Answer:
a(n) = 27*(2/3)^(n - 1)
Step-by-step explanation:
The first four terms are 27, 18, 12, 8.
Find the common ratio:
To do this, let that ratio = r, and write and solve 27r = 18. Thus, r = 2/3.
The general explicit formula for this sequence is
a(n) = a(1)*(2/3)^(n - 1), or, since a(1) = 27, a(n) = 27*(2/3)^(n - 1)
Answer:
The sequence is A(n) = 27*(1.5)^(n-1)
Step-by-step explanation:
First, we need to see which type of sequence we have:
Differences:
27 - 18 = 9
18 - 12 = 6
the differences are different, let's try with the ratios.
27/18 = 1.5
18/12 = 1.5
12/8 = 1.5
So we have that this ratio is constant, then the sequence can be:
A(n) = 27*(1.5)^(n-1)
For n an integger number
where:
A(0) = 27*1.5^0 = 27
A(1) = 27*1.5^1 = 18
A(2) = 27*1.5^2 = 12
A(3) = 27*1.5^3 = 8
please help asap! answer should be in polynomial in standard form
Answer:
-2[tex]y^{4}[/tex] - 5y² + 42
Step-by-step explanation:
Each term in the second factor is multiplied by each term in the first factor, that is
y²(- 2y² + 7) + 6(- 2y² + 7) ← distribute both parenthesis
= - 2[tex]y^{4}[/tex] + 7y² - 12y² + 42 ← collect like terms
= - 2[tex]y^{4}[/tex] - 5y² + 42 ← in standard form
[ standard form means the first term has the largest exponent of the variable, followed by other terms in descending powers of the variable. ]
suppose that 11 inches of wire cost 66 cents at the same rate how much (in cents) will 28 inches of wire cost
Answer:
168 cents or = $1.68
Step-by-step explanation:
11 inches of wire cost 66 cents
28 inches of wire cost x? cents
x = 28 * 66 / 11 = 168 cents or = $1.68
Answer
168 cents or = $1.68
Solve m + 2/3 = 1/2
1 1/6
1/6
-1
- 1/8
Answer:
m = - 1/6
Step-by-step explanation:
Since 2/3 is larger than 1/2, m is going to be less than 0 because you have to subtract 2/3 to get to the right. That makes a and b incorrect. I can tell you that the answer doesn't appear to be there.
m + 2/3 = 1/2 Subtract 2/3
m = 1/2 - 2/3 The common denominator is 6
m = 3/6 - 4/6 Do the subtraction
m = - 1/6
You might want to check out the - 1/8.
The Answer: m = - 1/6
The graph of f(x) is show below.
If f(x) and it’s inverse function f^-1(x) are both plotted on the same coordinate plane where is their point of intersection?
ANSWER
(2,2)
EXPLANATION
Since f(x) and its inverse function are symmetric about the line y=x, if (a,b) lies on the graph of f, then (b,a) must lie on f inverse.
The point (2,2) lies on f and the same time on f inverse.
The solution is a point that satisfies both equations.
Hence the correct choice is:
(2,2)
Answer:
Did the test. Answer is (2,2).
Find the domain of (f(g(x))) when f(x)= square root of x-1 and g(x)= 1/4x
Answer:
[tex]\large\boxed{Domain:\ x\in\left(0;\ \dfrac{1}{4}\right>\to0<x\leq\dfrac{1}{4}}[/tex]
Step-by-step explanation:
[tex]f(x)=\sqrt{x-1},\ g(x)=\dfrac{1}{4x}\\\\f\bigg(g(x)\bigg)-\text{instead of x in the function equation f(x) put}\ \dfrac{1}{4x}:\\\\f\bigg(g(x)\bigg)=\sqrt{\dfrac{1}{4x}-1}=\sqrt{\dfrac{1}{4x}-\dfrac{4x}{4x}}=\sqrt{\dfrac{1-4x}{4x}}\\\\\text{The domain}\ D:\\\\\dfrac{1-4x}{4x}\geq0\ \wedge\ 4x\neq0\\\\\dfrac{1-4x}{4x}\geq0\iff(1-4x)(4x)\geq0\\\\1-4x=0\to4x=1\to x=\dfrac{1}{4}\\\\4x=0\to x=0\\(look\ at\ the\ picture)\\\\(1)\qquadx\in\left<0,\ \dfrac{1}{4}\right>\\\\\\4x\neq0\qquad\text{divide both sides by 4}\\\\(2)\qquad x\neq0[/tex]
[tex]\text{From}\ (1)\ \text{and}\ (2)\ \text{We have}\ x\in\left(0,\ \dfrac{1}{4}\right>[/tex]
which pattern folds into the triangular prism above?
Answer:
the answer will be the letter Y
Step-by-step explanation:
because the darker shaded side are at the bottom and one is at the top and don't forget about the two triangles
Complete the table.
x
1 ___
7 ___
49 ___
log7 x
___ -1
___ -2
A.) 1/2
B.) 0
C.) 7
D.) 1
E.) 2
F.) 49
G.) 1/7
H.) 1/49
Answer:
x, log7(x)
1, 0 (B)
7, 1 (D)
49, 2 (E)
1/7, -1 (G)
1/49, -2 (H)
Step-by-step explanation:
Powers of 7 are ...
7^-2 = 1/7^2 = 1/49
7^-1 = 1/7^1 = 1/7
7^0 = 1
7^1 = 7
7^2 = 49
The log (base 7) of the number on the right is the exponent on the left. That is ...
log7(7) = log7(7^1) = 1
log7(1/49) = log7(7^-2) = -2
The fence is 68 feet long and 1/2 feet thick. 7 feet of space is between each post. How many posts are used for the fence. I think it’s basic division but I’m not sure what to divide by lol.
Answer:
We could say 10
Step-by-step explanation:
1) Remove unneeded info
2) Divide the length by the distance between posts
68/7
3) Will give you a decimal but ro7nd up to 10
For the function defined by R= 150/d², what is the constant of proportionality?
Answer: The constant of proportinality is 150.
Step-by-step explanation:
The equation of inverse proportion has the following form:
[tex]y=\frac{k}{x}[/tex]
Where "k" is the constant of proportionality.
In this case, you can observe that R is inversely proportional to d², because it has the form of inverse proportion:
[tex]R=\frac{150}{d^2}[/tex]
Therefore, you can identify that the constant of proportionality "k" is:
[tex]k=150[/tex]
Answer: A. 150
Step-by-step explanation:
This is my other I need help account. So I have the bigger picture now. I hope this is better . But still ! Urgent! Help!
Answer:
A. 12 in^2
Step-by-step explanation:
Polygon ABCD is a kite. The area of a kite is equal to the product of the diagonals divided by 2.
One diagonal is segment AC.
AC = AE + CE = 2 + 2 = 4
The other diagonal is segment BD.
BD = BE + ED
BD = BE + 2BE
BD = 3BE
BD = 3(2) = 6
The diagonals measure 4 inches and 6 inches.
area = diagonal1 * diagonal2/2
area = 4 * 6 /2
area = 24/2
area = 12
Answer: A. 12 in^2
The average man takes 7192 steps a day about how many steps does the average man take any year
Answer:
2625080
Step-by-step explanation:
just multiply by 365
Answer: 2,625,080
Explanation: 1 day = 7192, 365 days x 7192 = 2,625,080
I PROMISE BRAINLIST; 5-STARS; THANKS!! IT'S VERY SIMPLE; BELIEVE ME!!!!!
2. –4, 8, –16, 32, . . .
A. arithmetic, 64, 128, 256
B. geometric, –64, 128, –256
C. geometric, –48, 64, –80
D. The sequence is neither geometric nor arithmetic.
3. 81, 27, 9, 3, . . .
A. arithmetic, 0, –3, –6
B. geometric, 0, –3, –6
C. geometric, 1,
D. The sequence is neither geometric nor arithmetic.
4. What are the first four terms of an arithmetic sequence if the common difference is 1.5 and the first term is 15?
A. 15, 30, 45, 60
B. 15, 16.5, 18, 19.5
C. 15, 22.5, 33.75, 50.625
D. none of the above
5. What are the first four terms of a geometric sequence if the common ratio is 10 and the first term is 4.5?
A. 4.5, .45, .045, .0045
B. 4.5, 9.0, 13.5, 18.0
C. 4.5, 14.5, 24.5, 34.5
D. none of the above
Answer:
2. B
3. C
4. B
5. D
Step-by-step explanation:
2) The sequence is multiplying by -2 each time. This means that it is geometric.
The next two terms would be:
[tex]32*-2=-64\\-64*-2=128\\128*-2=-256[/tex]
This means that the answer is B
3) The sequence is being multiplied by [tex]\frac{1}{3}[/tex] each time. This means that it is geometric.
The next 3 terms would be:
[tex]3*\frac{1}{3} =1 \\\\1*\frac{1}{3} =\frac{1}{3} \\\\\frac{1}{3} *\frac{1}{3} =\frac{1}{9}[/tex]
I am assuming that the answer is C and that you were unable to type the fractions.
4) We know that the common difference is 1.5, so that is the coefficient of our variable and the starting value is 15. This means that we can write an equation as follows
[tex]f(x)=1.5(x-1)+15[/tex]
Now we can find the first 4 terms
[tex]f(1)=15.0\\f(2)=16.5\\f(3)=18.0\\f(4)=19.5[/tex]
This would mean that the answer is B
5) We know that this is a geometric series, we know the common ratio, and we know the first term. This means we can write the equation as follows
[tex]f(x)=4.5(10)^{x-1}[/tex]
Now we can find the first 4 terms
[tex]f(1)=4.5\\f(2)=45\\f(3)=450\\f(4)=4500[/tex]
Unless you meant that the ratio was [tex]\frac{1}{10}[/tex], the answer is D, none of the above
in a coordinate plane what is the length of the line segment that connects points (3, 3) and (8, 7)? round to the nearest hundredth
Answer:
6.40
Step-by-step explanation:
a^2 + b^2 = c^2X-values: 8 - 3 = 5 (length of a)Y-values: 7 - 3 = 4 (length of b)5^2 + 4^2 = c^225 + 16 = c^241 = c^2square root (41) = cc = 6.40When 5x2−5 is completely factored, which is one of its factors?
Answer:
5(x + 1)(x - 1)
Step-by-step explanation:
Given
5x² - 5 ← factor out 5 from each term
= 5(x² - 1) ← x² - 1 is a difference of squares
= 5(x + 1)(x - 1)
The factors are 5, (x + 1) and (x - 1)
Final answer:
When the expression 5x² − 5 is completely factored, one of its factors is 5, and after applying the difference of squares, the fully factored form is 5(x + 1)(x − 1).
Explanation:
When the expression 5x2 − 5 is completely factored, what we're looking for is a common factor that can be taken out of both terms. In this case, both terms have a factor of 5, so we can factor out 5 from the expression, yielding:
5(x² − 1).
This expression can be further factored as the difference of squares, which is a special factoring rule that applies to expressions in the form of a² − b²:
5(x + 1)(x − 1).
So, one of the factors is 5, another factor is (x + 1), and the last factor is (x − 1).
What is the value of x?enter your answer in the box.
Answer:
Hence final answer is x=46
Step-by-step explanation:
We need to find the value of x using given triangle.
Given that ED is angle bisector of angle E.
Then we can apply this formula
[tex]\frac{EG}{EH}=\frac{DG}{DH}[/tex]
[tex]\frac{63.8}{55}=\frac{58}{x+4}[/tex]
[tex]\frac{63.8}{55}=\frac{58}{x+4}[/tex]
Cross multiply
63.8(x+4)=55(58)
63.8(x+4)=3190[tex]x+4=\frac{3190}{63.8}[/tex]
x+4=50
x=50-4
x=46
Hence final answer is x=46
Tools
Question 12
The bottom of a garage door is 2.8 meters above the ground. When a button is pushed, the door moves down at a rate of 0.6 meter per second. W
A 0.6 + 2.8t = 0
B 0.6 – 2.8t = 0
C 2.8 + 0.6t = 0
D 2.8 – 0.6t = 0
Answer: D. 2.8 - 0.6t
Step-by-step explanation:
The t represents how much time it takes. So, it goes down by 0.6 per second until it gets to 0.
A garage door's bottom is 2.8 meters above the ground. The door descends at a pace of 0.6 meters per second when a button is pressed. The equation for the above situation is 2.8 + 0.6t = 0. Option C is correct.
What is an equation?Equations are statements that affirm the equivalence of two expressions that are joined by the equals symbol "=". An equal sign ("=") links two expressions together to form an equation.
It is given that, the bottom of a garage door is 2.8 meters above the ground. When a button is pushed, the door moves down at a rate of 0.6 meters per second.
The two expressions on each side of the equals sign are referred to as the "left-hand side" and "right-hand side" of the equation. The right side of an equation is typically assumed to be zero.
Suppose t represents the number of seconds, The equation for the given condition is,
2.8 + 0.6t = 0.
Thus, a garage door's bottom is 2.8 meters above the ground. The door descends at a pace of 0.6 meters per second when a button is pressed. The equation for the above situation is 2.8 + 0.6t = 0. Option C is correct.
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naoya read a book cover to cover in a single session, at a rate of 55 pages per hour. After 4 hours, he had 350 pages left to read
write the functions formula
Answer:
Step-by-step explanation:
The question here is "how many pages does this book have?"
In 4 hrs, at 55 pages/hr, he reads 220 pages.
Adding the number of pages read (220) to the number of pages left to read (350) yields a total of 570 pages in this book.
Next time, please try to be more specific about what you want to find. "functions formula" is very ambiguous and unhelpful.
The equation is [tex]\( y = 570 - 55x \)[/tex], where [tex]\( y \)[/tex] is pages left and [tex]\( x \)[/tex] is hours passed.
To complete the equation for the relationship between the number of pages left and the number of hours, we first need to determine the rate at which Naoya is reading the book.
Since he read 55 pages per hour, after 4 hours he would have read [tex]\( 55 \times 4 = 220 \)[/tex] pages.
Given that after 4 hours he still had 350 pages left to read, we can find out how many pages he had initially:
Initial number of pages = Total pages - Pages read
Initial number of pages = 350 pages + 220 pages
Initial number of pages = 570 pages
Now, let's use the formula for the relationship between the number of pages left and the number of hours:
[tex]\[ y = 570 - 55x \][/tex]
Where:
- [tex]\( y \)[/tex] represents the number of pages left to read after [tex]\( x \)[/tex] hours.
- [tex]\( x \)[/tex] represents the number of hours.
So, the complete equation for the relationship is:
[tex]\[ y = 570 - 55x \][/tex]
The complete question is here:
Naoya read a book cover to cover in a single session, at a rate of 55 pages per hour. After 4 hours, he had 350 pages left to read.
Let y represent the number of pages left to read after x hours.
Complete the equation for the relationship between the number of pages left and number of hours.
y=
find the exact values of sin pi/12
Answer:
[tex]\sin (\frac{\pi}{12})=\frac{\sqrt{6}-\sqrt{2}}{4}[/tex]
Step-by-step explanation:
We want to find the exact value of
[tex]\sin \frac{\pi}{12}[/tex]
We rewrite the given expression to obtain:
[tex]\sin \frac{\pi}{12}=\sin (\frac{\pi}{3}-\frac{\pi}{4})[/tex]
We use the identity:
[tex]\sin (A-B)=\sin A \cos B-\sin B \cos A[/tex]
[tex]\sin ( \frac{\pi}{3}- \frac{\pi}{4})=\sin \frac{\pi}{3} \cos \frac{\pi}{4}-\sin \frac{\pi}{4} \cos \frac{\pi}{3}[/tex]
[tex]\sin ( \frac{\pi}{3}- \frac{\pi}{4})=\frac{\sqrt{3}}{2} \times \frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2} \times \frac{1}{2}[/tex]
[tex]\sin ( \frac{\pi}{3}- \frac{\pi}{4})=\frac{\sqrt{6}-\sqrt{2}}{4}[/tex]
The exact value of sin(π/12) is ±√(2 - √3)/2 by using half-angle formula
To find the exact value of sin(π/12), we can use the half-angle formula for sine:
sin(x/2) = ±√[(1 - cos(x))/2]
In this case, x = π/6.
Therefore, we can use the half-angle formula with x = pi/6 to find the exact value of sin(π/12).
sin(pi/12) = ±√[(1 - cos(π/6))/2]
Let's calculate the value step by step:
cos(π/6) = √3/2
sin(π/12) = ±√[(1 - √3/2)/2]
To simplify further, let's rationalize the denominator:
sin(π/12) = ±√[(2 - √3)/4]
sin(π/12) = ±√(2 - √3)/2
Therefore, the exact value of sin(π/12) is ±√(2 - √3)/2.
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What is the area of the triangle rounded to nearest hundredth
ANSWER
The area of the triangle is 48.6 square feet to the nearest tenth.
EXPLANATION
The area of the triangle is calculated using the formula
[tex]Area= \frac{1}{2} bc \sin(A) [/tex]
where A=94° is the included angle, b=7.5 inches and c=13 inches.
We substitute the values into the formula to obtain:
[tex]Area= \frac{1}{2} \times 7.5 \times 13 \sin(94 \degree) [/tex]
Area=48.6 ft² to the nearest tenth.
Determine whether each table below models a linear, quadratic or exponential function
Answer:
Linear Quadratic Exponential
Step-by-step explanation:
Answer:
First table models Linear, second quadratic and third one exponential functions.
Step-by-step explanation:
To find whether the given table models a linear function there should be a constant change in y values with the constant change in x values of the table.
We take the example of first table written as linear.
Here change in x values is
6 - 5 = 1
7 - 6 = 1
8 - 7 = 1
Similarly change in y values is
1 - 4 = -3
-2 - 1 = -3
-5 -(-2) = -3
There is a common difference in y values = -3
So the given table models linear function.
We take the second table.
For quadratic function with the constant change in x values, difference of difference in y values is constant.
Change in x - values
6 - 5 = 1
7 - 6 = 1
8 - 7 = 1
Difference in y values
1 - 0 = 1
4 - 1 = 3
9 - 4 = 5
Now difference in difference of y values
3 - 1 = 2
5 - 3 = 2
Here, difference in difference of y values is 2
So the given table models a quadratic equation.
Now we take the third table.
For exponential function in the form of [tex]f(x) = a(r)^{n}[/tex] there should be a common ratio in the terms of y values.
[tex]\frac{\text{Second term of y}}{\text{First term of y }}= \frac{2}{1}=2[/tex]
[tex]\frac{\text{Third term of y}}{\text{Second term of y }}= \frac{4}{2}=2[/tex]
So there is a common ratio of 2 in each term.
Therefore, the given table models exponential equation.
First table models Linear, second quadratic and third one exponential functions.
Circle M has a radius of 7.0 cm. The shortest distance between P and Q on the
circle is 7.3 cm. What is the approximate area of the shaded portion of circle M? Please explain :)
Answer: C. [tex]25.6\ cm^2 [/tex]
Step-by-step explanation:
Given: Circle M has a radius = 7.0 cm.
The shortest distance between P and Q on the circle (arc length)= 7.3 cm.
Now, the central angle 'x' is given by :-
[tex]x=\dfrac{l}{r}\\\\\Rightarrow\ x=\dfrac{7.3}{7}=1.04285714286\ radian[/tex]
Now, the area of sector is given by :-
[tex]A=\dfrac{1}{2}r^2x\\\\\rightarrow\ A=\dfrac{1}{2}(7)^2(1.04285714286)\\\\\Rightarrow\ =25.55\approx25.6\ cm^2 [/tex]
Answer:
C.
Step-by-step explanation:
I did the test.
Number seven omg I am done with math!!! Please help to solve for m
Answer:
m∠1 = 123°
Step-by-step explanation:
Since a straight line is always a supplementary angle, it equals 180°. To solve for the unknown angle, we can subtract the known angle from 180°.
180° - 57° = 123°
So m∠1 = 123°
180-57= 123 is the measurement for angle 2
All straight line is equal to 180
The longest chord of a circle is?
Answer:
diameter
Step-by-step explanation:
A chord is a line segment connecting any 2 points on the circumference of the circle.
The diameter connects 2 points and also passes through the centre of the circle, making it the longest chord.
math help please ????
Answer:
4 (as in 25/4)
Step-by-step explanation:
Write and solve an equation of ratios:
x 15
------ = ------
10 24
Then 24x = 150, and x = 150/24 = 6.25. This is equivalent to 25/4.
Answer:
x = 25/4
Step-by-step explanation:
If the rectangles are similar, the ratio of the side lengths have to be similar
10 24
------ = --------
x 15
Using cross products
10*15 = 24*x
150=24x
Divide each side by 24
150/24=24x/24
150/24=x
Divide the top and bottom by 6
25/4 = x
explain why it is useful to write linear equations in equivalent form. what does each form reveal?
However, point slope equations can be awkward to use in some algebraic operations. In such cases, it may be helpful to convert the equation into a different form, the standard form. The standard form of an equation is Ax + By = C. In this kind of equation, x and y are variables and A, B, and C are integers.
A coral reef grows 0.13 m every week. How much does it grow in 15 weeks
0.13 times 15 is 1.95. Which means the coral reef grows 1.95 m in 15 weeks.
For this case we have reef coral grows 0.13 meters per week, if we want to indicate how much will have grown in 15 weeks we have the following rule three:
0.13 metrs ---------------> 1 week
x -------------------------------> 15 weeks
Where "x" is the number of meters reef coral grows in 15 weeks.
[tex]x = \frac {15 * 0.13} {1}\\x = 1.95 \ m[/tex]
Thus, in 15 weeks it grows 1.95 meters.
Answer:
[tex]1.95 \ m[/tex]
The sum of the angle measures of a triangle is 180°. Find the measure of each angle
Answer:
16 and 82 degrees
Step-by-step explanation:
You can sum all of the angles together and solve for x.
(x - 1) + (5x - 3) + (5x - 3) = 180
11x - 7 = 180
11x = 187
x = 17
The first angle is 16 degrees. (17 - 1)
The other two angles are 82 degrees(5(17) - 3)
Answer:
16 and 82 degrees
Step-by-step explanation:
You can sum all of the angles together and solve for x.
(x - 1) + (5x - 3) + (5x - 3) = 180
11x - 7 = 180
11x = 187
x = 17
The first angle is 16 degrees. (17 - 1)
The other two angles are 82 degrees(5(17) - 3)
given that (-3,6) is on the graph of f(x), find the corresponding point for the function 1/3f(x)
Answer:
The corresponding point of (-3 , 6) is (-3 , 2)
Step-by-step explanation:
* Lets talk about some transformation to solve the problem
- A vertical stretching is the stretching of the graph away from
the x-axis
- If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched
by multiplying each of its y-coordinates by k.
- A vertical compression is the squeezing of the graph toward
the x-axis.
- If 0 < k < 1 (a fraction), the graph is f(x) vertically compressed
by multiplying each of its y-coordinates by k.
* Now lets solve the problem
∵ f(x) transformed to be 1/3 f(x)
∴ The graph of f(x) is stretched or compressed vertically
∵ k = 1/3
∴ 0 < k < 1
∴ The graph is compressed vertically
- The y-coordinate must be multiplying by k
∵ The y-coordinate of the point is 6
∵ 6 × 1/3 = 2
∴ The image of the point (-3 , 6) is (-3 , 2)
* The corresponding point of (-3 , 6) is (-3 , 2)
The sum of three consecutive numbers is 72. What is the middle number?
Answer:
48
Step-by-step explanation:
Assuming that the numbers went in a pattern instead of a random order it would be 48 because 48 divided by 3 would be 24. 24 would be the first number though, so it would be 48 because 24 plus 24 is 48.
Hope this helps, have a great day!
Thhe answer is 48 :]
What is the slope of the function?
-10, -5, 5, 10
It is -10
Because when you take two points from the table and put it into the equation y=my+b...
So for example, take (-4,-16) from the table and substitute into x and y...
-16=m(-4) + b
And then substitute all the options given in the question, so I tried -10 first and put it in the place of m( in the equation) because m is the slope.
Then the equation would look like this:
-16= -10(-4) +b
Now solve for b
B= 24
And then check your answer by the RHS and LHS Method..
-16=-40 +24
Which is equal to:
-16=-16
There fore the the slope of this equation is 10
Answer: 5
Step-by-step explanation:
The formula to find slope is given by :-
[tex]\text{Slope}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the given table in picture,
Take [tex]x_1=0\ ;\ y_1=4\\\\x_2=2\ ;\ y_2=14[/tex]
Then, slope of the given function will be given by :-
[tex]\text{Slope}=\dfrac{14-4}{2-0}\\\\\Rightarrow\text{Slope}=\dfrac{10}{2}=5[/tex]
Hence, the slope of the given function = 5