Question 3 of 21
Which of the following are the domain and range that represent the inverse of
the function f(x), given the mapping diagram of f(x) below?

The circumcenter is the center of the circle which goes through the triangle's vertices, so the circumcenter of the triangle and the center of that circumscribed circle MUST be the same point.

The same goes for the incenter and the center of the inscribed circle, though these will not, in general, be the same point as the circumcenter.

Answer: Another name of circumcenter is, " Circumscribed circle ". The circumcenter is the center point of the circumcircle drawn around a polygon. The circumcircle of a polygon is the circle that passes through all of the polygon's vertices & the center of that circle is called the circumcenter. All polygons that have circumcircles are known as cyclic polygons. However, all polygons does not have a circumcircle. Only regular polygons, triangles, rectangles, and right-kites can have the circumcircle and thus the circumcenter as well.

You may find that the circumcenter of a triangle as the most common thing asked in exams and it is generally what schools begin with. So, some brief information about the circumcenter of a triangle is given below. You may safely ignore them if you haven't learned them yet.

The circumcenter of triangle can be found out as the intersection of the perpendicular bisectors (the lines that are at right angles to the midpoint of each side) of all sides of the triangle. This means that the perpendicular bisectors of the triangle are concurrent (meeting at one point). All triangles are cyclic and hence, can circumscribe a circle, therefore, every triangle has a circumcenter.

Property 1: All the vertices of the triangle are equidistant from the circumcenter.

Property 2: All the new triangles formed by joining O to the vertices are Isosceles triangles.

Property 3: Circumcenter lies at the midpoint of the hypotenuse side of a right-angled triangle

Property 4: In an acute-angled triangle, circumcenter lies inside the triangle

Property 5: In an obtuse-angled triangle, it lies outside of the triangle

Note- Location for the circumcenter is different for different types of triangles.

The circumcenter of any triangle can be constructed by drawing the perpendicular bisector of any of the two sides of that triangle. The steps to construct the circumcenter are:

P(X, Y) = [(x1 sin 2A + x2 sin 2B + x3 sin 2C)/ (sin 2A + sin 2B + sin 2C), (y1 sin 2A + y2 sin 2B + y3 sin 2C)/ (sin 2A + sin 2B + sin 2C)]

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Answer:

[tex]\sf x = \dfrac{\sqrt{19}+5}{3} \ ; \ x = \dfrac{-\sqrt{19}+5}{3}[/tex]

Step-by-step explanation:

(3x - 5)² = 19

To find the solution for the equation,  take square root on both sides.

    [tex]\sf 3x - 5 = \± \sqrt{19}\\\\ Add \ 5 \ to \ both \ sides \\\\ 3x = \±\sqrt{19} + 5\\\\ Divide \ both \sides \ by 3\\\\ x = \dfrac{\±\sqrt{19}+5}{3}\\\\x = \dfrac{\sqrt{19}+5}{3} \ ; \ x = \dfrac{-\sqrt{19}+5}{3}[/tex]

The area is given by f(x) = 10x² + 31x + 15.

The function is a rectangle's area function. We know that a rectangle is a flat, four-sided shape with straight sides and right-angled interior angles. Additionally, the opposing sides are parallel and of the same length.

Rectangle Area = Length * Width

The length of fabric scrap is 5x. So, the rectangular patchwork's length will be 5x + 3.

Since the width of the fabric scrap will be 2x, the rectangular patchwork's width will be 2x + 5.

Then area = f(x) = (5x + 3)(2x + 5) = 10x² + 25x + 6x + 15 = 10x² + 31x + 15

Therefore the area is given by f(x) = 10x² + 31x + 15.

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Answer:

A function is when each input has exactly one output

Step-by-step explanation:

Each input can only have one output, but an output can have multiple inputs.

The probability that the summer solstice will occur on a weekday is equal to 5/7.

Generally, there are seven days in a week and two among these days are weekends while five are weekdays. Thus, this can be represented as follows:

Therefore, the probability that the summer solstice will occur on a weekday is given by:

P = 5/7.

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Solving the exponential function, the resulting logarithmic expression is:

x = ln(4).

Considering an exponential equation involving Euler number e, the expression is solved applying the natural logarithm ln, which is the inverse function to the exponential function, to both sides of the equation.

Hence:

[tex]e^{x} = 4[/tex]

Applying ln to both sides:

[tex]\ln{e^x} = \ln{4}[/tex]

Since ln and e are inverse, we can isolate x, hence:

[tex]x = \ln{4}[/tex]

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Answer:

Jane is 11 1/4 years old.

Step-by-step explanation:

Subtract all of the numbers given.

[tex]13\frac{5}{6} -1\frac{1}{3} -1\frac{1}{4}[/tex].

To subtract this, we need to find a common denominator.

A common denominator in this situation is 12. To do this multiply the 5 and the 6 of 5/6 by 2. Multiply the 1 and the 3 of 1/3 by 4. And multiply the 1 and the 4 1/4 by 3.

The new expression will look like this:

[tex]13\frac{10}{12} -1\frac{4}{12} -1\frac{3}{12}[/tex].

Now we can subtract.

[tex]13\frac{10}{12} -1\frac{4}{12} -1\frac{3}{12}=11\frac{3}{12}[/tex]

Reduce the answer.

[tex]11\frac{3}{12}=11\frac{1}{4}[/tex]

In decimal form 11.25

Hope this helps!

If not, I am sorry.

Answer:

175000 km

Step-by-step explanation:

the 1:25000 essentially means that every centimeter represents 25000 kilometers. so the answer is 175000 by multiplying 7 and 25000

Answer:

Inequality Form:

b ≥ 1

Interval Notation:

[1,∞)

Step-by-step explanation:

The speed of Aro's paddling and speed of the river will be 1.56 miles per hour and 0.52 miles respectively.

Aro diagrams his river rafting trip, estimating the time it will take him to paddle upstream against the current, and then back downstream with the current. His campsite destination is 5.2 miles upstream. Determine how fast Aro can paddle and how fast the river water is moving. Round to the nearest hundredth as needed. Upstream: Downstream: Let x be the speed of Aro’s paddling and let y be the speed of the river. Upstream: 1.04 = x – y Downstream: 2.08 = x + y Aro can paddle at a speed of miles per hour. The river’s speed is miles per hour.

Based on the information given, the equations will be:

x + y = 1.04

x + y = 2.08

Add both equations together. This will be:

x = 1.56

Now substitute the value of x into equation ii. This will be:

1.56 + y = 2.08

y = 2.08 - 1.56

y = 0.52

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Answer:

-28

Step-by-step explanation:

put 3 where is x

f(x) = −5(3)^2 − (3) + 20

exponents flrst

(−5*9) − (3) + 20

-45 -3 +20

-48 + 20

-28

Answer:

The y-coordinates do not change under a horizontal stretch. The x-coordinates do not change under a vertical stretch.

Step-by-step explanation:

Answer:

2 days 21 hours and 50 minutes

Step-by-step explanation:

There are a couple of ways to solve this. Here is my approach

Convert everything to the lowest unit ie minutes, find the difference and then find the equivalent days, hours and minutes

Note

1 hour = 60 minutes

1 day = 24 hours * 60 minutes/hour = 1440 minutes

So,

7 days, 8 hours, 20 minutes = 7 * 24 * 60 + 8 * 60 + 20 = 10580 minutes
4 days, 10 hours, 30 minutes = 4 * 24 * 60 + 10 * 60 + 30 = 6390 minutes

Difference(elapsed time) = 10580 - 6390 = 4190 minutes

Convert 4190 to days, minutes and hours. This is a process of using whole division to find the quotient and remainder successively

For days, divide by 1440 which is the number of minutes in a day:
4190 minutes ÷ 1440 minutes = 2 whole days  with remainder of 1390 minutes

For hours divide by 60 which is the number of minutes in an hour:
the remainder 1390 minutes ÷ 60 minutes = 21 whole hours with remainder of 50 minutes

So 4190 minutes == 2 days, 21 hours and 50 minutes

The correct answer is option A which is segment D which is closer to home.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

From the given graph we can see that in segment D the distance between the home and the person is lesser than all the segments given in the graph.

Therefore the correct answer is option A which is segment D which is closer to home.

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The inequality x ≤ 88 represents the situation, and the line graph first represents the solution to the inequality option first is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

The missing options are in the picture, please refer to the picture.

We have:

An airplane can seat up to 175 passengers. The airline has already sold 87 tickets for a flight on the airplane.

Let's suppose the number of tickets is represented by x

Total number of passengers = 175

The inequality can be framed:

x + 87 ≤ 175

x ≤ 88

Thus, the inequality x ≤ 88 represents the situation, and the line graph first represents the solution to the inequality option first is correct.

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Step-by-step explanation:

Let, the given point of the equation of the line are (3,-1) and (0,3) i.e

(x1,y1)=(3,-1) and (x2,y2) = (0,3)

Now,

The slope of the line (m1) = y2-y1 ÷ x2-x1

= 3-(-1) ÷ 0-3

= 3+1 ÷ -3

= 4/-3

since, the lines are parallel i.e.

m1 = m2

or, m2 = -4/3

Again,

The required equation of the line passing through the point (-3,2)=(x1,y2) is

y-y1 = m2(x-x1)

or, y-2 = -4/3 ( x +3)

or, 3(y-2) = -4(x+3)

or, 3y-6 = -4x - 12

or, 4x+3y = -12+6

Therefore, 4x+3y = -6 is the right answer.

The true statement is (b) the random variable is x, the possible values are 0 to 3 and the values are numerical

The table is added as an attachment

From the attached image, we have:

Number of girls (x)          P(x)

0                                         0.125

1                                         0.375

2                                         0.375

3                                         0.125

In the above, the random variable is x, while P(x) represents its probabilities.

Also, the possible values are 0 to 3 as shown in the table.

0 to 3 are numerical digits, and the values are numerical

Hence, the true statement is (b)

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The relation written as a set of ordered pair is given as: : {(–2, 2), (0, 0), (3, –3)}. (Option D)

An ordered pair is a in math is one that comprises coordinates of one point in the coordinate system where the first is the x coordinate and the other is representative of the y coordinate.

Thus the correct ordered pair is option D. See the graph attached.

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1) Angles IDO and ILO are congruent, and both measure 122 degrees. So, as angles in a quadrilateral add to 360°, angle LOD measures 360-122-122-32=84°

2) As referred to in the first question, angle ODI measures 122°

3) In a kite, there are two pairs of disjoint congruent sides. This means that in this case, ID=IL=21 and LO=OD. As the perimeter is 74, this means LO=(74-21(2))/2=16

4) LI=ID, so ID=21

Answer: x²-59x+114=0

explanation:

If the roots are 2 and 57, then:-

sum of roots = 2+57 = 59

and, product of roots = 2×57 = 114

the quadratic equation is given by,

x²-(sum of roots)x+(product of roots)=0

so, x²-59x+114=0 will be the desired quadratic equation.

so, none of the options are correct.

the correct answer is x²-59x+114=0.

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Answer:

B

they both have equal probability of winning as both of them have a 50/50 chance of winning

Step-by-step explanation:

Yes, the game is fair because both friends have an equal probability of winning.

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

The game of Odds or Evens is not fair because Raul has a higher probability of winning than Luis.

In this game, the probability of both coins landing on heads or both coins landing on tails is 1/2 * 1/2 = 1/4.

Therefore, there is a 1/4 probability that Luis will win both coins.

However, there is a 1/2 probability that one coin will land on heads and the other will land on tails. In this case, Raul will win both coins because he chose "evens" and the sum of the numbers is even.

The sum of two random coin flips has an equal probability of being even or odd, so the probability of Raul winning both coins is 1/2.

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The equation equivalent to the simple interest formula A = P(1 + rt), that Celo used is P = A/(1 + rt). Hence, the first option is the right choice.

Equivalent equations are the equations that are transformed from one equation to another equation, but the final values they give are equal. It's just the change of the variable on which the equation is derived.

The simple interest equation that Celo used is A = P(1 + rt).

This is currently used to find the final amount A.

On isolating P to one side of the equation in the following ways:

A = P(1 + rt),

or, A/(1 + rt) = {P(1 + rt)}/(1 + rt) {Dividing both sides by (1 + rt)}.

or, A/(1 + rt) = P {Simplifying}.

or, P = A/(1 + rt) {Changing sides}.

Thus, the equation equivalent to the simple interest formula A = P(1 + rt), that Celo used is P = A/(1 + rt). Hence, the first option is the right choice.

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Answer:

Rate of Change = -77.9 feet/year

My interpretation: "Is Bad."

Step-by-step explanation:

The rate of change is the number of feet that Lake Powell dropped, divided by the number of years the drop took place.  We want a value with a unit of feet/year.

Year    Feet

1999     3893

2005    3425.6  

Change

Year = (2005 - 1999)  or 6 years

Feet = (3425.6 - 3893) or -467.4 feet

Rate of Change = (-467.4 feet)/(6 years)

Rate of Change = -77.9 feet/year

=======================

FYI:  Lake Powell is 22.39 feet lower today (June 23, 2022) than it was 1 year ago.

Answer:

EAD

Step-by-step explanation:

The result of the expression in exponential form is 9^-4

Given the expression below

[tex]9^2 \times 9^{-6}[/tex]

According the product law, since the base are equal, we will add the exponent to have:

[tex]9^2 \times 9^{-6}=9^{-6+2}\\9^2 \times 9^{-6} = 9^{-4}[/tex]

Hence the result of the expression in exponential form is 9^-4

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Hello!

Answer:

[tex]\Large \boxed{\sf A. -7}[/tex]

Step-by-step explanation:

We have this inequality:

[tex]\sf -5x - 7 \geq 28[/tex]

Let's solve this inequality:

◼ Add 7 to both sides:

[tex]\sf -5x - 7+7 \geq 28+7[/tex]

◼ Simplify both sides:

[tex]\sf -5x \geq 35[/tex]

◼ Divide both sides by -5, so also change the sign of the inequality

[tex]\sf \dfrac{-5x}{-5} \leq \dfrac{35}{-5}[/tex]

◼ Simplify both sides:

[tex]\boxed{\sf x \leq -7}[/tex]

So the correct answer is A. -7

Answer:

width=14 &Length = 70( can add unit behind the answer e.g.cm or mm etc..)

Step-by-step explanation:

we know that in a rectangle not all side are same compare to a square..

therefore:

1) write the formula for perimeter down

perimeter = the sum of all side

perimeter = 2x(width) + 2x(length)

P=2(w)+2(L)

2) substitute into the equation

P =2(w)+2(L)

84=2(w)+2(5*w)

3) perform opposite operation to make w become the subject of the formula inorder to find width

48=2(w)+2(5*w)

48=2w+10w

48=12w

48/12=12w/12( the twelves cancels out)

7=w or the width is 7

4) rewrite the formula and solve

P=2(w)+2(L)

P =2(7) + 2(5*7)

P = 14 + 70

P = 48