Consider the following inequality:x < -2Step 2 of 2: What type of interval does the following inequality represent?
Answers
You have the following inequality:
x≤2
the prevous inequality can be written in interval notation as follow:
(-oo, 2]
then, you can conclude that the inequality is represented by a half-open interval (this happens when you have an open parentheses and a close parentheses)
Related Questions
It takes Evelyn, traveling at 36 mph, 20 minutes longer to go a certain distance than it takes Sarah traveling at 60 mph. Find the distance
traveled.
Answers
The distance travelled by both Evelyn and Sarah is 30 miles.
Given,
The speed travelled by Evelyn = 30 mph
Time taken by Evelyn to cover a distance = 20 minutes
Speed travelled by Sarah = 60 mph
We have to find the distance travelled by both of them.
Speed = distance / time
Then,
Distance = speed x time
Lets take x as the distance.
Then,
36 × (x + 20) = 60x
36x + 720 = 60x
60x - 36x = 720
24x = 720
x = 720/24
x = 30
That is,
The distance travelled by both Evelyn and Sarah is 30 miles.
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The ratio of 1.2 to 32 is equal to the ratio of 3.6 to____.
Answers
Answer:
96
Step-by-step explanation:
let the number be x then
1.2x=32
x=80/3
again
3.6x
3.6×80/3
96
If a square has a perimeter of 28 inches, what is its area in square inches?
Answers
Remember that
The formula to calculate the perimeter of a square is
[tex]P=4*b[/tex]where
b is the length side of the square
we have
P=28 in
substitute in the formula
[tex]\begin{gathered} 28=4*b \\ sol\text{ve for b} \\ b=\frac{28}{4}=7\text{ in} \end{gathered}[/tex]The area of a square is
[tex]A=b^2[/tex]substitute the value of b
[tex]\begin{gathered} A=7^2 \\ A=49\text{ in}^2 \end{gathered}[/tex]The area is 49 square inchesoption CHow to tell if a sequence is linear, exponential, quadratic or absolute value as simply as possible without graphing (8th grade algebra) examples will be greatly appreciated
Answers
We will have the following:
We will be able to tel apart sequences as follows:
Linear sequence: We have that linear sequences follow the form:
[tex]y=mx+b[/tex]Here "x" represents the iteration value for the sequence, "m" the ratio (slope) and "b" a value that modifies the "position" of the sequence. This sequences grows in a linear manner.
Example:
[tex]\begin{cases}y_{}=2x+2 \\ \\ y_1=4 \\ y_2=6 \\ y_3=8 \\ \ldots\end{cases}[/tex]Exponential sequence: We have that exponential sequences follow the form:
[tex]y=a_1(r)^{x-1}[/tex]Here "a1" is the first term of the sequence, "r" is the ratio and "x" the iteration of the sequence.
We obtain the ratio as follows:
[tex]r=\frac{y_n}{y_{n-1}}[/tex]Example:
[tex]\begin{cases}y=1(5)^{x-1}_{} \\ \\ y_1=1 \\ y_2=5 \\ y_3=25 \\ \\ \ldots\end{cases}[/tex]The ratio for this case:
[tex]r=\frac{y_3}{y_2}\Rightarrow r=\frac{25}{5}\Rightarrow r=5[/tex]Quadratic sequence: A quadratic sequence follows the general form
Write the first 4 terms of the sequence defined by the given rule. f(n)=n^3-1
Answers
which expression is equivalent to 5^-2 x 5^5
Answers
Given the expression:
[tex]5^{-2}\ast5^5[/tex]To find the equivalent expression, let's simplify the expression using power rule.
[tex]a^m\ast a^n=a^{m+n}[/tex]Since they have the same base, we are to add the exponents.
We have:
[tex]5^{-2}\text{ }\ast5^5=5^{-2+5}=5^3[/tex]Therefore, the eqivalent expression is 5³
ANSWER:
[tex]5^3[/tex]We a
24. A rocket is launched into the air. Its height in feet, after x seconds, is given by the equation The starting height of the rocket is h(x)=-16x’ +300x + 20 The maximum height is The rocket hits the ground after seconds.
Answers
Well we just need to do the analise of the function h, so for the first question we need to know what is the value of h when x=0, so if we evaluate we see that
[tex]h(0)=-16(0)^2+300(0)^{}+20^{}=20^{}[/tex]So the first answer is that the start heigth of the rocket is 20.
Now for the second we need to do the derivate and see the critical ponit to know the maximum, we are going to calculate first the derivate, so
[tex]h^{\prime}(x)=-32x^{}+300[/tex]now we need to find the critical ponits so for this, we are going to see when h'(x) = 0, this meand when the derivate is equal to zero, so h'(x) = 0 when
[tex]\begin{gathered} -32x\text{ + 300 =0} \\ 300\text{ = 32x} \\ \frac{300}{32}=x \end{gathered}[/tex]to see if this critical poni is a maximum we need to calculate the secon derivate and see that the second derivate valued in 300/32 is smaller than 0, so
[tex]h^{\doubleprime}(x)\text{ = -32}[/tex]now when x= 300/32 we have that h''(x) is -32 because the second derivate is constant, in this case h''(300/32) < 0, because of this the answer is that 300/32 is the maximum, bur 300/32 = 75/8.
Now for the third question, we need to see the roots of h, so we need to see when h is zero, so for wich values of x we have that h(x) = 0, then
[tex]-16x^2+300x+20=0^{}[/tex]we can solve this with the quadratic equation to solve this kind of equations. This equation is
so we have that
[tex]\begin{gathered} x\text{ = }\frac{-300\text{ }\pm\sqrt[]{300^2\text{ -4(-16)20}}}{2(-16)} \\ x\text{ = }\frac{-300\text{ }\pm\sqrt[]{90000\text{ + 1280}}}{-32} \\ x\text{ = }\frac{-300\text{ }\pm\sqrt[]{91280}}{-32} \end{gathered}[/tex]the answer is x = (-300 - v/ 91280)/(-32) or x = (-300 + v/ 91280)/(-32) and this is equal to x = (300 + v/ 91280)/(32) or x = (300 - v/ 91280)/(32) if you prefer. We can also write the answer in a simpler way: x = (75 + v/ 5705)/(8) or x = (75 - v/ 5705)/(8), this is
[tex]x\text{ = }\frac{75\text{ }\pm\sqrt[]{5705}}{8}[/tex]Well we just need to do the analise of the function h, so for the first question we need to know what is the value of h when x=0, so if we evaluate we see that
[tex]h(0)=-16(0)^2+300(0)^{}+20^{}=20^{}[/tex]So the first answer is that the start heigth of the rocket is 20.
Now for the second we need to do the derivate and see the critical ponit to know the maximum, we are going to calculate first the derivate, so
[tex]h^{\prime}(x)=-32x^{}+300[/tex]now we need to find the critical ponits so for this, we are going to see when h'(x) = 0, this meand when the derivate is equal to zero, so h'(x) = 0 when
[tex]\begin{gathered} -32x\text{ + 300 =0} \\ 300\text{ = 32x} \\ \frac{300}{32}=x \end{gathered}[/tex]to see if this critical poni is a maximum we need to calculate the secon derivate and see that the second derivate valued in 300/32 is smaller than 0, so
[tex]h^{\doubleprime}(x)\text{ = -32}[/tex]now when x= 300/32 we have that h''(x) is -32 because the second derivate is constant, in this case h''(300/32) < 0, because of this the answer is that 300/32 is the maximum, bur 300/32 = 75/8.
Now for the third question, we need to see the roots of h, so we need to see when h is zero, so for wich values of x we have that h(x) = 0, then
[tex]-16x^2+300x+20=0^{}[/tex]we can solve this with the quadratic equation to solve this kind of equations. This equation is
so we have that
[tex]\begin{gathered} x\text{ = }\frac{-300\text{ }\pm\sqrt[]{300^2\text{ -4(-16)20}}}{2(-16)} \\ x\text{ = }\frac{-300\text{ }\pm\sqrt[]{90000\text{ + 1280}}}{-32} \\ x\text{ = }\frac{-300\text{ }\pm\sqrt[]{91280}}{-32} \end{gathered}[/tex]the answer is x = (-300 - v/ 91280)/(-32) or x = (-300 + v/ 91280)/(-32) and this is equal to x = (300 + v/ 91280)/(32) or x = (300 - v/ 91280)/(32) if you prefer. We can also write the answer in a simpler way: x = (75 + v/ 5705)/(8) or x = (75 - v/ 5705)/(8), this is
[tex]x\text{ = }\frac{75\text{ }\pm\sqrt[]{5705}}{8}[/tex]Which situation represents a proportional relationship?
O Renting a movie for $2 per day
O Renting a movie for $2 per day with a coupon for $0.50 off for the first day
O Renting a movie for $2 per day along with paying a $5 membership fee
O Renting a movie for $2 for the first day and $1 for each day after the first day
Answers
The option D that is "Renting a movie for $2 for the first day and $1 for each day after the first day" shows a proportional relationship as they are in proper ratio.
What is proportional relationship?Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportional relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.
What is ratio?A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
As they are in the right ratio, option D, "Renting a movie for $2 for the first day and $1 for each day after the first day," demonstrates a proportional relationship.
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In a right triangle, the side opposite angle β has a length of 16.4 cm. The hypotenuse of the triangle has a length of 25.1 cm. What is the approximate value of sin(β)?
Answers
Given
Length of hypotenuse= 25.1 cm
length of BC = 16.4 cm
Find
Value of
[tex]sin\beta[/tex]Explanation
As , we know
[tex]sin\beta=\frac{opposite}{hypotenuse}[/tex]now, put values
[tex]sin\beta=\frac{16.4}{25.1}=0.653[/tex]Final Answer
Value of
[tex]sin\beta=0.653\text{ approx}[/tex]What is the factored form of the expression 18x +12y -30?
Answers
Let's begin by listing out the information given to us:
[tex]18x+12y-30[/tex]Factoring means we will use the common factor of the elements to break down the expression into a simpler form:
[tex]6(3x+2y-5)[/tex]Simplify the problem and use the chart to find the answer.
Answers
When an exponent is a fraction, the number of the numerator is the exponent and the number of the denominator is the radical number:
Then, in this case:
Since
[tex]\sqrt[2]{x^3}=\sqrt[]{x^3}[/tex](when the number of the radical is 2 we can write it without the 2), then
[tex]\sqrt[2]{x^3}=\sqrt[]{x^3}[/tex]Then
Answer: III
copy and complete each problem
/20 = 11/55
Answers
Answer:
[tex]\frac{4}{20}[/tex] = [tex]\frac{11}{55}[/tex]
Step-by-step explanation:
[tex]\frac{x}{20}[/tex] = [tex]\frac{11}{55}[/tex] cross multiply and solve for x
55x = 11(22)
55x = 220 Divide both sides by 55
x = 4
The denominator of a fraction is five more than twice the numerator if both the numerator and the denominator are decreased by three the simplified result is 1/4 find the original fraction
Answers
Answer:
7/19
Step-by-step explanation: we could get two equations from the question if we set the denominator as x and the numerator as y:
1: x=2y+5
2:(y-3)/(x-3)=1/4
cross multiply
4(y-3)=1(x-3)
4y-12=x-3
x=4y-9
3: Then we can choose one of them and minus by another one
x-x=4y-2y-(9+5)
0=2y-14
2y=14
y=7
Then we only have to plug in
x=2*7+5
x=14+5
x=19
Johnny is going to use ASA to prove that VWX=YZX.Which of these is a necessary step in Johnny's proof? A. Prove that WX= XZby CPCTC.B. Prove that VW=YZ by CPCTC.C. Prove that VWX=YZX by alternate interior angles.D. Prove that VXW = YXZ by vertical angles.
Answers
In order to prove that two triangles are congruent using the ASA theorem, it is necessary to show two pairs of congruent angles and one pair of congruent sides of the triangles.
In the given diagram, there is already a pair of congruent triangles and a pair of congruent sides shown.
Then, in order to use the ASA theorem, we need to prove that there is another pair of congruent angles, one from each triangle.
Since the side VX must be adjacent to both angles involved in the procedure, then we need to show that the angle VXW is congruent to the angle YXZ, which is adjacent to the side YX.
This can be proven using the fact that VXW and YXZ are vertical angles.
Therefore, the necessary step in Johnny's proof is shown in option D)
[tex]\text{Prove that }\angle VXW\cong\angle YXZ\text{ by vertical angles}[/tex]Hello, I need some assistance with this homework question please for precalculusHW Q11
Answers
A polynomial has the following form:
[tex]P(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_2x^2+a_1x+a_0[/tex]Therefore, the function is a polynomial
Answer:
It is a polynomial of degree 3.
The standard form of a 3rd degree polynomial is given by:
[tex]P(x)=ax^3+bx^2+cx+d[/tex]So:
The polynomial in standard form is:
[tex]f(x)=x^3+3x[/tex]With the leading term x³ and the constant 0.
Review The measure of m
Answers
in the given image
m it is given that m
120 = 3x - 5 + 2x
120 = 5x - 5
5x = 120 + 5
x = 125/5
x = 25
so the value of x is 25
So, mm
m = 3 (25) - 5
= 75 - 5
mso, m
the, sum of the angles
so,
120 + mmm
what is the area of the regular 15-gon with radius 12mm?
Answers
The regular pentagon can divide into 5 congruent isosceles triangles
The equal sides of each triangle have length r and vertex angle of measure 72 degrees
Then we will use the sine rule of the area to find the area of each triangle, then multiply it by 5 to get the area of the pentagon
Since the radius is 7mm, then
r = 7
[tex]A=5\times\frac{1}{2}\times r\times r\times sin72[/tex]Substitute r by 7
[tex]\begin{gathered} A=5\times\frac{1}{2}\times7\times7\times sin72 \\ \\ A=116.5044232\text{ mm}^2 \end{gathered}[/tex]Round it to the nearest whole number
A = 117 mm^2
The area of the pentagon is 117 mm^2
Find the Z-score for which 5% of the distributions area lies between-z and z
Answers
The equation that will represent this situation will be:
[tex]\begin{gathered} P(-z\le x\le z)=P(x\le z)-(1-P(x\le z))=0.05 \\ \end{gathered}[/tex]Thus:
[tex]\begin{gathered} P(x\le z)-1+P(x\le z)=0.05 \\ 2\cdot P(x\le z)-1=0.05 \\ 2\cdot P(x\le z)=0.05+1 \\ 2\cdot P(x\le z)=1.05 \\ P(x\le z)=\frac{1.05}{2} \\ P(x\le z)=0.525 \end{gathered}[/tex]If we check in a standard normal table. the z-score that corresponds to a probability of 0.525 is 0.063.
Answer: z-score is 0.063.
what are the lenghths of the legs in the triangle?give your answer in simplest radical form or rounded to the nearest hundredth.
Answers
Here, we are given a 45°-45°-90° triangle.
Let's find the length of the legs.
A 45°-45°-90° triangle is an isosceles triangle, and the two legs of an isosceles triangle are of equal lengths.
To find the length of each leg apply the formula:
[tex]c=a\sqrt[]{2}[/tex]Where;
c = 12
Thus, we have:
[tex]12=a\sqrt[]{2}[/tex]Solve for a:
Divide both sides by √2
[tex]\begin{gathered} \frac{12}{\sqrt[]{2}}=\frac{a\sqrt[]{2}}{\sqrt[]{2}} \\ \\ \frac{12}{\sqrt[]{2}}=a \\ \\ a=\frac{12}{\sqrt[]{2}} \\ \\ \text{Simplify the denominator:} \\ a=\frac{12}{\sqrt[]{2}}\ast\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ \\ a=\frac{12\sqrt[]{2}}{2} \\ \\ a=6\sqrt[]{2} \end{gathered}[/tex]Therefore, the length of each leg in radical form is 6√2
ANSWER:
[tex]6\text{ }\sqrt[]{2}[/tex]make a conjecture about each value or geometric relationship.
The relationship between the angles of a triangle with all sides congruent.
Answers
Congruence of all sides implies congruence of all angles. All of the angles line up.
What is geometric conjecture?
According to Thurston's geometrization conjecture in mathematics, each of a select group of three-dimensional topological spaces has a distinctive geometric structure that can be connected to it.
How do the angles of a triangle with congruent sides relate to one another?
We refer to a triangle as being equilateral when its three sides are congruent. We add a slash mark to the sides that are congruent. An equilateral triangle always has 60° angles.Learn more about congruent
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Writing and evaluating a function modeling continuous exponential growth or decay given two outputs
Answers
Explanation
The model has the form
[tex]y=ae^{-kt}[/tex]Where a=initial amount
y= final amount
K= growth rate constant
t= time
When 140 kg of substance is left after 7 hours, the formula can be remodeled to be.
[tex]\begin{gathered} 140=400e^{-7k} \\ e^{-7k}=\frac{140}{400} \\ e^{-7k}=\frac{7}{20} \\ \ln (e^{-7k})=\ln (\frac{7}{20}) \\ -7k=\ln (\frac{7}{20}) \\ k=\frac{\ln(\frac{7}{20})}{-7} \\ \therefore k=\frac{\ln (\frac{20}{7})}{7} \end{gathered}[/tex]Therefore, the first solution is
[tex]y=400e^{-\ln (\frac{20}{7})\frac{t}{7}}[/tex]For part b we have 16 hours.
[tex]\begin{gathered} y=400e^{-\ln (\frac{20}{7})\frac{t}{7}}=400e^{-\ln (\frac{20}{7})\frac{16}{7}} \\ y=36.302\approx36\operatorname{kg}\text{ (To the nearest whole number)} \end{gathered}[/tex]Thus, the answer is 36kg
A cubic function has turning points at (-1,2) and (1,-2). Which could be its graph?
Answers
ANSWER
Graph D is the correct option
EXPLANATION
The turning points of a function are the points where its derivative changes sign - therefore the slope of the function changes sign. In other words, the turning points are the local maximums and local minimums of the function.
From these options, the one that has a local maximum/minimum at point (-1, 2) and another at point (1, -2) is option D.
State the domain using an appropriate notation and evaluate f(2)
Answers
The domain of a function or coordinates of a function are the input values of the function "x" for which the function exists.
For instance, given the coordinates of the function {(-7, 2), (0, -2), (2, 5), (8, 1)}, the corresponding value of the x-coordinates are the domain. Therefore the domain of the given coordinate points are given as;
[tex]\text{Domain}=\mleft\lbrace-7,0,2,8\mright\rbrace[/tex]Get the value of f(2).
To get the value of f(2), we will find the y-value of the coordinate with a domain of 2. From the given coordinates, we can see that the coordinate that has a domain of 2 is (2, 5) and the corresponding y-value of the coordinate is 5. Hence f(2) = 5
what is the rate change of the equation?Y=8x+20Remember Y=MX+B
Answers
The general equation of the line : y = m * x + b
where m is the slope , b is y -intercept
Given the function :
[tex]y=8x+20[/tex]The rate of change of the equation = the slope of the function
So, by comparing the given equation to the general from
The slope = m = 8
So, the rate of change = 8
Sophie has $4.20 worth of dimes and quarters. She has twice as many quarters asdimes. Write a system of equations that could be used to determine the number ofdimes and the number of quarters that Sophie has. Define the variables that you useto write the system.
Answers
d = 2q .........................................................................(1)
0.1d + 0.25q = 4.20 ................................................(2)
Explanation:Let d be the number of dimes, and q be the number of quarters Sophie has.
Since she has twice as many quarters as dimes, and they are worth $4.20, we have:
d = 2q .........................................................................(1)
Also, because:
1 dime = $0.1
1 quarter = $0.25
0.1d + 0.25q = 4.20 ..................................................(2)
Equation (1) and (2) can be solved to determine the number of dimes and quarters
Question 5 of 40Roxanne likes to fish. She estimates that 30% of the fish shecatches are trout, 20% are bass, and 10% are perch. Shedesigns a simulation.
Answers
30% are trout, 20% are bass, 10% are perch
what is the chance that one of the next 4 is a bass
20% are bass
100 - 20 = 80
0.8^4 = 0.4096
1 - 0.4096 = 0.5904
of the 20 simulation results, 12 had bass
12/20 = 0.6
B) 60% estimate
59.04% actual
Find the simple interest owed for the following loan. Principal = 2775 Rate = 7.5% Time = 5 1/2 years
Answers
We would apply the simple interest formula which is xpressed as
I = PRT/100
Where
I represents interest
P represents principal or amount borrowed
T represents time in years
R represents rate.
From the information given,
P = 2775
R = 7.5
T = 5 1/2 = 5.5
I = (2775 * 7.5 * 5.5)/100
I = 1144.6875
Rounding to the nearest cent,
I = 1144.69
A contractor bought 10.8 ft² of sheet metal. He has used 3.5 ft² so far and has $219 worth of sheetmetal remaining. The equation 10.8x - 3.5x = 219 represents how much sheet metal is remainingand the cost of the remaining amount. How much does sheet metal cost per square foot?
Answers
The first step to do is to combine 10.8x - 3.5x and that is equal to 7.3x.
[tex]7.3x=219[/tex]The next step is to divide both sides by 7.3 to solve for x.
[tex]\begin{gathered} \frac{7.3x}{7.3}=\frac{219}{7.3} \\ x=30 \end{gathered}[/tex]Therefore, the remaining sheet metal is 7.3 ft² and the cost per square foot of sheet metal is $30.
Calculating a rate of change
What is the vertical change form Point A to Point B?
What is the horizontal change from Point A to Point B ?
What is the rate of change shown on the graph? Give the answer as a decimal rounded to the nearest tenth, if necessary?
Answers
Hello there. To solve this question, we'll have to remember some properties about rate of change.
Given the points A and B from a line, we want to determine the vertical change and the horizontal change between the points and then, using these values, determine the rate of change of the function (the line passing through them).
For this, we first find the coordinates of the points.
[tex]A=(2,1)\text{ and }B=(4,2)[/tex]The vertical change is the difference between the y-coordinates of the points, hence
[tex]y(B)-y(A)=2-1=1[/tex]The horizontal change is given by the difference between the x-coordinates of the points, therefore
[tex]x(B)-x(A)=4-2=2[/tex]The rate of change of this function is, finally, given by the ratio between the vertical (rise) and horizontal (run) changes of the function:
[tex]\dfrac{1}{2}=0.5[/tex]This is the rate of change of this function.
Cilantro earns $17.43 per hour. If Cilantro works 27 hours in a week, what will Cilantro's earnings be for the week?
Answers
Let be "x" Cilantro's earnings (in dollars) for the week.
According to the explained in the exercise, Cilantro makes $17.43 per hour and works a total of 27 hours per week.
With that information, you can set up the following proportion:
[tex]\frac{$17.43\text{dollars}$}{1\text{hour}}=\frac{x}{27\text{hours}}[/tex]In order to find the value of "x", you need to solve for it. You can apply the Multiplication property of equality and multiply both sides of the equation by 27 hours.
Therefore, you get this result:
[tex]\begin{gathered} (27\text{hours)(}\frac{$17.43\text{dollars}$}{1\text{hour}})=(\frac{x}{27\text{hours}})(27\text{hours)} \\ x=470.61\text{dollars} \end{gathered}[/tex]Then, Cilantro's earnings for the week will be $470.61