Let l and w be the length and width of the rectangle, respectively; therefore, according to the question
[tex]\begin{gathered} l=2w+1 \\ and \\ l*w=45 \end{gathered}[/tex]Where l and w are in meters.
Substitute the first equation into the second one, as shown below
[tex]\begin{gathered} l=2w+1 \\ \Rightarrow(2w+1)*w=45 \\ \Rightarrow2w^2+w=45 \\ \Rightarrow2w^2+w-45=0 \end{gathered}[/tex]Solve for w using the quadratic formula,
[tex]\begin{gathered} \Rightarrow w=\frac{-1\pm\sqrt{1+4*2*45}}{2*2}=\frac{-1\pm\sqrt{361}}{4}=\frac{-1\pm19}{4} \\ \Rightarrow w=\frac{9}{2},-5 \end{gathered}[/tex]But w has to be positive since it is a measurement; therefore, w=9/2.
Finding l given the value of w=9/2,
[tex]\begin{gathered} w=\frac{9}{2} \\ \Rightarrow l=2(\frac{9}{2})+1=10 \\ \Rightarrow l=10 \end{gathered}[/tex]Thus, the answers are length=10 m, width=4.5m
Give the domain of definition of the function and find the asymptotes to the following function y = arctan 1/x - x
we have the function
[tex]y=arctan(\frac{1}{x}-x)[/tex]using a graphing tool
see the attached figure below
The domain is all real numbers except for x=0
The range is the interval (-pi/2, pi/2)
there are horizontal asymptotes at
y=pi/2 and y=-pi/2
A sofa regularly sells for $600. The sale price is $504.00. Find the percent decrease of the sale price from the regular price
STEP - BY - STEP EXPLANATION
What to find?
Percentage decreaase.
Given:
Original price = $600
new price = $504
Step 1
Recall the formula for percentage decrease.
[tex]\text{ \% decrease=}\frac{decrease}{original\text{ price}}\times100\text{ \%}[/tex]Step 2
Determine the value for the dcerease.
[tex]Decrease=new\text{ price - original price}[/tex][tex]Decrease=504-600=-96[/tex]Step 3
Substitute into the formula and simplify.
[tex]\text{ \% decrease=-}\frac{96}{600}\times100\text{ \%}[/tex][tex]=-16\text{ \%}[/tex]ANSWER
Percent decrease = 16% decrease
Help me with this math problem plsWrite the formula for g(x) in terms of f(x)
Given:
Given a graph of f(x) and g(x).
Required:
To write the formula for g(x) in terms of f(x).
Explanation:
The graph of g(x) is 5 units left and 1 units up gfrom the graph of f(x).
Therefore the function g(x) is
[tex]g(x)=f(x+5)+1[/tex]Final Answer:
[tex]g(x)=f(x+5)+1[/tex]Given sinx= 5/13 andπ/2 < x < π find the exact value of tan 2x
Given sin(x)=5/13
First, lets find cos(x).
It is known that:
[tex]\begin{gathered} \sin ^2(x)+\cos ^2(x)=1 \\ (\frac{5}{13})^2+\cos ^2(x)=1 \\ \cos ^2(x)=1-\frac{25}{169} \\ \cos ^2(x)=\frac{169-25}{169}=\frac{144}{169} \\ \cos (x)=\pm\sqrt[]{\frac{144}{169}}\text{ = }\frac{\sqrt[]{144}}{\sqrt[]{169}} \\ \cos (x)=\pm\frac{12}{13} \end{gathered}[/tex]Since π/2 < x < π, we are in 2nd quadrant. Then, cos(x) is negative.
[tex]\cos (x)=-\frac{12}{13}[/tex]Since we know the values for sin and cos, we can find tan(x):
[tex]\begin{gathered} \tan (x)=\frac{\sin(x)}{\cos(x)} \\ \tan (x)=\frac{\frac{5}{13}}{-\frac{12}{13}} \\ \tan (x)==-\frac{5}{12} \end{gathered}[/tex]Now, lets work with the expression tan(2x)
It is known that:
[tex]\tan (2x)=\frac{2\tan(x)}{1-\tan^2(x)}[/tex]
Since we know tan(x), we can substitute in the expression above and find the value of tan(2x):
[tex]\begin{gathered} \tan (2x)=\frac{2\tan(x)}{1-\tan^2(x)} \\ \tan (2x)=\frac{2\cdot(-\frac{5}{12}_{})}{1-(-\frac{5}{12})^2} \\ \tan (2x)=\frac{-\frac{10}{12}}{1-\frac{25}{144}}=\frac{-\frac{10}{12}}{\frac{144-25}{144}}=\frac{-\frac{10}{12}}{\frac{119}{144}}=-\frac{10}{12}\cdot\frac{144}{119} \\ \tan (2x)=-\frac{120}{119} \end{gathered}[/tex]Answer: -120/119
Find the area of the rectangle if the length is y + 4 inches and the width is y - 5 inches. Enter your answer as a polynomial in terms of variable y and in standard form, ay2 + by + c.
We have the following:
We have that the area of a rectangle is the following
[tex]\begin{gathered} A=l\cdot w \\ \text{In this case:} \\ l=y+4 \\ w=y-5 \end{gathered}[/tex]replacing:
[tex]\begin{gathered} A=(y+4)(y-5)=y^2-5y+4y-20 \\ A=y^2-y-20 \end{gathered}[/tex]Please help me with the question and explain your work! 16 through 19 thank you please please please help
We have the following:
A.
First we find the slope of the line with the following points:
(0, 3) and (5,0)
[tex]m=\frac{0-3}{5-0}=-\frac{3}{5}[/tex]now, for b, with the point (0,3)
[tex]\begin{gathered} 3=-\frac{3}{5}\cdot0+b \\ b=3 \end{gathered}[/tex]The equation is:
[tex]y=-\frac{3}{5}x+3[/tex]B.
The area is:
[tex]\begin{gathered} A=\frac{AC\cdot CB}{2} \\ A=\frac{3\cdot5}{2}=\frac{15}{2} \\ A=7.5 \end{gathered}[/tex]The area is 7.5 square units
for, perimeter:
[tex]\begin{gathered} p=AC+CB+AB \\ AB^2=AC^2+CB^2 \\ AB^2=3^2+5^2=9+25=34 \\ AB=\sqrt[]{34} \\ p=3+5+\sqrt[]{34} \\ p=13.83 \end{gathered}[/tex]The perimeter is 13.83 units
C.
when two lines are perpendicular they fulfill the following
[tex]m_1\cdot m_2=-1[/tex]therefore,
[tex]\begin{gathered} -\frac{3}{5}\cdot m_2=-1 \\ m_2=\frac{5}{3} \end{gathered}[/tex]Therefore, the equation is:
[tex]y=\frac{5}{3}x+3[/tex]The strength of a beam varies inversely with the square of its length. If a 10-foot beam can support 500 pounds how many pounds can a 13 foot beam support? Round the answer to the nearest pound.
The beam varies inversely with the square of it's length. Let's call S the strength and L the length.
Then we can write:
[tex]S=\frac{k}{L^2}[/tex]For a constant k.
Then, we know that if L = 10ft then S = 500 pounds
We write:
[tex]\begin{gathered} 500=\frac{k}{(10)^2} \\ \end{gathered}[/tex]And solve for k:
[tex]k=500\cdot10^2=500\cdot100=50,000[/tex]Then the inverse relation equation is:
[tex]S=\frac{50,000}{L^2}[/tex]Then, for L = 13ft, the strength is:
[tex]S=\frac{50,000}{13^2}=\frac{50,000}{169}=295.857[/tex]To the nearest pound, a beam of 13ft can support 296 pounds.
Suppose Piper eats out twice a week 15% of the time, she eats out once a week 35% of the time, and she does not eat out any time during the week 50% of the time.What is the expected value for the number of times Piper eats out during the week? Round your answer to the nearest hundredth if needed.
Solution
We are given
Probability of eating out twice in a week = 15% = 0.15
Probability of eating out once in a week = 35% = 0.35
Probability of not eating out in a week = 50% = 0.50
Let X be a random variable of the number of times Piper eats out in a week
So we have the table
Note: The Formula For finding the Expected value E(X) is given by
[tex]E(X)=\sum ^{}_{}xp(x)[/tex]Substituting we get
[tex]\begin{gathered} E(X)=0(0.50)+1(0.35)+2(0.15) \\ E(X)=0+0.35+0.30 \\ E(X)=0.65 \end{gathered}[/tex]Therefore, the expected value is
[tex]E(X)=0.65[/tex]define the imaginary unit, i
An imaginary unit, i is a solution to the quadratic equation:
[tex]\text{ x}^2\text{ + 1 = 0}[/tex]Or to simply say,
[tex]i\text{ = }\sqrt[]{-1}[/tex]It can
please help me ASAP!!!
can two rays be put together to form a line
ANSWER:
Only in the case that the rays are opposite.
STEP-BY-STEP EXPLANATION:
We have that a ray is part of a line that has an end point and continues infinitely in a single direction.
Therefore, a pair of opposite rays are two rays that have the same end point and extend in opposite directions. So together a pair of opposing rays always form a straight line.
Graphically a ray and a line are like this:
Answer: if the rays are opposite they will always form a straight line but if the are not opposite they will not form a line
Step-by-step explanation:
Find each value if f(x) = 2x - 1 and g(x) = 2 - x2.9. f(0)
ANSWER
f(0) = -1
EXPLANATION
We just have to replace x by 0 into f(x):
[tex]\begin{gathered} f(x)=2x-1 \\ f(0)=2\cdot0-1 \\ f(0)=0-1 \\ f(0)=-1 \end{gathered}[/tex]Find the sum: - 5/8 + 1/3
Answer:
-7/24
Explanation:
Given the expression:
[tex]-\frac{5}{8}+\frac{1}{3}[/tex]Step 1: Find the lowest common multiple of the denominators.
The L.C.M. of 8 and 3 = 24
Step 2: Use the LCM to combine the fractions.
[tex]=\frac{-5(3)+1(8)}{24}[/tex]Step 3: Simplify:
[tex]\begin{gathered} =\frac{-15+8}{24} \\ =-\frac{7}{24} \end{gathered}[/tex]The result of the sum is -7/24.
what decimals are between 0.82 and 0.83
Answer:
0.82 and 0.83
Which of the following measurements is greatest? O 6 yards O All of the measurements above are equal. O 19 feet O 187 inches
To answer this questions we have to remember the following rules
1 ft = 12 in
1 yd = 3 ft
Then we have to convert all our measurements to the same units, so we can compare them.
6 yd = 18 f
IF AB = (2x + 23). BC = (12 + 7x), and CD = 19 - 9x), find AD.
The addition of length of each line segment gives the value of AD.
[tex]\begin{gathered} \text{From the number line, AB+BC+CD=AD} \\ AD=(2x+23)+(12+7x)+(19-9x)=2x+7x-9x+23+12+19=54 \end{gathered}[/tex]The value of AD is 54.
I need help with this question... the correct answer choice
Since the polygon shown is a regular one, a rotation will carry it onto for every angle that makes a vertex to the place of another vertex.
So, we can fisrt figure the angle we need to rotate to get a vertex onto the next one, that is, we want to find the following angle:
We know tha the polygon is regular, so this angles is the same as the angles between the other consecutive vertexes. Since we have 5 vertexes, this angle is 1/5 of the role 360°. So, this angles is:
[tex]\frac{360\degree}{5}=72\degree[/tex]That means that a rotation of 72° will always endup in the same figure.
This also means that a rotation of any multiple of 72° will also end up in the same figure.
Thus, we just have to check which alternative is a multiple of 72°.
- 60° isn't a multiple, because it is lower.
- 108° also isn't because the 2*72 = 144, which is higher than 108°.
- 540° isn't, because 7*72 = 504 and 576, which passed through 540°
- 216° is a multiple because 3*72 = 216 exactly.
This means that if we rotate the figure by 210° it will end up in the same figure.
So, the correct alternative is the last one: 216°.
20 4/5 whats the decimal number
20 4/5
it means 20 integers and 4/5
4/5 = 0.8
so the number 20 4/5 is equal to 20.8
answer: 20.8
20 7/8 is 20 integers and 7/8
7/8 = 0.875
so 20 7/8 is equal to 20.875
2. Given that the indicated lines in figure 10.30(a) are parallel, determine the unknown angles without actually measuring them. Explain your reasoning briefly.
The opposie angles are equal
c is opposite to a, so
[tex]c=a=34^o[/tex]The angle p is opposite to that of n, so
[tex]p=118^o[/tex]The total angle of rotation in a line is 180°. so,
[tex]o=180-118=62[/tex]This o is the oppsite to m, and hence m=o.
similarly,
[tex]d=180-34=146[/tex]And hence, b=d=146
Find the domain and range of the relation Choose the correct domain below. a.) all real numbers b.) x=3c.) all real numbers except 3d.) none of the above Choose the correct range below a.) y=3b.)all real numbers except 3c.) all real numbers d.)none of the above
As this is a vertical line, its domain is just one point, x=3. And it's range is all the real numbers
In the diagram below, quadrilateral ABCD is inscribed in circle P.What is m< DCB?
ANSWER
A) 70º
EXPLANATION
In quadrilaterals inscribed in a circle, opposite angles are supplementary - their measures add up 180º. Therefore:
[tex]\begin{gathered} m\angle DAB+m\angle DCB=180º \\ 110º+m\angle DCB=180º \\ m\angle DCB=180º-110º \\ m\angle DCB=70º \end{gathered}[/tex]find an equation of the line having the given slope and containing the given point . Slope -2; through (6,-9) . type answer in slope-intercept form .
Given:
The slope of the line is m = -2.
The line passes throught the point (6,-9).
The objective is to find the equation of line.
Explanation:
Consider the point as,
[tex](x_1,y_1)=(6,-9)[/tex]The general equation to find the equation of line in slope intercept form is,
[tex]y-y_1=m(x-x_1)[/tex]Substitution:
On plugging the given values in the general equation,
[tex]\begin{gathered} y-(-9)=-2(x-6) \\ y+9=-2x+12 \\ y=-2x+12-9 \\ y=-2x+3 \end{gathered}[/tex]Here, slope of the line is -2 and y- intercept is 3.
Hence, the equation of the line in slope intercept form is y = -2x + 3.
1. Drag the fractions in order from least to greatest value L
Given the fractions 3/4 and 5/16
In order to determine which is less or greater, we need to first express them in percentage as shown;
3/4 = 3/4*100%
3/4 = 3*25 = 75%
5/16 = 5/16 * 100
5/16 = 500/16 = 31.25%
Since 75% is greater than 31.25% hence;
3/4 is greater than 5/16 and the sign that will be in the box will be the greater than sign i.e 3/4>5/16
Strategy: I compared the fraction to the bench mark of >
It is known that the lengths of trout (centimetres) in dams in North America is Normally distributed with a standard deviation of 5 cm. For monitoring purposes, a sample of 15 trout were captured, measured and released. The sample gave a mean of 50 cm and a standard deviation of 2 cm.The 99% confidence interval for the population average length of trout isSelect one:a.(49.3 ; 50.2)b.(49.2 ; 50.9)c.(46.7 ; 53.3)d.(47.8 ; 52.3)e.(46.2 ; 53.8)
The average length of the trout in the area with a 99% confidence interval is between 46.7 cm and 53.3 cm.
The distribution used should be t distribution as the sample standard deviation is to be used.
We need to build the 99% confidence interval for the population mean . The following information is provided:
Sample Mean = 50
Sample Standard Deviation = 2 cm
Sample Size = 15
The confidence interval for the trout population is computed as shown below:
[tex]\Pr \left({\bar {X}}-{\frac {cS}{\sqrt {n}}}\leq \mu \leq {\bar {X}}+{\frac {cS}{\sqrt {n}}}\right)=0.99\,[/tex]
now we will substitute the values in the equation of the CI.
[tex]{\bar {X}}-{\frac {2.7}{\sqrt {15}}}\leq \mu \leq {\bar {X}}+{\frac {2.7}{\sqrt {15}}}=0.99\,[/tex]
now solving for the confidence interval we get : 47.8 ; 52.3
Lower limit = 50 - 3.307 = 46.69 ≈ 46.7
upper limit = 50 + 3.307 = 53.307 ≈ 53.3
Hence the average length of the trout in the area is between 46.7 cm and 53.3 cm.
To learn more about confidence interval visit:
https://brainly.com/question/24131141
#SPJ9
Solve the following system of linear equations by graphing:4x + 4y = 2010x + 2y = 18
one solution: (1, 4)
The equations:
y = -x + 5
y = -5x + 9
Explanation:[tex]\begin{gathered} \text{Given equations:} \\ 4x+4y=20\text{ }\ldots(1) \\ 10x+2y=18\text{ }\ldots(2) \end{gathered}[/tex]To plot the graphs, we can assign values to x. The we get the corresponding values of y for each of the equation.
Rewritting the two equations by making y the subject of formula:
[tex]\begin{gathered} 4x+4y=20 \\ \text{divide through by 4:} \\ x\text{ + y = 5} \\ y\text{ = -x + 5} \end{gathered}[/tex][tex]\begin{gathered} 10x+2y=18 \\ \text{divide through by 2:} \\ 5x\text{ + y = 9} \\ y\text{ = -5x + 9} \end{gathered}[/tex]Plotting the graphs:
The point of intersection of the graphs is the solution.
There is one solution: (1, 4)
what are the coordinates of the library A (3,4)b. (4,3)c..(2,1)d.(1,2
To determine the coordinates of the library, for the x-coordinate, you have to draw a vertical line from the library to the x-axis and read where it intersects the x-axis. And to determine the y-coordinate you have to draw a horizontal line from the position of the library towards the y-axis, and read where the line intersects the y-axis:
The x-coordinate is 4 and the y-coordinate is 3, so the coordinates of the library are (4,3)
Fill in only the blanks. (Whatever that has an answer like the domain don’t do it)only do the empty blanks
From the graph, we can conclude:
[tex]Range\colon(-\infty,1)[/tex]As:
[tex]\begin{gathered} x\to0,f(x)\to-\infty \\ x\to\infty,f(x)\to1 \end{gathered}[/tex]x-intercept:
[tex](1,0)[/tex]Asymptote:
Vertical asymptote:
[tex]x=0[/tex]Horizontal asymptote:
[tex]y=1[/tex]Help me solve for equation 6x+3=33
Given:
[tex]6x+3=33[/tex]is given.
Required:
We need to solve this equation.
Explanation:
Here an equation given as
[tex]6x+3=33[/tex]now add both side negative 3 and we get
[tex]\begin{gathered} 6x+3-3=33-3 \\ 6x=30 \end{gathered}[/tex]now multiply both side with inverse 6
[tex]\begin{gathered} \frac{1}{6}*6x=30*\frac{1}{6} \\ x=5 \end{gathered}[/tex]Final answer:
Solution of given equation is
[tex]x=5[/tex]
5 Three pipes are connected to a water tank. One of the pipes can fill the tank in 30 minutes. The second pipe can fill it in 20 minutes. The third pipe can fill the tank in 40 minutes. How long will it take to fill the tank if all three pipes are opened together? If the slowest pipe is shut off after 3 minutes and the fastest pipe is shut off 3 minutes later, how long will it take the remaining open pipe to finish filling the tank?
Let's call the total volume of the tank as V. The rate each pipe fills the tank is given by the total volume of the tank divided by the amount of time it takes to fill the tank. Let's call the rate of the first pipe as r1, the rate of the second pipe as r2 and the rate of the third pipe as r3.
[tex]\begin{gathered} r_1=\frac{V}{30} \\ r_2=\frac{V}{20} \\ r_3=\frac{V}{40} \end{gathered}[/tex]The product between the rate and the time that has passed will give to us the fraction of the tank that has been filled. When we open the three pipes at once, we sum their rates. When the tank is filled, the product between the rate and the time passed must give the total volume of the tank, therefore, we have the following equation:
[tex]\begin{gathered} (\frac{V}{30}+\frac{V}{20}+\frac{V}{40})t=V \\ \frac{13V}{120}t=V \\ \frac{13}{120}t=1 \\ t=\frac{120}{13} \\ t=9.23076923077... \\ t\approx9.23 \end{gathered}[/tex]It will take approximately 9.23 minutes to fill the tank if all pipes are opened together.
When the three pipes are opened, the fraction that has been filled(let's call it as x) is given by:
[tex]\begin{gathered} (\frac{1}{30}+\frac{1}{20}+\frac{1}{40})\cdot3=x \\ x=\frac{13}{40} \end{gathered}[/tex]Then, the slowest pipe(the third pipe) is closed, then, after 3 more minutes we're going to fill an extra y amount of water, given by:
[tex]\begin{gathered} (\frac{1}{30}+\frac{1}{20})\cdot3=y \\ \frac{1}{10}+\frac{3}{20}=y \\ \frac{5}{20}=y \\ y=\frac{1}{4} \end{gathered}[/tex]Then, after a time t with the first pipe open, we're going to fill the tank(remember that it has been filled already by the amounts x and y, therefore, we must subtract it from the total volume).
[tex]\begin{gathered} \frac{1}{30}\cdot t=1-\frac{13}{40}-\frac{1}{4} \\ \frac{t}{30}=\frac{27}{40}-\frac{10}{40} \\ t=30\cdot\frac{17}{40} \\ t=12.75 \end{gathered}[/tex]If the slowest pipe is shut off after 3 minutes and the fastest pipe is shut off 3 minutes later, it will take 12.75 minutes for the remaining open pipe to finish filling the tank.
Can I get help with my math homework I’m struggling with ? 3
Step 1:
The slope intercept form formula is
y = mx + c
m = slope
c = intercept on the y-axis
Final answer
Slope Intercept
Step
Ton graph the function, find both x=intercept and y-intercept
[tex]\begin{gathered} \text{From y = }\frac{3}{2}x\text{ + 1} \\ y-\text{intercept c = 1} \\ \text{Make x subject of the formula} \\ 3x\text{ = 2y - 2} \\ x\text{ = }\frac{2}{3}y\text{ - }\frac{2}{3} \\ x-\text{intercept c = -}\frac{2}{3} \end{gathered}[/tex]Next plot the graph.