solving compound qualities
Answers
S = {x ∈ R : 3≤x≤12}
1) To solve a compound inequality, we must do it one by one.
Let's start with
1.1) 0≤1/3x -1
1≤1/3x-1+1
1≤1/3x Multiplying both sides by 3
3≤x Flipping it
x≥3
1.2) 1/3x -1≤3
1/3x -1+1≤3+1
1/3x≤4
x≤12
2) Let's find out the solution, by graphing on three lines. The first one for the first solution, the second for the second inequality's solution, and the third for the intersection of the above:
So the Solution set is S = {x ∈ R : 3≤x≤12}
Related Questions
solve the equation for all values of x by completing the square. x²+8x=-15
Answers
since (8/2)^2=16, we will add 16 in both sides of the equation, obtaining
[tex]x^2+8x+16=1[/tex]now, we factor the left side of the equation (it's a perfect square)
[tex](x+4)^2=1[/tex]then we have two options or x+4=1 or x+4=-1
solving both of the we have that the values for x are x=-3 and x=-5An office uses paper drinking cups in the shape of a cone, with dimensions as shown.-23 in.4 in.To the nearest tenth of a cubic inch, what is the volume of each drinking cup?A. 2.5B. 7.9C. 23.7D. 31.7
Answers
According to the formula for volume of a cone and rounding to the nearest tenth of cubic inch, we find out that the volume of each drinking cup is 7.9 cubic inch. Thus, option B is correct.
From the given figure, we have
Diameter of the cone-shaped cups, d = [tex]2\frac{3}{4}[/tex] in = 2.75 in
Height of the cone-shaped cups, h = 4 in
We have to find out the volume of each drinking cup.
Since, d = 2.75 in (Given), we can say that
The radius of the cone-shaped cups, r = [tex]\frac{1}{2}*2.75[/tex]
=> r = 1.375 in
We know that the volume of a cone can be represented as -
[tex]V = \frac{1}{3} \pi r^{2}h[/tex]
Putting the value of radius, r and height, h in the above equation of volume of the cone, we get
Volume, [tex]V = \frac{1}{3} \pi r^{2}h[/tex]
=> [tex]V = \frac{1}{3}\pi (1.375)^{2}*4\\= > V = 7.919 in^{3}[/tex]
Thus, using the formula for volume of a cone and rounding to the nearest tenth of cubic inch, we find out that the volume of each drinking cup is 7.9 cubic inch. Thus, option B is correct.
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Answer:According to the formula for volume of a cone and rounding to the nearest tenth of cubic inch, we find out that the volume of each drinking cup is 7.9 cubic inch. Thus, option B is correct.
Step-by-step explanation:
6.4 times m minus 12 equals 45.6
Answers
Given
6.4 times m minus 12 equals 45.6
To find: The value of m.
Explanation:
It is given that,
6.4 times m minus 12 equals 45.6.
Then,
[tex]\begin{gathered} 6.4m-12=45.6 \\ 6.4m=45.6+12 \\ 6.4m=57.6 \\ m=\frac{57.6}{6.4} \\ m=9 \end{gathered}[/tex]Hence, the value of m is 9.
Let's test out the prediction! On the coordinate plane below, plot the points from your table in Slide 4 and sketch the graph.Table from slide 4: Bounce Height after Bounce 1. 92. 8.13. 7.294. 6.561
Answers
Answer
Check Explanation
Explanation
To do this, we will let the bounce be represented on the x-axis as x and the height after bounce plotted on the y-axis as y
So, the table looks like
x | y
1 | 9
2 | 8.1
3 | 7.29
4 | 6.561
So, we plot these points on a graph and sketch a line of best fit to pass through them
Hope this Helps!!!
For what values of x is the expression below defined?A.-5 x < 1B.5 > x -1C.5 > x > 1D.5 x 1
Answers
Given:
There are given that the expression:
[tex]\frac{\sqrt{x+5}}{\sqrt{1-x}}[/tex]Explanation;
First, let's notice that we need positives to numbers inside both roots.
So,
The root of a negative number is a math error.
Then,
With that information, let us analyze the options.
From option A:
If we add 5 to this inequality, we have:
[tex]\begin{gathered} -5+5\leq x+5<1+5 \\ 0\leq x+5<6 \end{gathered}[/tex]That means the number in the first root is positive.
Now, we want 1-x to be positive:
[tex]\begin{gathered} -5\leq x<1 \\ 5\ge-x>-1 \\ 1+5\ge1-x>1-1 \\ 6\ge1-x>0 \end{gathered}[/tex]So, it is positive:
Final answer;
Hence, the correct option is A.
Two markers A and B on the same side of a canyon rim are 56 feet apart. A third marker C, located across the rim. is positioned so that BAC = 69º and ABC = 51° Complete parts (a) and (b) below (a) Find the distance between C and A.
Answers
To answer this question, it will be helpful to have a drawing of the situation to find the asked distance:
With this information, it will be easier to have all the information to solve for the distance CA.
Therefore, to find the distance CA, we can apply the Law of Sines, in which we have to find the angle C. We know that the sum of the interior angles of a triangle is equal to 180. Then, we have:
[tex]mNow, we can apply the Law of Sines to find the distance CA:[tex]\frac{AC}{\sin(51)}=\frac{56}{\sin(60)}\Rightarrow AC=\frac{56\cdot\sin (51)}{\sin (60)}[/tex]Then, we have:
[tex]AC=50.2527681652ft[/tex]Then, to round to one decimal place, we have that AC is approximately 50.3 ft.
To find the distance between the two rims, we have:
Now, we can also apply the Law of Sines to find the distance CD (the distance between the two rims):
[tex]\frac{CD}{\sin(69)}=\frac{CA}{\sin(90)}\Rightarrow CD=CA\cdot\sin (69),\sin (90)=1[/tex]Then, we have:
[tex]CD=50.2527681652\cdot\sin (69)\Rightarrow CD=46.9150007363ft[/tex]Therefore, the distance between the two canyon rims (round to one decimal place) is 46.9 ft.
If we take 50.3 ft (for CA), instead, we have 47 ft.
trig The last sub-problem of this section stumped me pls help
Answers
For this problem, we are given a triangle and we need to determine its height.
The distance of the UFO from point A is equal to the side c of the triangle, this side forms a right triangle with the height, where the height is the opposite cathetus from angle alpha and side c is the hypothenuse. We can use the sine relationship to determine the height, as shown below:
[tex]\begin{gathered} \sin(87.4)=\frac{h}{425.58}\\ \\ h=425.58\cdot\sin(87.4)\\ \\ h=425.58\cdot0.9989706=425.14 \end{gathered}[/tex]The height is approximately 425.14 km.
in the equation 4x^3=56, what is the value of x
Answers
The given equation is
[tex]4x^3=56_{}[/tex]First, we divide the equation by 4.
[tex]\begin{gathered} \frac{4x^3}{4}=\frac{56}{4} \\ x^3=14 \end{gathered}[/tex]At last, we take the cubic root on each side.
[tex]\begin{gathered} \sqrt[3]{x^3}=\sqrt[3]{14} \\ x\approx2.41 \end{gathered}[/tex]Therefore, the value of x is 2.41, approximately.solve the system by subsitution method
Answers
Substitute Y = 3X - 6
in second equation
-15X + 5•(3X - 6) = -30
Now solve for X, cancel parenthesis
use a(b+c) = ab + ac
-15X + 15 X - 30 = -30
. -30 = -30
Then we see that, have infinite solutions
In consecuence, ANSWER IS
OPTION D) (x , 3x - 6 )
please explain briefly..limits and derivatives
Answers
The logarithmic-radical expression √[㏒ₐ f(x)] is true for 0 < f(x) ≤ 1. (Correct choice: D)
What is the domain of a logarithmic-radical function?
Logarithms are trascendent expressions whose domain is described below:
Ran (logₐ f(x)) = (0, + ∞)
Since 0 < a < 1, then we find the following feature: logₐ f(x) > 0 for 0 < f(x) ≤ 1.
In addition, the domain of radical functions is described below:
Dom (√f(x)) = f(x) ≥ 0
Therefore, the logarithmic-radical expression defined in the statement is true for 0 < f(x) ≤ 1.
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Which of the following equations does the graph below represent?
A. 2x + 2y = 8
B. -2x - 2y = 8
C. -2x + y = 8
D. -2x + 2y = 8
Answers
Answer: D
Step-by-step explanation:
The answer is D, as seen on the graph, the Y-Intercept is at Y = 4, and the gradient is 1, so according to the equation y = mx + c,
"m" must equal 1, and "c" must equal 4, so the equation needs to be:
y = x + 4.
In Option D, the equation can be rearranged to 2y = 2x + 8, dividing both the LHS and RHS by 2, we get y = x + 4.
This type of question can be tough at first, however it's just a matter of practice, keep practicing, keep working hard, and you'll be an expert in no time!
Identify the following series as geometric or arithmetic. Also identify the series as infinite or finite.5, 10, 20, 40, 80, 160, 320geometricarithmeticinfinitefinite
Answers
the series is geometric and finite
Explanation:Given:
5, 10, 20, 40, 80, 160, 320
To find:
if the series is arithmetic or geometric; infinite or finite
a) For a series to be arithmetic, it must have a common difference
common difference = next term - previous term
For the series to be geometric, it must have a common ratio
common ratio = next term/previous term
We need to check if it has a common difference or common ratio
let next term = 10, previous term = 5
common difference = 10 - 5 = 5
let next term = 20, previous term = 10
common difference = 20 - 10 = 10
The difference is not common, it is different
common ratio = next term/previous term
let next term = 10, previous term = 5
common ratio = 10/5 = 2
let next term = 20, previous term = 10
common ratio = 20/10 = 2
The ratio is common
As a result, the series is geometric
b) Infinite series cannot be counted and totaled. This is because they do not end
Finite series can be counted and summed up. This is because the series has an end.
The series is finite
Answer:
geometric
finite
Step-by-step explanation:
Correct on Odyssey.
:)
Find a measurement of the complement for the angle 20
Answers
Given:
There are given that the angle is 20 degrees.
Explanation:
According to the concept:
The complementary angle is:
[tex]90^{\circ}-\theta[/tex]Then,
Put the value of an angle;
So,
[tex]\begin{gathered} 90^{\circ}-\theta=90^{\circ}-20 \\ =70^{\circ} \end{gathered}[/tex]Final answer:
Hence, the measure of the complement is 70 degrees.
936.1 ÷ 2.3how do i calculate this without a calculator
Answers
Using long division:
Move the decimal point in the divisor and the dividend 1 unit
set up an equation for your exterior angle, then use multi-step equation steps to solve for y.A. 15B. 17.4C. 5D. 10
Answers
In any triangle, the sum of the interior angles of two vertices is equal to the exterior angle of the other vertex.
Using this property, we can write the following equation:
[tex]\begin{gathered} \text{ABC+BAC=ACD}_{} \\ (4y+8)+(5y+3)=146 \\ 9y+11=146 \\ 9y=146-11 \\ 9y=135 \\ y=\frac{135}{9} \\ y=15 \end{gathered}[/tex]The value of y is equal to 15, therefore the correct option is A.
SCC Library667737985Based on the graph of this normal distribution,a. The mean isb. The median isThe mode isd. The standard deviation isCheck Answer
Answers
The Solution.
From the graph,
a. The mean = 73
b. The median = 73
c. The mode = 73
d. The standard deviation (S.D) is;
[tex]S.D=73-67=6[/tex]There is 1/5 of a foot of ribbon left onthe spool. If Brittany cuts it into 3equal pieces, how long (in feet) willeach piece be?
Answers
We know that
• There is 1/5 of a foot of ribbon.
If Brittany cuts it into 3 equal pieces, we have to divide to find the length of each piece.
[tex]\frac{\frac{1}{5}}{3}=\frac{1}{15}[/tex]Therefore, each piece is 1/15 of a foot long.Translate to a system of equations. Do not solve.Two angles are supplementary. One angle is 4 less than three times the other . Find the measures of the angles l.
Answers
Two angles are supplementary
That means they add to 180
x+y = 180
One angle is 4 less than three times the other
We know that is means equals and less than comes after
x = 3y-4
Sanjay attempts a 50-yard field goal in a football game. For his attempt to be a success, the football needs to pass through the uprights and over the crossbar that is 10 feet above the ground.Sanjay kicks the ball from the ground with an initial velocity of 64 feet per second, at an angle of 34° with the horizontal.Is Sanjay's attempt successful? If not, how many feet too low is the ball?
Answers
Let us draw a sketch to understand the situation
We will use some rules here
[tex]\begin{gathered} v_x=vcos\theta=64cos(34) \\ d_x=v_xt=64cos(34)t \end{gathered}[/tex]Since the horizontal distance is 50 yards
Since 1 yard = 3 feet, then
[tex]d_x=50\times3=150feet[/tex]We will use it to find the time t
[tex]\begin{gathered} d_x=150 \\ 64cos(34)t=150 \\ t=\frac{150}{64cos(34)}\text{ s} \end{gathered}[/tex]Now, we will find the vertical distance (h) by using this rule
[tex]\begin{gathered} v_y=vsin\theta=64sin(34) \\ d_y=h=v_yt-\frac{1}{2}at^2=64sin(34)t-\frac{1}{2}(32)t^2 \end{gathered}[/tex]Note that: a is the acceleration of gravity which is 32 ft/s^2
We will substitute t by its value
[tex]h=64sin(34)(\frac{150}{64cos(34)})-16(\frac{150}{64cos(34)})[/tex]We can simplify it by using sin34/cos34 = tan34, and 1/cos34 = sec34
But I will put it on the calculator to find the final answer
[tex]h=55.94\text{ ft}[/tex]Since the height of the crossbar is 10 feet, then
Sanjay's attempt successful
Leila bought a sofa on sale for $268. This price was 33% less than the original price.What was the original price?
Answers
Let P be the original price.
Since $268 is 33% less than the original price, then $268 is equal to 67% of the original price:
[tex]268=\frac{67}{100}\times P[/tex]Then:
[tex]\begin{gathered} P=\frac{100}{67}\times268 \\ =400 \end{gathered}[/tex]Therefore, the original price was $400.
Answer: $356.44
Step-by-step Explanation: To find the original price of the sofa you need to multiply 33% by $268, but you need to turn the percent into a decimal, to do so you need to divide 33 by 100 & that is 0.33. So 0.33 x $268 is 88.44. After, you add both $268 and $88.44 to get the original price & that is $356.44.
Find the slope of the secant line for the g(x) = -20 SQRT x between x = 2 and x = 3
Answers
Given:
Equation of line is,
[tex]g(x)=-20\sqrt[]{x}[/tex]The slope of the secant line between x =a and x= b is calculated as,
[tex]\begin{gathered} m=\frac{f(b)-f(a)}{b-a} \\ m=\frac{f(3)-f(2)}{3-2} \\ m=\frac{-20\sqrt[]{3}-(-20\sqrt[]{2})}{1} \\ m=-20\sqrt[]{3}+20\sqrt[]{2} \\ m=20(\sqrt[]{2}-\sqrt[]{3}) \\ m=-6.36 \end{gathered}[/tex]Answer: slope of the secant line is m = -6.36
Hello can someone help me in this pls i need it today now PLS i will give 25 points
Answers
Answer:
Look below
Step-by-step explanation:
Convert -8/5 into a decimal
-8/5 = -1 3/5 = -1.6
What is the image of (2,-3) after a 180 degree counterclockwise rotation about the origin?a. (-3, 2) b.(-2, 3) c. (-3, -2)d.(-2,3)
Answers
Answer:
b.(-2, 3)
Explanation:
A 180 roration transforms the coordinates of a point according to the following rule.
[tex](x,y)\rightarrow(-x,-y)[/tex]For our point (2, -3), applying the above rule gives.
[tex](2,-3)\rightarrow(-2,3)[/tex]Hence, the coordinates of the image are (-2, 3 ) which is choice B.
Use the table. What percentage of the people surveyed were teachers who wanted a later start time?
Answers
The Solution.
The percentage of the people survey that were teachers that voted yes to start later is
[tex]\text{ }\frac{\text{ number of teachers that voted YES}}{\text{ Total number of people surveyed}}\times100[/tex]Which is
[tex]\frac{20}{75}\times100=0.266667\times100=26.6667\approx26.67\text{ \%}[/tex]b. The percentage of the people surveyed that were teachers is
[tex]\frac{\text{ number of teachers surveyed}}{\text{ Total number of people surveyed}}\times100[/tex]Which is
[tex]\frac{30}{75}\times100=0.4\times100=40\text{ \%}[/tex]Hence, the correct answer are:
a. 26.67% b. 40%
With the exception of column one, all amounts are in dollars. Calculate the annual interest rate on this loan. Give your answer to the nearest hundredth percent. Do not include the % sign in your response.
Answers
Given:
Amortization table is given
Let r be the annual rate of interest.
[tex]\frac{r}{12}\text{ be the monthly rate of interest.}[/tex]Second payment:
P= $259873.20 ; interest = $539.24
[tex]\text{Interest for the 2nd payment = }P(\frac{r}{12}\times\frac{1}{100})[/tex][tex]539.24=259873.20(\frac{r}{1200})[/tex][tex]\frac{539.24}{259873.20}\times1200=r[/tex][tex]r=\frac{647088}{259873.20}[/tex][tex]r=2.49[/tex]Therefore, the annula rate of interest is 2.49%
limit using L'Hopital's rule . I just want to make sure if my answer is correct or not?
Answers
In order to use L'Hopital's rule, it is necessary to rewrite the limit as the quotient of two functions. Notice that:
[tex]\begin{gathered} 6x^{\sin (4x)}=e^{\ln (6x^{\sin (ex)})^{}} \\ =e^{\sin (4x)\cdot\ln (6x)} \end{gathered}[/tex]Since the exponential function is a continuous function, then:
[tex]\lim _{\text{x}\rightarrow0}e^{\sin (4x)\cdot\ln (6x)}=e^{\lim _{x\rightarrow0}\sin (4x)\cdot\ln (6x)}[/tex]Find the following limit using L'Hopital's rule:
[tex]\lim _{x\rightarrow0}\sin (4x)\cdot\ln (6x)[/tex]Write the function as a fraction:
[tex]\lim _{x\rightarrow0}\frac{\ln (6x)}{(\frac{1}{\sin (4x)})}[/tex]Use L'Hopital's rule to rewrite the limit as the limit of the quotient of the derivatives:
[tex]\begin{gathered} \lim _{x\rightarrow0}\frac{(\frac{1}{x})}{(-\frac{4\cos(4x)}{\sin^2(4x)})}=\lim _{x\rightarrow0}-\frac{\sin ^2(4x)}{4x\cdot\cos (4x)} \\ =\lim _{x\rightarrow0}\sin (4x)\cdot\frac{\sin(4x)}{4x}\cdot\frac{-1}{\cos (4x)} \\ =\lim _{x\rightarrow0}\sin (4x)\cdot\lim _{x\rightarrow0}\frac{\sin(4x)}{4x}\cdot\lim _{x\rightarrow0}\frac{-1}{\cos (4x)} \\ =0\cdot1\cdot-1 \\ =0 \end{gathered}[/tex]Therefore:
[tex]\lim _{x\rightarrow0}6x^{\sin (4x)}=e^0=1[/tex]How do I solve these?If f(x)=3xsquared + 9x-4 then evaluate the following:f(1)=3x^2+9x-4f(x+h)=3x^2+9x-4
Answers
a) We need to evaluate when x = 1
f(1): this means we will replace x with 1 in the given function
[tex]\begin{gathered} f\mleft(x\mright)=3x^2+9x-4 \\ f\mleft(1\mright)=3(1)^2+9(1)-4 \\ f(1)\text{ = 3(1) + 9 - 4 = 3 + 9 - 4} \\ f(1)\text{ = 8} \end{gathered}[/tex]b) We need to evaluate the function when x = x + h
[tex]\begin{gathered} f\mleft(x\mright)=3x^2+9x-4 \\ f(x\text{ + h): we will replace x with x + h in the given function} \\ f(x+h)=3(x+h)^2\text{ + 9(x + h) - 4} \end{gathered}[/tex]Expanding:
[tex]\begin{gathered} f(x\text{ + h) }=3(x^2+2xh+h^2)\text{ + 9(x + h) - 4} \\ f(x\text{ + h) }=3x^2+6xh+3h^2\text{ + 9x + 9h - 4} \\ \text{Since there are no like terms we can simplify, we can leave it in expanded form:} \\ f(x\text{ + h) }=3x^2+6xh+3h^2\text{ + 9x + 9h - 4} \\ \\ or\text{ the non expanded form:} \\ f(x+h)=3(x+h)^2\text{ + 9(x + h) - 4} \end{gathered}[/tex]Crystal earns $4.75 per hour mowing lawns. A. write a rule to describe how the amount of money M earned is a function of the number of hours H that mowing lawns. B. l how much does crystal earn if she works 1 hour and 15 minutes?
Answers
Given:
Crystal earns $4.75 per hour mowing lawns.
Let the money earned = M
And the number of hours = H
So, the relation between M and H will be :
[tex]M=4.75\cdot H[/tex]B. how much does crystal earn if she works 1 hour and 15 minutes?
Time = 1 hours and 15 minutes
AS 1 hour = 60 minutes
So,
[tex]H=1+\frac{15}{60}=1+\frac{1}{4}=1+0.25=1.25[/tex]Substitute with H to find M
So,
[tex]M=4.75\cdot1.25=5.9375[/tex]So, she will earn $5.9375
Solve for the remaining angles and side of the two triangles that can be created. Round to the nearest hundredth:B = 30 .b = 6,a = 7AnswerHow to enter your answer (opens in new window) 2 PointsTriangle 1: (where angle A is acute):Triangle 2: (where angle A is obtuse):AA:C =C:C:
Answers
ANSWER:
Triangle 1:
A = 35.69°
C = 114.31°
c = 10.94
Triangle 2:
A = 144.31°
C = 5.69°
c = 1.19
STEP-BY-STEP EXPLANATION:
Given:
B = 30°, b = 6, a = 7
We calculate the angle A by means of the law of sines:
[tex]\begin{gathered} \frac{a}{\sin A}=\frac{b}{\sin B} \\ \\ \text{ We replacing} \\ \\ \frac{7}{\sin A}=\frac{6}{\sin30} \\ \\ \sin A=\frac{7}{6}\cdot\sin30 \\ \\ \sin A=\frac{7}{12} \\ \\ A=\sin^{-1}\left(\frac{7}{12}\right)\: \\ \\ A_{acute}=35.69\degree \\ \\ A_{obtuse}=144.31\degree \end{gathered}[/tex]We calculate the value of angle C, knowing that the sum of all internal angles is equal to 180°
[tex]\begin{gathered} \text{ Acute} \\ \\ 180=35.69+30+C \\ \\ C=180-30-35.69=114.31\degree \\ \\ \text{ Obtuse} \\ \\ 180=144.31+30+C \\ \\ C=180-30-144.31=5.69\degree \end{gathered}[/tex]Side c is also calculated with the law of sines, like this:
[tex]\begin{gathered} \text{ Acute} \\ \\ \frac{b}{\sin B}=\frac{c}{\sin C} \\ \\ \frac{6}{\sin(30)}=\frac{c}{\sin114.31} \\ \\ c=\frac{6}{\sin(30)}\cdot\sin114.31 \\ \\ c=\:10.94 \\ \\ \text{ Obtuse} \\ \\ \frac{7}{\sin(A)}=\frac{c}{\sin(C)} \\ \\ c=\frac{6}{\sin(30)}\sin(5.69) \\ \\ c=1.19 \end{gathered}[/tex]Therefore;
Triangle 1:
A = 35.69°
C = 114.31°
c = 10.94
Triangle 2:
A = 144.31°
C = 5.69°
c = 1.19
Solve the given expression for x = -18:5x/3 - 2
Answers
ANSWER
[tex]-32[/tex]EXPLANATION
We want to solve the given expression for x = -18:
[tex]\frac{5x}{3}-2[/tex]To do this, substitute the given value of x into the expression and simplify. That is:
[tex]\begin{gathered} \frac{5(-18)}{3}-2 \\ \frac{-90}{3}-2 \\ -30-2 \\ \Rightarrow-32 \end{gathered}[/tex]That is the answer.