Answer:
To find the common difference of an arithmetic sequence, we compute the difference of an element of the sequence and its predecessor.
Example: Given the sequence 28, 18, 8, -2, the common difference is:
[tex]\begin{gathered} 18-28=-10, \\ 8-18=-10, \\ -2-8=-10. \end{gathered}[/tex]help me graduate please the graph of each function is shown . write the function in factored format. do not include complex numbers
Given the function of the graph:
[tex]g(x)=2x^4+x^3-47x^2-25x-75[/tex]Let's factor the given function.
Regroup the terms:
[tex]g(x)=x^3-25x+2x^4-47x^2-75[/tex][tex]\begin{gathered} \text{Factor x out of x}^3-25x\colon \\ \\ g(x)=x(x^2-25)+2x^4-47x^2-75 \end{gathered}[/tex][tex]g(x)=x(x^2-5^2)+2x^4-47x^2-75[/tex][tex]g(x)=x(x+5)(x-5)+2x^4-47x^2-75[/tex][tex]\begin{gathered} \text{ Rewrite x}^4as(x^2)^2\colon \\ \\ g(x)=x(x+5)(x-5)+2(x^2)^2-47x^2-75 \end{gathered}[/tex][tex]\begin{gathered} Letu=x^2 \\ \\ g(x)=x(x+5)(x-5)+2u^2-47u^{}-75 \end{gathered}[/tex][tex]\begin{gathered} Factor\text{ by grouping:} \\ g(x)=x(x+5)(x-5)+(2u+3)(u-25) \end{gathered}[/tex][tex]\begin{gathered} \text{ Repalce u with x}^2\colon \\ g(x)=x(x+5)(x-5)+(2x^2+3)(x^2-25) \end{gathered}[/tex][tex]g(x)=x(x+5)(x-5)+(2x^2+3)(x^2-5^2)[/tex][tex]g(x)=x(x+5)(x-5)+(2x^2+3)(x+5)(x-5)[/tex][tex]\begin{gathered} \text{Factor out (x+5)(x-5)} \\ \\ g(x)=(x+5)(x-5)(x+2x^2+3) \\ \\ g(x)=(x+5)(x-5)(2x^2+x+3) \end{gathered}[/tex]ANSWER:
[tex]g(x)=(x+5)(x-5)(2x^2+x+3)[/tex]Enter the range of values for x using the picture shown
We are asked to find a range for x. Let's start by finding the maximum value. We know, by definition, that a side opposite a larger angle has a longer length. For example, if you think about a right triangle, the hypotenuse (the longest side) is always opposite of the right angle (the largest angle). We are given two side lengths: 23 is opposite of 42 degrees, and 21 is opposite of 3x + 15. Because 42 is opposite the longer side, 42 degrees is a larger angle than 3x + 15. We can set up the inequality and solve for x:
[tex]\begin{gathered} 3x+15<42 \\ 3x<27 \\ x<9 \end{gathered}[/tex]Now, let's look at the minimum value. We know that the angle definitely has to be larger than 0. So, we can set up that inequality and solve for x:
[tex]\begin{gathered} 3x+15>0 \\ 3x>-15 \\ x>-5 \end{gathered}[/tex]Now, we have our final range: -5 < x < 9
What is 35/12 written as a Mixed Number?
Answer:
2 11/12
Explanation:
To write 35/12 as a mixed number we need to divide 35 by 12.
When we divide 35 by 12, we get 2 as a quotient and 11 as a remainder.
Additionally, 35 is the dividend, and 12 is the divisor:
Now, the mixed number can be written as:
It means that the mixed number is:
[tex]\text{quotient}\frac{\text{ remainder}}{\text{divisor}}=2\frac{11}{12}[/tex]Therefore, 35/12 written as a mixed number is 2 11/12
Represent the following sentence as an algebraic expression, where "anumber" is the letter x.The difference of a number and 8.
Given,
The difference of a number and 8
Let the number be x
The result of subtracting one number from another is called the "Difference"
The difference of a number and 8 can be expressed below as
[tex]x-8[/tex]Hence, the algebraic expression of the difference of a number (x) and 8 is x - 8
Milanputting money into a savings account. He starts with $350 in the savings account, and each week he adds $60.Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Milan has been adding money. Write anequation relating S to W. Then use this equation to find the total amount of money in the savings account after 17 weeks.
We know that he starts with $650 in the savings account, and each week he adds $30.
If S represents the total amount of money and w the number of weeks, an equation that realtes S to w is compounded by:
1. An constant value that is the value which he starts
S = 650
2. Multiplying the number of weeks by the money he adds weekly
S = 650 + w30
So, the equation that relates S to w is
[tex]S=650+w30[/tex]Now, we must calculate the total amount of money after 19 weeks.
In order to calculate this value we must replace w = 19 in the equaton
[tex]\begin{gathered} S=650+(19)(30) \\ S=1220 \end{gathered}[/tex]So, after 17 weeks there are $1220
ET 170 ivel -47 1) 0> Erol Name Kuta Software - Infinite Algebra 2 Solving Absolute Value Equations Solve each equation. 1) |3x| = 9 2) |–3r\ = 3 ond -3 Rasm
Question:
Solution:
Consider the following equation:
To solve the above equation, split the equation up into two separate equations:
Equation 1:
[tex]-2n\text{ + 6 = 6}[/tex]Equation 2:
[tex]-2n\text{ + 6 =- 6}[/tex]now, solve each of the equation:
For equation 1 we have that:
[tex]-2n\text{ = 0}[/tex]then n = 0
and for equation 2, we have that:
[tex]-2n\text{ = -12}[/tex]then n = 6.
Then, the correct answer is :
n = 6 and n = 0.
in circle C, BC = 6 and angle ACB = 120 degrees. what is the area of the shaded sector?
Area of sector = θ/360 × πr²
θ = m∠ACB = 120°
radius = r = 6
[tex]\text{Area of sector = }\frac{120}{360}\times\pi\times6^2[/tex][tex]\begin{gathered} \text{Area = }\frac{1}{3}\times\pi\times36 \\ Area\text{ = }\pi\times\frac{36}{3}\text{ } \end{gathered}[/tex][tex]\begin{gathered} Area\text{= }\pi\times12 \\ \text{Area of sector = 12}\pi\text{ (option C)} \end{gathered}[/tex]Given that lines b and care parallel, select all that apply.Which angles are congruent to 3?d123/4→b5/67/80 240270_226
We want to look which angles are congruent to 3 let's analyze the possible options:
Angle 4 is ot congruent since it's not a vertical angle respect to 3
Angle 7 is congruent since 7 and 3 are corresponding angles
Angle 2 is congruent since 2 and 3 are opposite angles
Angle 6 is congruent since 6 and 3 are consecutive interior angles
So
The perimeter of a rectangle measuring (2x + 2)cm by (3x -3) cm is 58cm. Calculate its area. 13. The perimeter
Given:
The length of the given rectangle is l =(2x+2) cm.
The width of the given rectangle is w =(3x-3) cm.
The perimeter of the given rectangle is P =58cm.
Required:
We need to find the area of the rectangle.
Explanation:
Consider the perimeter of the rectangle formula.
[tex]P=2(l+w)[/tex]Substitute l=2x+2, w =3x-3 and P=58 in the formula.
[tex]58=2(2x+2+3x-3)[/tex][tex]58=2(5x-1)[/tex][tex]58=10x-2[/tex]Add 2 to both sides of the equation.
[tex]58+2=10x-2+2[/tex][tex]60=10x[/tex]Divide both sides by 10.
[tex]\frac{60}{10}=\frac{10x}{10}[/tex][tex]x=6[/tex]Substitute x =6 in the equations l=2x+2.
[tex]l=2x+2=2(6)+2=12+2=14cm[/tex][tex]Substitute\text{ }x=6\text{ }in\text{ }the\text{ }equations\text{ }w=3x-3.[/tex][tex]w=3x-3=3(6)-3=18-3=15cm[/tex]The area of the rectangle is
[tex]A=lw[/tex]Substitute l=14cm and w =15cm in the formula.
[tex]A=14\times15[/tex][tex]A=210cm^2[/tex]Final answer:
The area of the given rectangle is 210 square cm.
If f(x) = x^2 + 3x, find f(-3). *
Answer:
The value of f(-3) is;
[tex]f(-3)=0[/tex]Explanation:
Given that;
[tex]f(x)=x^2+3x[/tex]To get f(-3), we will substitute -3 for x in the given function f(x);
[tex]\begin{gathered} f(x)=x^2+3x \\ f(-3)=(-3)^2+3(-3) \\ f(-3)=9^{}-9 \\ f\mleft(-3\mright)=0 \end{gathered}[/tex]Therefore, the value of f(-3) is;
[tex]f(-3)=0[/tex]If g is a linear function and g(2)=7 and g(-2)=-1, find g(-5)
Since the function is linear, it can be written in slope intercept form which is expressed as
y = mx + c
where
m = slope
c = y intercept
The formula for calculating slope is expressed as
m = (y2 - y1)/(x2 - x1)
From the information given,
g(2) = 7
This means that if x2 = 2, y2 = 7
Also,
g(- 2) = - 1
This means that if x1 = - 2, y1 = - 1
By substituting these values into the formula for calculating slope, we have
m = (7 - - 1)/(2 - - 2) = (7 + 1)/(2 + 2) = 8/4 = 2
We would find the y intercept, c by substituting x = 2, y = 7 and m = 2 into the slope intercept equation. We have
7 = 2 * 2 + c
7 = 4 + c
c = 7 - 4 = 3
By substituting m = 2 and c = 3 into the slope intercept equation, the linear function is
y = 2x + 3
Writing it as a function in terms of g, it is
g(x) = 2x + 3
To find g(- 5), we would substitue x = - 5 into g(x) = 2x + 3, we have
g(- 5) = 2(- 5) + 3 = - 10 + 3
g(- 5) = - 7
61.2 + 2x - 10 = -* - 71 + 4x
61.2 + 2x - 10 = - * - 71 + 4x
What do I have to do?
Write a rule to describe a transformation when a triangle hasbeen translated down 2 units and right 5 units.Using (x+10,y+10)
translated down 2 units and right 5 units.
The rule would be
(x + 5, y - 2)
Moving to the right is equal to adding 5 in the x-coordinate.
Translation down is equal to subtracting 2 in the y-coordinate.
17. Multistep The height of a trapezoid is 8 in. and its area is 96 in. Onebase of the trapezoid is 6 inches longer than the other base. What are thelengths of the bases? Explain how you found your answer.
The area of a trapezoid is computed as follows:
A = h*(a + b)/2
where h is the height, and a and b are the length of the bases.
One base of the trapezoid is 6 inches longer than the other base, then:
a = b + 6
Replacing with A = 96, h = 8, and a = b + 6, we get:
96 = 8*(b+ 6 + b)/2
96 = 8*(6 + 2b)/2
A quality control inspector found 9 defective machine parts out of 500 manufactured.a) What percent of the machine parts manufactured were defective? b) What percent of the machine parts manufactured were NOT defective?
a) In order to calculate what percent of the machine parts manufactured were defective, you proceed as follow:
divide the defective machine between the total number of machines:
9/500 = 0.018
next, you multiply the previous result by 100:
0.018 x 100 = 1.8%
Hence, 1.8% of the total number of machines were defective
b) In this case you have:
subtract total machine and defective ones:
500 - 9 = 491
divide the previoues result by the number of toal machine:
491/500 = 0.982
multiply the previoues result by 100:
0.982 x 100 = 98.2
Hence, 98.2% of the total number of machine were NOT defective.
A. Unfortunately, the precise data used by Eratosthenes was lost long ago. However, if Eratosthenes used a meter stick for his experiment today, then the stick’s shadow in Alexandria would be 127 mm long. Determine the angle 0 that the sunrays made with the meter stick. Remember that a meter stick is 1000 millimetres long.B. Assuming that the sun’s rays are essentially parallel, determine the central angle of the circle if the angle passes through Alexandria and Syene. How did you find your answer?
A
Answer:
Explanation:
The right triangle formed is shown below.
To find θ, we would apply the tangent trigonometric ratio which is expressed as
tan θ = opposite side /adjacent side
From the triangle,
opposite side = 127
adjacent side = 1000
tanθ = 127/1000 = 0.127
taking the tan inverse of 0.127
θ = tan^1(0.127)
θ = 7 degrees
hey can you tell me how to find a domain of a function and what does real numbers mean
Solution
Basically the domain represent all the possible values that the function can assume on the x axis
And the real numbers represent all the possible numbers from - infinity to infinity
For example:
f(x)= 2x+1
The domain is all the real numbers since the function is defined for all the possible values of x
In the other hand:
[tex]g(x)=\frac{1}{x-1}[/tex]For this new function the domain is all the real numbers except x=1 since we can' divide by 0
Sharma draws a floor plan of the local supermarket on a coordinate plane.
Solution
For this case we can do the following:
Coordinates
Dairy 1,0
Produce 3,3
Bakery 6,2
Frozen foods 2,6
Part A
B. (3,5)
Part B
D. (2,2)
Statement: Using the figure, determine the following ratios. ∆RTS is a right triangle with a right angle at
By definition:
[tex]\text{tan(angle)}=\frac{\text{opposite side}}{adjacent\text{ side}}[/tex]From the picture:
[tex]\begin{gathered} \tan (S)=\frac{80}{18}=4.4444 \\ \tan (R)=\frac{18}{80}=0.225 \end{gathered}[/tex]Harrison saved $38.97 from his first paycheck and $65.04 from his second paycheck. How much did he save from the paychecks?A.$26.07B.$94.01C.$94.91D.$104.01
Answer:
D.$104.01
Explanation:
Here is what we are told
Harrison got the following amount from his paychecks.
Paycheck 1: $38. 97
Paycheck 2: $65.04
Therefore total amount Harrison saved on his paychecks was
$38. 97 + $65.04 = $104.01
Now looking at the answer choices we see that choice D gives the correct answer.
Therefore choice D is the correct answer.
Answer:
it’s D sir =)
Step-by-step explanation:
The measure of angle a below is(Hint: Slide 3)42°78°
The measure of the angle = 78 - 42 = 36
The angle 78 is interior angle for the shown triangle
so, the angle 78 is the sum of the angles of the triangle except the adjacent angle to 78
I’m not sure if this correct is there no decimal? But it’s asking for a decimal format.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
1.6 x 10^7
decimal format = ?
Step 02:
decimal format:
10^7 ====> move decimal point 7 places right
1.6 x 10^7 = 16,000,000
The answer is:
16,000,000
Give each trig ratio as a fraction in simplest form. PQ is 48.
sin Q = 7/25
cos Q = 24/25
tan Q = 7/24
sin R = 24/25
cos R = 7/25
tan R = 24/7
Explanation:[tex]\begin{gathered} when\text{ Angle = Q} \\ \text{opposite = side opposite the angle= PR} \\ PR\text{ = 14} \\ \text{hypotenuse = 50} \\ \\ \sin \text{ Q = }\frac{opposite}{hypotenuse} \\ \sin \text{ Q = }\frac{14}{50} \\ \sin \text{ Q = 7/25} \end{gathered}[/tex][tex]\begin{gathered} \cos \text{ Q = }\frac{\text{adjacent}}{\text{hypotenuse}} \\ adjacent\text{ = PQ = ?} \\ \text{To get adjacent, we will apply pythagoras' theorem:} \\ \text{hypotenuse}^2=opposite^2+adjacent^2 \\ 50^2=14^2\text{ }+adjacent^2 \\ adjacent^2=50^2-14^2\text{ = 2500 - }196 \\ adjacent^2=\text{ 2304} \\ \text{adjacent = }\sqrt[]{2304}\text{ = 48} \\ \\ \cos \text{ Q = }\frac{48}{50} \\ \cos \text{ Q = 24/25} \end{gathered}[/tex][tex]\begin{gathered} \tan \text{ Q = }\frac{opposite}{adjacent} \\ \tan \text{ Q = }\frac{14}{48} \\ \tan \text{ Q = 7/24} \end{gathered}[/tex]when angle = R
opposite = side opposite the angle R = PQ
opposite = PQ = 48
adjacent = 14
hypotenuse = 50
[tex]\begin{gathered} \sin \text{ R = }\frac{opposite}{hypotenuse} \\ \sin \text{ R = }\frac{48}{50} \\ \sin \text{ R = 24/25} \end{gathered}[/tex][tex]\begin{gathered} \cos \text{ R = }\frac{\text{adjacent}}{\text{hypotenuse}} \\ \text{cos R = }\frac{14}{50} \\ \cos \text{ R = 7/25} \end{gathered}[/tex][tex]\begin{gathered} \tan \text{ R = }\frac{opposite}{hypotenuse} \\ \tan \text{ R = }\frac{48}{14} \\ \tan \text{ R = 24/7} \end{gathered}[/tex]solve by substitution You are planning a birthday party. You buy a total of 50 turkey burgers and veggie burgers for $90.00 . Yo pay $2.00 per Turkey burger and $1.50 per veggie burger. How many of each burger did you buy?*use verbal model to write a system of linear equations. Let "x" representthe number of turkey burgers and let "Y" represent the number of veggie burgers
Let,
t = Turkey burgers
v = veggie burgers
t + v = 50
$2.00 per Turkey burger
$1.50 per Veggie burger
2t + 1.5v = 90
Now we have a system of two equations with two unknowns
[tex]\begin{gathered} t+v=50 \\ 2t+1.5v=90 \end{gathered}[/tex]First equation
[tex]t=50-v[/tex][tex]\begin{gathered} 2(50-v)+1.5v=90 \\ 100-2v+1.5v=90 \\ -2v+1.5v=-100+90 \\ -0.5v=-10 \\ v=\frac{10}{0.5} \\ v=20 \end{gathered}[/tex]20 Veggie burgers
[tex]\begin{gathered} t=50-v \\ t=50-20 \\ t=30 \end{gathered}[/tex]30 Turkey burgers
I need help with this homework question please and thankyou
The formula for continuously compounded interest is
[tex]\begin{gathered} A=Pe^{rt} \\ \text{ Where }A\text{ is the Amount or future value} \\ P\text{ is the Principal, or initial value} \\ r\text{ is the interest rate, and} \\ t\text{ is the time} \end{gathered}[/tex]So, in this case, we have
[tex]\begin{gathered} A=\text{ \$}1,000 \\ P=\text{ \$}200 \\ r=4\text{\% }=\frac{4}{100}=0.04 \\ t=\text{ ?} \end{gathered}[/tex][tex]\begin{gathered} A=Pe^{rt} \\ \text{ Replace the know values} \\ \text{\$}1,000=\text{\$}200\cdot e^{0.04t} \\ \text{ Divide by \$200 from both sides of the equation} \\ \frac{\text{\$}1,000}{\text{\$}200}=\frac{\text{\$}200\cdot e^{0.04t}}{\text{\$}200} \\ 5=e^{0.04t} \\ \text{ Apply natural logarithm to both sides of the equation} \\ \ln (5)=\ln (e^{0.04t}) \\ \ln (5)=0.04t \\ \text{ Divide by 0.04 from both sides of the equation} \\ \frac{\ln(5)}{0.04}=\frac{0.04t}{0.04} \\ \boldsymbol{40.2\approx t} \end{gathered}[/tex]Therefore, it will take approximately 40 years for the account to reach $1,000.
Find the equation of the line passing through the points (-2,3) and (1, -3). Write the equation in slope-intercept form. A) y = -2x + 3 B) y = 2x + 7 C) y = 2x - 5 D) y = -2x - 1
The coordinates are given (-2,3) and (1, -3).
The equation formed from the coordinates is
[tex]y-3=\frac{-3-3}{1+2}(x+2)[/tex][tex]y-3=\frac{-6}{3}(x+2)[/tex][tex]y=-2x-4+3[/tex][tex]y=-2x-1[/tex]Hence the correct option is D .
One positive number is 5 more than another. The sum of their squares is 53. What is the larger number?
7
1) Let's write this
1st number: x
2nd number: y+5
So the positive number and the 1st number have the following relationship x = y +5
2) So we can write, and expand that binomial:
y² +(y+5)² = 53
y² + y² +10y +25 = 53 Combine like terms
2y² +10y -28 =0
We can now solve it:
[tex]\begin{gathered} y=\frac{-10\pm\sqrt[]{100-4(2)(-28)}}{2(2)} \\ y_1=2 \\ y_2=-7 \end{gathered}[/tex]3) As -7 is 9 units lower than 2, then it does not suits us. So let's use that prior relationship to find the other number
x =y+5
x = 2 +5
x=7
Hence, the larger number is 7 and the smaller one is 2
In the similar triangles below, what is the length of AB?
Given:
There are given two triangles, ABC and DEF.
Where,
[tex]\begin{gathered} AC=6cm \\ BC=4cm \\ DE=15cm \\ DF=18cm \end{gathered}[/tex]Explanation:
To find the value of two congruent triangles, we need to use the ratio properties:
So,
From the given congruent triangle:
[tex]\frac{AB}{DE}=\frac{AC}{DF}[/tex]Then,
Put the all values into the above ratio expression:
So,
[tex]\begin{gathered} \begin{equation*} \frac{AB}{DE}=\frac{AC}{DF} \end{equation*} \\ \frac{AB}{15}=\frac{6}{18} \\ \frac{AB}{15}=\frac{1}{3} \\ 3AB=15 \\ AB=\frac{15}{3} \\ AB=5 \end{gathered}[/tex]Final answer:
Hence, the correct option is D.
John and Amber work at an ice cream shop. The hours worked and wages earned are given for each person.
John's wages are proportional to time if every time that we divide wages by time, we get a constant, so we can make the following table:
Time Wages Wages/Time (y/x)
2 18 18/2 = 9
3 27 27/3 = 9
4 36 36/4 = 9
Since Wages/Time is always equal to 9, John's wages are proportional to time.
Answer: John's wages are proportional to time.
A rope is 60 inches in length must be cut into two pieces one piece must be twice as long as the other find the length of each piece round your answers to the nearest inch if necessary
Let x be the length of one piece and y be the length of the other piece. Then, we can write:
[tex]x+y=60\ldots(A)[/tex]since one piece must be twice long than the other, we can write
[tex]2x=y\ldots(B)[/tex]and we have 2 equations in 2 unknows.
Solving by substitution method.
By substituting equation B into equation A, we get
[tex]x+(2x)=60[/tex]which gives
[tex]\begin{gathered} 3x=60 \\ x=\frac{60}{3} \\ x=20 \end{gathered}[/tex]Now, in order to obtain y, we must substitute this result into equation B. It yields
[tex]\begin{gathered} y=2x\Rightarrow y=2(20) \\ y=40 \end{gathered}[/tex]Therefore, the answer is x= 20 inches and y= 40 inches.