The function g(x) is a continuous quadratic function defined for all real numbers, with some of its values given by the table below.The quadratic function ƒ(x) is represented by the parabola below. x g(x) -3 0 -2 5 0 9 2 5 3 0 Select all the statements that are true. The function ƒ(x) has a maximum value at x = 4.5. The function g(x) has a minimum value of 0. The maximum value of g(x) is twice the maximum value of ƒ(x). Neither function has a minimum value.

Answers

Answer 1

Though I almost broke my brain while solving what "-3 0 -2 5 0 9 2 5 3 0" means, I can tell you which statements is absolutely incorrect: it is "The function g(x) has a minimum value of 0" (it is incorrect because the maximum value is 9 as table provides).
To solve other problems, look at f(x): if it has the top, where y is the biggest, then it is the maximum value (so if y = 4.5 is the biggest y, first statement is correct); if it has the bottom, where y is the smallest, then it is minimum value (factually, statement 3 will be correct if statement 1 is correct because 9/4.5 = 2). Finally, if f(x) has the top, then statement 4 is correct because f(x) and g(x) would be both constantly decreasing functions.
Hope this helps.

Answer 2

Final answer:

The function g(x) has a minimum value of 0, but we cannot determine the maximum value of g(x) or compare it to the maximum value of f(x). The statements about the maximum value of ƒ(x) and the lack of minimum value for both functions are not supported by the given information.

Explanation:

The function g(x) is a continuous quadratic function that can be represented by a parabola. From the given table, we can observe that the minimum value of g(x) is 0 and it occurs when x = -3 or x = 3. Therefore, the statement 'The function g(x) has a minimum value of 0' is true.

To determine the maximum value of g(x), we need to find the vertex of the parabola representing g(x). Since the function is continuous and quadratic, the vertex occurs at the axis of symmetry. The axis of symmetry is given by x = -b/2a, where a and b are the coefficients of the quadratic function. In this case, the equation representing g(x) is not given, so we cannot determine the exact maximum value of g(x) or compare it to the maximum value of f(x).

Based on the given information, we cannot determine whether the function f(x) has a maximum value at x = 4.5 or if the maximum value of g(x) is twice the maximum value of f(x). Therefore, the statements 'The function ƒ(x) has a maximum value at x = 4.5' and 'The maximum value of g(x) is twice the maximum value of ƒ(x)' are false.

Regarding the statement 'Neither function has a minimum value,' it is not accurate based on the given information. We already established that g(x) has a minimum value of 0.

Related Questions

in 2003, a gallon of gas cost $1.75. In 2013 a gallon of gas cost $3.25. Write an equation to model this situation.

Answers

Final answer:

To model the situation of the gas prices in 2003 and 2013, we can use a linear equation. The equation to model this situation is y = $0.15x - $298.70.

Explanation:

To model the situation of the gas prices in 2003 and 2013, we can use the equation of a linear relationship between the year (x) and the cost of gas (y). We can use the formula y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope (m):

The change in cost of gas is $3.25 - $1.75 = $1.50The change in years is 2013 - 2003 = 10

Therefore, the slope (m) is $1.50 / 10 = $0.15.

Next, let's find the y-intercept (b):

Using the point (2003, $1.75), we can substitute the values into the equation and solve for b:

$1.75 = $0.15(2003) + b

b = $1.75 - $0.15(2003)

b = $1.75 - $300.45

b = -$298.70

Therefore, the equation to model this situation is y = $0.15x - $298.70, where x is the year and y is the cost of gas.

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Help me i hate word problems

Answers

Is that all? My Algebra is freackin hard compared to this. Anyways, The way I understand this, is that we will have 3 (liters of water) +0.5 (half a liter of lemonade) =3.5 liters of liquid

so the question would be: how many times does fit into 3.5?

if you want to divide by a fraction, you need to multiply by the reverse of it.

so the answer is: 10 servings of lemonade ( and a little bit will be left over for half a serving).
Hope this helps!

Which statement is true about the equations –3x + 4y = 12 and x – y = 1?

The system of the equations has exactly one solution at (–8, 3).
The system of the equations has exactly one solution at (–4, 3).
The system of the equations has no solution; the two lines are parallel.
The system of the equations has an infinite number of solutions represented by either equation.

Answers

The system of the equations has no solution; the two lines are parallel.

Answer:

Step-by-step explanation:

Its C just did the test

2.What is the correct equation of the line shown below ?

Answers

The correct answer would be the first choice, y=3/2x+3.

Since the line enters the y-axis at (0,3) the y-intercept of the equation would be 3 (as according to the y=mx+b format where b is the y-intercept and m is the slope). The slope would be 3/2 since when you find two perfect points (I used (0,3) and (2,6)) and you use the rise over run method (move up 3 from (0,3) and 2 to the right to get to (2,6)), your slope is 3/2.

The equation of the line shown is y = (3/2)x + 3.

What is the equation of line?

The general equation of a straight line is

y = mx + c,

where m is the gradient or slope, and

y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

Now given points from the line passes are (0,3) and (-4,-3)

Therefore we have,

x₁ = 0

y₁ = 3

x₂ = -4

y₂ = -3

Now since the slope of the line is given as,

m = (y₂ - y₁)/(x₂ - x₁)

⇒ m = (-3 - 3)/ (-4-0)

⇒ m = -6/(-4)

⇒ m = 6/4

or, ⇒ m = 3/2

Now, for intercept c we can put any of points in the equation of line.

So, put (0,3)in the equation of line

3 = m(0) + c

3 = 0 + c

⇒ c = 3

Hence the required equation of line is given as,

y = mx + c

put the values of m and c,

y = (3/2)x + 3

which is the required equation of the line shown

Hence,the equation of the line shown is y = (3/2)x + 3.

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Um cone reto tem 24cm de altura e o raio da base é igual a 18cm. Calcule
A) a medida de sua geratriz
B) a área total lateral (aproximadamente)
C) a área total (aproximadamente)
+volume

Answers

A)
A geratriz pode ser encontrada através dum teorema de Pitágoras. Tendo a altura e o raio, podemos chegar à medida da geratriz. Soma-se o quadrado da altura com o quadrado do raio para se obter o quadrado da geratriz. depois basta fazer a raíz quadrada do quadrado da geratriz para encontrar a medida da geratriz.
[tex]\sqrt{24^{2}+ 18^{2} } = g [/tex] ⇔ 30 = g
A medida da geratriz é 30cm

B)
A área total lateral é obtida multiplicando o raio pela geratriz e pelo π.
Área total lateral = r×g×π ⇔ Atl = 18cm×30cm×π ⇔ Atl ≈ 1696,5cm²

C)
A área total é calculada somando a área da base e a área lateral. A área da base é calculada multiplicando o quadrado do raio pelo π.
Área total ≈ 1696,5cm²+(18²cm×π) ≈ 1696,5cm²+1017,9cm² ≈ 2714,4cm²

O volume do cone é dado pela área da base vezes a altura a dividir por três.
Volume do cone = (área da base×altura do cone)÷3 ≈ (1017,9cm²×24cm)÷3 ≈ 24429,6cm³÷3 ≈ 8143,2cm³

8 less than one third of x is y

Answers

y = 1/3x -8
I think this is what you were looking for seeing that you cannot solve this problem without an 'x' or 'y'.

Help with math please.
Select the correct rate of change and y -intercept for the linear function that contains the points (4, 6) and (5, 3).

Question 1 options:

The rate of change is –3, and the y -intercept is 18.

The rate of change is 3, and the y -intercept is –6.

The rate of change is 1/3, and the y intercept is 4 2/3

The rate of change is -1/3, and the y intercept is 7 1/3

Answers

Hello,

The rate of change is the slope (rise/run, y/x). To find that, we use the equation (y2-y1) over (x2-x1). It means take the second "y" and subtract it from the first "y" and the same to "x". If I plug in the numbers, it would be (3-6) over (5-4), and after you subtract, the answer simplifies to: -3/ 1 which is -3. Yay! We got the slope (rate of change) done.

Now let's find the y-intercept by using the formula of point-slope form,
y-y1= m (slope) (x-x1). This is saying you "y" is subtracted from the first
"y" of the points which equals the slope (m) times the quantity of "x" subtracted by the first "x" of the points.

Let's plug the numbers in: y-6 = -3 (x-4). Let's distribute -3 to the parenthesis, and after that it should simplify to: y-6 = -3x + 12. To get "y" by itself, add 6 to both sides: y = -3x +18. We have finally found the slope-intercept equation for those two points (4,6) and (5,3). To then find the y-intercept in this equation, it would be the 18, because -3 is the slope, so that makes 18 the y-intercept.

In conclusion, the rate of change is -3 and the y-intercept is 18.

I hope this helps!

May

..........................................

Deidre is 5 feet 4 inches tall and her weight is 135 pounds. her bmi is closest to _____ kg/m2.

Answers

Deidre bmi is 23.73.

1. Multiply the weight by .45:

135 X .45 = 60.75kg

2. Multiply the height in INCHES by .025

Convert 5feet 4inches to only inches (5*12+4) = 64 inches

Now multiply 64 X .025 = 1.6 m

3. Square the answer from the above step.

1.6 X 1.6 = 2.56m

4. Divide the answer from the first step by the answer from the third step.
60.75kg/2.56m = 23.73.

Deidre bmi is 23.73.

Let r1 and r2 be relations on a set a represented by the matrices mr1 = ⎡ ⎣ 0 1 0 1 1 1 1 0 0 ⎤ ⎦ and mr2 = ⎡ ⎣ 0 1 0 0 1 1 1 1 1 ⎤ ⎦. find the matrices that represent
a.r1 ∪ r2.
b.r1 ∩ r2.
c.r2 ◦r1.
d.r1 ◦r1.
e.r1 ⊕ r2.

Answers

Given:
[tex]r1 = \left[\begin{array}{ccc}0&1&0\\1&1&1\\1&0&0\end{array}\right] \,\, and \,\, r2= \left[\begin{array}{ccc}0&1&0\\0&1&1\\1&1&1\end{array}\right] [/tex]

Part a. r1 ∪ r2
This assembles matrix elements from either r1 and/or r2.
[tex]r1 \cup r2 = \left[\begin{array}{ccc}0&1&0\\1&1&1\\1&1&1\end{array}\right] [/tex]

Part b. r1 ∩ r2
This assembles matrix elements common to both r1 and r2.
[tex]r1 \cap r2 = \left[\begin{array}{ccc}0&1&0\\0&1&1\\1&0&0\end{array}\right] [/tex]

Part c. r2 . r1
[tex]r2 \circ r1 = \left[\begin{array}{ccc}0&1&0\\0&1&1\\1&1&1\end{array}\right] \left[\begin{array}{ccc}0&1&0\\1&1&1\\1&0&0\end{array}\right] = \left[\begin{array}{ccc}1&1&1\\2&1&1\\2&2&1\end{array}\right] [/tex]

Part d. r1 . r1
[tex]r1 \circ r1 = \left[\begin{array}{ccc}0&1&0\\1&1&1\\1&0&0\end{array}\right] \left[\begin{array}{ccc}0&1&0\\1&1&1\\1&0&0\end{array}\right] = \left[\begin{array}{ccc}1&1&1\\2&2&1\\0&1&0\end{array}\right] [/tex]

Part e. r1 ⊕ r2 (Direct sum)
[tex]r1 \oplus r2 = \begin{bmatrix} r1&0\\0&r2\end{bmatrix} = \begin{bmatrix} 0&1&0 &0&0&0\\ 1&1&1 &0&0&0\\ 1&0&0 &0&0&0\\ 0&0&0 &0&1&0\\0&0&0 &0&1&1\\ 0&0&0 &1&1&1\end{bmatrix}[/tex]

Final answer:

The operation results on the matrices representing relations r1 and r2 are beautiful illustrations of how relations are manipulated in set theory. Given the limitations imposed by the data available, only three of the five stipulated operations can be carried out.

Explanation:

In the given question, the student needs to perform different operations on the matrices that represent relations r1 and r2. Here is the solution:

r1 ∪ r2 (Union of r1 and r2): It's obtained by taking the union of the corresponding elements in the two matrices. If either or both of the matrices have a 1 in a position, then put a 1, else 0. So the matrix for r1 ∪ r2 is ⎡ ⎣ 0 1 0 1 1 1 1 1 1 ⎤ ⎦ r1 ∩ r2 (Intersection of r1 and r2): It's obtained by taking the intersection of the corresponding elements in the two matrices. If both of the matrices have a 1 in a position, then put a 1, else 0. So the matrix for r1 ∩ r2 is ⎡ ⎣ 0 1 0 0 1 1 1 0 0 ⎤ ⎦ r2 ◦r1 (Composition of r2 and r1): If there exists an element in the set such that (a, b) is in r1 and (b, c) is in r2, then put a 1 in A[ac] else put a 0. Due to this, the matrix comprehension is studied in higher mathematics, and it can't be calculated from the given matrices. r1 ◦r1 (Composition of r1 and r1): Same as the previous operation but with both relations being r1. It also requires the full set of elements to calculate and can't be derived from the given matrices. r1 ⊕ r2 (Symmetric difference of r1 and r2): It is obtained by taking the XOR of each element in the matrices. So if the two elements are the same, put a 0, else put a 1. So the matrix for r1 ⊕ r2 is ⎡ ⎣ 0 0 0 1 0 0 0 1 1 ⎤ ⎦

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The african bush elephant weighs between 4.4 tons and 7.7 tons. What are its least and greatest wieghts rounded to the nearest ton

Answers

4.4=4 tons rounded

7.7=8 tons rounded

4.4 rounds to 4.

7.7 rounds to i

based on the pattern of the drawings which conjecture is reasonable to make?

A. when a pair of parallel lines is intersected by a third line, the corresponding angles are complementary
B. when a pair of parallel lines is intersected by a third line, all of the angles formed are congruent.
C. when a pair of parallel lines is intersected by a third line, the corresponding angles are congruent
D. when a pair of parallel lines is intersected by a third line, the corresponding angles are supplementary.

Answers

the 2 angles in each picture are the same - meaning they are congruent,

so the answer is:

C. when a pair of parallel lines is intersected by a third line, the corresponding angles are congruent

Conjectures are simply opinions from a given information.

The conjecture that can be formed is: C. when a pair of parallel lines is intersected by a third line, the corresponding angles are congruent

From the three diagrams, we can see that:

[tex]\mathbf{30^o = 30^o}[/tex][tex]\mathbf{35^o = 35^o}[/tex][tex]\mathbf{50^o = 50^o}[/tex]

From the figures above, we have the following observations

The angles are congruentThe angles are correspondingThe congruence of the angles is based on parallel lines, intersected by a third line (i.e. the transversal)

Hence, the conjecture that can be formed is: option (c)

Answers

So the composite solid has a rectangular pyramid top with a rectangular box below.
We can find the total vol. by adding the two together: Vol (v)total = vol (pyra) + vol (box)
vol (tot) = (1/3×base×height) + (l×w×h)
In order to find the height (h) of the triangle, we imagine a string dropped straight down from the apex (tip), which falls perfectly to center of the base of pyramid. Now the distance from the bottom of that string to edge is 1/2×6.7 = 3.35. Use Pythagorean Theorem to determine the pyramid height:
[tex] {5.8}^{2} = {h}^{2} + {3.35}^{2} \\ {h}^{2} = {5.8}^{2} - {3.35}^{2} \\ h \: = \sqrt{({5.8}^{2} - {3.35}^{2})} \\ h = \sqrt{(33.64 - 11.22)} \\ h = \sqrt{22.42} = 4.73 \: cm[/tex]
Now we can solve our volume, so the base of pyra = l×w = 6.2×6.7 = 41.54
vol (tot) = (1/3×base×height) + (l×w×h)
vol = (1/3×41.54×4.73) + (6.7×6.2×5.5)
vol = (65.49) + (228.47) = 293.96
[tex]vol = 294 \: {cm}^{3} > > \: answer \: (c)[/tex]

On average, how many times must a 6-sided die be rolled until a 6 turns up twice in a row?

Answers

Chance of one 6: 1/6
Chance of two 6s: (1/6)² = 1/36

Hello There!

The chance of rolling a 6 on 2 dice is 1/6 x 1/6.
1/6 x 1/6 = 1/36.
The average number of times for the first 6 would be 6
I'm not sure how to explain this part
But the average number of times for the second one would be 7.
To get the consecutive number of times, multiply them together:
6 x 7 = 42.
It would take an average of 42 times.

Hope This Helps You!
Good Luck :)

- Hannah ❤

a store manager orders t-shirts so that 15 out of every 35 are medium. how many medium t-shirts would you expect to find when there are 105 t-shirts on the rack. explain how to get

Answers

I'm pretty sure you do 15/35 (fifteen over thirty-five) times x/105 (x over one hundred and five) and cross multiply. If you get a calculator and multiply, you'll find that 15x105 is 1,575, and 35 times x is 35x. Your equation is then 35x=1,575. If you divide 1,575 by 35 you get 45. Another way to check this is by putting 15/35= in a calculator. It'll tell you 3/7. The same thing will happen with 45/105. Also, 105 divided by 35 is three, so you can multiply 15 by three. Either way, the answer is 45 medium per every 105 a rack.

Write the next two terms in the pattern. 3, 10, 17, 24, . . .

Answers

the pattern is +7.
So next values would be 31 and 38

10-3 =7

each term increases by 7

so 24 +7 = 31

31+7 = 38

next 2 terms are 31 & 38

PLEASE HELP

Solve for x.

−32>−5+9x

Enter your answer, as an inequality, in the box.

Answers

-32 > - 5 + 9x

-32 + 5 < 9x

-27 < 9x

-3 < x

x > -3

hope that helps, God bless!

Inequality is a statement of an ordered relationship

The value of x as inequality is less than -3.

x < -3 is our answer.

What is inequality?

It is a statement of an ordered relationship

- greater than,

- greater than or equal to,

- less than,

- less than or equal to between two numbers or algebraic expressions.

Example:

x > 3

y < 5

x ≤ 6

y ≥ 2

We have,

-32 > -5 + 9x

Add 5 on both sides.

-32 + 5 > -5 + 9x + 5

[ -32 + 5 = -27 ]

-27 > 9x

Divide both sides by 9.

-27/9 > 9x/9

-9 x 3 / 9 > 9x / 9

-3 > x

This can be written as:

x < -3

Thus,

The value of x as inequality is less than -3.

i.e x < -3

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What is the average of 5.24,6.875,3.298,5.7,4.98? Round the answer to 2 decimal points

Answers

The original answer is 5.2186. After you round, your answer should become 5.22

The relative frequency of a car travelling through a road junction having exactly two occupants is 0.26.If 5,000 cars are observed passing through the junction, how many of the cars could be expected to have only two occupants?

Answers

5000 cars x 0.26 frequency of a car with 2 occupants = the number of cars that have 2 occupants at the junction

5000 x 0.26 = ??

Which transformation is not isometric?

Answers

the answer would be A since the squares are different sizes in each figure

How is an emulsion different from a solution?
:The components are mixed unevenly instead of evenly within the emulsion.
:Insoluble instead of soluble particles are suspended within the emulsion.
:Two liquids that normally are not mixable are mixed in the emulsion.
:The components of an emulsion are single elements or compounds instead of a mixture of compounds.

Answers

Emulsion is a liquid suspended in a liquid while solution is liquid and solid

A new truck that sells for $25,000 depreciates (decreases in value) 11% each year. What will be the value of the truck in 2 years

Answers

Original price =$25,000
Depreciation rate = 11%

Note that 1 - 0.11 = 0.89.
Value after 1 year = $25,000 (0.89) = $22,250
Value after 2 years = $22,250 (0.89) = $19,802.50

Answer: $19,802.50

Answer:

Price of Truck after 2 year = $ 19802.50

Step-by-step explanation:

Given: Price of truck = $ 25,000

Price depreciate at rate of 11% in a year

To find: Price of truck after 2 years

If we let Price of truck to be P = $ 25000

And Rate of deprecation to be R = 11%

And time to be n = 2

now by using formula of deprecation, we get

[tex]A=P\times(1-\frac{R}{100})^n[/tex]

[tex]A=25000\times(1-\frac{11}{100})^2[/tex]

[tex]A=25000\times0.7921[/tex]

A = $ 19802.50

Therefore, Price of Truck after 2 year = $ 19802.50

14-3x=4x solve and explain

Answers

14 - 3x = 4x
Flip
4x = 14 - 3x
Add both sides by 3x
7x = 14
Divide both sides by 7
x = 2
Have an awesome day! :)

Ronald walks from home to Taco Bell to eat everyday. It takes him 30 minutes to walk the 2 mile distance. A) write a function for Ronald’s wall. Let x be the number of minutes he walks.
B) what should the domain of the function be?

Answers

a) We know that

[tex]d=vt[/tex]

where d[tex]y= \frac{1}{15}x [/tex]= distance,
v = velocity,
t = time

In this case, d = 2 mi., t = 30 min. So we get

[tex]2=30v[/tex]

Dividing both sides by 30, we get

[tex]v= \frac{2}{30}= \frac{1}{15} [/tex]

Thus a function for his walk would be

[tex]y= \frac{1}{15} x[/tex]
where y = distance and x = number of minutes he walks.

b) Domain of a function is a set of x-values on which the function defined. In this case, the number of minutes is 30 at maximum. So the domain of the function is [0, 30].

Six students measure the acceleration (in meters per second per second) of an object in free fall. The measured values are: 10.56, 9.52, 9.73, 9.80, 9.78, 10.91.The students want to state that the absolute deviation of each measured value xfrom the mean is at most
d. Find the value of
d.

Answers

The measured data is
x = [10.56, 9.52, 9.73, 9.80, 9.78, 10.91]

There are 6 measurements.
Calculate the mean.
m = (10.56+9.52+9.73+9.80+9.78+10.91)/6 = 10.05

Calculate deviations from the mean.
y = |x - m|
= [0.51, 0.53, 0.32, 0.25, 0.27, 0.86]

The greatest deviation from the mean is d = 0.86.

Calculate the average absolute deviation.
(0.51+0.53+0.32+0.25+0.27+0.86)/6 = 0.4567

Answer:
d = 0.86

What is the surface area of a cylinder whose radius is 3 inches and whose height is 10 inches? Round to the nearest tenth.

SA = 2π r2 + 2π rh
A. 226.1 square inches
B. 241.8 square inches
C. 244.9 square inches
D. 543.3 square inches

Answers

The answer is C. 244.9

A scatterplot is produced to compare the size of a lake to the number of fish that are in it. There are 15 data points, each representing a different lake. The points are widely dispersed on the scatterplot with no pattern of grouping. Interpret what the results of the scatterplot tell you about the relationship between the two variables.

Answers

There is no relation between the size of a lake and the number of fish in the lake.

Answer:

Since there is no cluster formed in the scatterplot, the two variables are not related. Therefore, based on the data shown in the scatterplot, the number of fish in a lake is not dependent on the size of the lake.

Step-by-step explanation:

Sharon needs 64 credits to graduate from her community college. So far she has earned 24 credits. What percent of the required credits does she have?

Answers

She has 37.5 % of her answers because 64/124 is 37.5

A percentage is a number or ratio expressed as a fraction [tex]100[/tex]. Hence, Sharon has [tex]12.5[/tex]% of the credits required.

What is the percentage?

A percentage is a number or ratio expressed as a fraction [tex]100[/tex]. It is often denoted using the percent sign, "%".

Here given information:-

Sharon needs [tex]64[/tex] credits and he earned [tex]24[/tex] credits.

So,

[tex](\frac{24}{64})[/tex]×[tex]100[/tex][tex]=\frac{1}{8}[/tex]×[tex]100[/tex]

[tex]=0.125[/tex]×[tex]100[/tex]

[tex]=12.5[/tex]%

Hence, Sharon has [tex]12.5[/tex]% of the credits required.

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Bill Payne visits his local bank to see how long it will take for $1,000 to amount to $1,900 at a simple interest rate of 12 ½%. Provide Bill with the solution to his problem in years. A. 6.5 years B. 7.2 years C. 12.5 years D. 10.2 years

Answers

Your monthly deposit of $0.00 for 6 years with an interest rate of 12.05% compounded Annually
with an initial starting balance of $1,000.00Balance after 6 years with annual interest of 12.05% $1,979.12
7 years- 2,217.60$
12 years- 3,916.90

The domain for f(x) and g(x) is the set of all real numbers. Let f(x) = 2x2 + x − 3 and g(x) = x − 1. Find f(x) • g(x).

A. 2x3 − x2 + 4x − 3

B. x2 − 4x + 3

C. 2x3 − x2 − 4x + 3

D. 2x3 − 4x2 + 3

Answers

f(x)*g(x)=(2x^2+x-3)(x-1)=(2X^3+x^2-3x)-(2x^2+x-3)=2x^3-x^2-4x-3
so the answer should be C

Find the sum of a 9-term geometric sequence when the first term is 4 and the last term is 1,024 and select the correct answer below.

A.682

B.2044

C.2048

D.678

Answers

The answer is 4+8+16+32+64+128+256+512+1024: This is equivalent to 2044

Answer: The correct option is (B) 2044.

Step-by-step explanation: We are given to find the sum of a 9-term geometric sequence when the first term is 4 and the last term is 1,024.

We know that

the n-th term of a geometric sequence with first term a and common ratio r is given by

[tex]a_n=ar^{n-1}.[/tex]

According to the given information, we have

[tex]a=4[/tex]

and

[tex]ar^{9-1}=1024\\\\\Rightarrow 4\times r^8=1024\\\\\Rightarrow r^8=\dfrac{1024}{4}\\\\\Rightarrow r^8=256\\\\\Rightarrow r^8=2^8\\\\\Rightarrow r=2.[/tex]

Therefore, the sum of the 9-term geometric sequence is given by

[tex]S_9\\\\\\=\dfrac{a(r^9-1)}{r-1}\\\\\\=\dfrac{4\times(2^9-1)}{2-1}\\\\\\=\dfrac{4\times(512-1)}{1}\\\\=4\times511\\\\=2044.[/tex]

Thus, the required sum of the 9-term sequence is 2044.

Option (B) is CORRECT.

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