Answers
The value of equation P (x) = [tex]2[/tex] + [tex]\frac{x}{2}[/tex] + [tex]x^{2}[/tex] - [tex]\frac{x^{2} }{3}[/tex] when x = (-1) is P(-1) = [tex]\frac{13}{6}[/tex]
P (x) = [tex]2[/tex] + [tex]\frac{x}{2}[/tex] + [tex]x^{2}[/tex] - [tex]\frac{x^{2} }{3}[/tex]
If the value of x = -1
P (-1) = 2 + [tex]\frac{-1}{2}[/tex] + [tex](-1)^{2}[/tex] - [tex]\frac{(-1)^{2} }{3}[/tex]
P (-1) = 2 - [tex]\frac{1}{2}[/tex] + 1 - [tex]\frac{1}{3}[/tex]
The above equation consist of fractional numbers as well as the whole numbers to therefore it is not possible to apply the operations in this particular conditions.
Equation is statement which equates two algebraic expressions.On taking LCM for the denominators of the fractional numbers (2 , 3), we get 6 as the Least Common Multiple.
To apply the sum and difference operation, we need to make the denominators of all the terms same.
[tex]2 * \frac{6}{6} = \frac{12}{6}[/tex][tex]\frac{1}{2} * \frac{3}{3} = \frac{3}{6}[/tex][tex]1 * \frac{6}{6} = \frac{6}{6}[/tex][tex]\frac{1}{3} * \frac{2}{2} = \frac{2}{6}[/tex]P (-1) = [tex]\frac{12}{6} - \frac{3}{6} + \frac{6}{6} - \frac{2}{6}[/tex]
P (-1) = [tex]\frac{12-3+6-2}{6}[/tex]
P (-1) = [tex]\frac{13}{6}[/tex]
Value of the equation P when 'x' is replaced by (-1) will be [tex]\frac{13}{6}[/tex]
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Related Questions
what is the missing value in x^2 y^8 times x^3 y^? = x^5 y^5?
Answers
Hence , the missing value y in x^2 y^8 times x²y⁸ x³ y = x⁵ y⁵ is -3 .
Definition of law of exponents
- one in every of a collection of rules in algebra: exponents of numbers are additional once the numbers are increased, subtracted once the numbers are divided, and increased once raised by still another exponent: a^m × aⁿ = a^(m+n)
We have given an expression x²y⁸ x³ y = x⁵ y⁵ .
LHS = x²y⁸ x³ yⁿ
Let the power of y in LHS be "n" .
On using exponents rule , we get
LHS = x⁵y⁹⁺ⁿ
RHS = x⁵ y⁵
As LHS = RHS
x⁵y⁹⁺ⁿ = x⁵ y⁵
On comparing power of y , we get
9 + n = 5
n = -3
Hence , the power of y in LHS is -3 .
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Find 55% of 60 kilometers.
Answers
Answer:
33
Step-by-step explanation:
Convert the percentage to a decimal.
55 ÷ 100 = 0.55
Multiply 60 by 0.55
60 × 0.55 = 33
Answer:
33
Step-by-step explanation:
55 x 60 divided by 100
= 33
[tex]-61 = 8 - 1/3 (12w + 42) - w[/tex]
Answers
The variable w is as follows:
[tex]w = \frac{393+\sqrt{189221} }{12}[/tex][tex]w = \frac{393-\sqrt{189221} }{12}[/tex]How to find the variable in an equation?We have to find the variable w in the equation.
-61 = 8 - 1 / 3(12w + 42) - w
subtract 8 from both sides of the equation
-61 = 8 - 1 / 3(12w + 42) - w
-61 - 8 = 8 - 8 - 1 / 3(12w + 42) - w
-69 = - 1 / 3(12w + 42) - w
69 = 1 / 3(12w + 42) + w
Therefore,
[tex]\frac{1}{3(12w+42)}+w[/tex] = 69
[tex]\frac{1+3w(12w+42)}{3(12w+42)}[/tex] = 69
[tex]\frac{1 + 36w^{2} +126w}{3(12w+42)}[/tex] = 69
cross multiply
1 + 36w² + 126w = 2484w + 8694
36w² + 126w - 2484w - 8694 + 1 = 0
36w² - 2358w - 8693 = 0
using,
[tex]\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex] and [tex]\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]
a = 36
b = -2358
c = -8693
Hence,
[tex]\frac{2358+\sqrt{(-2358)^{2}-4(36)(-8693) } }{2(36)}[/tex] and [tex]\frac{2358-\sqrt{(-2358)^{2}-4(36)(-8693) } }{2(36)}[/tex]
Therefore,
[tex]w = \frac{393+\sqrt{189221} }{12}[/tex] and [tex]w = \frac{393-\sqrt{189221} }{12}[/tex]
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Your friend invested $ 1000 in an account that pays 6 % annual interest. How much interest will your friend have after her college graduation in 4 years?
a. Is an exponential model reasonable for this situation?
Answers
The interest the friend will have after her college graduation in 4 years is $240 and an exponential model is not reasonable for this situation.
The formula to be used to is given as :
I = Prt (1)
where, I = simple interest
P = principal amount or amount initially deposited.
r = annual interest rate
t = time
According to the question we have been given that
P = $1000
r = 0.06
t = 4 years
Putting the required values in equation (1) we get
I = 1000*0.06*4
I = 240
Thus $240 interest the friend will have after her college graduation in 4 years.
a) the exponential model is not reasonable for this situation as simple interest is not an exponential function.
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pls help guys i have no clue whats going on
Answers
Answer:D
Step-by-step explanation:Hope that helped
18-2x = 4x
Drag and drop the reasons into the boxes to correctly complete the table.
18-2z=4r
18=6z
Combine Like Terms Division Property of Equality Given Addition Property of Equality
Dist
Answers
Answer:
18-2x=4x is given
18=6x is addition property of equality
3=x is I think division property of equality bc you divided to get x=3
Simplify each number. 4¹/₂
Answers
The simplified form of number is 2
To find the simplified form of the number, we will find the number whose square is equal to 4. As per the known fact, only 2 is the number whose square is 4.
Firstly rewriting the number -
Number = [tex]4^{1/2}[/tex]
Now, rewriting the number with base as 2 and exponent also as 2, as stated in theory above -
Number = [tex]2^{2(1/2)}[/tex]
Cancelling 2 from the exponent as it is present in both numerator and denominator. Rewriting the number with 2 as base and 1 as exponent to find the simplified form of the number.
Number = 2
Hence, the simplified number is 2
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The area of a blue circle is 15 square yards less than five times the area of a tan circle. The blue circle has an area of 1,335 square yards. Use approximation to find the radius of the tan circle.
Answers
Based on the given task content, the approximate radius of the tan circle given the area of the blue circle is 9.27 yards.
Area of a circleArea of the tan circle = xArea of the blue circle = (5x - 15) Area of blue circle = 1,335 square yards1,335 = 5x - 15
Add 15 to both sides1,335 + 15 = 5x
1,350 = 5x
divide both sides by 5x = 1350/5
x = 270 square yards
Area of the tan circle = πr²
270 = 3.14 × r²
270 = 3.14r²
divide both sides by 3.14r² = 270 / 3.14
r² = 85.98726114649681
r = √85.98726114649681
Approximately,
r = 9.27 yards
Therefore, the approximate radius of the tan circle given the area of the blue circle is 9.27 yards.
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In which of the following combination, both fractions can be simplified as a whole number?
2/2 , 3/2
4/2 , 3/6
2/2 , 6/2
5/2 , 3/2
Answers
because 2/2=1 and 6/2 = 3
Answer:
2/2, 6/2
Step-by-step explanation:
2/2 can be simplified as 1 and 6/2 can be simplified as 3
Determine whether each function is an example of exponential growth or decay. Then, find the y -intercept. y=25/7(7/5) x
Answers
y = 25x / 5 is each function is an example of exponential growth or decay.
What does exponential growth look like in math?
A typical illustration of exponential expansion is population increase. Take a population of bacteria as an example. It seems sense that the rate of population increase would be inversely correlated with the population's size. After all, the number of bacteria grows more quickly the more there are for them to reproduce.y= 25/7(7/5) x
y = 25/5 x
y = 25x / 5
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How much should you invest in an account that pays 6 % annual interest compounded continuously if you want exactly $ 8000 after four years? Show your work.
Answers
We must invest $6294.256 if we want exactly $ 8000 after four years.
The formula for calculating the amount (A) on a principal (P) invested at the rate of r%, compounded continuously, after t years is-
[tex]A = Pe^{rt}[/tex]
Here, we are given that rate of interest = 6% and we need exactly $8000 after four years.
Thus r = 6/100 = 0.06 and t = 4
Putting the values in the compound interest formula we get,
8000 = P[tex]e^{(0.06*4)}[/tex]
8000 = P[tex]e^{(0.24)}[/tex]
P[tex]e^{(0.24)}[/tex] = 8000
[tex]e^{(0.24)}[/tex] = 1.271
⇒ 1.271P = 8000P
= 8000/ 1.271P
= 6294.256
Thus, we must invest $6294.256 if we want exactly $ 8000 after four years.
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What does the 150 in the equation represent?
What does the 9 in the equation represent?
Answers
Max rides his scooter toward Kim and then passes her at a constant speed. His distance in feet, d, from Kim t seconds after he started riding his scooter is given by d = |150 – 9t|. Then 150 in the equation represents the initial distance between Max and Kim. 150 is how far Max is from Kim before he starts and 9 in the equation represents the rate at which Max is closing in on Kim. 9 feet per second is Max's rate.
What is Equation?
Two expressions with equal sign is called as equation.
Max rides his scooter toward Kim and then passes her at a constant speed. His distance in feet, d, from Kim t seconds after he started riding his scooter is given by d = |150 – 9t|.
Then 150 in the equation represents the initial distance between Max and Kim. 150 is how far Max is from Kim before he starts and 9 in the equation represents the rate at which Max is closing in on Kim. 9 feet per second is Max's rate.
Therefore Then 150 in the equation represents the initial distance between Max and Kim. 150 is how far Max is from Kim before he starts and 9 in the equation represents the rate at which Max is closing in on Kim. 9 feet per second is Max's rate.
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1. Which equation is not an example of a direct variation?
5
A. y = x + 1
B.y = -x
C. y = 4x
D.y = -9x
3
16
Answers
Answer: D
Step-by-step explanation:
Write each expression as a single natural logarithm. ln 9+ln 2
Answers
We have expression ln 9+ln 2 as a single natural logarithm ln 18
What is a natural logarithm?A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.
Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.
The power to which e would need to be raised in order to equal x is the natural logarithm of x.
For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.
Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.
We have been asked to express ln 9+ln 2 as a single natural logarithm.
⇒ ln 9 + ln 2
⇒ ln (9) = ln (2)
Use the quotient property of logarithms
⇒ ln (9 × 2)
⇒ ln 18
Finally, we have expressed ln 9+ln 2 as a single natural logarithm ln 18
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Domain-Functions
state the domain and range of the function
Answers
The domain of the function is [-2, 2] and the range of the function is [-1, 2].
If there is a function y = x + a, then the domain is the set of all values that x can take and the range is the set of all the values that y can take for the function to exist.
Here, we are given a function as shown in the graph.
As we can see the function is defined only for the given points, that is, it has 2 endpoints.
Just by looking at the graph we can see that x can take values from -2 to 2. Thus, the domain of the function is [-2, 2].
We use closed brackets as x can be -2 and 2 as well. Similarly, we can see that y can take values from -1 to 2.
Thus, the range of the function is [-1, 2].
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A soup company ordered 57 shipments of carrots. There were 901 carrots in each shipment. How many carrots did the company order in all?
Answers
hope this helps ♡
Answer: 51357
901×57=51357
Kathy loves the K-Pop group BTS. She wants to buy their World Tour DVD for $27.80.
a) The tax for the album is 0.15 of the cost. How much is tax?
b) if Kathy has $35, how much will change will she get back after buying the album and paying tax
Answers
Tax levied is $4.17 if the price of album is $27.80.
Kathy will get $3.03 after buying the album and paying the tax.
What is tax?A tax is a mandatory financial charge or other sort of levy that is placed on a taxpayer by a governmental entity in order to pay for public services and other expenses.
The total amount is calculated by adding the tax on the cost of product or service.
How are Total Amount and Tax related?The pre-tax price of an item must first be multiplied by the sales tax percentage once it has been translated to a decimal form in order to determine the amount of sales tax that will apply to the purchase. To determine the item's Total Amount, the sales tax must be computed and then added to the pre-tax price.
a) Given data: Tax%=0.15 of cost of album
Selling Price=$27.80.
Tax=Tax%×Selling Price
=0.15×27.80
=$4.17
b) Given data: Amount given by Kathy = $35
Tax=$4.17
Total Amount = Selling Price + Tax
=$4.17+$29.80
=$31.97
Amount left can be calculated by subtracting the amount given by Kathy from the Total Amount.
Amount=$35-$31.97
=$31.97
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Please answer with work
Answers
Answer:
7. 17
8. -7
9. 64/3 or 21 1/3
Step-by-step explanation:
7. 3x-4 and the value of x is 7. Plug 7 into the x values in the expression that is given.
3x-4 --> 3(7) - 4
When simplified, 3(7) - 4 becomes 21-4 which is 17.
8. -5x+8 and the value of x is 3. Same as before, but this time you'll plug 3 into the x values in the given expression.
-5x+8 --> -5(3) + 8
When simplified, -5(3) + 8 becomes -15+8 which is -7.
9. 10x+18 and the value of x is 1/3. Plug in 1/3 into the x values in the expression.
10x+18 --> 10(1/3)+18
When simplified, 10(1/3)+18 becomes 10/3+18. To solve this, turn 18 in a fraction over 3. 3x18=54 and that gives you the numerator. 10/3+54/3= 64/3. If you wanted it in a mixed fraction, it would be 21 1/3.
Dante is baking two different recipes, cookies and brownies. The cookie recipe requires 1.5
cups of sugar, and the brownie recipe requires 1.25
cups of sugar.
Answers
3. Kaitlin has two puppies. Puppy A
weighs 12 pounds and is gaining
1.5 pounds each week. Puppy B
weighs 18 pounds and is gaining
0.75 pounds each week. How
many weeks, x, will it take for
the two puppies to weight the
same amount? put in a equation or inequality
Answers
Answer:
X = 8
Step-by-step explanation:
what would be 12+3.4x-5.4x-x simplified?
Answers
Answer:
12−3x
Step-by-step explanation:
12+3.4x−5.4x−x
Combine 3.4x and −5.4x to get −2x.
12−2x−x
Combine −2x and −x to get −3x.
12−3x
After simplification of given expression. We get, the value of x is 4.
To simplify this 12 + 3.4x - 5.4x - x,
12 + 3.4x - 5.4x - x = 0
3.4x - 5.4x = - 2x
12 - 2x - x
-2x - x = -3x
-3x + 12 = 0
-3x = -12,
x = 4
Therefore, the value of x is 4.
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Simplify each radical expression. Use absolute value symbols when needed. ∛-0.027
Answers
The simplified form is -0.3.
As an instance, 3√(8) method to locate the diced root of 8. If there may be no superscript range, the novel expression is asking for the rectangular root. The term underneath the unconventional image is referred to as the radicand.
An intensive expression is an expression containing a rectangular root. Radicand - a variety of expressions in the radical symbol. Radical equation - An equation containing radical expressions with variables inside the radicands.
A few examples of radicals are √7, √2y+1, etc. an intensive also can be associated with the subsequent terms: An equation this is inside a radical is referred to as a thorough equation. An expression that lies interior a rectangular root is referred to as an intensive expression.
Applying radical rule,
[tex]\sqrt[n]{-a} =-\sqrt[n]{a} \\\sqrt[3]{-0.027}=-\sqrt[3]{0.027}\\ = -0.3[/tex].
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Please help me out please please please
Answers
- hope this helps ♡
Which best explains the relationship between the two triangles below?
Answers
Answer:1.
Step-by-step explanation: 1. because , and Step-by-step explanation:We have been given two triangles and . We are asked to find the relationship between these triangles.By angle sum property let us find measure of angle C of triangle ADC.Let us find measure of angle T of triangle RTS.We can see that , and . Therefore, and 1st option is the correct choice.
determine whether an observational study or an experimental study is used. a study was done on two groups of overweight individuals. group 1 was placed on a healthy, moderate diet. group 2 was not given any diet instructions. after 1 month, the members were asked how many times they engaged in binge eating. the results of the two groups were compared.
Answers
An experimental study is used in the given situation.
Observational Study is defined as the type of study where there is no influence on the response of the participant.
Experimental Study is defined as the type of study where the participant is put into a setup and then the participants are observed .
In the given question ,
As the individual are first categorized into to two groups , one on a healthy, moderate diet and the other group not on any diet.
So, we can see that in this a setup has been created , they are put in different conditions , and then they are observed .
Therefore , an experimental study is used in the given situation.
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Dionne slides a flag shaped like an isosceles triangle up to the top of a 9-meter flagpole. How many congruent angles does the flag have now? congruent angles
Answers
Answer:
So There will be 2 congruent angle
determine algebraically, whether the following function is ever, odd, or neither. g(x)= x^ square root of 1+x
Answers
The function g(x)= x^ square root of 1+x is neither an even function nor an odd function
How to determine the function type?The function is given as
g(x)= x^ square root of 1+x
Rewrite the above function equation properly
So, we have
g(x) = x^(√x+1)
Calculate g(-x)
So, we have
g(-x) = -x^(√-x+1)
Evaluate
g(-x) = -x^(√-x+1)
Calculate -g(x)
So, we have
-g(x) = -x^(√x+1)
In the above computations;
g(x) does not equal g(-x) and -g(x)
Hence, the function g(x)= x^ square root of 1+x is neither an even function nor an odd function
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In triangle DAB, D = x, m
Answers
Answer:
Step-by-step explanation:
It is not possible for a triangle to have more than one vertex with internal angle greater than or equal to 90°, or it would no longer be a triangle.
Mr raymond teaches dance he has 18 6th graders students and 24/7 grader students he wants to put the students in equal groups each group will have students of only one grade level how many students should be in each group how many of each group will be there very nice thank you
Answers
Using greatest common factor (GCF), Mr. Raymond should put 6 students in each group. If that happens, he will have 3 groups of 6th graders and 4 groups of 7th graders.
The greatest common factor (GCF) of a set of numbers is defined as the largest common positive integer that divides each number into equal parts with zero remainder.
If Mr. Raymond has 18 6th graders students and 24 7th grader students he wants to put in equal groups wherein each group will have students of only one grade level, find the GCF of 18 and 24 to find how many students he will put in each group.
18 : 1, 2, 3, 6, 9, 18
24 : 1, 2, 3, 4, 6, 8, 12, 24
GCF = 6
Hence, he should put 6 students in each group.
Dividing each level of students to groups of 6.
6th graders = 18/6
6th graders = 3 groups
7th graders = 24/6
7th graders = 4 groups
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5. What is the additive inverse of 3/4
Answers
Answer:
Step-by-step explanation:
0.75