The equation for the profit from selling the items is P = 40x-0.5x²-300. The values of x are 10 and 70.
How to solve for the expressionWe have the cost function in this question to be
Cx = 60x+300
Revenue = 100x−0.5x²
A. The revenue function is stated as the revenue - cost
= (100x−0.5x²)-60x+300
We have to open the equation
40x-0.5x²-300
B. when profit is 50 dollars
50 = 40x-0.5x²-300
We have to multiply both sides by 10
500 = 400x - 5x² - 3000
We have to collect like terms and form a quadratic equation
5x² - 400x - 3500 = 0
We have to solve the quadratic equation above using a quadratic calculator.
Hence
x = 10, 70
So the two values that would create a profit of 50 dollars is 10 and 70.
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Which of the following is a valid probability distribution? Probability distribution A is shown. The probabilities of 1, 2, 3, 4, 5 and 6 are all 0.2. Probability distribution B is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.3; 4 is 0.3; 5 is 0.2; 6 is 0.1. Probability distribution C is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.4; 5 is 0.1; 6 is 0.1. Probability distribution D is shown. The probability of 1 is 0.2; 2 is 0.1; 3 is 0.1; 4 is 0.5; 5 is 0.1.
Considering the given probability distribution, distribution D is valid.
When a probability distribution is valid?A probability distribution is valid if:
There are no negative probabilities.,The sum of all probabilities is of 1.In this problem:
For distribution A, the sum is of 1.2, hence it is not valid.For distribution B, the sum is of 1.2, hence it is not valid.For distribution C, the sum is of 0.9, hence it is not valid.For distribution D, the sum is of 1, hence it is valid.More can be learned about probability distributions at https://brainly.com/question/23670007
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Choose the most convenient method to graph the line x=8.
Select the correct answer below:
Recognize the equation as that of a vertical line passing through the x-axis at 8
Recognize the equation as that of a horizontal line passing through the y-axis at 8
Identify the slope and y-intercept and then graph
Find the x- and y-intercepts and then graph
Answer:
Recognize the equation as that of a vertical line passing through the x-axis at 8
Answer:
the first option : vertical line passing through the x-axis at 8.
Step-by-step explanation:
x = 8
is a special case of a line equation.
it means that it contains all points for which x = 8.
so, e.g.
(8, -26), (8, - 7), (8, 0), (8, 3), (8, 57), ...
in other words, any y value is possible, but x is constant 8.
therefore, it is one vertical line going through 8 on the x-axis.
the is therefore no y-intercept.
this line equation maps all y values from -infinty to +infinity to the x value of 8. and FYI - it is therefore not a function (where each x value has exactly one assigned y value).
the slope of such a line is infinite or even more accurate undefined.
as the slope is y difference / x difference, x difference is always 0. something divided by 0 is officially undefined and often considered as infinite.
the opposite extreme is something like
y = 8
this is now the line that contains all points with y = 8.
any x-value is possible, but y is always 8.
that is a horizontal line that goes through the y-axis at 8.
and in fact, this is a function, as every x value has exactly one assigned y value (they are all 8, but that does not matter).
there is no x-intercept, of course.
and the slope is 0, as the slope is y difference / x difference, and the y difference is always 0. 0 divided by something is 0.
Which of the numbers below are some potential roots of p(x) = x3 6x2 − 7x − 60 according to the rational root theorem?
The potential roots of the function p(x)=[tex]x^{3}+6x^{2} -7x-60[/tex] are -10,-5,3,15.
Given function p(x)=[tex]x^{3}+6x^{2} -7x-60[/tex]
We have to find the potential roots of the function according to rational root theorem.
Root is the solution of an equation usually expressed as a number or an algebraic formula.
The rational root theorem is used to find the potential roots of function.
For a polynomial function:
p(x)=p[tex]x^{n}[/tex]+..............................+q
The potential roots are:
Roots =±factors of q/factors of p
Th factors of 60 are =±1,±2,±3,±4,±5,±6,±10,±12.
The factors of 1 is ±1.
So we have factors are:±1,±2,±3,±4,±5,±6,±10,±12,±15,±20/±1
The roots are =±1,±2,±3,±4,±5,±6,±0.
Factors:-10,-5,3,15.
Hence the potential roots are -10,-5,3,15.
Question is incomplete as it should includes options :-10,-7,-5,3,15,24
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how to find compound rate from given values, 10 years after, and initial
The formula that calculates the compound rate from the given values is [tex]r = n(-1 + \sqrt[10n]{\frac{P + I}{P}})[/tex]
How to determine the compound interest rate?The compound interest formula is:
[tex]I = P(1 + \frac rn)^{nt} - P[/tex]
Where:
P represents the principal amountr represents the compound interest raten represents the number of times the interest is compoundedt represents the time in yearsI represents the interestWe start by adding P to both sides
[tex]P + I = P(1 + \frac rn)^{nt}[/tex]
Divide through by P
[tex]\frac{P + I}{P} = (1 + \frac rn)^{nt}[/tex]
Take the nt-th root of both sides
[tex]\sqrt[nt]{\frac{P + I}{P}} = 1 + \frac rn[/tex]
Subtract 1 from both sides
[tex]-1 + \sqrt[nt]{\frac{P + I}{P}} = \frac rn[/tex]
Multiply through by n
[tex]r = n(-1 + \sqrt[nt]{\frac{P + I}{P}})[/tex]
In this case, t = 10
So, we have:
[tex]r = n(-1 + \sqrt[10n]{\frac{P + I}{P}})[/tex]
Hence, the formula that calculates the compound rate is [tex]r = n(-1 + \sqrt[10n]{\frac{P + I}{P}})[/tex]
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The fine schedule for overdue books at the county library is modeled by the values in the table.
Library Fines for Overdue Books
Days overdue
Amount of fine
0
0 ¢
2
5 ¢
4
10 ¢
6
15 ¢
8
20 ¢
10
25 ¢
Which equation best models the fine schedule for overdue books?
Thus, the required equation is given by Y = 5/2X.
Given data can tabulate is
Days overdue(x) = 0 2 4 6 8 10
Amount of fine(y) = 0 5 10 15 20 25
What is equation?equation is the relationship between variable and represented as is example of polynomial equation.
Since, the as for every value of x, y grows linerely.
Equation can be given as for every 2 step of x, y increase 5 steps
therefore, y = 5/2x
Thus, The required equation is given by y = 5/2x
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Consider the relationship 3r+8t=3
The function r =f(t) is f(t) = 1 - 8t/3
How to evaluate the function?The function is given as:
3r + 8t = 3
Make r the subject
3r = 3 - 8t
Divide by 3
r = 1 - 8t/3
This means that:
f(t) = 1 - 8t/3
To calculate f(-3), we have:
f(3) = 1 - 8 * 3/3
Evaluate
f(3) = -7
Also, we have:
1 - 8t/3 = 2
Add 2 to both sides
-8t/3 = 3
Solve for t
t = -9/8
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Complete question
Consider the relationship 3r+8t=3
Write the relationship as a function r = f(t)
Evalute f(-3)
Solve for f(t) = 2
What is the measure of 2 if 1 is (4x - 4) and 2 is (4x)?
The measure of <2 is 92 degrees
How to solve for 2?The complete question is in the attached image
The angles are given as:
<1 = 4x - 4
<2 = 4x
The sum of angles on a straight line is
<1 + <2 = 180
So, we have:
4x - 4 + 4x = 180
Evaluate the like terms
8x = 184
Divide by 8
x = 23
Substitute x = 23 in <2 = 4x
<2 = 4 * 23
Evaluate
<2 = 92
Hence, the measure of <2 is 92 degrees
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The age of undergraduate students at the U of A has a mean (µ) of 20.66 and a population standard deviation (s) of 2.4. What percentage of students are 21 or older and thus old enough to legally order alcohol at Griff's?
Using the normal distribution, it is found that 44.43% of students are 21 or older and thus old enough to legally order alcohol at Griff's.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 20.66, \sigma = 2.4[/tex]
The proportion of students that are 21 or older is one subtracted by the p-value of Z when X = 21, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{21 - 20.66}{2.4}[/tex]
Z = 0.14
Z = 0.14 has a p-value of 0.5557.
1 - 0.5557 = 0.4443 = 44.43% of students are 21 or older and thus old enough to legally order alcohol at Griff's.
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The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.9 minutes and a standard deviation of 2.8 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)
(a) less than 10 minutes
(b) longer than 5 minutes
(c) between 8 and 15 minutes
Using the normal distribution, the probabilities are given as follows:
a) 0.6517 = 65.17%
b) 0.0823 = 8.23%.
c) 0.6109 = 61.09%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 8.9, \sigma = 2.8[/tex]
Item a:
The probability is the p-value of Z when X = 10, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{10 - 8.9}{2.8}[/tex]
Z = 0.39
Z = 0.39 has a p-value of 0.6517.
0.6517 = 65.17% probability that the time is less than 10 minutes.
Item b:
The probability is the one subtracted by the p-value of Z when X = 5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5 - 8.9}{2.8}[/tex]
Z = -1.39
Z = -1.39 has a p-value of 0.0823.
0.0823 = 8.23% probability that the time is more than 5 minutes.
Item c:
The probability is the p-value of Z when X = 15 subtracted by the p-value of Z when X = 8, hence:
X = 15:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15 - 8.9}{2.8}[/tex]
Z = 2.18
Z = 2.18 has a p-value of 0.9854.
X = 8:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{8 - 8.9}{2.8}[/tex]
Z = -0.32
Z = -0.32 has a p-value of 0.3745.
0.9854 - 0.3745 = 0.6109 = 61.09%.
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Find the sum of the measures of the interior angles of the figure.
Answer:
[tex]\huge\boxed{\sf 900}[/tex]
Step-by-step explanation:
Sides of the figure = n = 7
Formula for measuring the interior angles of a polygon:(n - 2)×180
Where n is the number of sides in the polygon
So,
Measure of interior angles in the figure:= (n - 2) × 180
= (7 - 2) × 180
= 5 × 180
= 900
[tex]\rule[225]{225}{2}[/tex]
Answer: 720°
Step-by-step explanation:
- Assuming this is a regular hexagon, all the sides are equal and all the angles are equal
- One of the properties of a regular hexagon is that the sum of all the interior angles is 720°
- Since the sum of all the interior angles is 720°, this means each interior angle is 120°
hope this helps :)
Be sure that you show all of your work to reach your answer. Each step must be on a separate line. Your method to reach your answer must be clear and include explanations.
Be sure to only round at the last step for your final answer.
You plan to purchase a house for $525,000 and you will make a 20% down payment. You are evaluating two mortgages a 30-year fixed mortgage at 2.72% and a 15-year fixed mortgage at 2.25%. Your goal is to have a monthly payment that fits within your budget.
a. Which mortgage will give you the lowest monthly payment? What will that payment be? How much less will this be than the other monthly mortgage payment?
b. Assuming you take the full term of the mortgage, which mortgage will result in you paying the most interest? What will that interest be? How much more will this be than the interest on the other mortgage?
R= regular monthly payment
p= amount financed, or principal
r= rate written as a decimal
n= number of payments per year
t= number of years
Needs to be easy to read.
The mortgage that will give the lowest monthly payment is EMI1 which translates to $ 1,708.16; and method one will require payment of the highest interest.
What is mortgage?A mortgage is an arrangement between you and a lender that provides the lender the right to repossess your property if you fail to repay the loan plus interest.
Mortgage loans are used to purchase a property or to borrow money against the value of an existing home.
What is the calculation for the above?Given that:
Total amount = $525,000
Down payment = 20% = 0.2
Method 1: Time is 30 years and rate is 2.72%
Method 2: Time is 15 years and the rate is 2.25%
Loan amount = total amount less down-payment
= 525,000 - (0.2 * 525,000)
= $420, 000
Using Method 1Given that t = 30 year or 360 months
r = 2.72% or 0.0272
EMI1 = [ 420, 000 * (0.0272/12) * ( 1 + (0.0272/12)³⁶⁰]/ [( 1 + (0.0272/12)³⁶⁰ -1]
= [952 * 2.259]/1.259
EMI1 = $ 1,708.16
Using Method 2
t = 15 years or 180 months
Rate = 2.25% or 0.0225
EMI2 = [420,000 * (0.0225/12) * ( 1 + (0.0225/12)¹⁸⁰]/ [( 1 + (0.0225/12)¹⁸⁰ --1]
= [787.5 * 1.401]/0.401
EMI2 = $2,751.34
Assuming you take the full term of the mortgage, which mortgage will result in you paying the most interest?
Method 1
Interest = EMI1 x total months - loan amount
= 1,708.16 x 360 - 420,000
= $194, 937.6
Method 2
Interest = EMI2 x total months - loan amount
2,751.34 x 180 - 420,000
= $75,241.2
From the above method 1 requires the highest interest.
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Identify the underline place 75.733
Answer: Digit Place Value
7 Tens
5 Ones
.
7 Tenths
3 Hundredths
3 Thousandths
Step-by-step explanation: this should help its not the answer but it's support
In Washington county , 850 homes were sold in 2017 . How many homes was sold in the southwest region.
The number of homes sold in the Southwest region in 2017was B. 102.
What are Regional Sales?Regional sales refer to the sales recorded by marketing and sales regions through which an organization distributes its products and services.
Recording sales by region helps management to determine regional managers' performances and contributions to the sales efforts.
Data and CalculationsSales in Washington county:
Southeast = 48%
Southwest = 12%
Northwest = 25%
Northeast = 15%
Sales of homes in the Southwest region = 102 (850 x 12%)
Question Completion with Answer Options:A. 1,020
B. 102
C. 588
D. 1,231
Thus, the homes sold in the Southwest region in 2017 were B. 102.
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gary cycled a total of 8 kilometers by making 4 trips to work. How many trips will gary have to make to cycle a total of 10 kilometers?
Answer:
5
Step-by-step explanation:
Each trip adds up to 8/4 = 2 km
According to this, to travel 10 km is required:
10/2 = 5 trips
Hope this helps
John and 2 friends are going out for pizza for lunch. They split one pizza and 3 large drinks. The pizza cost $14.00. After using a $7.00 gift certificate, they spend a total of $12.10. Write an equation to model this situation, and find the cost of one large drink.
Answer:
$2.55
Step-by-step explanation:
2d + $14.00 – $7.00 = $12.10; $2.55
Different types of angels
Step-by-step explanation:
assuming you are looking for angles and not angels:
Zero Angle (0° in Measure)
Acute Angle (0 to 90° in Measure)
Right Angle (90° in Measure)
Obtuse Angle (90 to 180° in Measure)
Straight Angle (180° in Measure)
Reflex Angle (180 to 360° in Measure)
Complete Angle (360° in Measure)
Solve for x
x - 20 + 2x = 35
[tex] \sf{\red{ANSWER \: \: :}}[/tex]
x = 18 1/3
[tex] \sf{\purple{EXPLANATION \: \: :}}[/tex]
x - 20 + 2x = 35
- 20 + 3x = 35
3x = 35 + 20
3x = 55
x = 55/3
x = 18 1/3
Suppose that you and a friend are playing cards and you decide to make a friendly wager. the bet is that you will dr6aw two cards without replacement from a standard deck. if both cards are hearts, your friend will pay you $16. otherwise, you have to pay your friend $3. suppose that you and a friend are playing cards and you decide to make a friendly wager. the bet is that you will draw two cards without replacement from a standard deck. if both cards are hearts, your friend will pay you $16. otherwise, you have to pay your friend $3. step 2 of 2 : if this same bet is made 762 times, how much would you expect to win or lose? round your answer to two decimal places. losses must be expressed as negative values. round your answer to two decimal places. losses must be expressed as negative values.
If the bet is done 762 times then expected value is that we may have a loss of $1562.1if the bet is that is heart comes we will get $16 and lose $3 if not comes.
Given We will get $16 if hearts come and lose $3 when not comes and bet is made 762 times. We have to calculate the expected win after 762 times.
We know that there are 13 hearts in the standard deck of cards.
Probability is the chance of happening an event among all the events possible. The formula of calculating probability is as under:
Probability= number of items/ total number of items.
When two cards are chosen at random without replacement then the probability of getting two hearts is 13/52*12/51
=156/2652
=0.05
When two cards are chosen at random without replacement then the probability of not getting two hearts is 1-0.05
=0.95
When bet is made only 1 time expected value will be 0.05*16-0.95*3
=0.8-2.85
=-2.05 means we are expecting to lose $2.05.
When bet is made 762 times then the expected value will be -2.05*762=-1562.1.
Hence the expected value when bet is made 762 times is that we will lose $1562.1 .
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In which quadrants do solutions for the inequality y≤x-4 exist?
OI, III, and IV
OI, II, and III
OI and IV
All four quadrants
Answer:
(a) I, III, and IV
Step-by-step explanation:
We want to identify areas on a graph where the solutions to an inequality might be found.
Boundary lineThe boundary line for the inequality y ≤ 2/3x -4 has a positive slope and a negative y-intercept. That means it must pass through quadrants I, III, and IV.
Solution setQuadrant II is above the line, but the y ≤ () inequality tells you the shading is below the line, where y-values are less than those on the line. There can be no solutions in quadrant II.
Solutions are found in quadrants I, III, and IV.
___
For reference, the second attachments shows the quadrant numbering.
If xm/x5=x7 and (x)=x¹2, then the value of m-r= A. 3 B. 4 C. 8 D. 12 If xm / x5 = x7 and ( x ) = x¹2 , then the value of m - r = A. 3 B. 4 C. 8 D. 12
The difference between m and r from the given expressions is 8
Indices and exponentsGiven the following exponents
x^m/x^5=x^7
x^m = x^5 * x^7
x^m = x^12
Equate the powers
m = 12
For the expression
(x^r)³ = x^12
x^3r = x^12
3r = 12
r = 4
Take the difference
m - r = 12 - 4
m - r = 8
Hence the difference between m and r is 8
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hello please help with my question, I will give brainlyest!
No, John is incorrect.
Correct work shown:
[tex]\sf x^2 - 6x - 7 = 0[/tex]
[tex]\sf x^2 - 6x = 7[/tex]
[tex]\sf x^2 - 6x + 9= 7 + 9[/tex]
[tex]\sf (x-3)^2= 16[/tex]
[tex]\sf x-3=\pm \sqrt{16}[/tex]
[tex]\sf x-3= \pm 4[/tex]
[tex]\sf x= + 4 + 3 \quad or \quad x = -4 + 3[/tex]
[tex]\sf x= 7 \quad or \quad x = -1[/tex]
The correct answer should be x = 7 or x = -1
The next number in the series 0,7, 26, 63 is?
Answer:
124
Step-by-step explanation:
1^3-1=0
2^3-1=7
3^3-1=26
4^3-1=63
5^3-1=124
Hence the next one in the pattern is 124.
Find the quotient: 40 ÷ 7
Answer:
5.71428571429
Step-by-step explanation:
A square has a perimeter of 12x+25 units. Which expression represents the side length of a square and units
Answer:
3x+13 units
Step-by-step explanation:
square perimeter of 12x +52 units
perimeter= 12x +52
12x + 52= 4(sides)
divide both sides by 4 = 12x/4 + 52/4= 3x+13
which give you 3x +13 units
PLESE HELP ME ASAP!!!
Answer:
Square Root of 7 = 7^1/2 = 2.646
Cubed Root of 7 = 7^1/3 = 1.913
Square Root of 7^3 = 7^3/2 = 3.659
Hi- I need help please to get my HS diploma...did not graduate :(
For the inequality y+4x≤x2+2, where is the graph shaded and is the curve solid or dotted?
Answer:
B
Step-by-step explanation:
first for the easy one : the curve line is dotted, if the line points are NOT part of the solution. and it is solid, if the points are included.
you know what the curve line indicates ? it indicates the points for which there is equality.
so, if there is a ">=" or "<=" relation, then that includes equality, and the curve is solid.
if there is only a true inequality ("<", ">"), then the curve is dotted, as the equality is not included.
so, I how this is now really clear.
in our case here (I suspect it really looks like this)
y + 4x <= x² + 2
we have a "<=" sign, so, the curve is ..., well ? ... well ? ...
well ? ... well ? ... solid !
and we still treat inequalities as much as possible as regular equalities.
so,
y <= x² - 4x + 2 (after subtracting 4x from both sides).
and now you see it, right ?
all y values that are smaller or equal to the quadratic expression.
SMALLER ! so, BELOW the curve (as the smaller y values are represented by the lower part of the y-axis).
Which choice is equivalent to the quotient shown here for acceptable values of X?
√7x² ÷ √3x
A x(√7x/3)
B √21x³
C (√7x/3)
D (√7x³/3)
The choice that is equivalent to the quotient values of X in √7x² ÷ √3x is Option C : (√7x/3).
What is the quotient about?Since the expression is √7x² ÷ √3x
So, one need to rationalize the denominator and thus:
√7x² ÷ √3x x √3x ÷ √3x
or write as √7x² x√3x ÷ √3x
or write as√(21x³)/3x
or write as √3*7*x³/3x
or write as √3*7*x/3
= √7x/√3
Therefore, The choice that is equivalent to the quotient values of X in √7x² ÷ √3x is Option C : (√7x/3).
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Here are the ages (in years) of 10 professors at a college. 49, 43, 53, 41, 33, 67, 55, 34, 75, 55 What is the percentage of these professors who are younger than 55?
Answer:
60%
Step-by-step explanation:
There are 6 professors younger than 55 (49, 43, 53, 41, 33, 34).
6/10 = 60%
A number line going from negative 3 to positive 5. A closed circle is at negative 1.5. Everything to the left of the circle is shaded. Which inequalities have the solution set graphed on the number line? Check all that apply. x Greater-than-or-equal-to -1.5 x Less-than-or-equal-to -1.5 -1.5 Less-than-or-equal-to x -1.5 Greater-than-or-equal-to x x Less-than-or-equal-to -2.5 x Greater-than-or-equal-to -2.5 -2.5 Greater-than-or-equal-to x
the inequality in the number-line is:
x ≤ -1.5
Which inequality is represented?We know that we have a closed circle at -1.5, this means that the value is a solution of the inequality.
Then we have a line that goes to the left of that circle, so the inequality will have solutions that are less than or equal to -1.5
Then the inequality is:
x ≤ -1.5
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Answer:c
Step-by-step explanation:
trust me
cting Polynomials: Practice
Question 1 of 5
Select the correct answer.
Let p(x) be a polynomial as shown below, and let b be an integer.
p(=) = a₁ + a₁ + a₂=² + ... + an In
Which of the following is true regarding the sum and difference of p(x) and b?
O
The sum-and difference of p(x) and b are integers.
The sum and difference of p(x) and b are polynomials.
The sum of p(x) and b is a polynomial, and the difference is an integer.
The sum of plx) and b is an integer, and the difference is a polynomial.
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The option that's true regarding the sum and difference of the polynomial p(x) and b is B. The sum and difference of p(x) and b are polynomials.
How to illustrate the information?From the information given, it was stated that p(x) is a polynomial and is given as p(=) = a₁ + a₁ + a₂=² + ... + an.
In this case, it should be noted that the sum and difference of p(x) and b are polynomials.
They can't be integers as the function given is represented as a polynomial.
In conclusion, the correct option is B.
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