Answer:
2
Step-by-step explanation:
The slope of a line is defined by the formula:
[tex]m=\dfrac{\Delta \, y}{\Delta \, x} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
In this problem, we are given two points in the form [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex].
So, we can define the x's and y's as:
[tex]x_1 = 1[/tex], [tex]y_1 = 2[/tex], [tex]x_2 = 5[/tex], [tex]y_2 = 10[/tex].
Hence, the slope of the line can be solved for.
[tex]m = \dfrac{10-2}{5-1}[/tex]
[tex]m = \dfrac{8}{4}[/tex]
[tex]m = 2[/tex]
The slope of the line with points (1, 2) and (5, 10) is 2.
Which graph represents the function f(x) = -x] -2?
The third graph or option 3 represents the function f(x) = - l x l - 2.
Given:
f(x) = - l x l - 2
Table
x y = - l x l - 2
0 -2
1 -3
2 -4
3 -5
-1 -3
-2 -4
-3 -5
On plotting above points or the above points shown in figure 3 or third graph.
Therefore the third graph or option 3 represents the function f(x) = - l x l - 2.
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friendly and kind personality and likes to help people but like Hyde, he becomes mysterious and violent
I need to know what NM is
The length of NM is 10 units
What are similar triangles?
If two triangles' corresponding angles and sides are identical and their corresponding sides are proportional, or if the ratios between the lengths of the corresponding sides are comparable, then two triangles are said to be similar.
Similar triangles are triangles with the same shape but different sizes. Examples of related objects are all equilateral triangles and squares with any side length.
The triangles ONP and LNM are similar triangles.
So, the following is true.
(ON/LN)=(NP)/(NM)
(3.6/6)=(6)/(NM) ( LN=LO+ON=2.4+3.6=6 )
3.6 NM=6*6 =36
NM=36/3.6 = 10
So, the length of NM is 10 units
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At a time t seconds after an object is tossed vertically upward, it reaches a height s in feet given by the equation:
s=64t-16t^2
In how many seconds does the object reach its maximum height?
The time it takes the object to attain maximum height is 2 seconds
Time to Attain Maximum HeightTo find the time it takes the object to attain maximum height, we have to use the quadratic equation to do so. The formula can be given as
t = -b/2a
But let's write and define our quadratic equation with it's variables.
S = 64t - 16t²
To attain maximum height;
t = -b/2a
a = -16, b = 64,c = 0
Substituting the values
t = -64/2(-16)
t = 2
The time is 2 seconds
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The cost to replace a water pump in a sports car was $899. This included $365 for the water pump and $89 per hour for labor. How many hours of labor were required to replace the water pump?
By solving a linear equation we will see that there were 6 hours of labor.
How many hours of labor were required?We know that the total cost is composed by a fixed amount of $365 plus $89 per hour of labor, so if there are x hours of labor, the total cost will be:
c(x) = $365 + x*$89
We know that the total cost is $899, then we can write the linear equation:
$899 = $365 + x*$89
$899 - $365 = x*$89
($899 - $365)/$89 = x = 6
So there were 6 hours of labor.
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10] Salim walked 1 1/2 miles to school and then 2 1/2 miles to work after school. How far did he walk in all?
Answer:
4
Step-by-step explanation:
Solution by separating parts
Rewriting our equation with parts separated
=1 + 1/2 + 2 + 1/2
Solving the whole number parts
1 + 2 = 3
Solving the fraction parts
1/2 +1/2 = 2/2
Reducing the fraction part, 2/2,
2/2 = 1/1
Simplifying the fraction part, 1/1,
1/1 = 1
Combining the whole and fraction parts
3 + 1 = 4
Answer:
4 miles
Step-by-step explanation:
1 1/2 = 1.5
2 1/2 = 2.5
1.5 + 2.5 = 4 miles
Rewrite the equation in vertex form. (Include fractions in final answer).
y=-3x^2 -7x+4
For the given equation y = 3x² -7x + 4 the vertex form is given by
( 7/6, -1/12).
As given in the question,
Equation is given by :
y = 3x² -7x + 4
Standard form of the equation to get the vertex form is given by :
y = a ( x - h )² + k
Where ( h, k ) represents the vertex of the equation,
Now,
Simplify the given equation y = 3x² -7x + 4 into standard form to get vertex form,
y = 3x² -7x + 4
⇒ y = 3 [x² -2×(7/6)] + 4
⇒ y = 3 [ x² - 2×(7/6) + (49/36) - (49/36) ] + 4
⇒ y = 3 [ x² - 2×(7/6) + (49/36) ] - 3(49/36) + 4
⇒ y = 3 [x - (7/6)]² - (49/12) + 4
⇒ y = 3[x - (7/6)]² - (1/12)
Compare it with standard form ,
a = 3, h = (7/6) , k = -(1 /12)
Vertex form ( h, k) = ( 7/6 , -1/12 )
Therefore, for the given equation y = 3x² -7x + 4 the vertex form is given by ( 7/6, -1/12).
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Karen, a 52-year-old female, bought a $75,000, 20-year life insurance policy through her employer. Karen is paid weekly.
How much is deducted from her paycheck for life insurance? (Use the table.)
ABC Term Life Insurance Company
Annual premium
Age at issue
Male Female 10-year
per $1000 of coverage
20-24 23-27 $2.50
25-29 28-32 $3.25
30-34 33-37 $3.82
35-39 38-42 $4.55
40-44 43-47 $5.78
45-49 48-52 $7.53
20-year
$3.80
$5.84
$7.93
$10.33
$13.68
$17.56
As Karen age is 52- year old and she is a female and her life insurance policy is for 20- years , then amount to be deducted from her life insurance paycheck is equal to $1317.
As given in the question,
Information given about Karen,
Age = 52- year old
Gender = female
Policy = 20 -year life insurance policy
Annual premium given per $1000 for coverage
Karen policy amount = $75,000
From the table it is given that,
Amount deducted per $1000 for 20year policy in the age limit of 48 -52
= $17.56
⇒ $1000 = $17.56
⇒ $75,000 = $( 17.56 × 75,000)/ 1000
= $1317.
Therefore, as Karen age is 52- year old and she is a female and her life insurance policy is for 20- years , then amount to be deducted from her life insurance paycheck is equal to $1317.
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PLEASE HELP SOLVE!!!
Answer:
positive, positive, zero, zero, negative, negative, positive
Step-by-step explanation:
The derivative is positive when a function is increasing.
The derivative is zero when a function is neither increasing nor decreasing.
The derivative is negative when the function is decreasing.
Graph g(x) = |x − 3|.
Answer: x+3
Step-by-step explanation:
since it has the absolute value, it will be x+3 and you can graph that in your calculator!
78 children attended a trip to the fair. 60 of them were girls. Find the ratio of the number of girls to boys.
Do not put in simplest form.
Answer:
First, find the number of boys: [tex]78-60=18[/tex]
The ratio of the number of girls to boys would be 60 : 18.
The functions r and s are defined as follows.
r(x) = 2x+1
s(x) = -x²
Find the value of r (s (4)).
r(s(4))=
Answer:
[tex]33[/tex]
Step-by-step explanation:
Define functions:
[tex]r(x) = 2x+1\\s(x) = -x^2[/tex]
Substitute [tex]s(x)[/tex] into [tex]r(x)[/tex]:
[tex]2(-x^2) + 1[/tex]
Solve for value:
[tex]= 2((-4)^2)+1\\= 2(16) + 1\\= 32 + 1\\= 33[/tex]
** assuming that the function of [tex]s(x)[/tex] the x value is squared with the negative sign.
A poster measuring 150cm by 180cm is enlarged in the ratio 8:5. Find the length and breadth of the enlarged poster
Answer:
240 cm by 288 cm
Step-by-step explanation:
You want the dimensions of a 150 cm by 180 cm poster enlarged by the ratio 8:5.
SolutionThe enlargement ratio, expressed as a fraction, multiplies each of the original dimensions to get the new dimensions. The new dimensions are ...
(8/5)·150 cm by (8/5)·180 cm = 240 cm by 288 cm
Find the savings plan balance after 2 years with an APR of 3% and monthly payments of $300.
The balance is $
(Do not round until the final answer. Then round to the nearest cent as needed.)
Answer:
Step-by-step explanation:
The balance of the savings plan after 2 years will be=$7,410.85 at 3% compounded monthly.
The balance of the savings plan after 2 years will be=$7,407.95 at 3% compounded annually.
The formula you use to calculate this is:FV=P{[1 + R]^N - 1/ R}=FV OF $1 PER PERIOD, Where R=Interest rate per period, N=number of periods, P=periodic payment, FV=Future value.
If tan(t)=3/4 what’s cos(t)
well, let's notice our tangent is positive, that only happens on the 1st and 3rd Quadrants
[tex]tan(t )=\cfrac{\stackrel{opposite}{3}}{\underset{adjacent}{4}}\hspace{5em} \textit{now let's find the hypotenuse} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{4^2 + 3^2}\implies c=5\hspace{5em} \stackrel{I~Quadrant}{cos(t)= \cfrac{\stackrel{adjacent}{4}}{\underset{hypotenuse}{5}}}\qquad \stackrel{III~Quadrant}{cos(t)=-\cfrac{4}{5}}[/tex]
A dog breeder is planning to buy more dog food. He makes a table showing how
many pounds of food he will have after shopping. The table is based on how much he
spends and how much food he already has. Which equation generates the table?
Money Spent (x) $0 $20 $40 $60
Pounds of Food (v) 4 12 20 28
x=y-4
y=8x-4
x=8y +4
y=x+4
The equation that generates the table is
y = (2/5)x + 4.
What is an equation of a line?
The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
Money Spent (x) $0 $20 $40 $60
Pounds of Food (v) 4 12 20 28
We can have the following points from the table.
(0, 4), (20, 12), (40, 20), and (60, 28).
Now,
Choose two points:
(0, 4) and (20, 12)
m = (12 - 4) / (20 - 0)
m = 8 / 20
m = 2/5
Now,
(0, 4) = (x, y)
y = mx + c
4 = (2/5) x 0 + c
4 = c
c = 4
Now,
The equation is given as,
y = mx + c
y = (2/5)x + 4
The equation that generates the table is
y = (2/5)x + 4.
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The scatter plot shows the winning times, in seconds, in a 50-meter race over eight consecutive years.
Scatter plot with x axis labeled Time in Years and y axis labeled Winning Time with points at 1 comma 5 and 4 tenths, 2 comma 5, 3 comma 4 and 6 tenths, 4 comma 4 and 9 tenths, 5 comma 4 and 1 tenth, 6 comma 3 and 9 tenths, 7 comma 3 and 6 tenths, and 8 comma 3 and 3 tenths.
Which of the following is an appropriate line of best fit?
y hat equals negative 29 hundredths times x plus 5 and 67 hundredths.
y hat equals 29 hundredths times x plus 5 and 67 hundredths.
y hat equals negative 45 hundredths times x plus 7 and 69 hundredths.
y hat equals 45 hundredths times x plus 7 and 69 hundredths.
Answer:
[tex]\hat{y}=-0.29x+5.67[/tex]
Step-by-step explanation:
Given points on the scatter plot:
(1, 5.4)(2, 5)(3, 4.6)(4, 4.9)(5, 4.1)(6, 3.9)(7, 3.6)(8, 3.3)Plot the given points and draw a line of best fit (see attachment).
As the y-values decrease as the x-values increase, the slope of the line of best fit is negative.
From inspection of the plotted line of best fit, we can see that the y-intercept is approximately 5.7.
Therefore, the equation that is appropriate for the line of best fit is:
[tex]\boxed{\hat{y}=-0.29x+5.67}[/tex]
Answer:
y hat equals negative 29 hundredths times x plus 5 and 67 hundredths.
Step-by-step explanation:
i took the test :)
Prizes in a raffle are determined by taking a ball from a bag. There are 15 balls in the bag, 12 of them are green, two of them with black stars. There are two silver balls, one with a black star, and one gold ball. If you draw the green ball, without the black star, you win a small prize. If you get a green ball with the black star, you get a medium prize. If you get the silver ball without the star, you get a large prize. If you get the silver ball with the black star, you get the extra-large prize. If you get the gold ball, you get the super deluxe prize.
If you get a ball, what is the probability of getting the green with the black star?
The probability of getting the green ball with the star is
a.) 0.1333
b.) 0.1133
c.) 0.0123
d.) 0.0333
This is an example of:
a.) a joint event
b.) an elementary event
The probability of winning the small prize is:
a. 0.7666
b. 0.6666
c. 0.6667
d. 0.6777
This is an example of:
a.) a joint event
b.) an elementary event
What is the probability of winning the super deluxe prize?
The probability of winning the super deluxe prize is:
a.) 6.6677
b.) 0.6667
c.) 0.7667
d.) 0.0667
This is an example of:
a.) a joint event
b.) an elementary event
Answer:
a. )
Step-by-step explanation:
There are 15 balls ...... two are green with a star
2 out of 15 = 2/15 = .1333
A neighborhood planner uses a coordinate plane to design a new neighborhood. The coordinates A(1,−1) , B(1,−2) , and C(2,−1) represent House A, House B, and House C. The planner decides to place a playground centered at the origin, and moves the houses to make space. House A is now located at A′(3,−4) . What are the new coordinates of House B and House C when each house is moved using the same translation?
The new coordinates of House B and House C are
B' ( 3 , -5 ) and C' ( 4 , -4 ) respectively
What is Translation?
A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.
Given data ,
Let the 3 houses be A , B ,C
The coordinate of House A = A ( 1 , -1 )
The coordinate of House B = B ( 1 , -2 )
The coordinate of House C = C ( 2 , -1 )
Now , the houses are relocated to new coordinates with
The new coordinate of House A = A' ( 3 , -4 )
The translation of Point A can be expressed in the form of x and y coordinate as there is a translation occurred with a scale factor
So ,
A ( x₁ , y₁ ) to A' ( x₂ , y₂ )
A ( 1 , -1 ) to A' ( 3 , -4 )
x₂ = x₁ + 2
y₂ = y₁ - 3
From the figure , we can clearly see that the coordinates of the houses A , B and C are translated by a scale factor and the new coordinates are
x₂ = x₁ + 2
y₂ = y₁ - 3
Therefore ,
B ( x₁ , y₁ ) to B' ( x₂ , y₂ )
B' ( x₂ , y₂ ) = B' ( 3 , -5 )
C ( x₁ , y₁ ) to C' ( x₂ , y₂ )
C' ( x₂ , y₂ ) = C' ( 4 , -4 )
Hence , the new coordinates of House B and House C are B' ( 3 , -5 ) and C' ( 4 , -4 ) respectively
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#11 i
PROBLEM SOLVING The table shows the heights y of a competitive water-skier x seconds after jumping off a ramp.
Time (seconds), x 0 0.25 0.75 1 1.1
Height (feet), y
22 22.5 17.5 12 9.24
Write a function that models the height of the water-skier over time.
The function y =
Interpret the y-intercept.
B
22
I U
models the height.
T' T₂
When is the water-skier 5 feet above the water? Round your answer to the nearest hundredth.
70°F
Cloudy
The skier is 5 feet above the water after about
second(s).
O Search the web
J
O
L
D
(
1/10000 Word L
The function modelled for the given condition is [tex]y = -16x^{2} + 6x +22[/tex] and the time after which the skier is 5 feet above the water is 1.23 seconds.
A competitive water skier's heights y, x seconds after soaring off a ramp.
For x = 0, y = 22
for x = 0.25, y = 22.5
For x = 0.75, y = 17.5
For x = 1, y = 12
For x = 1.1, y = 9.24
The general equation of a quadratic equation is y = [tex]ax^{2} + bx +c[/tex]
Putting x = 0 and y = 22 in the equation, we get :
[tex]y = ax^{2} +bx +c[/tex]
c = 22
Now, putting x = 1 and y =12, we get,
12 = a*1 + b*1 + 22
a +b = 12 - 22 = -10 equation (1)
Putting x = 0.25, y = 22.5,
22.5 = a* [tex]22.5^{2}[/tex] +b*22.5 +22
506.25 a +22.5b = 0.5 equation(2)
Solving equation (1) and equation(2), we get :
a = -16 and b = 6 and c = 22
So, the quadratic equation becomes,
[tex]y = -16x^{2} + 6x +22[/tex]
Now, Time when the skier is 5 feet above the water,
[tex]x = \frac{3 +\sqrt{281} }{16} = 1.23 seconds[/tex]
Hence, the function modelled for the given condition is [tex]y = -16x^{2} + 6x +22[/tex] and the time after which the skier is 5 feet above the water is 1.23 seconds.
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30 POINTS AND BRAINLIEST!! PLEASE HURRY I HAVE 20 MIN LEFT. <3 tysm (:
25. doubled
26. doubled
27. increases 4 times
28. remains unchanged
29. increases 6 times
Consider the following linear equation.
y=2+34x
Step 1 of 2 : Determine the slope and the y-intercept (entered as an ordered pair) of the equation above. Reduce all fractions to lowest terms.
The slope of the function y = 2 + 34x is 34 and the y-intercept of the function y = 2 + 34x is 2.
First, let us understand the slope intercept form;
The slope intercept form is simply a way of writing a line's equation so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are obvious.
We know that the slope intercept form of a line is y = mx + c where m is the slope of the line and b is the y-intercept of the line.
We are given:
y = 2 + 34x
y = 34x + 2
Compare with y = mx + c, we will get;
m = 34
b = 2
So, the slope is 34 and the y-intercept is 2.
Thus, the slope of the function y = 2 + 34x is 34 and the y-intercept of the function y = 2 + 34x is 2.
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See question in screenshot below:
The value of P is $2,000.
The value of r is 2.8%
The value of n is 4.
The amount of money that Allision will have in 8 years is $2,500.19.
How much will he have in 8 years?When the account is compounded quarterly, it means that the amount invested and the interest that has already been earned would increase in value four times in a year. A compound growth rate can be modelled as an exponential equation.
The equation that can be used to determine the future value with quarterly compounding is:
S(t) = P( 1 + r /n)^(n x t)
Where:
P = amount deposited r = interest rate n = number of compounding t = number of yearsS(t) = 2,000 x ( 1 + 0.028 / 4)^(4 x 8)
S(t) = 2,000 x 1.007^32 = $2,500.19
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Read the problem below on the picture. It's Geometry by the way. Also if u can answer my other one its in my profile.
Answer:
x = 18. y = 54
Step-by-step explanation:
first we we figure out the degrees of the spot where N is.
(I know N references the line but ill be using it to call the spot)
72 + N = 90
subtract 72 from both sides
N = 18
So since opposite angles are the same
2x + N = 3x
2x + 18 = 3x
subtract 2x from both sides
18 = 1x
divide by 1 both sides
18 = x
______
now we add all the angles from the left sides to make 180
2x + N + 72 + y = 180
we know x is equal to 18 and N is also 18
2(18) + 18 + 72 + y = 180
simplify
36 + 18 + 72 + y = 180
add
126 + y = 180
subtract both sides by 126
y = 54
One year consumers spent an average of $23 on a meal at a restaurant. Assume that the amount spent on a restaurant meal is normally distributed and that the standard deviation is $5.
A) What is the probability that a randomly selected person spent more than $25?
B) What is the probability that a randomly selected person spent between $12 and $21?
C) Between what two values, symmetrically distributed around the mean, will the middle 95% of the amounts of cash spent fall?
Using the normal distribution, it is found that:
a) The probability that a randomly selected person spent more than $25 is of 0.3446 = 34.46%.
b) The probability that a randomly selected person spent between $12 and $21 is of 0.3307 = 33.07%.
c) The middle 95% of the amounts are between $13.2 and $32.8.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for the costs of the meal are given as follows:
[tex]\mu = 23, \sigma = 5[/tex]
The probability that a randomly selected person spent more than $25 is one subtracted by the p-value of Z when X = 25, hence:
Z = (25 - 23)/5
Z = 0.4
Z = 0.4 has a p-value of 0.6554.
1 - 0.6554 = 0.3446 = 34.46%.
The probability that a randomly selected person spent between $12 and $21 is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 12, hence:
X = 21:
Z = (21 - 23)/5
Z = -0.4
Z = -0.4 has a p-value of 0.3446.
X = 12:
Z = (12 - 23)/5
Z = -2.2
Z = -2.2 has a p-value of 0.0139.
0.3446 - 0.0139 = 0.3307 = 33.07%.
The normal distribution is symmetric, meaning that the bounds of the middle 95% of values are given as follows:
2.5th percentile: X when Z = -1.96.97.5th percentile: X when Z = 1.96.-1.96 = (X - 23)/5
X - 23 = -1.96 x 5
X = $13.2
1.96 = (X - 23)/5
X - 23 = 1.96 x 5
X = $32.8
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7. For the piecewise defined function {f(x)=1 x<3
{1/2x+7 x_>3
(1) 7
(2) 10
3x-1 x<3
[//x+7 _x23²)
(3) 17
(4) 27
which of the following is the value of f(6)?
Answer:
I think it's 10 idek I just search it
A student 6ft tall is standing 20ft away from a 35ft tall flagpole.
The flagpole is 60ft away from a building.
From the students point of view, the flagpole is lined up perfectly with the top of the building.
What's the height of the building?
PLEASE HELP MEEEE!!!!!
A student 6ft tall is standing 20ft away from a 35ft tall flagpole.
The flagpole is 60ft away from a building.
From the students point of view, the flagpole is lined up perfectly with the top of the building.
What's the height of the building?
PLS HELP GUYS LIKE FR I NEED HELP THIS IS MY LAST PROBLEM FOR MY SHEET. SHOW THE DRAWING PLS
Answer/Step-by-step explanation:
Use the given drawing and scale to find out how big the building is in real life. See image. Then use the scale they asked for to make the new drawing. See image.
- Jacob Elementary School had a book drive. On
Monday, the students collected 95 books. They
collected 78 more books on Tuesday. How many
books did the students collect?
The students collected
books.
The Grover family went on a spring vacation. Th
cabin is 305 miles away. If they drive 98 miles
first day, how many more miles do they have to
Step-by-step explanation:
1. 95+78 as its asking how many bools all together. 173 books
2. 305-98 ita asking how many miles LEFT.
Can some one please help me do these work sheets before I fail my class♀️
Answer of the given question are respectively,
[tex]-x^2y , 2w ,\\\\h^6 , -14a^5b^2\\x^6 , 4m^8\\9x^4/14 , y^2\\-5/x^2 , 1/2k\\7 , 1[/tex]
Exponent:
A quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression.
Example:
[tex]2^3[/tex] = 2 × 2 × 2
Combine like term:
1. [tex]9x^2y -10x^2y[/tex] = [tex]-x^2y[/tex]
2. Subtract 6w from 8w
8w -6w = 2w
Rule:
[tex]x^{a} * x^{b} = x^{a+b} \\\\[/tex]
1.
[tex]h^2 * h^4 = h^{2+4} \\ \\\\= h^6[/tex]
2.
[tex](-2a^2b).(7a^3b)\\\\-14 a^{2+3} b^{1+1} \\\\= -14 a^5 b^2[/tex]
Rule:
[tex](x^a)^b = x^{ab}[/tex]
1. [tex](x^2)^3 = x^6[/tex]
2.
[tex](-2m^3)^2 * m^2 \\\\4m^6*m^2\\\\4m^8[/tex]
Rule:
[tex]x^a/x^b = x^{a-b}[/tex]
1.
[tex]27x^5/42x\\\\= 9x^4 /14[/tex]
2.
[tex](y^3)^2/y^4\\\\y^6/y^4\\\\y^2\\[/tex]
Rule:
[tex]x^{-a}= 1/x^a[/tex]
1.
[tex]-5x^{-2} \\\\= -5/x^2[/tex]
2.
[tex]4k^2/8k^3\\\\= k^{-1} /2\\\\= 1/2k[/tex]
Rule:
[tex]x^0 =1[/tex]
1.
[tex]7x^0\\\\= 7[/tex]
2.
[tex](w^4)^2/w^8\\\\w^8/w^8\\\\w^0\\\\=1[/tex]
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