Answers
For the upper line:
[tex]\begin{gathered} (x1,y1)=(0,2) \\ (x2,y2)=(2,3) \\ m=\frac{y2-y1}{x2-x1}=\frac{3-2}{2-0}=\frac{1}{2} \\ \text{ using the point-slope equation:} \\ y-y1=m(x-x1) \\ y-2=\frac{1}{2}(x-0) \\ y=\frac{1}{2}x+2 \end{gathered}[/tex]For the lower line:
[tex]\begin{gathered} (x1,y1)=(0,-3) \\ (x2,y2)=(2,-2) \\ m=\frac{-2-(-3)}{2}=\frac{1}{2} \\ \text{ Using the point-slope equation:} \\ y-y1=m(x-x1) \\ y-(-3)=\frac{1}{2}(x-0) \\ y+3=\frac{1}{2}x \\ y=\frac{1}{2}x-3 \end{gathered}[/tex]Therefore, the system of inequalities is given by:
[tex]\begin{gathered} y\le\frac{1}{2}x+2 \\ y\ge\frac{1}{2}x-3 \end{gathered}[/tex]
Related Questions
In the picture below, line PQ is parallel to line RS, and the lines are cut by a transversal, line TO. The transversal is not perpendicular to the parallel lines.
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Congruent angles = ?
Step 02:
We must analyze the diagram to find the solution.
Congruent angles:
∠ Y ≅ ∠ E
The answer is:
∠ Y ≅ ∠ E : are congruent
Reflect triangle YWZ across line YW. Which of these is a valid reason why the image of Z will coincide with X?
Answers
Triangle WYZ
line YW
then YW is a bisector of, ZX
Scatter PlotWhich statement best describes the association betweenvariable X and variable Y?.moderate negative association. Perfect negative association. Moderate positive association. Perfect positive association
Answers
It's moderate negative association
Find the slope of the tangent line when x=3 using the limit definition f(x) = X^2 - 5
Answers
SOLUTION
From the limit definition, we have that
[tex]f^{\prime}(x)=\lim _{h\to0}\frac{f(x+h)-f(x)}{h}[/tex]Now applying we have
[tex]\begin{gathered} f\mleft(x\mright)=x^2-5 \\ f^{\prime}(x)=\lim _{h\to0}\frac{f(x+h)-f(x)}{h} \\ =\lim _{h\to0}\frac{((x+h)^2-5)-(x^2-5)}{h} \\ =\lim _{h\to0}\frac{x^2+2xh+h^2^{}-5-(x^2-5)}{h} \\ =\lim _{h\to0}\frac{x^2+2xh+h^2-5-x^2+5}{h} \\ =\lim _{h\to0}\frac{x^2-x^2+2xh+h^2-5+5}{h} \\ =\lim _{h\to0}\frac{2xh+h^2}{h} \end{gathered}[/tex]factorizing for h, we have
[tex]\begin{gathered} =\lim _{h\to0}\frac{h(2x+h)^{}}{h} \\ \text{cancelling h} \\ =\lim _{h\to0}2x+h \\ =2x \end{gathered}[/tex]So, when x = 3, we have
[tex]\begin{gathered} =2x \\ =2\times3 \\ =6 \end{gathered}[/tex]Hence, the answer is 6
The first quartile of a data set is 32, and the third quartile is 52. Which of
these values in the data set is an outlier?
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Answer: As we know that the formula of outlier is
IQR = Q3 - Q1
= 52 - 32
= 20
52 + 1.5(20) = 82...
so anything above 82 is an outlier
now
32 - 1.5(20) = 2.
..anything below 2 is an outlier
so...the 83 is outlier
so correct option is D
hope it helps
Step-by-step explanation:
Two people out of a group of 75 will win tickets to an upcoming concert. How many different groups of two are possible?
Answers
To calculate the combinations of groups of 2, since the order doesn't matter, we can use combination. In this case we have a total of 75 to choose from and will choose 2, so this is "75 choose 2".
The equation to use is (n choose k):
[tex]C(n,k)=\frac{n!}{(n-k)!k!}[/tex]In this case, we have n = 75 and k = 2, so:
[tex]C(75,2)=\frac{75!}{73!2!}[/tex]For the property of factorials, 75! / 73! = 75*74, because the terms less or equal 73 cancel out. so:
[tex]C(75,2)=\frac{75\cdot74}{2!}=\frac{75\cdot74}{2}=75\cdot\frac{74}{2}=75\cdot37=2775[/tex]So, there are 2775 different groups of 2 in this case.
Another way of doing this calculation is by thinking of choosing one at a time.
At first, we can choose from 75 possible people, so we start at 75.
When we choose the second one, we already picked the first, so there are only 74 people left. So we get:
[tex]75\cdot74[/tex]This are the two first people, but, in this way we are considering too many groups, since here we considere the order matter, to fix this we divide by k!, where k is the number of picks, which is 2 in this case (so, permutation of 2). So:
[tex]\frac{75}{2}\frac{74}{1}=\frac{75\cdot74}{2}=2775[/tex]6. Find the distance from A to B for the hexagonal nut shown below: А 1.50 in BYo I've asked tutors and they have been unable to answer, after all it's only given one side and I need some help.
Answers
Let
x ------> the length side of the regular polygon
we have a regular hexagon
that means
the interior angle of this polygon is
180(6-2)/6=120 degrees
A regular hexagon can be divided into 6 congruent equilateral triangles
see the attached figure to better understand the problem
in the right triangle of the figure
we have that
sin(60)=0.75/x
solve for x
x=0.75/sin(60)
Remember that
[tex]\sin (60^o)=\frac{\sqrt[]{3}}{2}[/tex]substitute
[tex]\begin{gathered} x=0.75\colon\frac{\sqrt[]{3}}{2} \\ \\ x=\frac{1.50}{\sqrt[]{3}}\cdot\frac{\sqrt[]{3}}{\sqrt[]{3}}=\frac{1.50\sqrt[]{3}}{3}=\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]Part 2
Find the distance AB
Applying the Pythagorean Theorem
AB^2=1.5^2+x^2
substitute the value of x
AB^2=2.25+(3/4)
AB^2=3
[tex]AB=\sqrt[]{3}\text{ in}[/tex]the distance AB is the square root of 3 inchesBy what factor does the population grow every 2 years? Use rhis information to fill out the table.By what factor does the population grow every year? explain how you know, and use this information to complete the table.
Answers
From the table, we see that:
• Year 0 has a population of 10,
,• Year 2 has a population of 20.
So after two years, the population of fish is doubled.
1) By year 4, we will have double the population of year 2, so the population will be 2*20 = 40.
2) To function that describes the growth of the population is:
[tex]P(t)=P_0\cdot r^t._{}[/tex]Where P_0 is the initial population and r is the growth factor.
We know that after two years, the population of fish is doubled:
[tex]P(t+2)=2\cdot P(t)\text{.}[/tex]Using the formula above evaluated in t + 2, we have:
[tex]P(t+2)=P_0\cdot r^{t+2}=(P_0\cdot r^t)\cdot r^2=P(t)\cdot r^2[/tex]Equalling the last two equations, we have:
[tex]P(t+2)=2\cdot P(t)=P(t)\cdot r^2\text{.}[/tex]Solving for r the last equation, we have:
[tex]\begin{gathered} 2=r^2, \\ r=\sqrt[]{2}\text{.} \end{gathered}[/tex]So the growth factor is r = √2.
Answer:
1. 40
2. √2
Exercises Complete the following: 11. Find the intercepts and (a) 9x² - 164 = 144 (c) 25x - 4y = 100 (e) x² + y² = 1 29x² + 16y² = 144
Answers
The intercepts for a function can be on either of the two axis, y or x.
when finding the intercepts of x, means that y = 0
when finding the intercepts of y, means that x = 0
finding the x intercepts
[tex]\begin{gathered} -x^2+(0)^2=1 \\ -x^2=1 \\ x^2=-1 \\ x=\sqrt[]{-1} \end{gathered}[/tex]since the solution for the square root of -1 has not any solution on the real numbers, we can say that there is no intercept over the x axis.
finding the y intercepts
[tex]\begin{gathered} -(0)^2+y^2=1 \\ y^2=1 \\ y=\pm\sqrt[]{1} \\ y=1;y=-1 \end{gathered}[/tex]there are 2 intercepts on the y axis, these are at y=1 and y=-1
information can be proven by graphing the function
pls help i Dont get it
Answers
Answer:
what do you need
Step-by-step explanation:
Use the graphs below to help you answer the question.
Which of the following is the best approximation to a solution of the equation e* = 4x+1?
A. 10
B. 2
C. 3
D. 1
Answers
Answer:
I would say the answer is D.
Step-by-step explanation:
If you solve for x you get 1/4.
In decimal form that is 0.4
If possible, give the input and output variables of the equation f(r) = 兀r2.
Answers
The input variable of the function is r, while the output variable is f(r)
How to determine the variables?The definition of the function is given as
f(r) = πr²
In the above function definition, we have the function to be
f(r)
The definition f(r) implies that
r represents the input variablef(r) represents the output variableThe above is true because, the variable π has its constant value of 22/7
i.e. π= 22/7
While the variable r can change its value
Take for instance:
If r = 7, then we have
f(7) = π x 7²
Evaluate
f(7) = 154
If r = 14, then we have
f(14) = π x 14²
Evaluate
f(14) = 616
See that the value of f(r) changes as r changes
This means that, the stated parameters above are true i.e.
r represents the input variablef(r) represents the output variableRead more about functions at
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Insert three arithmetic means between -16 and 4
Answers
To answer this question we will use the following formulas to compute n arithmetic means between 'a' and 'b':
[tex]\begin{gathered} A_1=a+\frac{b-a}{n+1}, \\ A_2=a+2\cdot\frac{b-a}{n+1}, \\ \ldots \\ A_n=a+n\cdot\frac{b-a}{n+1}\text{.} \end{gathered}[/tex]Substituting n=3, a=-16, and b=4 we get:
[tex]\begin{gathered} A_1=-16+\frac{4-(-16)}{3+1}, \\ A_2=-16+2\cdot\frac{4-(-16)}{3+1}, \\ A_3=-16+3\cdot\frac{4-(-16)}{3+1}\text{.} \end{gathered}[/tex]Simplifying the above results we get:
[tex]\begin{gathered} A_1=-16+\frac{4+16}{4}=-16+\frac{20}{4}=-11, \\ A_2=-16+2\cdot\frac{4+16}{4}=-16+\frac{40}{4}=-6, \\ A_3=-16+3\cdot\frac{4+16}{4}=-16+\frac{60}{4}=-1. \end{gathered}[/tex]Answer: -11, -6, and -1.
f(-9)=7x+6
what would the value of F(-9) be?
Answers
Hope it’s helps
The area of a triangle is 5. two of the sides lengths are 4.1 and 2.5 and the included angle is obtuse. find the measure of the included angle, to the nearest tenth of a degree.
Answers
Given data:
The given area of the triangle is A=5.
The first side given is a=4.1.
The second side given is b=2.5.
The expression for the area of triangle is,
[tex]A=\frac{1}{2}ab\sin C[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} 5=\frac{1}{2}(4.1)(2.5)\text{ sin C} \\ \sin C=0.97561 \\ C=102.7^{\circ} \end{gathered}[/tex]Thus, the value of the angle is 102.7 degrees.
Please help me, i struggle with these types of problems
Answers
Solution
[tex]\begin{gathered} 11x-3=9x+15 \\ \\ 2x=18 \\ \\ x=9 \end{gathered}[/tex]Therefore, we find m < 7
[tex]\begin{gathered} 11x-3 \\ \\ 11(9)-3 \\ \\ 99-3 \\ \\ 96\degree \end{gathered}[/tex]what is 3 8/9 + 8 1/2
Answers
rst builds ons 3 Veronda has a bag of mixed shapes. She chooses 3 shapes and fits them together to form a figure as shown. 17 cm What is the area of the figure Veronda creates? Use 1 = 3.14 5 Holly A 136 cm? B 107.14 cm C 96.56 cm D 76.57 cm?
Answers
We have three different figures
Semicircle
r = 4cm
[tex]\begin{gathered} A_r=\frac{\pi\cdot r^2}{4} \\ A_r=\frac{3.14\cdot4^2}{4} \\ A_r=\frac{3.14\cdot16}{4} \\ A_r=12.56 \end{gathered}[/tex]Square
l = 8cm+
2. In the xy-plane above, ABCD is a square and point E is the center of the square. The coordinates of points C and E are (7,2) and (1,0), respectively. Write an equation of the line that passes through points A, E, and C. B 1 2 -С E X -6 2 4. 16 A -2
Answers
Ready
Points A = (-5, -2) C = (7, 2) E = (1, 0)
1.- Find the slope
m = (y2 - y1) / (x2 - x1)
m = (2 + 2) / (7 + 5)
m = 4/ 12
m = 1/3
2.- Find the equation of the line
y - y1 = m(x - x1)
y + 2 = 1/3(x + 5)
y + 2 = 1/3x + 5/3
y = 1/3x + 5/3 - 2
y = 1/3 x + 5/3 - 6/3
This is the equation:
y = 1/3 x - 1/3
my pleausre
log 2x = 3 what is x
Answers
The value of x is 10.04 using log properties.
What is the log in math?The power to which a number must be increased in order to obtain another number is known as a logarithm. The exponential function is thought of as the inverse of the logarithmic function because of their close relationship. The logarithmic function logₐN = x is created from the exponential function [tex]a^{x}[/tex] = N. For instance, since ten raised to the power of two equals 100, the base ten logarithms of 100 is 2: log 100 = 2.
logₐ xy = logₐ x + logₐ y (product property)
logₐ x/y = logₐ x - logₐ y (quotient property)
logₐ [tex]x^{y}[/tex] = ylogₐ x (power property)
log2x = 3
2x = e³
x = e³/2
= 10.04
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Find the coordinates of the stationary points of the curve and use the secondderivative to determine the type of each.
Answers
Calculate the derivative of the function, as shown below
[tex]\begin{gathered} y=3x+\frac{108}{x}=3x+108x^{-1} \\ \Rightarrow y^{\prime}=3+108((-1)x^{-1-1})=3-108x^{-2} \\ \Rightarrow y^{\prime}=3-108x^{-2} \end{gathered}[/tex]Set y'=0 and solve for x, as shown below
[tex]\begin{gathered} y^{\prime}=0 \\ \Rightarrow3-108x^{-2}=0,x\ne0 \\ \Rightarrow3=\frac{108}{x^2} \\ \Rightarrow x^2=\frac{108}{3} \\ \Rightarrow x^2=36 \\ \Rightarrow x=\pm\sqrt[]{36} \\ \Rightarrow x=\pm6 \end{gathered}[/tex]Their corresponding y-coordinates are
[tex]\begin{gathered} x=\pm6 \\ \Rightarrow y=3(6)+\frac{108}{6}=18+18=36 \\ \Rightarrow(6,36) \\ \text{and} \\ 3(-6)+\frac{108}{-6}=-18-18=-36 \\ \Rightarrow(-6,36) \end{gathered}[/tex]Therefore, the two stationary points are (6,36) and (-6,-36).
Using the second derivative test,
[tex]\begin{gathered} y^{\prime}=3-108x^{-2} \\ \Rightarrow y^{\doubleprime}=-108(-2x^{-2-1})=216x^{-3} \end{gathered}[/tex]Then,
[tex]\begin{gathered} y^{\doubleprime}(6)=\frac{216}{(6)^3}=1>0\to\text{ local minimum at x=6} \\ \text{and} \\ y^{\doubleprime}(-6)=\frac{216}{(-6)^3}=-1<0\to\text{ local maximum at x=-6} \end{gathered}[/tex](6,36) is a local minimum and (-6,-36) is a local maximum.
An item is regularly priced at $85. Yolanda bought it at a discount of 65% off the regular price?
Answers
Solve for the hypotenuse and then determine the ratios below (show all work)
Answers
hypotenuse=29
[tex]\sin x=\frac{20}{29}[/tex][tex]\cos y=\frac{20}{29}[/tex]
Explanation
Step 1
a) hypotenuse
to find the hypotenuse we can use the Pythagorean theorem ,it statse that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)
so
[tex]\begin{gathered} 21^2+20^2\text{= hypotenuse}^2 \\ 441+400=\text{ hypotenuse}^2 \\ 841=\text{hypotenuse}^2 \\ taking\text{ the square root in both sides} \\ \sqrt{841}=\sqrt{(hypotenuse)^2} \\ 29=hypotenuse \end{gathered}[/tex]so
hypotenuse=29
Step 2
now, sin x
the sin of an angle is the ratio of the opposite side ( the one in front of the angel) to the hypotenuse
[tex]\sin\theta=\frac{opposite\text{ side}}{hypotenuse}[/tex]hence, replace
[tex]\sin x=\frac{20}{29}[/tex]Step 3
finally, cos of y
the cos of an angle is the ratio of the adjancent side( the side the makes the angle) to the hypotenuse
[tex]cos\theta=\frac{adjacent\text{ side}}{hypotenuse}[/tex]so,replace
[tex]\cos y=\frac{20}{29}[/tex]I hope this helps you
I inserted a picture of the questionPlease state whether it’s A B C or DCheck all that apply
Answers
Given the initial function,
[tex]f(x)=2^x[/tex]In general, a vertical stretch/compression is expressed by
[tex]f(x)\to k\cdot f(x)[/tex]If k>1, the function gets a vertical stretch; on the other hand, if 0Therefore, in our case,
[tex]g_1(x)=\frac{1}{3}f(x)\to\text{vertical compression by a factor of 1/3}[/tex]A vertical shift is given by the following formula
[tex]\begin{gathered} f(x)+k \\ k>0\to\text{shifted up} \\ k<0\to\text{shifted down} \end{gathered}[/tex]In our case,
[tex]g(x)=g_1(x)-7\to\text{vertical shift down by 7 units.}[/tex]Therefore, the answers are B and D.
I’ve been working on these similar questions but coming to this question. I found myself being stuck.
Answers
Solution:
If the variation in pressure is P pounds per square inch, then the Loudness L in decibels is;
[tex]L=20\log _{10}(121.3P)[/tex]When L=115 decibels;
[tex]\begin{gathered} 115=20\log _{10}(121.3P) \\ \text{Divide both sides by 20;} \\ \frac{115}{20}=\frac{20\log_{10}(121.3P)}{20} \\ \log _{10}(121.3P)=5.75 \end{gathered}[/tex]But from the logarithmic law, we have;
[tex]\log _ba=c\leftrightarrow a=b^c[/tex]Thus,
[tex]\begin{gathered} \log _{10}(121.3P)=5.75 \\ 121.3P=10^{5.75} \\ 121.3P=562341.33 \end{gathered}[/tex][tex]\begin{gathered} \text{Divide both sides by 121.3;} \\ \frac{121.3P}{121.3}=\frac{562341.33}{121.3} \\ P\cong4635.95 \end{gathered}[/tex]FINAL ANSWER:
[tex]4636.0\text{ pounds per square inch.}[/tex]Find the slope of the line that passes through (8, 7) and (6, 2).
Answers
[tex]m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{2 - 7}{6 - 8} \\ m = \frac{ - 5}{ - 2} \\ m = \frac{5}{2} [/tex]
ATTACHED IS THE SOLUTION WITH THE FORMULA TO CALCULATE THE SLOPE BETWEEN POINTS.
Solve the following simultaneous equation with elimination or substitution method
Answers
So, to solve the system:
To solve it, we could substitute the first equation in the second one and then solve for x:
We could solve the previous quadratic by factoring:
To find the values of y, just replace each vaue of x:
Therefore, the solutions of the system are
(x,y) = (-3,-1)
(x,y)=(1,3)
how is the metric system important to a pharmacy Technician?
Answers
The metric system is a system of decimals in which all the measurements are taken as multiples or divisions based on a factor of 10. We have to convert between different units of measurements while working in a pharmacy. Metric system helps to make fast and easy conversions of units of measurements. Therefore, metric system is important to a pharmacy technician.
Graph the solution of the linear inequality and answer the questions on the bottom
Answers
The inequality is given
[tex]-2y\leq6x+18[/tex]To draw the graph of the inequality which is less than equal to
which number below comes first when the numbers are listed from least to greatest? Explain. Then write the numbers in order from least to greatest 1/6, -3, the square root of 5, -9 / 2, 4.6 which number comes first when the numbers are listed from least to greatest?A. 1/6B.-3C.-9/2D.Square root of 5E. 4.6
Answers
Answer:
The number that comes first when the numbers are listed from least to greatest is;
[tex]\frac{-9}{2}[/tex]And, arranging the numbers from least to greatest will give;
[tex]\frac{-9}{2},-3,\frac{1}{6},\sqrt{5},4.6[/tex]Explanation:
We want to arrange the number given below from least to greatest;
[tex]\frac{1}{6},-3,\frac{-9}{2},\sqrt{5},4.6[/tex]From the list of numbers, let us simplify each of them to their approximate decimal.
[tex]\begin{gathered} \frac{1}{6}=0.1667 \\ -3 \\ \frac{-9}{2}=-4.5 \\ \sqrt{5}=2.236 \\ 4.6 \end{gathered}[/tex]From the given number, the highest negative number will be the least number.
Because the higher a negative number the lower it becomes.
The highest negative is -4.5 followed by -3.
So, arranging from the least to the greatest we have;
[tex]-4.5,-3,0.1667,2.236,4.6[/tex]Rewriting it in its initial form we have;
[tex]\frac{-9}{2},-3,\frac{1}{6},\sqrt{5},4.6[/tex]Therefore, The number that comes first when the numbers are listed from least to greatest is;
[tex]\frac{-9}{2}[/tex]And, arranging the numbers from least to greatest will give;
[tex]\frac{-9}{2},-3,\frac{1}{6},\sqrt{5},4.6[/tex]