A cat is stuck in the tree and the fire department needs a ladder to rescue the cat. The fire truck available has a 95-foot ladder, which starts 8 feet above ground. Unfortunately, the fire truck must park 75 feet away from the tree. If the cat is 60 feet up the tree, does the cat get rescued? If not, what ladder length is need to allow the cat to be rescued?
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Draw the given scenario
STEP 2: Describe how to answer the question
The question forms a right angle triangle. where the height of the cat on the tree is the opposite side of the triangle. The distance between the cat and the tree is the adjacent side of the triangle .
Recall the 95 foot ladder can only start 8 feet above the ground .The diagram is represented above:
The ladder height should be the hypotenuse of the triangle.
using Pythagoras's theorem,
[tex]hypotenuse^2=opposite^2+adjacent^2[/tex]STEP 3: Write the given sides
[tex]\begin{gathered} adjacent=75fto \\ opposite=52ft \\ hypotenuse=x\text{ ft} \end{gathered}[/tex]STEP 4: find x
[tex]\begin{gathered} x^2=75^2+52^2 \\ x^2=5625+2704 \\ x^2=8329 \\ x=\sqrt{8329}=91.26335519 \\ x\approx91.26ft \end{gathered}[/tex]The expected length of the ladder should be approximately 91.26ft. Since the ladder is 95 foot, therefore the cat will be rescued with the given ladder.
Related Questions
flying against the wind, an airplane travels 7840 kilometers in 8 hours. flying with the wind, the same plane travels 5280 kilometers in 4 hours. what is the rate of the plane in still air and what is the rate of the wind?
Answers
The rate of the plane in still air is 1150km/hr and the rate of the plane in the wind is 170km/hr.
Explanations:The formula for calculating distance is expressed as:
[tex]\begin{gathered} dis\tan ce=\text{speed}\times\text{time} \\ d=st \end{gathered}[/tex]Let the rate of the plane in still air be "x"
Let the rate of the plane in the wind be "y"
if flying against the wind, an airplane travels 7840 kilometers in 8 hours, then;
8 (x - y) = 7840
x - y = 980 ........................ 1
If flying with the wind, the same plane travels 5280 kilometers in 4 hours
4 (x + y) = 5280
x + y = 1,320 ......................2
Add both equations:
x + x = 980 + 1320
2x = 2,300
x = 2300/2
x = 1150 km/hr
Substract x = 1150km/hr into equation 1.
x - y = 1320
1150 + y = 1320
y = 1320 - 1150
y = 170km/hr
Hence the rate of the plane in still air is 1150km/hr and the rate of the plane in the wind is 170km/hr
Points that lie on the same line are called: a) opposite rays b) coplanar and non-collinear c) non-collinear and non-coplanar d) collin ear and coplanar
Answers
Given:
Points that lie on the same line.
Opposite rays
Question 125 ptsA raffle sells 1000 tickets at $5 per ticket. The possible prizes are given below. Find the expectedvalue of each ticket (from the perspective of the person buying the ticket). Include signs in youranswer as appropriate.1 ticket wins $10005 tickets win $10010 tickets win $20
Answers
The answer is $0.5
Explanation:
⇒ Total amount of tickets sold = 1000 x $5 = $5000
⇒ Expected value E(X) =∑X.P(x)
⇒ 1 x (1000/5000) + 5 x (100/5000) + 10 x (20/1000)
= 0.2 + 0.1 + 0.2
= $0.5
A study shows that 28% of the population has high blood pressure. The study also shows that 86% of those who do not have high blood pressure exercise at least 90 minutes per week, while 32% of those with high blood pressure exercise at least 90 minutes per week. Which of the following relative frequency tables could the study provide?
Answers
The study can provide relative frequency table 2 (starting from the top)
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. The word per cent means per 100. It is denoted by the symbol “%”.
The total percentage of two or more ratios in a thesame entity is 100. For example, In a population, 28% has HBP (high blood pressure)
This means that number of those that do not have HBP will be 100 - 28 = 72%
86% of those who did not have HBP exercise at least 90 minute per week i.e
86% of no HBP ,exercise >or = 90 = (86/100) × 72 = 62%( nearest whole number)
Those that do exercise <90 minute per week = 72-62= 10%
32% of those with HBP exercise at least 90 minute( >or = 90 minutes) =( 32\100) × 28= 9%( nearest whole number)
Those with HBP and exercise <90= 28- 9= 19%
Therefore Table 2 starting from the top clearly shows this data.
learn more about percentages from
https://brainly.com/question/24877689
#SPJ1
How is this wrong can someone explain, and what is the correct answer
Answers
Answer:
Step-by-step explanation:
find and classify the global extrema of the following function
f(x)=(x-2)^2+5
compute the critical points of (x-2)^2+5
to find all critical points, first compute f(x)
f(x)=2(x-2)
solving 2(x-2)=0 yields x=2
x=2
f(x) exists everyhere
2(x-2) exists everyhere
the only critical point of (x-2)^2+5 is at x=2
x=2
the domain of (x-2)^2+ 5 is R
the endpints of R are x = -∞ and ∞
Evalute (x-2)^2+5 at x = -∞, 2 and ∞
the open endpoints of the domain are marked in gray
x () f(x)
-∞ ∞
2 5
∞ ∞
the largest value corresponds to a global maximum, and the smallest value corresponds to a global minimum:
the open endpoints of the domain are marked in gray
x () f(x) extrema type
-∞ ∞ global max
2 5 global min
∞ ∞ global max
remove the points x = -∞ and ∞ from the table
These cannot be global extrema, as the value of f(x) here is never achieved
x () f(x) () extrema type
2 5 global min
f(x) = (x-2)^2+5 has one global minimum
Answer:
f(x) has a global minimum at x = 2
Answer:
Step-by-step explanation:
A parabola that passes through the point (8, 28) has vertex (-2, 8). Its line of symmetry is parallel to the y-
axis.
Find equation of the parabola: y =
When x 18, what is the value of y:
What is the average rate of change between x = -2 and x = 18:
Answers
The equation of the parabola is y = 1/5( x + 2 )² + 8.
When x = 18 the value of y is 88 and the average rate of change between x = - 2 and x = 18 is 4.
The general equation of the parabola is given as:
y = a(x – h)² + k where ( h, k ) is the vertex of the parabola.
We have, the vertex as ( - 2, 8 ) and the parabola passes through ( 8, 28 ).
Then,
y = a(x – h)² + k
28 = a( 8 - (-2) )² + 8
28 = a(10)² + 8
28 - 8 = a(10)²
100a = 20
a = 20/100 = 1/5
Therefore, the equation of the parabola will be:
y = a(x – h)² + k
y = 1/5( x + 2 )² + 8
Now, when x = 18:
y = 1/5( x + 2 )² + 8
y = 1/5( 18 + 2 )² + 8
y = 1/5( 20 )² + 8
y = 80 + 8 = 88
Now, the change between x = - 2 and x = 18:
Then,
y = f(18) = y = 1/5( 18 + 2 )² + 8 = 1/5(20)² + 8 = 88
And;
y = f( - 2) = 1/5( -2 + 2 )² + 8 = 1/5(0)² + 8 = 8
Therefore the average rate of change between x = - 2 and x = 18 will be:
= [ f(18) - f(-2) / ( 18 - (-2) ) ]
= ( 88 - 8 ) / 20
= 80/20
= 4
Learn more about equation of parabola here:
brainly.com/question/9647095
#SPJ1
0896. Calculate the atomic mass of copper if copper-63 is 69.17% abundant and copper-65 is30.83% abundant.
Answers
The atomic mass of the copper is
[tex]63\times69.17\text{ \% + 65}\times30.83\text{ \%}[/tex]solve the above expression
[tex]63\times\frac{69.17}{100}+65\times\frac{30.83}{100}[/tex][tex]63\times\frac{6917}{10000}+65\times\frac{3083}{10000}[/tex][tex]46.35+20.03=66.38[/tex]So the atomic weight of the mixture is 66.36 .
what digit is in the
Answers
Let:
Mp = Marked price = $310
r = Rate of discount = 20% = 0.2
D = Discount
Sp = Sale price
The discount will be given by:
[tex]\begin{gathered} D=r\cdot Mp \\ D=0.2\cdot310 \\ D=62 \end{gathered}[/tex]And the sale price will be:
[tex]\begin{gathered} Sp=Mp-D \\ Sp=310-62 \\ Sp=248 \end{gathered}[/tex]please help me I dont understand A number is less than or equal to - 7 or greater than 12.
Answers
To translate the sentence as an inequality, we have:
[tex]x\leq-7,x>12[/tex]Since the number is less or equal ( < = ) we use this symbol to represent it as inequality, and greater than using the symbol ( > ).
Then, we can answer the question as:
x < = -7 or x > 12.
need help with this answer in a quick and clear response
Answers
ANSWER
Yes
EXPLANATION
The system of inequalities shows that y is greater than or equal to the first line and less than or equal to the second line. This means that any point on both lines is a solution to the system.
Hence, the intersection of the boundary lines is part of the solution.
Solve for a side in right triangles. AC = ?. Round to the nearest hundredth
Answers
The length of segment AC is 2.96 units
How to determine the side length AC?From the question, the given parameters are
Line segment AB = 7 units
Angle A = 65 degrees
The line segment AC can be calculated using the following cosine ratio
cos(Angle) = Adjacent/Hypotenuse
Where
Adjacent = Side length AC
Hypotenuse = Side length AB
So, we have
cos(65) = AC/AB
This gives
cos(65) = AC/7
Make AC the subject
AC =7 * cos(65)
Evaluate
AC = 2.96
Hence, the side length AC has a value of 2.96 units
Read more about right triangles at
https://brainly.com/question/2437195
#SPJ1
Alani want to buy a 3366 buycie She reconsidering e payment options. The image shows Option A, which consists of making an initial down payment then smallet. equesized weekly payments. Option consists of making 6 equal payments over a week WE Weekly Bike Payments A-What factors should Alanl take into consideration before deciding between Option A and Option B? B- Communicate Precisely Suppose Alani could modify Option A and still pay off the bike in 5 weeks. Describe the relationship between the down payment and the weekly payments.
Answers
[tex]4(2 \times - 1) \ \textless \ (4 \times - 3)[/tex]That is the Math problem
Answers
Which statement correctly describes the relationship between the graph of f(x) and g(x)=f(x+2)? Responses The graph of g(x) is the graph of f(x) translated 2 units right. The graph of , g begin argument x end argument, is the graph of , , f open argument x close argument, , translated 2 units right. The graph of g(x) is the graph of f(x) translated 2 units down. The graph of , g begin argument x end argument, is the graph of , , f open argument x close argument, , translated 2 units down. The graph of g(x) is the graph of f(x) translated 2 units up. The graph of , g begin argument x end argument, is the graph of , , f open argument x close argument, , translated 2 units up. The graph of g(x) is the graph of f(x) translated 2 units left.
Answers
The graph of g(x) is the graph of f(x) translated 2 units left by the operation g(x)=f(x+2) so option (D) is correct.
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.
If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).
If a function f(x) is transformed by funciton g(x) as shown,
g(x) = f(x+a)
For a>0, then the graph of f(x) shifts left by "a" unit, while if a<0, then the graph of f(x) shifts right side by "a"units.
As per the given function,
g(x) = f(x + 2)
Since 2 > 0 therefore the function will shift 2 units left.
Hence "The graph of g(x) is the graph of f(x) translated 2 units left by the operation g(x)=f(x+2)".
To learn more about the transformation of graphs,
brainly.com/question/3099136
#SPJ1
Determine the x-intercept for 3x + 2y = 14.A) (7,0) B) (0,7) C) (14/3,0) D) (0,14/3)
Answers
By definition, when the line intersects the x-axis, the value of "y" is:
[tex]y=0[/tex]Knowing this, you can substitute that value of "y" into ithe equation given in the exercise:
[tex]\begin{gathered} 3x+2y=14 \\ 3x+2(0)=14 \end{gathered}[/tex]Now you must solve for the variable "x" in order to find the x-intercept. This is:
[tex]\begin{gathered} 3x+0=14 \\ 3x=14 \\ x=\frac{14}{3} \end{gathered}[/tex]Then, you get this point:
[tex](\frac{14}{3},0)[/tex]The answer is: Option C.
the score on the right is a scaled copy of the square on the left identify the scale factor express your answer in the simplest form
Answers
Answer
Scale factor = 3.5
Explanation
Scale factor expresses how much the copy/image of the original figure is bigger or smaller than the original figure.
If the scale factor is more than 1, then the image is an enlargement of the original figure.
But if the scale factor is less than 1, then the image is a reduction of the original figure.
Mathematically,
Scale factor = (Length of a side of the image or scaled copy)/(Corresponding length of that side on the original figure)
Length of a side of the image or scaled copy = 56
Corresponding length of that side on the original figure = 16
Scale factor = (Length of a side of the image or scaled copy)/(Corresponding length of that side on the original figure)
Scale factor = (56/16) = (7/2) = 3.5
Hope this Helps!!!
Answer
Scale factor = 3.5
Explanation
Scale factor expresses how much the copy/image of the original figure is bigger or smaller than the original figure.
If the scale factor is more than 1, then the image is an enlargement of the original figure.
But if the scale factor is less than 1, then the image is a reduction of the original figure.
Mathematically,
Scale factor = (Length of a side of the image or scaled copy)/(Corresponding length of that side on the original figure)
Length of a side of the image or scaled copy = 56
Corresponding length of that side on the original figure = 16
Scale factor = (Length of a side of the image or scaled copy)/(Corresponding length of that side on the original figure)
Scale factor = (56/16) = (7/2) = 3.5
Hope this Helps!!!
Ji min's grandmother asked him to pick up some ginger on his way home .He knows that she wants to get 2 meals(4oz/ meal)out of it and it costs $2.99 per root. how much will he spend if each root is approximately 6 oz?
Answers
Since 1 meal is equivalent to 4oz, then 2 meals are equivalent to 8oz (4*2=8).
Now, one root (6oz) cost $2.99 and we need 8oz, then Ji-min must buy 2 roots because he cant buy parts of the root, that is
[tex]2.99\cdot2=5.98[/tex]that is, Jim will spend $5.98 approximately.
How many radians are equal to 360 degrees 2 2pi 1 Pi
Answers
Answer:
2pi
Explanation:
By definition, 360 degrees are equal to 2π radians.
This follows from the fact that the circumference of a circle is 2π times the radius. Therefore, if radius = 1, then
circumference = 2π
Since the circumference is the distance around a circle, and degrees are the "angular distance " around the circle, these two quantities can be related.
So if you think of the circle in terms of the circumference, a circle measures 2π. If you think in terms of degrees, a circle measures 360 degrees.
Therefore, we say
360 degrees = 2π (radians)
A 43-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first
piece, and the third piece is three inches more than five times the length of the first piece. Find the
lengths of the pieces.
What is the length of the first piece?
Answers
The length of the first piece is 5 inches when a 43-inch piece of steel is cut into three pieces.
According to the question,
We have the following information:
A 43-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is three inches more than five times the length of the first piece.
Now, let's take the length of the first piece to be x inches (as shown in the figure).
Length of second piece = 2x inches
Length of third piece = (3+5x) inches
Now, we have the following expression for addition:
x + 2x + 3 + 5x = 43
8x+3 = 43
8x = 43-3
8x = 40
x = 40/8
x = 5 inches
Hence, the length of the first piece is 5 inches.
To know more about length of the first piece here
https://brainly.com/question/20661763
#SPJ1
Which ordered pair is a solution tothe system of inequalities shown?
Answers
We want to know which ordered pair is a solution of the system of inequalities shown:
[tex]\begin{cases}x-4y\ge0 \\ x-y<-1\end{cases}[/tex]For doing so, we will try to solve both inequalities for one variable, in this case, we will use y.
On the first equation:
[tex]\begin{gathered} x-4y\ge0 \\ x\ge4y \\ y\le\frac{x}{4} \end{gathered}[/tex]On the second equation:
[tex]\begin{gathered} x-y<-1 \\ x+1-y<0 \\ x+1And joining those two results we get:[tex]x+1Now we check each of the ordered pairs, if they hold the condition above:For (0, 2)
We have that x=0, and y=2. Thus,
[tex]\begin{gathered} x+1=1 \\ \frac{x}{4}=0 \\ \text{And as }2>0,\text{ (0, 2) is NOT a solution of the system.} \end{gathered}[/tex]For (-3, 8)
In this case, x=-3 and y=8.
[tex]\begin{gathered} x+1=-2 \\ \frac{x}{4}=-\frac{3}{4} \\ \text{As }8>-\frac{3}{4},\text{ this means that (-3, 8) is NOT a solution of the system.} \end{gathered}[/tex]For (2,5)
In this case, x=2 and y=5.
[tex]\begin{gathered} x+1=3 \\ \frac{x}{4}=\frac{2}{4}=\frac{1}{2} \\ \text{As }5>\frac{1}{2}\text{ this means that (2, 5) is NOT a solution of the system.} \end{gathered}[/tex]For (-7, -4)
In this case, x=-7 and y=-4.
[tex]\begin{gathered} x+1=-6 \\ \frac{x}{4}=-\frac{7}{4} \\ \text{As }-6<-4\le-\frac{7}{4},\text{ (-7, -4) is a SOLUTION of the system.} \end{gathered}[/tex]For (6, -1)
We have that x=6 and y=-1.
[tex]\begin{gathered} x+1=7 \\ \frac{x}{4}=\frac{6}{4}=\frac{3}{2} \\ \text{As }7>-1,\text{ (6, -1) is NOT a solution of the system. } \end{gathered}[/tex]Thus, the ordered pair which is a solution of the system is (-7, -4).What is the coordinate point location of the y-intercept of the graph below?
Answers
The y-intercept is located at the coordinate (0, 4) as shown below. Y-intercept is the point where a line or a graph crosses the y-axis.
Which of the following systems of equations is an example of one where elimination is the best method?A) {y=27x+11 {3x−4y=−24 B) {4x+5y=20 {−4x+6y=24 C) {y=13x+15 {2x−2y=18 D) {x = 11 {y = -8
Answers
Answer:
Explanation:
When solving a system of equations, the elimination method is best used when the system is given in such a way that the coefficients of one variable can be eliminated by addition or subtraction.
Of the given system of equations, the example of where elimination is the best method is:
[tex]\begin{gathered} 4x+5y=20 \\ -4x+6y=24 \end{gathered}[/tex]In this example, we see that the variable 'x' can be directly eliminated by adding the two equations.
The correct option is B.
Suppose that the functions f and g are defined as follows. f(x)= x-6/x+5 g(x)= x/x+5. find f/g. Then, give its domain using an interval or union of intervals. simplify your answers.
Answers
STEP 1:
To find f/g we divide f(x) by g(x)
[tex]\frac{f}{g}=\frac{\frac{x-6}{x+5}}{\frac{x}{x+5}}\text{ = }\frac{x-6}{x+5}\text{ }\times\text{ }\frac{x+5}{x}\text{ =}\frac{x-6}{x}[/tex]Therefore the value of f/g is
[tex]\frac{f}{g}=\frac{x-6}{x}[/tex]STEP 2:
Also, the domain is the set of all possible x-values which will make the function "work", and will output real values.
The domain of this function is
[tex]-\inftyThis implies that the function would exist for all values of x except when x=0The above domain can also be represented as :
[tex](-\infty,0)\text{ and (0,}\infty)[/tex]the circumference of a circle is 18pi ft. what is the area in square feet.
Answers
We have first the formula of the circumference of a circle
[tex]C=2\pi r[/tex]In order to know the area we need to know the radius of the circle, it can be obtained using the formula above and the next information.
C=18pi
r is the radius
[tex]18\pi=2\pi r[/tex]then we isolate the r
[tex]\begin{gathered} r=\frac{18\pi}{2\pi} \\ r=9 \end{gathered}[/tex]the radius is 9 ft
then we can calculate the area using the next formula
[tex]A=\pi r^2[/tex]we substitute the value of the radius
[tex]\begin{gathered} A=\pi(9)^2 \\ A=81\pi ft^2 \\ A=254.47ft^2 \end{gathered}[/tex]Two segments of Parallelogram ABCD are shown below.  Which coordinate pair BEST represents the location of Point D, the fourth vertex of Parallelogram ABCD? A. (6, 1) B. (7, 0) C. (8,2) D. (7,1)
Answers
Given coordinates of A(2,-1), B(1,3), C(6,5)
Let the coordinates of D(x,y)
Let join AC and BD:
SO by mid point rule:
Coordinates of midpoint by AC are:
[tex](\frac{2+6}{2},\text{ }\frac{-1+5}{2})\rightarrow(4,2)[/tex]And the midpoint of BD are same as AC:
[tex]\begin{gathered} \frac{1+x}{2}=4 \\ 1+x=8 \\ x=7 \end{gathered}[/tex][tex]\begin{gathered} \frac{3+y}{2}=2 \\ 3+y=4 \\ y=4-3 \\ y=1 \end{gathered}[/tex]hence the coordinates of D are (7,1)
Option D is correct.
SKIPPYTHEWALRUS U CAN'T ANSWER THIS QUESTIONI NEED CORRECT ANSWER 100 POINTS ONLY ANSWER CORRECTLY
A line passes through the points (7,9) and (10,1). What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
Answers
Answer:
y - 1 = -8/3(x - 10)
also valid:
y - 9 = -8/3(x - 7)
Step-by-step explanation:
Point-slope equation is a fill-in-the-blank formula that is sort of a shortcut for writing the equation of a line. Point-slope is named that bc you fill in a point and the slope.
Point-slope Eq:
y - Y = m(x - X)
fill in the slope for the m and fill in any point on the line for the X,Y.
First slope:
Slope is y-y over x-x
9-1 / 7-10
= 8/ -3
= -8/3
So slope is -8/3 fill that in for the m.
y -Y = -8/3(x-X)
Pick one of the points (either one it totally doesn't matter)
Let's use (10,1)
fill in 10 for X and 1 in place of Y.
the y in the very front stays a y and the first x in the parentheses stays an x, so there will be two variables in your completed answer.
y - 1 = -8/3(x - 10)
make sure the parentheses on the right is beside the -8/3 fraction and is NOT written on the bottom, beside the 3 only.
Consider the complex number 2 = V17 (cos(104°) + i sin(104°)).Plot z in the complex plane below.If necessary, round the point's coordinates to the nearest integer.Im5+4+3+2+1 +ReA+-5+-4-3-2-112345-1+-2-3 +-4+-5 +
Answers
Recall that to plot a point in the complex plane we have to know its real part and its imaginary part.
The real part of the given number is
[tex]\sqrt[]{17}\cos 104^{\circ},[/tex]and its imaginary part is
[tex]\sqrt[]{17}\sin 104^{\circ}.[/tex]Simplifying the above expressions, and rounding to the nearest integer we get that:
[tex]\begin{gathered} \operatorname{Re}(z)=-1, \\ \operatorname{Im}(z)=4. \end{gathered}[/tex]Therefore, the point has coordinates (-1,4).
Answer:
Divide polynomial and monomial 49c^2 d^2 - 70c^3 d^3 - 35c^2d^4 /7cd^2
Answers
start separating the fraction into smaller fractions
[tex]\frac{49c^2d^2}{7cd^2}-\frac{70c^3d^3}{7cd^2}-\frac{35c^2d^4}{7cd^2}[/tex]then, divide each of the fractions
[tex]7c-10c^2d-5cd^2[/tex]identify the constant of proportionality in the following questions. 1) y= 2x + 32) y= -3x - 4
Answers
Answer:
0. k=2
,1. k=-3
Explanation:
The constant of proportionality is the number that is beside the variable x in both equations.
(1)For the equation:
[tex]y=2x+3[/tex]The constant of proportionality is 2.
(2)For the equation:
[tex]y=-3x-4[/tex]The constant of proportionality is -3.
find the average rate of change on the interval (SHOW ALL WORK)
Answers
First, evaluate the function at the ends of the interval:
[tex]\begin{gathered} g(x)=x^3-2x \\ g(-1)=(-1)^3-2(-1) \\ g(-1)=-1^{}+2 \\ g(-1)=1 \end{gathered}[/tex][tex]\begin{gathered} g(x)=x^3-2x \\ g(2)=2^3-2(2) \\ g(2)=8-4 \\ g(2)=4 \end{gathered}[/tex]Now, the average rate of change will be
[tex]\begin{gathered} \text{Average rate of change }=\frac{g(2)-g(-1)}{2-(-1)} \\ \text{Average rate of change }=\frac{4-1}{2-(-1)} \\ \text{Average rate of change }=\frac{3}{2+1} \\ \text{Average rate of change }=\frac{3}{3} \\ \text{Average rate of change }=1 \end{gathered}[/tex]