f(x) = x/2 - 3 and g(x) = 3x² + x − 6, find (f+ g)(x)

Answer: 1/12

Step-by-step explanation:

The total area of the rectangle needs to be 1.

Since 20-8=12, the height needs to be 1/12.

The surface area of trapezoidal prism is: D. 385.6 yd².

Surface area = (b1 + b2)h + PH.

The parameters are:

b1 = 10 yd

b2 = 6 yd

h = 4.6 yd

Perimeter of base (P) = 6 + 10 + 5 + 5 = 26 yd

H = 12 yd

Plug in the values

Surface area = (10 + 6)4.6 + (26)(12)

Surface area = 385.6 yd²

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The value f x when y= 5 is 2

Let the given equation be y = k/x

where k is the constant

if y = 2 when x= 5, then;

k = xy

k= 2(5)

k = 10

In order to determine the value of x when y = 5

x = k/y

x = 10/5

x = 2

Hence the value f x when y= 5 is 2

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Given that, one digit of a two digit number is three times the other digit.

Let assume that digit at ones place be x.

digit at ones place be x.So, digit at tens place be 3x.

digit at ones place be x.So, digit at tens place be 3x.So, two digit original number = 10 × 3x + 1 × x = 30x + x = 31x

Now, number formed on interchanging its digits, i.e.

Reverse number = 10 × x + 1 × 3x = 10x + 3x = 13x

According to statement, if we interchange the digits of this two digit number and add the resulting number to the original number, we get 88.

[tex]\begin{gathered}\sf \: 31x + 13x = 88 \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf \: 44x = 88 \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf \: x = \dfrac{88}{44} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf\implies \: x = 2 \\ \\ \end{gathered}[/tex]

So, two digit number is 31 × 2 = 62

Hence,

[tex]\begin{gathered}\sf\implies \: \boxed{ \bf{ \:Original \: number \: = \: 62 \: \: }} \\ \\ \end{gathered}[/tex]

[tex]\rule{190pt}{2pt}[/tex]

Answer:

26 or 62

Step-by-step explanation:

If one of the two digits of a two-digit number is three times the other digit, then the options for the two-digit number are:

If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88.

From inspection of the listed pairs of numbers, the only pair that sums to 88 is 26 and 62:

⇒ 26 + 62 = 88

Therefore, the original number is either 26 or 62.

Answer:

  -4sin(2x)

Step-by-step explanation:

Angle sum identities can be used to simplify this expression.

The cosine function is even, so cos(-x) = cos(x). The cosine of the sum is ...

  cos(90°+x) = cos(90°)cos(x) -sin(90°)sin(x) = -sin(x)

Then the numerator simplifies to ...

  4cos(-x)cos(90°+x) = -4cos(x)sin(x) = -2sin(2x)

Matching the denominator expression to the sine of a sum relation, we see

  sin(30° -x)cos(x) +sin(x)cos(30° -x) = sin((30°-x) +x) = sin(30°) = 1/2

The simplified expression is the ratio of the simplified numerator to the simplified denominator:

  = -sin(2x)/(1/2)

  = -4sin(2x)

f(x) = x^4 - 5x^3 + x^2 + 21x - 18

=======================================================

Explanation:

The root x = -2 means x+2 is a factor. This is because we add 2 to both sides of x = -2 to get x+2 = 0.

Similarly, x = 3 leads to x-3 being another factor. It's a double root so we really have two copies of (x-3)

The last root is x = 1 which gives the factor x-1.

The four factors are: (x+2)(x-3)(x-3)(x-1)

Let's use the FOIL rule to expand out the first two factors

(x+2)(x-3) = x^2-3x+2x-6 = x^2-x-6

Do the same for the last two factors

(x-3)(x-1) = x^2-1x-3x+3 = x^2-4x+3

--------------------

So far we have:

(x+2)(x-3) = x^2-x-6

(x-3)(x-1) = x^2-4x+3

which leads to  

(x+2)(x-3)(x-3)(x-1) = (x^2-x-6)(x^2-4x+3)

From here I'll use the box method to multiply these trinomials. Check out the diagram below. Each inner cell is the result of multiplying the headers. Example: x^2 times x^2 = x^4 in the upper left corner.

I've color-coded the inner cells to show the like terms. Add up those like terms:

Therefore we end up with

(x^2-x-6)(x^2-4x+3) = x^4 - 5x^3 + x^2 + 21x - 18 which is choice B

--------------------

To verify this answer, plug in x = 0 and you should get y = -18 to show that we have the correct y intercept. If we tried this with choice A, then we'd get y = 18 which helps eliminate choice A.

Furthermore, plug in x = -2 into choice B and you should get y = 0 as an output. The same applies to x = 3 and x = 1. This confirms that they are roots or x intercepts of the polynomial.

Another way to verify the answer is to use something like WolframAlpha to type in (x+2)(x-3)(x-3)(x-1). Under the "expanded form" subsection, it says x^4 - 5x^3 + x^2 + 21x - 18

The coordinates plane is illustrated below.

A coordinate plane simply means the graphing system for points and lines.

Based on the information given, the area of teb triangle will be:

= 1/2 × b × h

= 1/2 × 11 × 20

= 110

Other information are attached.

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According to the internet it states, The median of a triangle is a line segment joining the vertex of the triangle to the mid-point of its opposite side.

It bisects the opposite side, dividing it into two equal parts.

The median of a triangle further divides the triangle into two triangles having the same area

Answer:

you can use the spreadsheet

Answer:

only the first one

Step-by-step explanation:

all the others sign to at least one x value 2 different y values. and that violates the definition of a function.

the sequence is:

Translation, then reflection.

The correct option is the second one.

We start with figure 1.

In the image, we can see that the image is shifted 4 units up and 4 units left to make figure 2.

Then you can see that the image is reflected across a horizontal line to make figure 3, you can see that because now the "L" is facing upwards.

Then the sequence is:

Translation, then reflection.

The correct option is the second one.

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Answer:

1.  Vertical shrink by a factor of ¹/₅

2.  Right 5

3.  Up 5

Step-by-step explanation:

Transformations of Graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.

Transformations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]

[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]

[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]

[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]

Identify the transformations that take the parent function to the given function.

Question 1

[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]

[tex]\textsf{Given function}: \quad f(x)=\dfrac{1}{5}x^3[/tex]

Comparing the parent function with the given function, we can see that the parent function has been multiplied by ¹/₅.

Therefore, the transformation is:

[tex]y=\dfrac{1}{5}\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:\dfrac{1}{5}[/tex]

As 0 < a < 1, the transformation visually is a compression in the y-direction, so we can also say:  Vertical shrink by a factor of ¹/₅

Question 2

[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]

[tex]\textsf{Given function}: \quad f(x)=(x-5)^3[/tex]

Comparing the parent function with the given function, we can see that 5 has been subtracted from the x-value of the parent function.

Therefore, the transformation is:

[tex]f(x-5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units right}[/tex]

Question 3

[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]

[tex]\textsf{Given function}: \quad f(x)=x^3+5[/tex]

Comparing the parent function with the given function, we can see that  5 has been added to the parent function.

Therefore, the transformation is:

[tex]f(x)+5 \implies f(x) \: \textsf{translated}\:5\:\textsf{units up}[/tex]

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Answer:

1) Vertical shrink by a factor of 1/5

2) Right 5

3) Up 5

Explanation:

Given main function: f(x) = x³

1.) f(x) = 1/5 (x³)

Comparing with a(f(x)) which gives vertical stretch or compression.

Here the function f(x) has been shrinked vertically by a factor of 1/5

2.) f(x) = (x - 5)³

Comparing with f(x - c) which gives horizontal translation c units right.

Here the function f(x) has been shifted 5 units to the right.

3.) f(x)= x³ + 5​

Comparing it with f(x) + d which gives vertical translation d units up.

Here the function f(x) has been moved 5 units up.

Answer:

Option D

Step-by-step explanation:

This function has vertex at origin

Let's verify

Put (0,0)

Hence verified

Answer:

[tex]f(x)=-x^2[/tex]

Step-by-step explanation:

Vertex form of a quadratic function:

  [tex]y=a(x-h)^2+k[/tex]  

where:

If the vertex is at the origin:

Substituting the vertex into the equation:

[tex]\implies y=a(x-0)^2+0[/tex]

[tex]\implies y= ax^2[/tex]

Comparing with the available answer options:

[tex]f(x)=-x^2[/tex]  has its vertex at the origin.

Additional Information:

[tex]\textsf{The vertex of }\:f(x)=(x+4)^2 \: \textsf{ is }\:(-4,0)[/tex]

[tex]\textsf{The vertex of }\:f(x)=x(x-4) \: \textsf{ is }\:(2,-4)[/tex]

[tex]\textsf{The vertex of }\:f(x)=(x-4)(x+4) \: \textsf{ is }\:(0,-16)[/tex]

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Answer:

diameter =7 cm

Step-by-step explanation:

circum=2pi×r

[tex]2\pi \times r[/tex]

2×pi×r=22

2×22÷7×r=22

r=22×7÷44

r=7÷2

r=3.5

d=2×r=2×3.5=7

Answer:

Step-by-step explanation:

let he drives at 21 m/hr=x gallons

gas used at 18 m/hr=15.5-x

21x+18(15.5-x)=300

divide by 3

7x+6(15.5-x)=100

7x+93-6x=100

x=100-93=7 gallons

gas used in city=15.5-7=8.5 gallons

distance travelled in city=18×8.5=153 miles

The distance from the second destination back to Dallas is 918 miles

A triangle has points Dallas, destination 1, and destination 2.

The distance from Dallas to destination 1 is 720 miles

The distance from destination 1 and destination 2 is 290 miles

the angle formed between Dallas, destination 1, and destination 2 is 125 degrees.

He moves from destination 1 to Dallas then destination 2

We could use cosine law to find the distance

The Law of cosines or cosine law means the relation between the length of sides of a triangle with respect to the cosine of its angle. It is also called the cosine rule

[tex]b^{2}=a^2+c^2-2ac*cosB[/tex]

=[tex]290^2+720^2-2*720*290*cos125[/tex]

=84100+518400-417600 cos 125

=602500-417600*(-0.5735)

=602500+239493.6

=841993.6

b=917.6 miles

≅918 miles

The distance is 918 miles  he will fly from the second destination back to Dallas

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Answer:

918 miles

Step-by-step explanation:

got it right on edge

Answer:

it's-3

Step-by-step explanation:

please mark me as brainlist

The correct answer is D

The mean is also called average. The arithmetic mean is found by adding the numbers in the list and dividing the sum by the number of numbers in the list.

Mean = (Sum of all the observations/Total number of observations)

Darryl's credit scores are Experian score is 719, Equifax's score is 741, and Transunion's score is 780.

To find the mean we have to add the given values i.e., the sum of Experian score, Equifax's score, and Transunion's score.

719+741+780

there are a total of 3 scores so we have to divide them by 3.

[tex]\frac{719+741+780}{3}[/tex]

≅[tex]746.67[/tex]

The nearest whole point is 747.

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By using Geogebra online graphing calculator, the solution to this system of inequalities are plotted in the image attached below.

An inequality is a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:

Given the following system of inequalities:

3y > 2x + 12  ⇒ 3y - 2x > 12

2x + y ≤ -5

By using Geogebra online graphing calculator, the solution to this system of inequalities are plotted in the image attached below.

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Answer:

6x^5-5x^4+6x^3-x^2+12x-31

Step-by-step explanation:

(−5x^4+6x^3−43)+(6x^5−x^2+12x+12)

To add, combine like terms

6x^5-5x^4+6x^3-x^2+12x-43+12

6x^5-5x^4+6x^3-x^2+12x-31

Standard form means from the highest power of x to the lowest power of x

Answer:

4.5

Hope it helps

Answer:

max=50

min=41

Step-by-step explanation:

graph

1. The Year-0 net cash flow is -$1,061,500.

2. The net operating cash flows in Years 1, 2, and 3 are as follows:

Year 1: $288,750 ($386,000 x 1 - 0.25)

Year 2: $288,750 ($386,000 x 1 - 0.25)

Year 3: $288,750 ($386,000 x 1 - 0.25)

3. The additional Year-3 cash flow (i.e, the after-tax salvage and the return of working capital) is $468,750 {($599,000 x 1 - 0.25) + $19,500}.

4. The NPV of the project is ($13,139).

5. The machine should not be purchased because it does not yield a positive NPV.

The net present value (NPV) shows the difference between the present value of cash inflows and the present value of cash outflows over a period of time.

It is determined by calculating the present values of cash flows using their present value factors as below:

Initial cash outlay = $1,061,500 ($1,020,000 + $22,000 + $19,500)

Salvage value = $599,000

Increase in net working capital = $19,500

Annual savings before tax = $386,000

Tax rate = 25%

Annuial savings after tax = $288,750 ($386,000 x 1 - 0.25)

Year      Cashflows        PV Factor     Present Value

0          -$1,061,500               1             -$1,061,500

1              $288,750          0.901           $260,164

2             $288,750          0.812          $234,465

3             $288,750          0.731            $211,076

3             $468,750          0.731          $342,656

Net present value                                -$13,139

Thus, the project should not be undertaken by The Campbell Company due to the negative NPV that it yields.

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The quotient of the division operation is [tex]\frac{5}{9}[/tex]

From the question, we are to find the quotient of the division operation

The given division operation is

[tex]\frac{2}{3} \div \frac{6}{5}[/tex]

1. The divided is [tex]\frac{2}{3}[/tex]

2. The divisor is [tex]\frac{6}{5}[/tex]

3. The reciprocal of the divisor is [tex]\frac{5}{6}[/tex]

4. The equivalent multiplication of the division problem is

[tex]\frac{2}{3} \times \frac{5}{6}[/tex]

5. The multiplication gives

[tex]\frac{2}{3} \times \frac{5}{6}=\frac{10}{18}[/tex]

6. Simplifying the quotient, we get

[tex]\frac{10}{18}=\frac{5}{9}[/tex]

Hence, the quotient of the division operation is [tex]\frac{5}{9}[/tex]

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See below for the changes when the exponential function is transformed

The exponential functions are given as:

[tex]y = \sqrt x[/tex]

[tex]y = 5\sqrt x[/tex]

[tex]y = 14\sqrt{x[/tex]

[tex]y = -2\sqrt{x[/tex]

An exponential function of the above form is represented as:

[tex]y = a\sqrt{x[/tex]

See attachment for the graph of the four functions.

When a is large

This is represented by [tex]y = 14\sqrt{x[/tex]

In this case, the curve of the base form [tex]y = \sqrt x[/tex] is vertically stretched and it moves closer to the y-axis

When a is small

This is represented by [tex]y = 5\sqrt x[/tex]

In this case, the curve of the base form [tex]y = \sqrt x[/tex] is vertically stretched and it moves away from the x-axis

When a is negative

This is represented by [tex]y = -2\sqrt{x[/tex]

In this case, the curve of the base form [tex]y = \sqrt x[/tex] is vertically stretched and is reflected across the y-axis.

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Answer:

1) All real numbers n such that [tex]n < 5.5[/tex]

2) All real numbers n such that [tex]n > -\frac{19}{7}[/tex]

Step-by-step explanation: How did I come up with such answers? Let me show you!

For the first problem, we just solve the inequality easily.

Subtracting 3 from both sides, we get:

4n < 22

Dividing by 4 from both sides, we get:

n < 5.5

Thus, all real numbers n that is less than 5.5 when plugged in for x will be less than 25.

For the next problem, it will be slightly trickier.

Subtracting 5 from both sides, we get:

-7n < 19

Dividing -7 from both sides, we get:

n > -19/7

Did you catch that? We just flipped the inequality sign and turned it from less than to a greater than. Whenever we divide by a negative number, the signs always change.

Thus, for all real numbers n greater than -19/7, when plugging in for x, you will get less than 24.

Hope this helped!

Answer:

mark on day three can use up to 4 cans of blue paint and 5 cans of yellow paint

Step-by-step explanation:

given--started with 14 cans of blue paint

given--started with 20 cans of yellow paint

given--used 10 cans of blue paint and 15 cans of yellow paint in total

by subtracting the blue paint he used with the amount he started with you get an answer of 4 blue paint cans--- vice verse--20 yellow paint cans minus 15 yellow paint cans equal 5 yellow paint cans.

The number sentence that applies the commutative property to the example is 4 × 3 = 12

Commutative property can be additive or multiplicative. It is a way of changing the position of a function or value in an expression without affecting the result

Examples are

A +B = B +A

AB = BA

Although the value were interchanged, the result were not affected. Hence the number sentence that applies the commutative property to the example is 4 × 3 = 12 since changing 3 and 4 does not affect the result

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Answer:

Russia is so vast that it has eleven time zones.

Explanation:

"Russia has 11 time zones across its vast territory - and its leaders believe that's just too many hours in the day." - NBC News