In order to determine the equation of the line, use the following general expression for the equation:
y - yo = m(x - xo)
where m is the slope of the line and (xo,yo) is any point of the line.
To calculate m use the following espression:
m = (y2 - y1)/(x2 - x1)
where, for this case (x1,y1) = (2,5) and (x2,y2) = (8,2):
m = (2 - 5)/(8 - 2) = -3/(6)
m = -1/2
next, replace m and (xo,yo) = (2,5) into the general expression, and solve for y, as follow:
y - 5 = -1/2(x - 2)
y - 5 = -1/2x + 1
y = -1/2 x + 6 this is the euqation of the line
At the train station, the cost for parking is based on an hourly fee. Patrons that park for 2 hours or less are charged at the short termparking fee but patrons that park for more than 2 hours are charged at the long term parking fee. The parking cost can be modeledwith the following piecewise equation, where x represents the number of hours.f(x) = {12x, x ≤ 2 15x, x > 2How much would it cost to park at the train station for 7 hours?Enter your answer in the box.$
We have a fee that is modeled by the piecewise function:
[tex]f(x)=\begin{cases}12x,x\le2 \\ 15x,x>2\end{cases}[/tex]We have to find the total fee for x = 7 hours.
As x = 7 > 2, we use the second part of the function, 15x.
Then, we can calculate the fee as:
[tex]f(7)=15(7)=107[/tex]Answer: $107
Linda goes for a run every day after school, but she likes to make some workouts easier than others. On Monday, Linda ran 3.5 miles in 35 minutes. On Tuesday, she ran 3 miles in 40 minutes. On which day did Linda run at a faster pace? Monday Tuesday Submit
1) Gathering the data
Monday 3.5 miles in 35 minutes
Tuesday 3 miles in 40 minutes
Faster pace?
2) To find out the pace let's calculate the average speed.
And we can find it by a formula:
Average Speed on Monday = 3.5 / 35 =0.1 miles per minute
Average speed on Tuesday = 3 / 40 = 0.075 miles per minute
So, Linda runs on Monday at a faster pace.
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Spencer Fuel Stop (cheaper) Gas World
Saturday
Sunday
Since at Fuel Stop the gasoline is cheaper than at Gas World, then Spencer will be able to buy more gas at Fuel Stop with his $20 than at the Gas world
Refer to the figure below. Then find the indicated values:A) f(7)B) g(0) + f(3)C) f(g(7))D) g(f(8))E) x if f(x) =2
Given the graph in the image question, it can be seen that:
[tex]\begin{gathered} y=f(x) \\ y=g(x) \end{gathered}[/tex]To answer the questions, we have:
a. f(7)
[tex]f(7)=1[/tex]b. g(0)+f(3)
[tex]\begin{gathered} g(0)=6 \\ f(3)=-1 \\ g(0)+f(3)=6+(-1)_{} \\ =6-1 \\ =5 \end{gathered}[/tex]c. f(g(7))
[tex]\begin{gathered} We\text{ do }g(7)\text{ first and then do the f(x) of the result:} \\ g(7)=6 \\ f(g(7))=f(6) \\ =1 \end{gathered}[/tex]d. g(f(8))
[tex]\begin{gathered} We\text{ do f}(8)\text{ first and then do the f(x) of the result:} \\ f(8)=1 \\ g(f(8))=g(1) \\ =6 \end{gathered}[/tex]e. x if f(x)=2
[tex]\begin{gathered} f(x)=2 \\ \text{ To get }f(x),\text{ we look at the point 2 on the y axis and trace it to x} \\ f(x)=2\text{ at point }-7\text{ on the x axis} \\ \text{Hence, x=-7} \end{gathered}[/tex]The area of Seth's bedroom is 1/2 of the area of his mom's living room. Seth also has a closet with an area of 12 square feet. If the total area Seth has at his disposal is 132 square feet, what is the area of the living room?
Let S be the area of Seth's bedroom and let M be the area of his mom's living room.
Let's first set-up the e
From the question, "The area of Seth's bedroom is 1/2 of the area of his mom's living room" can be written mathematically as;
S = 1/2 M ---------------------------------------------(1)
Also, "the total area Seth has at his disposal is 132 square feet" implies;
S + 12 = 132 -----------------------------------------------------(2)
graph the equation y equals 4x - 5 by plotting points
Given the equation:
y = 4x - 5
Use the slope intercept form:
y = mx + b
Where m is the slope and b is the y-intercept.
To plot the points, first make a point on the y-intercept, y = -5
At y-intercept, x = 0.
Thus, we have the point (0, -5)
Let's find the value of y, when x = 1.
y = 4(-1) -5
y = 4 - 5 =
y = -1
When x = 1, y = -1
We have the point (1, -1)
When x = 2
y = 4(2) - 5
y = 8 - 5
y = 3
When x = 2, y = 3
We have the point (2, 3)
Thus, mark the following points:
(0, -5)
(1, -1)
(2, 3)
Then connect the plotted points with a straight line.
We have the graph attached below:
G(x) =x^2+3 Use the transformation to graph the following function
The graph of a function h(x) translated n units up is represented by the following function:
[tex]l(x)=h(x)+n\text{.}[/tex]Therefore, the graph of g(x) is the graph of f(x) translated 3 units up.
The graph of f(x) is:
Therefore, the graph of g(x) is:
Answer:
find an angle between 0 and 2π that is coterminal with 33π/10
The Solution.
Coterminal angles are angles that differ by a whole number of complete circles.
So, The coterminal angles of the given angle in the interval [0,2pi} is obtained as below:
[tex]\frac{33\pi}{10}-2\pi=3\frac{3\pi}{10}-2\pi=1\frac{3}{10}\pi[/tex]Thus, the coterminal angle within the given range is
[tex]1\frac{3}{10}\pi\text{ or }\frac{13}{10}\pi[/tex]lake Question Find the value of x to the nearest degree. 8 4 Not drawn to scale 59 b. 63 54 d. 27 A
We can relate the sides and the angle of right triangles with trigonometric ratios.
In this case, we can write:
[tex]\begin{gathered} \tan (x)=\frac{\text{Opposite}}{\text{Adyacent}}=\frac{8}{4}=2 \\ x=\arctan (2)\approx63\degree \end{gathered}[/tex]Answer: x = 63°
What are the factors after you do yhr 4th step?
Here given that
[tex](x-\frac{2}{3})(x+\frac{9}{3})[/tex]Further simplification we have to take lcm first
[tex](\frac{3x}{3}-\frac{2}{3})(\frac{3x}{3}+\frac{9}{3})=\frac{(3x-2)}{3}\times\frac{(3x+9)}{3}=\frac{(3x-2)(3x+9)}{9}[/tex]Also
So finally we get the factors are
[tex](3x-2)(3x+9)[/tex]Determine the exact value of cos 135 degrees and explain how you knew to use the side lengths you used
Explanation
We are required to determine the exact value of cos 135°.
Since the angle lies in the second quadrant, we have:
[tex]\begin{gathered} \cos135\degree=\cos(180\degree-45\degree) \\ \cos135\degree=-\cos45\degree \end{gathered}[/tex]To determine the value of x, we have:
[tex]\begin{gathered} \text{ Using the Pythagorean theorem,} \\ x^2=1^2+1^2 \\ x=\sqrt{1^2+1^2} \\ x=\sqrt{1+1} \\ x=\sqrt{2} \end{gathered}[/tex]Therefore, the value of cos 135° is:
[tex]\begin{gathered} \text{ We know that }cos\theta=\frac{adj}{hyp} \\ \therefore\cos135\degree=-\cos45\degree=-\frac{1}{\sqrt{2}} \\ \cos135\degree=-\frac{1}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}} \\ \cos135\degree=-\frac{\sqrt{2}}{2} \end{gathered}[/tex]Hence, the answer is:
[tex]\cos(135)\operatorname{\degree}=-\frac{\sqrt{2}}{2}[/tex]The lengths used is the lowest length of sides that can be used.
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (suchas printing). The one-time fixed costs will total $39.160. The variable costs will be $11 per book. The publisher will sell the finished product to bookstores at aprice of $24.75 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?
Given:
The one-time fixed costs = $39.160.
The variable costs = $11 per book.
The price of the book = $24.75 per book.
Let x be the number of books.
The production cost of the x number of books is
[tex]=39.160+11x[/tex]The sales price of the x number of books is
[tex]=24.75x[/tex]Given that the production cost = the sales cost.
[tex]=39.160+11x[/tex]A figure is shownselect all the statements that are true
Vertical angles are the opposite angles when a "X" (cross) is formed.
They are equal.
Adjacent angles are angles next to one another. They add to 180 degrees.
Complementary angles are angles that add to 90 degrees.
From the figure, we can say the following:
• B and C are vertical angles
,• A and D are vertical angles
,• A and B are adjacent angles
,• B and D are adjacent angles
,• D and C are adjacent angles
,• C and A are adjacent angles
The first statement is false. Since C is vertical angles to B, it should be equal to B, 50 degrees.
The second statement is true. Since B and D are adjacent angles, 50 + D = 180, So, D = 130.
Third statement is true. B and C are vertical angles.
Fourth statement is false. B and C are not adjacent angles, they are vertical.
Fifth statement is true. B and D are adjacent angles.
Sixth statement is false. B and A aren't complementary. They are rather supplementary (two angles that add to 180 degrees).
Thus,
The true statements are:
2nd
3rd
5th
Describe the effect of the transformation on (x,y) and describe the transformation in words: (x, y) → ( )
The effect of the transformation on (x,y) , it will make a similar images but at different coordinates of x and y , as shown in the image, two similar figures but at different places
To describe the given transformation, at first, we need to find the rule of transformation
Take the point as a reference and find its image
Let the point is the vertex of the image which is (1 , 2 )
the image of the point is ( 3 , 1 )
So, x coordinates changed from 1 to 3, which mean the image moved 2 units to the right
And, y- coordinates changed from 2 to 1, which mean the image moved 1 units down
So, the desciption of the transformation is:
The total image moved 2 units right and 1 unit down
Simplify to determine the number of solutions 8(5b+3)=10(4b+2)
We will solve as follows:
[tex]8(5b+3)=10(4b+2)\Rightarrow40b+24=40b+20[/tex][tex]\Rightarrow40b-40b=20-24\Rightarrow0\ne-4[/tex]The problem has no real solutions.
Answer:
no solution
Step-by-step explanation:
8(5b + 3) = 10(4b + 2) ← distribute parenthesis on both sides
40b + 24 = 40b + 20 ( subtract 24 from both sides )
40b = 40b - 4 ( subtract 40b from both sides )
0 = - 4 ← not possible
this indicates the equation has no solution
x is an acute angle. Find the value of x in degrees. cos (x)= 0.8
So, given:
The answer is 36.87°.
Find the equation that represents the proportional relationship in this graph, for y in terms of x.
Answer:
2x=y
Step-by-step explanation:
0.2/0.1 using rise over run method
2x=y
Please mark brainliest and comment if you need more explanation
What is the greatest common factor of 10b^2 and 30? A. 2 B. 5b C. 10b D. 10
Answer:
D. 10
what's the domain of [tex] \frac{5x}{6 - 4x} [/tex]
SOLUTION
A fraction will be undefined when its denominator is zero.
The given function will be undefined when
[tex]\begin{gathered} 6-4x=0 \\ 4x=6 \\ x=\frac{6}{4} \\ x=\frac{3}{2} \end{gathered}[/tex]The function will be defined at all point except when x=3/2
The domain of a function refers to all possible values of x on which the function is defined.
This is given as ;
list the sides in order from largest to shortest JKL
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
∠ J = 71
∠ K = 41
∠ L = 68
sides from largest to shortest = ?
Step 02:
We must apply relationship between sides and angles.
The sides from largest to shortest :
1 . ∠ J = 71 ===> side KL
2. ∠ L = 68 ===> side JK
3. ∠ K = 41 ===> side JL
This is the solution.
KL , JK , JL
1) Find perimeter and area of a rectangle with width 7 in and length 12 in. P = A found the decimeter of a square wi with area 64 cm?
To solve the exercise, let us first draw the rectangle:
The formula to find the area of a rectangle is
[tex]\begin{gathered} A=l\cdot w \\ \text{ Where } \\ A\text{ is the area,} \\ l\text{ is the length and} \\ w\text{ is the width of the rectangle} \end{gathered}[/tex]So, in this case, you have
[tex]\begin{gathered} l=12\text{ in} \\ w=7\text{ in} \\ A=l\cdot w \\ A=12\text{ in}\cdot7\text{ in} \\ A=84in^2 \end{gathered}[/tex]On the other hand, the perimeter is the sum of all the sides of a geometric figure. Then, in this case, you have
[tex]\begin{gathered} P=12\text{ in }+7\text{ in }+12\text{ in }+7\text{ in} \\ P=38\text{ in} \end{gathered}[/tex]Therefore, the perimeter and area of this rectangle are:
[tex]\begin{gathered} A=84in^2 \\ P=38\text{ in} \end{gathered}[/tex]#3: Explain if the triangles are similar using AA-. If they are similar, which angles are congruent and how do you know? (Explain your reasoning using evidence like a paragraph proof NOT a rigid motion proof!)
AS shown in the figure :
There are two right triangles
For the triangle SYE :
m∠ Y = 90
m∠ E = 39
So, m∠S = 180 - ( 90 + 39 ) = 51
For the triangle WCH :
m∠ C = 90
m∠ W = 51
m∠ H = 180 - ( 90 + 51 ) = 39
So, the triangles SYE and WCH have the following :
m∠ Y = m∠ C = 90
m∠ E = m∠ H = 39
m∠ S = m∠ W = 51
So, the triangles are similar by AAA [ angle - angle - angle Postulate ]
If ABCD is dilated by a factor of 3, thecoordinate of B' would be:5С43B.21-5 4 3-2 -1 012345-1-2DB' = ([?],[])-3
First, find coordinate B.
B= ( -2,2 )
Multiply each coordinate by the dilation factor 1/2
B'= ( -2 * 1/2 , 2 * 1/2 )
B'= ( -1, 1 )
How do I find the zeros using synthetic division when the highest degree is 4
Answer:
Explanation:
Given f(x) defined below:
[tex]f\mleft(x\mright)=x^4-11x^3+40x^2-48x[/tex]To find the zeros, set f(x) equal to 0.
[tex]x^4-11x^3+40x^2-48x=0[/tex]First, observe that we can factor out x.
[tex]\begin{gathered} x(x^3-11x^2+40x-48)=0 \\ \implies x=0\text{ or }x^3-11x^2+40x-48=0 \end{gathered}[/tex]Given that x=3 is a zero of the function, we divide using synthetic division to find the other factors.
Find an ordered pair(X, Y) that is a solution to the equationX minus 5Y equals five
To solve this problem, the first step is to find the slope intercept form of the equation:
[tex]\begin{gathered} x-5y=5 \\ 5y+5=x \\ 5y=x-5 \\ y=\frac{1}{5}x-1 \end{gathered}[/tex]Now, use a random value of x and find y, for example in this case we can use x=5 :
[tex]\begin{gathered} y=\frac{1}{5}(5)-1 \\ y=1-1 \\ y=0 \end{gathered}[/tex]The ordered pair that is a solution for the given equation is (5,0).
write the first four terms of a decreasing arithmetic sequence. use this to describe, in your own words, how to write the formula for the sequence. then use the formula to calculate the 20th term. show all work
The 20th term = -34
Explanation:An arithmetic sequence is one which has a common difference.
For example, the sequence below has a common difference of -2, and first term of 4
4, 2, 0, -2........
The first term, a = 4
The common difference, d = 2 - 4 = -2
The formula for nth term of an arithmetic sequence
[tex]\begin{gathered} a_n=a+(n-1)d \\ \\ a_n=4+(n-1)(-2) \\ \\ a_n=4-2n+2 \\ \\ a_n=6-2n \end{gathered}[/tex]The 20th term is:
[tex]\begin{gathered} a_{20}=6-2(20) \\ \\ a_{20}=6-40 \\ \\ a_{20}=-34 \end{gathered}[/tex]The 20th term = -34
The length of a photograph of Mr. Lemley playing golf is 1 4/5 inches. If the area of the photo is 33/20 square inches, what is the width of the photograph? * Your answer
Take into account that the area of a rectangular shape, is given by the following formula:
A = l·w
w: width = ?
l: length = 1 4/5 in
A: area = 33/20 in²
In order to determine the width of the photo, solve the previous formula for w:
w = A/l
convert 1 4/5 to a normal fraction:
1 4/5 = (5 + 4)/5 = 9/5
replace the values of A and l into the expression for w:
w = (33/20)/(9/5)
w = 165/180
simplify the previos fraction:
w = 165/180 = 33/36 = 11/12
Hence, the width of the photograp is 11/12 in
|In8Word problem on unit rates associated with ratios of fractions1days, a construction crew built miles of road.4What is the unit rate in miles per day?Write your answer in simplest form.miles per dayI need help solving this problem
ANSWER :
2 miles per day
EXPLANATION :
In 1/8 day, they finished 1/4 miles of the road.
We just need to divide the work done by the time to get the rate :
[tex]\frac{1}{4}\div\frac{1}{8}[/tex]Division can be expressed as multiplication by taking the reciprocal of the divisor.
That will be :
[tex]\frac{1}{4}\times\frac{8}{1}=2[/tex]Write fractions for points A and B on the number line
Given: The line from 0 to 1 is divided in 6 parts and has two points. A and B marked on it.
To find:The fraction for point A and B.
Explanation: The length from 0 to 1 is divided into 6 parts.
Therefore, the length of one part will be 1/6.
The point A is markes at the second division.
Since, 1 division= 1/6
therefore, 2 divisions will be = 2x(1/6)
Therefore, the point A will correspond to the fraction
[tex]\begin{gathered} A=2\times\frac{1}{6} \\ =\frac{2}{6} \\ =\frac{1}{3} \end{gathered}[/tex]Now the next pint B lets count its division.
It is marked at the fifth division.
Therefore, the fraction representing B can be written as:
[tex]\begin{gathered} B=5\times(1\text{ division\rparen} \\ =5\times\frac{1}{6} \\ =\frac{5}{6} \end{gathered}[/tex]Therefore, the point B can be represented as 5/6.
Final answer : Point A = 1/3
and point B = 5/6.
Rosanne has $9,716 in a savings account. The interest rate is 4%, compounded annually.To the nearest cent, how much will she have in 2 years?
To answer this question, we will use the following formula for annually compounded interest:
[tex]F=A(1+r)^t,[/tex]where A is the initial amount, r is the interest rate in decimal form, and t is the time in years.
Substituting A=9716, r=0.04, and t=2, we get:
[tex]F=9716(1+0.04)^2.[/tex]Simplifying the above result, we get:
[tex]F=9716(1.04)^2=10508.83[/tex]dollars.
Answer: $10508.83
Order the intervals based on the average rates of change of the function below over theintervals. Place the interval corresponding to the greatest average rate of change on top.f(x) = x2[0, 8][2, 7][4, 6]
for a function f defined on an interval, the average rate of change is
[0,8]
[tex]AV=\frac{8^2-0^2}{8-0}=\frac{64}{8}=8[/tex][2,7]
[tex]AV=\frac{7^2-2^2}{7-2}=\frac{49-4}{5}=\frac{45}{5}=9[/tex][4,6]
[tex]AV=\frac{6^2-4^2}{6-4}=\frac{36-16}{2}=\frac{20}{2}=10[/tex]order interval:
[4,6] [2,7] and [0,8]