· A circular safety sign at a manufacturing plant has a diameter of 28 inches. Which measurement is closest to the area of the sign in square inches? A 87.92 in 2 B 43.96 in.? C 615.44 in. D 246.18 in.​

Two lines that form a right angle at their point of intersection are perpendicular to each other.

The negative reciprocal is equal to the slope of the perpendicular lines. A transversal line is a line that is perpendicular to two parallel lines. Equal pairs of alternate angles and matching angles are created in the case of the transversal line.

When two lines intersect at a right angle, they are perpendicular to each other. The junction is referred to as the point of perpendicularity. The perpendicular lines form a 90-degree angle, and they can be used to create a coordinate system or used in geometric constructions. Such lines are called perpendicular lines.

Correct Question :

Two lines that form a right angle at their point of intersection are called what?

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The value of \(\frac{x + 1}{x}\), when \(x = (2 +\sqrt{5} )\), is \(-4\).

To find the value of \(\frac{x + 1}{x}\), we substitute the given value of x into the expression and perform the necessary calculations.

Let's start by substituting \(x= (2 + \sqrt{5} )\) into \(\frac{x + 1 }{x}\):

\(\frac{x + 1}{x} = (2 +\sqrt{5} ) + \frac{1}{ (2 + \sqrt{5} )}\)

To simplify the expression, we need to rationalize the denominator of the second term.

Multiply the numerator and denominator of the second term by the conjugate of the denominator:

\(\frac{x + 1}{x } = \frac{(2+\sqrt{5} )+1 \times (2 - \sqrt{5}) }{(2 + \sqrt{5} )) \times (2 - \sqrt{5} )}\)

Multiplying the numerator and denominator of the second term:

\(\frac{x + 1}{x} = \frac{ (2 + \sqrt{5})+(2-\sqrt{5} ) }{ [4 - 5]}\)

Simplifying further:

x + 1 / x = (2 + sqrt(5)) + (2 - sqrt(5)) / (-1)

\(\frac{x + 1 }{x} = \frac{(1+\sqrt{5}) +(2-\sqrt{5} ) }{ (-1)}\)

Combining the like terms in the numerator:

\(\frac{x + 1 }{x} =\frac{4}{ (-1)}\)

Simplifying the expression:

\(\frac{x + 1 }{x} = -4\)

Therefore, the value of \(\frac{x + 1 }{x}\), when \(x=(2+\sqrt{5} )\), is \(-4\).

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Answer:

f(3)=0, f(4)=-60

f(n) = f(n-1) + (-60)

Step-by-step explanation:

Arithmetic Sequences

The arithmetic sequences are identified because any term n is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.

The equation to calculate the nth term of an arithmetic sequence is:

f(n)=f(1)+(n-1)r

Where

f(n) = nth term

f(1) = first term

r   = common difference

n  = number of the term

The given sequence has two known terms: 120, 60, ...

The common difference is found by subtracting consecutive terms:

r = 60 - 120 = -60

Thus the next two terms are:

f(3)=120+(3-1)(-60)=120-120 = 0

f(4)=120+(4-1)(-60)=120-180 = -60

Since each term is calculated as the previous term plus -60, then the recursive formula is:

f(n) = f(n-1) + (-60)

Answer:

That would be 14 miles ÷ 6 hours which would be 2.3333 or 2 and 1/3

Answer:

Step-by-step explanation:

/D. There is not enough information to awnser this question

The total cost next year will be: $10,613.10

Solving:

The total cost of this year

Simply just add up everything that has been given which wouold give you 10,405

The total cost of next year

multiply the total cost of this year by 1.02 to find what the cost would be with a 2% increase which should give you 10,613.1

Answer:

1/6

Step-by-step explanation:

Since it's a OR statement, find a probability of each event and add

Another way would be count the ones that give u the sum of 4 and 10 which I got 6.

Total number of outcomes is 36.

So 6/36 = 1/6

Answer:

To use the vertical line test, take a ruler or other straight edge and draw a line parallel to the y-axis for any chosen value of x. If the vertical line you drew intersects the graph more than once for any value of x then the graph is not the graph of a function.

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Hope it helps you

Mark and Henry have a ratio of 1:4 so there are 5 parts in total. We can conclude each ratio is $5 each since 25/5 is 5. Hence:

Mark - $5

Jume - $45

Henry - $20

Answer:

15 multiple choice 5 true false

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The inverse Laplace transform of \(\( \frac{2s}{(s^2+4)(s^2+9)} \) is \( \frac{2}{5} \cos 3t \)\).

The inverse Laplace transform of \(\( \frac{e^{-2s}}{s^3} \) is \( t^2e^{2t} \)\). This can be obtained using the properties and formulas of Laplace transforms.

To find the Laplace transform of \( \int_{0}^{t} \sin 2(t-\tau) \cos 3 \tau d \tau \), we can utilize the convolution theorem. The convolution theorem states that the Laplace transform of a convolution of two functions is equal to the product of their individual Laplace transforms.

First, we take the Laplace transform of each component separately. The Laplace transform of \( \sin 2(t-\tau) \) is \( \frac{2}{s^2+4} \), and the Laplace transform of \( \cos 3 \tau \) is \( \frac{s}{s^2+9} \).

Multiplying these two transforms together, we obtain \( \frac{2s}{(s^2+4)(s^2+9)} \).

Now, we need to find the inverse Laplace transform of this expression. By utilizing partial fraction decomposition, we can rewrite \( \frac{2s}{(s^2+4)(s^2+9)} \) as \( \frac{As+B}{s^2+4} + \frac{Cs+D}{s^2+9} \).

Solving for the unknown coefficients A, B, C, and D, we find that \( A = 0 \), \( B = 0 \), \( C = \frac{2}{5} \), and \( D = 0 \).

Therefore, the inverse Laplace transform of \( \frac{2s}{(s^2+4)(s^2+9)} \) is \( \frac{2}{5} \cos 3t \).

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The given paragraph states that a stationery shop has been running for 10 years near campus in Jakarta.

Students like the asker often visit this store to purchase stationery, markers, rulers, and photocopiers.

The word "been" is a past participle of the verb "be." It is used to show the completion of an action in the past.

In this case, it implies that the stationery shop has been operating for the past 10 years near the campus.

The sentence can be rewritten as follows to make use of the word "been":

"The stationery shop has been providing stationery, markers, rulers, and photocopiers to students near the campus for 10 years."

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The probability that the diameter of a selected bearing is greater than 123 millimeters is 0.8944 = 89.4400%.

The Problems of normally distributed samples can be solved using the z-score formula.

In a set the Z-score of a measure X is given by:

Z = ( X - μ )/σ

Here , μ is Mean, σ is the standard deviation and X is Z-score of a measure.

Z-score measures that how many standard deviations the measure is from the mean. After finding Z-score, we will look at the z-score table and find the p-value associated with this z-score. The p-value is the probability that value of the measure is smaller than X, i.e., the percentile of X. On subtracting 1 by the p-value, we will get the probability that the value of the measure is greater than X.

We have, μ = 71 millimeters and σ = 4millimeters

The probability that the diameter of a selected bearing is greater than 66 millimeters,

This is 1 subtracted by the p-value of Z when X = 66. So

Z = ( 66 - 71 )/4

Z = -5/4

Z = -5/4 has a p-value of 0.1056.

1-0.1056 = 0.8944

0.8944 = 89.4400% is the probability that the diameter of a selected bearing is greater than 66 millimeters.

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Therefore, the gardener can plant 48 tulips in one hour.

We can start by using a proportion to find out how many tulips the gardener can plant in one hour.

If the gardener planted 36 tulips in 45 minutes, then we can represent that as:

\(36 tulips / 45 minutes = x tulips / 60 minutes\)

where x is the number of tulips the gardener can plant in one hour.

To solve for x, we can cross-multiply and simplify:

\(36 tulips * 60 minutes = 45 minutes * x tulips\)

2,160 tulip-minutes = 45x

Dividing both sides by 45, we get:

x = 2,160 tulip-minutes / 45 = 48 tulips

Therefore, the gardener can plant 48 tulips in one hour.

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*see attachment for the diagram of the information given

Answer:

115.8°

Step-by-step explanation:

Due west = 83 miles

Northwest = 111 miles

Distance to its original position = 165 miles

Let x represent the degree north of west that it turned when it changed direction which is the opposite angle of 165 miles.

Thus, to find x, we'd apply the Law of Cosine which is given as:

c² = a² + b² - 2ab*cos C

Where,

C = x

a = 83 miles

b = 111 miles

c = 165 miles

Plug in the values

165² = 83² + 111² - 2*83*111*Cos x

27,225 = 19,210 - 18,426*Cos x

27,225 - 19,210 = - 18,426*Cos x

8,015 = -18,426*Cos x

8,015 = -18,426*Cos x

8,015/-18,426 = Cos x

-0.434983176 = Cos Cmx

Cos x = -0.434983176

x = cos^{-1}(-0.434983176)

x = 115.784223°

x = 115.8°

Answer:

The ordered pair to represent the second term as an ordered pair is:

Step-by-step explanation:

Background knowledge about the sequence function

A sequence is defined as the function whose domain is the set of natural numbers (counting numbers).

1,        2,        3,       4,     ....        n,   ....  

↓

a₁,       a₂,      a₃,      a₄,    ....       aₙ,   ....

Here,

1 gets mapped onto a₁,

2 gets mapped onto a₂, and so on

The numbers a₁,       a₂,      a₃,      a₄,    ....       aₙ,   .... are the terms of the sequence.

The number aₙ is the nth term of a sequence.

And the sequence function is denoted by {aₙ}.

Given the sequence

3, 9, 15, 21, ...

Here,

a₁ = 3 is the first term

a₂ = 9 is the second term

Thus, the ordered pair to represent the second term as an ordered pair is:

Answer:

m = variables

+4 = Coefficients

-7 = Coefficients

and 2 and 6 are Constants

Hope this helps!

Step-by-step explanation:

Answer:

\(\frac{104}{100}\)

Step-by-step explanation:

You would multiply 104/100 to the price because it would be 100%, (basically the price), plus the 4/100, the tax.

Answer:

The cost increases by $8.50 for each person who attends the event.

Step-by-step explanation:

The company charges an initial fee of $45.00

The cost increases by $8.50 for each person who attends the event.

The correct options are B and C

As per the given data:

The equation y = 8.50x + 45.00 can be used to predict the cost of the meals if x people attend the event.

By comparing this equation with the slope intercept form y = mx + c

slope(m) = 8.50

We can find out the initial fee charged by the company by substituting

x = 0 {zero people}

y = 8.50(0) + 45.00

y = $45.00

For increase in cost with each person attending the event:

Cost for 2 persons - Cost for 1 person

= 8.50(2) + 45.00 - [8.50(1) + 45.00]

= 8.50(2) - 8.50(1)

= $8.50

This is the slope of the line

Hence, The company charges an initial fee of $45.00 and the cost increases by $8.50 for each person who attends the event.

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Answer:

speed is given by:

speed=distance/time

given that:

1 mile=1,760 yards

1 hour=60 min

then the speed in yards/sec will be:

distance Ashley covered is 15 miles

time=2 hours

thus;

speed=(15x1760)/(2x60)

=220 yards/ min

Step-by-step explanation:

Hi hope helps you :)

To show that the vector v = ai + bj is perpendicular to the line ax + by = c, we establish that the slope of the vector v is the negative reciprocal of the slope of the given line. The slope of the vector v is determined by the coefficient b divided by the coefficient a.

The given line ax + by = c can be rewritten in slope-intercept form as y = (-a/b)x + (c/b). The slope of this line is given by -a/b.

To determine the slope of the vector v = ai + bj, we note that the coefficient b corresponds to the y-component and the coefficient a corresponds to the x-component. Therefore, the slope of the vector v is given by b/a.

To show that v is perpendicular to the line, we need to establish that the slope of the vector v is the negative reciprocal of the slope of the line. In other words, we need to show that -(a/b) = -(b/a).

By simplifying both sides of the equation, we can see that -(a/b) = -(b/a) is indeed true. This implies that the vector v = ai + bj is perpendicular to the line ax + by = c.

This perpendicular relationship between the vector v and the line can be visualized geometrically, as the negative reciprocal slopes indicate that the vector v is orthogonal (perpendicular) to the line.

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Answer:

x=9

Step-by-step explanation:

side opposite to 90 degree is hypotenuse(longest side of a triangle) . And other two are the legs of the triangle.

using pythagoras theorem

a^2 + b^2 = c^2

12^2 + x^2 = 15^2

144 + x^2 = 225

x^2 = 225 - 144

x^2 = 81

x = \(\sqrt{81}\)

x = 9

The lines that are parallel and the converse theorem that justifies each statement are:

4. a. x║y

b. AEA converse.

5 a. a║b

b. CIA converse.

If two alternate exterior angles on two lines are said to be congruent to each other, the two lines they lie on are proven to be parallel lines based on the alternate exterior angles converse (AEA).

If two interior angels on the same side of a transversal are congruent to each other, the lines they are found on can be proven to be parallel lines based on the consecutive interior angles converse (CIA).

Therefore, we have the following deductions:

4. a. If <9 ≅ <15, then the lines that are parallel are, x║y

b. The correct justification for this is, AEA converse.

5 a. If m<3 + m<10 = 180°, then the lines that are parallel are, a║b

b. The correct justification for this is, CIA converse.

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The slope of the table is 2

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

to determine the slope:

From the table, we have the following points:

(x,y) = (0, 4) and (1,7)

The slope is then calculated as:

m = (y2 - y1)/(x2 - x1)

Substitute known values

m = (7 - 4)/(1 - 0)

Evaluate the differences

m = 3/1

Divide

m = 2

Hence, the slope of the table is 2

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Answer: AECD

Step-by-step explanation:

Answer:AECD

Step-by-step explanation:

The solution is : Second option is correct. O B. a circle, can not form a perpendicular bisector.

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. The perimeter around the circle is known as the circumference.

here, we have,

Since we know that to form perpendicular bisector .

We need atleast two lines which form right angle.

So, right triangle can form perpendicular bisector with base and height.

Parallel lines can also form perpendicular bisector if a line is drawn from mid point of one line to mid point of another line.

A line segment can form perpendicular bisector.

But circle can't as it is curved shape it needs line to make perpendicular bisector.

Hence, Second option is correct. O B. a circle, can not form a perpendicular bisector.

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Answer:

Step-by-step explanation:

In this exercise, we are expected to convert a mathematical expression to a word problem

Given the expresion

3(x - 7) + 10

we can see that the expression has two parts or terms

the first term is 3(x - 7)

which can be translated as three times the difference of x and 7

the second part is a constant term of 10, it carries a positive sign

so we have to add it up to the first term hence the first term plus 10

In all the word to expression the mathematical relation is

Three times the difference of x and seven plus ten

Answer:

Ste p-by-step explanation:

Answer: 8=4+4, 50=25+25