For the required linear function , the height of the candle when the amount of time for burning a candle is 16 hours is equal to 18.8 centimeters.
Let 'h' be the height of the candle.
And 't' be the amount of time used for burning.
Required linear function is :
h = mt + c
When t = 8 hours , h = 20.4centimeters
20.4 = 8m + c ___(1)
When t = 19 hours , h = 18.2centimeters
18.2 = 19m + c ___(2)
Subtract (2) from (1) we get,
20.4 = 8m + c
18.2 = 19m + c
2.2 = -11m
⇒ m = -2.2 / 11
⇒ m = -0.2
Substitute in (1) we get,
20.4 = 8( -0.2 ) + c
⇒ c = 20.4 + 1.6
⇒ c = 22
Now , h = -0.2t + 22
When t = 16 hours
⇒ h = -0.2(16) + 22
⇒ h = -3.2 + 22
⇒ h = 18.8 centimeters
Therefore, the height of the candle when amount of time of burning is 16 hours is equal to 18.8 centimeters.
The above question is incomplete, the complete question is:
Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 8 hours of burning, a candle has a height of 20.4 centimeters. After 19 hours of burning, its height is 18.2 centimeters. What is the height of the candle after 16
hours?
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Solve the system of equations by graphing.
x+y = -7
4x + y = 19
Answer:
(8.666666667, -15.66666667)
or in fraction form
(26/3, -47/3)
Step-by-step explanation:
First we want to get both of the equations into y-intercept form
x + y = -7
subtract x from both sides
y = -x - 7
and the other
4x + y = 19
subtract 4x from both sides
y = -4x +19
now we can graph them
(See attached screenshot)
Cindy spent $65. 25 on ingredients
for blueberry pies and $62. 84 on
ingredients for cherry pies. Each slice
of pie sells for $3. 50
Cindy spent a total of $128.09 on ingredients for pies. She will be able to make 18 slices of pie with this amount of ingredients.
1. Cindy spent $65.25 on ingredients for blueberry pies and $62.84 on ingredients for cherry pies.
2. Add the two amounts together: $65.25 + $62.84 = $128.09
3. Each slice of pie sells for $3.50.
4. Divide the total spent on ingredients by the cost of a slice of pie: $128.09 / $3.50 = 18 slices of pie.
the complete question is :
Cindy spent $65. 25 on ingredients for blueberry pies and $62. 84 on
ingredients for cherry pies. Each slice of pie sells for $3. 50.How much did Cindy spend on ingredients for blueberry and cherry pies, and how many pies can she make from that?
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sufficient and necessary? 1 point possible (graded) suppose that we have some loss function that may or may not have multiple critical points. we have found a critical point such that f''(w)>0 , so that we know that it is a minimum. what can we say about it being a global minimum?
In order to determine whether a critical point of a loss function is a global minimum, it is necessary to consider the second derivative of the function.
If the second derivative is positive at the critical point, then we can say with certainty that the critical point is a local minimum. However, this does not necessarily mean that it is a function function. This is because there may be other local minima at points which the second derivative is negative, and in this case, the critical point must be compared to these points to determine if it is indeed the global minimum.
In order to assess whether a local minimum is a global minimum, we must first identify any other local minima. This can be done by locating the points at which the first derivative of the function is equal to zero and then evaluating the second derivative of the function at these points. If the second derivative is negative at any of the points, then we have identified a local minimum. Then, we can compare the value of the loss function at the points function as local minima to the value of the loss function at the critical point. If the value of the loss function at the critical point is lower than the value of the loss function at the other local minima, then the critical point is the global minimum. If the values are equal, then the critical point is a global minimum if and only if it is the only local minimum.Overall, identifying whether a critical point of a loss function is a global minimum requires both sufficiency and necessity. It is necessary to evaluate the second derivative of the function at the critical point in order to determine whether it is a local minimum, and it is also necessary to identify any other local minima and compare the value of the loss function at the critical point to the value of the function at the other local minima in order to determine whether the critical point is the global minimum.
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help me solve this please (please provide work)
Answer:
2x^2 - 12*x/2= Area For Shaded Region
Step-by-step explanation:
This works because you find tha area of both and subtract the shaded area by the unshaded area
Answer: Expression for the area of shades region of the figure = 2[tex]x^{2}[/tex] - 6x
Step-by-step explanation: Area of shaded region = Area of big rectangle - Area of small rectangle
Area of rectangle = length.breadth
Area of big rectangle = 2x.x { . means multiply}
= 2[tex]x^{2}[/tex]
Area of small rectangle = 12.(x/2)
=6x
∴ Area of shaded region = 2[tex]x^{2}[/tex] - 6x
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how many times larger is a centigram than a milligram? 10times | 100 times| 1000 times| 0.1 time
Answer: 10 times
Step-by-step explanation:
Please help me with this!! ( please answer thinking wuestion
1. In his newspaper, Peter Zenger published articles criticizing the Governor's use of arbitrary power
2. Because it was against the law to criticize the king or his appointees, the Attorney General accused Peter Zenger of committing" libel.
3. Hamilton believed Zenger was not guilty of this charge because in Zenger's newspaper articles the "truth is told
4. Hamilton felt that more than just Peter Zenger was on trial. He felt that the larger concept of American" liberty was at stake.
How to convey the informationHamilton and Morris agreed that the trial of Peter Zenger was important for American freedom and the defense of liberty.
As for the question about television and newspaper reporters, it is a matter of opinion. Some people believe that the freedom of the press is an important part of democracy, and that reporters should be able to criticize anyone in power, including the president. Others believe that criticism of the president should be limited to protect the dignity and stability of the office. In either case, it is important to strike a balance between free speech and responsible journalism.
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Sarah earned a 4% commission on all of her sales in December. Her total sales for December were $80,000. How much money did she cam in commission?
On solving the provided question, we can say that Amount of commission = Total sales value x Rate of commission = 3,200
what is amount ?aggregate attempting to calculate the time required, total number or quantity. The quantity at hand or under consideration is incredibly energetic. the overall result, importance, or import. Principal, interest, and a third accounting. amounts, amounting, and amounted are word forms. flexible noun The quantity of something is how much there is, how much you have, how much you require, or how much you obtain. He requires that sum of money to get by.
[tex]Amount of commission = 3,200\\Total sales value = 80,000//[/tex]
Rate of commission = 4% on sales
Amount of commission = Total sales value x Rate of commission
Amount of commission = 80,000 x 4%
Amount of commission = 3,200
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Please help as soon as possible
The number of hours taken to have the same number of pages completed is 5 hours.
The solution to the system of equations is (5, 50).
How to write the system of equations for this system?In order to write a system of linear equations that could be used to model the situation and determine the number of hours it would take to complete the workbook, we would assign variables to the number of hours and the number of pages respectively as follows:
Let the variable x represent the number of hours.Let the variable y represent the number of pages.Next, we would translate the word problem into system of linear equations as follows:
Isaiah: y = x + 45
Brenna: y = 9x + 5
When the same number of pages are completed, the number of hours taken can be calculated as follows;
x + 45 = 9x + 5
9x - x = 45 - 5
8x = 40
x = 5 hours.
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A concert venue wants to make at least $3,150.00 profit for their Saturday night show.
Adult tickets cost $12.00 and children's tickets cost $6.00. The venue can seat up to
350 people. Find three combinations of adult and children's tickets that will make the
profit goal and not be more than 350 total people. Enter your answer as ordered pairs
(A,C) separated by a comma where A is the number of adult tickets sold and Cis
the number of children's tickets sold.
Answer:
(175, 175) -> $3,150
(200, 150) -> $3,300
(225, 125) -> $3,450
Explain: I hope this helps
Answer two questions about Systems AAA and BBB:
System AAA \text{\quad}start text, end text System BBB
\begin{cases}-3x+12y=15\\\\7x-10y=-2\end{cases}
⎩
⎪
⎪
⎨
⎪
⎪
⎧
−3x+12y=15
7x−10y=−2
\begin{cases}-x+4y=5\\\\7x-10y=-2\end{cases}
⎩
⎪
⎪
⎨
⎪
⎪
⎧
−x+4y=5
7x−10y=−2
1) How can we get System BBB from System AAA?
1. To get System BBB from System AAA, we can divide both sides of the first equation in System AAA by -3:
-3x + 12y = 15
-3x/ -3 + 12y/ -3 = 15/ -3
x + 4y = -5
So System BBB is obtained by dividing both sides of the first equation in System AAA by -3.
2. Are Systems AAA and BBB equivalent?
Yes, Systems AAA and BBB are equivalent. This means that they have the same solution set, despite having different coefficients in their equations. Equivalent systems of linear equations are systems that have the same solution set, regardless of the coefficients of the equations.
While playing a game of chance, Mei rolled a regular six-sided die 100 times and noticed that it landed on the number 4 exactly 48 times. What could Mei conclude about the die?
We are 90% confident that the true proportion of times the die would land on the number 4 is between 0. 398 and 0. 562. Since this includes 0. 5, the die appears to be fair. We are 90% confident that the true proportion of times the die would land on the number 4 is between 0. 398 and 0. 562. Since this is much greater than 1 out of 6, the die appears to be unfair. We are 90% confident that the true proportion of times the die would land on the number 4 is between 0. 382 and 0. 578. Since this is much greater than 1 out of 6, the die appears to be unfair. We are 90% confident that the true proportion of times the die would land on the number 4 is between 0. 382 and 0. 578. Since this includes 0. 5, the die appears to be fair
Mei concluded that
We are 90% confident that the true proportion of times the die would land on the number 4 is between 0.398 and 0.562. Since this includes 0.5, the die appears to be fair.
It is based on a statistical analysis of the data collected by Mei.
The proportion of times the die landed on the number 4 is calculated as 48/100 = 0.48.
Using a statistical method called a confidence interval, we can estimate the range of values that the true proportion of times the die would land on the number 4 is likely to fall within, with 90% confidence.
The confidence interval calculated for this data is 0.398 to 0.562.
Since this interval includes the value of 0.5 (which would be the proportion of times a fair die would land on the number 4), By using statistical method we cannot reject the hypothesis that the die is fair.
Hence,
By using statistical method, we can conclude that the die would land on the number 4 is between 0.398 and 0.562 as 0.5 the die appears to be fair.
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help please it's for today
2. In this institute, 150 students are in 1st year of ESO; 148, 2nd of ESO; 73, 3rd of ESO; 60, 4th of ESO; 150, high school and 204, training cycles. What percentage of students do cycles?
3. A merchant gives a clearance discount of 20% on all items. Indicate what the prices of the following items will be:
a) Skirt: €40
b) Jacket: €55
c) Pants: €35
d) Sweater: €28
4. I want to buy a 60 horsepower Seat Ibiza that costs €12,400. If I get a 15% dealer discount, how much will I pay for the car?
5. The price of a television has risen by 25% compared to last year. What is the current price if last year it was €510.80?
6. The Netflix connection is €17.25, we get a 20% discount. How much will the connection cost us?
7. A family buys a refrigerator that costs €840. Pay 30% in cash and the rest in 6 monthly installments. What is the amount of each term?
8. I paid €48 for a video game that cost €60. What percentage have I been discounted?
9. A car cost €12,000 at the beginning of the year. The Central Government gives a subsidy to buyers of €3000 for the old car, if it is more than 10 years old. How much will the car cost with the bonus and what % will we save?
10. What interest does a capital of €3000 produce at 4.5% per annum over 5 years?
11. What is the capital that a bank will return to us after 6 months to deposit €3700 at 7.5% per annum?
The percentage of students doing cycles is 37.98% ((204/535)*100).
What is a Percentage?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent symbol, "%," is frequently used to indicate it.
A % is a number without dimensions and without a measurement system.
The other answers are:
a) The skirt will cost €32 after the discount.b) The jacket will cost €44 after the discount.c) The pants will cost €28 after the discount.d) The sweater will cost €22.40 after the discount.After the dealer discount, the car will cost €10,540 (€12,400 * 0.85).
The current price of the television is €638.50 (€510.80 * 1.25).
The Netflix connection will cost €13.80 after the discount (€17.25 * 0.8).
The family will pay €252 in cash (30% of €840), and the amount of each monthly installment will be €126.
You have been discounted by 20% ((60-48)/60*100).
The car will cost €9,000 with the bonus (€12,000 - €3,000), and the family will save 25% of the original price (€3,000/€12,000*100).
The capital will produce €683.10 of interest (€3000 * 0.045 * 5).
The capital that the bank will return is €3,855 (€3700 + (€3700 * 0.075 * 6/12)).
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[tex]\frac{-3x+6}{x-2}[/tex] = 0
solve for x. if there is no solution, write no solution.
Answer:
there is no solution
Step-by-step explanation:
The diagram shows a prism
Draw the front elevation and the side elevation of the prism on the grids.
Use a scale of 2 squares to 1m
The sketch of the front elevation and the side elevation of the prism are added as an attachment
How to draw the front elevation and the side elevation of the prismFrom the question, we have the following parameters that can be used in our computation:
The prism
Using the figure as a guide, we understand that:
The front elevation is a rectangle of 2m by 0.5m
While the side elevation is a rectangle merged with a trapezoid
Next, we draw the elevations (see attachment)
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Write a matrix to represent the following system: -x+5y=7, 7x-2y=3
[tex]\left[\begin{array}{ccc}-1&5\\7&-2\end{array}\right]\left[\begin{array}{ccc}x\\y&\end{array}\right] =\left[\begin{array}{ccc}7\\3&\end{array}\right][/tex] is the representation of system of equation x+5y=7, 7x-2y=3
What is Matrix?A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.
The system of linear equations
-x + 5y = 7
7x - 2y = 3
can be represented in matrix form as:
[tex]\left[\begin{array}{ccc}-1&5\\7&-2\end{array}\right]\left[\begin{array}{ccc}x\\y&\end{array}\right] =\left[\begin{array}{ccc}7\\3&\end{array}\right][/tex]
The matrix on the left represents the coefficients of the variables x and y, and the matrix on the right represents the constants on the right-hand side of each equation.
The vector on the left contains the variables x and y, and the vector on the right contains the constants.
Hence, [tex]\left[\begin{array}{ccc}-1&5\\7&-2\end{array}\right]\left[\begin{array}{ccc}x\\y&\end{array}\right] =\left[\begin{array}{ccc}7\\3&\end{array}\right][/tex] is the representation of system of equation x+5y=7, 7x-2y=3
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pls help its due on monday...
cylinder has a volume of 157 cm³. If the radius of the cylinder is 1 cm, what is its height? 3.14
The height of the cylinder whose volume has been given above would be = 50cm
How to calculate the height of a cylinder?The volume of a cylinder can be calculated with the formula = πr²h
Where Volume = 157cm³
radius = 1 cm
height = X cm
π = 3.14
That is, 157 = 3.14 × 1² × X
make X the subject of formula;
X = 157 /3.14
X = 50cm
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use subsitution to solve the system y=2x-8 and -3x+4y=-22 x= and y=
(will give branliest)
Answer:
x = 2 and y = -4
Step-by-step explanation:
To solve using substitution, we define one unknown variable in terms of another and sub this into a second equation with both.
We are told y=2x-8 and -3x+4y=-22, so let's sub '2x-8' in for y in -3x+4y=-22:
-3x+4y=-22
-3x+4(2x-8)=-22
-3x+8x-32=-22
5x=10
x=2
If x=2 and y=2x-8, let's sub 2 in for x to find y:
y=2x-8
y=2(2)-8=4-8=-4
Help me asap it is due soon pls
The solution of the system of equation y - 10 = 2x and 1/2 y = x + 5 is
A. (0, 10)How to solve the simultaneous equationThe simultaneous equation is solved by substitution method as follows
y - 10 = 2x and
1/2 y = x + 5
Isolate y in the first equation to get
y = 2x + 10
substitute y in 1/2 y = x + 5
1/2 (2x + 10) = x + 5
x + 5 = x + 5
x = 0
substitute x = 0 into y = 2x + 10
y = 2(0) + 10
y = 10
hence the solution is (0, 10)
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In February, Dawn's monthly allowance and Evelyn's monthly allowance were in the ratio 5: 8. In March, Mother increased Dawn's monthly allowance by 20% and decreased Evelyn's monthly allowance. Dawn and Evelyn then had the same amount of allowance. What was the percentage decrease in Evelyn's allowance in March?
Answer:
25%
Step-by-step explanation:
Let Dawn’s monthly allowance be 5x. Let Evelyn’s monthly allowance then be 8x.
Percentage increase by 20% is the same as multiplying a number by 1.2
To find the percentage decrease of Evelyn’s monthly allowance, we can equate their allowances after the change of their initial allowance.
1.2 * 5x = k/100 * 8x
k represents the percentage
6x = 8xk/100
Cancel the x’s from both sides
6 = 8k/100
600 = 8k
k = 75
Therefore since 75% of Evelyn’s monthly allowance is equal to Dawn’s increased monthly allowance, this means Evelyn’s monthly allowance was decreased by 25%.
Best buy is having a 15% off sale on all brands of computers. Jerome buys a computer regularly priced at $2250. How much does jerome save on the computer? if the sales tax is 7. 5%what is the amount of tax on the computer? how much is the total cost for the computer? what would be the total price for the computer not on sale?
Jerome saves 337.5$ on the computer.
Jerome buys the computer for 1912.5$.
The total cost of the computer is 2056$ including sales tax.
The total price of the computer not on sale is 2418.75$.
The discount is 15% of the original price:
0.15 x $2250 = $337.50.
If the sales tax is 7.5%,
The price of the computer after the discount is $2250 - $337.50 = $1912.50.
The amount of tax on the computer is 7.5% of $1912.50:
0.075 x $1912.50 = $143.44.
The total cost for the computer is the discounted price plus the tax: $1912.50 + $143.44 = $2055.94.
The total price for the computer not on sale would be the original price plus the tax:
$2250 + $169.13 = $2419.13 (where tax is 7.5% of $2250).
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A spinner and a fair number cube are used in a game. The spinner has an equal chance of landing on 1 of 6 colors: red, purple, blue, green, white, or orange. The faces of the cube are labeled 1 through 6. What is the probability of a player spinning the color green and then rolling an even number?
The probability of a player spinning the color green and then rolling an even number is 1/12.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Spinner:
= {red, purple, blue, green, white, orange}
Cube:
= {1, 2, 3, 4, 5, 6}
Now,
The sample space of spinning and rolling a cube.
= {red, purple, blue, green, white, orange} x {1, 2, 3, 4, 5, 6}
The number of outcomes.
= 6 x 6
= 36
Now,
The outcome of spinning a green and an even number.
= (green, 2), (green, 4), (green, 6)
Number of outcomes = 3
Now,
The probability of a player spinning the color green and then rolling an even number.
= 3/36
= 1/12
Thus,
The probability of a player spinning the color green and then rolling an even number is 1/12.
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Sarah's cell phone company charges her $35 a month for phone service plus $0.25 for
every text message. How many text messages does Sarah send in one month if her bill
was $99?
Answer:
256 text
Step-by-step explanation:
Let's call the number of text messages Sarah sends in a month as "x".
So, the total cost of the text messages is $0.25 * x.
The total cost of the phone service and text messages is $35 + $0.25 * x = $99.
So, $35 + $0.25 * x = $99.
Subtracting $35 from both sides, we have:$0.25 * x = $99 - $35 = $64
Dividing both sides by $0.25, we have:x = 256
So, Sarah sent 256 text messages in one month.
Lamar and Allie are organizing a car wash to raise money to buy new hockey sticks for their school's hockey team. The number of hockey sticks they will be able to purchase for the team depends on the number of cars they wash.
s = the number of hockey sticks Lamar and Allie will be able to purchase
c = the number of cars Lamar and Allie wash
Which of the variables is independent and which is dependent?
The independent variable of the question is c:the number of cars Lamar and Allie wash while the dependent variable is s: the number of hockey sticks Lamar and Allie will be able to purchase
How to find the independent and dependent variables?The independent variable is defined as the variable that you change and control in your experiment. The dependent variable is defined as the variable that you don't have control over and is affected by the way that the independent variable reacts.
The parameters given are;
s = the number of hockey sticks Lamar and Allie will be able to purchase
c = the number of cars Lamar and Allie wash
Now, since the number of cars they wash determines how much money they will get to buy a new car, then we can say that c is the independent variable while s is the dependent variable as it depends on c to be actualized.
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Shopping Two friends shop for fresh fruit. Jackson buys a watermelon for $6.25 and 5 pounds of cherries. Tim buys a pineapple for $3.15 and 4 pounds of cherries. Use the variable p to represent the price, in dollars, per pound of cherries. Write and simplify an expression to represent how much more Jackson spent.
Answer:44
Step-by-step explanation:44444444
Can someone please pelass help with the attached image
Answer:
C) E=118°, T=118°
Step-by-step explanation:
The angles inside a quadrilateral (shape with four sides) always add to 360°. So this means:
W+E+S+T=360°
29°+E+95°+T=360°
E+T=360°-124°=236°
Note that the shape contains two congruent triangles (they share equal sides) ΔEWS and ΔTWS. This means their angles are the same so E=T
If E=T and E+T=236°, then E=T=236°/2=118°
Answer:
C) E-118°, T=118° is the answer
The point N lies on the segment MP.
Find the coordinates of N so that MN is of MP.
2/5
The coordinates of N are (-38.4, -18.4)
How to determine the coordinatesFrom the question, we have the following parameters that can be used in our computation:
M = (-26, -14)
P = (6, -2).
m : n = 2 : 3 i.e. 2/5
The coordinate is then calculated as
N = 1/(m + n) * (mx2 + nx1, my2 + ny1)
substitute the known values in the above equation, so, we have the following representation
N = 2/5 * (2 * 6 + 3 * -36, 2 * -2 + 3 * -14)
Evaluate
N = (-38.4, -18.4)
Hence, the coordinate is (-38.4, -18.4)
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Complete question
The point N lies on the segment MP.
Find the coordinates of N so that MN is of MP. 2/5
M- (-26, 14) P- (6,-2)
N(?,?)
The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.50, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
A. Equally likely and unlikely
B. Likely
C. Unlikely
D. This value is not possible to represent probability of a chance event.
The probability that it is likely that a randomly selected cookie from the batch will be a chocolate chip cookie.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
If P(chocolate chip) = 0.50, it means that the probability of randomly selecting a chocolate chip cookie from the batch is 0.50 or 50%.
Interpreting this probability, we can say that it is likely that a randomly selected cookie from the batch will be a chocolate chip cookie since the probability is relatively high.
Therefore, the correct answer would be an option (B) Likely.
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Graph each inequality.
7. yz|x+2
The graph of the inequality is added as an attachment
How to determine the graphFrom the question, we have the following parameters that can be used in our computation:
yz|x+2
Express properly
So, we have the following representation
y < x + 2
The above expression is an inequality that implies that
The value of y does not exceed 2 added to x
Next, we plot the graph
See attachment for the graph of the inequality
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i need help with this for math class
The expression that shows an equivalent expression include the following:
1/4(14x - 8 + 6x) = 5x - 2.
What is an expression?In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).
Based on the information provided above, we have the following mathematical expression:
1/4(14x - 8 + 6x)
By opening and expanding the bracket, we have the following mathematical expression:
1/4(14x - 8 + 6x) = 1/4(20x - 8)
1/4(20x - 8) = 5x - 2
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