You need to catch two different buses to get to the shops Bus 1 is due to leave at 2 o'clock and arrive at 2.30. You have a half hour wail between getting off the first bus and getting on the second bus.

Bus 2 is due to arrive at the shops at 3.15.

(a) What time is bus 2 scheduled to leave? Bus 2 leaves 15 minutes early
(b) What time does it leave? () What time does it anive?
Bus 1 is 15 minutes late.
(c) What time does it arrive?​

Answer:

18 and 19

Step-by-step explanation:

Consecutive positive integers have a difference of 1 between them

let n and n + 1 be the 2 integers, then

n(n + 1) = 342, that is

n² + n = 342 ( subtract 342 from both sides )

n² + n - 342 = 0 ← quadratic equation in standard form

(n + 19)(n - 18) = 0 ← in factored form

Equate each factor to zero and solve for n

n + 19 = 0 ⇒ n = - 19

n - 18 = 0 ⇒ n = 18

However, n > 0 ⇒ n = 18 and n + 1 = 18 + 1 = 19

The 2 integers are 18 and 19

Answer:

I have to assume that the 24, the 72, and the 18 are feet.

If those are the dimensions of a rectangular prism, like a box, a crate,

or a humongous block of ice, then

           Volume = (length) x (width) x (height) =

                            (24-ft) x (72-ft) x (18-ft) =  31,104 cubic ft

If those numbers are inches, then here's the easy way to handle it:

      24 inches  =  2 ft

      72 inches  =  6 ft

      18 inches  =  1.5 ft

              Volume  =  (length) x (width) x (height) =

                                    (2ft) x (6ft) x (1.5ft)  =  18 cubic feet

Answer:

A 15

Step-by-step explanation:

In an isosceles trapezoid, each pair of base angles is congruent.

In this isosceles trapezoid, angles B and C are congruent, so their measures are equal.

m<B = m<C

60 = 3x + 15

Subtract 15 from both sides.

45 = 3x

Divide both sides by 3.

15 = x

x = 15

Answer:  The correct option is (A) 15.

Step-by-step explanation:  As shown in the attached figure below, ABCD is an isosceles trapezoid with AD parallel to BC.

Also, m∠B = 60°  and  ∠C = (3x +15)°.

We are to find the value of x.

Since ABCD is an isosceles trapezoid with AB and CD as the two legs, so we have

[tex]AB=CD\\\\\Rightarrow m\angle C=m\angle B~~~~~~~~~~~~~~~~~~~[\textup{Angles opposite to equal legs are equal}]\\\\\Rightarrow (3x+15)^\circ=60^\circ\\\\\Rightarrow 3x+15=60\\\\\Rightarrow 3x=60-15\\\\\Rightarrow 3x=45\\\\\Rightarrow x=\dfrac{45}{3}\\\\\Rightarrow x=15.[/tex]

Thus, the required value of x is 15.

Option (A) is CORRECT.

Answer:

fff

Step-by-step explanation:

By pythagorean theorum we calculate the height:

[tex]\sqrt{5^2-1^2}[/tex]

=[tex]\sqrt{24}[/tex] = height of triangle

area of triangle = base * height

area = [tex]2*\sqrt{24}[/tex]

There are two triangles so:

[tex]2*2*\sqrt{24}=4\sqrt{24}[/tex]

Multiply this by 13.25 to get total cost:

=$259.65

Answer:

$ 129.82 because it is to the nearest cent

we use divsion, 10 divided by 5 is 2, everyone get 2 yumy cupcakes.

Answers: Ten millions

Answer:

Step-by-step explanation:

The sum of the interior angles of an n gon is found by using the following formula.

(n-2)*180 = sum of the interior angles.

(n - 2) * 180 = 3960                     Divide by 180

(n - 2) 180/180 = 3960/180         Show the division

n - 2 = 22                                     Add 2 to both sides.

n -2+2=22+2                               Combine

n = 24

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

To find the size of each angle, use

(n - 2)*180/n

(24 - 2)*180/24

22 * 180/24

3960/24 = 165

===========

another way

===========

You already know there are 24 sides. You are given the sum of the interior angles as 3960

All you really need to do is 3960/24 = 165

Answer:

5.

Step-by-step explanation:

There are a total of  21 items so the median is the mean of the 10th and 11th .

This lies on the highest column so the median is  5.

Answer:

See picture.

In the picture I graphed (0,1) and then graphed (1,3).

I connected the points with a straight-edge.

Step-by-step explanation:

This question is asking us to use slope-intercept form of a line to answer it.

Slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.

Your equation is y=2x+1 so our m=2 and b=1.

So our y-intercept is 1.  This is the first point we graph.

The slope is 2 or as a fraction 2/1. Recall that slope=rise/run.  So this tells us after we plot (0,1) we need to go up 2 units and right 1 unit to get one more point to graph.  This point will be (0+1,1+2) or just (1,3).

I will draw a graph also to show you this:

Answer:

Graph Attached Below

Step-by-step explanation:

Hello!

To graph a line, we just need any two points that belong to that line.

We know the y-intercept, (0,1), given in the equation itself. We can plot that point as our first point.

The second point can be found by using the slope. The slope is 2/1, and we can go up 2 units and to the right 1 unit to find the second point.

The second point is (1,3).

In the given scenario regarding a toy sinking in a pool, the constraints related to the depth of the pool and the rate of sinking of the toy could be part of the scenario, which illustrates a system of inequality related to the depth of the toy in the pool over time.

The question requires understanding of the constraints in a scenario that involve a system of inequalities related to the depth of a toy in a pool over time. In this case, the toy is falling, or sinking, into the pool. Therefore, the scenario will involve the depth of the pool and the rate at which the toy is falling.

Firstly, The depth of the pool is important because the toy cannot sink deeper than the pool is. Therefore, both constraints A) The pool is 1 meter deep and B) The pool is 2 meters deep could both be part of the scenario, depending on the actual depth of the pool involved.

Secondly, The rate at which the toy is falling (sinking) is also important. Both constraints C) The toy falls at a rate of at least a 1/2 meter per second and D) The toy sinks at a rate of no more than a 1/2 meter per second could be part of the scenario, depending on the actual sinking rate of the toy.

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The constraint that could be part of the scenario is that the D) toy sinks at a rate of no more than a 1/2 meter per second.

A system of inequalities is a set of two or more inequalities involving the same variables. The solution to the system is the set of values that satisfy all the inequalities simultaneously. Graphically, the solution represents the overlapping region of the individual inequalities on a coordinate plane.

The constraint that could be part of the scenario is that the toy sinks at a rate of no more than a 1/2 meter per second. This constraint ensures that the depth of the toy in the pool does not change too rapidly. If the toy sank at a faster rate than 1/2 meter per second, it would quickly reach the bottom of the pool.

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The correct answer is [tex]\(\boxed{\frac{1919}{16} - \frac{481\pi}{128}}\)[/tex] cubic inches.

To determine the volume of the empty space in the box, we need to calculate the volume of the box and the volume of the basketball, and then subtract the volume of the basketball from the volume of the box.

First, let's calculate the volume of the cubic box. Since the edge of the cube is given as 9.5 inches, the volume of the cube [tex]\( V_{box} \)[/tex] is the edge length cubed:

[tex]\[ V_{box} = 9.5^3 \][/tex]

[tex]\[ V_{box} = \left(\frac{95}{10}\right)^3 \][/tex]

[tex]\[ V_{box} = \frac{95^3}{10^3} \][/tex]

[tex]\[ V_{box} = \frac{95^3}{1000} \][/tex]

[tex]\[ V_{box} = \frac{857375}{1000} \][/tex]

[tex]\[ V_{box} = \frac{1919}{4} \][/tex] cubic inches.

 Next, we calculate the volume of the basketball. The basketball is a sphere with a diameter of 9.5 inches, so its radius [tex]\( r \)[/tex] is half of that:

[tex]\[ r = \frac{9.5}{2} \][/tex]

[tex]\[ r = \frac{95}{20} \][/tex]

[tex]\[ r = \frac{19}{4} \] inches.[/tex]

The volume of a sphere [tex]\( V_{sphere} \)[/tex] is given by the formula:

[tex]\[ V_{sphere} = \frac{4}{3}\pi r^3 \][/tex]

[tex]\[ V_{sphere} = \frac{4}{3}\pi \left(\frac{19}{4}\right)^3 \][/tex]

[tex]\[ V_{sphere} = \frac{4}{3}\pi \left(\frac{19^3}{4^3}\right) \][/tex]

[tex]\[ V_{sphere} = \frac{4}{3}\pi \left(\frac{6859}{64}\right) \][/tex]

[tex]\[ V_{sphere} = \frac{481\pi}{128} \] cubic inches.[/tex]

Now, we subtract the volume of the basketball from the volume of the box to find the volume of the empty space [tex]\( V_{empty} \):[/tex]

[tex]\[ V_{empty} = V_{box} - V_{sphere} \][/tex]

[tex]\[ V_{empty} = \frac{1919}{4} - \frac{481\pi}{128} \] cubic inches.[/tex]

 To simplify the expression, we can multiply the terms by a common denominator of 128 to combine them:

[tex]\[ V_{empty} = \frac{1919 \times 32}{128} - \frac{481\pi}{128} \][/tex]

[tex]\[ V_{empty} = \frac{61408}{128} - \frac{481\pi}{128} \][/tex]

[tex]\[ V_{empty} = \frac{61408 - 481\pi}{128} \] cubic inches.[/tex]

 However, we notice that the denominator of 128 can be simplified by dividing both numerator and denominator by 4, which gives us the final

[tex]\[ V_{empty} = \frac{1919}{16} - \frac{481\pi}{128} \][/tex] cubic inches.

Therefore, the volume of the empty space in the box is [tex]\(\boxed{\frac{1919}{16} - \frac{481\pi}{128}}\)[/tex] cubic inches.

Answer:

The average rate of change is -6

Step-by-step explanation:

The formula for average rate of change is

[tex]=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

where

x₁=-1 and x₂=2

In this case we replace f(x) with z(x)

Substitute values of x₁ and x₂ in the formula given the function as

[tex]z(x)=-6x+2+3\\z(x)=-6x+5\\\\\\=\frac{z(x_2)-z(x_1)}{x_2-x_1} \\\\\\z(x_1)=z(-1)=-6*-1+5=6+5=11\\\\\\z(x_2)=z(2)=-6*2+5=-12+5=-7\\\\\\x_2-x_1=2--1=3\\\\Rateofchange=\frac{-7-11}{3} =\frac{-18}{3} =-6[/tex]

Answer:

[tex]3x^2-2x-6[/tex]

Step-by-step explanation:

[tex](f-g)(x)[/tex]

[tex]f(x)-g(x)[/tex]

So plug in your functions:

[tex][3x^2-2]-[2x+4][/tex]

Distribute:

[tex]3x^2-2-2x-4[/tex]

Combine like terms:

[tex]3x^2-2x-6[/tex]  There was only one pair of like terms -2 and -4.

Answer: C≈50.27cm

if u want the solution then here u go

C=2πr=2·π·8≈50.26548cm

The transformation which do not describe a rigid motion transformation is:

           Option: C

   C. dilating a figure by a scale factor of 1/4

Rigid motion transformation is a transformation in which the shape and size of the figure is preserved i.e. it remains the same.

A)

Translating a figure 5 units right.

We know that in the translation transformation the shape and size of the figure remains the same only the location of points are changed.

B)

Rotating a figure 90 degrees.

In rotation the shape and size is preserved.

Hence it is a rigid transformation.

C)

dilating a figure by a scale factor of 1/4

This is not a rigid transformation because the size of the figure is changed.

since the scale factor is less than 1.

Hence, the transformation is a reduction of the original figure.

D)

reflecting a figure across the x-axis.

The reflection is also a rigid transformation.

since it preserves the shape and size of the object.

Answer:

The correct answer is C.

Answer:

a = 12

b = 22

c = 25.96186

Angle A = 27.417°

Angle B = 57.583°

Angle C = 95°

Area = 131.4977

Perimeter = 59.96186

a = 12,b = 22,c = 25.96186

∠A = 27.417°,∠B = 57.583°,∠C = 95°

Law of sine states that the ratio sine of an angle and its opposite side in a triangle is same for all 3 angles and their corresponding sides.

sinA/a=sinB/b=sinC/c

Law of cosine is the generalized Pythagoras theorem is applied. It is applied for measuring one side where the opposite angle and other two sides are given.

c²=a²+b²-2abcosC

here given,

a = 12

b = 22

∠C = 95°

Applying law of cosine,

c²=a²+b²-2abcosC

=12²+22²-2.12.22.cos95°

=674.018

⇒c=√674.018

⇒c=25.96

Applying law of sine

sinA/a=sinC/c

⇒sinA=(a/c)sinC

⇒sinA=(12/25.96)sin95°=0.46

⇒A=sin⁻¹(0.46)

⇒A=27.417°

As we know sum of the 3 angles in a triangles are 180°.

∠B=180°-(∠A+∠C)=180°-(27.417°+95°)=180°-(122.42)

⇒∠B=57.583°

Therefore a = 12,b = 22,c = 25.96186

∠A = 27.417°,∠B = 57.583°,∠C = 95°

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Answer: 88

Step-by-step explanation:

(8x2)=16/2=8

8x6=48

8x4=32

48+32+8=88

Answer:

112

Step-by-step explanation:

Answer:

Option A 50-page photo album holds 400 photographs.

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

step 1

Find the value of k

For the point (3,24)

x=3,y=24

k=y/x

k=24/3=8

The equation is equal to

y=8x

step 2

Verify each statement

case A) 50-page photo album holds 400 photographs.

For x=50

substitute in the equation

y=8(50)=400 -----> is correct

case B) 80-page photo album holds 560 photographs.

For x=80

substitute in the equation

y=8(80)=640 -----> is not correct

case C) 100-page photo album holds 8,000 photographs.

For x=100

substitute in the equation

y=8(100)=800 -----> is not correct

case D) 900-page photo album holds 8,400 photographs.

For x=900

substitute in the equation

y=8(900)=7,200 -----> is not correct

Answer:

Yes ! The correct answer is A.) 50-page photo album holds 400 photographs.

Step-by-step explanation:

I did the Unit Test and i got it correct.

Answer:

$102.29 is the original price of the suit.

Explanation:

$x ------- 100% price (full price)

$35.80 --------------- 35% of the original price (100%-65%=35%).

To find x, use cross-products.

x=(35.80×100)/35 =3580/35 = approximately $102.29.

Answer:

The original price of the suit was $102.29.

Step-by-step explanation:

Alex purchased a new suit discounted by 65%.

He paid $35.80 for the suit.

Let the original price (100% price) be x.

After discount the price is given = 100% - 65% = 35%

35% of x = 35.80

0.35x = 35.80

x = [tex]\frac{35.80}{0.35}[/tex]

x = 102.2857 rounded to $102.29

The original price of the suit was $102.29.

Answer:

Step-by-step explanation:

His chances of getting the purple one are 1/6

His chances of getting the blue one after drawing the purple one and not replacing are 1/5

The probability of both happening are 1/6 * 1/5 = 1/30

Answer:

the required answer is 125/24.

Answer:

The cost price of one calculator is Rs.750.

The cost price of other calculator is Rs.500.        

Step-by-step explanation:

Cost price of 1'st calculator = x

Cost price of 2'nd calculator = 1250-x

He sold one at a profit of 2%.

The selling price of one calculator is

[tex]SP_1=CP(1+\frac{P\%}{100})[/tex]

[tex]SP_1=x(1+\frac{2}{100})[/tex]          

[tex]SP_1=x(1+0.02)[/tex]      

[tex]SP_1=1.02x[/tex]    

He sold other at a loss of 3%.

The selling price of other calculator is

[tex]SP_2=CP(1-\frac{L\%}{100})[/tex]

[tex]SP_2=(1250-x)(1-\frac{3}{100})[/tex]          

[tex]SP_2=(1250-x)(1-0.03)[/tex]      

[tex]SP_2=(1250-x)(0.97)[/tex]

[tex]SP_2=1212.5-0.97x[/tex]  

According to given condition,

[tex]SP_1+SP_2=1250[/tex]

[tex]1.02x+1212.5-0.97x=1250[/tex]

[tex]0.05x=1250-1212.5[/tex]

[tex]0.05x=37.5[/tex]

[tex]x=\frac{37.5}{0.05}[/tex]

[tex]x=750[/tex]

The cost price of one calculator is Rs.750.

The cost price of other calculator is 1250-750=Rs.500.

Answer:

40 combinations

Step-by-step explanation:

We just multiply the outcomes.

4*2*5=40

There are 40 different ways to redecorate.

4 colors of paint * 2 kinds of curtains * 5 colors of carpet

= 40 outcomes.

In the possibility principle, an outcome is a probable result of a test or trial. every possible final result of a selected experiment is precise, and one-of-a-kind results are together one of a kind (most effective final results will occur on each trial of the experiment).

To locate the total wide variety of consequences for two or greater occasions, multiply the variety of effects for every occasion collectively. that is referred to as the product rule for counting because it involves multiplying to discover a product.

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Answer:

D. ABC = DBC

Step-by-step explanation:

They are the same length and congruent.

Answer:

d) ABC ≅ DBC

Step-by-step explanation:

∠B in ΔABC and ∠B in ΔDBC is 90°. BC is a common side in both triangles which mean that both triangles have one side of the same length. Side AC in ΔABC is the same length as side DC in ΔDBC. Therefore ∠C in both ΔABC and ΔDBC are the same size. Therefore ΔDBC is a mirror image of ΔABC, which is a form of congruent triangles.

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables, and then solve for "y".

[tex]\bf y = 4x^2-8\implies \stackrel{\textit{quick switcheroo}}{\underline{x} = 4\underline{y}^2-8}\implies x+8=4y^2\implies \cfrac{x+8}{4}=y^2 \\\\\\ \sqrt{\cfrac{x+8}{4}}=y\implies \cfrac{\sqrt{x+8}}{\sqrt{4}}=y\implies \cfrac{\sqrt{x+8}}{2}=\stackrel{f^{-1}(x)}{y}[/tex]

Answer:

C

Step-by-step explanation:

The surface area (A) of a sphere is calculated as

A = 4πr² ← r is the radius, here r = 12, hence

A = 4π × 12²

  = 4π × 144 = 576π units² → C

The surface area of the sphere is  576 square units. The correct option is B.

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called as the surface area.

The surface area (A) of a sphere is calculated as

A = 4πr² ← r is the radius, here r = 12, hence

A = 4π × 12²

A= 4π × 144

A = 576π units²

Hence, the correct option is B.

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Answer:

You need to draw a horizontal line that goes through the point (0,4).

Step-by-step explanation:

Slope of zero means it does not go up or down. It looks like this ↔, but stretched out to the two sides of the graph.

A line with a slope of zero is flat and does not rise or fall. To graph this line, draw a horizontal line through the given y-coordinate.

A line with a slope of zero means that the line is flat and has no rise or fall. To graph a line with a slope of zero passing through the point (0,4), you would draw a horizontal line through the y-coordinate 4. Since the slope is zero, the line will not change in the vertical direction.

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Answer:

$11,700

Step-by-step explanation:

If Cary earns $975 each month on his part-time job, he would earn $11,700 in a year.

1 year = 12 months

$975 per month

975 x 12 = 11700

In this question, we're going to need to find out how much Cary earns in a year.

To do this, we need to go back to the problem to see if we can get some valuable information.

We know that Cary earns $975 each month.

With the information above, we can solve the problem.

There are 12 months in a year, so that means we're going to multiply 975 by 12 in order to find out how much Cary earns in a year.

975 × 12 = 11,700

When you multiply, you would end up with the answer "11,700"

This means that Cary earns $11,700 in a year

since we know the endpoints of the circle, we know then that distance from one to another is really the diameter, and half of that is its radius.

we can also find the midpoint of those two endpoints and we'll be landing right on the center of the circle.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{diameter}{d}=\sqrt{[-2-(-4)]^2+[-5-(-7)]^2}\implies d=\sqrt{(-2+4)^2+(-5+7)^2} \\\\\\ d=\sqrt{2^2+2^2}\implies d=\sqrt{2\cdot 2^2}\implies d=2\sqrt{2}~\hfill \stackrel{~\hfill radius}{\cfrac{2\sqrt{2}}{2}\implies\boxed{ \sqrt{2}}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-5})\qquad \qquad \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{-2-4}{2}~~,~~\cfrac{-5-7}{2} \right)\implies \left( \cfrac{-6}{2}~,~\cfrac{-12}{2} \right)\implies \stackrel{center}{\boxed{(-3,-6)}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-3}{ h},\stackrel{-6}{ k})\qquad \qquad radius=\stackrel{\sqrt{2}}{ r} \\[2em] [x-(-3)]^2+[y-(-6)]^2=(\sqrt{2})^2\implies (x+3)^2+(y+6)^2=2[/tex]

Answer:

FIRST OPTION: [tex](x+3)^2+ (y+6)^2 =2[/tex]

Step-by-step explanation:

The equation of the circle in center-radius form is:

[tex](x- h)^2 + (y- k)^2 = r^2[/tex]

Where the center is at the point (h, k) and the radius is "r".

We know that the endpoints of the diameter of this circle are (-4, -7) and (-2, -5), so we can find the radius and the center of the circle.

In order to find the radius, we need to find the diameter. To do this, we need to use the formula for calculate the distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Then, substituting the coordinates of the endpoints of the diameter into this formula, we get:

[tex]d=\sqrt{(-4-(-2))^2+(-7-(-5))^2}=2\sqrt{2}[/tex]

Since the radius is half the diameter, this is:

[tex]r=\frac{2\sqrt{2}}{2}=\sqrt{2}[/tex]

To find the center, given the endpoints of the diameter, we need to find the midpoint with this formula:

[tex]M=(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})[/tex]

This is:

[tex]M=(\frac{-4-2}{2},\frac{-7-5}{2})=(-3,-6)[/tex]

Then:

[tex]h=-3\\k=-6[/tex]

Finally, substituting values  into  [tex](x- h)^2 + (y- k)^2 = r^2[/tex], we get the following equation:

 [tex](x- (-3))^2 + (y- (-6))^2 = (\sqrt{2})^2[/tex]

[tex](x+3)^2+ (y+6)^2 =2[/tex]

Answer:

slope = 0

Step-by-step explanation:

The line with equation x = - 3 is a vertical line parallel to the y- axis

A perpendicular line is therefore a horizontal line parallel to the x- axis

The slope of the x- axis is zero, hence the slope of the horizontal line is

slope = 0

We have the following function:

[tex]f(x)=-\frac{3}{x}[/tex]

The graph of this function has been plotted below. So lets analyze each statement:

As you can see x increases from -∞ to 0 and decreases from 0 to +∞

The function is undefined for [tex]x=0[/tex] since x is in the denominator.

Statement is unclear but the range is the set of all real numbers except zero.

The function is a reflection in the x axis of the function [tex]g(x)=\frac{3}{x}[/tex]

This is false since:

[tex]f(3)=-1\neq -27[/tex]

Note. As you can see those statements are false, so any of them is true, except item 3 that is unclear.

Answer:

its b and d

Step-by-step explanation:

i know