Answer:
slope of perpendicular line = - 2
Step-by-step explanation:
calculate the slope of YZ using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = Y (- 7, - 4 ) and (x₂, y₂ ) = Z (5, 2 )
[tex]m_{YZ}[/tex] = [tex]\frac{2-(-4)}{5-(-7)}[/tex] = [tex]\frac{2+4}{5+7}[/tex] = [tex]\frac{6}{12}[/tex] = [tex]\frac{1}{2}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2
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The probability that the customer came for lunch and did not order dessert is 7/113
The probability that the customer came for lunch or did not order dessert is 93/113
What is probability?It is the chance of an event to occur from a number of possible outcomes.
It is given by:
Probability = Number of required events / Total number of outcomes
We have,
Total number of customers = 113
Desert Non desert
Lunch 7 1 3
Dinner 30 63
The probability that the customer came for lunch and did not order dessert:
= 7 / 113
The probability that the customer came for lunch or did not order dessert:
= (7+13)/113 + (13 + 63)/113
= 20/113 + 73/113
= 93/113
Thus,
The probability that the customer came for lunch and did not order dessert is 7/113
The probability that the customer came for lunch or did not order dessert is 93/113
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hlp
A jacket costs $50.50 more than a pair of sneakers. If the total cost of both items is $200.00, find the cost of each
The total cost of a Jacket is $124.75 and the cost of pair of sneaker is $74.75.
Let us say that the cost of the pair of sneakers is X dollars.
According to the given situation,
Cost of One jacket is 50 dollars more than the cost of a pair of sneakers.
Cost of one jacket = $(50 + X).
Total cost of one jacket and one pair of sneakers is $200.
Total cost of jacket and sneakers = $200
We get,
X + (X+50.5) = 200
2X + 50.5 = 200
The above equation that we have got is linear equation in one variable because it has degree 1 and one 1 variable.
Further solving the equation,
2X + 50.5 = 200
2X = 149.5
X = 74.75
So, the cost of one pair of sneakers is $74.75
Cost of One jacket is $(X + 50.5).
Cost of one jacket = $124.75.
So, one jacket costs $124.75 and sneakers cost $74.75.
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What is Pythagoras Theorem? What is the formula for the same?
The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem can be expressed as, c2 = a2 + b2; where 'c' is the hypotenuse and 'a' and 'b' are the two legs of the triangle.
Answer:
Pythagoras theorem is a theorem attributed to Pythagoras that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
The Pythagoras theorem equation is expressed as,
c²=a²+b²
where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two angles(opposite and adjacent)
Step-by-step explanation:
rate as brainliest
help meeeeeee pleaseee !!!!
Answer:
See below
Step-by-step explanation:
Use points given in hint to find slope, m = (2000 -1000) /( 6- 8) = -500
then y = - 500x + b sub i oneof the points to calculate b = 5000
so y = - 500x + 5000
if x = 7.5
y = -500(7.5) + 5000 = 1250 dollars
A sheriff patrols several neighborhoods in her patrol car it requires 3/15 of an hour to patrol an entire neighborhood how many neighborhoods can the sheriff patrol in 5/8 of an hour
Based on the time it takes to patrol one neighborhood, the number of neighborhoods that the sheriff can patrol in 5/8 of an hour is 3.125 neighborhoods
How to find the number of neighborhoods?The number of neighborhoods that the sheriff can patrol in 5/8 hours depends on the number of hours that it takes the sheriff to patrol one neighborhood.
The number of neighborhoods she can patrol can therefore be found by the formula:
= Number of hours sheriff has / Number of hours required to patrol one neighborhood
= 5/8 ÷ 3/15
= 5/8 x 15/ 3
= 75 / 24
= 3.125 neighborhoods
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The Sanchez family had dinner at their favorite restaurant. A 9% salestax was added to their bill. Amy paid the bill with a $10 gift certificateplus $30.60. How much did the family's dinner cost before tax? Roundyour answer to the nearest penny.Hint: Use the equation P+rP=T,where P is the price before tax, r is the sales tax rate, and T is the totalprice, including tax.
The formula indicates how the price of the meal after taxes is calculated.
[tex]T=P+rP[/tex]Where
T is the total price
P is the price without taxes
r is the tax rate, this value is always expressed as a decimal value.
Amy paid a total of $30.60 plus a $10 gift certificate, the total cost of the bill is:
[tex]\begin{gathered} T=30.6+10 \\ T=40.6 \end{gathered}[/tex]To express the tax rate as a decimal value you have to divide the percentage by 100:
[tex]\begin{gathered} r=\frac{9}{100} \\ r=0.09 \end{gathered}[/tex]Replace both values on the formula:
[tex]P+0.09P=40.60[/tex]Now we have established an equation with one unknown "P", to solve the equation for P, the first step is to simplify both terms on the left side of the equation. To do so, add both terms:
[tex]\begin{gathered} P+0.09P=40.60 \\ 1.09P=40.60 \end{gathered}[/tex]Divide both sides by 1.09 to determine the value of P
[tex]\begin{gathered} \frac{1.09P}{1.09}=\frac{40.60}{1.09} \\ P=37.249\approx37.25 \end{gathered}[/tex]The cost of the family's dinner before taxes w
Twelve less than seven times a number is sixteen. Find the number.
Answer:
4
Step-by-step explanation:
put in equation form
7x - 12 = 16
solve for x
7x = 28
x = 4
Write the correct equation for the following statement and then solve for the given number of
miles.
You decide to rent a limo for prom. The rate is $200 plus $5 per mile
traveled. Write an equation to calculate your total cost (c) at the end of
the evening for a given number of miles (m).
If you travel 45 miles what will be your total bill at the end
of the evening?
Answer:
$425
Step-by-step explanation:
Equation can be written as follows:
c = 200 + 5m
Plug 45 in for m to get this:
c = 200 + 5(45)
Simplify!
c = 200 + 225
c = 425
Hope this helps :)
In the figure, CA and CE are opposite rays, CH bisects
Which of the following are linear pairs involving point F? Select all that apply.
last choices are
e)
f)
pls help im crying
The angles that form a linear pair involving point F are:
a. ∠DFC and ∠CFG
d. ∠HFD and ∠CFD
What is the Definition of a Linear Pair?A linear pair can be defined as the set of two angles that are adjacent to each other and share a common vertex and a common side, and also lie on a straight line.
Given the image in the question above, we see that:
Angle DFC and angle CFG share a common side FC and a common vertex point F, hence, they are adjacent angles that lie on a straight line, thus, they are a linear pair.
Angle HFD and angle CFD also share a common side FD and a common vertex point F. This makes them adjacent to each other. Also they are on a straight line. Therefore, angle HFD and angle CFD are a linear pair.
Thus, we can conclude that the angles that form a pair of angles that are classified as a linear pair are:
a. Angle DFC and angle CFG
d. Angle HFD and angle CFD
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PLS HELP ME WITH THIS
you need to use the y=mx+b
Hello!
What is a slope-intercept form:
y = mx + b
m: slope[tex]Slope = \dfrac{y_2-y_1}{x_2-x_1} =\dfrac{1--3}{1-0} =\dfrac{4}{1} =4[/tex]
b: y-intercept or point that has an x-coordinate value of 0==> thus is -3
So our equation is [tex]y=4x-3[/tex]
Hope that helps!
A note with a face value of $8200 was discounted at If the discount was $200 find the length of the loan in days.
A note with a face value of $8200 was discounted If the discount was $200, the length of the loan in days will be 178 Days.
A loan is when money is lent to another person with the understanding that it would be repaid, along with interest. Before agreeing to provide a borrower with a loan, lenders will take into account the borrower's income, credit score, and degree of debt.
Let us consider the number of days to be 'D'
8200 * 5% * (D / 365) = $200
D = (200 * 365) / (8200 * 0.05)
D = 7300 / 41
D = 178 Days.
Therefore, the loan's duration in days will be 178 Days.
COMPLETE QUESTION: A note with a face value of $8200 was discounted at 5% If the discount was $200 find the length of the loan in days
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What is a rule for the translatiARST? Select all that apply.R
Explanation:
Let's identify the coordinates of the initial and final triangle.
R = (-4, 5)
S = (-2, 5)
T = (-4, 1)
In the same way,
R' = (3, 2)
S' = (5, 2)
T' = (3, -2)
So, we can say that the translation was 7 units to the right and 3 units down, so the rule will be:
(x, y) ---> (x + 7, y - 3)
If we apply this rule to the points R, S, and T, we get:
R(-4, 5) ---> (-4 + 7, 5 - 3) = R'(3, 2)
R(-4, 5) ---> (-4 + 7, 5 - 3) = R'(3, 2)
R(-4, 5) ---> (-4 + 7, 5 - 3) = R'(3, 2)
Under her cell phone plan, Mei Mei pays a flat cost of $46 per month and $5 per gigabyte. She wants to keep her bill under $70 per month. Write and solve an inequality which can be used to determine gg, the number of gigabytes Mei Mei can use while staying within her budget.
Answer:
Step-by-step explanation:
Under her cell phone plan, Mei Mei pays a flat cost of $46 per month and $5 per gigabyte. She wants to keep her bill under $70 per month. Write and solve an inequality which can be used to determine gg, the number of gigabytes Mei Mei can use while staying within her budget.
The
inequality
for the required
condition
will be 46+5x<70 as she want to keep the
bill
under $70 according to question. Also she can buy 5 gg that is number of
gigabytes
in a month.
What is inequality?
An
inequality
in mathematics is a relationship that makes a non-equal
comparison
between two numbers or other
mathematical
expressions. It is most commonly used to compare the
sizes
of two numbers on a
number
line.
How to solve the inequality?
To solve an inequality, follow these steps: Remove fractions by
multiplying
all terms by the fractions' least common
denominator
.
Simplify
the
inequality
by combining like terms on each side.
Subtract
or add
amounts
to get the unknown on one side and the numbers on the other.
according to the question,
$46 is the fix cost that she has to pay.
$5 is the cost of gg she buys that is variable.
let us assume that x gigabytes she can buy in a month.
$70 is the maximum bill amount she want.
so the inequality would be,
46+5x<70
5x<70-46
5x<26
x<26/5
x<5.2
so, she can
buy
5 gg at
maximum
in a month with the inequality 46+5x<70 for the given conditions.
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Which statement explains how you could use coordinate geometry to prove the diagonals of a quadrilateral are perpendicular?
To demonstrate that the diagonal slopes are opposing reciprocals, use the slope formula from coordinate geometry.
What is coordinate geometry?
The science of geometry using coordinate points is known as coordinate geometry (also known as analytical geometry).
Finding the difference between two points, breaking lines into m:n segments, locating a line's midpoint, computing a triangle's area in the Cartesian plane, and other operations are all feasible using coordinate geometry.
m=(rise/run) = (y2-y1)/(x2-x1)
(x1,y1) = coordinates of the line's first point
(x2,y2) = coordinates of the line's second point
To demonstrate that the diagonal slopes are opposing reciprocals, use the slope formula from coordinate geometry.
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Find the volume of this cone. Use 3 for TT. V = 7 r26 3 8ft V [?]ft V 1 6ft Enter SRI nhte. Das
The diameter of the cone is d = 6 ft.
The height of cone is h = 8 ft.
Determine the radius of cone.
[tex]\begin{gathered} r=\frac{d}{2} \\ =\frac{6}{2} \\ =3 \end{gathered}[/tex]Determine the volume of cone.
[tex]\begin{gathered} V=\frac{\pi(3)^28}{3} \\ =\frac{\pi\cdot9\cdot8}{3} \\ =3\cdot3\cdot8 \\ =72 \end{gathered}[/tex]So volume of cone is 72 feet cube.
Answer: 72
2 Kenedi has a piece of ribbon that measures24 inches long. She cuts the ribbon into15 equal pieces to attach to her dancecostume. Kenedi uses the expression shown tocalculate the length of each piece of ribbon sheuses on her costume.241 - 15Which of the following expressions CANNOT beused to determine the length of each piece ofribbon?15F99=G (242) (15)H7+15J 241-15
Notice that the option F cannot be used to determine the lengths of each piece of ribbon because:
[tex]\frac{(\frac{97}{4})}{\frac{1}{15}}=15\cdot\frac{97}{4}\ne\frac{24\text{ 1/4}}{15}[/tex]Kevin measured how many times he arrived to work late if he took subway. the results are provided in the following table. Find the probability that Kevin will arrive on-time tomorrow if he plans to take subway. (round the answer to 2 decimal places)
ANSWER
86.67%
EXPLANATION
We want to find the probability that Kevin will arrive on time if he plans to take the subway.
To find this, we have to divide the number of times that Kevin was on-time by the total number of times that he took the measurement.
We have that out of 30 days that Kevin was on-time on 26 occasions.
Therefore, the probability that Kevin will arrive on-time the next day is:
[tex]\begin{gathered} P(on-\text{time) = }\frac{26}{30}\text{ = }\frac{13}{15} \\ P(on-\text{time) = 86.67\%} \end{gathered}[/tex]That is the answer.
Simplify the expression.
the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths
negative 37 over 24 times j minus 17 over 12
negative 37 over 24 times j plus 17 over 12
43 over 24 times j plus 1 over 12
negative 43 over 24 times j plus negative 1 over 12
Simplify the expression.
the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths
negative 37 over 24 times j minus 17 over 12
negative 37 over 24 times j plus 17 over 12
43 over 24 times j plus 1 over 12
negative 43 over 24 times j plus negative 1 over 12
Which expression is equivalent to 3(−4.5b − 2.1) − (6b + 0.6)?
19.5b + 1.5
−19.5b − 1.5
−19.5b − 6.9
19.5b − 6.9
1.The value of the expression after simplify will be,
''negative 43 over 24 times j plus negative 1 over 12.''
Option D is true.
2. The equivalent expression will be;
⇒ - 19.5b - 6.9
What is mathematical expression?
Expression in math is defined as the collection of the numbers, variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is;
''The expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths.''
Now, We can write the expression in mathematical form as;
⇒ (- 1/8 j + 2/3) - (5/3 j + 9/12)
Solve the expression as;
⇒ - 1/8 j + 2/3 - 5/3 j - 9/12
⇒ - 1/8 j - 5/3 j + 2/3 - 9/12
⇒ j (-1/8 - 5/3) + 2/3 - 3/4
⇒ j (- 3 - 40)/24 + (8 - 9)/12
⇒ j (-43/24) + (- 1/12 )
This can be written as;
''negative 43 over 24 times j plus negative 1 over 12''
Therefore, The value of the expression after simplify will be,
''negative 43 over 24 times j plus negative 1 over 12.''
Option D is true.
2. The expression is given as;
3(−4.5b − 2.1) − (6b + 0.6)
Solve the expression as;
3(−4.5b − 2.1) − (6b + 0.6)
3 x -4.5b - 3 x 2.1 - 6b - 0.6
- 13.5b - 6.3 - 6b - 0.6
- 13.5b - 6b - 6.3 - 0.6
- 19.5b - 6.9
Thus, The expression is equivalent to 3(−4.5b − 2.1) − (6b + 0.6) will be;
⇒ - 19.5b - 6.9
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Find the selling price of a $249.50 cell phone with a 30% markup. Round to the nearest cent when necessary.$74.85$72.22$324.35$174.65
Answer:
$324.35
Explanation:
Given a $249.50 cell phone with a 30% markup, to determine the selling price of the cell phone we need to first calculate 30% of $249.50 as seen below;
[tex]\frac{30}{100}\times249.5=0.3\times249.5=74.85[/tex]We'll now add $74.85 to $249.50 to finally get the selling price of the cell phone;
[tex]74.85+249.5=324.35[/tex]Therefore, the selling price of the cell phone is $324.35.
What is the distance between the points (−3, −5) and (−3, −7)?
The distance between the points (−3, −5) and (−3, −7) is 2 units.
How to use distance formula?The distance formula gives the shortest distance between two points in a two-dimensional plane.
The distance formula is a useful tool for calculating the distance between two points.
Therefore,
d = √(x₂ - x₁)²+(y₂ - y₁)²
Let's find the distance between the points (−3, −5) and (−3, −7).
Hence,
x₁ = -3
x₂ = -3
y₁ = -5
y₂ = -7
d = √(-3 + 3)² + (-7 + 5)²
d = √(-2)²
d = √4
d = 2
Therefore, the distance between the point is 2 units.
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HELP ASAP WILL GIVE BRAINLIEST FOR THE CORRECT ANSWER
Answer:
(4,-4)
Step-by-step explanation:
(x,y)→(x+2,y−5)
A(2,1) -> (4,-4)
:]
The length of a rectangle is 1 units more than the width. The area of the rectangle is 72 units. What is the length, in units, of the rectangle?
Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs.
You need a $140,000 loan.
Option 1: a 30-year loan at an APR of 9%.
Option 2: a 15-year loan at an APR of 8.5%
Monthly payments and total loan costs on a 30-year loan at an APR of 9% are 1027.27 and for a 15-year loan at an APR of 8.5% are 1297.82.
Formula to computer the periodic payment for a loan with principal P, periodic interest rate R, and several payments T:
(P × R)([tex](1-(1+r)) ^{-T}[/tex])
Option 1, there are 30×12=360 monthly payments, and the monthly interest rate is 8%÷12.
By applying all the given values P=140000, R= 8%÷12 and T = 360 in P÷([tex](1-(1+r)) ^{-T}[/tex]),
(140000 × (9% ÷ 12))÷(1 - [tex](1 + \frac{9}{12} )^{-360}[/tex] ) = 1027.27
In option 2, there are 12 × 15 = 180 monthly payments, and the monthly interest rate is 7.5% ÷ 12. Applying the formula (P × R)([tex](1-(1+r)) ^{-T}[/tex]), the monthly payment is:
(140000 × (8.5% ÷ 12))÷(1 - [tex](1 + \frac{8.5}{12} )^{-180}[/tex] ) = 1297.82
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Which table shows a relationship with a constant rate of change of 9?
Option C
Explanations:The rate of change is given by the equation:
[tex]\text{Rate of change = }\frac{\triangle y}{\triangle x}[/tex]For the rate of change to be constant, Δy / Δx must be the same for all parts of the table.
In table A, the constant rate of change is (9-9)/(4-2) = 0
In table B, the constant rate of change is (13-11)/(4-2) = 2/2 = 1
In table C, the constant rate of change is (36-18)/(4-2) = 18/2 = 9
In table D, the constant rate of change is (10-9) / (4-2) = 1/2
Only table C has a constant rate of change of 9
I need help with this practice problem The subject is complex numbers and vectors
we have the expression
[tex]12\sqrt{2}cis(\frac{7pi}{6})\colon3\sqrt{3}cis(\frac{pi}{4})[/tex]therefore
[tex]12\sqrt{2}c\imaginaryI s(\frac{7p\imaginaryI}{6})\operatorname{\colon}3\sqrt{3}c\imaginaryI s(\frac{p\imaginaryI}{4})=\frac{12\sqrt{2}}{3\sqrt{3}}cis(\frac{7pi}{6}-\frac{pi}{4})=4\sqrt{\frac{2}{3}}cis(\frac{11pi}{12})[/tex]Simplify
[tex]4\frac{\sqrt{6}}{3}cis(\frac{11pi}{12})[/tex]please help me i need it asp
The solution of the system of equation is as follows:
x = 10 / 7y = - 5How to solve system of equation?The system of equation can be solved as follows:
6x + 4y = 10
-7x - 3y = 5
Hence, let's multiply equation(i) by 3 and multiply equation(ii) by 4
Therefore,
18x + 12y = 30
-28x - 12y = 20
add equation(ii) to equation(ii)
-10x = 50
y = 50 / -10
y = -5
Hence,
-7x - 3y = 5
-7x - 3(-5) = 5
-7x + 15 = 5
-7x = 5 - 15
-7x = - 10
x = 10 / 7
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A standard pair of six-sided dice is rolled. What is the probability of rolling a sum greater than or equal to 10? Express your answer as a fraction or a decimal number rounded to four decimal places.
The probability of rolling a sum greater than or equal to 10 in rolling dice will be 1/6 or 0.1667.
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
A standard pair of six-sided dice is rolled.
Since, All the possible outcomes are;
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6, 1), (6, 2), (6, 3), (6, 4), (6,5), (6,6).
So, Total possible outcomes = 6 x 6 = 36
Now, The favorable outcomes which has sum greater than or equal to 10 are;
(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)
So, Number of favorable outcomes = 6
Thus, The probability of rolling a sum greater than or equal to 10 in rolling dice
= 6/36 = 1/6 = 0.1667
Therefore, The probability of rolling a sum greater than or equal to 10 in rolling dice will be 1/6 or 0.1667.
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Conrad has two willow trees in his backyard. The first tree is 4 feet taller than the second one. If the second one is 28 feet tall, what is the height, in feet, of the first tree?
The first tree is 28ft tall, and the second tree is 4 ft higher than the second one. Then we need to add 4ft to the height of the second tree:
[tex]28ft+4ft=32ft[/tex]The heigh of the first tree is 32ft
how much wood is needed to make the circular bottom of a bird house if the diameter of the bottom is 12 inches
We are asked to find out how much wood is needed to make the circular bottom of a birdhouse if the diameter of the bottom is 12 inches.
Recall that the circumference of a circular shape is given by
[tex]C=2\cdot\pi\cdot r[/tex]Where π is a constant and r is the radius.
The radius and diameter of a circle are related as
[tex]r=\frac{D}{2}[/tex]So, the circumference of the circle becomes
[tex]\begin{gathered} C=2\cdot\pi\cdot r \\ C=2\cdot\pi\cdot\frac{D}{2} \\ C=\pi\cdot D \\ C=\pi\cdot12 \\ C=36.7\: in \end{gathered}[/tex]Therefore, 36.7 inches of wood is needed to make the circular bottom of a birdhouse.
What are the degree and leading coefficient of the polynomial?Y^3+8y+12y^5-6
Solution
- The question asks us for the leading coefficient of the following polynomial
[tex]y^3+8y+12y^5-6[/tex]Explanation
Leading Coefficient:
- The Leading Coefficient is defined as the number multiplying the variable with the highest degree or exponent.
- In the case of this question, the variable is "y".
- The y-variable with the highest power is "y⁵", thus, the Leading coefficient is the number multiplying "y⁵". In this case, that number is 12.
- Thus, the Leading Coefficient is 12
Degree of the Polynomial:
- The degree of a polynomial is the highest power of the variable in the polynomial.
- This variable with the highest number is usually multiplying the Leading Coefficient.
- Thus, the Degree of the Polynomial is 5.
Final Answer
- The Leading Coefficient is 12.
- The Degree of the Polynomial is 5.