The solution to the expression with decimals rounded to the nearest tenth is: -2
Examine the hundredth number to round the decimal number to the nearest tenth. If the number is more than 5, multiply it by one. If it is less than 5, leave the tenth place value alone and eliminate any numbers after the tenth. 4.624, for example, is 4.6 rounded to the closest tenth.
Thus, given the expression:
2.29 + 9.11 + 15.381 - 5.414 - 7.631.11 + 5.99 - 5.734 + 6.893 - 18.355 -4.411
We first round them up to the nearest tenths is:
2.1 + 9.1 + 15.4 - 5.4 - 7.6 + 6.0 - 5.7 + 6.9 - 18.4 - 4.4 = -2
Thus, it is correct to state that the version of the above-given expression resolved to the nearest tenths (2.1 + 9.1 + 15.4 - 5.4 - 7.6 + 6.0 - 5.7 + 6.9 - 18.4 - 4.4) = -2
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Help me ASAP math question.
The client should invest $8889 in AAA bonds, $4444 in A bonds, and $5667 in B bonds.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example: 2x + 4 = 8 is an equation.
We have,
Amount invested in AAA bond = 2x
Amount invested in A bond = y
Amount invested in B bond = x
Now,
Average yield:
AAA bond = 4%
A bond = 5%
B bond = 8%
Now,
Total amount = $19,000
Total yield = $990
Now,
Two equations can be made:
2x + y + x = 19000
3x + y = 19000 _____(1)
0.04 x (2x) + 0.05 x y + 0.08x = 990
0.08x + 0.05y + 0.08x = 990
0.16x + 0.05y = 990 ______(2)
From (1) and (2),
3x = 19000 - y
x = (19000 - y)/3
Substituting in (2)
0.16 x (19000 - y)/3 + 0.05y = 990
0.053 x 19000 - 0.053y + 0.05y = 990
1007 - 0.003y = 990
1007 - 990 = 0.003y
y = 17/0.003
y = 5666.6
y = 5667
Now,
x = (19000 - y)/3
x = (19000 - 5667)/3
x = 4444.333
x = 4444
Now,
x = $4444
y = $5667
2x = $8889
Thus,
Amount invested in AAA bond = $8889
Amount invested in A bond = $5667
Amount invested in B bond = $4444
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Read the following prompt and type your response in the space provided.
Explain how to model the division of –24 by –4 on a number line.
To model the division of -24 by -4 on a number line, we can start at -24 and move to the left by -4 units at a time, counting the number of times we move until we reach 0.
How to explain the number line?A number line is a diagram of a graduated straight line used to represent real numbers in elementary mathematics. It is assumed that each real number and each point on a number line correspond to one another.
Since -24 divided by -4 is 6, we would move to the left 6 times and end at 0 on the number line. The negative signs of the dividend and divisor indicate that the quotient will be a negative number.
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Simplify. Need ASAP. show work
The solutions to the simplification of the following surds are:[tex]-12\sqrt[3]{3}+4\sqrt[3]{2}[/tex] and [tex]-5x^2 y^2\sqrt[3]{3x^2y^2}[/tex]
Simplification of surd forms:A number without a root is simply referred to as a surd. These surds illustration comprises fractions as powers if presented in exponential form. There are three main forms of surds, according to the definition of surds.
Pure surds, which are surds that include just one irrational number. Surd that comprises both rational and irrational numbers is called Mixed surds. Compound surds are two surds combined into one.The simplification of the given surds is carried out as follows:
[tex]-2\sqrt[3]{81} +2\sqrt[3]{16}-2\sqrt[3]{81}[/tex]
Factor 27 out of 81
[tex]-2\sqrt[3]{27*3} +2\sqrt[3]{16}-2\sqrt[3]{27*3}[/tex]
Rewrite it as 3³*3
[tex]-2\sqrt[3]{3^3*3} +2\sqrt[3]{16}-2\sqrt[3]{3^3*3}[/tex]
Rearrange and simplify
[tex]-2\sqrt[3]{3^3*3} -2\sqrt[3]{3^3*3}+2\sqrt[3]{16}[/tex]
Pull term out from the radical
[tex]-2*3\sqrt[3]{3} -2*3\sqrt[3]{3}+2\sqrt[3]{16}[/tex]
[tex]-6\sqrt[3]{3} -6\sqrt[3]{3}+2\sqrt[3]{16}[/tex]
Rewrite 16 as 2³*2
[tex]-6\sqrt[3]{3} -6\sqrt[3]{3}+2\sqrt[3]{2^3*2}[/tex]
Pull term out of the radical
[tex]-6\sqrt[3]{3} -6\sqrt[3]{3}+2*2\sqrt[3]{2}[/tex]
[tex]-6\sqrt[3]{3} -6\sqrt[3]{3}+4\sqrt[3]{2}[/tex]
Simplify altogether;
[tex]-12\sqrt[3]{3}+4\sqrt[3]{2}[/tex]
In [tex]\sqrt[3]{-375x^8y^8}[/tex]; simplify the radical by breaking the radicand up into a product of known factors, assuming real numbers.
[tex]\sqrt[3]{(-5) ^3(x^2)^3 (y^2)^3*3x^2y^2}[/tex]
[tex]\sqrt[3]{(-5x^2y^2) ^3*3(x^2y^2)}[/tex]
[tex]-5x^2 y^2\sqrt[3]{3x^2y^2}[/tex]
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The label on a car's antifreeze container claims to protect the car at temperatures greater than −40°C and less than 140°C. To convert Celsius temperature to Fahrenheit temperature, the formula is C equals five ninths times the quantity F minus thirty two.. Write a compound inequality to determine the Fahrenheit temperature range at which the antifreeze protects the car
Answer:
-40F to 284F
Step-by-step explanation:
C = 5/9F -32
so F = 32+9/5*C
so the range is
F= 32+9/5*(-40) = 32-72 = -40F
F= 32+9/5*(140) = 32+252 = 284F
billy makes $20 a week in allowance plus $5 for each lawn that he mows. this week billy wants to make over $50. select the inequality for the number of lawns he needs to mow.
The inequality for the number of lawns he needs to mow is: $50 < $20 + $5n
The correct answer is an option (b)
Let n represents the number of lawns he needs to mow.
Here, Billy needs to make more than $50 between his allowance and the lawns that he mows. This means that an inequality should include 50 <
As Billy will make $5 for each lawn that he mows, for 'n' number of lawns the cost would be = 5n
Based on the mentioned conditions we formulate an inequality,
50 < 20 + 5n
20 + 5n > 50
20 + 5n - 20 > 50 - 20 ...........(subtract 20 from each side)
5n/5 > 30/5 .............(divide each side by 5)
n > 6
This means, he needs to mow more that 6 lawns.
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The complete question is:
Billy makes $20 a week in allowance plus $5 for each lawn that he mows. this week billy wants to make over $50. select the inequality for the number of lawns he needs to mow.
a) $50 < $20+$5
b) $50 > $20+$5n
c) $50 < $20n+$5
d) $50 > $20n+$5
e) $50 < $20+$5n
In the pattern below, the cat moves clockwise through the four squares, and the mouse moves counterclockwise through the eight exterior segments of the four squares.
If the pattern is continued, where would the cat and mouse be after the 247th move?
Only setup A places the mouse on the bottom right square and the cat there.
The pattern is continued, so we have to define where the cat and mouse would be after the 247th move.
Divide the issue into two parts: the location of the mouse and the location of the cat after the 247th move.
Every cycle, which consists of four different positions for the cat, is repeated once every four movements. When 247 is divided by 4, the remainder is 3. This matches the bottom right corner, where the cat is located after the third move.
Similar to the mouse, which repeats every eight moves, the mouse has eight possible places in a single cycle. When 247 is divided by 8, the remainder is 7. This matches the rat's bottom left corner position after the seventh motion.
The only configuration with the cat in the bottom right square and the mouse in that position is A.
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The complete question is given below:
Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
An equation 6(2x+4)²=(2x+4)+2 has degree 2, so it is quadratic equation. Therefore, option D is the correct answer.
What is a quadratic function in standard form?The standard form of a quadratic equation is given as:
ax² + bx + c = 0 where a, b, c are real numbers and a ≠ 0.
Quadratics are the polynomial equation which has highest degree of 2.
A) x⁴-6x²-27=0
Here, the highest degree is 4 so, it is biquadratic equation.
B) 3x⁴=2x
3x³=2
Here, the highest degree is 3 so, it is cubic equation.
C) 2(x + 5)⁴+2x²+5=0
Here, the highest degree is 4 so, it is biquadratic equation.
D) 6(2x+4)²=(2x+4)+2
6(4x²+16x+16)=(2x+4)+2
24x²+96x+96=2x+4+2
24x²+94x+90=0
Here, the highest degree is 2 so, it is quadratic equation.
E) 6x⁴= -x²+5
6x⁴+x²+5=0
Here, the highest degree is 4 so, it is biquadratic equation.
F) 8x⁴+2x²-4x=0
Here, the highest degree is 4 so, it is biquadratic equation.
Therefore, option D is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
Select all of the following equation(s) that are quadratic in form.
a) x⁴-6x²-27=0
b) 3x⁴=2x
c) 2(x + 5)⁴+2x²+5=0
d) 6(2x+4)²=(2x+4)+2
e) 6x⁴= -x²+5
f) 8x⁴+2x²-4x=0
Graph the line y=−54x−3.
Use the line tool and select two points on the line.
The two points on the line y = − 54x − 3 will be (1, −57) and (−1, 51).
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
y = − 56x − 4
Let x = 1, the value of y will be
y = − 54 (1) − 3
y = − 54 − 3
y = − 57
Let x = − 1, the value of y will be
y = − 54(−1) − 3
y = 54 − 3
y = 51
The two points on the line y = − 56x − 4 will be (1, −57) and (−1, 51). Then the diagram of the line is given below.
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The store owner put 10 Tshirts on clearance. The Tshirts were originally priced at $22.00 each. The owner marked down the price of the Tshirts by 40%.
How much money did the store owner receive for selling all 10 Tshirts?
Answer:
$132
Step-by-step explanation:
Looks like $22.00 was the price at 100%
The owner marks the price down by 40%, making the total price 60% of $22 because 100%-40% is 60%
We can set up a ratio
60%. X
-------. =. ------
100%. $22
Cross multiplying makes it (100)(x) = (60)(22)
100x = 1,320
Dividing both by 100 to get X alone
x = 13.2
Each shirt is now $13.20
Last, but not least, we multiply by 10 because he sold 10 shirts
= $132
a white cylindrical silo has a diameter of $30$ feet and a height of $80$ feet. a red stripe with a horizontal width of $3$ feet is painted on the silo, as shown, making two complete revolutions around it. what is the area of the stripe in square feet?
So, the area of the stripe is 394.25= 282.75 square feet.
Silo Stripe Area CalculationThe stripe is a rectangle, with a width of 3 feet and a length that is the circumference of the cylinder. The diameter of the cylinder is 30 feet, so the circumference is 30pi=94.25 feet. So, the area of the stripe is 394.25= 282.75 square feet.
The white cylindrical silo has a red stripe painted on it, which makes two complete revolutions around the silo. The stripe is a horizontal rectangle with a width of 3 feet and a length equal to the circumference of the cylinder, which is calculated by multiplying the diameter of 30 feet by pi. The area of the stripe is the width of 3 feet multiplied by the length of 94.25 feet, which equals 282.75 square feet.
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A file that is 237 megabytes is being downloaded. If the download is 17.6% complete, how many megabytes have been downloaded?
Answer:
Step-by-step explanation:
The answer is 42 MB.If it's round to nearest tenth than it's 40 MB
13.) 5x − 2 – (8x − 1) =
14.) 1-(2-x) =
15.) 2x + 1 + (x + 3) =
16.) -1(3 + 2x) =
An equation is said to be linear if each term has a maximum of one degree.The system of linear equations is solved by (2,6).
What is a linear equation?An equation is said to be linear if each term has a maximum of one degree.
It is possible to formulate linear equations in the form y=mx+c.
A straight line results from a linear equation with two variables when its axes are plotted on the cartesian plane.
When the second equation for x is solved,
x + 5y = 32
x = 32 - 5y
Add the value of x to the first equation now,
2(32 - 5y) + 5y = 34
64 - 10y + 5y = 34
-5y = -30
y = 6
the value of y should be replaced in any one of the equations,
x + 5y = 32
x + 5(6) = 32
x = 2
Consequently, the system of linear equations' solution is (2,6).
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Helpppppppppppppppppppppppppppppppp
Answer:
Step-by-step explanation:
Its the second one
Answer: -1/3 > -2/5
Step-by-step explanation:
If we put them as common denominators we can solve this. To do that look at this:
-1/3 = -5/15
-2/5 = -6/15
So we can see that -2/5 is smaller
I hope this was able to help you :D
The floor of a rectangular room is to be covered with tiles 1-foot sides. The floor of the room is 18 feet long and 12 feet wide. How much would it cost at $4 a tile?
The cost for the flooring of the rectangular room is $864.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
Given that,
Dimension of each time = 1 foot
Length of the room = 18 feet
Width of the room = 12 feet
Number of tiles needed for the room = 18 × 12 = 216
Cost of one tile = $4
Total cost for the tile = 216 × $4 = $864
Hence the total cost for the tiles is $864.
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When using the multiplication method, it is important to multiply all the terms on both sides of the equation—not just the one term you are trying to eliminate
As per the elimination method, in order to solve a system of equations when multiplication is necessary to eliminate a variable.
The term equation is known as algebra is a statement of equality that contains one or more unknown quantities or variables.
Here we have given that When using the multiplication method, it is important to multiply all the terms on both sides of the equation, then here we do not just the one term you are trying to eliminate.
According to the rule of elimination method we all know while solving systems of linear equations uses the addition property of equality. You can add the same value to each side of an equation.
So in order to multiplying to solve linear systems is to find a number to multiply to one or both of the equations so that the x or y terms in one of the equations will have opposite coefficients from the x or y in the other equation.
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How do u solve: 4x-(9-3x)=8x-1
Answer:
x=-8
Brief explanation:
Well I simplify first
4x-(9-3x)=8x-1
4x-9+3x=8x-1
then you do this operation called collecting similar terms
4x+3x-9=8x-1
7x-9=8x-1
7x-8x=-1+9
7x-8x=8
-x=8
x=-8 should be ur solution--
Answer:
[tex] \sf \: x = - 8[/tex]
Step-by-step explanation:
Given equation,
→ 4x - (9 - 3x) = 8x - 1
Now the value of x will be,
→ 4x - (9 - 3x) = 8x - 1
→ 4x - 9 + 3x = 8x - 1
→ (4x + 3x) - 9 = 8x - 1
→ 7x - 9 = 8x - 1
→ 7x - 8x = -1 + 9
→ -x = 8
→ [ x = -8 ]
Hence, the value of x is -8.
If each of these runners travels the indicated number of spaces in the same amount of time, at which numbered spot will all of the runners be next to one another?
The numbered spot at which all the runners will be next to one another is spot 19.
What is the LCM?Least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.
Starting with the runner on the outside track, the provided parameters are;
The runner covered n₁ = 5 places on the outside track, which is the number of spaces.
Next, the inner runner will traverse n₂ spaces, which equals one space.
The following inner runner will cover n₃ = 3 spaces.
The subsequent runner will traverse n₄ = 2 spaces.
The Lowest Common Multiple, or LCM, of all the runners' speeds or the total number of spaces they cover in the same amount of time, determines where all the runners will be placed next to one another.
LCM(5, 1, 3, 2) = 30 is the LCM of 5, 1, 3, and 2.
Time = 30/ = 6
Consequently, when the first runner has covered 30 places, we have;
Six time units have been expended.
The runner comes to a stop at position 30- (30 -19) = Position 19.
First runner's new destination is Spot 19.
The distance covered simultaneously by runner 2 is 6 x 1 = 6.
The distance covered by two runners running simultaneously equals six spaces.
Second runner's new position: 6 spaces plus spot 13 equals spot 19.
The combined distance covered by the three runners is 6 x 3 = 18.
The distance runner 3 covers 18 spaces simultaneously.
Third runner's new position: 18 spaces + Spot 1 = 19 spaces
Runner 4 covers a distance of 6 x 2 = 12 at the same time.
Distance runner 4 journeys equals 12 spaces
Runner 4's new position is now 12 spaces Plus Spot 7 = Spot 19.
Therefore, all the runners will be next to one another is spot 19.
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Which of the values make 4x<45 true?
A 12
B. 11
C. 13.5
D. 16
Answer: B - 11
Step-by-step explanation: Hello! How you can do this is by substituting A, B, C, and D for x.
D:
4(16)<45
64<45
64 is not less than 45, so this is false. D is not the answer.
C:
4(13.5)<45
54<45
54 is not less than 45, so this is false. C is not the answer.
A:
4(12)<45
48<45
48 is not less than 45, so this is false. A is not the answer.
B:
4(11)<45
44<45
44 is less than 45 so this is true.
The answer is B - 11.
if Kis the smallest positive integer such that(2k)(5200) has 303digits. Find the sum of the digits of that number when expanded.
The sum of the digits of the number 10302k, when k = 151, is 157.
The smallest positive integer such that (2k)(5200) has 303 digits is k = 151. In order to calculate the sum of the digits of this number, we will first expand the expression (2k)(5200). This expression can be expanded to 10302k. The sum of the digits of this number is equal to 1 + 0 + 3 + 0 + 2 + k. Since k = 151, the sum of the digits of this number is equal to 1 + 0 + 3 + 0 + 2 + 151 = 157. Therefore, the sum of the digits of the number 10302k, when k = 151, is 157.
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the base company has assets other than investment securities, that cost $50,000. The current market value of the assets is $75 million. The assets will be recorded and reported as assets at
As the company asset other than investment securities cost $50,000 and market value of the assets is $75 million. The assets will be recorded and reported as at $75,050,000.
How are asset recorded and reported?An asset is a resource with monetary value that an individual, corporation, or country owns or controls with the expectation of future benefit. An asset is anything that can generate cash flow, reduce expenses, or increase sales in the future, whether it's manufacturing equipment or a patent.
A company's assets are reported on its balance sheet. They are divided into four categories: current, fixed, financial, and intangible. They are purchased or created in order to increase the value of a company or to benefit its operations.
The reported asset of the company will be:
= $50,000 + $75 million
= $75,050,000
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Complete the calculation in step 3 and drag the appropriate solute amounts to the ECF and ICF columns. Drag the appropriate labels to their respective targets.
The types of solutes and their distribution between the ICF and ECF are not the same for the appropriate solute amounts to the ECF and ICF columns.
Intracellular fluids are fluids found inside the cell's cytoplasm while extracellular fluid are fluids the flow outside the cells which consist of plasma, interstitial and trancellular fluid
The types of solutes and their distribution between the ICF and ECF are not the same because intracellular fluid of the cystosol is composed of water, dissolved ions, small molecules, and large, water-soluble molecules while extracellular fluid consist of plasma, interstitial fluid and cytosol have high potassium concentration and low sodium Concentration.
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Of the following statements, which one or ones describe actions harmful to your credit score?
I. Owing a lot of money
II. Having many lines of credit
III. Making steady payments
Answer:
I
Step-by-step explanation:
owing a lot of money bc it hurts your credit score
Given that z is a standard normal random variable, compute the following probabilities (to 4 decimals).
P(z ? -1.0)
P(z ? -1.0)
P(z ? -1.5)
P(z ? -2.5)
P(-3 < z ? 0)
Computed the probabilities P(z < -1.0)=0.1587, P(z > -1.0)=0.8413, P(z < -1.5)=0.0668, P(z < -2.5)=0.0062, P(-3 < z < 0)=0.4987.
What is deviation ?
Deviation refers to how far a value or set of values is from the mean or average. In statistics, the standard deviation is a measure of the spread of a dataset, calculated as the square root of the variance. It represents the average distance of each data point from the mean. A low standard deviation indicates that the data points tend to be close to the mean.
To compute the probabilities for a standard normal random variable, we can use a standard normal table or a calculator with standard normal distribution functions.
P(z ? -1.0) = P(z < -1.0) = 0.1587
P(z ? -1.0) = P(z > -1.0) = 1 - 0.1587 = 0.8413
P(z ? -1.5) = P(z < -1.5) = 0.0668
P(z ? -2.5) = P(z < -2.5) = 0.0062
P(-3 < z ? 0) = P(-3 < z < 0) = P(z < 0) - P(z < -3) = 0.5 - 0.0013 = 0.4987,
Computed the probabilities P(z < -1.0)=0.1587, P(z > -1.0)=0.8413, P(z < -1.5)=0.0668, P(z < -2.5)=0.0062, P(-3 < z < 0)=0.4987.
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Maleri Designs sells cartons of cloth face masks ($12) and cartons of hand-sanitizer ($6) on eBay. One of their customers, Mod World, purchased 22 cartons for $216. How many of cartons of each did Mod World purchase? Check your answer. Hint: Let F = Face masks.
The customer purchased 14 face masks and 8 hand sanitizers.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Given that, Maleri Designs sells cartons of cloth face masks ($12) and cartons of hand-sanitizer ($6) on eBay.
Let the number of face masks be f an the number of hand-sanitizers be h.
One of their customers, Mod World, purchased 22 cartons for $216.
Now, f+h=22 --------(I) and
12f+6h=216 --------(II)
f=22-h
Substitute f=22-h in equation (II), we get
12(22-h)+6h=216
264-12h+6h=216
264-216=6h
6h=48
h=8
Substitute h=8 in equation (I), we get
f+8=22
f=14
Hence, the customer purchased 14 face masks and 8 hand sanitizers.
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What is the constant of proportionality in this proportional relationship?
X 2 2/1 3 3 1/2
Y 5/2 25/8 15/4 35/8
The constant of proportionality in this proportional relationship is 5/4.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x = 5 is an equation.
We have,
Let the proportional equation be y ∝ x.
y = kx
From the table,
When x = 2, y = 5/2
This means,
5/2 = 2k
k = (5/2)/2
k = 5/4
Now,
When x = 2(1/2), y = 25/8
k = y/x
k = (25/8)/(5/2)
k = 25/8 x 2/5
k = 5/4
We see that,
k = 5/4
Thus,
The constant of proportionality is 5/4.
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#8 i need help with this problems.
ΔABD and ΔBCD are congruent by AAS congruence theorem.
The proof is given below.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
From the figure below,
ΔABD and ΔBCD are congruent.
∠BCD = ∠BAD [ 90 degrees ]
∠CDB = ∠ABD [ alternate angles ]
BD = BD [ Common ]
ΔABD ≈ ΔBCD [ AAS ]
Thus,
ΔABD and ΔBCD are congruent by AAS congruence theorem.
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Suppose that y varies directly with x, and y=4 when x=20. (a) Write a direct variation equation that relates and y Equation: (b) Find y when x=9. y=
Answer:
(a) Since y varies directly with x, hence, y = kx, where k is a constant.
(b) When x = 20, y = 4
20k = 4
∴ k = 0.2
∴ When x = 9,
y = 9(0.2)
y = 1.8
pls help me with this 4(x−2+y)
Answer: 4x + 4y - 8
Step-by-step explanation:
4(x−2+y)
4x -8 +4y
4x + 4y - 8
NO LINKS!!!
Find the solution set for each inequality.
Answer:
41. (-∞, -1] ∪ [2, 3)
42. (2, 5) ∪ (5, ∞)
Step-by-step explanation:
Question 41Given rational inequality:
[tex]\dfrac{x^2-x-2}{x-3} \leq 0[/tex]
Factor the numerator:
[tex]\dfrac{(x-2)(x+1)}{x-3} \leq 0[/tex]
Find the roots by solving f(x) = 0 (set the numerator to zero):
[tex]\implies (x-2)(x+1)=0[/tex]
[tex]\implies x-2=0 \implies x=2[/tex]
[tex]\implies x+1=0 \implies x=-1[/tex]
Find the restrictions by solving f(x) = undefined (set the denominator to zero):
[tex]\implies x-3=0 \implies x=3[/tex]
Create a sign chart, using closed dots for the roots and open dots for the restrictions (see attachment 1).
Choose a test value for each region, including one to the left of all the critical values and one to the right of all the critical values.
Test values: -2, 0, 2.5, 4For each test value, determine if the function is positive or negative:
[tex]f(-2)=\dfrac{(-2)^2-(-2)-2}{(-2)-3} =\dfrac{+}{-}=-[/tex]
[tex]f(0)=\dfrac{(0)^2-(0)-2}{(0)-3} =\dfrac{-}{-}=+[/tex]
[tex]f(2.5)=\dfrac{(2.5)^2-(2.5)-2}{(2.5)-3} =\dfrac{+}{-}=-[/tex]
[tex]f(4)=\dfrac{(4)^2-(4)-2}{(4)-3} =\dfrac{+}{+}=+[/tex]
Record the results on the sign chart for each region (see attachment 1).
As we need to find the values for which f(x) ≤ 0, shade the appropriate regions (zero or negative) on the sign chart (see attached).
Therefore, the solution set is:
x ≤ -1 or 2 ≤ x < 3As interval notation:
(-∞, -1] ∪ [2, 3)Question 42Given rational inequality:
[tex]\dfrac{\sqrt{x}}{(x-2)|x-5|} > 0[/tex]
Find the roots by solving f(x) = 0 (set the numerator to zero):
[tex]\implies \sqrt{x}=0 \implies x=0[/tex]
Find the restrictions by solving f(x) = undefined (set the denominator to zero):
[tex]\implies (x-2)|x-5|=0[/tex]
[tex]\implies x-2=0 \implies x=2[/tex]
[tex]\implies |x-5|=0 \implies x=5[/tex]
Create a sign chart, using closed dots for the roots and open dots for the restrictions (see attachment 1).
Choose a test value for each region, including one to the left of all the critical values and one to the right of all the critical values.
Test values: -1, 1, 3, 6For each test value, determine if the function is positive or negative:
[tex]f(-1)=\dfrac{\sqrt{-1}}{(-1-2)|-1-5|}=\dfrac{\sf unde\:\!fined}{-}=\sf unde\:\!fined[/tex]
[tex]f(1)=\dfrac{\sqrt{1}}{(1-2)|1-5|}=\dfrac{+}{-}=-[/tex]
[tex]f(3)=\dfrac{\sqrt{3}}{(3-2)|3-5|}=\dfrac{+}{+}=+[/tex]
[tex]f(6)=\dfrac{\sqrt{6}}{(6-2)|6-5|}=\dfrac{+}{+}=+[/tex]
Record the results on the sign chart for each region (see attachment 2).
As we need to find the values for which f(x) > 0, shade the appropriate regions (positive) on the sign chart (see attached).
Therefore, the solution set is:
2 < x < 5 or x > 5As interval notation:
(2, 5) ∪ (5, ∞)4. Juan cotiza un motor generador de ondas estacionarias para cuerdas en 50 almacenes
eléctricos. Obteniendo los siguientes datos:
300 mil pesos en un almacén y esta con el 10% de descuento; en el almacén dos, costaba 400
mil pesos con un 14% de descuento; en el almacén 3, tenía un costo de 500 mil pero le bajaban
el 20%, en el cuarto almacén, valía 700 mil pesos pero rebajan el 22%; en el almacén 5, costaba
750 mil pesos con un 12% de descuento; en el almacén 6, tenía un precio de 800 mil y le
bajaban el 10%; en el séptimo almacén, tiene un precio de 1000 y le hacen el descuento del 6%;
en almacén 8, cuesta 1200 y bajan el 4%; en el último almacén cobran 1500 y hacen el 2% de
rebaja.
De acuerdo con lo anterior, la respuesta correcta serían 270,000 es el precio más bajo que obtuvo para comprar un motor generador de ondas estacionarias para cuerdas en el primer almacén.
¿Cómo calcular cuál almacén le ofrece el precio más bajo a Juan?
Para calcular cuál es el almacén que le ofrece el precio más bajo a Juan debemos identificar a cuanto equivale el descuento y restarlo del precio total. Cuando sepamos el precio final comparamos para saber cuál de todos es el menor.
300,000 / 100 = 3,000
3,000 * 10 = 30,000
300,000 - 30,000 = 270,000
400,000 / 100 = 4,000
4,000 * 14 = 56,000
400,000 - 56,000 = 344,000
500,000 / 100 = 5,000
5,000 * 20 = 100,000
500,000 - 100,000 = 400,000
700,000 / 100 = 7,000
7,000 * 22 = 154,000
700,000 - 154,000 = 546,000
750,000 / 100 = 7,500
7,500 * 12 = 90,000
750,000 - 90,000 = 660,000
800,000 / 100 = 8,000
8,000 * 10 = 80,000
800,000 - 80,000 = 720,000
1'000.0000 / 100 = 10,000
10,000 * 6 = 60,000
1'000.000 - 60,000 = 940,000
1'200.000 / 100 = 12,000
12,000 * 4 = 48,000
1'200,000 - 48,000 = 1'152.000
1'500.000 / 100 = 15,000
15,000 * 2 = 30,000
1'500,000 - 30,000 = 1'270,000
De acuerdo a lo anterior, el precio más bajo para comprar un motor generador de ondas estacionarias para cuerdas es 270,000 en el primer almacén.
Nota: Esta pregunta está incompleta y tiene errores en los valores. A continuación esta la información completa y correcta.
Pregunta
¿Cuál tienda le ofrece el precio más bajo a Juan?
Precios
Almacén 1: 300 mil pesos con el 10% de descuento.
Almacén 2: 400 mil pesos con el 14% de descuento.
Almacén 3: 500 mil pero con el 20% de descuento.
Almacén 4: 700 mil pesos con el 22% de descuento.
Almacén 5: 750 mil pesos con el 12% de descuento.
Almacén 6: 800 mil pesos con el 10% de descuento.
Almacén 7: 1'000.000 de pesos con el 6% de descuento.
Almacén 8: 1'200.000 de pesos con el 4% de descuento.
Almacén 9: 1'500.000 de pesos con el 2% de descuento.
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