Answer:
2d=90
d=45
Explanation: Complementary angles add up to 90 degrees. If the two angles are congruent, it means that both angles have the same measurements.
Write the following expression using the fewest possible terms.
(−5x − 12) + (14 + 7x)
2x + (−2)
2x + 2
17x + (−26)
17x + 26
The expression which can be used to represent the given using the fewest possible terms is 2x + 2
The correct answer choice is option B.
How to write expression using fewest possible terms?(−5x − 12) + (14 + 7x)
open parenthesis
-5x - 12 + 14 + 7x
collect like terms
-5x + 7x - 12 + 14
2x + 2
In conclusion, 2x + 2 is the expression which represents the fewest possible terms of (−5x − 12) + (14 + 7x)
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Answer:
its C
Step-by-step explanation:
other guy wasn't reasonable and chose the actual shortest one possible instead of the one that made sense
∠X and ∠Y are supplementary angles. The measure of ∠X=3n−18 . The measure of ∠Y=2n−27
The measure of the supplementary angles is:
∠X = 117°
∠Y = 63°
How to find the measures of the angles?Here we know that angles ∠X and ∠Y are supplementary angles. Remember that two angles are supplementary if their measures add up to 180°.
Here we know that the measures are:
∠X = 3n − 18
∠Y = 2n − 27
We can write:
∠X + ∠Y = 180°
(3n - 18) + (2n - 27) = 180
Then we can solve that for n.
3n + 2n - 18 - 27 = 180
5n = 180 + 45
n = 225/5 = 45
Then the measures of tha angles are:
∠X = 3n − 18 = 3*45 - 18 = 117°
∠Y = 2n − 27 = 2*45 - 27 = 63°
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A store buys 15 sweaters for $90 and sells them for $405. If p represents the total profit in dollars and cents when the store buys any number of sweaters, s, write a proportional equation for p in terms of s that matches the context.
If p represents the total profit in dollars and cents when the store buys any number of sweaters, s, then the proportional equation for p in terms of s is, p = $21 x s
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Let's call the selling price of each sweater "sp".
The store buys 15 sweaters for $90, so each sweater must cost
=$90 / 15
= $6
The store sells each sweater for
= $405 / 15
= $27,
so sp = $27
The total profit is equal to the selling price minus the buying price, so the equation for the total profit, p, in terms of the number of sweaters sold, s, is:
p = sp x s - $6 x s
We can simplify this equation to:
p = ($27 - $6) x s
p = $21 x s
So, the proportional equation for the total profit in dollars and cents when the store buys any number of sweaters, s, is:
p = $21 x s
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Task 1 Table, Equation, and Evaluate
Mo takes potato salad with her when she goes camping but doesn’t pack it in a cooler. When she sits down to eat, it has been at 75 ⁰F for 6 hours. At that warmer temperature the bacteria Salmonella in the potato salad reproduces quickly, with an exponential growth rate of 8.
Assume Mo’s potato salad starts in the first hour with one single bacterium and grows exponentially. Make a table of values showing the number of bacteria that will be present after each hour for the first six hours using the exponential hourly growth rate of 8.
Hours
0
1
2
3
4
5
6
Bacteria Count
1
8
16
32
96
480
2,880
Write the equation that models the Bacteria Count as a function of Hours with the growth rate of 8. Remember that for exponential growth y = a(b)x where a is the starting value and b is the growth rate.
Evaluate - what is the Bacterial Count for Mo’s potato salad after 6 hours?
Task 2 Graph
Graph your equation from Task 1b. Your graph must include:
A title
Labels for your x and y axis
An x and y axis scale that allows the data from the table to be shown in the graph
The bacterial count at 6 hours marked and labeled
Graph Submission: You may create the graph in any format you are comfortable with and can easily submit to me as long as the requirements listed in the task are met. Some format options include...
Desmos, one screenshot with title, equation, point and graph in the picture.
Desmos, Share Graph (top right) and copy the link for the graph. Then paste the link into your portfolio submission. Or export it, but then add your title in the portfolio.
Graph paper (NOT notebook paper), take a pic and submit. This is actually very tricky because of the numbers involved in exponential equations so please be accurate with your axes steps
Any other free graphing app, site or software you can easily access that will let you create graphs you can download, screen shot or take a pic of. But you must include information listed in above rubric
The amounts of bacteria are given as follows:
Hour 0: 1 bacteria.Hour 1: 8 bacteria.Hour 2: 64 bacteria.Hour 3: 512 bacteria.Hour 4: 4096 bacteria.Hour 5: 32768 bacteria.Hour 6: 262144 bacteria.The exponential function y = 8^x is graphed by the image presented at the end of the answer.
How to define the exponential function?An exponential function is defined as follows:
y = ab^x.
In which:
a is the initial value.b is the rate of change.The parameters for this problem are given as follows:
a = 1 -> initial number of bacteria.b = 8 -> number of bacteria is multiplied by 8 each hour.Hence the function is defined as follows:
y = 8^x.
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You are making a sand art bottle. You
Fill 1/6 of the bottle with pink sand ,3/6 with red sand, and 2/6 with white sand. How
much of the bottle is filled?
The amount of the bottle that is filled with sand is; The whole bottle is full of sand
How to solve Fraction Word Problems?When talking about fraction word problems we are simply referring to fraction parameters being represented in the form of word problems.
The parameters given are;
Fraction with pink sand = 1/6
Fraction with red sand = 3/6
Fraction with white sand = 2/6
Thus;
Total sand = 1/6 + 2/6 + 3/6
= 6/6 = 1
Thus, the bottle will be full
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A right circular cylinder has a volume of 10 cubic centimeters. a new right circular cylinder is created by increasing both the radius and the height of the original cylinder by a factor of 4. what is the volume of the new cylinder?
The new volume of the cylinder is 39.94cm³
What is volume of a cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder.
The volume of a cylinder is expressed as V = πr²h
The volume of the original cylinder = 10cm³
The radius and height of the new cylinder = 4r and 4h
10 = 3.14 × r²h
V 2= 3.14 × 4r²4h
V2 = 3.14× 4( r²h)
10=3.14 × r²h
r²h = 10/3.14
r²h = 3.18
from
V2 = 3.14 × 4(r²h)
represent 3.18 by r²h in the equation
V2 = 3.14 × 4 ( 3.18)
V2 = 39.94cm³
therefore the volume of the new cylinder is 39.94 cm³
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3 A zoo keeper thinks there may be a problem with the Mole Rat population at the zoo. He starts keeping track of the animals in the tunnels. 7 days into his monitoring he counts 120 mole rats, 13 days in he counts 108.
Independent Quantity:
dependent quantity:
I NEED HELP
The independent quantity is the number of days into the monitoring and the dependent quantity is the number of mole rats counted.
What is an independent quantity?The independent quantity refers to a variable that is not influenced by any other factor and can be changed freely in an experiment or study.
In this case, the number of days into the monitoring is the independent quantity because it can be varied at the discretion of the zoo keeper.
The dependent quantity, on the other hand, is a variable that depends on the independent quantity and is affected by changes in it.
In this case, the number of mole rats counted is the dependent quantity because it is determined by the number of days into the monitoring. The zoo keeper counts a different number of mole rats based on how many days have passed, which is determined by the independent quantity.
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A zoo keeper thinks there is a problem with the Mole-Rat population at the zoo. He starts keeping track of the animals in the tunnels. 7 days into his monitoring he counts 120 mole rats, 13 days in he counts 108.
what information is provided?
why does it require less work to raise one end of a log to shoulder height than to raise the whole log to the same height?
Work is defined as the product of force and distance, and can be calculated using the equation W = F * d, where W is work, F is force, and d is distance.
When lifting the whole log, the force required is equal to the weight of the log, and the distance over which the force is applied is the distance from the ground to the height of the shoulder.
When lifting one end of the log, the force required is still equal to the weight of the log, but the distance over which the force is applied is reduced. This is because the lever arm (the distance from the axis of rotation, which is the shoulder joint, to the point where the force is applied, which is the end of the log) is reduced.
So the equation for work done in lifting the whole log would be W = m * g * h, where m is the mass of the log, g is the acceleration due to gravity, and h is the height from the ground to the shoulder. The equation for work done in lifting one end of the log would be W = (m/2) * g * h', where h' is the reduced height.
It can be seen that the work done in lifting one end of the log is equal to half the work done in lifting the whole log, because the force applied is the same, but the distance over which it is applied is reduced.
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Liam opened a savings account and deposited $6000. The account earns 5% percent in interest annually. He makes no further deposits and does not withdraw any money.
What is the initial value?
Answer: $6000
Step-by-step explanation:
The initial value will be what the person deposits before the interest. Because Liam deposited $6000 the initial value would be $6000.
Hope this helps!
ve the following problems.
ven: AAFD,
m/F=90°,
AD = 14,
mZD=30°
d: Area of AAFD
A
F
D
W
If ∆AFD, m ∠F = 90° AD = 14, m ∠D = 30° .The Area of ∆AFD is 49 square units.
What is area?To find the area of triangle AFD, we can use the formula for the area of a triangle given its base and height. In this case, the base is AD, and the height can be found by constructing an altitude from F to AD.
First, we will find the length of FD. Since m ∠D = 30°, we can use the trigonometric function sine to find the length of FD. Using the sine formula:
FD = AD * sin(∠D) = 14 * sin(30°) = 14 * 1/2 = 7
Next, we will find the length of A.F. Since m ∠F = 90°, FD is the height of the triangle. So, the area of triangle AFD is given by:
Area = (AD * FD) / 2 = (14 * 7) / 2 = 49 square units
Therefore the area of ∆AFD is 49 square units.
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A product is currently made in a process-focused shop, where fixed costs are $9000 per year and variable cost is $50 per unit. The firm is considering a fundamental shift in process, to repetitive manufacture. The new process would have fixed costs of $90,000, and variable costs of $5. What is the crossover point for these processes?
Every year, 1800 units crossover point. The process focus is less expensive for volumes over 1800.
What is the crossover point?When all tax credits have been used up by a limited partnership and the limited partners are left with a tax burden, that moment is known as the crossover point.
When both projects have positive values, the crossover point is formed by the intersection of two IRR curves.
The weighted average cost of capital, also known as the crossover rate, is the rate of return at which the net present values (NPV) of two projects are equal.
The rate of return at which the net present value profiles of two projects cross each other is what this term denotes.
So, annual crossover sales are 1800 units.
Process emphasis is less expensive and less important for volumes under 1800 units; repeated manufacturing concentration is less expensive and less important for volumes exceeding 1800 units.
Fixed cost ÷ variable cost
$90000÷50 =$1800
$9,000÷5=$1800
Therefore, every year, 1800 units cross over. The process focus is less expensive for volumes over 1800.
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Correct question:
A product is currently made in a process-focused shop, where fixed costs are $9,000 per year and variable costs are $50 per unit. The firm is considering a fundamental shift in process, to repetitive manufacturing. The new process would have fixed costs of $90,000, and variable costs of $5. The cross over is at 1800 units annually. for volumes over 1800, the process focus is cheaper.
During the ceremony, a printing
company received a very large order to
carry out the production of campaign
material. It was estimated that the 3
machines would take 24 hours to
perform the entire service. Assuming
that one of these machines breaks
down before starting the service, how
long will it take to meet this demand?
If one of the three machines breaks down before starting the service, it would take the remaining two machines longer to meet the demand. If each machine can produce the same amount of material, it would take each machine 24 hours / 3 machines = 8 hours to perform the entire service.
So, with two machines working, it would take each machine 8 hours / 2 machines = 4 hours to complete the job. Thus, the total time to meet the demand would be 4 hours * 2 machines = 8 hours.
find the parametric equation of the line through a parallel to b, using t as the parameter!
The parametric equations of a line can be determined using a point on the line and a direction vector. To find the parametric equation of a line that passes through a point A and is parallel to a direction vector b, we can use the following formula:
x = x0 + tbx
y = y0 + tby
z = z0 + tbz
where (x0, y0, z0) is the position vector of point A, (bx, by, bz) is the direction vector, and t is the parameter that varies along the line.
What is equation?An algebraic equation, also known as a polynomial equation, is a mathematical equation of the form P=0, where P is a polynomial with coefficients in some field, most commonly the field of rational numbers. An algebraic equation is a mathematical statement that sets two expressions equal to each other. An algebraic equation is typically made up of a variable, coefficients, and constants.
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the length of a rectangle is six inches more than eight times the width. the perimeter is 120 inches. find the length and width.
The length and width of a rectangle are 36cm and 4.5cm
Finding the Width:
The formula to find the perimeter of the rectangle is:
P=2(l+w),
where P is the perimeter, l be the length, and w be the width.
Now substitute the given values to solve for w, since we need to find the width.
The given information is:
the length of a rectangle is six inches more than eight times the width so the equation becomes:
L=8w+6
P=120
w=8w
now plug the values in the above formula:
P=2(l+w),
120=2(8w+6)+8w
120=16w+12+8w
120=24w+12
24w=108
w=4.5
To find the length just substitute in the L.
L=8(4.5)+6
L=30+6
L=36
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use pictures,numbers, or words to explain how you can use the adding-on strategy to find the difference 120.45-116.9. What is the difference?
The difference 120.45-116.9 is 3.55.
What is subtraction?Subtraction is a mathematic operation. Which is used to remove terms or objects in an expression.
Given:
The two decimal numbers,
120.45 and 116.9.
Applying subtraction operation,
the difference 120.45-116.9.
By adding on strategy,
116.9 is 3.55 left to the number 120.45 on the number line.
That means,
116.9 + 3.55 = 120.45.
Therefore, the difference is 3.55.
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PLS HELP ASAP I NEED IT PLS PLS PLS
I WILL MARK BRAINLIST AND SET THIS 100 POINTS BUT PLS ANSWER CORRECTLY.THIS IS GRADED OUT OF 100% I need 80% to pass for an A- PLS YALL!
Answer:
x=105
Step-by-step explanation:
The angles of a triangle add up to 180 degrees.
[tex]180 = 30 +45+x[/tex]
[tex]x=105[/tex]
Solve for arc x
Thxs and hurry
The value of arc x is solved to be 120 degrees
How to find the value of arc xThe Arc x is solved using the knowledge of linear pair
A linear pair of angles forms a straight line, and the two angles are said to be "linear" because they are next to each other and their measures add up to 180 degrees.
Applying this we have that
60 + x = 180
x = 180 - 60
x = 120 degrees
hence we can say that x is 120 degrees
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What is the lateral surface area of the rectangular prism below?
72 cm²
3 * ( 6+2+2) + 2 * (2 * 6) + 6 * 3
For each ordered pair, determine whether it is a solution to 2x+7y=-5.
The correct options of the solution of the equation 2x+7y=-5 is (a) -6,1 and (c) 8,-3.
What is called equation?In mathematics, two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign.
In order to determine whether an ordered pair is a solution, all we have to do is plug in the values of x and y and see if we end up with a true statement.
(a) for (-6, 1)
put the value of 1 for y and -6 for x:
2(-6)+7(1)=-5
-12+7=-5
-5=-5
Yes! Here we have a true statement. Therefore, this ordered pair is a solution.
(b) for (9, 2)
put the value of 2 for y and 9 for x:
2(9)+7(2)=-5
18+14=-5
32≠-5
Well, we can see that we have a false statement, because ≠ means "not equal to". Therefore, this ordered pair is not a solution.
(c) for (8, -3)
put the value of -3 for y and 8 for x:
2(8)+7(-3)=-5
16-21=-5
-5=-5
Yes! Here we have a true statement. Therefore, this ordered pair is a solution.
Let's try the last option.
(d) for (-5, -4)
put the value of -4 for y and -5 for x:
2(-5)+7(-4)=-5
-10-28=-5
-38≠-5
Well, we can see that we have a false statement, because ≠ means "not equal to". Therefore, this ordered pair is not a solution.
Hence, the correct options of the solution of the equation 2x+7y=-5 is (a) -6,1 and (c) 8,-3.
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How much of a radioactive kind of neodymium will be left after 44 days if the half-life is
11 days and you start with 120 grams?
There will be left 7.5 grams of the radioactive kind of neodymium after 44 days, with half life of 11 days.
What is half life?Half-life is the time required for a quantity to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential decay.
Given that, a radioactive kind of neodymium have the half-life is 11 days, and with 120 grams
We need to find the remaining after 44 days,
The formula to calculate half life =
[tex]N(t) = N(1/2)^\frac{t}{t_{1/2} }[/tex]
N(t) = quantity of the substance remaining
N = initial quantity of the substance
t = time elapsed
t{1/2} = half life of the substance
N(t) = 120(1/2)⁴⁴/₁₁
= 120(1/2)⁴
= 120(1/16)
= 7.5
Hence, there will be left 7.5 grams of the radioactive kind of neodymium after 44 days, with half life of 11 days.
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Find 3 ratios that are equivalent to the given ratio 7 over 6
Question 8(Multiple Choice Worth 1 points)
(04.07 LC)
Data were collected and showed an increase in ice cream sales as the weather gets warmer.
Which of the following best describes this situation?
Based on the data, this is an example of correlation and causation.
Based on the data, this is an example of correlation.
Based on the data, this is an example of causation.
Based on the data, this is not an example of causation or correlation.
Based on the data of increase in ice cream sales as the weather gets warmer the data is
B. Based on the data, this is an example of correlation.What is correlation?A statistical measure known as correlation expresses how linearly connected two variables are (meaning they change together at a constant rate). It is frequently used to describe straightforward relationships without explicitly stating cause and effect.
In this case, the data shows a relationship between the weather (one variable) getting warmer and an increase in ice cream sales (another variable). However, just because two variables are correlated does not necessarily mean that one causes the other.
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Write the slope-intercept form of the line containing the
point (5, −3) and is parallel to: = − 2/5 − 3/4
The slope-intercept form of the line containing the point (5, −3) and is parallel to y = − 2/5x − 3/4 is y = -2/5x - 1.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given, line containing the point (5, −3) and is parallel to: y = − 2/5x − 3/4
The slope-intercept form of the equation of a line
y=mx+b,
where m is the slope
b is the y-intercept
In our case Line is parallel to the Line y = − 2/5x − 3/4,
So the slope would be the same.
m = -2/5
Thus, the equation of the line:
y = -2/5x + b
Since the line passes through the point (5, -3)
-3 = -2/5 * 5 + b
b = -1
Thus the final equation of a line:
y = -2/5x - 1
Therefore, The slope-intercept form of the line containing the point (5, −3) and is parallel to y = − 2/5x − 3/4 is y = -2/5x - 1.
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Helpppppp pleaseeeee !!!
Based on each given quadrilateral, we know that:
Rectangle ABCD has:
DC = 12BC = 5DE = 6.5∠DBA = 35°∠DAC = 55°∠DEC = 110°∠CEB = 70°Rhombus FGHJ:
∠JGH = 120°∠FJH = 120°∠KFG = 30°GH = 10KG = 5F.K = 5√3FH = 10√3Square LMNO:
∠OMN = 45°PM = 8LN = 16∠OPL = 90°Let's discuss each quadrilateral we have:
ABCD is a rectangle; then:
AD // BC and AD = BCAB // CD and AB = CDAC = BD but not perpendicular to each otherAC bisects BDDC = AB = 12
BD² = BC² + CD²
13² = BC² + 12²
169 = BC² + 144
BC² = 25
BC = 5
DE = 1/2 BD
DE = 1/2 (13)
DE = 6.5
∠DBA and ∠BDC are alternate interior angles and congruent, then:
∠DBA = ∠BDC = 35°
∠DBA = ∠BAC because triangle BAE is isosceles triangle.
∠BAC is the alternate interior angle of ∠DCA; then:
∠BAC = ∠DCA = 35°
∠DAB = ∠DAC + ∠BAC
90° = ∠DAC + 35°
∠DAC = 55°
Focus on triangle DEC:
∠DEC + ∠EDC + ∠ECD = 180°
∠DEC + 35° + 35° = 180°
∠DEC = 110°
Focus on triangle CEB:
∠CEB + ∠EBC + ∠CBE = 180°
∠CEB + 55° + 55° = 180°
∠CEB = 70°
FGHJ is a rhombus; then:
All sides share the same lengthIts diagonals are perpendicular and bisect each otherIts diagonals bisect its respective anglesHave 2 pairs of opposite angles and congruentThe sum of angles is 360°∠JGH = ∠FJH = 2∠FJG
∠JGH = ∠FJH = 2(60)
∠JGH = ∠FJH = 120°
Since FGHJ is a rhombus, then:
∠JGH + ∠JHG + ∠FGH + ∠JFG = 360°
120° + ∠JHG + 120° + ∠JGH = 360°
240° + 2∠JHG = 360°
2∠JHG = 120°
∠JHG = 60°
∠KFG = 1/2∠JHG
∠KFG = 1/2 (60)
∠KFG = 30°
GH = FG = 10
To find KG, we need to focus on triangle F.KG. Under the Sines Law:
KG / sin 30 = FG / sin 90 = F.K / sin 60
KG / √3/2 = 10 / 1 = F.K / 1/2
KG = 5
F.K = 5√3
FH = 2F.K
FH = 2(5√3)
FH = 10√3
LMNO is a square, then:
All sides share the same lengthBoth diagonals are perpendicular and bisect each otherBoth diagonals share the same lengthAll diagonals bisect its respective anglesThe sum of angles is 360°All sides angle are 90°∠OMN = 45°
Please focus on triangle MNP. Under the Sines Law:
PM / sin 45 = MN / sin 90
PM / √2/2 = 8√2 / 1
PM = 8
LN = 2PM
LN = 2(8)
LN = 16
∠OPL = 90°
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a woman is traveling in her car at 25 miles per hour. how far will that woman travel in thirty minutes? (distance
In 30 minutes, the woman will travel 12.5 miles.
This is due to the fact that the rate (25 mph) times the time equals the distance traveled. Mathematically, this can be expressed as d = rt, where d represents the distance, r represents the rate (speed), and t represents the time. In this instance, the distance can be calculated as d = 12.5 miles by multiplying d = 25 mph by 30 minutes/60 minutes.
The distance between two points is measured in distance. The rate, or the amount of distance traveled per unit of time, is the speed at which a person or vehicle travels. The woman in the car is traveling at a rate of 25 miles per hour (mph).
In this instance, the time is. The formula d = rt can be used to determine the distance traveled by multiplying her rate by the time. Given the rate and duration of travel, this formula can be used to determine the distance traveled by any object or person.
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Evaluate:
10³ +5² +2²=
A. 10,029
B. 1,029
C. 10,254
D. 129
Answer:
B
Step-by-step explanation:
10*10*10 =1000
5*5 =25
2*2 =4
1000+25+4 =1029
11) show all ur equation steps
The number of solutions that the system has is
One Solution
How do we solve the equations?To solve the system algebraically, we can substitute the first equation into the second equation to eliminate one of the variables. We'll use y:
x=2y-5
7x-14y=10
Substitute x=2y-5 into 7x-14y=10:
7(2y-5)-14y=10
Expand the left side:
14y-35-14y=10
Combine like terms:
-35=10
Solve for y:
y = -7.5
Substitute y = -7.5 back into x=2y-5:
x = 2(-7.5) - 5
Solve for x:
x = -10
So the solution to the system of equations is (x, y) = (-10, -7.5).
Since there is one unique solution, the system has One Solution.
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a diamond ring was purchased ten years ago for 300. the value of the ring increased by 7% each year. what is the value of the ring today
Answer:
Below
Step-by-step explanation:
Value will be original value * ( 1 + i)^n i = decimal annual interest
n = years
Value = 300 ( 1 + .07)^10 = 590.15 (dollars ?)
Let sets A and B be defined as follows.
A is the set of integers greater than or equal to -9 and less than or equal to - 3
B=1-29, -26, -23, 30}
(a) Find the cardinalities of A and B.
n(A) =
n (B) =
The cardinalities:
n(A) = 3
n (B) = 1.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Let sets A and B be defined as follows.
A is the set of integers greater than or equal to -9 and less than or equal to - 3
Set A can be expressed as,
A = {n ≥ -9 or n ≤ -3}
And set B is given,
B = {1-29, -26, -23, 30}
Simplifying,
B = {-28, -26, -23, 30}
The cardinalities:
n(A) = 3
n (B) = 1.
Therefore, n(A) = 3 and n (B) = 1.
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Order these numbers from least to greatest.
7 19/25, 8.44, 31/4, 7.765
The order of the numbers from least to greatest is as follows:
7, 31/4,7¹⁹/₂₅,7.765,8.44
What is a decimal number?A decimal number is a number that consists of a whole number and a fractional part separated by a point. For example – 3.5, 6.79, 78.32, etc.
Given here: The numbers containing fractions and decimal numbers.
To get a clarity on the magnitude of the numbers, let's convert every fraction to decimal numbers
Thus 7¹⁹/₂₅=7.76
31/4=7.75
Hence, The order of the numbers from least to greatest is as follows:
7, 31/4,7¹⁹/₂₅,7.765,8.44
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