The formula for expected mean is :

E ( X ) = μ = ∑ x P ( x )

Where:

x = values of the random variable X

P(x) = Corresponding probability

∑ =Sum of all products xP(x)

μ = mean

Therefore the expected mean is 168.5 pounds.

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Answer:

Step-by-step explanation:

A=60

B=75

C=45

D=60

E=75

F=45

G=90

Answer:

Step-by-step explanation:

Answer:

a = 41°

b = 57°

c = 82°

Step-by-step explanation:

all angles in a triangle must add up to equal 180°

The value of cos 2A/cos A-sin A = cos A + sin A is proved

cos 2A =  2cos²A - 1

= 2cos²A - (sin²A + cos²A)

= 2cos²A - sin²A - cos²A

= cos²A - sin²A

We need to prove that

cos 2A/cos A-sin A = cos A + sin A

L.H.S

cos 2A/cos A-sin A

= cos²A - sin²A/ cos A-sin A

= (cos A + sin A)(cos A-sin A)/ cos A-sin A

= cos A + sin A

R.H.S

LHS = RHS proved

Therefore, cos 2A/cos A-sin A = cos A + sin A is proved

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The width of the rectangle is given as w = p/2 - l which is derived from perimeter of rectangle

The perimeter of a rectangle is the total distance covered by its boundaries or the sides. Since there are four sides of a rectangle, thus, the perimeter of the rectangle will be the sum of all four sides.

In this question, we simply need to make the width (w) the subject of formula.

The equation given is

p = 2w + 2l

p = 2w + 2l

p = 2(w + l)

p / 2 = w + l

w = p/2 - l

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The solutions to the financial ratio requirements based on the supplied facts are:

A. Current ratio is 1.125.

B. Acid test is 1.

C. Average days' collection is 26.7 days.

D. Asset turnover is 1.4x.

E. Profit margin on sales is 14.63%.

Financial ratios are ratios that show the relative magnitude of one financial account to another.

Financial ratios are used to compare or represent an entity's financial performance or position in relative terms.

Current Ratio = Current Assets ÷ Current Liabilities

= $18,000 ÷ $16,000

= 1.125

Acid Test Ratio = (Current Assets - Inventory) ÷ Current Liabilities

= ($18,000 - 2,000) ÷ $16,000

= $16,000 ÷ $16,000

= 1

Average Days' Collection = Accounts Receivable ÷ Net Sales x 365 days

= $3,000 ÷ $41,000 x 365

= 26.7 days

Asset Turnover = Net Sales ÷ Total Assets

= $41,000 ÷ $29,000

= 1.4x

Profit Margin on Sales = Net Income ÷ Net Sales x 100

= $6,000 ÷ $41,000 x 100

= 14.63%

Current Assets = $18,000

Accounts Receivable = $3,000

Current Liabilities = $16,000

Inventory = $2,000

Net Sales = $41,000

Total Assets = $29,000

Net Income = $6,000

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a) The amount of money in the account at the beginning is $222,222.222.

b) The total amount of money withdrawn from the account is $400,000.

c) The amount of interest earned is $177,777.778.

It is given that we want to be able to withdraw $20,000 per year for 20 years. The account earns 9% interest annually. Let the total amount of money withdrawn in the twenty years be represented by the variable "A".

A = $20,000*20 = $400,000

Let the amount of money in the account at the beginning be represented by the variable "P".

A = P*R*T

400,000 = P*0.09*20

400,000 = P*1.8

P = 222,222.222

The interest earned is the difference between the initial and the final amount in the bank. Let the interest earned be represented by the variable "I".

I = A - P = $400,000 - $222,222.222 = $177,777.778

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Answer: x=-2, x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]

Step-by-step explanation:

f(x) = x³ - 4x² - 5x + 14

-2    |    1    -4     -5     14

                -2      12   -14

           1    -6       7     0

x³ - 4x² - 5x + 14 = (x+2)(x²-6x+7)

x²-6x+7=0

x²-6x+9-2=0

(x²-6x+9)-2=0

x²-6x+9=2

x²-3x-3x+9=2

x(x-3)-3(x-3)=2

(x-3)²=2

x-3=[tex]\sqrt{2}[/tex], -[tex]\sqrt{2}[/tex]

x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]

Hence, zeroes are x=-2, x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]

Step-by-step explanation:

our first "suspicion" for a factoring is an integer factor of the constant term : 14.

14 = 2 × 7 or -2 × -7

I started to try 2 or -2 and found that -2 is indeed a zero solution.

so, the first factors are

f(x) = (x + 2)(x² + ...)

let's divide (x³ - 4x² - 5x + 14) by (x + 2) to get the x² term.

x³ - 4x² - 5x + 14 ÷ x + 2 = x² - 6x + 7

- x³ + 2x²

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

0 -6x² - 5x

- -6x² - 12x

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

0 7x + 14

- 7x + 14

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

0 0

f(x) = (x + 2)(x² - 6x + 7)

the zeros for x² - 6x + 7 we get from the general solution for a quadratic equation

ax² + bx + c = 0

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (6 ± sqrt((-6)² - 4×1×7))/(2×1) =

= (6 ± sqrt(36 - 28))/2 = (6 ± sqrt(8))/2 =

= 3 ± sqrt(8/4) = 3 ± sqrt(2)

x1 = 3 + sqrt(2)

x2 = 3 - sqrt(2)

so, the zeros are

-2, 3 - sqrt(2), 3 + sqrt(2)

Graph for the modulus function is as follows.

What is modulus function?

A modulus function is a function that determines a number or variable's absolute value.

Main body:

Given that,

Which graph represents the function f(x) = 4⌈x⌉?

Now,

to represent the graph of Y =  IxI-4 .

So,

Taking x = 0, we get

Y =  IxI -4

Y =  I0I -4

Y = -4

Taking x = 1, we get

Y =  IxI - 4

Y =  I1I -4

Y = -3

Taking x = 2, we get

Y =  IxI - 4

Y =  I2I - 4

Y = -2.

Taking x = -1, we get

Y =  IxI - 4

Y =  I-1I - 4

Y = 1 -4

Y = -3

Taking x = -2, we get

Y =  IxI - 4

Y =  I-2I - 4

Y = -2

Hence the graph for the function is as follows.

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The total cost is $1.75

Given that we've done it:

The total price is shown by:

Now, let's display the following in a number line:

So, after seven hops, we arrive at 1.75, which is the correct response.

Hence, the total cost is $1.75

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