Solve the following compound inequalities. Use both a line graph and interval notation to write each solution set.
Answers
The required value of t is (-∞, -6) U (4, ∞).
What is a linear inequality and how is it solved?
Expressions with linear inequalities compare any two values using inequality symbols like "<" and ">." The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. Polynomial inequality, rational inequality, and absolute value inequality are the several types of inequalities that exist in mathematics.
First, create an equation for the inequality. The given equation must be solved for one or more values. Represent all of the values that you found on the number line now. On the number line, use open circles to symbolize the excluded values. the interval, then. To determine whether the values satisfy the inequality equation, substitute any random value from the interval into the inequality equation. The solutions of the given inequality equation are intervals that fulfil the inequality equation.
Given, the linear inequalities are t + 1 < -5 and t + 1 > 5
Solving the first inequality, t + 1 < -5 ⇒ t < -5 -1 ⇒ t < -6
Again, solving second inequality, t + 1 > 5 ⇒ t > 5 - 1 ⇒ t > 4
Combining the solution of both the inequalities, we have;
the value of t can take any value in (-∞, -6) U (4, ∞).
Therefore, the required value of t is (-∞, -6) U (4, ∞).
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Related Questions
write an equation of the line in the point- slope form that passes through the given points in the table. Then write the equation in slope-intercept form. (10,80) (5,65)
Answers
To write the equation of the line that passes through (10,80) (5,65)
we will use the formula;
[tex]y-y_1\text{ =}\frac{y_{2-}y_1}{x_2-x_1}(x-x_1)[/tex]x₁ = 10 y₁ = 80 x₂ = 5 y₂ = 65
substituting the above into the formula;
[tex]y\text{ - 80 = }\frac{65\text{ - 80}}{5\text{ - 10}}(\text{ x - 10)}[/tex]we will go ahead and simplify
[tex]y\text{ - 80 = }\frac{-15}{-5}(x-10)[/tex]y- 80 = 3(x - 10)
y- 80 = 3x - 30
y -3x -80 + 30 = 0
y - 3x - 50 = 0
The above is the equation of the line.
To write in a slope-intercept form simply means to write it in the form;
y = mx + b
where m is the slope and b is the intercept
Hence;
y = 3x + 50
The above is the equation of the line in a slope-intercept form
the sum of negative three and a number, divided by seven, is negative two
Answers
Answer:
-3+x/7=-2 is equation, 7 is the answer
Step-by-step explanation:
-3+x/7=-2 add 3 to both sides.
x/7=1 multiply 7 to both sides
x=7 this is the answer
Dilate the figure by the scale factor. Then enterthe new coordinates.A(1,3)B(4,2)K=3A’([?],[]).B'([10]C'([],[:]C(1,-3)Enter
Answers
The new coordinates after the dilation are as follows;
[tex]\begin{gathered} A^{\prime}\text{ (3,9)} \\ B^{\prime}\text{ (12,6)} \\ C^{\prime}\text{ (3,-9)} \end{gathered}[/tex]Here, we want to perform a dilation
Given a pre-image with coordinates (x,y) and a scale factor of k, the coordinates of the image will be;
[tex](x,y)\text{ = (kx,ky)}[/tex]Applying this to the given coordinates, we have;
[tex]\begin{gathered} A^{\prime}\text{ = }(3\times1,3\times3)\text{ = (3,9)} \\ B^{\prime}=\text{ (4}\times3,\text{ 2}\times3)\text{ = (12,6)} \\ C^{\prime}\text{ = (1}\times3,\text{ -3}\times3)\text{ = (3,-9)} \end{gathered}[/tex]D Question 6 6) sin A С 39 36 15 B 5 12 A) B) 12 13
Answers
B) 12/13
1) In this triangle, the sine of angle A is given by the opposite leg over the hypotenuse, so we can write it out. Since the hypotenuse is opposite to the right angle:
[tex]\begin{gathered} \sin (A)=\frac{36}{39} \\ \sin (A)\text{ = }\frac{12}{13} \end{gathered}[/tex]Note that we simplified that original ratio 36/39 dividing both numerator and denominator by 3
2) Hence, the answer is B) 12/13
2) Create the first four terms based on the given recursive formulas below. Also determine if the
sequence you made is an arithmetic or geometric sequence:
G(1) = 18, G(n) = 2 · G(n − 1). H(1) = 3,H(n) = 5 · H(n − 1)
-
-
J(1) = 3, J(n) = J(n − 1) + 5 M(1) = 3, M(n) = 2 · (n − 1)
Answers
The first 4 terms of given recursive formulas will be as follows
G(n) = 18,36,72,144 (geometric sequence)H(n) = 3, 15, 75, 325 (geometric sequence)J(n) = 3, 8, 13, 18 (arithmetic sequence)M(n) = 3, 6, 12, 24 (geometric sequence)Recursive Expression:The recursive expression provides two pieces of information:
the first term in the sequence.
the pattern rule that takes each term from the previous term.
As we have G(1) = 18, G(n) = 2 · G(n − 1).
It's A geometric sequence with r as 2
∴ G(2) = 2 · G(2 − 1) = 2 · G(1) = 2(18) = 36.
∴ G(3) = 2 · G(3 − 1) = 2 · G(2) = 2(36) = 72.
∴ G(4) = 2 · G(4 − 1) = 2 · G(3) = 2(72) = 144.
As we have H(1) = 3, H(n) = 5 · H(n − 1).
It's A geometric sequence with r as 5
H(2) = 5 · H(2 − 1) = 5 . H(1) = 5(3) = 15.
H(3) = 5 · H(3 − 1) = 5 . H(2) = 5(15) = 75.
H(4) = 5 · H(4 − 1) = 5 . H(3) = 5(75) = 325.
As we have J(1) = 3, J(n) = J(n − 1) + 5
It's an arithmetic sequence with d as 5
J(2) = J(2 − 1) + 5 = J(1) + 5 = 3+5 = 8.
J(3) = J(3 − 1) + 5 = J(2) + 5 = 8+5 = 13.
J(4) = J(4 − 1) + 5 = J(3) + 5 = 13+5 = 18.
As we have M(1) = 3, M(n) = 2 · M(n − 1)
It's A geometric sequence with r as 2
M(2) = 2 · M(2 − 1) = 2 · M(1) = 2(3) = 6.
M(3) = 2 · M(3 - 1) = 2 · M(2) = 2(6) = 12.
M(4) = 2 · M(4 - 1) = 2 · M(3) = 2(12) = 24.
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HELP PLEASEEEEE!!!!!!
Answers
A rational number between the two given ones is -2/5, such that:
-1/3 > -2/5 > -1/2.
How to find a rational number between the two given ones?Rememeber that a rational number is any number that can be written as a quotient between two integer numbers.
Here we want to find a rational number between -1/3 and 1/-2, we can rewrite the second one as -1/2.
Now we want to find a number x such that:
-1/3 > x > --1/2
Remember that:
-1/3 ≈ -0.33...
-1/2 ≈ -0.5
So a number between these two is -0.4 which can be written as -2/5 (this is also rational).
That is the number we wanted to find.
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Find the distance between: (6,12) and (7,-4)
Answers
The formula for determining the distance betwwen two points is expressed as
[tex]\begin{gathered} \text{Distance = }\sqrt{(y2-y1)^2+(x2-x1)^2} \\ \text{From the information given,} \\ x1\text{ = 6, x2 = 7} \\ y1\text{ = 12, y2 = - 4} \\ \text{Distance = }\sqrt{(-4-12)^2+(7-6)^2} \\ \text{Distance = }\sqrt{-16^2+1^2}=\sqrt{257} \\ \text{Distance = 16.03} \end{gathered}[/tex]The distance is 16.03
1 i Solve the system of linear equations. y = -2x - 4 y = 2x - 4
Answers
In order to solve the system, we can compare both y values from each equation:
[tex]\begin{gathered} \begin{cases}y=-2x-4 \\ y=2x-4\end{cases} \\ -2x-4=2x-4 \\ 4x=0 \\ x=0 \\ \\ y=2x-4 \\ y=0-4 \\ y=-4 \end{gathered}[/tex]So the solution for this system is the pair (0, -4), that is, x = 0 and y = -4.
create your own systems of equations that has a solution of (-2,4)
Answers
In this case we have the point (-2,4), since this represents the x and y coordinates of the solution of the system of equations, then:
x= -2
y= 4
Let's create the pair of equations:
1. ax+by=c
2. ex+fy=g
Randomly let's define the values of the coefficients a, b, e and f:
a= 1
b=2
e= -1
f= 4
With these values and the known coordinates of the solution, let's replace into the expressions of the system of equations and solve for c and g, like this:
It costs $5,600 to manufacture a Jet Ski. If the desired percent markup based on cost is 48%, how much should each Jet Ski sell for?
Answers
Each Jet Ski should sell for $8288.
What is selling price?
The amount a buyer pays for a good or service is known as the selling price. It may differ based on the price that buyers are prepared to pay, the seller's acceptance threshold, and how competitive the price is in relation to those of other companies in the market.
Let the selling price be x.
Therefore according to the question,
( x - 5600/ 5600) 100 = 48
=> x - 5600 = 48 . 56
=> x = 2688 + 5600
=> x = 8288
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Write the equation of the line that passes through the given points.
(0, 1) and (2, 2)
Answers
The equation of the line passing through points (0,1) and (2,2) will be y = ( 1 / 2) x + 1
What is an equation of the line?
An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope= 2-1 / 2-0 = 1 /2
Now pick one of the points and put in for y and x use (2,2).
2= 1/2(2) +b
2=1 + b
2-1 =1-1 +b subtract 1 from each side
1 = b This is your y-intercept
The equation will be written as:-
y = ( 1 / 2) x + 1
The probability distribution for arandom variable x is given in the table.Find the probability that x>5
Answers
The probability that x≥5
P (x≥5) = P(5)+P(10)+P(15)+ P(20)
P (x≥5)= 0.1+0.25+0.1+0.15
P (x≥5)= 0.6
HELP PLEASEEEEE!!!!!!
Answers
Negatives act the opposite for positives so be careful for this.
A jet flies at an average speed of 230
miles per hour. How long will it take to
fly from New York to Amsterdam, a
distance of 3,647 miles? (distance =
rate time)
.
Answers
Answer:
15
Step-by-step explanation:
Speed= 230 per hour
Distance=3,647
Formula
Time=Distance upon speed
divide 230 into 3,647=15 time
Which is equivalent to multiplying a number by 10 to the power of 4
Answers
Answer: 10,000
Step-by-step explanation:
the figure above represents a closed cylindrical tank of height 15m.the radius of the Cross-section is 7m. Calculate a) the curved surface area of the tank. b) the volume of the tank. use π=22/7
Answers
Answer:
a) The curved surface area is;
[tex]660\text{ }m^2[/tex]b) The volume of the cylindrical tank is;
[tex]2310\text{ }m^3[/tex]Explanation:
Given that the cylindrical tank has height 15m and radius 7m.
[tex]\begin{gathered} h=15\text{ m} \\ r=7\text{ m} \\ \pi=\frac{22}{7} \end{gathered}[/tex]The curved surface area of a cylinder can be calculated using the formula;
[tex]A=2\pi rh[/tex]substituting the given values;
[tex]\begin{gathered} A=2\times\frac{22}{7}\times7\times15 \\ A=660m^2 \end{gathered}[/tex]Therefore, the curved surface area is;
[tex]660\text{ }m^2[/tex]The volume of the cylindrical tank can be calculated using the formula;
[tex]V=\pi r^2h[/tex]Substituting the given values;
[tex]\begin{gathered} V=\frac{22}{7}\times7^2\times15 \\ V=2310m^3 \end{gathered}[/tex]Therefore, the volume of the cylindrical tank is;
[tex]2310\text{ }m^3[/tex]If EFGH is a parallelogram, what is the value of x?F(4-2)340HGA. 82B. 30.5cC. 36D. 37E. 34F. 9
Answers
x = 36° (option C)
Explanation:The adjacent angles in a parallelogram are supplementary. This means the sum of the angles is equal to 180 degrees
The adjacent angles in this paralllelogram are (4x + 2)° and 34°
(4x + 2)° + 34° = 180°
4x + 2 + 34 = 180
4x + 36 = 180
4x = 180 - 36
4x = 144
Divide both sides by 4:
4x/4 = 144/4
x = 36° (option C)
The table shows the proportional relationship between the number of uniform shirts for a soccer team and the cost. Number of Uniform Shirts Cost (in dollars) 9 148.50 15 247.50 21 346.50 Determine the constant of proportionality. 99.50 54 16.50 6
Answers
The constant of proportionality that lies in all of the pairs of values that we have here is given as 17.5
What is the constant of proportionality?This is the term that is used to refer to the ratio that is known for the fact that it helps to relate two values that are given in a proportional way.
For instance we are to find the constant proportionality of (9, 148.50)
This is given as 9 + 148.5 / 9
= 157.5 / 9
= 17.5
Then the second pair is (15 ,247.50)
In the same way 15 + 247.50 / 15 = 17.5
Hence we can see that the constant of proportionality in all of the pairs is 17.5
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Answer:
its 16.50 i literally just took the test trust me.
Step-by-step explanation:
9 x 16.50 = 148.50
15 x 16.50= 247.50
21 x 16.50 = 346.50!
hope this helps! =)
a) Find the exact solution of
log 3(2x - 1) + log 3(2x + 1) = log 3(x + 2)
While x = 1
Answers
The exact solution of log 3(2x - 1) + log 3(2x + 1) = log 3(x + 2) While x = 1 is 0.954.
Given:
log 3(2x - 1) + log 3(2x + 1) = log 3(x + 2)
= log 3(x + 2)
putting x = 1
= log 3( 1 + 2 )
= log 3 . 3
= log 3 + log 3
= 0.477 + 0.477
=0.954
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the income for selling x units of a video game is R=257x. The cost to produce the game is C =193x +5248. In order to make a profit the income must be greater than the cost. find the vaule of X
Answers
The value of x when the income for selling x units of a video game is R=257x is x > 82.
What is the value of x?From the information given, it was stated that the income for selling x units of a video game is R=257x and that the cost to produce the game is C =193x +5248.
To make a profit the income must be greater than the cost. The value of x will be:
257x > 193x + 5248
Collect like terms
257x - 193x > 5248
64x > 5258
Divide
x > 5248/64
x > 82
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Cylinder 1 is congruent to cylinder 2. The dimensions of the cylinders are given inunits.Cylinder 1Cylinder 238What is the volume of cylinder 2?
Answers
Since the two cylinders are congruent, it means that their dimensions are exactly the same thing.
In other words, the radius of cylinder 1 is the same as that of cylinder 2, and the height of cylinder 2 is the same as that of cylinder 1. This is what it means for two solid shapes to be congruent.
Now, to find the volume of cylinder 2, we apply the frmula for the volume of a tyical cylnder:
[tex]\text{Volume}=\pi\times r^2\times h[/tex]Now,
radius of cylinder 2 = radius of cylinder 1 = 3
height of cylinder 2 = 8
Thus: r = 3, h= 8
Therefore:
[tex]\begin{gathered} \text{Volume}=\pi\times r^2\times h \\ \text{Volume}=\pi\times3^2\times8 \\ \text{Volume}=\pi\times9^{}\times8 \\ \text{Volume}=\pi\times72 \\ \text{Volume}=72\pi\text{ cubic units} \end{gathered}[/tex]Therefore the volume of cylinder 2 is 72pi cubic units (Option D)
Sketch the graph of the line whose equation, in point-slope form, is y-3=9/5 (x+1). Also write the equation of this line in slope- intercept form .(y=mx+b )
Answers
Given the equation of the line in point-slope form:
[tex]y-3=\frac{9}{5}(x+1)[/tex]Based on this, one point of the line is (-1, 3). Now, the slope-intercept form of the equation is:
[tex]\begin{gathered} y-3=\frac{9x}{5}+\frac{9}{5} \\ y=\frac{9}{5}x+\frac{9}{5}+3 \\ \Rightarrow y=\frac{9}{5}x+\frac{24}{5} \end{gathered}[/tex]Then, another point of the line is (0, 24/5) = (0, 4.8). Finally, the graph of the equation is:
If f(x)= x² + 5x and g(x) = 3x + 2, finda. (f+g)(2) by evaluating f(2) and g(2).f(2)= g(2)=ƒ(2) + g(2) =b. (f+g)(x)=c. Evaluate your formula from part b at x = 2 to verify your answer to part a.(f+g)(2)=
Answers
Given:
f(x)= x² + 5x and g(x) = 3x + 2
Required:
To calculate
f(2)= g(2)=
(f+g)(x)=
(f+g)(2)=
Explanation:
a)-
[tex]\begin{gathered} f(2)=(x^2+5x)(2) \\ \\ =((2)^2+5(2)) \\ \\ =(4+10)=14 \\ \\ g(2)=(3x+2) \\ \\ =(3\times2+2) \\ \\ =(6+2)=(8) \end{gathered}[/tex][tex]\begin{gathered} f(2)+g(2) \\ \\ =(2^2+5\times2)+(3\times2+2) \\ \\ =(4+5\times2)+(3\times2+2) \\ \\ =(4+10)+(6+2) \\ \\ =(14)+(8) \\ \\ =22 \end{gathered}[/tex]b)-
[tex]\begin{gathered} f(x)+g(x) \\ \\ f(x)+g(x)=(x^2+5x)+(3x+2) \\ \\ determine\text{ the sign} \\ \\ x^2+5x+3x+2 \\ \\ \\ x^2+8x+2 \end{gathered}[/tex]c)-
[tex]\begin{gathered} (f+g)(x) \\ \\ (x^2+5x+3x+2)(2) \\ \\ (x^2+8x+2)(2) \\ \\ ((2)^2+8(2)+2) \\ \\ (4+16+2) \\ \\ (22) \end{gathered}[/tex]Required answer:
[tex]\begin{gathered} a)-22\text{ } \\ \\ b)-x^2+8x+2 \\ \\ c)-22 \end{gathered}[/tex]Question
Marco is writing a coordinate proof involving a right isosceles triangle. Marco places his triangle on the coordinate plane such that the base of the triangle lies along the x-axis.
What coordinates should he assign to this third vertex of the isosceles triangle?
Responses
(2a, 2b)
begin ordered pair 2 a comma 2 b end ordered pair
(a, b)
begin ordered pair a comma b end ordered pair
(b, a)
begin ordered pair b comma a end ordered pair
(b, b)
Answers
Given mn, find the value of x.
(x+14)°
(9x-4)º
Answers
Answer: x = 17
Step-by-step explanation:
We can tell that these two angles are supplementary angles because we can use corresponding angles. See attached.
(x + 14)° + (9x - 4)° = 180°
x° + 14° + 9x° - 4° = 180°
14°- 4° + x° + 9x° = 180°
10° + 10x° = 180°
10x° = 170°
x = 17
Write 0.00128 in scientific notation
Answers
Given:
[tex]0.00128[/tex]To write it in scientific notation:
It can be written as,
[tex]\begin{gathered} 0.00128=\frac{1.28}{1000} \\ =\frac{1.28}{10^3} \\ =1.28\times10^{-3} \end{gathered}[/tex]Hence, the scientific notation is,
[tex]1.28\times10^{-3}[/tex]III Comprehensive Mid term Review Part Question 2 of 60 (1 point) | Question Attempt: 1 of Unlimited 2 6 3 4 Convert 35°F to degrees Celsius. If necessary, round your answer to the nearest tenth of a degree. Here are the formulas. 5 C (F-32) 9 FC + 32 5 25 OF
Answers
Here, we want to make a unit conversion
Since we want to move from Fahrenheit to celsius, we are going to use the first formula
We simply are going to substitute the value of F = 35 into the equation
Thus, we have it that;
[tex]\begin{gathered} C\text{ = }\frac{5}{9}(35-32) \\ C\text{ = }\frac{5\times3}{9} \\ \\ C\text{ =}\frac{5}{3} \\ C\text{ = 1.7 deg celsius} \end{gathered}[/tex]I need help finding at least three solutions 10 8 7 6 4 = 2 you can add subtract and/or divide
Answers
You can only subtract or divide?
Juanita works at a telemarketing company. She makes 12 sales calls per hour. Employees are encouraged to make more than 480 calls per week. Juanita has already made 180 calls this week. How many more hours, x, does Juanita need to work this week to reach the weekly goal of sales calls?
Answers
Using the mathematical operations of subtraction and division, Dan needs more than 25 hours to make more than 300 sales calls for this week to achieve the weekly goal.
What are the mathematical operations?Subtraction and division operations are two of the basic mathematical operations.
The subtraction operation involves operating on the minuend using the subtrahend to arrive at the difference.
In other words, the difference from a subtraction operation is the minuend minus the subtrahend.
The division operation is then applied to the difference above to arrive at the quotient.
The number of sales calls per hour = 12
The expected sales calls per week > 480
The number of sales calls already made by Juanita = 180
The more hours required to make more than 300, x, is 25 or more hours (480 - 180)/12
Thus, the number of more hours, using mathematical operations, that Juanita needs to reach the weekly sales calls goal is 25 or more hours.
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Find BC.
Round to the nearest tenth.
C
12
A
87°
9
B
Answers
Answer:
C-10
A-90
B-10
Step-by-step explanation:
For rounding off to nearest tens, we compare the last digit.