The journal entry to record the sale of the equipment would be:Cash $105,800,Loss on Sale of Equipment $35,650,Equipment $212,000
Accumulated Depreciation $66,000
How to solve the question?
a. To calculate the book value of the equipment at December 31 of the fifth year, we need to determine the accumulated depreciation for the first five years. The annual depreciation expense is calculated as follows:
Depreciation Expense = (Cost - Residual Value) / Useful Life
Depreciation Expense = ($212,000 - $14,000) / 15
Depreciation Expense = $13,200 per year
The accumulated depreciation for five years is therefore:
Accumulated Depreciation = Depreciation Expense x Number of Years
Accumulated Depreciation = $13,200 x 5
Accumulated Depreciation = $66,000
The book value of the equipment at December 31 of the fifth year is calculated as follows:
Book Value = Cost - Accumulated Depreciation
Book Value = $212,000 - $66,000
Book Value = $146,000
b.
To record depreciation for the three months until the sale date, we need to calculate the depreciation expense for the sixth year. The annual depreciation expense remains the same at $13,200, but since the equipment was sold on April 1, we need to prorate the depreciation for the first three months of the year.
Depreciation Expense for the Sixth Year = Depreciation Expense x (Months Remaining / 12)
Depreciation Expense for the Sixth Year = $13,200 x (9 / 12)
Depreciation Expense for the Sixth Year = $9,900
The journal entry to record depreciation for the three months until the sale date would be:
Depreciation Expense $9,900
Accumulated Depreciation $9,900
To record the sale of the equipment, we need to compare the sale price to the book value of the equipment at the time of the sale.
The book value of the equipment at the time of the sale is calculated as follows:
Book Value = Cost - Accumulated Depreciation
Book Value = $212,000 - ($13,200 x 5.25)
Book Value = $141,450
Since the sale price of $105,800 is less than the book value of $141,450, we need to record a loss on the sale of the equipment. The journal entry to record the sale of the equipment would be:
Cash $105,800
Loss on Sale of Equipment $35,650
Equipment $212,000
Accumulated Depreciation $66,000
The cash received from the sale is debited, and the difference between the sale price and the book value is recorded as a loss on the sale of the equipment. The equipment and its accumulated depreciation are removed from the books.
To know more about cost estimate visit :-
https://brainly.com/question/27993465
#SPJ1
There are three colored cookie jars. One jar is blue, another green and the last one pink. The blue jar contains 7 chocolate chip and 12 sugar cookies. The green jar contains 6 chocolate chip, 8 sugar and 5 peanut butter cookies. The pink jar contains 15 chocolate chip, 9 sugar and 13 peanut butter cookies. One of the three cookie jars is chosen at random. The probabilities that the blue jar, green jar, or pink jar will be chosen are 1⁄2 , 1⁄4 , and 1⁄4 , respectively. A cookie is then chosen at random from the chosen jar. What is the probability that the pink jar was chosen, if it is known that the cookie was a sugar cookie?
The probability that the pink can was chosen because the cookie was a sugar cookie is about 0.282, or about 28.2%.
Why do you think probability?Probability is simply how likely something is to happen. When we are uncertain about the outcome of an event, we can talk about the probability of certain outcomes - how likely they are. The analysis of events driven by probabilities is called statistics.
We can use Bayes' theorem to calculate the probability that the pink can was chosen because the cookie was a sugar cookie. Let P(P) be the probability that the pink jar was chosen, P(S) be the probability that the chosen cookie was a sugar cookie, and P(S|P) be the probability that a sugar cookie was chosen given that the pink one was chosen. Then we have:
P(P|S) = P(S|P) * P(P) / P(S)
We can calculate all these probabilities as follows:
P(S|P) = 9 / (15 9 13) = 9/37
This is the probability of choosing a sugar cookie, given that the pink can was chosen.
P(P) = 1/4
This is the probability of choosing the pink can.
To calculate P(S), we need to consider all possible options for choosing a sugar cookie. We can choose a sugar loaf from a blue, green or pink jar. So:
P(S) = P(S|B) * P(B) P(S|G) * P(G) P(S|P) * P(P)
where P(S|B) is the probability of choosing a sugar cookie from the blue jar, P(G) is the probability of choosing the green jar, and so on. We can calculate all these probabilities as follows:
P(S|B) = 12 / (7 12) = 12/19
P(S|G) = 8 / (6 8 5) = 8/19
P(S|P) = 9 / (15 9 13) = 9/37
P(B) = 1/2
P(G) = 1/4
P(P) = 1/4
So,
P(S) = (12/19) * (1/2) (8/19) * (1/4) (9/37) * (1/4) = 271/444
We can now calculate P(P|S) using Bayes' theorem:
P(P|S) = (9/37) * (1/4) / (271/444) ≈ 0.282
Therefore, the probability that the pink can was chosen because the cookie was a sugar cookie is about 0.282, or about 28.2%.
Learn more about Probability here
https://brainly.com/question/30034780
#SPJ1
What part of the proof uses the justification that angles with a combined degree measure of 90⁰ are complementary?
The justification of the angles with a combined degree measure of 90⁰ are complementary angles is proved by part 3. ∠1 is complementary to ∠2.
In the figure,
Measure of angle 1 = 40 degrees.
Measure of angle 2 = 50 degrees
Angle 2 is complementary to angle 3.
Proof of the result,
Measure of ∠1 = 40 degrees ( given )
Measure of ∠2 = 50 degrees ( given )
Measure of ∠1 + measure of ∠2 = 40° + 50°
⇒ Measure of ∠1 + measure of ∠2 = 90°
⇒ Angle 1 and angle 2 are complementary to each other.
Complementary angles are such pairs of angles whose sum is equal to 90°.
It is given that
Angle 2 is complementary to angle 3.
This implies ,
m ∠1 + m ∠2 = m ∠2 + m ∠3
⇒ m ∠1 = m ∠3
⇒ m ∠1 ≅ m ∠3
Therefore, the part 3 . ∠1 is complementary to ∠2 gives the justification for the proof of complementary angles.
learn more about complementary angles here
brainly.com/question/1882199
#SPJ1
What is the work done on an object if a force of 4 x − x 2 is applied from x = 0 to 3?
The work done on an object if a force of 4 x − x^2 is applied from x = 0 to 3 is 9J
What is the workdone?Work Done serves as the quantity of energy which is been moved by the force so that a particular energy can move howver the relation between Work and Energy can be seen as a direct one.
Give that force= 4 x − x^2 from x = 0 to 3
Work done by force , F= ∫(4 x − x^2 )dx (0-3)
F= (4x^2/2 - x^3/3)
=[2x^2 -x^3/3]
= [2*3^2 -3^3/3 - 2*0^2 -0^3/3]
18 -9= 9
9J
Learn more about work done at:
https://brainly.com/question/25573309
#SPJ1
The owners of Applewood Farmstead tracked their fruit sales over the weekend. The graph below shows the relative frequencies of the sales of each fruit. Applewood Farmstand sold a total of 320 pieces of fruit over the weekend. How many of those were apples?
Applewood Farmstand sold 102 pieces of apples over the weekend.
What is graph?Graph is a data structure which consists of nodes (vertices) that are connected with each other. Graphs are used to represent relationships between different objects, such as networks, social connections, and pathways. Graphs are useful for representing data as they can provide a visual representation that is easy to interpret, and can be used to analyse patterns in the data. Graphs can also be used to represent problems such as shortest path problems, and can be used to solve problems such as finding the most efficient route between two points.
The graph shows that apples accounted for 32% of the total fruit sales. To find the exact number of apples sold, we can calculate the following:
Apples = (320 pieces of fruit) x (0.32)
Apples = 102 pieces
Therefore, Applewood Farmstand sold 102 pieces of apples over the weekend.
To know more about graph click-
http://brainly.com/question/19040584
#SPJ1
plot 1 2/5 - 1/2 - 2 1/10 on a number line
A graph of the data set is shown in the image attached below.
What is a number line?In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
In this scenario and exercise, we would use an online graphing calculator to graphically represent the given data set on a number line as shown in the image attached below.
Read more on number line here: brainly.com/question/22515080
#SPJ1
(2a² b c³) (-a² b⁵)
pls help asap!
Answer:
-2a⁴ b⁶ c³
Step-by-step explanation:
2a² b c³ (-a² b⁵)
determine the signs for multiplication or division
-2a²bc³a²b⁵
multiply the monomials
-2a⁴b⁶c³
(then done)
Which values should be added
The missing values of h(x) to show it is a linear function are:
X=1, h(x)=3
X=3, h(x)=17
X=5, h(X)=31
So, the correct answer is (c)
What is linear function?A linear function is a mathematical relationship between two variables that produces a straight line when plotted on a graph, with a constant rate of change between them.
What is function?A function is a mathematical rule that assigns each input value to a unique output value. It can be represented graphically, algebraically, or with a table of values.
According to the given information:
To prove that h(x) is a linear function, we need to show that the difference in h(x) values between any two points is proportional to the difference in their corresponding x values.
Using the given values in the table, we can calculate the differences in h(x) values and x values:
Δh(x) = h(x) - h(x-1)
Δx = x - (x-1) = 1
Δh(x=1) = h(x=1) - h(x=0) = ? - (-4) = ?
Δh(x=3) = h(x=3) - h(x=2) = ? - 10 = ?
Δh(x=5) = h(x=5) - h(x=4) = ? - 24 = ?
If h(x) is a linear function, then the ratio of Δh(x) to Δx should be the same for all pairs of consecutive x values. We can use the given values of Δh(x=2) and Δx=1 to calculate this ratio:
Δh(x=2)/Δx = (10 - (-4))/2 = 7
We can now use this ratio to find the missing values of h(x):
Δh(x=1)/Δx = ?/1 = 7
Δh(x=3)/Δx = ?/1 = 7
Δh(x=5)/Δx = ?/1 = 7
?/1 = 7 => ? = 7
Therefore, the missing values of h(x) are:
X=1, h(x)=3
X=3, h(x)=17
X=5, h(X)=31
So, the correct answer is (c)
To know more about Function and linear function visit:
https://brainly.com/question/20286983
#SPJ1
PLSSS HELPP
This figure represents the base of a fish tank that is 8 inches high.
What is the volume of the fish tank?
Responses
378 in³
378 in³
408 in³
408 in³
480 in³
480 in³
768 in³
The volume of the fish tank is 408in³
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
The volume of regular object is given as;
V = base area × height
base area = 13 × 6
= 78in²
The area of the cut out section = 1/2(a+b) h
= 1/2 × (3+6) × 6
= 9× 3 = 27in²
The actual area of the base shown = 78-27
= 51 in²
therefore the volume of the tank will be
V = 51 × 8
= 408in³
therefore the volume of the tank is 408in³
learn more about volume from
https://brainly.com/question/27710307
#SPJ1
Simplify (m2n)3. .... that is M to the 2nd power times n in parenthesis to the 3rd power
70+15=85 125+85=210 Write into an equation.
Answer:
Brother asked a very good question.
We can write the given arithmetic expressions into equations as follows:
70 + 15 = 85
This can be written as an equation: x + 15 = 85, where x is the unknown value that needs to be determined.
125 + 85 = 210
This can be written as an equation: y + 85 = 210, where y is the unknown value that needs to be determined.
These equations can be used to solve for the unknown values x and y by performing inverse operations (such as subtraction or division) to isolate the unknown variable on one side of the equation.
100 Points! Algebra question, photo attached. Please show as much work as possible. Thank you!
Answer is down below!
Step-by-step explanation:
5 x2 =`5 xj2
Luka and Dana are making cookies for the Westland pantry. They only have up to 6 hours to bake! They can bake 32 chocolate chip cookies in an hour(x), and 20 snickerdoodle cookies in an hour(y). They need it make at least 150 cookies. Which inequality represents the situation?
Option 3. x+y≤6 , 32x + 20y ≥ 150. The inequality 32x + 20y ≥ 150 ensures that they bake enough cookies to meet the requirement of making at least 150 cookies.
The right disparity that addresses what is happening is:
32x + 20y ≥ 150
To see the reason why, we want to consider the quantity of treats Luka and Dana can heat in every hour and the all out number of hours they need to prepare. We should expect they have H hours to prepare, where H = 6 for this situation.
Luka and Dana can prepare 32 chocolate chip treats in 60 minutes, so they can heat a sum of 32x treats in x hours. Likewise, they can prepare a sum of 20y snickerdoodle treats in y hours. To make no less than 150 treats, they need to prepare a mix of chocolate chip and snickerdoodle treats in every hour, with the end goal that the complete number of treats they make in H hours is something like 150.
Thus, the imbalance 32x + 20y ≥ 150 guarantees that they heat an adequate number of treats to meet the necessity of making somewhere around 150 treats.
To learn more about inequality, refer:
https://brainly.com/question/21746543
#SPJ1
Barry buys a plot of land that measures 1/4 acre. He divides the plot into 3 equal pieces
The calculated area of each piece is 1/12 acre
Calculating the area of each pieceIf Barry buys a plot of land that measures 1/4 acre, then the total area of the land is 1/4 acre.
If he divides the land into 3 equal pieces, then each piece will have 1/3 of the total area.
So the area of each piece will be:
Area of each piece = (1/3) x (1/4) acre
Multiplying the fractions, we get:
Area of each piece = 1/12 acre
Therefore, each piece of land will have an area of 1/12 acre.
Read more about area at
https://brainly.com/question/24487155
#SPJ1
Point B has coordinates (1,2). The x-coordinate of point A is -11. The distance between point A and point B is 15 units. What are the possible coordinates of point A?
Answer:
We know that the x-coordinate of point A is -11, and that the distance between point A and point B is 15 units. Let's call the y-coordinate of point A "y". Then we can use the distance formula to find the two possible values of y:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1,y1) = (-11,y) is the coordinates of point A, and (x2,y2) = (1,2) is the coordinates of point B. Substituting the values, we get:
15 = sqrt((-11 - 1)^2 + (y - 2)^2)
15 = sqrt(144 + (y - 2)^2)
15^2 = 144 + (y - 2)^2
225 = 144 + (y - 2)^2
81 = (y - 2)^2
y - 2 = ±9
y = 2 ± 9
So the possible coordinates of point A are (-11,11) and (-11,-7).
A digital thermometer in Olivia's car says the temperature outside is –5°C. Which statement BEST describes the meaning of the value –5 in this context?
The value -5°C represents the temperature outside as measured by the digital thermometer in Olivia's car.
Which statement describes the meaning of the valueIn this context, the value -5 represents the temperature outside in Celsius degrees.
The minus sign indicates that the temperature is below freezing point. The Celsius scale is a temperature scale that uses the freezing point of water (0°C) and the boiling point of water (100°C) at standard atmospheric pressure as its reference points.
Thus, a temperature of -5°C means that it is five degrees Celsius below the freezing point of water.
The negative sign indicates that the temperature is below zero degrees Celsius, which is the freezing point of water.
Read more about expression at
https://brainly.com/question/15775046
#SPJ1
100 Points!!! Determine if the equation (2x²+y²)²=(2x²-y²)²+(2xy√2)² is a polynomial identity. Photo attached. Please show as much work as possible. Thank you!
Answer:
Yes, it is a polynomial identity (work below).
Step-by-step explanation:
Let's start by expanding the left side of the equation.
[tex](2x^2+y^2)^2=\\4x^4+y^4+4x^2y^2[/tex]
Now, let's expand the second side.
[tex](2x^2-y^2)^2+(2xy\sqrt{2} )^2=\\4x^4+y^4-4x^2y^2+4x^2y^2(2)=\\4x^4+y^4-4x^2y^2+8x^2y^2[/tex]
There are no like terms on the left side, so let's combine the like terms on the right side.
[tex]4x^4+y^4-4x^2y^2+8x^2y^2=\\4x^4+y^4+4x^2y^2[/tex]
Now, let's check if the left and right sides are equal:
[tex]4x^4+y^4+4x^2y^2= 4x^2+y^4+4x^2y^2[/tex]
Both sides are the same. Thus, the equation is a polynomial identity.
. The formula 9x - 5y = -160 relates the
temperature in degrees Fahrenheit y to
the temperature in degrees Celsius x.
Tell whether the relationship is a direct
variation. Explain your answer.
Answer: formula 9x - 5y = -160 is not a direct variation.
Step-by-step explanation: The provided expression, 9x - 5y = -160, does not exemplify direct variation.
Direct variation is a correlation existing between two variables, wherein one is a constant scalar multiple of the other. Stated differently, should one variable increase by a defined magnitude, the corresponding variable will also experience a commensurate increase of identical magnitude.
The formula provided indicates the absence of a constant proportionality between the temperature in degrees Celsius (x) and the temperature in degrees Fahrenheit (y). It is noteworthy that the correlation amidst the variables x and y is non-linear in nature, thereby precluding its representation in the form of a direct proportionality.
Answer: It is not a direct variation.
Step-by-step explanation:
While a linear equation is a direct variation, the y-intercept of a direct variation relationship must be 0. Here, that is not the case. Let us manipulate this equation into a slope-intercept equation.
Given:
9x - 5y = -160
Add 5y and 160 to both sides of the equation:
5y = 9x + 160
Divide both sides of the equation by 5:
y = [tex]\frac{9}{5}[/tex]x + 32
32 ≠ 0
Find the percent of increase. Round to the nearest tenth.
125 to 240
A. 104.0%
B. 92.0%
C. 115.0%
D. 143.8%
x^2+16=(x+4)^2 true or false?
Answer:
False
Step-by-step explanation:
(x+4)^2 = x^2 + 8x + 16
A laptop has a listed price of 639.99 before tax. If the sales tax rate is 9.75%, find the total cost of the laptop with sales tax included. Round your answer to the nearest cent, if necessary.
Answer: $702.39
Step-by-step explanation: To find the total cost of the laptop with sales tax included, we need to add the sales tax to the listed price.
First, we need to calculate the amount of sales tax.
Sales tax = 9.75% of 639.99
Sales tax = 0.0975 x 639.99
Sales tax = 62.40
Now we can find the total cost of the laptop with sales tax included:
Total cost = listed price + sales tax
Total cost = 639.99 + 62.40
Total cost = 702.39
Therefore, the total cost of the laptop with sales tax included is $702.39.
In •A find CE if BA=7.35.
The value of CE is 14.7 units.
What if the diameter of a circle?The diameter of a given circle is a straight line which passes through the center of the circle and divides it into two equal semi-circles.
So that in the given circle with center A, we have;
CE = BD (diameter of a given circle)
BA = EA = CA = DA (radius of a given circle)
CE is the diameter of the circle, and BA is the radius, so that;
CE = 2*BA
= 2*7.35
= 14.7
CE = 14.7
Learn more about the diameter of a circle at https://brainly.com/question/28162977
#SPJ1
What is the numerical coefficient in the expression 2x³y?
Answer:
2
Step-by-step explanation:
The numerical coefficient is the number that is multiplied to a variable.
Example.
2x^2 + 7y^3
The numerical coefficients would be 2 and 7.
So for your problem it would be 2 since 2 is the number being multiplied to x and y.
a rectangular prism is 12 units high and 5 units wide an 10 units long
Answer:
To find the surface area of a rectangular prism, we can use the formula:
Surface Area = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the rectangular prism, respectively.
Given that the rectangular prism is 12 units high, 5 units wide, and 10 units long, we can substitute these values into the formula:
Surface Area = 2(10)(5) + 2(10)(12) + 2(5)(12)
Surface Area = 100 + 240 + 120
Surface Area = 460 square units
Therefore, the surface area of the rectangular prism is 460 square units
How much property tax must be paid
each month when the property tax is
$1,176 a year?
Answer:
$98 a month
Step-by-step explanation:
1,176 divided by 12
please help me
a!!!!!!!!
Answer:
Step-by-step explanation:
Hopefully this is right.
Area = r²
Which is pi times the the radius squared
The radius is 2, so 2² is 4, So we multiply 3.14, which is pi, by 4.
Multiply 3.14 by 4, and the answer is 12.56, the question says round to the nearest tenth, so the final answer will be 12.6
My math teacher back in 7th grade gave us this sentence to help us memorize the equations.
Cherry Pie Delicious (C=d), Apple Pie Are Too (A=r²)
Do the same with the other two questions, and the answer for question two will be 3.14, rounded to the nearest tenth will be 3.1
Hope this helps!
For a circle with a radius of 2, the area can be calculated using the formula:
Area = π x r^2
where π is approximately 3.14 and r is the radius.
Plugging in the values, we get:
Area = 3.14 x 2^2
Area = 3.14 x 4
Area = 12.56
Rounding to the nearest tenth, we get:
Area ≈ 12.6
Therefore, the area of the circle with radius 2 is approximately 12.6.
For a circle with a radius of 1, the area can be calculated using the same formula:
Area = π x r^2
Plugging in the values, we get:
Area = 3.14 x 1^2
Area = 3.14
Rounding to the nearest tenth, we get:
Area ≈ 3.1
Therefore, the area of the circle with radius 1 is approximately 3.1.
7x³+5x² - 2 = [?]
X = -1
An engine does 62 J of work each cycle as it absorbs 2 times as much heat as it discharges to the environment. A) Determine the efficiency of the engine in percent. B) What quantity of heat is discharged to the environment each cycle in Joules?
Answer:
A) 150%
B) 20.67 J
Step-by-step explanation:
A) To determine the efficiency of the engine, we can use the formula:
efficiency = (work output / heat input) x 100%
In this case, the engine does 62 J of work each cycle, so the work output is 62 J. We're also given that the engine absorbs 2 times as much heat as it discharges to the environment, so we can express the heat input as 2 times the heat discharged:
heat input = 2 x heat discharged
Therefore, we can rewrite the efficiency formula as:
efficiency = (62 J / (2 x heat discharged)) x 100%
Simplifying this expression, we get:
efficiency = 31 J / heat discharged
Now we need to determine the value of heat discharged. We know that the engine absorbs 2 times as much heat as it discharges, so the net heat input is 3 times the heat discharged:
net heat input = heat input - heat discharged = 2 x heat discharged - heat discharged = heat discharged
Therefore, we can express the net heat input as:
net heat input = 3 x heat discharged
Now we can use the first law of thermodynamics, which states that the net heat input is equal to the work output plus the heat discharged:
net heat input = work output + heat discharged
Substituting the given values, we get:
3 x heat discharged = 62 J + heat discharged
Solving for heat discharged, we get:
heat discharged = 20.67 J
Now we can calculate the efficiency:
efficiency = 31 J / 20.67 J = 1.50 or 150%
Therefore, the efficiency of the engine is 150%.
B) To determine the quantity of heat discharged to the environment each cycle in Joules, we can use the value we calculated above for heat discharged:
heat discharged = 20.67 J
Therefore, the quantity of heat discharged to the environment each cycle is 20.67 J.
Hope this helps!
The top three prices for works of art sold at auction in 2013 totaled $308.0 million. These three works of art were a sculpture, a painting, and a photograph. The selling price of the painting was $49.4 million more than that of the photograph. Together, the painting and the photograph sold for $24.4 million more than the sculpture. What was the selling price of each work?
The selling prices of the sculpture, painting, and photograph were 166.5 million, 107.0 million, and 57.6 million respectively.
How to Determine the Selling Price?Let's call the selling prices of the sculpture, painting, and photograph as S, P, and Ph respectively.
From the first sentence, we know that:
S + P + Ph = 308.0 million
From the second sentence, we know that:
P = Ph + 49.4 million
And from the third sentence, we know that:
P + Ph = S + 24.4 million
Now we can substitute the second equation into the third equation:
(Ph + 49.4 million) + Ph = S + 24.4 million
Simplifying:
2Ph + 49.4 million = S + 24.4 million
2Ph = S - 25 million
Substituting this into the first equation:
S + P + Ph = 308.0 million
S + (Ph + 49.4 million) + Ph = 308.0 million
2Ph + S = 258.6 million
Now we can substitute the equation we derived earlier:
S + 2Ph - 49.4 million = 258.6 million
S + 2Ph = 308.0 million
Substituting 2Ph = S - 25 million:
S + S - 25 million = 308.0 million
2S = 333.0 million
S = 166.5 million
Now we can use this value to find P and Ph:
P = Ph + 49.4 million
P + Ph = S + 24.4 million
Substituting S = 166.5 million in both equations:
P + Ph = 190.9 million
P = Ph + 49.4 million
Solving these two equations simultaneously:
Ph = 57.6 million
P = 107.0 million
Learn more about selling price on:
https://brainly.com/question/26008313
#SPJ1
< ^2 − 3
^2 ≥ x^2/2 -12
Is this a system of linear inequalities?
The linear inequalities in the given graph is y ≥ x/2 -1 and y< -1/2x -3.
What is Linear inequalities ?Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. These quantities may be numerical, algebraic, or a combination of the two.
Here, we have,
The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities. A linear inequality has the same appearance as a linear equation, but uses a different symbol to link the two expressions.
we have,
In the given graph, the area above solid line,
points, (-2 , -2) , (0 , -1)
slope = 1/2
so, y ≥ x/2 -1
The area below dashed line ,
points, (-2 ,-2) , (0 ,-3)
slope= -1/2
so, y< -1/2x -3.
To know more about linear inequalities, visit:
brainly.com/question/28971384
#SPJ1
One cubic foot of a crushed mineral weighs 150 pounds. How many pounds of the crushed mineral can a container with the dimensions shown hold?
Therefore , the solution of the given problem of volume comes out to be 4500 pounds of the crushed mineral can fit inside the container.
What exactly does volume mean?The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Litre and in3 are the symbols for cubic measurements. However, in order to determine an object's dimensions, you must be aware of its volume. It's common practise to translate an object's weight onto metric units like kilogrammes.
Here,
We must first determine the container's volume, then multiply it by the crushed mineral's weight per cubic foot.
The container's measurements in the image are as follows:
=> 5 feet in length
=> Size: 3 feet wide
=> Height is two feet.
The following formula determines the container's volume:
=> Volume = length* width*height
Inserting the values:
=> 5 feet * 3 feet * 2 feet = volume.
=> 30 cubic feet is the volume.
=> Volume of container x Weight per cubic foot = Weight of crushed mineral
=> Weight of crushed mineral = 30 cubic feet x 150 pounds/cubic foot
=> The crushed mineral weighs 4500 pounds.
Therefore, 4500 pounds of the crushed mineral can fit inside the container.
To know more about volume , visit:
https://brainly.com/question/13338592
#SPJ1