Answer:
We can use the half-angle formula for sine to find the exact value of sin(a/2) in terms of sin(a):
sin(a/2) = ±√[(1 - cos(a))/2]
where the ± sign depends on the quadrant of a/2.
To use this formula, we first need to find cos(a). We can do this using the identity:
sin^2(a) + cos^2(a) = 1
Substituting sin(a) = 7/9, we get:
(7/9)^2 + cos^2(a) = 1
Simplifying and solving for cos(a), we get:
cos(a) = ±4/9
Since a is in quadrant I, we take the positive value of cos(a):
cos(a) = 4/9
Now we can use the half-angle formula for sine to find sin(a/2):
sin(a/2) = ±√[(1 - cos(a))/2]
Substituting cos(a) = 4/9, we get:
sin(a/2) = ±√[(1 - 4/9)/2]
Simplifying, we get:
sin(a/2) = ±√(5/18)
Since a is in quadrant I, a/2 is also in quadrant I, so we take the positive value of sin(a/2):
sin(a/2) = √(5/18)
Therefore, the exact value of sin(a/2) is √(5/18)
What is the GCF in simplify form
Answer: 9x^2y
the gcf of -63 , 9 and 90 is 9
And the gcf of the variables is x^2 and y
So, 9x^2y
State an equation you could use to find the value of X. Then solve for X
In the circle , the value οf x is 50°.
What is secant line in circle?A secant in geοmetry is a line that tοuches a curve at at least twο different pοints. The Latin wοrd secare, which means tο cut, is where the wοrd secant derives. A secant crοsses a circle at precisely twο pοints when it is a circle. A chοrd is the line segment that the twο pοints determine, i.e., the interval οn the secant whοse ends are the twο pοints.
Remember that a tangent line is οne that crοsses a circle at precisely οne pοint. The term "secant line" describes a line that passes thrοugh twο pοints οn a circle. Secant is a Latin wοrd that means "tο cut," and it is derived frοm secare. A chοrd is the line segment defined by the twο pοints where a secant tοuches a circle in a given space.
Here in the given circle using secant line fοrmula ,
=> 75° = [tex]\frac{1}{2}[/tex] (100°+x)
=> 2×75 = 100+x
=> 150 = 100+x
=> x= 150-100= 50°.
Hence the value of x is 50°.
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I need to know how to solve this problem and the answer of it.
Answer:
P = 8g⁵ - 15g + 14
Step-by-step explanation:
This question has expressions to represent the side lengths of a triangle.
The side lengths are:
-8g⁵ - 7g
10g⁵ - 8g
6g⁵ + 14
They ask for a simplified expression for the perimeter. The purpose of this question is to combine like terms.
P = s₁ + s₂ + s₃ where s is a side length of the triangle.
P = (-8g⁵ - 7g) + (10g⁵ - 8g) + (6g⁵ + 14)
P = 8g⁵ - 15g + 14
Lola hosts a podcast about computers, and Franco hosts a podcast about parenting. Both podcasts have a set duration for each episode. Last year, Lola released 17 episodes and Franco released 43 episodes, for a total of 5,645 minutes of content. This year, Lola released 36 episodes and Franco released 43 episodes, which lasted a total of 6,956 minutes. How long is each episode?
Answer:
Let's denote the duration of each episode of Lola's podcast by "L" and the duration of each episode of Franco's podcast by "F".
From the information given, we can write two equations based on the total duration of content for the two years:
17L + 43F = 5,645 (equation 1)
36L + 43F = 6,956 (equation 2)
To solve for L and F, we can eliminate F by subtracting equation 1 from equation 2:
(36L + 43F) - (17L + 43F) = 6,956 - 5,645
Simplifying, we get:
19L = 1,311
Therefore, the duration of each episode of Lola's podcast (L) is:
L = 1,311 / 19
L ≈ 69.0 minutes
To find the duration of each episode of Franco's podcast (F), we can substitute the value of L into either equation 1 or 2:
17L + 43F = 5,645
17(69.0) + 43F = 5,645
1,173 + 43F = 5,645
43F = 4,472
F = 4,472 / 43
F ≈ 104.0 minutes
Therefore, each episode of Lola's podcast is approximately 69.0 minutes long, and each episode of Franco's podcast is approximately 104.0 minutes long.
HELP ASAP WILL GIVE 100 PTS AND BRAINLYEST FOR CORRECT ANSWER
the answers and questions are all in the attachment box
Answer:
Picture number 1: y=1/2x+2
Picture number 2: y=3x-5
Picture number 3 : y=-x
Picture number 4: y=(x+3)^2-2
A cruise ship weighs 3.83×107 kilograms. A horse weighs 7.1×102 kilograms. Approximately how many horses weigh as much as one cruise ship?
Give your answer in scientific notation using only whole numbers.
5.394366197183099*10^4
Step-by-step explanation:1. Write the number as a decimal 53943.66197183099
2. Make it a new number between 1 and 10
Move the decimal point to make 53943.66197183099 a new number between 1 and 10. Because our number is greater than 10, we move the decimal point to the left. Drop any trailing zeros and place the decimal point after the first non-zero digit. Keep track of how many times we move the decimal point.
53943.66197183099 -> 5.394366197183099
Our new number is 5.394366197183099. We moved the decimal point 4 times.
Use a calculator and get the values from both equations, 3.83×10^7 and 7.1×10^2 then put the first value 38300000 into a calculator, then divide 38300000/710 and you will get the value 53,943.66197183099. Then run that through a scientific notion calculator to get 5.394366197183099*10^4.
There you go.
Approximately 54,000 horses weigh as much as one cruise ship.
Explanation:To find out how many horses weigh as much as one cruise ship, we need to divide the weight of the cruise ship by the weight of a horse. In scientific notation, the weight of the cruise ship is 3.83x107 kg and the weight of a horse is 7.1x102 kg.
Dividing the weight of the cruise ship by the weight of a horse, we get:
(3.83x107 kg) ÷ (7.1x102 kg) = 5.4x104
So approximately 54,000 horses weigh as much as one cruise ship.
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What is the total surface area for the square pyramid below? Responses 144 in2 144 in, 2 288 in2 288 in, 2 352 in2 352 in, 2 208 in2 208 in, 2 (Image)
Answer:
To find the total surface area of the square pyramid, we need to find the area of each of its faces and add them up.
The pyramid has a square base with sides of 8 inches and each triangular face has an isosceles right triangle shape with two sides of 8 inches and a hypotenuse of 2 x 8 = 16 inches (using the Pythagorean theorem).
The total surface area is then:
Area of the square base: 8 x 8 = 64 square inches
Area of each triangular face: 1/2 x 8 x 8 = 32 square inches (since each triangle is isosceles with base and height of 8 inches)
Total surface area: 4 x 32 + 64 = 192 + 64 = 256 square inches
Therefore, the total surface area of the square pyramid is 256 in². So, the closest answer option is 256 in, 2.
change 3 5 to a decimal fraction
Answer:
7/20
its the answer to your question
48805 rounded to the nearest thousand
Answer: 49,000
48805 is greater than 48500, so it rounds to 49,000
In 10-12, use the table.
10. Higher Order Thinking Complete the
table. Show some different ways that a
rectangular prism can have a volume of
12 cubic units.
11. Use Patterns and Structure Look across
each row of the table. What pattern do
you see?
12. Use the table to help. How many unit
cubes are needed to make a model of
a rectangular prism that is 4 units long,
10. The table is mentioned below 11. the product of the number of cubes long and the number of cubes wide is equal to 12. 12. The number of unit cubes needed to make this model is 24.
Describe Cubes?A cube is a three-dimensional geometric shape that has six square faces, 12 edges, and eight vertices (corners). All six faces of a cube are congruent squares, and all edges have the same length. The cube is a regular polyhedron, meaning that it has congruent faces and angles, and its symmetry group is the group of rotations and reflections that preserve the cube's structure. Cubes are widely used in geometry, mathematics, and physics because of their symmetry and regularity, and they also have practical applications in fields such as architecture and engineering.
10. Different ways a rectangular prism can have a volume of 12 cubic units:
Number of Cubes Long Number of Cubes Wide Number of Cubes Tall
1 1 12
2 2 1.5
2 3 1
3 2 2
4 3 1
6 2 1
11. The pattern we see is that for each row, the product of the number of cubes long and the number of cubes wide is equal to 12.
12. A rectangular prism that is 4 units long, 2 units wide, and 1 unit tall would have a volume of 8 cubic units. To make a rectangular prism with a volume of 12 cubic units, we can add another layer of 4 cubes to the top of this prism. Therefore, a rectangular prism that is 4 units long, 2 units wide, and 2 units tall would have a volume of 12 cubic units. The number of unit cubes needed to make this model is 24.
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Un cilindro cuya altura es de 1 pie tiene un volumen de 10 pies". ¿Cuál sería el volumen en pies cúbicos para un cilindro con la misma altura pero tres veces el diámetro?
The volume of the second cylinder is 90 square feet.
How to find the volume of the larger cylinder?Here we know that a cylinder whose height is 1 ft has a volume of 10 ft², remember that the volume for a cylinder of radius R and height H is:
V =pi*R²*H
Where p = 3.14
Then the radius here is:
10 = 3.14*R²*1
√(10/3.14) = R
If we triple the diameter we also triple the radius, then the volume of the other cylinder will be:
V = 3.14*(3*√(10/3.14))²*1
V = 90
The volume is 90 square feet.
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Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 145 subjects with positive test results, there are 21 false positive results; among 156 negative results, there are 4 false negative results. If one of the test subjects is randomly selected, find the probability that the subject tested negative or did not use marijuana. (Hint: Construct a table.)
Question content area bottom
Part 1
The probability that a randomly selected subject tested negative or did not use marijuana is enter your response here.
(Do not round until the final answer. Then round to three decimal places as needed.)
Answer:
The probability that a randomly selected subject tested negative or did not use marijuana is 0.589.
Step-by-step explanation:
Read the story. A group of sixth-grade students volunteered to pick up garbage at Elver Park for Earth Day. To make it more fun, they set up a contest to see whether girls or boys could pick up the most garbage. The girls won, picking up 8 pieces of garbage for every 5 pieces the boys picked up. Pick the diagram that models the ratio in the story.
We may conclude after answering the presented question that This ratio indicates that the guys picked up 5 pieces of rubbish for every 8 pieces of rubbish picked up by the girls.
what is ratio?In mathematics, ratios demonstrate how frequently one number is contained in another. For example, if there are 8 oranges and 6 lemons in a fruit plate, the ratio of oranges to lemons is 8 to 6. In a similar vein, the orange-to-whole-fruit ratio is 8, whereas the lemon-to-orange ratio is 6:8. A ratio is an ordered pair of integers a and b represented as a / b, where b is not zero. A ratio is an equation that equates two ratios. For example, if there is one male and three girls (for every boy she has three daughters), 3/4 are girls and 1/4 are boys.
The ratio in the narrative is represented by the following diagram:
Girls : Boys=8:5
This indicates that the guys picked up 5 pieces of rubbish for every 8 pieces of rubbish picked up by the girls.
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Grace The Brand Jewelry generated the following information from its financial statements:
Earnings after interest and taxes R600 000
Earnings per share R2,50 per share
Shareholder equity R1000 000
Market to book ratio 2,60
What is the company’s market price per share?
Answer:
Step-by-step explanation:
We can use the market-to-book ratio to calculate the company's market price per share.
Market-to-book ratio = Market value per share / Book value per share
Book value per share = Shareholder equity / Number of shares outstanding
We are given the market-to-book ratio as 2.60, and the shareholder equity as R1000 000. We can calculate the book value per share as follows:
Book value per share = R1000 000 / Number of shares outstanding
To calculate the number of shares outstanding, we can use the earnings per share (EPS) formula:
EPS = Earnings / Number of shares outstanding
We are given the earnings per share as R2.50, and the earnings after interest and taxes as R600 000. Substituting these values, we get:
R2.50 = R600 000 / Number of shares outstanding
Solving for Number of shares outstanding:
Number of shares outstanding = R600 000 / R2.50 = 240,000 shares
Now, we can calculate the book value per share:
Book value per share = R1000 000 / 240,000 = R4.17 per share
Finally, we can calculate the market value per share using the market-to-book ratio:
Market-to-book ratio = Market value per share / Book value per share
2.60 = Market value per share / R4.17
Market value per share = 2.60 x R4.17 = R10.83 per share
Therefore, the company's market price per share is R10.83.
HELPPPPP PLEASEEEEEE
18. A business invests $10,000 in an
account that earns 3.2% interest
that is compounded quarterly.
What type of function best
represents the growth of the
investment?
◻ linear
◻ quadratic
◻ exponential
19. What is the value of the account
described in Item 18 after 5 years?
Round to the nearest cent.
Answer: Exponential & $11,709.83
Step-by-step explanation:
The growth of the investment can be represented by an exponential function because the interest is being compounded quarterly, which means that the interest is being added to the account balance and the account balance is growing exponentially over time.
The formula for the future value of an investment with continuous compounding is:
A = P e^(rt)
Where A is the future value, P is the principal investment, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate expressed as a decimal, and t is the time in years.
In this case, the principal investment is $10,000, the annual interest rate is 3.2%, and the interest is compounded quarterly, so the quarterly interest rate is 3.2%/4 = 0.8%. The time period is 5 years, so t = 5.
The formula for the future value of an investment with quarterly compounding is: A = P (1 + r/n)^(nt)
Where n is the number of compounding periods per year, which is 4 in this case.
Substituting the values, we get:A = $10,000 (1 + 0.032/4)^(4*5) = $11,709.83
Therefore, the value of the account after 5 years is $11,709.83 rounded to the nearest cent.
each classroom has 6 rows of 5 desks. how many desks are thre in 45 classrooms?
There are 1,350 desks in 45 classrooms that each have 6 rows of 5 desks.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Each classroom has 6 rows of 5 desks.
So the total number of desks in one classroom.
= 6 rows x 5 desks per row
= 30 desks
To find the total number of desks in 45 classrooms, we can multiply the number of desks in one classroom by the number of classrooms.
= 30 desks per classroom x 45 classrooms
= 1,350 desks
Therefore,
There are 1,350 desks in 45 classrooms that each have 6 rows of 5 desks.
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Write a linear equation in y=mx+b form to represent the scenario.Todd has $450 in his savings. He withdraws $10 per week.
The linear equation in y=mx+b form that represents this scenario is:
y = -10x + 450.
What is a linear equation?
A linear equation is a mathematical equation in which the highest power of the variable(s) is one.
ax + b = 0
or
y = mx + b
where a, b, and m are constants and x and y are variables. In the first form, x is a variable and a and b are constants. In the second form, x and y are variables, m is the slope of the line, and b is the y-intercept.
Let x be the number of weeks that have passed since Todd started withdrawing money from his savings account. Initially, Todd had $450 in his savings, so the amount of money he has left after x weeks is:
450 - 10x
The rate of change of the amount of money Todd has with respect to time is -10, since he is withdrawing $10 per week. Therefore, the slope of the line that represents this situation is -10.
The y-intercept represents the initial amount of money Todd had in his savings, which is $450. Therefore, the linear equation in y=mx+b form that represents this scenario is:
y = -10x + 450
where y is the amount of money Todd has in his savings after x weeks.
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evaluate [(- 5/4) ^ - 2] ^ 3
Answer:
4096/15625 or
0.262144 or
(4/5)^6
the soccer team manager plans to have 2 gallons of water for every 4 players on the team during practice. determine whether the statements about ratios are true or false.
A. The team manager needs 1 gallon of water for every 1 player
` true or false
B. The ratio of number of players to gallons of water is 2:1
` true or false
C. The team manager ould need 4 gallons of water for 10 players
` true or false
D. For 30 players, the team manager would need 15 gallons of water ` true or false
Answer:
A.=False
B.=True
C.=False
D.=True
Step-by-step explanation:
The original ration is 2 gallons of water for 4 players.
Each player requires 1/2 gallon of water.
To get the amount of water needed multiply 1/2 by the amount of players.
1*(1/2) does not equal 1
2*(1/2) equals 1
10*(1/2) does not equal 4
30*(1/2) equals 15
Y=3x^2-4x-1 what is the sign of leading coefficient
Answer:The leading term in a polynomial is the term with the highest degree.
Step-by-step explanation:
Step-by-step explanation:
y = 3 x^2 - 4 x - 1
leading coefficient is 3 and its sign is ' + ' or positive
If sin a = -1/4 and π < a <3pi/2 and cos b= 5/9 and 0 < b < pi/2, find the exact value of the following. Show all your work and simplify your answers.
sin(a + B) =
Answer:
Step-by-step explanation:
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Answer:
There is 5% of the juice left.
Step-by-step explanation:
We know that originally, the container had 80 oz of orange juice, this is 100% in our case.
Then we can write a relation:
80 oz = 100%
Now there are 4 ounces left, in the same way as before, we can write this as:
4 oz = X%
We want to find X%
First, let's write our equations:
4 oz = X%
80 oz = 100%
We can take the quotient between these two equations to get:
(4oz/80oz) = (X%/100%)
We need to solve this for X%, then we get:
(4oz/80oz)*100% = X% = 5%
This means that 4 oz is 5% of the initial volume of the juice container.
Then we can conclude that there is 5% of the juice left.
Please HELP DUE IN AN HOUR
Answer:
It is not true (equal sign with a slash in it) one side’s 23 and the other side is 20
Please help me w my trig
Answer:
Assuming that the expression is asking for the tangent of 1 radian, we can use the tangent half-angle formula to find an exact value:
tan(1) = 2tan(1/2) / (1 - tan^2(1/2))
To find tan(1/2), we can use the half-angle formula for tangent:
tan(1/2) = sin(1) / (1 + cos(1))
We cannot simplify this expression any further without a calculator. Therefore, the exact value of tan(1) is:
tan(1) = 2sin(1) / (cos(1) - cos^2(1) + 1)
Again, we cannot simplify this expression any further without a calculator.
For the second expression, we are asked to find the value of:
tan(arctan(6/4))
By definition, tan(arctan(x)) = x for all x, so we have:
tan(arctan(6/4)) = 6/4 = 3/2
Therefore, the exact value of the expression tan(6/4) is 3/2.
Investing $1,000 at a 5% annual interest rate for 6 years, compounded every two months,
yields $1,348.18. Without doing any calculations, rank these four possible changes in order
of the increase in the interest they would yield from the greatest increase to the least
increase:
• Increase the starting amount by $100.
• Increase the interest rate by 1%.
• Let the account increase for one more year.
• Compound the interest every month instead of every two months.
Once you have made your predictions, calculate the value of each option to see if your
ranking was correct.
Answer:
Step-by-step explanation:
Ranking:
Compound the interest every month instead of every two months.
Increase the interest rate by 1%.
Let the account increase for one more year.
Increase the starting amount by $100.
Calculations:
If the interest is compounded monthly instead of every two months, the final value would be $1,357.36, which is an increase of $9.18 compared to the original value.
If the interest rate is increased to 6%, the final value would be $1,411.58, which is an increase of $63.40 compared to the original value.
If the account increases for one more year at the same interest rate, the final value would be $1,435.09, which is an increase of $86.91 compared to the original value.
If the starting amount is increased by $100, the final value would be $1,421.61, which is an increase of $73.43 compared to the original value.
Make calculations for a 5-year loan of $20,000 with an annual interest rate of 6% compounded monthly. Calculate the balance owed if the loan had to be paid in full at the end of the 5-year period, and no monthly payments were required.
Answer: $28,383.68.
Step-by-step explanation:
The first step is to determine the number of monthly payments over the 5-year period, which is 5 years x 12 months/year = 60 months.
Next, we can use the formula for the future value of an annuity, which is:
FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)
where:
FV is the future value of the loan (the amount owed at the end of the 5-year period)
P is the initial principal amount ($20,000 in this case)
r is the annual interest rate (6%)
n is the number of compounding periods per year (12 for monthly compounding)
t is the total number of years (5)
Plugging in these values, we get:
FV = $20,000 * ((1 + 0.06/12)^(12*5) - 1) / (0.06/12)
FV = $28,383.68
Therefore, the balance owed at the end of the 5-year period would be $28,383.68.
Write down the equations of the asymptotes of the functions below g() = 3tan (2x) where x = [-90°; 90°]
The equatiοns οf the asymptοtes fοr g(x) = 3tan(2x) x = -π/8, π/8, 3π/8, 5π/8, and 7π/8.
What are asymptοtes?The asymptοte is a line οr curve that a functiοn apprοaches but never crοsses as the independent variable gets clοser tο a specific number οr infinity. A line οr curve that the graph οf a functiοn apprοaches steadily but never meets is referred tο as an asymptοte.
The fοllοwing is the expressiοn fοr the vertical asymptοtes οf the functiοn g(x) = 3tan(2x):
x = (2n + 1)π/4
where n is an integer.
This is because the tangent function approaches infinite when 2x is an odd multiple of [tex]\pi[/tex]/2,
The tangent function, on the other hand, has vertical asymptotes at odd multiples of [tex]\pi[/tex]/2.
So the vertical asymptotes of g(x) in the range of x = [-90°; 90°] are:
x = -π/8, π/8, 3π/8, 5π/8, and 7π/8.
Examining the behavior of the tangent function as x approaches positive or negative infinity can reveal the horizontal asymptotes of the function g(x) = 3tan(2x).
As x approaches odd multiples of /2, the tangent function oscillates between positive and negative infinity, so no horizontal asymptotes exist.
As a result, in the given range, the formulae for the vertical asymptotes of the function g(x) = 3tan(2x) are:
x = -π/8, π/8, 3π/8, 5π/8, and 7π/8.
Therefore, no horizontal asymptotes exist.
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K
The principal P is borrowed and the loan's future value A at time t is given. Determine the loan's simple interest rater.
P = $7000.00, A = $7280.00, t = 1 year
The loan's simple interest rate is 4%.
What is simple interest ?
Simple interest can be defined as a technique used to calculate the proportion of interest paid on a sum over a set time period at a set rate.
To determine the loan's simple interest rate, we can use the simple interest formula:
A = P(1 + rt)
Where
A is the future valueP is the principal r is the interest rate t is the time periodWe can rearrange this formula to solve for the interest rate r:
r = (A/P - 1) / t
Plugging in the given values, we get:
r = ($7280.00/$7000.00 - 1) / 1
r = 0.04 or 4%
Therefore, the loan's simple interest rate is 4%.
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Trevor used about half of a 5-lb bag of potatoes (2 lb 6 oz). How much did the remaining potatoes weigh?
Answer:
Step-by-step explanation:
f Trevor used 2 lb 6 oz of a 5-lb bag of potatoes, then the weight of the remaining potatoes is:
5 lb = 80 oz (since 1 lb = 16 oz)
Remaining potatoes = Total potatoes - Used potatoes
Remaining potatoes = 80 oz - 2 lb 6 oz
Remaining potatoes = 80 oz - (2 × 16 oz + 6 oz)
Remaining potatoes = 80 oz - 38 oz
Remaining potatoes = 42 oz
Therefore, the remaining potatoes weighed 2 lb 10 oz (or 42 oz).
Show your work.
Are the expressions (4c + 8) + 3c - 2 and 4c + 2(0.5c + 1) equivalent?
First, let's simplify the expression (4c + 8) + 3c - 2:
(4c + 8) + 3c - 2
= 4c + 3c + 8 - 2 (rearrange terms)
= 7c + 6 (combine like terms)
So the first expression simplifies to 7c + 6.
Next, let's simplify the expression 4c + 2(0.5c + 1):
4c + 2(0.5c + 1)
= 4c + 2(0.5c) + 2(1) (distribute the 2)
= 4c + c + 2 (simplify the parenthesis)
= 5c + 2 (combine like terms)
So the second expression simplifies to 5c + 2.
Now we can compare the two expressions:
7c + 6 vs. 5c + 2
These expressions are not equivalent because they do not have the same coefficients or constants.