Answer
Width of the parking lot = 4 miles
Explanation
The area of a rectangle is given as
Area = L × W
where
L = Length of the rectangle = (1/6) mile
W = Width of the rectangle = ?
Area = (2/3) square miles
Area = L × W
(2/3) = (1/6) × W
[tex]\begin{gathered} \frac{2}{3}=\frac{1}{6}\times W \\ \frac{2}{3}=\frac{W}{6} \\ \text{Cross multiply} \end{gathered}[/tex]3W = (2)(6)
3W = 12
Divide both sides by 3
(3W/3) = (12/3)
W = 4 miles
Hope this Helps!!!
Out the following equation in the slope-intercept form by solving the equation for y. Fill in blank one
Given: The equation below
[tex]6x-2y=12[/tex]To Determine: The slope-intercept form of the equation
Solution:
The slope-intercept form of a linear equation is given as
[tex]\begin{gathered} y=mx+c \\ Where \\ m=slope \\ c=intercept \end{gathered}[/tex]From the given equation, make y the subject
[tex]\begin{gathered} 6x-2y=12 \\ 6x-12=2y \\ 2y=6x-12 \\ Divide\text{ through by 2} \\ \frac{2y}{2}=\frac{6x}{2}-\frac{12}{2} \\ y=3x-6 \\ slope=3 \\ intercept=-6 \end{gathered}[/tex]Hence, the slope-intercept form of the given equation is
y = 3x - 6
What is the period of the graph of y = 2 cos (7x)+ 3?O A. 2O B.klaalO C.O D. 4
Given the following function:
[tex]\text{ y = 2cos(}\frac{\pi}{2}x)\text{ + 3}[/tex]We will be using the standard formula aCos (bx - c) + d to find the variables used to find the period.
We get,
aCos (bx - c) + d = 2 cos (π/2x) + 3
a = 2
b = π/2
c = 0
d = 3
Finding the period, we will be using the following formula:
[tex]\text{ Period = }\frac{2\pi}{b}[/tex]We get,
[tex]\text{ Period = }\frac{2\pi}{b}[/tex][tex]\text{ = }\frac{2\pi}{\frac{\pi}{2}}[/tex][tex]\text{ = 2(}\pi)\text{ x }\frac{2}{(\pi)}[/tex][tex]\text{ = 2 x 2}[/tex][tex]\text{ Period = 4}[/tex]Therefore, the period of y = 2 cos (π/2x) + 3 is 4. The answer is letter D.
If AACB = ADCE, ZABC = 61°,ZBCA = 57°, and ZCDE = 2xDEСx = [?]BEnter
We have two congruent triangles. This means they have corresponding sides and angles.
We assume that DE and AB are parallel segments. Then
Then, we can write:
[tex]\begin{gathered} m\angle\text{ABC}=m\angle\text{CDE} \\ 61=2x \\ x=\frac{61}{2} \\ x=30.5\degree \end{gathered}[/tex]Answer: x = 30.5°
f (x) = 3x and g(x) = Vx + 4tep 1 of 2: Find the formula for (f + g)(x) and simplify your answer.
Given the following question:
Perform the indicated operation. (5 - 21 a 22 29 - 201 c 49 b 21 d 29
We have to perform this operation with this complex number:
[tex]\begin{gathered} (5-2i)^2 \\ (5-2i)(5-2i) \\ 5^2+2\cdot(-2i)\cdot5+(-2i)^2 \\ 25-20i+4\cdot i^2 \\ 25-20i+4(-1) \\ 25-20i-4 \\ 21-20i \end{gathered}[/tex]Answer: 21 - 20i
-4 less than greater to and less than greater to 1
The inequality shown in the question means the number n is greater than or equal the number -4, but it is also (at the same time) lesser than or equal the number 1.
So, graphing the possible values of n in the number line (in blue), we have:
The dots on -4 and 1 are filled, since these numbers are also part of the solution.
The number of music CDs sold in 2003 by one company was approximately 1.5 x 10^5. The number of music CDs sold by thesame company in 2013 was approximately 7.1 x 10^7. What is the difference in CDs sold between 2003 and 2013?
Given:
[tex]\begin{gathered} \text{Number of music CDs sold in 2003 = 1.5 }\times10^5 \\ \text{Number of music CDs sold in 2013 = 7.1 }\times10^7 \end{gathered}[/tex]Solution
The difference between the number of CDs sold between 2003 and 2103:
[tex]\text{Difference = Number of CDs in 2013 - Number of CDs in 2003}[/tex]Substituting, we have:
[tex]\begin{gathered} \text{Difference = 7.1 }\times10^7\text{ - 1.5 }\times10^5 \\ =\text{ 7.1 }\times10^2\text{ }\times10^5\text{ - 1.5 }\times10^5 \\ =10^5(710-1.5) \\ =\text{ 708.5 }\times10^5 \\ =\text{ 7.085 }\times10^7 \end{gathered}[/tex]Answer: 7.085 x 10^7
A person chooses 2 different numbers from a set of the integers from −5 to −1, inclusive. The result of the experiment is the sum of the two chosen numbers. Find the set representing the event E that the sum is less than −6. Give your answer as a set, e.g. {1,2,3}, and do not include E= in your answer.
Given a set of integers from -5 to -1
[tex]\mleft\lbrace-5,-4,-3,-2,-1\mright\rbrace[/tex]The experiment is "choose two numbers at random from the set and add them"
The possible combinations are:
[tex]\begin{gathered} -1;-2\to(-1)+(-2)=-3 \\ -1;-3\to(-1)+(-3)=-4 \\ -1;-4\to(-1)+(-4)=-5 \\ -1;-5\to(-1)+(-5)=-6 \\ -2;-3\to(-2)+(-3)=-5 \\ -2;-4\to(-2)+(-4)=-6 \\ -2;-5\to(-2)+(-5)=-7 \\ -3;-4\to(-3)+(-4)=-7 \\ -3;-5\to(-3)+(-5)=-8 \\ -4;-5\to(-4)+(-5)=-9 \end{gathered}[/tex]Event E is defined as "all sums whose results are less than -6"
As you can see, there are only 3 results of the possible combinations that are less than -6, those are:
[tex]\mleft\lbrace-3,-4,-5\mright\rbrace[/tex]Maria is running a 20-kg race .the graph at the right shows her distance remaining and the race in kilograms over time and hours find a rate of changing for distance remaining during the race
Answer:
-5/2 km/hr
Explanation:
We can find the rate of change for the distance remaining over time at points (2, 15) and (8, 0) using the below formula;
[tex]\text{Rate of Change = }\frac{y_2-y_1}{x_2-x_1}[/tex]where our x1 = 2, y1 = 15, x2 = 8, and y2 = 0.
Let's go ahead and substitute these values into our formula;
[tex]\begin{gathered} \text{Rate of Change = }\frac{0-15}{8-2} \\ =\frac{-15}{6} \\ =-\frac{5}{2} \end{gathered}[/tex]So this means that the distance decreases by 5km in every 2hours.
please help me with my question
f(x) = -4x2 – 7x +4Find f(-7)
Given the function
[tex]f(x)=-4x^2-7x+4[/tex]You have to calculate f(x=-7). To do so you have to replace the x terms in the variable by -7 and solve:
[tex]\begin{gathered} f(-7)=-4(-7)^2-7(-7)+4 \\ f(-7)=-4(49)+49+4 \\ f(-7)=-196+49+4 \\ f(-7)=-143 \end{gathered}[/tex]If the orbit of this the moon Can be modeled using the equationx^2/63,500 + y^2/50,900 = 1, what is the shape of the moons orbit?
ANSWER:
Ellipse
STEP-BY-STEP EXPLANATION:
The equation that models the situation is the following:
[tex]\frac{x^2}{63500}+\frac{y^2}{50900}=1[/tex]We have that this corresponds to the following form of equation:
[tex]\frac{\left(x-h\right)^2}{a^2}+\frac{\left(y-k\right)^2}{b^2}=1[/tex]This corresponds to the equation of the ellipse and in this case, has the center at the origin.
Therefore, the correct answer is an ellipse
Consider the density curve plotted below:0.81.62.43.240.10.20.30.40.5XPDF(X)Density CurveFind P(X<0.8) : Find P(X>3.2) :
First, find the equation of the red line in the image, as shown below
[tex]\begin{gathered} (0,0),(0.8,0.1) \\ \Rightarrow y=\frac{0.1}{0.8}(x) \\ \Rightarrow y=\frac{1}{8}x \\ \Rightarrow PDF(X)=\frac{1}{8}X \end{gathered}[/tex]Then, integrate the obtained function for each question, as shown below
1)
[tex]P(X<0.8)=\int_0^{0.8}PDF(X)dX=\int_0^{0.8}\frac{1}{8}XdX=\frac{1}{8}\lbrack\frac{X^2}{2}\rbrack_0^{0.8}=\frac{1}{16}(0.8)^2=0.04[/tex]Thus, the answer to the first part is 0.042) Similarly,
[tex]P(X>3.2)=\frac{1}{8}\int_{3.2}^4XdX=\frac{1}{16}(4^2-3.2^2)=\frac{1}{16}(5.76)=0.36[/tex]The answer to the second part is 0.36here are the nets of three cardboard boxes that are rectangular prism the boxes will be packed with 1 centimeter cube all lengths are centimeters Find the surface area
the surface area = 42cm²
Explanation:
We apply the formula for surface area of rectangular prism:
Area = l * w + l*h + l* w + h * l + w * h + w * h
Area = 3cm × 2cm + 3cm×3cm + 2cm× 3cm + 3cm×3cm + 3cm × 2cm + 3cm × 2cm
Area = 6cm² + 9cm² + 6cm² + 9cm² + 6cm² + 6cm²
Area = 42cm²
Therefore, the surface area = 42cm²
Which is an equation of the line that passes throughthe points (5, 2) and (10, -3)?
Given two points on a line, use the formula below to find its equation
[tex]\begin{gathered} (x_1,y_1),(x_2,y_2) \\ \Rightarrow y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} (5,2),(10,-3) \\ \Rightarrow y-2=\frac{-3-2}{10-5}(x-5) \\ \Rightarrow y-2=-\frac{5}{5}(x-5) \\ \Rightarrow y-2=-(x-5)=-x+5 \\ \Rightarrow y=-x+5+2 \\ \Rightarrow y=-x+7 \end{gathered}[/tex]Thus, the equation is y=-x+7
Use the inequality to answer the following question. 4(x-3) -9≤10-7-6x+2x
Answer:
Explanation:
Before graphing the solution set of the inequality:
[tex]undefined[/tex]Can you help me with number 3 and do it just as the paper says so I can understand it better.
r = 7.2
z = 7.2 cis 73π/90
See explanation below
Explanation:r is given as |z|
z = -6 + 4i
[tex]\begin{gathered} r\text{ = }\sqrt[]{(-6)^2+(4)^2} \\ r\text{ = }\sqrt[]{36\text{ + 16}} \\ r\text{ = }\sqrt[]{52} \\ r\text{ }\approx\text{ }7.2\text{ (nearest tenth)} \end{gathered}[/tex]tan α = 4/-6 = 2/-3
[tex]\begin{gathered} \tan \alpha\text{= }\frac{-2}{3} \\ \alpha=tan^{-1}(\frac{-2}{3})\text{ }\approx\text{ -33.69}\degree \\ \\ \sin ce\text{ z = -6 + 4i is in the second quadrant, add 180}\degree\colon \\ \text{-33.69}\degree\text{ + 180}\degree\text{ = 146.31}\degree\text{ }\approx\text{146.3}\degree \end{gathered}[/tex]convert to radians:
1π rad = 180°
[tex]\begin{gathered} \text{146.3}\degree\text{ }\times\text{ }\frac{\pi}{180\degree}\text{ = }\frac{\text{146.3}\degree\text{ }\times\pi}{180\degree} \\ \text{146.3}\degree\text{ }\times\text{ }\frac{\pi}{180\degree}\text{ = }0.81\pi \\ OR \\ \text{ 146.3}\degree\text{ }\times\text{ }\frac{\pi}{180\degree}\text{ = }\frac{73\pi}{90}\text{ (approx i}mately) \end{gathered}[/tex][tex]\begin{gathered} \text{Polar form:} \\ z\text{ = r cis }\theta \\ |z|=\text{ r }\approx\text{ }7.2 \\ \\ \theta\text{ = }\frac{73\pi}{90} \\ z\text{ = 7.2 cis }\frac{73\pi}{90} \end{gathered}[/tex]Hello! Please look at the picture to see the question, thank you!
As given by the question
There are given that the polynomial function:
[tex]f(x)=2x^2+3x^3+x+4[/tex]Now,
From the equation, first, rearrange the function:
[tex]\begin{gathered} f(x)=2x^2+3x^3+x+4 \\ f(x)=3x^3+2x^2+x+4 \end{gathered}[/tex]Hence, the leading coefficient of the given polynomial function is 3.
You got 85% of the questions on the test correct. What fraction of the questions did you get correct? Write in lowest terms.
you got 85% of the questions on the test correct, this means if the total amount of questions was 100, you got 85 of them correct
So the fraction is 85/100
and to write it in lowest terms we can divide each term by 5:
[tex]\frac{\frac{85}{5}}{\frac{100}{5}}=\frac{17}{20}[/tex]So the answer is: 17/20
If f(x)=x^2+3xAnd g(x)=4-xWhat is (f/g)(x)= (f/g)(5)=
Given: A function
[tex]f(x)=x^2+3x[/tex]and
[tex]g(x)=4-x[/tex]Required: To find the function-
[tex](\frac{f}{g})(x)\text{ and }(\frac{f}{g})(5)[/tex]Explanation: The required function can be calculated as
[tex]\begin{gathered} (\frac{f}{g})(x)=\frac{f(x)}{g(x)} \\ =\frac{x^2+3x}{4-x} \\ =\frac{x(x+3)}{4-x} \end{gathered}[/tex]Now putting x=5 gives-
[tex]\begin{gathered} (\frac{f}{g})(5)=\frac{5^2+3(5)}{4-5} \\ =\frac{25+15}{-1} \\ =-40 \end{gathered}[/tex]Final Answer: The required function is
[tex](\frac{f}{g})(x)=\frac{x(x+3)}{4-x}[/tex]and
[tex](\frac{f}{g})(5)=-40[/tex]
What 3-dimensional shape will the net fold into? (pic attached)
We need to find which 3-dimensional shape will the net fold into the given figure:
As shown:
The given figure has 6 sides,
So, it will be cube or rectangular prism
But, the sides are: 2 squares and 4 rectangles
So, the answer is : rectangular prism
State if the triangles are similar. If so, how do you know they are similar and complete the similarity statement.LKJ
Explanation
For the given question, we are asked to determine if the triangles are similar
If two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
From the given questions, the two triangles are similar because the ratio of the corresponding sides of triangles LKJ and LQR are similar.
Also
The SAS Postulate tells us If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
Thus, we have that
The two triangles are similar
SAS similarity
Triangle LQR
Thus, option B is correct
i’m really sick on this promise and i really need help
Solution:
Analysis: We have an initial inequation; we need to isolate x in order to graph the solution.
[tex]-4.4\ge1.6x-3.6[/tex]Let's add 3.6 on both sides:
[tex]\begin{gathered} -4.4+3.6\geqslant1.6x-3.6+3.6 \\ -0.8\ge1.6x \end{gathered}[/tex]Now, let's divide by 1.6 into both sides to isolate x.
[tex]\begin{gathered} \frac{-0.8}{1.6}\ge\frac{1.6x}{1.6} \\ -0.5\ge x \\ x\leq-0.5 \end{gathered}[/tex]After we simplify the inequation until x is less or equal to -0.5, now we can graph the solution.
X has to be equal to or less than -0.5. That graph corresponds to the first option.
20 ping pong balls are numbered 1-20, with no repetition of any of the numbers. What is the probability of selecting one ball that is either odd or a number 4 ball?Need answer as a percentage amountMy choices are: 50, 5, 45, or 55
The answer in percentage is %55
The total amount of balls is 20. Half of them are odd, but also we need to add the probability of picking the 4.
Then,
[tex]\begin{gathered} 20\cdot\frac{1}{2}=10 \\ 10+1=11 \end{gathered}[/tex]So of the 20 possible outcomes, we want to know the probablity of 11 of them. That's a probability of 11/20. Thus,
11/20 = 0.55
To convert the result in percentage, we multiply by 100:
0.55 * 100 = %55
The following two sets of parametric functions both represent the same ellipse, Explain the difference between the graphs.x = 3 cost and y = 8 sin tx= 3 cos 4t and y = 8 sin 4t
Answer:
The graphs of both equations will have different slopes and periods
Explanation:
Given:
[tex]\begin{gathered} x=3\cos t\text{ and }y=8\sin t \\ x=3\cos4t\text{ and }y=8\sin4t \end{gathered}[/tex]Recall that the equation of an eclipse is generally given as;
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]We can go ahead and express both equations in the above as seen below;
[tex]\begin{gathered} x^2=3^2\cos^2t\text{ and }y^2=8^2\sin^2t \\ \frac{x^2}{3^2}+\frac{y^2}{8^2}=\cos^2t+\sin^2t \\ \frac{x^2}{3^2}+\frac{y^2}{8^2}=1 \\ OR \\ x^2=3^2\cos^24t\text{ and }y^2=8^2\sin^24t \\ \frac{x^{2}}{3^{2}}+\frac{y^{2}}{8^{2}}=\cos^24t+\sin^24t \\ \frac{x^2}{3^2}+\frac{y^2}{8^2}=1 \end{gathered}[/tex]So we can see that both equations represent the same eclipse.
Recall the below sine function;
[tex]y=a\sin(bx-c)+d[/tex]where;
a = amplitude
2pi/b = period
If we compare the given equations, we can see that x = 3 cos t and y = 8 sin t, have 3 and 8 as amplitudes respectively and pi as period.
While x= 3 cos 4t and y = 8 sin 4t have 3 and 8 as amplitudes respectively and pi/4 as period.
If we express the equations as linear functions we'll have;
For x = 3 cos t and y = 8 sin t;
[tex]\begin{gathered} \frac{y}{x}=\frac{8\sin t}{3\cos t} \\ y=\frac{8}{3}x\tan t \end{gathered}[/tex][tex]\begin{gathered} \frac{y}{x}=\frac{8\sin t}{3\cos t} \\ y=\frac{8}{3}\tan t*x \end{gathered}[/tex]For x = 3 cos 4t and y = 8 sin 4t
[tex]\begin{gathered} \frac{y}{x}=\frac{8\sin4t}{3\cos4t} \\ y=\frac{8}{3}\tan4t*x \end{gathered}[/tex]We can see that both equations have different slopes
Let p be "The two numbers are negative" and q be "Their product is positive" Which of the following statements best represents the statement p⟺q?Select the correct answer below:None of the aboveIf their product is positive, then the two numbers are negative.Their product is positive and the two numbers are negative.The two numbers are negative only if their product is positive.
We have the following facts:
p = The two numbers are negative
q = Their product is positive
We have the following statement:
[tex]p\Leftrightarrow q[/tex]We see that in the statement appears the symbol ⟺, this symbol must be interpreted as "if and only if".
Now, let's see the meaning of the options. Taking into account that the symbol ⇒ means "then".
1) If their product is positive, then the two numbers are negative. Is equivalent to:
[tex]p\Rightarrow q[/tex]So this is not the answer because we don't have a ⟺.
2) Their product is positive and the two numbers are negative.
[tex]p\wedge q[/tex]We see that in the sentence we an "and", we express that with the symbol ∧.
3) The two numbers are negative only if their product is positive.
This option is not correct because we don't have an "if and only if", we only have "only if".
Answer
Because none of options 1, 2 or 3 are equivalent to the statement of the question, we conclude that the correct option is: None of the above.
1. Points A and B are to be mapped onto a number line according to two equations.
ANSWERS
(a) A = -36
(b) B = -100
(c) 64
EXPLANATION
(a) To solve the first equation we have to multiply both sides by 3,
[tex]\begin{gathered} \frac{2}{3}\cdot3\cdot A=-24\cdot3 \\ 2A=-72 \end{gathered}[/tex]And divide both sides by 2,
[tex]\begin{gathered} \frac{2A}{2}=\frac{-72}{2} \\ A=-36 \end{gathered}[/tex](b) For the second equation, we have to multiply both sides by -0.2,
[tex]\begin{gathered} 20\cdot(-0.2)=-\frac{B}{0.2}(-0.2) \\ -100=B \end{gathered}[/tex](c) The distance between two points on a number line is the difference between the two values, in absolute value,
[tex]d=|A-B|=|-36-(-100)|=|-36+100|=64[/tex]So the distance between A and B is 64.
The recycling center pays $0.25 per pound for aluminum and $0.11 per pound for glass. David received $5.75 for his aluminum cans and $2.53 for his glass bottles How many pounds of glass and aluminum did he recycle? (Hint: Change dollars to cents first.)
Answer:
He recycles 23 pounds of glass and 23 pounds of aluminum.
Explanation:
To know the number of pounds of glass, we need to divide the amount received for his glass bottles by the amount per pound of glass, so:
[tex]\frac{2.53}{0.11}=23\text{ pounds of glass}[/tex]In the same way, to know the number of pounds of aluminum, we need to divide the amount received by the amount per pound, so:
[tex]\frac{5.75}{0.25}=23\text{ pounds of aluminum}[/tex]Therefore, he recycles 23 pounds of glass and 23 pounds of aluminum
5 Type the correct answer in the box Round your answer to the nearest hundredth Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the top of the dam to be 26° Scarlett's height is 1.65 meters, so the height of the dam is meters
I sletched Scarlets position (S), her distance from the dam and the angle of elevation
As you can see, they form a rigth triangle.
The side represented by the dam is the opposite side to the angle of elevation
Using the trigonometric ratios you can calculate the height of the dam
The ratio that relates the oposite and adjacent sides of an angle is the tangent
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \text{opposite}=\tan \theta\cdot adjacent \end{gathered}[/tex][tex]\begin{gathered} \text{opposite=tan26}\cdot90 \\ \text{opposite}=43.895\cong43.90m \end{gathered}[/tex]The dam is 43.90m
Consider the following functions.Sx) = x + 4 and g(x) = x - 7Step 4 of 4: Find(3)).x). Simplify your answerAnswerKeyboards(2)) =Submit Ang
Given:
[tex]f(x)=x+4\text{ and }g(x)=x-7[/tex]Required:
[tex]\text{We need to find }(\frac{f}{g})(x).[/tex]Explanation:
[tex]\text{We know that }(\frac{f}{g})(x)=\frac{f(x)}{g(x)}.[/tex][tex]Substitute\text{ }f(x)=x+4\text{ and }g(x)=x-7\text{ in the equation.}[/tex][tex](\frac{f}{g})(x)=\frac{x+4}{x-7}[/tex]Final answer:
[tex](\frac{f}{g})(x)=\frac{x+4}{x-7}[/tex]