Answers
Answer:
Solution given:
sin 52°=perpendicular/base
sin52°=AB/AC
AC=12/sin52°=15.23is your answer
Related Questions
21. If 2 < a < 5, and 3 < b < 6, what are the possible values of a + b?
(A) a + b must equal 8.
(B) a + b must be between 2 and 6.
(C) a + b must be between 3 and 5.
(D) a + b must be between 5 and 8.
(E) a + b must be between 5 and 11.
Answers
The value of a + b must be between 5 and 11. If the value of a 3 or 4, and b will be 4 or 5.
How to find unknown value ?An unknown in mathematics is a number that we are unsure of. In algebra, where they are also known as variables and denoted by symbols like x, y, and z, they are frequently utilised.
In science, a letter from the Roman or Greek alphabet stands in for an undetermined value. They are most frequently employed in physics, where equations are used to explain how different physical qualities relate to one another.
Given that
2 < a < 5, and 3 < b < 6
a is greater than 2 and lesser than 5 , so the value will be 4 or 3.
b is greater than 3 and lesser than 6, so the value will be 4 or 5.
a + b is
3 + 4 = 7 or 4 + 5 = 9
so the product of sum will be 7 or 9, it is between 5 and 11
Therefore, a + b must be between 5 and 11.
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2. (5 pts) An angle, A, is 11 times larger than its supplement, B. Find the angles (be sure to say which is which).
Answers
Answer:
So, a+2a=180°
Simplify.
3a=180°
To isolate a , divide both sides of the equation by 3 .
3a3=180°3 a=60°
The measure of the second angle is,
2a=2×60° =120°
So, the measures of the two supplementary angles are 60° and 120° .
Strontium 90 decays at a constant rate of 2.44% per year. Therefore, the equation for the amount P of strontium 90 after t years is P = Po e^-0.0244t, How long will it take for 15 grams of strontium to decay to 5 grams? Round answer to 2 decimal places.
Answers
45 years will take for 15 grams of strontium to decay to 5 grams
What is strontium?
The chemical element strontium has the atomic number 38 and the symbol Sr. Strontium is a soft, silver-white, yellowish metallic element that is an alkaline earth metal and has a strong reactivity to chemicals. When the metal is exposed to air, a thick layer of dark oxide forms.
Equation Given.
[tex]P = Po e^{-0.0244t}[/tex]
given P = 5 gram
[tex]P_o = 15 gram[/tex]
Hence ,time taken
[tex]5 = 15 e^{-0.0244t}[/tex]
[tex]\frac{5}{15} = e^{-0.0244t}[/tex]
Taking log both side,
[tex]ln(\frac{1}{3} )=ln (e^{-0.0244t})\\\\-1.098 = -0.0244t\\\\t=\frac{1.098}{0.0244}\\\\t=45years[/tex]
Hence, 45 years will take for 15 grams of strontium to decay to 5 grams.
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Use the graph below to find the domain and range.
Answers
The domain and the range of the graphed function are given as follows:
Domain D: (-9, -1] U (0, 4].Range R: (-6, 8.6].How to obtain the domain and the range of the function?The domain of a function is composed by the set that contains all possible values assumed by the input of the function. Hence, considering the graph of the function, the domain is given by the values of x of the graph.
Thus the domain of this function is given as follows:
D: (-9, -1] U (0, 4].
As there is an interval between -1 and 0 for which the function is not defined, and open circle defines that the interval is open at x = -9 and at x = 0.
The range of a function is composed by the set that contains all possible values assumed by the output of the function. Hence, considering the graph of the function, the range is given by the values of y of the graph.
Then the range of the function is given as follows:
R: (-6, 8.6].
Open interval due to the open circle at y = -6, closed at the value between 8 and 10 which is of 8.6.
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Find the value of x.
If necessary, you may learn what the markings on a figure indicate.
Check
71°
X
x =
Answers
Tables and figures must all be labelled with numbered captions that clearly identify and describe them.
What do the marks on shapes mean?Little tick marks are used to show that two sides are the same length (congruent). You can use just one tick mark, two or three or more -- just as long as you use the same number on sides that are equal. Notation for congruent angles in a triangle: This works a lot like congruent sides Tick marks (shown in orange) indicate sides of a shape that have equal length (sides of a shape that are congruent or that match). The single lines show that the two vertical lines are the same length while the double lines show that the two diagonal lines are the same length.We mark the congruent sides by a slash mark. The angles in an equilateral triangle are always 60°. When a triangle has two congruent sides it is called an isosceles triangle.While "hash marks" are used to represent segments of equal length on diagrams, "arcs" are used to represent angles of equal measure.Indicator marks for sides and angles in a triangle diagram. Indicator marks are used to show whether two or more sides are congruent (equal in measure).x = 61
Left hand triangle containing 1 angle of 74
Label the other angle opposite the marked side also as 74
Find the third angle. Call it y.
y + 74 + 74 = 180 Combine like terms
y + 148 = 180 Subtract 148 from both sides.
y = 180 - 148
y = 32
Now work with the triangle on the right.
label the angle making up the right angle = z
32 + z = 90 These two angles are complementary = 90
32 - 32 + z = 90 - 32 Subtract 32 from both sides
z = 58 Use 58 wherever you see z
x + x + z = 180 Substitute
2x + 58 = 180 Subtract 58 from both sides
2x = 122 Divide by 2
x = 61
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Help me out pls someone
Answers
Convert 1/2 to 5/10 and 1/5 to 2/10.
Now subtract from left to right. Start with the whole numbers, 9 and 6.
9-6=3, move on the their fractions, 8/10 - 5/10 =3/10.
So now you have 3 3/10. Subtract the last number from your answer. 3-1=2 and 3/10 - 2/10= 1/10.
So your final answer would be 2 1/10
Draco steals and throws Neville's red ball straight up at 54 feet per second from about 7 feet above the ground. The ball's height in feet above the ground after tt seconds is given by
h(t)=â16t2+54t+7
How long does he have until the ball reaches the ground? seconds
Answers
Answer:
3.5
Step-by-step explanation:
The ball reaches the ground when [tex]h(t)=0[/tex].
[tex]-16t^2+54t+7=0 \\ \\ 16t^2-54t-7=0 \\ \\ (8t+1)(2t-7)=0 \\ \\ t=-1/8, t=7/2 \\ \\ t>0 \implies t=3.5[/tex]
y=-1/2x-3 how to graph
Answers
Given line:
y = - 1/2x - 3Plot two points and connect.
One point is the y-intercept:
x = 0 ⇒ y = - 3, the point is (0, - 3)Another point with an even value of x as its slope is a fraction with denominator of 2:
x = 6 ⇒ y = - 1/2*6 - 3 = - 3 - 3 = - 6, the point is (6, - 6)Plot these two points and connect.
See below graph.
the measure of one angle of a right is 23 degrees. Find the measure of the other angle
Answers
Answer: The measure of the three angles is 23, 67, and 90.
Step-by-step explanation:
The sum of three angles is equal to 180. We set the equation as:
x + 23 + 90 = 180
x + 113 = 180
x = 67
The measure of the three angles is 23, 67, and 90.
Suppose we want to choose 4 objects, without replacement, from 17 distinct objects.
(a) How many ways can this be done, if the order of the choices is taken into consideration?
(b) How many ways can this be done, if the order of the choices is not taken into consideration?
Answers
a) If we select without taking the order into consideration there are 2380.
b) If we take the order into consideration, we have 57120 ways
What is selection?We talk about the selection when we are talking about how a material can be chosen in the midst of many other materials that we have. In this case we are told that we want to choose 4 objects, without replacement, from 17 distinct objects.
If the order is not important then we need to do a combination and we have;
n!/r! (n - r)!
17!/4!(17 - 4)!
17 * 16 * 15 * 14 * 13!/4! * 13!
= 57120/24
= 2380
If we are looking at the order we have;
n!/(n-r)!
17!/(17 - 4)!
17 * 16 * 15 * 14 * 13!/13!
= 17 * 16 * 15 * 14
= 57120
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Let me know by Thursday pls
Answers
The angle relationships formed in the diagram are as follows;
∠1 and ∠5 are corresponding angles.∠4 and ∠7 are corresponding angles∠3 and ∠5 are alternate interior angles.∠1 and ∠8 are alternate exterior angles.∠2 and ∠7 are alternate exterior angles ∠3 and ∠6 are same interior anglesHow to find angles when parallel line s are cut by transversal ?When parallel lines are cut by a transversal, angle relationships can be formed such as corresponding angles, alternate interior angles, alternate exterior angles, vertically opposite angles, linear angles, etc.
Therefore, let's find the angles relationship formed in the diagram as follows:
∠1 and ∠5 are corresponding angles.
∠4 and ∠7 are corresponding angles
Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line.
∠3 and ∠5 are alternate interior angles.
Alternate interior angles are the angles formed when a transversal intersects two coplanar lines.
∠1 and ∠8 are alternate exterior angles.
∠2 and ∠7 are alternate exterior angles.
Alternate exterior angles are the pair of angles that are formed on the outer side of the parallel lines but on the opposite side of the transversal.
∠3 and ∠6 are same interior angles. Same interior angles are supplementary angles.
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Please Help. Thank you
Answers
Answer:
Look below
Step-by-step explanation:
Example for A
1/5 y= 3/5 x
1/5 y= 3/5 x +4
Example for B
0x=0y
0x=0y+3
Answer for C
add statement for the y not to be equal to 0
(15points) Let 21, 22, ..., Ik be linearly independ vectors in a vector space V. If we add a vector Ik+1 to the collection, will we still have a linear independent collection of vectors? Explain. If we delete a vector, say, 2k , from the collection, will we still have a linearly independent collection of vectors? Explain.
Answers
If we add a vector I{k+1} to the collection of 21, 22, ... I{k}, the collection will no longer be linearly independent and yes, we will still have a linearly independent collection of vectors if we delete a vector {say 2k}.
What are linearly independent vectors? What is a mathematical function, equation and expression?linearly independent vectors : In the theory of vector spaces, a set of vectors is said to be linearly dependent if there is a nontrivial linear combination of the vectors that equals the zero vector. If no such linear combination exists, then the vectors are said to be linearly independent. These concepts are central to the definition of dimension
Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function
Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators
Equation : A mathematical equation is used to equate two expressions.
Given is a linearly independent vectors in a vector space V.
If we add a vector I{k+1} to the collection of 21, 22, ... I{k}, the collection will no longer be linearly independent.
If we delete a vector {say 2k}, from the collection, yes, we will still have a linearly independent collection of vectors
Therefore, if we add a vector I{k+1} to the collection of 21, 22, ... I{k}, the collection will no longer be linearly independent and yes, we will still have a linearly independent collection of vectors if we delete a vector {say 2k}.
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x + 2y=-6
y = 2z =2
-2x- 6y + 5z =26
Answers
To eliminate y from the first equation, we can multiply the entire equation by -2. This will give us:
-2x - 4y = -12
Now, if we add this equation to the second equation, the y terms will cancel out, leaving us with:
-2x - 4(2) + 5z = 26
-2x + 5z = 26
Now we have two equations in two variables, x and z. We can solve this system of equations by substituting the value of y from the second equation into the first equation. This gives us:
x + 2(2) = -6
x = -10
Substituting this value of x into the second equation, we get:
-2(-10) + 5z = 26
20 + 5z = 26
5z = 6
z = 1.2
Finally, we can substitute the values of x and z back into the second equation to find the value of y:
-2(-10) - 6(1.2) + 5(1.2) = 26
20 - 7.2 + 6 = 26
12.8 = 26
This system of equations has no solution, since we have found values of x and z that make the second equation true, but substituting these values into the first equation results in a false statement. This means that there is no set of values for x, y, and z that will make all three equations true at the same time.
A jacket is normally priced at $120. At the end of the winter season, the jacket is offered with a
discount of $18 off the normal price. What percentage of the normal price is the discount?
Answers
Answer:
15%
Step-by-step explanation:
18/120 = 0.15
0.15*100 = 15%
...
The solution is 15 %
The percentage of discount on the normal price of the jacket is given by the equation A = 15 %
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the percentage of discount be represented as A
Now , the equation will be
The normal price of the jacket = $ 120
The discounted price of the jacket = $ 18
So ,
Discounted price of the jacket = A % of normal price of the jacket
Substituting the values in the equation , we get
18 = A % x 120
On simplifying the equation , we get
( A / 100 ) x 120 = 18
Divide by 120 on both sides of the equation , we get
A / 100 = 18/120
A / 100 = 0.15
Multiply by 100 on both sides of the equation , we get
A = 15 %
Therefore , the value of A is 15 %
Hence , the discounted percentage is 15 %
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ShivamG yt where r u
Answers
Answer:
Somoeone can talk here boring
Answer:
this a quesy=tion?
Step-by-step explanation:
1. The graph of a quadratic function is called a(an)
Copy and complete the table of values for the function.
2.
y=-1/3 x²
Answers
The graph of a quadratic function is called a parabola
The complete table is
x = -6, -3, 0, 3 6
y = -12 -3 0 -3 -12
How to complete the table of values?From the question, we have the following equation that can be used in our computation:
y=-1/3 x²
From the table of values , we have the following x values
x = -6, -3, 0, 3 and 6
Substitute x = -6, -3, 0, 3 and 6 in y=-1/3 x²
So, we have the following representation
y = -1/3 (-6)² = -12
y = -1/3 (-3)² = -3
y = -1/3 (0)² = 0
y = -1/3 (3)² = -3
y = -1/3 (6)² = -12
So, the complete table of values is
x = -6, -3, 0, 3 6
y = -12 -3 0 -3 -12
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Value Determination: Determine the values that x cannot be equal for the rational expression.
(5x-2)/(x^2-5x)
with steps please.
Answers
The values of x that can't be equal for the expression are 0 and 5
How to determine the values of x that can't be equal?From the question, we have the following parameters that can be used in our computation:
(5x-2)/(x^2-5x)
This means that we set the denominator to 0
So, we have
x^2 - 5x = 0
Factorize
(x - 5)x = 0
So, we have
x - 5 = 0 and x = 0
Solve for x
x = 5 and x = 0
Hence, the solution is x = 5 and x = 0
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What is the answer to the question??
Answers
Answer:you need to show the diagram in order for me to
Step-by-step explanation:
Determine if the following equation has one, none, or many solutions
3x-6=x+6-5x
Answers
The equation 3x - 6 = x + 6 - 5x has one solution, which is x = 12/7.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equation is,
3x - 6 = x + 6 - 5x
To determine the solutions, solve the equation,
3x - 6 = 6 - 4x
7x = 12
x = 12/ 7
The equation has one solution, which is 12/7.
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R 0, -180(x, y) maps to the same point as R 0, 180(x, y).
O True
O False
Answers
Answer:
True.
Step-by-step explanation:
Whether you do a rotation 180 degrees clockwise( [tex]R__(-180,O)[/tex]), or a rotation 180 degrees counterclockwise ([tex]R__(180,O)[/tex]), the image will always end up in the coordinate diagonal from the pre-image.
How much would you need to deposit in an account now in order to have $5,000.00 in the account in 821 days?
Assume the account earns 5-% simple interest.
You would need to deposit ___
in your account now.
Answers
Answer:
A = principal +interest
P = Principal Amount
r = rate
t = time
A = P(1 + rt)
5 000 = P[(1 + 0.05(821/364.25)]
5 000 = P(1 + 0.05(2.254)
5 000 = P(1 + 0.1127)
5 000 = 1.1127P
P = 4 493.5742
Therefore, you need to deposit an amount of $4 493.5742 to have $5 000 in 821 days.
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-What is the solution for x in the equation? 5/3x+4=2/3r A.x=12/7 B.x=12/7C.x=4 D.x=-4
Answers
Answer:
D
Step-by-step explanation:
5/3 x - 2/3 x = -4
3/3 x = -4
x = -4
The sum of the lengths of the sides of this triangle is 30cm.
What is the length of the LONGEST side of the triangle in centimeters?
Answers
The longest side of the triangle has a length of 11 cm.
How to Find the Length of the Longest Side of a Triangle?Given that the sum of the lengths of the triangle is equal to 30 cm, and the sides are:
(x + 6)
(x + 4)
2x
Create an equation to find the value of x:
(x + 6) + (x + 4) + 2x = 30
x + 6 + x + 4 + 2x = 30
Combine like terms
4x + 10 = 30
4x = 30 - 10
4x = 20
4x/4 = 20/4
x = 5
Find the length of each of the sides of the triangle:
(x + 6) = 5 + 6 = 11 cm
(x + 4) = 5 + 4 = 9 cm
2x = 2(5) = 10 cm
The longest side is 11 cm.
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write an equation of the line below.
Answers
Answer:
y = (1/2)x + 2
Step-by-step explanation:
Go from point (-2,1) to (0, 2).
Start at point (-2, 1). First, go up 1 unit. That is a rise of 1.
Now go 2 units right. That is a run of 2.
slope = rise/run = 1/2 = m
The graph intersects the y-axis at 2, so the y-intercept = b= 2.
y = mx + b
y = (1/2)x + 2
What are two motion that are illustrated as a horizontal line on a speed time graph?
Answers
A horizontal line indicates that the thing is travelling steadily. A line that slopes downhill indicates that an object is slowing down.
What is horizontal line?The difference between a horizontal and vertical line is that a horizontal line is drawn from left to right, while a vertical line is drawn from top to bottom. Lines parallel to the x-axis and the y-axis are referred to as horizontal and vertical, respectively, in coordinate geometry.A left to right line is referred to as a horizontal line. The sunrise is visible as it crosses a horizontal line as you look toward the horizon. Examples of horizontal lines include the x-axis.Whether drawn from the right to the left or the left to the right, a horizontal line is a simple straight line (as opposed to down-up or up-down).To learn more about horizontal line refer to:
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find a power series representation for the function. determine the interval of convergence. (give your power series representation centered at x
Answers
The interval of convergence for this series is [tex]$x \in \left(-1, 1\right)$[/tex].
What is Power Series Representation for the Function ?
To find a power series representation for a function, we need to express the function as an infinite series of the form
[tex]$$f(x) = \sum_{n=0}^{\infty} a_n (x-x_0)^n$$[/tex]
where [tex]$x_0$[/tex] is the center of the series, and the [tex]$a_n$[/tex] are the coefficients of the series. To determine the interval of convergence for the series, we need to find the values of [tex]$x$[/tex] for which the series converges.
To find the power series representation for a given function, we can use the process of Taylor series expansion. This involves finding the derivative of the function at the point [tex]$x_0$[/tex], and using the derivative to find the coefficients of the series.
For example, suppose we want to find a power series representation for the function [tex]$f(x) = \frac{1}{1-x}$[/tex] centered at [tex]$x_0 = 0$[/tex]. We can use the process of Taylor series expansion to find the power series representation as follows:
[tex]$$f(x) = \frac{1}{1-x} = \frac{1}{1-0} + \frac{0-1}{(1-0)^2}x + \frac{2 \cdot 0 - 1 \cdot 1}{(1-0)^3}x^2 + \dotsb$$[/tex]
Simplifying this expression, we get
[tex]$$f(x) = 1 + x + x^2 + x^3 + \dotsb$$[/tex]
This is the power series representation of [tex]$f(x)$[/tex] centered at [tex]$x_0 = 0$[/tex].
To determine the interval of convergence for this series, we can use the ratio test. If we let [tex]$a_n = 1$[/tex] for all [tex]$n$[/tex], then the series becomes
[tex]$$\sum_{n=0}^{\infty} a_n (x-x_0)^n = \sum_{n=0}^{\infty} x^n$$[/tex]
If we take the limit of the absolute value of the ratio of successive terms, we get,
[tex]$$\lim_{n \to \infty} \left| \frac{x^{n+1}}{x^n} \right| = \left| x \right|$$[/tex]
If [tex]$|x| < 1$[/tex], then the series converges. If [tex]$|x| > 1$[/tex], then the series diverges. If [tex]$|x| = 1$[/tex], then the test is inconclusive and we need to use another method to determine convergence.
Therefore, the interval of convergence for this series is [tex]$x \in \left(-1, 1\right)$[/tex].
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Find the measure of ∠BCD in degrees.
(Answer as fast as possible would be appreciated!)
Answers
Answer:
106*
Step-by-step explanation:
a triangle is 180*
to find angle BCA, you do 180 - (64+42)
that =74*
a straight line is also 180* so you do 180 - BCA
180-74=106
106
NO LINKS!!!
Complete the table by finding the balance A when P dollars is invested at rate r for t years and compounded n times per year. (Round your answers to the nearest cent)
P = $2100, r= 8.5%, t = 9 years
n A
1 $
2 $
4 $
12 $
365 $
Continuous $
Answers
Answer:
[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} n&A \\\cline{1-2}\vphantom{\dfrac12} 1& \$4376.10\\\vphantom{\dfrac12} 2& \$4442.10\\\vphantom{\dfrac12} 4& \$4476.86\\\vphantom{\dfrac12} 12& \$4500.73\\\vphantom{\dfrac12} 365& \$4512.49\\\vphantom{\dfrac12} \sf Continuous& \$4512.89 \\\cline{1-2} \end{array}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given:
P = $2100r = 8.5% = 0.085t = 9 yearsSubstitute the given values into the formula to create an equation for A in terms of n:
[tex]\implies A=2100\left(1+\dfrac{0.085}{n}\right)^{9n}[/tex]
Substitute each value of n into the equation:
[tex]\begin{aligned}n=1 \implies A&=2100\left(1+\dfrac{0.085}{1}\right)^{9 \times 1}\\&=2100\left(1.085\right)^{9}\\&=\$4376.10\end{aligned}[/tex]
[tex]\begin{aligned}n=2 \implies A&=2100\left(1+\dfrac{0.085}{2}\right)^{9 \times 2}\\&=2100\left(1.0425\right)^{18}\\&=\$4442.10\end{aligned}[/tex]
[tex]\begin{aligned}n=4 \implies A&=2100\left(1+\dfrac{0.085}{4}\right)^{9 \times 4}\\&=2100\left(1.02125\right)^{36}\\&=\$4476.86\end{aligned}[/tex]
[tex]\begin{aligned}n=12 \implies A&=2100\left(1+\dfrac{0.085}{12}\right)^{9 \times 12}\\&=2100\left(1.00708333...\right)^{108}\\&=\$4500.73\end{aligned}[/tex]
[tex]\begin{aligned}n=365 \implies A&=2100\left(1+\dfrac{0.085}{365}\right)^{9 \times 365}\\&=2100\left(1.00023287...\right)^{3285}\\&=\$4512.49\end{aligned}[/tex]
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]
[tex]\implies A=2100e^{0.085 \times 9}[/tex]
[tex]\implies A=2100e^{0.765}[/tex]
[tex]\implies A=2100(2.14899437...)[/tex]
[tex]\implies A=\$4512.89[/tex]
Input the calculated values into the table:
[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} n&A \\\cline{1-2}\vphantom{\dfrac12} 1& \$4376.10\\\vphantom{\dfrac12} 2& \$4442.10\\\vphantom{\dfrac12} 4& \$4476.86\\\vphantom{\dfrac12} 12& \$4500.73\\\vphantom{\dfrac12} 365& \$4512.49\\\vphantom{\dfrac12} \sf Continuous& \$4512.89 \\\cline{1-2} \end{array}[/tex]
Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. f(x) = x² - 2x - 7 O minimum; -8 Omaximum: 1 O minimum; 1 O maximum; -8
Answers
Quadratic function has minimum value which is -8.
correct option: 1
What is quadratic equation?A variable with the largest power of two in a quadratic equation is called a variable. Quad, which signifies square, is the root of the term quadratic. The phrase must be two times its own strength, neither higher nor lower.
Given that they are the x values for which f(x) = 0, the roots of the function f(x) = ax² + bx + c correspond to the solutions of the quadratic equation ax² + bx + c = 0.
The term ax² is known as the quadratic term (hence the function's name), the word bx is known as the linear term, and the value c is known as the constant term.
Here, the given function,
f(x) = x² - 2x - 7 .......... (i)
now, differentiate with respect to x
d/dx {f(x)} = d/dx ( x²) - d/dx (2x) - d/dx (7)
or, f'(x) = 2x - 2 ............. (ii)
Now, put f'(x) = 0
so, 0 = 2x - 2
or, 2x - 2 = 0
or, 2x = 2
or, x = 1
From equation (ii)
f'(x) = 2x - 2
now, differentiate with respect to x
f''(x) = 2 > 0
So, it implies that, the function has minimum value at x = 1
Now, putting x = 1 in equation (i), we get -
f(1) = (1)² - 2×(1) - 7
f(1) = - 8
Function has minimum value is: - 8.
Thus, correct option is : (1)
To know more about quadratic function refer to:
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