Let F(x) = Vw. Find G(x), The Function That Is F(x) Shifted Up 5 Units And Left 4 Units.=g(2)help (formulas) (2024)

In order to add these two complex numbers, we need to add the real parts together and the imaginary parts together.

The real part is the number without the "i", and the imaginary part is the number together with the "i".

So we have:

[tex]\begin{gathered} (-4+9i)+(-2-7i)\\ \\ =-4+9i-2-7i\\ \\ =(-4-2)+(9i-7i)\\ \\ =-6+2i \end{gathered}[/tex]

Solution:

Given:

Part A:

[tex]\begin{gathered} P=\text{ \$7,700} \\ r=7.3\text{ \%}=\frac{7.3}{100}=0.073 \\ n=365...............compounded\text{ daily} \end{gathered}[/tex]

Using the compound interest formula,

[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ Thus, \\ A=7700(1+\frac{0.073}{365})^{365\times t} \\ A=7700(1+0.0002)^{365t} \\ A=7700(1.0002)^{365t} \end{gathered}[/tex]

Therefore, the function showing the value of the account after t-years is:

[tex]A=7700(1.0002)^{365t}[/tex]

Part B:

To get the percentage growth per year, we get the amount in the account at the end of two successive years.

At the end of year 1:

[tex]\begin{gathered} A=7700(1.0002)^{365t} \\ \\ when\text{ }t=1 \\ A=7700(1.0002)^{365\times1} \\ A=7700(1.0002)^{365} \\ A=\text{ \$}8283.06 \end{gathered}[/tex]

At the end of year 2:

[tex]\begin{gathered} A=7700(1.0002)^{365t} \\ \\ when\text{ }t=2 \\ A=7700(1.0002)^{365\times2} \\ A=7700(1.0002)^{730} \\ A=\text{ \$}8910.28 \end{gathered}[/tex]

The percentage growth is gotten using the formula:

[tex]\begin{gathered} PGR=(\frac{Ending\text{ value}}{Beginning\text{ value}}-1)\times100\text{ \%} \\ PGR=(\frac{8910.28}{8283.06}-1)\times100\text{ \%} \\ PGR=(1.0757-1)\times100\text{ \%} \\ PGR=0.0757\times100\text{ \%} \\ PGR=7.57\% \end{gathered}[/tex]

Therefore, the percentage of growth per year (APY) is 7.57%

The area of the rectangular prism above is derived as

[tex]\text{Area}=2(\lbrack width\times length\rbrack+\lbrack height\times length\rbrack+\lbrack height\times width\rbrack)[/tex]

The volume of the rectangular prism is derived as

[tex]\text{Vol}=length\times width\times height[/tex]

The area is denoted as "squared." For example, if the area is 10, then you write it out as "10 feet squared," OR "10 square feet."

The volume is written out as cubed, or cubic units

For example if the volume is now 10, your answer would be written out as "10 cubic feet."

SOLUTION:

The points (or stars) from the graph include: (9,5), (10,5.5), (12.5,3.5) and (14.5,1)

So using desmos calculator,

The resulting graph

Showing the plotting:

Final answer:

The resulting equation is:

[tex]y=-0.175x^2\text{ + 3.33x-10.65}[/tex]

The answer is:

B. the statement is false bacuase 8 is not an element of the set.

The set only has the elemnets 1,2,5,7

The blue fabrics used by Frank is 5/8.

The red fabrics used by Frank is 3/8.

PART A:

Plot the fraction 3/8 and 5/8 on the number line.

From the number line it can be observed that 5/8 lies after 3/8. So 5/8 is more than 3/8 means that blue fabric is used more as compare to red fabrics.

PART B:

Multiply the numerator and denominator fraction of 3/4 by 2 to obtain equivalent fraction.

[tex]\frac{3}{4}\cdot\frac{2}{2}=\frac{6}{8}[/tex]

The numerator of fraction 6/8 is 6 and numerator of fraction 3/8 is 3. So fraction 6/8 represent the large value as compare to fraction 3/8.

[tex]\frac{3}{4}>\frac{3}{8}[/tex]

Thus amount of gold fabric is used more as compare to red fabrics.

Given that you spin the spinner twice, the 9 possible outcomes are:

AA, AB, AC, BA, BB, BC, CA, CB, and CC

5 of them have at least one A. Then,

P(at least one A) = 5/9

SOLUTION

We want to solve

[tex]\begin{gathered} 4x^2+x-5=-6x \\ bringing\text{ 6x to the other side, we have } \\ 4x^2+x+6x-5=0 \\ 4x^2+7x-5=0 \\ This\text{ is in the form of the quatric equation } \\ ax^2+bx+c=0 \\ So,\text{ it means } \\ a=4,b=7,c=-5 \end{gathered}[/tex]

Using the quadratic formula

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

We have

[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ x=\frac{-7\pm\sqrt{(-7)^2-4\times4\times-5}}{2\times4} \\ x=\frac{-7\pm\sqrt{49+80}}{8} \\ x=\frac{-7\pm\sqrt{129}}{8} \end{gathered}[/tex]

So, either

[tex]\begin{gathered} x=\frac{-7+\sqrt{129}}{8} \\ x=\frac{-7+11.35781669}{8} \\ x=0.544727 \\ x=0.5 \end{gathered}[/tex]

Or

[tex]\begin{gathered} x=\frac{-7-\sqrt{129}}{8} \\ x=\frac{-7-11.35781669}{8} \\ x=-2.294727 \\ x=-2.3 \end{gathered}[/tex]

Hence the answer is x = 0.5 or -2.3 to the nearest tenth

[tex]\begin{gathered} \text{ Since NM = NR+RM then, } \\ 7x+2=4x+7+x+3 \\ 7x+2=5x+10 \\ 2x=8 \\ x=4 \end{gathered}[/tex][tex]\begin{gathered} \text{Therefore } \\ NM=7\cdot4+2=30 \end{gathered}[/tex]

Solution:

We are to determine the number of triangles ABC possible with the given parts.

a=24, b=20, A=46°

Note that there are only 3 ways of constructing a triangle. They are:

SAS - Side Angle Side.

ASA - Angle Side Angle.

SSS - Side Side Side.

The information given for the triangle does not conform to any of the three ways listed above. Thus,

No triangle can be formed with the given part.

The correct answer is 0.

Given:

[tex]\begin{bmatrix}{1} & {0} & {x} \\ {y} & {-1} & {4} \\ {-3} & {5} & {1}\end{bmatrix}=\begin{bmatrix}{3} & {0} & {-9} \\ {6} & {-3} & {12} \\ {-9} & {15} & {3}\end{bmatrix}[/tex]

Find-: Value of "x" and "y"

Sol:

[tex]\begin{gathered} =\begin{bmatrix}{1} & {0} & {x} \\ {y} & {-1} & {4} \\ {-3} & {5} & {1}\end{bmatrix} \\ \\ \text{ Multiply by 3 then:} \\ \\ =3\times\begin{bmatrix}{1} & {0} & {x} \\ {y} & {-1} & {4} \\ {-3} & {5} & {1}\end{bmatrix} \\ \\ =\begin{bmatrix}{3} & {0} & {3x} \\ {3y} & {-3} & {12} \\ {-9} & {15} & {3}\end{bmatrix} \end{gathered}[/tex]

So, value of x and y is:

[tex]\begin{bmatrix}{3} & {0} & {3x} \\ {3y} & {-3} & {12} \\ {-9} & {15} & {3}\end{bmatrix}=\begin{bmatrix}{3} & {0} & {-9} \\ {6} & {-3} & {12} \\ {-9} & {15} & {3}\end{bmatrix}[/tex][tex]\begin{gathered} 3x=-9 \\ \\ x=-\frac{9}{3} \\ \\ x=-3 \\ \\ 3y=6 \\ \\ y=\frac{6}{3} \\ \\ y=2 \end{gathered}[/tex]

The value of "x" is -3 and value of "y" is 2.

To solve this problem, we need to apply the formula for the equation of a straight line.

One of the forms of this formula, which is appropriate for this problem, is as follows:

[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where (x1 , y1) and (x2 , y2), are the coordinates of any two points that lie on the line.

In this case, the coordinates are: ( -5,-2), and (3, -4)

Now:

[tex]\frac{y-(-2)_{}}{x-(-5)_{}}=\frac{-4_{}-(-2)_{}}{3_{}-(-5)_{}}[/tex][tex]\frac{y+2_{}}{x+5_{}}=\frac{-4_{}+2_{}}{3_{}+5_{}}[/tex][tex]\frac{y+2_{}}{x+5_{}}=\frac{-2_{}}{8_{}}[/tex]

[tex]\frac{y+2_{}}{x+5_{}}=\frac{-1_{}}{4_{}}[/tex][tex]\frac{y+2_{}}{x+5_{}}=-0.25[/tex][tex]\begin{gathered} y+2_{}=-0.25(x+5)\text{ (OPTION C is correct)} \\ y+2_{}=-0.25x-1.25\text{ Option D is also correct} \\ y=-0.25x-3,25\text{ } \end{gathered}[/tex]

We were given the following information:

Cole has 181 songs on a playlist

31 gospel, 20 blues, 36 classical, 24 rap, 16 rock, 9 pop, and 45 jazz

If Cole begins listening to his playlist on shuffle, the probability that the first song played is a classical song is given by:

[tex]\begin{gathered} Pr=\text{obability} \\ P(classical)=\frac{\text{Number of classical songs}}{Total\text{ no. songs}} \\ \text{Number of classical songs}=36 \\ \text{Total = 181} \\ P\mleft(classical\mright)=\frac{36}{181} \\ \\ \therefore P(classical)=\frac{36}{181} \end{gathered}[/tex]

You need to determine which of the given options is equivalent to the expression

[tex](11x-8)+(7-4x)[/tex]

To determine the equivalent expression you have to simplify the equation.

-First, erase the parentheses and group the like terms together:

[tex]\begin{gathered} 11x-8+7-4x \\ 11x-4x-8+7 \end{gathered}[/tex]

-Then, solve the operations between the like terms to simplify the expression:

[tex]\begin{gathered} 11x-4x-8+7 \\ 7x-1 \end{gathered}[/tex]

The equivalent expression is 7x-1 (option C)

Let's first draw a diagram of the situation

Let's call the missing angle a, then using the definition of the sine function, we have that

[tex]\sin (a)=\frac{75}{120}[/tex]

then, we can take inverse sine in both sides of the equality to clear a

[tex]a=\sin ^{-1}(\frac{75}{120})=38,68218745[/tex]

and rounding to the nearest degree, the answer will be 39 degrees.

Given:

a.) They bought a lawnmower for 425 and plan to charge 25.00 an hour.

Question 1: How many hours did the boys work if their profit was more than 4,000.

[tex]\text{ No. of hours the boys worked }>\text{ }\frac{4,000\text{ + cost of lawnmower}}{\text{ charge for doing the job}}[/tex][tex]\text{ No. of hours the boys worked }>\text{ }\frac{4,000\text{ + 4}25}{\text{ 2}5}[/tex]

Let,

x = the number of hours the boys worked.

[tex]\text{ x }>\text{ }\frac{4,425}{\text{ 2}5}[/tex][tex]\text{ x }>\text{ 177 hours}[/tex]

Therefore, for the boys' profit to be more than 4,000, they must work for more than 177 hours.

Question 2: How many hours did the boys work if their profit was between 2,300 and 2,900.

For a profit of more than 2,300:

[tex]\text{ No. of hours the boys worked }>\text{ }\frac{2,300\text{ + cost of lawnmower}}{\text{ charge for doing the job}}[/tex][tex]\text{ x }>\text{ }\frac{2,300\text{ + 425}}{\text{ 2}5}[/tex][tex]\text{ x }>\text{ }\frac{2,725}{\text{ 2}5}[/tex][tex]\text{ x }>\text{ }109[/tex]

For a profit of less than 2,900:

[tex]\text{ No. of hours the boys worked }<\text{ }\frac{2,900\text{ + cost of lawnmower}}{\text{ charge for doing the job}}[/tex][tex]\text{x }<\text{ }\frac{2,900\text{ + 4}25}{\text{ 2}5}[/tex][tex]\text{x }<\text{ }\frac{3,325}{\text{ 2}5}[/tex][tex]\text{x }<\text{ }133[/tex]

Therefore, for a profit between 2,300 and 2,900, the inequality of how many hours must the boys work is:

[tex]\text{ 109 }<\text{ x }<\text{ 133}[/tex]

Given the equation:

[tex]x-1=\sqrt[]{4x-4}[/tex]

Let's solve the equation for x.

To solve for x, take the following steps:

• Step 1.

Square both sides:

[tex]\begin{gathered} (x-1)^2=\sqrt[]{4x-4}^2 \\ \\ (x-1)(x-1)=4x-4 \\ \end{gathered}[/tex]

• Step 2.

Expand using FOIL method and distributive property

[tex]\begin{gathered} x(x-1)-1(x-1)=4x-4 \\ \\ x(x)+x(-1)-1(x)-1(-1)=4x-4 \\ \\ x^2-x-x+1=4x-4 \\ \\ x^2-2x+1=4x-4 \end{gathered}[/tex]

• Step 3.

Add 4 to both sides and also subtract 4x from both sides:

[tex]\begin{gathered} x^2-2x-4x+1+4=4x-4x-4+4 \\ \\ x^2-6x+5=0 \end{gathered}[/tex]

• Step 4.

Factor the left side of the equation using the AC method.

Find two numbers whose sum is -6 and whose product is 5.

Thus, we have:

-5 - 1 = -6

-5 x -1 = 5

Therefore, the numbers are:

-5, and -1

Hence, we have:

[tex](x-5)(x-1)=0[/tex]

Equate trhe individual factors to zero and solve for x:

[tex]\begin{gathered} x-5=0 \\ \text{Add 5 to both sides}\colon \\ x-5+5=0+5 \\ x=5 \\ \\ \\ x-1=0 \\ \text{Add 1 to both sides:} \\ x-1+1=0+1 \\ x=1 \end{gathered}[/tex]

Therefore, the solutions to the given equation is:

[tex]x=5,\text{ and 1}[/tex]

ANSWER:

x = 5, 1

The reference angle is the smallest angle associated with a given angle, measured with respect to the X axis.

Draw each angle to identify the reference angle:

5π/4

The reference angle is π/4.

7π/6

The reference angle is π/6.

-π/9

The reference angle is -π/9.

15π/8

The reference angle is -π/8.

Answer:

4 ( 12 + b)

Explanations:

The given expression is " 4 times the sum of 12 and b"​

"The sum of 12 and b" can be written mathematically as:

12 + b

"4 times the sum of 12 and b" can then be written as:

4 x (12 + b)

Which is also 4 (12 + b)

The formula given is;

[tex]s=\sqrt[]{24d}[/tex]

We can now input the distance d, to obtain;

[tex]\begin{gathered} s=\sqrt[]{24\times245} \\ s=76.7ft\text{ /s} \end{gathered}[/tex]

Therefore, the speed of the vehicle before the brakes were applied is 76.7ft/s

Answer: $4524.56

Work Shown:

A = P*(1+r/n)^(n*t)

5000 = P*(1+0.02/12)^(12*5)

5000 = P*1.105079

P = 5000/1.105079

P = 4524.5634022545

P = 4524.56

Given

To find:

a) The median of each data set.

b) Compare the median values of the data sets.

Explanation:

It is given that,

a) From the above figure.

The median of the data set X is 13, and the median of the data set Y is 16.

b) Also,

The median of the data set X is less than the median of the data set Y.

That implies, the brand Y has a battery life that lasts longer than brand X.

Since the selling price of $585 is marked down by 20%, then, the sale price is

[tex]\begin{gathered} 585-585(0.20)= \\ 585(1-0.20)= \\ 585(0.8) \end{gathered}[/tex]

which is equal to $468.

Now, the cost is $360, then the markup is

[tex]468-360[/tex]

which is equal to $108. Then, answer is $108.

we have the following:

[tex]1\text{foot}=12\text{inches}[/tex]

therefore:

[tex]2.52ft\cdot\frac{12in}{1ft}=30.24in[/tex]

the answer is 30.24 inches

we have the expression

1/2 (4×5)-2³​

so

Applying PEMDAS

P ----> Parentheses first

E -----> Exponents (Powers and Square Roots, etc.)

MD ----> Multiplication and Division (left-to-right)

AS ----> Addition and Subtraction (left-to-right)

step 1

Parentheses first

(4x5)=20

substitute

1/2*20-2³​

step 2

Exponents

2³​=8

substitute

1/2*20-8

step 3

Multiplication

1/2*20=10

substitute

10-8

step 4

Subtraction

10-8=2

answer is 2

To simplify the radical, factorize the number under it using the prime number

Since 252 is an even number, then let us divide it by the 1st prime number 2

[tex]\frac{252}{2}=126[/tex]

since 126 is an even number, then divide it by 2 again

[tex]\frac{126}{2}=63[/tex]

Now 63 is an odd number and sum of its digit = 6 + 3 = 9, then

Divide it by the 2nd prime number 3

[tex]\frac{63}{3}=21[/tex]

Since 21 is divisible by 3, divide it by 3 again

[tex]\frac{21}{3}=7[/tex]

Then 252 = 2 x 2 x 3 x 3 x 7, put them under the radical

[tex]\sqrt[]{252}=\sqrt[]{2\times2\times3\times3\times7}[/tex]

Each number repeated twice can go out the radical, then

2 and 3 will go out the radical

[tex]\begin{gathered} \sqrt[]{252}=2\times3\times\sqrt[]{7} \\ \sqrt[]{252}=6\sqrt[]{7} \end{gathered}[/tex]

The simplest form of the radical is 6 square root 7

[tex]\begin{gathered} \sqrt[]{252}=\sqrt[]{4}\times\sqrt[]{63} \\ =2\times\sqrt[]{63} \\ =2\times\sqrt[]{9}\times\sqrt[]{7} \\ =2\times3\times\sqrt[]{7} \\ =6\times\sqrt[]{7} \\ =6\sqrt[]{7} \end{gathered}[/tex]

A linear function has the form

[tex]y=mx+b[/tex]

so number 2 is a linear function. The graph of the linear is

and it models constant growth.

A quadratic function has the form

[tex]y=ax^2+bx+c[/tex]

so number 1 is quadratic. The graph of the quadratic is

and is decreasing in

[tex](-\infty,-4)[/tex]

An exponential function has the form

[tex]y=a^x,\text{ a>0}[/tex]

then the number 3 is exponential. The graph of the exponential is

and eventually excedees the other functions.

Looking at the figure, we need the reason for angle AED being congruent to angle ACB.

Since the segments ED and CB are parallel, the angles AED and ACB are corresponding angles, therefore they are congruent.

Therefore the correct option is B.

Answer:

67,600,000 possible license plates

Explanation:

The license plates contain 5 numbers followed by 2 letters.

• You can choose a number in 10 ways (that is any number from 0,1,2,3,4,5,6,7,8,9).

,

• There are 26 letters so, you can choose a letter in 26 ways.

Thus, the number of possible license plates that can be issued using this system is:

[tex]\begin{gathered} 10\times10\times10\times10\times10\times26\times26 \\ =10^5\times26^2 \\ =67,600,000 \end{gathered}[/tex]

There are 67,600,000 possible license plates.