The product of the functions f(x) and g(x), where the functions f(x) = [tex]x+2[/tex] and g(x) = [tex]-x^{2}[/tex] is
As per the given question statement, we are supposed to find and simplify the product of the functions f(x) and g(x), where the functions f(x) = [tex]x+2[/tex]and g(x) = [tex]-x^{2}[/tex].
Let's assume [tex]m(x)[/tex] be the product of the functions [tex]f(x)[/tex] and [tex]g(x)[/tex]
So, [tex]m(x) = f(x) * g(x)\\m(x)= (x+2)*(-x^{2} )\\m(x)=-x^{3} -2x^{2}[/tex]
Therefore the product of the functions f(x) and g(x), where the functions f(x) = [tex]x+2[/tex]and g(x) = [tex]-x^{2}[/tex] is [tex]m(x)=-x^{3} -2x^{2}[/tex]
This question is a classic example of how to solve functions using different mathematical operations and using the concept of algebraic expressions.
Algebraic Expressions: An algebraic symbol or set of symbols that includes one or more integers, variables, and arithmetic operations.To learn more about algebraic expressions, click on the link given below:
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two cars travel the same distance car one travels at 50 mph and car 2 at 65 mph if it takes car 1 one more hour to travel than car two how far did the cars travel
Huai take out a 2$2600 to be on at 6.8% to help him with a two-year community college after finishing the two years he transferred to State University and Brows another $12,300 to defray expenses for the five semesters he needs to graduate. He graduates for years and four months after acquiring the first song and payments are deferred for three months after graduation the second long was acquired two years after the first and had an interest rate of 7.6% find the total amount of interest that we are acquire until payments begin
If the amount of loan taken in community college is $2900 and the rate of interest is 6.8% then the amount of interest that will accrue for loan 1 is $364.
Given that the amount of loan in community college is $2900 and the rate of interest is 6.8%.
We are required to find the amount of interest that will accrue for
loan 1.
Compound interest is the amount of interest that is calculated on the aggregate of principal and interest of previous years.
Compounded amount=P[tex](1+r)^{n}[/tex]
To find out the amount of interest for the loan 1,we have to find the compounded amount after 2 years.
Compounded amount=2600([tex](1+0.068)^{2}[/tex]
=2600*[tex](1.068)^{2}[/tex]
=2600*1.14
=$2964
Interest=2964-2600=$364
Hence if the amount of loan in community college is $2900 and the rate of interest is 6.8% then the amount of interest that will accrue for loan 1 is $364.
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somebody please help me
Answer:
4
Step-by-step explanation:
[tex] \frac{(2 {)}^{3}(2 {)}^{4} }{(2 {)}^{5} } [/tex]
→[tex] {2}^{3 + 4 + 5} [/tex]
→[tex] {2}^{2} = 4[/tex]
Hope it helpsIdentify the property that justifies the following
statement. If AB = CD, then CD = AB.
Answer:
Transitive property for equality
Step-by-step explanation:
125 tickets at $6 and $10 were sold for $1,022. How many $6 tickets and how many $10 tickets were sold?
Answer:
This is the answer :20 5/6 and 102.2
What kind of numbers are −5 and 7?
-5 and 7 are real and rational numbers also they are integers.
What is a rational number ?Numbers which can be written in the form of p/q are rational numbers where q must not be zero.
According to the given question we have to determine what kind of numbers are -5 and 7.
In a most simple way we can say that - 5 is an negative integer and 7 is a positive integer.
But -5 can be written as -5/1 which is a rational number also and 7 can also be written as 7/1 so we can also say they are integers al well as rational numbers.Lastly they are real numbers as they don't have any imaginary part 'i' in it.
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Could you show the work so I can learn? Thank you!
Answer:
38363
Step-by-step explanation:
Kent Fuller is in the 26 percent tax bracket. A nontaxable employee benefit with a value of $2,400 would have a tax-equivalent value of: (Round your
answer to the nearest whole number.)
The tax equivalent value will be $3243. The third option is correct
Tax bracket Kent Fuller is currently in is 26 percent
Nontaxable employee benefits value: $2400
The return that a taxable benefit would need to provide in order to match the yield on a comparable tax-exempt benefit is known as the tax-equivalent value. This is very useful for investors to compare the return between a tax-free and a taxable alternative.
Finding out the tax equivalent value using the formula:
Tax equivalent value = Tax exempt value/(1 - Tax Rate)
Tax equivalent value = 2400/(1 - 0.26)
= 2400/0.74
Tax equivalent value = 3243.24 or 3243
Therefore, the tax equivalent value will be $3243. Hence, the third option is correct
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Alfonso borrowed $2500 total from two different banks. One bank charged 4% simple interest, the other charged 3.5% simple interest. After one year, the amount of interest that Alfonso owed was $91.25. How much money did Alfonso borrow from each bank.
Alfonso borrowed $750 from the bank with 4% simple interest and borrowed $1,750 from the bank with 3.5% simple interest.
How do we calculate the amount borrowed?
Let:
x = amount borrowed from the bank that charged 4% simple interest
y = amount borrowed from the bank that charged 3.5% simple interest
Therefore, we have:
x + y = 2,500 ............................... (1)
0.04x + 0.035y = 91.25 ............................. (2)
From equation (1), we have:
x = 2,500 - y ....................... (3)
Substituting equation (3) into (2) and solving for y, we have:
0.04(2,500 - y) + 0.035y = 91.25
100 - 0.04y + 0.035y = 91.25
100 - 0.005y = 91.25
-0.005y = 91.25 - 100
-0.005y = -8.75
y = -8.75 / -0.005
y = $1,750
Substituting for y in equation (3), we have;
x = 2,500 - 1,750
x = $750
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For each value of 1 ≤ n ≤ 100, the highest common factor of 8n + 3 and 5n + 4 is written down. What is the sum of these values
Highest common factor of 8n + 3 and 5n + 4 is either 1 or 17 for all n and its sum is 18
what is greatest integer divisor ?
The greatest common divisor (GCD) of two nonzero integers a and b is the greatest positive integer d such that d is a divisor of both a and b; that is, there are integers e and f such that a = de and b = df, and d is the largest such integer. The GCD of a and b is generally denoted gcd(a, b).
For each value of 1 ≤ n ≤ 100, the highest common factor of 8n + 3 and 5n + 4 is written down. What is the sum of these values
Let gcd(8n + 3, 5n + 4) = d
⟹d|8n+3∧d|5n+4
⟹d|8(5n+4)−5(8n+3)
⟹d|17
Therefore highest common factor of 8n + 3 and 5n + 4 is either 1 or 17 for all n and its sum is 18
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Pls answer this question
Answer: 1/4
Step-by-step explanation:
The easiest way to solve this is to make them all common denominators.
The common denominator for this problem is 24.
Change the denominators:
1/4 = 6/24
4/12 = 8/24
3/8 = 9/24
2/6 = 8/24
This way it is easier to see which one is smaller and closest to 0. In this case, it is 6/24 or 1/4 because 6/24 is the smallest out of all of them.
If LM = 22 and MN = 15, find LK
1. If the length and width of the rectangle are doubled, then what is the value of the new area? 4ft 10ft
O 160
040
80
120
4ft
10ft
Answer: I think the answer you are looming for is 80 feet.
Step-by-step explanation:
4 x 10 = 40
To double means to multiply by 2 so
40 x 2 = 80
Which expression has the same value as 4^2 - 6 x 2?
A. 1 - 8^0 + 2^2
B. 3^2 x 6^-2
C. 10 - 3 x 2 + 4^1
The expression which has the same value as the given expression; 4² - 6 × 2 among the answer choices is; Choice C; 10 - 3 x 2 + 4¹.
Which expression has the same value as the given expression?According to the task content; the given expression whose equivalent is to be determined is;
Given;
4² -6 ×2.
It follows from PEMDAS that the exponent should be evaluated and then the multiplication.
Hence, the value of the expression is; 16 - 8
= 8.
For answer choice C, which is correct, the evaluation is as follows;
10 - 3 × 2 + 4¹
= 10 -6 + 4
= 8.
Ultimately, choice C has the same value as the given expression.
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Suppose the spinner shown to the right is spun once, to determine a single-digit number, and we
are interested in the event E that the resulting number is even. Give each of the following.
(a) the sample space
(b) the number of favorable outcomes
(c) the number of unfavorable outcomes
(d) the total number of possible outcomes
(e) the probability of an even number
(f) the odds in favor of an even number
The sample space for the event is given by {2,3,4}
The sample space is a collection of all possible outcomes of an experiment. The sample space is used in probability where the it represents all possible outcomes.
a) In the spinner there are only three possibilities.
The sample space is represented by {2,3,4} .
b)The favorable outcomes in this case is 2 and 4.
Hence the number of favorable outcome is 2.
c)There is only 1 unfavorable outcome which is 3.
d)The total number of possible outcomes is 3 , as we see in the sample space there are 3 numbers.
e)The probability is defined as the fraction of favorable outcome to the
total number of outcome. Therefore the probability in this case is given
by [tex]P(even)=\frac{2}{3}[/tex]
f) The ratio of the number of possible outcomes to the number of possible outcomes that do not occur is known as the odds in favor.
Therefore odds in favor = 2:1
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An airline offers discounted flights from Atlanta to five American cities . Below is a frequency distribution of the number of tickets purchased for each location based on a random sample of purchased tickets. Complete parts (a) through (f)
-(a) construct a relative frequency distribution of the data. (round to three decimal places as needed)
According to the given statement The relative frequency distribution of the data is = 964.400
What is the data's relative frequency distribution?A relative frequency distribution, which is connected to a probability distribution and is widely used in statistics, illustrates the percentage of the total number of observations associated with each value or class of values.
What is the purpose of using relative frequency distribution?Relative frequency distributions are particularly valuable because they show how common a value is in a dataset in comparison to all other values.
According to the given information:The relative frequency distribution of the data:
= the frequency/ total number of data.
So,
the frequency of the data is:
1227 + 884 + 1160 + 634 + 917
= 4,822
The total number of data: = 5
Now applying the formula we get:
= 4822/5
= 964.400
According to the given statement the frequency of the data is = 964.400
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Use the given conditions to write an equation for the line in point-slope form and general form.
Passing through (-4,3) and parallel to the line whose equation is 3x - 4y-5-0
The equation of the line in point-slope form is.
(Type an equation. Use integers or fractions for any numbers in the equation.)
Answer:
I don't know it this question
Step-by-step explanation:
rfhdwhjgdshmfsaghjjdsdbj
Help with my geometry problem (included as image)
Answer:
40°
Step-by-step explanation:
We know that
[tex]m\angle 2=28^{\circ}+m\angle 1[/tex]
Thus, by the angle addition postulate,
[tex]28+m\angle 1+m\angle 1=108^{\circ} \\ \\ 2m\angle 1=80^{\circ} \\ \\ m\angle 1=40^{\circ}[/tex]
Let [tex] \rm|M|[/tex] denote the determinant of a square matrix M. Let [tex] \rm g : \bigg[0, \dfrac{\pi}{2} \bigg] \to \mathbb{R}[/tex] be the function defined by [tex] \rm g( \theta) = \sqrt{f( \theta) - 1} + \sqrt{f \bigg( \dfrac{\pi}{2} - \theta\bigg) - 1} [/tex] where
[tex] \rm f( \theta) = \dfrac{1}{2} \left| \begin{matrix} 1& \sin( \theta) &1 \\ - \sin( \theta) &1& \sin( \theta) \\ - 1& - \sin( \theta)&1 \end{matrix} \right | + \left| \begin{matrix} \sin(\pi) & \cos( \theta + \frac{\pi}{4} ) & \tan( \theta - \frac{\pi}{4} ) \\ \sin( \theta - \frac{\pi}{4} ) & - \cos( \frac{\pi}2 ) & \log_{e} ( \frac{4}\pi ) \\ \cot( \theta + \frac{\pi}{4} ) & \log_{e} ( \frac{\pi}4 )& \tan(\pi) \end{matrix} \right | [/tex]
Let p(x) be a quadratic polynomial whose roots are the maximum and minimum values of the function g([tex]\theta [/tex]) , and p(2)=2-[tex]\sqrt{2}[/tex]. Then which of the following is True?
[tex] \rm(1) \: p \bigg( \frac{3 + \sqrt{2} }{4} \bigg) < 0 \\ \rm(2) \: p \bigg( \frac{1 + 3 \sqrt{2} }{4} \bigg) > 0 \\ \rm(3) \: p \bigg( \frac{5\sqrt{2} - 1 }{4} \bigg) > 0 \\ \rm(4) \: p \bigg( \frac{5 - \sqrt{2} }{4} \bigg) < 0[/tex]
The second matrix in the definition of [tex]f[/tex] is singular, since
[tex]\sin(\pi) = -\cos\left(\dfrac\pi2\right) = \tan(\pi) = 0[/tex]
[tex]\cos\left(\theta+\dfrac\pi4\right) = \sin\left(\dfrac\pi2 - \left(\theta+\dfrac\pi4\right)\right) = \sin\left(\dfrac\pi4-\theta\right)=-\sin\left(\theta-\dfrac\pi4\right)[/tex]
[tex]\cot\left(\theta+\dfrac\pi4\right) = \tan\left(\dfrac\pi2 - \left(\theta+\dfrac\pi4\right)\right) = \tan\left(\dfrac\pi4 - \theta\right) = -\tan\left(\theta-\dfrac\pi4\right)[/tex]
[tex]\ln\left(\dfrac4\pi\right) = -\ln\left(\dfrac\pi4\right)[/tex]
In other words, it's antisymmetric; [tex]A^\top=-A[/tex]. It's easy to show that [tex]\det(A)=0[/tex] if [tex]A[/tex] is 3x3 and antisymmetric.
The other determinant reduces to
[tex]\begin{vmatrix}1 & \sin(\theta) & 1 \\ - \sin(\theta) & 1 & \sin(\theta) \\ -1 & -\sin(\theta) & 1 \end{vmatrix} = 2 + 2\sin^2(\theta)[/tex]
Hence
[tex]f(\theta) = 1 + \sin^2(\theta) \implies f\left(\dfrac\pi2\right) = 1 + \cos^2(\theta)[/tex]
With [tex]g[/tex] defined on [tex]\left[0,\frac\pi2\right][/tex], both [tex]\sin(\theta)[/tex] and [tex]\cos(\theta)[/tex] are non-negative. So
[tex]g(\theta) = \sqrt{f(\theta)-1} + \sqrt{f\left(\dfrac\pi2-\theta\right)-1} \\\\ ~~~~ = \sqrt{\sin^2(\theta)} + \sqrt{\cos^2(\theta)} \\\\ ~~~~ = |\sin(\theta)| + |\cos(\theta)| \\\\ ~~~~ = \sin(\theta) + \cos(\theta) \\\\ ~~~~ = \sqrt2\,\sin\left(\theta + \dfrac\pi4\right)[/tex]
which is maximized at [tex]t=\frac\pi4[/tex] with a value of [tex]\sqrt2\,\sin\left(\frac\pi2\right)=\sqrt2[/tex], and minimized at [tex]t=0[/tex] and [tex]t=\frac\pi2[/tex] with a value of [tex]\sqrt2\,\sin\left(\frac{3\pi}4\right)=1[/tex].
Edit: The rest of my answer wouldn't fit. Continued in attachment.
Calculate the length of a chord of a circle of radius 26cm if the chord is 10cm from the center of the circle
Answer: see explanation
Step-by-step explanation:
The 10 cm distance is measured perpendicularly to the chord, forming a right angle and bisecting the chord. Thus half of the chord, the segment from the center of the chord, and a radius to the end of the chord form a right triangle. The hypotenuse is 26 cm and one leg is 10 cm, so the other leg is given by the Pythagorean theorem: a^2 + 10^2 = 26^2, giving a = 24 cm. Since a is half the chord, the chord is 2a = 48 cm in length.
Hence, the length of a chord of a circle is [tex]48cm[/tex].
What is the circle?
A circle is defined as a two-dimensional figure, which is round in shape where all the points on the surface of the circle are equidistant from the center point is called “[tex]P[/tex]”.
Here given that,
A circle of radius [tex]26[/tex]cm if the chord is [tex]10[/tex]cm from the center of the circle.
So,
The [tex]10[/tex]cm from the center of the circle is perpendicular of the chord and the hypotenuse is [tex]26[/tex]cm .
As we know
[tex]H^2=B^2+P^2[/tex] .......[tex](1)[/tex]
Substituting the values in the equation [tex](1)[/tex], we get
[tex](26)^2=(10)^2+B^2\\B^2=676-100\\B^2=576\\B=\sqrt{576}\\B=24cm[/tex]
Hence, the length of a chord of a circle is [tex]48cm[/tex].
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A company produces a logic board for computers. The annual fixed cost for the board is $323,902, and the variable
cost is $109 per board. If the logic board sells for $479, write an inequality that gives the number of logic boards that
will give a profit for the product.
Write the linear inequality?
The inequality that give the number of logic boards that will give a profit for the product is profit = x($479-$109)-$323,902.
Given that, a company produces a logic board for computers. The annual fixed cost for the board is $323,902, and the variable cost is $109 per board. So, we have to write an inequality which will gives the number of logic boards that will give a profit for the product, if the logic board sells for $479.
We simply use the formula that,
profit + annual fixed cost = number of logic board sold x (logic board sales price-variable cost of logic board)
Let the number of logic board sold be x.
profit + $323,902 = x($479-$109)
profit = x($479-$109)-$323,902
Therefore, we can denote the above listed information in profit = x($479-$109)-$323,902 term. This is the required answer.
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i will give brianliest to however gets it right
Please help
Write the equation of the line shown
Answer:
Equation of line is y = 8 as it is horizontal
Samera is asked to find the multiples of 24. Her work is shown below.
m/NMG = 46°, m/NML = 11x + 11, and m/GML = 8x-5. Find x.
we get that, the value of x for the given angles in the diagram is 10°.
We can see that:
∠ NMG + ∠ GML = ∠ NML
Substituting the values of the angles in the equation, we get that:
46 ° + 8 x - 5° = 11 x + 11 °
Combining the like terms:
8 x + 41° = 11 x + 11°
Taking variables on one side:
11 x - 8 x = 41° - 11°
Combining the like terms again:
3 x = 30°
Divide both sides by 3:
x = 30° / 3
x = 10°
Therefore, we get that, the value of x for the given angles in the diagram is 10°.
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Your question was incomplete. Please refer the content below:
∠ NMG = 46°, ∠ NML = 11x + 11, and ∠ GML = 8x-5. Find x.
Is the slope of a linear demand curve positive or nega-
tive?
The slope of a linear demand curve is negative
The demand curve's negative slope indicates that there is an inverse link between price and demand.
It is true that the demand curve's negative slope indicates an inverse link between price and quantity desired. According to the demand curve, demand declines as prices increase and rises as prices decrease.
This statement is false since it only applies to Giffen products, where the demand curve has a positive slope and a direct correlation between price and quantity desired.
Because unit requests rise when prices decrease and decline when prices rise, the demand curve often slopes downward (i.e., is negative). Demand increases when prices are low, but demand decreases when prices are high.
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4xº
(3x + 8)°
B
Find m
If angle BAD=4x° and angle DAC=(3x+8)° then the equation showing angle BAC is equal to (7x+8)°.
Given that angle BAD=4x° and angle DAC=(3x+8)°.
We are required to find the equation showing the angle BAC.
Angle is basically the figure formed by two rays which is called the sides of the angle and sharing a common endpoint called the vertex of the angle.
∠BAD=4x° and ∠DAC=(3x+8)°
To find the equation showing angle BAC we have to just add the two expressions given in the equation.
∠BAC=∠BAD+∠DAC
∠BAC=4x+3x+8
∠BAC=(7x+8)°
Hence if angle BAD=4x° and angle DAC=(3x+8)° then the equation showing angle BAC is equal to (7x+8)°.
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A car rental agency advertised renting a car for $27.95 per day and $0.25 per mile. If Greg rents this car for 3 days, how many whole miles can he drive on a $150 budget?
Answer: 264.6 miles
Step-by-step explanation: Let's put the info we got from the problem into an equation. If the car is rented for three days, we need to multiply 27.95 by 3, which will give us 83.85. Now let's use the equation 150=83.85 + 0.25x, where x represents miles. Subtract 83.85 from both sides and we get 66.15 = 0.25x. Now divide both sides by 0.25 and we get x = 264.6.
Answer:
264 miles
Step-by-step explanation:
y = 27.95x + 0.25n where:
y = budget
x = days rented
n = miles driven
150 = 27.95(3) + 0.25n
150 = 83.85 + 0.25n
150 - 83. 85 = 0.25n
66.15 = 0.25n
66.15 / 0.25 = n
n = 264.6 miles
27.95(3) + 0.25(246.6) = $150
You decide you need a new computer. The cost of the computer is $864. However, the store also offers a rent to own option which will cost $41 per week for 24 weeksHow much more will the rent to own option cost after you have made all of the payments? $
The rent option will cost 120 more dollars than the outright cost of the computer .
How to find how much more the rent to own option cost?The outright cost of the computer is $864.
The store also offers a rent to own option which will cost $41 per week for 24 weeks.
Therefore, the total cost for the rent option is as follows:
cost of the computer for rent option = 41 × 24
cost of the computer for rent option = 984 dollars
Therefore,
difference in cost = 984 - 864
difference in cost = 120 dollars
Therefore, the rent option will cost 120 more dollars than the outright cost of the computer.
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what type of number is 16/14
Answer:
fraction..............................
or improper fraction.