Question:
Write a linear function f with f (- 1/2) = 1 and f (0) = -4
The linear function f with f (- 1/2) = 1 and f (0) = -4 would be ; y = -5x -4.
What is a linear equation?
A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form
y = mx + c
Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.
We are asked to write the linear function f with f (- 1/2) = 1 and f (0) = -4
Let the equation in variables x and y can be written in the form y = mx + c
So f (- 1/2) = 1
this gives, 1 = -1/2m+c -----------eq 1
Also f (0) = -4
This gives -4 = c. --------------eq2
Now Putting the value of c in the equation in eq1 we get m=0.
So 1 = -1/2m+c
1 = -1/2m - 4
m = -5
Then we get;
y = -5x -4.
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If x is 60% of y and y is 30% of z, x is what percent of z?
Answer:
18%
Step-by-step explanation:
x is 60% of y[tex]x = y*\frac{60}{100} =y*0.6=0.6y\\x=0.6y[/tex]
y is 30% of z[tex]y = z*\frac{30}{100} =z*0.3=0.3z\\y=0.3z[/tex]
x is what percent of z?
Since x = 0.6y and y = 0.3z:
[tex]\%=\frac{x}{z} *100\\\\\%=\frac{0.6y}{z}*100\\ \\\%=\frac{0.6(0.3z)}{z} *100\\\\\%=\frac{0.18z}{z} *100\\\\\%=0.18*100\\\\\%=18[/tex]
Special right triangles
In the special right triangle, x has a value of √3/2
Special Right TriangleA special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called an "angle-based" right triangle.
To find the value of x, we should take into consideration that two of the sides of the triangle are equal to each other.
Using Pythagoras theorem;
[tex](\sqrt{3}) ^2 = x^2 + x^2\\3 = 2x^2\\x^2 = \frac{3}{2} \\x = \sqrt{\frac{3}{2} }[/tex]
The value of x in the triangle is √3/2
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Find a polynomial function with real coefficients that has the given zeros
-1, 8,3 - 21,
A polynomial function with real coefficients that has the given zeros -1, 8, 3, -21 is x^4−11x^3−197x^2−297x+504.
In the given question we have to find a polynomial function with real coefficient that has the given zeros -1, 8,3, -21.
The given zeros are -1, 8,3 - 21.
Let the variable is x.
So the factor from the given zeros are
(x-1), (x+8), (x+3), (x-21)
To find the polynomial we multiply the factors to each other.
=(x-1)(x+8)(x+3)(x-21)
We firstly multiply the factor with the pair of two using the distributive property.
={x(x-1)+8(x-1)}{x(x+3)-21(x+3)}
=(x^2-x+8x-8)(x^2+3x-21x+63)
Simplifying
=(x^2+7x-8)(x^2-18x+63)
=x^2(x^2+7x-8)-18x(x^2+7x-8)+63(x^2+7x-8)
=(x^4+7x^3-8x^2)-(18x^3+126x^2-144x)+(63x^2+441x-504)
=x^4+7x^3-8x^2-18x^3-126x^2+144x+63x^2+441x-504
=x^4−11x^3−197x^2−297x+504
Hence, a polynomial function with real coefficients that has the given zeros -1, 8, 3, -21 is x^4−11x^3−197x^2−297x+504.
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The surface area of this cylinder is 6,732.16 square feet. What is the height? Use 3.14 and round your answer to the nearest hundredth 16 ft=radius h feet
The height of the cylinder whose surface area and radius are as given in the task content is; 67 ft.
What is the surface area of the cylinder?It follows from the task content that the height of the cylinder as described by the surface area and radius above be determined.
On this note, recall that the surface area of a cylinder is given by the formula;
Surface area = 2πrh
Therefore;
6732.16 = 2 × 3.14 × 16 × h
h = 6732.16/100.48
h = 67.
Consequently, the height of the cylinder which is as described is; 67 ft.
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There are two more quarters than dimes and as many nickles as quarters and dimes together. The total amount of money is 3.75. How many quarters, dimes and nickles are there?
Answer: 9 quarters, 7 dimes, & 16 nickels
Step-by-step explanation:
We set number of dimes as d:
Number of quarters: d + 2Number of nickels: d + 2 + d = 2d + 2So, set up the equation to solve:
[tex]0.10d+0.25(d+2)+0.05(2d+2)=3.75\\\\0.10d+0.25d+0.5+0.1d+0.1=3.75\\\\0.45d=3.75-0.5-0.1=3.15\\\\d=7[/tex]
So now that we know there're seven dimes, we can plug them in our initial equations to find the number of quarters and nickels:
Number of quarters: d + 2 = 7 + 2 = 9Number of nickels: d + 2 + d = 2d + 2 = 2(7) + 2 = 16Lourdes is reading a biography for her history class. She reads 30 pages each day. After 9 days, Lourdes has read (3)/(5) of the biography. Write a linear equation to represent the number of pages Lourdes still has to read after x days.
The linear equation is z = 450 - 30 x, where z is the number of pages Lourdes has left to read after x days
We need to write a linear equation to represent the number of pages
Lourdes has left the number of pages to read after x days
Lourdes reads 30 pages each day
Lourdes will read for x days
The number of pages Lourdes will read in x day = 30 x
The left pages will be the difference between the total pages of the
book and the pages Lourdes read.
After 9 days Lourdes completes 3/5 of the total number of pages.
So the number of pages Lourdes reads after 9 days = 30×9 = 270 pages.
Let The total number of pages in the book = y
Therefore 3/5 × y = 270.
So y = 270 × (5/3) = 450 pages.
The total number of pages in the book = 450 pages.
Lourdes will read 30 x in x days
The number of pages left = 450 - 30 x
Assume that z represents the number of pages Lourdes has left to read after x days
z = 450 - 30 x
The linear equation is z = 450 - 30 x, where z is the number of pages Lourdes has left to read after x days
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Shivani won the raffle at the zoo and gets to feed the dolphins! The dolphin trainer gives
Shivani a bucket of fish to divide evenly among 3 dolphins. Each dolphin gets 6 fish.
Which equation can you use to find the number of fish f in the bucket before Shivani feeds
the dolphins?
Pls help ASAP
Answer:
Step-by-step explanation:
f/4 = 3
A & B = (A + B) x A + (A - B) divided by B. find the value of 4 & - 2.
Answer:
-7
Step-by-step explanation:
A= 4
B= -2
((4-2) × 4 + (4+2))/-2
14/-2
-7
100 PONTS FOR ANSWERING 5-6 Q'S THANK YOU
11. Tell whether the sequence is arithmetic. If it is, what is the common difference?
19, 11, 3, negative 5 (1 point)
No
Yes; one-eighth
Yes; 8
Yes; negative 8
12. Grass seeds grow rapidly. A grass seed has grown to a 12 millimeter tall blade of grass. Tomorrow it will be 23 millimeters tall, the next day it will be 34 millimeters tall, and on the next day it will be 45 millimeters tall. Write a rule to represent the height of the blade of grass as an arithmetic sequence. How tall will the blade of grass be in 15 days? (1 point)
A(n) = 16 + (n – 1)11; 194 millimeters
A(n) = 12 + (n – 1)11; 166 millimeters
A(n) = 13n; 195 millimeters
A(n) = 12n; 180 millimeters
13. A magician charges $50.00 for a visit and an additional $7.50 for each hour he performs. The function rule C = 7.50h + 50.00 describes the relationship between the number of hours h and the total cost of the visit C. If the magician will only visit a maximum of 8 hours, what is a reasonable graph of the function rule? (1 point)
14. What is the graph of the function rule?
y = |3x| – 1 (1 point)
Answer:
Step-by-step explanation:
11 = D. Yes ; -8
12 = A(n) = 12+ (n-1) 11 ;166 milliliters
13 = The first plot graphed is located nearest 50 to resemble the initial charge.
The last plot graphed should be located at the top of the graph vertical to 8 - the maximum hours he'll work.
Therefore, the answer is C.
14 = you have to select x-values and plug them into the equation. Once you plug those values into the equation, you will get a y-value. Your x-values and your y-values make up your coordinates for a single point
Suppose conditional p→ q is true and conditional q→ r is false. Must the conditional p →r also be false? Explain.
Answer:
no
Step-by-step explanation:
the conditional p-> r is the basically both of the beginning 2 conditionals combined
3/8 x 4/3 please help me I’ve been stuck at this
Answer:
1/2
Step-by-step explanation:
Answer:
1/2
Step-by-step explanation:
3/8*4/3
The 3 can be cancel out
you can also cancel out 8 and 4
leaving you with 1/2
Darnelle has a $10,000, three-year loan with an APR of 5%. She uses the table below to compute information on the loan.
a. What is her monthly payment?
b. What is the total of all her monthly payments?
c. What is the total finance charge?
Between 10 P.M. and 7:54 A.M., the water level in a swimming pool decreased by 11/40 . Assuming that the water level decreased at a constant rate, how much did the water level drop each hour?
Answer:
It approximately dropped 0.027777 per hour.
Step-by-step explanation:
First, we calculate the decrease.
Decrease = 11/40 = 0.275
Then, we calculate the time interval.
From 10 pm to 7:54 hours will be 9.54 hours
Time interval= (9 + 54/60) hours
Time interval=9.9 hours
Finally, we calculate how much it dropped each hour
0.275/9.9 ≈ 0.027777
So it approximately dropped 0.027777 per hour.
Answer:
7:54 A.M to 10 P.M is = 14 hrs and 6 mins
60 mins = 1 hour
therefore 6 mins = 0.1 hour
14 hrs plus 0.1 hrs = 14.1 hours
if 14.1 hrs = 11/40
1 HR = x
cross multiply
14.1x = 11/40
divide both sides by 14.1
14.1x / 14.1 = 11/40 / 14.1
X = 11/564 or 0.0195 times every hourQUICK!! EMERGENCY!! PLEASE HELP ME!!
As shown in the graph, Jane has a car payment of $200 a month. Her loan amount is $3,000. Assume there is no interest.
A. What is the slope of the line?
What does this slope in this situation mean?
B. What is the y-intercept of the line?
What does the y-intercept mean in this situation?
C. How many months will it take Jane to pay off the loan?
Show your work.
Answer:
A ) What is the slope of the line? What does this slope in this situation mean?
The equation of the line is y = -200x +3000 so the slope of the line would be -200x.
This means that as x ( Month ) increases, y ( Loan ) decreases.
B ) What is the y-intercept of the line? What does the y-intercept mean in this situation?
As stated above the equation of the line is y = -200x +3000 so the y-intercept would be +3000.
In this case the y-intercept represents the cost of the loan before Jane's first payment.
C ) How many months will it take Jane to pay off the loan? Show your work.
It will take 15 months to pay off Jane's car loan.
On the graph we can see when x ( month ) equals fifteen, y ( loan ) equals zero. This means that it will take fifteen months for Jane to pay off the loan.
We can check this by putting it into our equation...
y = -200( 15 ) +3000 = 0
Hope this helps! :)
Lucy owes three of her friends 5.60 each how much money does Lucy owe in total
Answer:
16.80
Step-by-step explanation:
The ratio is 1:5.60. Where 1 is the amount of friends and 5.60 is the amount owed. Since there are 3 friends, multiply 5.60 by 3.
Answer: 16.8
Step-by-step explanation: basically multiply 5.60 by 3 (5.60 x 3 = 16.8) or add 5.60 3 times (5.60 + 5.60 + 5.60 = 16.8)
X Use FOIL to solve (x+2)(x+1): Write x squared as x2
x2+3x+2
x+2x+2
Ox-2x-2
0/2
X
After using FOIL, the final answer will be
x2 + 3x + 2
What is the FOIL method?
The typical way of multiplying two binomials is known as the FOIL method since FOIL is a shorthand for it. The acronym FOIL stands for the following four terms that describe the item: (Each binomial "initial" term is multiplied together.) The FOIL method is a memory aid for the procedures involved in multiplying two binomials. The result of multiplying the first term, outer term, inner term, and last term is the product of two binomials: (a+b)(c+d)=ac+ad+bc+bd.
Solution explained:
A/Q we have
(x+2)(x-1)
= x * x + x + 2x + 2 (After expanding and applying distributive property)
= x2 + x + 2x + 2
= x2 + 3x + 2
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5.03 exam Solve three and two fifths plus three and four sixths
Answer:
seven and two thirtieths
Step-by-step explanation:
3 2/5 + 3 4/6 find an equal value between 5 and 6
3 12/30 + 3 20/30
12+20=32
32/30=1 2/30
3+3+1=7
7 2/30
The mean of a normal distribution is 400 kilos. The standard deviation is 10 kilos. What is the probability of a weight between 420 kilos and the mean of 400
kilos?
****
0.1932
O 0.4772
0.4332
O0.5000
Second option is correct 0.04772.
The probability of a weight between 420 kilos and the mean of 400
kilos = 0.4772
Mean of a normal probability distribution is μ = 400 kilos
And standard deviation σ = 10 kilos
Let x be the variable in kilos.
X is between 400 kilos and 420 kilos
P( 400 < X < 420 ) = P ( 400 - μ < X - μ < 420 - μ)
= P ( (400-μ)/σ < (X-μ)/σ < (420-μ)/σ )
= P ( (400 - 400) /10 < Z < (420 - 400)/10 )
= P ( 0 < Z < 2 )
= 0.4777 from the table appendix B1.
The link for the appendix table B1 :
www.webassign.net%2Faswsbe13%2Fappendix-b.pdf&usg=AOvVaw3QlkaDTdGZ1Z01YZPYCL6h
The probability of a weight between 420 kilos and the mean of 400
kilos = 0.4772
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Find the value of x.
The value of x on the given sides of the rectangles is 4.
What are the area and perimeter of a rectangle?The area of a rectangle is the product of its length and width.
The perimeter of a rectangle is the sum of the lengths of all the sides.
Given, The area of the shaded region is 39.
As the smaller rectangle is inside the whole larger rectangle,
∴The area of the smaller rectangle subtracted from the area of the whole larger rectangle is the area of the shaded region.
So, (2x - 1)(x + 3) - (x - 2)(x + 1) = 39.
2x² + 6x - x - 3 - x² - x + 2x + 2 = 39.
x² + 6x - 1 = 39.
x² + 6x - 40 = 0.
x² + 10x - 4x - 40 = 0.
x(x + 10) - 4(x + `10) = 0.
(x + 10)(x - 4) = 0.
(x + 10) = 0 Or (x - 4) = 0.
x = - 10 Or x = 4.
Now if we put x = - 10 the lengths will be negative which is inappropriate.
So, the value of x that satisfies is 4.
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In 2015, sarah spent $800 buying lunches. In 2017, she spent $550 buying lunches. What was the rate of change from 2015 to 2017?.
As per the Sarah buying pattern, the rate of change from 2015 to 2017 is $250
Rate of change
Rate of change refers the speed at which a variable changes over a specific period of time.
Given,
In 2015, sarah spent $800 buying lunches. In 2017, she spent $550 buying lunches.
Here we need to find the rate of change from 2015 to 2017.
While we looking into the given question, we have identified that,
Buying lunch cost for 2015 = $800
Buying lunch cost for 2017 = $550
Now, the rate of change from 2015 to 2017 is calculated by finding the difference between them,
So, rate of change is,
=> 800 - 550
=> 250
Therefore, the rate of change from 2015 to 2017 is $250
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Finding Angle Measures When Parallel Lines Are Cut By a Transversal
Answer:
Since angle 8 is 95 degrees, we will have to either subtract or use the rules to solve this!
Lets find angle 1 first!
Since opposite angles are the same, angle 1 will be 95 degrees!
Angle 2 will wave subtracting used to find it!
180 - 95 = 85
Angle 2: 85 degrees
Angle 3 is the same as angle 2 so 85 degrees!
Angle 4 is the same as angle 8 and 1 so 95 degrees!
Angle 5 is the same as 8, 4, and 1 so 95 degrees!
Angle 6 is the same as angle 3 and 2 degrees!
Angle 7 will be 85 by subtraction!
Angle 8 is given and it is 95!
Have an amazing day!!
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Q5.
Heres a formula
r = √(w² − h² )
Work out the value of r when w=9√2 and h=5root6.
Give your answer in the form
a√b
where a and b are integers greater than 1.
Answer:
r = 2[tex]\sqrt{3}[/tex]
Step-by-step explanation:
using the rules of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
([tex]\sqrt{x}[/tex] )² = x
substitute the given values of w and h into the equation
r = [tex]\sqrt{w^2-h^2}[/tex]
= [tex]\sqrt{(9\sqrt{2})^2-(5\sqrt{6})^2 }[/tex]
= [tex]\sqrt{162-150}[/tex]
= [tex]\sqrt{12}[/tex]
= [tex]\sqrt{4(3)}[/tex]
= [tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex]
= 2[tex]\sqrt{3}[/tex]
a fair 6-sided die is repeatedly rolled until an odd number appears. what is the probability that every even number appears at least once before the first occurrence of an odd number?
The probability that every even number appears at least once before the first occurrence of an odd number is [tex]\frac{1}{20}[/tex]
Take [tex]A_{k}[/tex] - the event that odd number appeared on the k-th throw, B - every even number appeared at least once.
Let’s find P(B|[tex]A_{k}[/tex]) . Note that this probability is 0 for k∈{1,2,3} as you need k≥4 to place all distinct even numbers before the odd one.
Now for k≥4 we need to use the formula of inclusions and exclusions: P(B¯|[tex]A_{k}[/tex])=P(C2+C4+C6|[tex]A_{k}[/tex])=
=P(C2|[tex]A_{k}[/tex])+P(C4|[tex]A_{k}[/tex])+P(C6|[tex]A_{k}[/tex])−P(C2C4|[tex]A_{k}[/tex])−P(C2C6|[tex]A_{k}[/tex])−P(C4C6|[tex]A_{k}[/tex]) where Ci is the event that the dice i is missing.
These probabilities are:
P(Ci/[tex]A_{k}[/tex])=[tex](\frac{2}{3} )^{k-1}[/tex]
P(CiCj|[tex]A_{k}[/tex])=[tex](\frac{1}{3} )^{k-1}[/tex]
So
P(B|[tex]A_{k}[/tex])=1–P(B¯|[tex]A_{k}[/tex])=1−3⋅[tex](\frac{2}{3} )^{k-1}[/tex]+3[tex](\frac{2}{3} )^{k-1}[/tex].= 1 − [tex]\frac{9}{2}[/tex].[tex](\frac{2}{3} )^{k}[/tex]+9[tex](\frac{1}{3} )^{k}[/tex]
Now as P([tex]A_{k}[/tex])= [tex]\frac{1}{2^{k} }[/tex]we conclude that
P(B) = ∞∑k=4P(B/[tex]A_{k}[/tex])P([tex]A_{k}[/tex])= ∞∑k=4([tex](\frac{1}{2} )^{k}[/tex]−[tex]\frac{9}{2}[/tex][tex](\frac{1}{3} )^{k}[/tex]+9.[tex](\frac{1}{6} )^{k}[/tex])=
=[tex]\frac{\frac{1}{16} }{\frac{1}{2} }[/tex]−[tex]\frac{\frac{1}{18} }{\frac{2}{3} }[/tex]+[tex]\frac{\frac{1}{144} }{\frac{5}{6} }[/tex] = [tex]\frac{1}{8}[/tex] -[tex]\frac{1}{12}[/tex] + [tex]\frac{1}{120}[/tex] =[tex]\frac{6}{120}[/tex] = [tex]\frac{1}{20}[/tex]
the probability that every even number appears at least once before the first occurrence of an odd number is [tex]\frac{1}{20}[/tex]
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A group of friends wants to go to the amusement park. They have $89.50 to spend on parking and admission. Parking is $7.75, and tickets cost $27.25 per person, including tax. Write and solve an equation which can be used to determine p, the number of people who can go to the amusement park.
I had trusted a VERIFIED answer and got it wrong, so for everyone in the future, here is the correct answer.
Answers:
Equation: 27.25p + 7.75 = 89.5
Answer: p = 3
The equation which can be used to determine p is 7.75 + 27.25p = 89.50, then the number of people who can go to the amusement park is 3
The total amount that they have to spend on parking and admission = $89.50
The parking cost = $7.75
The ticket cost including tax = $27.25
Consider the number of people who can go to amusement park as p
Then the equation will be
7.75 + 27.25p = 89.50
Subtract both side of the equation by 7.75
27.25p + 7.75 - 7.75 = 89.50 - 7.75
27.25p = 81.75
Divide both side of the equation by 27.25
27.25p / 27.25 = 81.75 / 27.25
p = 3
Hence, the equation which can be used to determine p is 7.75 + 27.25p = 89.50, then the number of people who can go to the amusement park is 3
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Solve the equation: 12x+18=16x
Answer:
Step-by-step explanation:
answer is: x=9/2
marley's bank charges a $3 service fee each time money is whithdrawn from another bank's atm. Marley is traveling and must withdraw money from another bank's atm 4 times. Which expressions model the charge in the balance of her account due to service fees?
The expressions represent the service fee charge on her account balance is 4x+3.
Given that,
Every time money is withdrawn from an ATM run by a different bank, Marley's Bank levies a $3 service fee. Marley needs to make four ATM withdrawals from a different bank while she is abroad.
We have to find which expressions represent the service fee charge on her account balance.
The expression we can write as,
4x+3
Because 4 times he has taken from ATM money and adding the service fee $3.
Therefore, The expressions represent the service fee charge on her account balance is 4x+3.
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Choose the expression that is equivalent to 1/5 x 3
Answer:
0.2
Step-by-step explanation:
1/5 is equvalent with 10/5=0.2
I need help please please
In the given triangle LMN, measure of side LM = 18in. and measure of angle MLN is 28° then the measure of side LN = 18in. , m ∠M = 76° and
m ∠N = 76°.
As given in the question,
In the given triangle LMN,
Measure of side LM = 18in.
Measure of angle MLN is equal to 28°
It is given that side LM ≅ LN
LM = 18 in.
LN = 18in.
In a triangle LMN ,
In a triangle opposite sides are congruent to each other then angle opposite to them also congruent to each other.
LM ≅LN
⇒m ∠N = m ∠M
In a ΔLMN,
Let x° be the measure of angle M and N each.
m ∠M + m ∠N + m ∠L = 180°
⇒ x° + x° + 28° = 180°
⇒ 2x° = 180° -28°
⇒2x° = 152°
⇒ x = 76°
Therefore, in the given triangle LMN, measure of side LM = 18in. and measure of angle MLN is 28° then the measure of side LN = 18in. , m ∠M = 76° and m ∠N = 76°.
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what is
S+2c=47
5s+8c=201
s=?
c=?
step by step answer
The values of the variables s and c are 13 and 17, respectively.
We are given a system of two equations. The equations are linear in nature. Each equation represents a straight line. We need to find the solution to the system of linear equations. The coordinates of the intersection point of the straight lines are the solution. The equations are given below.
s + 2c = 47
5s + 8c = 201
We will substitute the value of s from the first equation into the second equation.
s = 47 - 2c
5s + 8c = 201
5(47 - 2c) + 8c = 201
235 - 10c + 8c = 201
235 - 2c = 201
2c = 235 - 201
2c = 34
c = 17
We will substitute the value of c into the first equation to find the value of s.
s = 47 -2c
s = 47 - 2(17)
s = 47 - 34
s = 13
Hence, the values of s and c are 13 and 17, respectively.
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Determine whether the expression is a monomial. 1/2(c^3)(d^6)
A. Monomial
B. Not a monomial
Answer:
not a monomial
Step-by-step explanation:
monomial
Prefix mono- means 1 so, monomial means one term
This has more than one term so it’s not a monomial
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