12 - 2^2 x 2
---Remember: PEMDAS
---In this case exponents are first, then multiplication, then subtraction
12 - 4 x 2
12 - 8
4
Answer: 4
Hope this helps!
For the following exercises, convert the angle measures to radians.
-236° (the exact answer) b) 601° (round to two decimal places)
The calculated values of the angle measures when converted to radians are 1.31π rad and 3.34π rad
Converting the angle measures to radians.To convert angles from degrees to radians, we multiply the number of degrees by π/180.
This means that
Angle = Degree measure * π/180
Using the above as a guide, we have the following:
Angle 236 = 236 * π/180
Evaluate the products
Angle 236 = 1.31π rad
Next, we repeat the same process for the second angle 601 degrees
Angle 601 = 601 * π/180
Evaluate the products
Angle 601 = 3.34π rad
Hence, the angles are 1.31π rad and 3.34π rad
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Less than 53% of adults would erase all of their personal information online if they could . The hypothesis test results in a p-value of 0.0059
A conclusion on the null hypothesis is C. Reject H_{0} because the P-value is less than or equal to a.
What should happen to the null hypothesis ?Stated in the initial description is the null hypothesis, establishing that adults who possess a desire to eliminate all personal information available online would equate to or exceed 53%, while the alternative conjecture rests on this percentage being under 53%.
The statistical significance level at hand designated as alpha equals 0.05 indicates that a P-Value having less than or equal value of 0.05 is necessary for declining the null hypothesis. As provided by the task's question, the computed P-value registers a score of 0.0059 which falls below the established significance level of 0.50 and thus resulting in null hypothesis rejection.
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People, I need to figure out a question
Is the sun of 7/10 + 1/5 closer to 0, 1/2 or 1?
Answer:
1
Step-by-step explanation:
7+10+1/5
7/10 = 0.7
1/5 = 0.2
0.7+0.2=0.9
Therefore it would be closest to 1.
Answer: 1
Step-by-step explanation:
To find an estimate, you need to round your fractions. Let's start with 7/10. First let's look at the numerator, 7. 7 is a number greater than 5, so we'll round it to 10 and you keep your denominator. so now we have 10/10, or 1. Then round 1/5. 1/5 is lower than 5, so we'll round it to 0. Now, for the final step add them. 1 + 0 = 1, so 1 is the answer
Cual es mayor
1 or 1
_ _
4 3
Answer:
Step-by-step explanation:
1/3 is greater.
Can someone help me with dosage calculation problems #46 and #47.
Would greatly appreciate if you explain how it was solved. Thanks!
46. There are 9 complete doses available from the bottle. 47. There are 8 full doses available in the 120 mL bottle.
What is weight and mass?Although weight and mass are frequently used interchangeably, they have distinct meanings in the study of physics. Weight is a measurement of the force of gravity acting on an item, whereas mass is a measure of the amount of matter that makes up an object. Weight is typically expressed in newtons (N) or pounds, while mass is typically expressed in kilogrammes (kg) (lb). While an object's mass remains constant, its weight can change depending on how strongly gravity is pulling on it.
46. We know that,
1 fluid ounce = 29.5735 mL
4 fluid ounces = 4 x 29.5735 = 118.294 mL
Each dose is 12.5 mL:
118.294 / 12.5 = 9.46
So there are 9 complete doses available from the bottle.
47. Given, 1 tablespoon is equal to 15 mL.
Thus, doses of 15 mL are in a 120 mL bottle:
120 / 15 = 8
So there are 8 full doses available in the 120 mL bottle.
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Jermaine invested $3,200 in a defined-contribution account. Assuming he is in a 20% marginal tax bracket, how much did he lower his income taxes with the investment
Jermaine's income tax was lowered by $640 as a result of the investment.
Investment calculationAssuming that the defined contribution account is a tax-deferred retirement account, Jermaine can lower his income taxes by the amount of his contribution multiplied by his marginal tax rate. The formula for this tax savings is:
Tax savings = Contribution × Marginal tax rate
Using the given values, Jermaine's contribution to the account is $3,200 and his marginal tax rate is 20%. Substituting these values into the formula, we get:
Tax savings = $3,200 × 0.20 = $640
Therefore, Jermaine can lower his income taxes by $640 by contributing $3,200 to the defined contribution account.
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ACTIVITY 1: Solve the following rational equation.
The solutions to the rational equations are
(1) x = 14/3 (2) x = -2/3 (3) x = 4(4) x = 0 or x = 3(5) x = 0 or x = -2(6) x = 4/5(7) x = √(17/5)(8) x = 11/9(9) x = -1 or x = 2 (10) x = 1 or x = 2Solving the rational equationsThe rational equations can be solved as follows
(1)
(x - 2)/(2x + 4) = 1/5
This gives
5x - 10 = 2x + 4
So, we have
3x = 14
x = 14/3
(2)
For equation (2), we have
(x + 3)/2 - x/4 = 4/3
So, we have
[2(x + 3) - x]/4 = 4/3
[x + 6]/4 = 4/3
So, we have
3x + 18 = 16
x = -2/3
(3)
For equation (3), we have
3/(x + 1) - 2/(x - 1) = 1/(x² - 1)
So, we have
3(x - 1) - 2(x + 1) = 1
This gives
3x - 3 - 2x - 2 = 1
x = 4
(4)
For equation (4), we have
18/(x² - 3x) = 2x/(x - 3) - 6/x
So, we have
18 = 2x² - 6(x - 3)
This gives
x = 0 or x = 3
(5)
For equation (5), we have
3x/(x + 2) + 6/x + 4 = 12/(x² + 2x)
Multiiply through by x² + 2x
3x² + 6(x + 2) + 4(x² + 2x) = 12
Evaluate
x = 0 or x = -2
(6)
For equation (6), we have
1/(x - 2) + 4/(x + 9) = 3/(x² + 7x - 18)
Multiiply through by (x² + 7x - 18)
x - 9 + 4x + 8 = 3
So, we have
5x = 4
Evaluate
x = 4/5
(7)
For equation (7), we have
3/5x² - 1/5 = 2/25x²
Multiiply through by 25x²
15 - 5x² = 2
So, we have
5x² = 17
Evaluate
x = √(17/5)
(8)
For equation (8), we have
9/(x + 1) = 2/(x² - 1)
Multiiply through by 25x²
9x - 9 = 2
So, we have
9x = 11
Evaluate
x = 11/9
(9)
For equation (9), we have
3/(x³ - 8) = 1/(x - 2)
Cross multiiply
(x³ - 8) = 3(x - 2)
Evaluate
x = -1 and x = 2
(10)
For equation (10), we have
x²/2 - 3x/2 + 1 = 0
Multiiply through by 2
x² - 3x + 2 = 0
Factoize
(x - 1)(x - 2) = 0
So, we have
x = 1 and x = 2
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7 A right rectangular prism is sliced by a plane perpendicular to its bases. A right cylinder is sliced the same way. Which statement about the plane sections that result is correct?
A Both plane sections have two pairs of parallel sides.
B The plane section of the prism has only straight sides, but the plane section of the cylinder does not.
C The plane section of the prism has four right angles, but the plane section of the cylinder does not.
D Both plane sections are the same shape as the bases of the three-dimensional figures from which they resulted.
9. Which of the following functions represents a vertical shift of the function f(x) = x? a. f(x) = 2x b. f(x) = x + 5
c. f(x) = x2 d. none of the above 9.____________________
10. Which of the following functions represents a horizontal shift of the function f(x) = x2?
a. f(x) = (x+2)2 b.f(x) = 3x2
c. f(x) = x2 + 2 d. none of the above
b. f(x) = x + 5, which represents a vertical shift of 5 units upwards. f(x-a) = (x-a)^2, where a is a constant.
How to find the functions that represents a vertical shift9) The function f(x) = x represents a linear function with a slope of 1 and y-intercept of 0. To shift the graph vertically, we need to add or subtract a constant from the function. Thus, the function that represents a vertical shift of f(x) = x would be of the form f(x) = x + b, where b is a constant.
Out of the given options, the correct answer is b. f(x) = x + 5, which represents a vertical shift of 5 units upwards.
10) To shift the graph of f(x) = x^2 horizontally, we need to add or subtract a constant inside the function, affecting the position of the vertex of the parabola. Thus, the function that represents a horizontal shift of f(x) = x^2 would be of the form f(x-a) = (x-a)^2, where a is a constant.
Out of the given options, the correct answer is a. f(x) = (x+2)^2, which represents a horizontal shift of 2 units to the left.
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Solve the system of equations.
y=4x2+3x−5y=2x2+x+7
What is the sum of the y-coordinates of the solutions to the system?
Enter your answer in the box.
Answer:
37
Step-by-step explanation:
We are given the system of equations:
y = 4x^2 + 3x - 5
y = 2x^2 + x + 7
We can set the two equations equal to each other to get:
4x^2 + 3x - 5 = 2x^2 + x + 7
Simplifying, we get:
2x^2 + 2x - 12 = 0
Dividing both sides by 2, we get:
x^2 + x - 6 = 0
Factoring the left-hand side, we get:
(x + 3)(x - 2) = 0
Therefore, the solutions are x = -3 and x = 2.
To find the corresponding y-coordinates, we can plug these values of x into either of the original equations. Using the first equation, we get:
y = 4(-3)^2 + 3(-3) - 5 = 16
and
y = 4(2)^2 + 3(2) - 5 = 21
Therefore, the sum of the y-coordinates of the solutions is:
16 + 21 = 37
Answer: 37.
What is the average of the two bases in the following trapezoid in feet? 22 ft 14.75 ft 11 ft 18 ft
Answer: 18 feet.
Step-by-step explanation:
Average of bases = (22 + 14.75) / 2
Average of bases = 18.375
18.375 to the nearest tenth is = 18ft
Therefore, the average of the two bases of the trapezoid is 18 feet.
You’re planning to buy a car and you want to have $25,000 to purchase a car in cash in 5 years. If you’re able to receive 10% interest rate for investing the money, how much money should you invest today in order to have $25,000 in 5 years?
You have to invest $15,506.08
How to solve for the investmentPV = FV / (1 + r)^n
where:
PV = present value (amount of money you need to invest today)
FV = future value (amount of money you want to have in 5 years, which is $25,000)
r = interest rate (10% or 0.1)
n = number of periods (5 years)
Plugging in the values into the formula:
PV = $25,000 / (1 + 0.1)^5
PV = $25,000 / 1.61051
PV = $15,506.08
Therefore, you need to invest approximately $15,506.08 today at a 10% interest rate in order to have $25,000 in 5 years to purchase a car in cash.
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Lia deposits $100 into a savings account that earns simple interest at a rate
of 5%. If she makes no withdrawals, how much interest has Lia's savings account earned after 5 years?
A. 45
B. 25
C. 75
D. 15
Please explain. I’ll give brainly
Answer:
[tex]100( {1.05}^{5} ) = 127.63[/tex]
[tex]127.63 - 100 = 27.63[/tex]
The closest answer here is B. $25
Answer:
B is the answer of the given above question
What is the circumference of the following circle? What is the answer?
Answer:31.42
Step-by-step explanation:
C=2πr=2·π·5≈31.41593
a sample of what size would be needed to estimate a population mean to within 4 units with 95 percent confidence if the population has a standard deviation of 12?
A sample of at least 139 individuals would need to be taken to estimate the population mean to within 4 units with 95% confidence.
Understanding the Population EstimateTo estimate the sample size needed to estimate the population mean to within 4 units with 95% confidence, we can use the formula:
n = (z * σ / E)²
where:
n = sample size
z = z-score for the desired level of confidence (95% in this case), which can be found using a standard normal distribution table or calculator. For 95% confidence, the z-score is approximately 1.96.
σ = population standard deviation (12 in this case)
E = margin of error (4 in this case)
Plugging in the values, we get:
n = (1.96 * 12 / 4)²
n = 34.5744
Rounding up to the nearest whole number, we get a sample size of 35. Therefore, a sample of at least 35 individuals would need to be taken to estimate the population mean to within 4 units with 95% confidence.
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Select the correct answer.
Which set of coordinates satisfies the equations x − 2y = -1 and 2x + 3y = 12?
A.
(1, 2)
B.
(3, 1)
C.
(3, 2)
D.
(-3, -2)
E.
(3, -2)
The set of coordinates that satisfy the equation are as follows:
(2, 3)
How to solve equation?The equation given is as follows:
x - 2y = -1
2x + 3y = 12
Therefore, let's find the set of coordinates that satisfies the equation. Hence,
x - 2y = -1
2x + 3y = 12
multiply equation(i) by 2
Hence,
2x - 4y = -2
2x + 3y = 12
Therefore, subtract the equations
7y = 14
divide both sides of the equation by 7
y = 14 / 7
y = 2
Let's find x as follows
x - 2y = -1
x = -1 + 2(2)
x = -1 + 4
x = 3
Therefore, the solution is (2, 3)
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if you increase your current quality score of 85% by 7%, you will have a score of?
Answer:
90.95%
Step-by-step explanation:
85 * 0.07 = 5.95 5.95 + 85= 90.95
Answer:
The answer to your problem is, 90.95%
Step-by-step explanation:
Calculation:
In order to find the answer we need to
= Old score + New Score
= 85 + 7% of 85
= 85 + ( [tex]\frac{7}{100}[/tex] x 85 )
= 85 + ( 0.07 x 85 )
= 85 + 5.95
= 90.95
Which 90.95% is our answer.
Thus the answer to your problem is, 90.95%
One positive integer is 2 less than twice another. The sum of their squares is 260 . Find the integers.
Hence, 8 and 14 are the two positive integers as Y must be 8 because we are seeking for positive integers.
what is integers ?All entire numbers (optimistic, negative, and zero) as well as their opposites are included in the category of integers. These can be visualised as evenly spaced-apart points with zero in the middle on a number line. The following numbers are part of the set of integers, which is represented by the symbol Z . The numbers of pupils in an educational setting, the weather in degrees Celsius, or the location of an object in relation to a reference point are all examples of quantities that can be represented by integers and are counted or measured in whole units. They adhere to specific arithmetic laws and can be added, deducted, multiplied, and divided.
given
Assume that x and y are the two positive integers, with x being the greater of the two. Finally, we may convert the provided data into equations:
In order to remove x, we can replace the first equation with the second equation as follows:
[tex](2y-2)^2 + y^2 = 260[/tex]
Adding and subtracting:
[tex]4y^2 - 8y + 4 + y^2 = 260[/tex]
combining comparable phrases
[tex]5y^2 - 8y - 256 = 0[/tex]
Using the quadratic formula, we can solve this quadratic equation:
y = [8 ± sqrt(8^2 - 45(-256))] / (2*5)
y = [8 ± sqrt(3368)] / 10
y ≈ 8.6 or y ≈ -9.4
Y must be 8 because we are seeking for positive integers. The first equation can then be used to determine x:
x = 2y - 2 = 2(8) - 2 = 14
Hence, 8 and 14 are the two positive integers as Y must be 8 because we are seeking for positive integers.
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1 Place an X in the table to show the solution that makes each equation true. 6+x=15 244 X 9x = 18 x=9
Step-by-step explanation:
| Equation | Solution |
| 6+x=15 | x = 9 |
| 9x = 18 | x = 2 |
The table would look like:
| Equation | Solution |
| 6+x=15 | X |
| 9x = 18 | X |
helppp I need help pleaseeeeeee
The new matrix from an elementary row operation to get a 1, in row 1 column 1 will have:
R₁ = [1 -10 2] and R₂ = [-12 7 -13]
What is a matrix row operationRow operations are a set of operations that can be performed on the rows of a matrix in order to transform it into a row equivalent matrix, which has the same solution set as the original matrix.
The row operation R₁ - 6 — R₁ will be carried out as follows:
7 - 6 = 1 {row 1 column 1}
-4 - 6 = 5 {row column 2}
8 - 6 = -8 {row column 3}
Therefore, the resulting matrix from an elementary row operation to get a 1, in row 1 column 1 will have:
R₁ = [1 -10 2] and R₂ = [-12 7 -13]
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what is x?
a. 100
b. 120
c. 60
d. 50
Michael invests $1,000 in an account that earns a 4.75% annual percentage rate compounded continuously. Peter invests$1,200 in an account that earns a 4.25% annual percentage rate compounded continuously. Which person's account will grow to $1,800 first?
Answer:
Step-by-step explanation:
We can use the formula for continuous compounding to determine how long it will take each account to reach $1,800.
For Michael's account, the formula is:
A = P*e^(rt)
where:
A is the amount in the account after t years
P is the principal
r is the annual interest rate
t is the time in years
Plugging in the values given, we get:
1,800 = 1,000*e^(0.0475t)
Taking the natural logarithm of both sides, we get:
ln(1,800/1,000) = 0.0475t
t = ln(1,800/1,000)/0.0475
t ≈ 8.55 years
So it will take approximately 8.55 years for Michael's account to reach $1,800.
Similarly, for Peter's account, the formula is:
A = P*e^(rt)
where:
A is the amount in the account after t years
P is the principal
r is the annual interest rate
t is the time in years
Plugging in the values given, we get:
1,800 = 1,200*e^(0.0425t)
Taking the natural logarithm of both sides, we get:
ln(1,800/1,200) = 0.0425t
t = ln(1,800/1,200)/0.0425
t ≈ 9.03 years
So it will take approximately 9.03 years for Peter's account to reach $1,800.
Therefore, Michael's account will grow to $1,800 first as it will take less time (8.55 years) compared to Peter's account (9.03 years).
Please HELPP!!!!! Angles !! Marking brainliest whoever awnsers
Answer: IN ORDER FROM TOP LEFT OVER
Step-by-step explanation:
1. Example
2. Already correct
3. 43
4. 82
5. Supplementary
6. 68
7. 33
8. Adjacent (could be wrong)
9. 51
10. 128
11. 54
12. Complimentary
13. Parallel
14. 29
15. 117
HOPE THIS HELPS. I MAY HAVE GOTTEN 1 OR 2 WRONG.
I need help please
I need to answer the white box i don't know the answer
The expression of the matrix row operation is 1/4 Row 1 ⇒ Row 1
Determing the matrix row operation and expressionFrom the question, we have the following parameters that can be used in our computation:
[tex]\left[\begin{array}{cccc}-24&-24&12&20\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex] into [tex]\left[\begin{array}{cccc}-6&-6&3&5\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex]
From the above matrices, we understand that
Dividing the first row of the first matrix by 4 gives the first row of the second matrix Other corresponding row elements of the second and third rows remain unchangedThis means that
row 1 = 1/4(row 1)
This in other words means that
row 1 = (row 1)/4
When these values are evaluated, we have
[tex]\left[\begin{array}{cccc}-24&-24&12&20\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex] into [tex]\left[\begin{array}{cccc}-6&-6&3&5\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex]
This means that we replace -24, -24, 12, and 20 in row 1 with -6, -6, 3 and 5
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Alexia is cutting construction paper into rectangles for a projects. She needs to cut one rectangle that is a 9 inches x 14 1/3 inches. she needs to cut another that is 10 1/4 inches by 10 1/3 inches. How many total square inches of construction paper does Alexia need for her project?
Answer:
234.8525 square inches
Step-by-step explanation:
To find the total area of construction paper needed for the project, we need to find the area of each rectangle and add them together.
For the first rectangle, the dimensions are:
Length = 9 inches
Width = 14 1/3 inches
Area of the first rectangle = Length x Width
Area of the first rectangle = 9 inches x (43/3) inches
Area of the first rectangle = 9 inches x 14.33 inches
Area of the first rectangle = 128.97 square inches (rounded to two decimal places)
For the second rectangle, the dimensions are:
Length = 10 1/4 inches
Width = 10 1/3 inches
Area of the second rectangle = Length x Width
Area of the second rectangle = (41/4) inches x (31/3) inches
Area of the second rectangle = 10.25 inches x 10.33 inches
Area of the second rectangle = 105.8825 square inches (rounded to four decimal places)
Therefore, the total area of construction paper needed for the project is:
Total area = Area of first rectangle + Area of second rectangle
Total area = 128.97 square inches + 105.8825 square inches
Total area = 234.8525 square inches (rounded to four decimal places)
Therefore, Alexia needs a total of approximately 234.8525 square inches of construction paper for her project.
find two numbers who’s product is -9 and who’s sum is -8
Answer:
1, -9
Step-by-step explanation:
xy = -9
x + y = -8 solve this for x and substitute into the 1st equation
x = -8 - y
(-8 - y)y = -9
-y² - 8y + 9 = 0
y² + 8y -9 = 0
Solve for y by factoring:
(y - 1)(y + 9) = 0
y = 1, -9
x(1) = -9
x = -9
x(-9) = -9
x = -9/-9 = 1
PLEASE HELP ME QUICK!!!
Answer:
Option D. [tex]g(x)=5(0.8)^{x}+2[/tex]
Step-by-step explanation:
Main concepts
Concept 1: identifying horizontal asymptote
Concept 2: assuring decreasing exponential function
Concept 1. identifying horizontal asymptote
Any exponential function of the form [tex]y=a*b^x[/tex] has a horizontal asymptote on the x-axis. A constant (positive or negative) added to the end of the exponential expression will shift the graph of the exponential function up (if positive) or down (if negative) the number of units equal to the magnitude of the number. Since the original function f(x) has a "+2" at the end, it has been shifted up 2 units. Thus, we can eliminate answers A and C from feasible answers since they each shift the exponential function up 3 units, not 2.
Concept 2. assuring decreasing exponential function
Exponential functions of the form [tex]y=a*b^x[/tex] increase or decrease based on the value of "b".
If "b" is between 0 and 1 (a "small" number), the function will decrease.If "b" is larger than 1 (a "big" number), the function will increase.Observe that the graph of the function f(x) is decreasing, and the value of b=0.5.
To ensure that g(x) also decreases, the b-value must be between 0 and 1, which eliminates option B.
Option D is the correct answer because the value of "b" is between 0 and 1 (making the graph of the function a decreasing exponential), and the number added at the end is "+2", causing the horizontal asymptote to be at a height of positive 2.
what is the nearest tenth to 3.5
Answer: 3.5
Step-by-step explanation: i got it right on the quiz
Help pleasee
here is the picture is about Row Ops
The result of the carrying out the operation, Add -4(row 1) to row 3, on the given matrix is:
[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]
Reducing row matricesFrom the question, we are to perform the given row operation on the given matrix
The given matrix is:
[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\4&-1&6&-8\end{array}\right][/tex]
Now,
From the given information,
The operation we are to carry out is:
Add -4(row 1) to row 3
This means we are to multiply the first row by -4. Then, we will add the results to the corresponding elements on the third row (row)
Multiplying by -4
-4 × [ 1 2 1 | -5
-4 -8 -4 | 20
Now, we will add the result from the multiplication to the corresponding elements in row 3
Adding the results to corresponding elements in row 3
4 -1 6 | -8
+ -4 -8 -4 | 20
------------------------
0 -9 2 | 12
Hence,
The resulting matrix becomes
[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]
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Solve the inequality then list 5 numbers that fit in the solution set_,_,_,_,_ 4 - 5g > 39
The values that fit in the solution are -4, -3, -2, -1 , 0
g > - 5
How to solve the inequalityInequalities are described as expressions that are used to represent an unequal relationship between numbers or variables.
They are represented with the symbols;
< is less than> represents the greater than≥ represents the greater than or equal≤ represents the less than or equal toFrom the information given, we have that;
4 - 5g > 39
collect the like terms, we get;
-5g > 39 - 4
subtract the values
-5g > 35
Divide by the coefficient of g, we get;
g > -5
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