Given:
The area of the rectangle, A=65ft^2.
Let l be the length of the rectangle and w be the width of the rectangle.
It is given that the length of the rectangle is two feet less than 3 times the width.
Hence, the expression for the length of the rectangle is,
[tex]l=3w-2\text{ ----(A)}[/tex]Now, the expression for the area of the rectangle can be written as,
[tex]\begin{gathered} A=\text{length}\times width \\ A=l\times w \\ A=(3w-2)\times w \\ A=3w^2-2w \end{gathered}[/tex]Since A=65ft^2, we get
[tex]\begin{gathered} 65=3w^2-2w \\ 3w^2-2w-65=0\text{ ---(1)} \end{gathered}[/tex]Equation (1) is similar to a quadratic equation given by,
[tex]aw^2+bw+c=0\text{ ---(2)}[/tex]Comparing equations (1) and (2), we get a=3, b=-2 and c=-65.
Using discriminant method, the solution of equation (1) is,
[tex]\begin{gathered} w=\frac{-b\pm\sqrt[]{^{}b^2-4ac}}{2a} \\ w=\frac{-(-2)\pm\sqrt[]{(-2)^2-4\times3\times(-65)}}{2\times3} \\ w=\frac{2\pm\sqrt[]{4^{}+780}}{2\times3} \\ w=\frac{2\pm\sqrt[]{784}}{6} \\ w=\frac{2\pm28}{6} \end{gathered}[/tex]Since w cannot be negative, we consider only the positive value for w. Hence,
[tex]\begin{gathered} w=\frac{2+28}{6} \\ w=\frac{30}{6} \\ w=5\text{ ft} \end{gathered}[/tex]Now, put w=5 in equation (A) to obtain the value of l.
[tex]\begin{gathered} l=3w-2 \\ =3\times5-2 \\ =15-2 \\ =13ft \end{gathered}[/tex]Therefore, the length of the rectangle is l=13 ft and the width is w=5 ft.
Solve the system by elimination. 2x+3y=06x+9y=0
We have the next system of equations
2x+3y=0 ...(1)
6x+9y=0 ...(2)
I order to solve this system by elimination we will multiply the first equation by -3
So we will have
-6x-9x=0
then we add the equation above with the second equation
-6x-9x=0
+6x+9y=0
As we can see we obtain 0=0 which means that we have infinity solutions
ANSWER
Infinity solutions
suppose there are two types of tickets to a show . advance and same day. advance tickets cost $15 and same day tickets cost 30. for one more performance there are 55 tickets sold in all and the total amount paid for them was 1275. how many tickets of each typer were sold?
Advanced tickets(x): $15
Same day tickets(y) : $30
For one more performance there are 55 tickets sold
x+ y= 55 (a)
The total amount paid for them was 1275
15x+30y= 1275 (b)
System of equations:
x+y= 55 (a)
15x+30y = 1275 (b)
Solve for x in (a)
x=55-y
Replace x on (b)
15(55-y)+30y = 1275
82
which system of equations can be used to determine how many quarters, x, and how many nickels, y, he has?
Given: Alfred has 12 coins in his piggy bank. Some of the coins are quarters, some are nickels, and have a total of $3.15.
Required: To determine the system of linear equations for the given situation.:
i am supposed to find the volume of this pyramid
For this type of problems we use the formula for the volume of a pyramid:
[tex]\begin{gathered} V=\text{ }\frac{1}{3}A_bh \\ A_b\text{ is the area of the base} \\ h\text{ is the height of the pyramid} \end{gathered}[/tex]Substituting h=12 yd and knowing that the area of a square is side*side we get that:
[tex]\begin{gathered} A_b=\text{ 10yd }\cdot10yd=100yd^2 \\ V=\frac{1}{3}100yd^212yd=100yd^24yd=400yd^3 \end{gathered}[/tex]Classify the following triangle. Check all that apply.A. ScaleneB. IsoscelesC. AcuteO D. RightE. EquilateralF. Obtuse
Answer
Options A and C are correct.
The triangle is a Scalen triangle and it is also an Acute triangle.
Explanation
To answer this question, we first explain what these type of triangles are
According to side lengths,
- Scalene triangle has none of its three sides having the same length as another. All the three sides have different lengths. To use angle to know this, all the three angles of a Scalene triangle have different values.
- Isoscelles triangle has two of its sides with the same lengths. In terms of angles, an Isoscelles triangle has two of its angles equal to each other.
- Equilateral triangle has all of its sides equal to one another. In terms of angles, all of the angles of an Equilateral triangle are equal to one another. Each of the angle is equal to 60°.
According to the angles,
- Acute triangle has all of the angles in the triangle being less than 90 degrees.
- Right angle triangle has one of the angles in the triangles being equal to 90 degrees.
- Obtuse triangle has one of the angles in the triangle being greater than 90 degrees but obviously less than 180 degrees.
For this triangle,
We can see that all of its sides have different lengths. Hence, the triangle is a Scalene triangle.
Also, each of the angles of the triangle is less than 90 degrees. Hence, the triangle is an Acute triangle.
Hope this Helps!!!
I need help with thisIt asks to graph the functionIf you can, use Desmos to graph
Given the function
[tex]f(x)=\cot (x+\frac{\pi}{6})[/tex]The graph of the function is dhoe below
3/3=_/21Fill the blank space with the answer
In the expression 3/3=_/21, it can be observed that 7 is multipled by denominator 3 in order to obtain 21 in in denominator. So same number, 7 is also multiplied with the numerator also.
[tex]\frac{3}{3}\times\frac{7}{7}=\frac{21}{21}[/tex]So, 21 is to be filled at blank space.
A remodeling project calls for sanding a chair with a disksander. The sanding disk used on the sander has a radiusof 4.5 Inches. Find the area of the disk. Use 3.14 for
Which of the following equations represents a line that passes through thepoints (6,-5) and (-6, -7)?
Problem
Which of the following equations represents a line that passes through the
points (6,-5) and (-6, -7)?
Solution
For this case the equation for a line is given by:
y= mx +b
And we can find the slope m with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]And replacing we got:
[tex]m=\frac{-7+5}{-6-6}=\frac{-2}{-12}=\frac{1}{6}[/tex]Then we can find the intercept with this formula:
-5 = 1/6 (6)+b
And solving for b we got:
b= -5-1 =-6
And our equation would be:
y= 1/6 x -6
And the best option would be:
I.
5|x +1| + 7 = -38
Solve for x
Answer: No solutions
Step-by-step explanation:
[tex]5|x+1|+7=-38\\\\5|x+1|=-45\\\\|x+1|=-9[/tex]
However, as absolute value is non-negative, there are no solutions.
Solve for x8x-11=6x-5Simplify your answer as much as possible
Solve the given equation for x as shown below
[tex]\begin{gathered} 8x-11=6x-5 \\ \Rightarrow8x-11-6x=6x-5-6x \\ \Rightarrow2x-11=-5 \\ \Rightarrow2x-11+11=-5+11 \\ \Rightarrow2x=6 \\ \Rightarrow\frac{2x}{2}=\frac{6}{2} \\ \Rightarrow x=3 \end{gathered}[/tex]Therefore, the solution to 8x-11=6x-5 is x=3.Question 4 of 10 In the function y + 3 = (2x)2+1, what effect does the number 2 have on the graph, as compared to the graph of y=x"? 2 A. It shrinks the graph vertically to 1/2 the original height. B. It stretches the graph vertically by a factor of 2. C. It stretches the graph horizontally by a factor of 2. O OD. It shrinks the graph horizontally to 1/2 the original width
The parental function of the graph is,
[tex]y+3=(x)^2+1[/tex]The transformed function of the graph is,
[tex]y+3=(2x)^2+1[/tex]The transformation between the parent function and the transformed function will be resolved graphically.
From the graph above, the parent function is represented with red while the transformed image is represented with green colour.
We can conclude that the parent function was shrinked horizontally by 1/2.
Hence, it shrinks the graph horizontally to 1/2 the original width.
The correct option is Option
Hi I need help with this thank you! Previous question that may help answer this one : Line of best fit: ^y1=−0.02 x+4.68 ● Curve of best fit: ^y2=−0.09 x2+1.09 x+2.83 Section 2 Question 1 Using a curve to make a prediction of the y value for an x value between two existing x values in your data set is called interpolation. Suppose the year is 2005, where x = 5 years: (a) Use the equation for the line of best fit to predict the number of cell phones sold during that year. Round answers to one decimal place and be sure to include the appropriate units. Your Answer: we have the linear equation: y1=-0.02x+4.68Where x is the number of years since the year 2000, y1 ----> is the number of cell phones sold. So for the year 2005, x=2005-2000=5 years.substitute:y1=-0.02(5)+4.68y1=4.58Therefore, the answer is 4.6 cell phones sold.(b) Use the equation for the non-linear curve of best fit to predict the number of cell phones sold during that year. Round answers to one decimal place and be sure to include the appropriate units. Your Answer: We have the equation y2=-0.09x^2+1.09x+2.83For x=5 yearssubstitute:y2=-0.09(5)^2+1.09(5)+2.83y2=6.03Therefore, the answer is 6.0 cell phones sold.
From the information provided we will have that the predictions will be:
*Line of best fit:
[tex]y_1=0.02(13)+4.68\Rightarrow y_1=4.94\Rightarrow y_1\approx4.9[/tex]So, the extrapolation from the line of best fit is 4.9 sold.
*Curve of best fit:
[tex]y_2=0.09(13)^2+1.09(13)+2.83\Rightarrow y_2=32.21\Rightarrow y_2\approx32.2[/tex]So, the extrapolation for the curve of best fit is 32.2 sold.
Today, October 20, 2022, seven friends ate lunch together at Chipotle.
Friend #1 eats there every day - including weekends.
Friend #2 eats there every other day - including weekends
Friend #3 eats there every third day - including weekends
Friend #4 eats there every fourth day - including weekends
Friend #5 eats there every fifth day - including weekends
Friend #6 eats there every sixth day - including weekends
Friend #7 eats there every seventh day - including weekends
Assuming that none of them catch Covid or miss any days, what will be the date when the friends again all eat lunch together at Chipotle?
The most appropriate choice for LCM of two numbers will be given by -
All the friends together can eat lunch on 14th December 2023.
What is LCM?
LCM means Lowest Common Multiple. LCM of two numbers a and b is the least number that is divisible by both a and b.
Friend 1 eats lunch together at Chipotle everyday including weekends
Friend 2 eats lunch together at Chipotle every other day including weekends
Friend 3 eats lunch together at Chipotle every third day including weekends
Friend 4 eats lunch together at Chipotle every fourth day including weekends
Friend 5 eats lunch together at Chipotle every fifth day including weekends
Friend 6 eats lunch together at Chipotle every sixth day including weekends
Friend 7 eats lunch together at Chipotle every seventh day including weekends
Number of days after which all the friends together can eat lunch
= LCM of 1, 2, 3, 4, 5, 6, 7 = 420 days
All the friends together can eat lunch after 420 days
All the friends together can eat lunch on =
(31 - 20) + 30 + 31 + 31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 +14 = 14th December 2023
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metres> -21,23Sup10f3: Wandere first rareAnswerTeir wiced data prosto w will be whermerson is us. There will stand er is danfromGoethe type of boundary lineDashedEnter two points on the boundary lineSelect the repon you wish to be shaded:
Given
[tex]\begin{gathered} x>-2 \\ y\ge3 \end{gathered}[/tex]The graph
[tex]\begin{gathered} x>-3\text{ the pink colour} \\ y\ge3\text{ the blue colour} \end{gathered}[/tex]Two boundary points
[tex]\begin{gathered} \lparen-2,3) \\ \lparen-2,0) \end{gathered}[/tex]
Find (fog)(x) and (gof)(-1) for the functions f(x) = 3x² + 5 and g(x) = -x + 1
Answer:
Step-by-step explanation:
fog(x)=3(-x+1)^2+5
=3(x^2+2x+1)+5
=3x^2+6x+3+5
fog(x) =3x^2+6x+8
gof(x)=-(3x^2+5)+1
=-3x^2-5+1
gof(x)=-3x^2-4
gof(-1)=-3(-1)^2-4
=-3-4
gof(-1) =-7
Write a sine function that has a midline of 4 , an amplitude of 3 and a period of 2/3
Given a midline of 4, an amplitude of 3 and a period of 2/3 we are asked to write a sine function.
Explanation
The equation of a sine function is given as
[tex]y=Asin(\frac{2\pi x}{T})+B[/tex]Where A is the amplitude, T is the period and B is the midline of the sine function.
Therefore, we will have;
[tex]\begin{gathered} y=3sin(2\pi x\div\frac{2}{3})+4 \\ y=3sin(2\pi x\times\frac{3}{2}_)+4 \\ y=3s\imaginaryI n(3\pi x)+4 \end{gathered}[/tex]Answer:
[tex]y=3s\imaginaryI n(3\pi x)+4[/tex]Text-to-Speech6.For the expression, combine like terms and write an equivalentexpression with fewer terms.4- 2x + 5xВ ІΣSave answer and go to next question
hello
the question given request we write an equivalent expression as the one given which is
[tex]4-2x+5x[/tex]an equivalent expression to the one above would be
[tex]4+3x[/tex]so, we can say
[tex]4-2x+5x=4+3x[/tex]A line has the given slope m and passes through the first point listed in the table. Complete the table so that each point on the table lies on the line.
A line can be written as an equation in the slope-intercept form:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
We know the slope:
[tex]m=3[/tex]The y-intercept is the y value of the graph where it intercepts the y-axis, which happens when x = 0.
We know that the point x = 0 and y = 3 is on the line and, since the value of x is 0. the y value is the y-interceot, so:
[tex]b=3[/tex]Thus, we have the equation:
[tex]y=3x+3[/tex]To calculate the other points, we just need to substitute their x values and get their y values:
x = 1:
[tex]y=3\cdot1+3=3+3=6[/tex]So, when x = 1, y = 6
x = 2:
[tex]y=3\cdot2+3=6+3=9[/tex]So, when x = 2, y = 9.
x = 3:
[tex]y=3\cdot3+3=9+3=12[/tex]So, when x = 3, y = 12;
So, the complete table is:
x | 0 | 1 | 2 | 3
y | 3 | 6 | 9 | 12
can you please help me solve this practice problem I really need help
Question:
Solution:
Step 1: Find the equation of a line:
Notice that the line passes through the point (x2,y2)= (4,-2) and (x1,y1)=(0,3). Then, the slope of this line would be:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}=\text{ }\frac{-2-3}{4-0}\text{ = }\frac{-5}{4}\text{ =-}\frac{5}{4}[/tex]now, notice that the y-intercept of this line is b=3. Then, the equation for this line is:
[tex]y\text{ = -}\frac{5}{4}x+3[/tex]Step 2:
note that the shaded region is all points on the line and those above it. So, the shaded region can be represented by the following inequality:
[tex]y\text{ }\ge\text{ -}\frac{5}{4}x+3[/tex]and it is shown graphically like this:
So that, we can conclude that the correct answer is:
[tex]y\text{ }\ge\text{ -}\frac{5}{4}x+3[/tex]Set up the equation for the following word problem and solve the equation. Let x be the unknown number. -26 times a number minus 5 is equal to 56 less than the number. Step 2 of 2: Solve the equation for x. Express your answer as an integer, a reduced fraction, or a decimal number rounded to two pl Answer
Answer:
Step 1 of 2:
-26x - 5 = x - 56
Step 2 of 2:
17/9 or 1.89
Step-by-step explanation:
1. Putting word statement in algebraic form
Step 1:
Let x be the unknown number ==> x is the unknown variable to be used in the equation and to be solved for
Step 2:
-26 times a number minus 5 ==> -26x - 5
Step 3:
is equal to 56 less than the number ==> = x - 56
Putting it all together:
-26x - 5 = x - 56
2. Solving the equation
-26x - 5 = x - 56
1. Subtract x from both sides:
-26x - 5 - x = x - x -56
-26x -x - 5 = -56
-27x - 5 = -56
2. Add 5 to both sides
-27x - 5 + 5 = -56+ 5
-27x = -51
x = -51/-27 (dividing both sides by -27)
x = 51/27 (negative divide by negative results in positive)
Reduce 51/27 by dividing numerator and denominator by 3
x = (51 ÷ 3)/(27 ÷ 3) = 17/9
= 1.88888.... = 1.89 rounded to two decimal places
The cost of renting a bicycle from Dan's Bike Shop is $2 for 1 hour plus $1 for each additional hour of rental time. Which of the following graphs shows the cost, in dollars, of renting a bicycle from Dan's Bike Shop for 1, 2, 3, and 4 hours? Bicycle Rental Cost Bicycle Rental Cost 7 6 Rental Cost (dollars) Rental Cout (dollars) 2. 1 Hetalia A B. Rental Time Chours) Bicycle Rental Cosi Bicycle Rental 7 7 Rental Cost dollars) 1 Rental Time (hours) Rental Tiene Chours) D.
option B
Explanation:The cost of renting per hour = $2
For 1 hour = $2
For each additional hour, it is $1
For 2 hours = First hour + 1(additional hour)
For 2 hours = $2 + $1(1) = 2+1 = $3
For 3 hours = $2 + $1 (2) = 2+2 = $4
For 4 hours = $2 + $1(3) = 2+3 = $5
The graph which shows this rental cost as 2, 3, 4, 5 is option B
Can you please help me out with a question
The formula for the area of a sector of a circle is:
[tex]A=\frac{\theta}{360}\cdot\pi r^2[/tex]Where
θ is the angle
r is the radius
Given,
θ = 100
r = 7
We substitute into the formula and figure the answer out [remembering to use 3.14159 as π]:
[tex]\begin{gathered} A=\frac{\theta}{360}\cdot\pi r^2 \\ A=\frac{100}{360}\cdot(3.14159)(7)^2 \\ A=\frac{5}{18}\cdot(3.14159)(49) \\ A\approx42.76053 \end{gathered}[/tex]Rounding to the nearest thousandth [3 decimal places], we have:
Area = 42.761 square centimetersHelppppppppppppppppppp
Perpendicular line are reciprocals
slope of the original line = -1/9
slope of the perpendicular line = 9
i432--5-4-3-2-1(3.1)2 3 45 X(0,-1)What is the equation of the line that is parallel to thegiven line and has an x-intercept of -3?Oy=x+3Oy=x+2Oy=-x+3Oy=-³x+2
Explanation:
Step 1. We are given the graph of a line and we need to find the equation of the line parallel to it that has an x-intercept of -3.
Since the new line will be a parallel line it means that it will have the same slope. Therefore, our first step is to find the slope of the current line.
Given any line, we find the slope as shown in the following example diagram:
Step 2. Using the previous method, the slope of our line is:
The new line will have the same slope of 2/3.
Step 3. We are also told that the x-intercept of the new line is -3, which means that the new line will cross the y-axis at x=-3, that point is:
(-3,0)
We will label that point of our new line as (x1,y1):
[tex]\begin{gathered} (x_1,y_1)\rightarrow(-3,0) \\ \downarrow \\ x_1=-3 \\ y_1=0 \end{gathered}[/tex]Step 4. So far, we know that the new line will have a slope of 2/3:
[tex]m=\frac{2}{3}[/tex]And that it includes the point (-3,0) where x1=-3 and y1=0.
To find the equation, we use the point-slope equation:
[tex]y-y_1=m(x-x_1)[/tex]Step 5. Substituting the known values into the formula:
[tex]y-0=\frac{2}{3}(x-(-3))[/tex]Solving the operations:
[tex]\begin{gathered} y=\frac{2}{3}(x+3) \\ \downarrow \\ \boxed{y=\frac{2}{3}x+2} \end{gathered}[/tex]Answer:
[tex]\boxed{y=\frac{2}{3}x+2}[/tex]The period T(In seconds) of a pendulum is given by T=2PI(Square root of L/32) Where L stands for length (in feet) of the pendulum If pi =3.14 and the period is 6.28 what is the length
Let me check your question
[tex]T\text{ = 2}\cdot\text{ 3.14}\cdot\text{ }\sqrt[]{L/\text{ 32}}[/tex][tex]\frac{T}{2\cdot\text{ 3.14}}\text{ = }\sqrt[]{L/\text{ 32}}[/tex]T= the period = 6.28
[tex]\frac{6.28}{6.28}\text{ = }\sqrt[]{L/\text{ 32}}[/tex][tex]L/32=1^2[/tex][tex]L=32[/tex]_________________
Answer
L= 32
Are they inverses?f(x) = 6x - 6, g(x) = 1/6x + 1
Given function,
f(x) = 6x - 6
or
y = 6x -6
The inverse of a function is calculated by replacing the values of x and y
therefore
Inverse (y = 6x - 6)
x = 6y - 6
x + 6 = 6y
6y = x + 6
y = x/6 + 6/6
y = 1/6*x + 1
or
g(x) = 1/6*x + 1
Hence, both are inverse of each other.
What’s the correct answer answer asap for brainlist please
Answer:
c. you can't be feeling alive with wearing,weakness of body and mind.
Consider function f, where B is a real number.
f(z) = tan (Bz)
Complete the statement describing the transformations to function f as the value of B is changed.
As the value of B increases, the period of the function
When the value of B is negative, the graph of the function
shy
and the frequency of the function
If the value of B increases, the period of the function decreases, and the frequency of the function increases. When the value of B is negative, the graph of the function reflects over the y-axis.
How to estimate the graph and the frequency of the function?Let the tangent function be f(z) = tan (Bz)
The period exists [tex]$P=\frac{\pi}{|B|}$[/tex]
The frequency exists [tex]$F=\frac{1}{P}=\frac{|B|}{\pi}$[/tex].
The period exists inversely proportional to B, therefore, as B increases, the period decreases.
Frequency exists inversely proportional to the period, therefore, as the period decreases, the frequency increases.
When B is negative, we get f(z) = tan -Bz = f(-z), therefore, the function exists reflected over the y-axis, as the graph at the end of the answer shows, with f(z) exists red(B positive) and f(-z) exists blue(B negative).
As the value of B increases, the period of the function decreases, and the frequency of the function increases. When the value of B exists negative, the graph of the function reflects over the y-axis.
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Which value of n makes the following equation true?√n=4020408O 16
Solution
- The solution steps are given below:
[tex]\begin{gathered} \sqrt{n}=4 \\ \text{ Square both sides} \\ n=4^2 \\ n=16 \end{gathered}[/tex]Final Answer
The answer is 16