Answer:
y = 36
Step-by-step explanation:
given y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the condition when x = 5 , y = 15
15 = 5k ( divide both sides by 5 )
3 = k
y = 3x ← equation of variation
when x = 12 , then
y = 3 × 12 = 36
Four identical cubes are joined to make a new shape.
What is the new shape's surface area?
PRL
The PTO is selling raffle tickets to raise money for classroom supplies. A raffle ticket costs $3. There is 1 winning ticket out of the 300 tickets sold. The winner gets a prize worth $76. Round your answers to the nearest cent.
What is the expected value (to you) of one raffle ticket? $
Calculate the expected value (to you) if you purchase 12 raffle tickets.
What is the expected value (to the PTO) of one raffle ticket? $
If the PTO sells all 300 raffle tickets, how much money will they raise for the classroom supplies?
The expected value (to you) of one raffle ticket is -$2.737.
The expected value (to you) if you purchase 12 raffle tickets is -$32.84.
The expected value (to the PTO) of one raffle ticket is $2.737.
Amount of money raised if 300 tickets are sold is $821.1.
Cost of a ticket = $3
P(winning a ticket) = 1/300
Winning amount = $76
Prize value = 1/300 × $76 = $0.253
Expected value (to you) for 1 ticket = $0.253 + (299/300 × -$3) = -$2.737
Expected value (to you) if you purchase 12 tickets = 12 × -$2.737
= -$32.84
Expected value (to the PTO) of raffle ticket = -$0.253 + (299/300 × $3)
= $2.737
If they sell 300 tickets,
Expected value = 300 × $2.737 = $821.1
Amount raised = $821.1
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Which of the following is not a Pythagorean triple?
A. (6, 8, 10)
B. (9, 12, 15)
C. (7, 24, 25)
D. (4, 5, 6)
Answer:
D. 4, 5, 6, then
H² = P² + B²
6² = 5² + 4²
36 = 25 + 16
36 ≠ 41
This is not Pythagorean triple.
Statistics question
Considering the given information, we fail to reject the null hypothesis that the proportion of men who own cats is less than or equal to 23% at the 0.10 significance level.
How did we arrive at this assertion?The null and alternative hypotheses are as follows:
H o: p ≤ 0.23 (proportion of men who own cats is less than or equal to 23%)
H a: p > 0.23 (proportion of men who own cats is larger than 23%)
The test is right-tailed because the alternative hypothesis states that the proportion is larger than 23%.
Based on a sample of 40 people, with 15% of them owning cats, we can calculate the p-value.
To find the p-value, we need to use the binomial distribution and calculate the probability of observing a result as extreme or more extreme than the one obtained under the null hypothesis.
Let's calculate the p-value:
p = 0.15 (proportion of men in the sample who own cats)
n = 40 (sample size)
p-value = P(X ≥ 0.15 x 40) = P(X ≥ 6)
Using a binomial calculator or software, we can find that P(X ≥ 6) is approximately 0.162.
Since the p-value (0.162) is greater than the significance level of 0.10, we fail to reject the null hypothesis.
Therefore, based on the given information, we fail to reject the null hypothesis that the proportion of men who own cats is less than or equal to 23% at the 0.10 significance level.
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For each equation, choose the statement that describes its solution.
If applicable, give the solution.
-4 (u + 1) + 6u = 2(u + 2) - 8
No solution
O "=0
O All real numbers are solutions
2(y-1) + 4y= 3(y-1) + 7
No solution
O y = 0
O All real numbers are solutions
Answer:
1,-4(u+1)+6u=2(u+2)-8
Step-by-step explanation:
=-4u-4+6u=2u+4-8
=2u-4=2u-4
=2u-2u=-4+4
=0=0
2,2(y-1)+4y=3(y-1)+7
=2y-2+4y=3y-3+7
=6y-2=3y+4
=6y-3y=4+2
=3y/3=6/3=y=2
: all real numbers are solutions
Using the following information, find the sum of the given arithmetic series.
a1= 16, d = -9, n = 18
Answer:
Sn = n÷2[2a+(n-1)d]
=18÷2[2(16)+(18-1)(-9)]
Sn=-1089
Step-by-step explanation:
First write out the formula for sum in arithmetic series
Then substitute the given information
Then punch everything as it is together with the signs to get the answer
formula for percentage of growth
Answer:
How to calculate growth rate percentage?
To calculate the percentage growth rate, use the basic growth rate formula:
Subtract the original from the new value and divide the results by the original value. To turn that into a percent increase, multiply the results by 100.
división of decimals using the number problem
1. The demand of calculators when its price per unit is Rs 1200,is Rs 4000. When the price increases to Rs 1500, only 3000 calculators are demanded. a.Find the demand equation in the form of p = f(Q)
b.Obtain the number of calculations demanded when the price per unit calculators is Rs 1650
c. If 4500 calculations are demanded, what should be the price per unit of calculator?
a) the demand equation in the form of p = f(Q) is p = -10/3Q + 14533.33
b) when the price per unit of calculators is Rs 1650, approximately 3865 calculators are demanded.
c) when 4500 calculators are demanded, the price per unit should be approximately Rs 3010.
To find the demand equation in the form of p = f(Q), we need to determine the relationship between the price per unit (p) and the quantity demanded (Q) based on the given information.
Let's use the two data points provided:
Point 1: Price (p1) = Rs 1200, Quantity (Q1) = 4000
Point 2: Price (p2) = Rs 1500, Quantity (Q2) = 3000
First, we calculate the slope of the demand equation using the formula:
Slope = (Q2 - Q1) / (p2 - p1)
Substituting the values, we get:
Slope = (3000 - 4000) / (1500 - 1200) = -1000 / 300 = -10/3
Next, we use one of the data points and the slope to find the y-intercept (b). Let's use Point 1:
p1 = Rs 1200, Q1 = 4000
Using the equation of a straight line (y = mx + b), we can rearrange it to solve for b:
b = y - mx
b = 1200 - (-10/3)(4000) = 1200 + 40000/3 = 1200 + 13333.33 = 14533.33
Therefore, the demand equation in the form of p = f(Q) is:
p = -10/3Q + 14533.33
To find the number of calculators demanded (Q) when the price per unit is Rs 1650, we can rearrange the equation and solve for Q:
1650 = -10/3Q + 14533.33
-10/3Q = 1650 - 14533.33
-10/3Q = -12883.33
Q = (-12883.33) / (-10/3)
Q = 12883.33 * 3/10
Q ≈ 3865
Therefore, when the price per unit of calculators is Rs 1650, approximately 3865 calculators are demanded.
Now, let's determine the price per unit (p) when 4500 calculators are demanded. We rearrange the equation and solve for p:
4500 = -10/3Q + 14533.33
-10/3Q = 4500 - 14533.33
-10/3Q = -10033.33
Q = (-10033.33) / (-10/3)
Q = 10033.33 * 3/10
Q ≈ 3010
Therefore, when 4500 calculators are demanded, the price per unit should be approximately Rs 3010.
By using the slope-intercept form of a linear equation and the given data points, we can determine the demand equation and solve for various scenarios, including finding quantities demanded at specific prices and determining the appropriate price for a given quantity demanded.
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what is the area of the triangle whose vertices are A (0, 0) B(-10, 0) and C(0, -6)
5
5 points
In A, the m/BAD = 106°. Find the measure of DE
B
3.
E
In the circle if ∠BAD is 106 degrees then the measure of arc DE is 74 degrees
In the circle the measure of ∠BAD is 106 degrees
We have to find the measure of the arc DE
∠BAD is equal to ∠CEA because these are vertical angles
106+106=212 degrees
Now let us find the measure of ∠DAE
212 degrees +∠DAE + ∠ABC = 360
212 degrees+∠DAE+∠DAE=360 (∠DAE =∠ABC)
212 degrees+2∠DAE =360
2∠DAE = 360-212
2∠DAE = 148
Divide both sides by 2
∠DAE = 74 degrees
The ∠DAE is equal to measure of arc DE
arc DE = 74 degrees
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Pls someone help me with this
Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{AB}\\ a=\stackrel{adjacent}{6}\\ o=\stackrel{opposite}{6} \end{cases} \\\\\\ AB=\sqrt{ 6^2 + 6^2}\implies AB=\sqrt{ 36 + 36 } \implies AB=\sqrt{ 72 }\implies AB=6\sqrt{2}[/tex]
if P={1,2,3,4,5,6,7} , Q= {5,6,7}, and R= {0,7,11},find a: QnR, b:Pn{ QuR} and c: PnR
[tex]Q\cap R=\{7\}\\\\Q\cup R=\{0,5,6,7,11\}\\P\cap(Q\cup R)=\{5,6,7\}\\\\P\cap R=\{7\}[/tex]
High school students are pledging hours to help clean up streets and parks around their neighborhood. Tim pledged 27 hours to help clean 3 parks and 6 streets. Susan pledged 42 hours to help clean 6 parks and 8 streets. How long are either of them planning to clean each street and park?
Learning Goal: I can use the substitution method to solve linear systems of equations
They plan to clean the street for 3 hours.
They plan to clean the park for 3 hours.
How many hours do they plan to clean the street and the park?The first step is to set up a set of linear equations that describe the information in the question.
3p + 6s = 27 equation 1
6p + 8s = 42 equation 2
Where:
p = number of hours spent cleaning one park
s = number of hours spent cleaning on street
In order to determine the value of s, take the following steps:
Multiply equation 1 by 2
6p + 12s = 54 equation 3
Subtract equation 2 from equation 3
4s = 12
Divide both sides of the equation by 4
s = 12 / 4
s = 3 hours
Substitute for s in equation 1:
3p + 6(3) = 27
3p + 18 = 27
3p = 27 - 18
3p = 9
p = 9/3
p = 3
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What’s the 6th term of 23,92,368
Answer:
23552
Step-by-step explanation:
23, 92, 368... is a geometric sequence.
first term = a = 23
common ratio = r = 2 term ÷ first term = 92 ÷ 23 = 4
nth term = [tex]ar^n^-^1[/tex]
6th term = [tex]23*(4)^6^-^1[/tex]
[tex]=23*4^5[/tex]
[tex]=23*1024[/tex]
[tex]=23552[/tex]
Hope this helps :)
Pls brainliest...
Hadey is planning an advertising blitz for his new amusement park, but
he’s aware that the park will be much more appealing in warm weather
than when it’s rainy and cold. He doesn’t want to try to operate the
park if there won’t be a crowd, so he needs to iron out when exactly to
open and close the park each year. Hadey is a goat, and doesn’t
understand climate change (who does?) so he just uses the most recent
twelve months as a guideline. The temperature in Los Angeles peaked in
2022 on September 9 at around 102°F, followed by a low of about 57°F
approximately 6 months later. Hadey is confident that he’ll get good
turnout as long as the high temp any given day is at least 72°F.
Assuming that the high temperature is periodic, what day should he
open and close the park each year?
Hadey should open the park when the high temperature consistently reaches or exceeds 72°F and close it when it falls below.
To determine the best day to open and close the park each year, Hadey should consider the temperature patterns based on the given information. The temperature in Los Angeles peaked on September 9 at 102°F and reached a low approximately 6 months later, suggesting a periodic pattern.
To find the optimal opening and closing days, Hadey should look for the days when the high temperature is consistently above 72°F. This would ensure a good turnout for the amusement park. He should open the park when the high temperature consistently reaches or exceeds 72°F and close it when the high temperature consistently falls below this threshold. Using the temperature data from the most recent twelve months, Hadey should analyze the high temperature records for each day and identify the earliest day when the high temperature consistently reaches or exceeds 72°F. This would be the opening day of the park. Similarly, he should find the latest day when the high temperature consistently falls below 72°F, which would be the closing day.
It's important to note that Hadey's approach assumes that temperature patterns will remain consistent in the future. However, climate change and other factors can affect temperature variations, so it would be wise to consider long-term climate trends and consult with meteorological experts to ensure the park's success.
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What the meaning of statement this?
The axiom of regularity is a set theory principle which states that every non-empty set C contains an element that is disjoint from C.
Axiom of RegularityThe set theory concept rules that for every non-empty set C there is an element x of C such that x does not intersect C. The regularity axiom aims to establish that no non-empty set will have itself as an element.
The principle which is also called the axiom of foundation is a fundamental concept in set theory and credited to Zermelo–Fraenkel.
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tudy the Road to Health Chart contained in ANNEXURE G and answer the following uestions. How old is the baby whose weight of 26 lb places her at the 75th percentile curve? 3.2 Jay's baby who is 29 months old has a weight that places her at the 50th percentile curve and a length which places her at the 97th percentile curve. Calculate her BMI in the form kg/cm². (Do not round-off your answer.) .3.1 You may use the following formula: weight BMI = height²
Once you have the weight and length, you can use the formula:
BMI = weight (in kg) / height² (in meters²).
The weight from lb to kg and the length from inches to meters before applying the formula.
The specific Road to Health Chart contained in ANNEXURE G.
The Road to Health Chart and calculate BMI.
The age of a baby at a specific weight percentile:
To determine the age of a baby whose weight places her at the 75th percentile curve you would need to refer to the specific chart.
Locate the weight of 26 lb on the chart and find the corresponding age.
The chart typically provides a range of ages for each percentile curve, allowing you to estimate the age of the baby.
Calculating BMI:
To calculate the BMI (Body Mass Index) for Jay's baby you need both the weight and the length of the baby.
Since the length is given in percentile you would need to find the corresponding measurement value on the chart.
By plugging in the appropriate values you can calculate the BMI in the form of kg/cm².
Remember not to round off the answer as specified.
The specific Road to Health Chart in ANNEXURE G to obtain accurate information for these calculations.
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At a local market, the cost of apples is derectly proportional to the weight of the apples. The graph shows the relationship between the weight of apples in pounds and the cost in dollars
Answer:
The statement you provided describes a situation in which the cost of apples at a local market is directly proportional to the weight of the apples. This means that as the weight of the apples increases, the cost also increases at a constant rate. The graph mentioned in the statement would show this relationship between the weight of apples in pounds and the cost in dollars.
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A tank in the shape of a hemisphere has a radius of 4 feet. If the liquid that fills the tank has a density of 75 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
The weight of the liquid can be found by multiplying its volume by its density. The volume will be that of a hemisphere, which can be found using the appropriate formula.
Hemisphere volumeThe volume of a hemisphere with radius r is given by ...
[tex]\sf V = \huge \text(\dfrac{2\pi}{3}\huge \text)r^3[/tex]
When the radius is 4 ft, the volume is ...
[tex]\sf V = \huge \text(\dfrac{2\pi}{3}\huge \text)(4 \ ft)^3 = \dfrac{128\pi }{3} \ ft^3[/tex]
WeightThe weight of the liquid in the tank is found using the density.
[tex]\sf W = \rho V[/tex]
[tex]\sf W = (75 \ lb/ft^3)\huge \text(\dfrac{128\pi}{3} \ ft^3\huge \text) = 3200\pi \ lb \thickapprox 10,053 \ lb[/tex]
The total weight of the liquid in the tank is about 10,053 pounds.
FCPS Bookmarks
Launch realize. 8-2: Find Volume of Cylinders (LMS graded)
8.2.PS-13
The cylinder shown has a volume of 824 cubic inches.
a. What is the radius of the cylinder? Use 3.14 for .
b. If the height of the cylinder is changed, but the volume
stays the same, then how will the radius change? Explain.
a. The radius of the cylinder is about 8.2 in³.
(Type an integer or decimal rounded to the nearest tenth as needed.)
10.7 in.
Question Help
◇
To find the radius of the cylinder, we can use the formula for the volume of a cylinder:
V = πr²h
Given that the volume is 824 cubic inches, we can rearrange the formula to solve for the radius:
824 = πr²h
Since the height is not given, we cannot find the exact radius. However, we can still determine the relationship between the height and radius if the volume remains the same.
b. If the height of the cylinder is changed, but the volume stays the same, the radius will change inversely proportional to the height. This means that as the height increases, the radius will decrease, and vice versa. This relationship ensures that the volume remains constant.
Therefore, we cannot determine the exact radius without knowing the height, but we can conclude that the radius and height have an inverse relationship.
can some one please solve the attached image for me?
Step-by-step explanation:
Area of circle (pi r^2 ) - area of rectangle (W x H) = shaded area
pi (4^2) - (5 x 6 ) = 20.3 in^2
4.1.3. What is the General direction of Pretoria from Cape Town?
Combining the information from the Latitude and longitude, we can conclude that Pretoria is situated in a north-eastern direction from Cape Town.
The general direction of Pretoria from Cape Town is North-East.
Cape Town is a coastal city located in the southwestern part of South Africa, while Pretoria is an inland city situated in the northeastern part of the country. To determine the general direction between the two cities, we consider their geographic coordinates.
Cape Town is approximately at a latitude of 33.9249° S and a longitude of 18.4241° E, while Pretoria is around 25.7479° S latitude and 28.2293° E longitude.
When we compare the latitude values, we see that Cape Town is situated further south than Pretoria. Therefore, the general direction from Cape Town to Pretoria is north.
Next, if we compare the longitude values, we observe that Cape Town has a significantly smaller longitude value compared to Pretoria. This indicates that Pretoria is situated more to the east.
Combining the information from the latitude and longitude, we can conclude that Pretoria is situated in a north-eastern direction from Cape Town.
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A can has 5 marbles in it.
The radius of each ball (marble) is 1.2 cm and the radius of the can is 1.50cm.
The height of this can is 4 cm. How much empty space is in this can?
The empty space is -7.92 cm^3 (rounded to two decimal places).The result is negative, indicating that there is not enough space in the can to fit all the marbles.
To calculate the empty space in the can, we first need to calculate the volume occupied by the marbles and then subtract it from the total volume of the can.
The volume of each marble can be calculated using the formula for the volume of a sphere:
V_marble = (4/3) * π * r^3
where r is the radius of the marble.
Given that the radius of each marble is 1.2 cm, we can calculate the volume of one marble as follows:
V_marble = (4/3) * π * (1.2 cm)^3
≈ 7.238 cm^3 (rounded to three decimal places)
Since there are 5 marbles in the can, the total volume occupied by the marbles is:
V_total_marbles = 5 * V_marble
≈ 5 * 7.238 cm^3
≈ 36.19 cm^3 (rounded to two decimal places)
The volume of the can can be calculated using the formula for the volume of a cylinder:
V_can = π * r^2 * h
where r is the radius of the can and h is the height of the can.
Given that the radius of the can is 1.5 cm and the height of the can is 4 cm, we can calculate the volume of the can as follows:
V_can = π * (1.5 cm)^2 * 4 cm
≈ 28.27 cm^3 (rounded to two decimal places)
To find the empty space in the can, we subtract the volume occupied by the marbles from the total volume of the can:
Empty space = V_can - V_total_marbles
≈ 28.27 cm^3 - 36.19 cm^3
≈ -7.92 cm^3 (rounded to two decimal places)
The result is negative, indicating that there is not enough space in the can to fit all the marbles.
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PLEASE HELP and show work thank you !
Suppose that two identical mass planets are sitting a million miles apart. At that distance, the planets have a gravitational force of 1,000,000 N. If the planets are moved to two million miles apart, what is the new gravitational force between them?
The new gravitational force between the two planets, when they are moved to two million miles apart, is 250,000 N.
The new gravitational force between the two planets, when they are moved to two million miles apart, can be calculated using the inverse square law of gravity, resulting in a gravitational force of 250,000 N.
Let's denote the initial distance between the planets as d1 (1 million miles) and the corresponding gravitational force as F1 (1,000,000 N).
The final distance between the planets is denoted as d2 (2 million miles), and we need to find the new gravitational force, F2.
According to the inverse square law of gravity, the relationship between distance and gravitational force is as follows:
[tex]F1 / F2 = (d2^2) / (d1^2)[/tex]
Substituting the given values:
[tex]1,000,000 N / F2 = (2,000,000^2) / (1,000,000^2)[/tex]
Simplifying:
1,000,000 N / F2 = 4
Cross-multiplying:
F2 = 1,000,000 N / 4
F2 = 250,000 N.
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The graph of y = f(x) is shown.
a) Give the coordinates of the
turning point of the graph.
b) Find the roots of f(x) = 0
Note: Please use a comma between your answers.
c) Find f(0)
-3
-2
4
3-
2-
O
-1-
-2-
-~
2
COL
3
X
s+
Answer:
a) (1, 4)
b) -1, 3
c) 3
Step-by-step explanation:
The turning point is the point when the function changes direction.
The roots are the x-intercepts.
f(0) is the y-intercept.
how do u do this and give me the answer 16q2–8q+1
Answer:
[tex]\huge\boxed{\sf (4q - 1)\²}[/tex]
Step-by-step explanation:
Given expression:= 16q² - 8q + 1
We can also write it as:
= (4q)² - 2(4q)(1) + (1)²
Using formula:a² - 2ab + b² = (a - b)²
So, the above expression becomes:
= (4q - 1)²[tex]\rule[225]{225}{2}[/tex]
solve the following proportion for x
Step-by-step explanation:
Cross multiply to get
8 (x-1) = 2 (x+2)
8x -8 = 2x + 4
6x = 12
x = 2
Translate the sentence into an equation.
Eight more than the quotient of a number and 7 is equal to 3.
The " Eight further than the Quotient of a number and 7 is equal to 3," and the result to the equation is x = -35.
The equation 8( x/ 7) = 3 represents the judgment " Eight further than the Quotient of a number and 7 is equal to 3," and the result to the equation is x = -35.
" Eight further than" implies addition, so we've 8 " The quotient of a number and 7" means dividing a number by 7, so we've x/ 7 " is equal to" means that the expression on the left side is equal to the expression on the right side, so we've = " 3" is the value to which the expression on the left side is equal, so we've 3 Putting it all together the judgment " Eight further than the quotient of a number and 7 is equal to 3" can be restated into the equation ( x/ 7) = 3
In this equation, x represents the number we're trying to find. To break for x, we can manipulate the equation using algebraic operations to insulate x on one side of the equation. By abating 8 from both sides of the equation, we get ( x/ 7)- 8 = 3- 8 Simplifying, we have x/ 7 = -5
To insulate x, we can multiply both sides of the equation by 7 *( x/ 7) = -5 * 7 This gives us x = -35 thus, the equation 8( x/ 7) = 3 represents the judgment " Eight further than the quotient of a number and 7 is equal to 3," and the result to the equation is x = -35.
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Which expression is equivalent to (7x - 4) - (2 - 1/2x)? A. 11/2x + 6 B. 11/2x - 6 C. 5/2x + 6 D. 15/2x - 6
The expression (7x - 4) - (2 - 1/2x) simplifies to 3/2 is equivalent to 11/2x + 6. A.
To simplify the expression (7x - 4) - (2 - 1/2x), we can remove the parentheses and combine like terms.
(7x - 4) - (2 - 1/2x) = 7x - 4 - 2 + 1/2x
Now, let's combine the like terms:
= 7x + 1/2x - 6
To add the terms with the same variable, we need to have a common denominator.
The common denominator for x and 1/2x is 2x.
= (14x + x) / (2x) - 6
= (15x) / (2x) - 6
= 15/2 - 6
= (15 - 12) / 2
= 3/2
The brackets and merge related words in order to make the statement (7x - 4) - (2 - 1/2x) simpler.
(7x - 4) - (2 - 1/2x) = 7x - 4 - 2 + 1/2x
Let's now mix similar terms:
= 7x + 1/2x - 6
We need a common denominator so that we may sum the words that share the same variable.
2x serves as the common denominator for x and 1/2x.
= (14x + x) / (2x) - 6
= (15x) / (2x) - 6
= 15/2 - 6
= (15 - 12) / 2
= 3/2
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