The ____?____ of “ sets A and B, “ denoted by ____?____ , is the set of elements that belong to “ A or B “ or “both A or B. “
We will have the following:
*The "Union" of sets A and B, denoted by A U B is the set of elements that belong to A or B, or both A or B.
[Option A]
Solve the following compound inequalities. Use both a line graph and interval notation to write each solution set.
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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Mr. Cumme has 8 3/4 yards of material for her class. he needs to use 1/3 of the material to make an example. How many yards of material will he need to make the example?
Given:
Mr. Cumme has 8 3/4 yards of material for her class.
he needs to use 1/3 of the material to make an example.
To find the number of yards of material that he will need, we will multiply 1/3 by 8 3/4 to get the answer.
[tex]\frac{1}{3}\times8\frac{3}{4}=\frac{1}{3}\times\frac{35}{4}=\frac{35}{12}=2\frac{11}{12}[/tex]So, the answer will be 2 11/12 yards.
Create an example of a difference of
polynomials and explain how to simplify
your expression.
(9x² + 8x) - (2x²+ 3x) = 7x² + 5x .
By simplifying we get x( 7x + 5) .
What is polynomial ?Polynomials are algebraic expressions with variables and coefficients. Variables are also known as indeterminates. For polynomial expressions, we can perform arithmetic operations such as addition, subtraction, multiplication, and positive integer exponents, but not division by variable.The variables and exponents of polynomials do not change when they are subtracted. Only their coefficients are subject to change. This ensures that the difference has variables and exponents that are already classified as polynomials. As a result, the difference is always a polynomial.Consider two polynomials,
(9x² + 8x) and (2x² + 3x)
The difference of polynomials is,
(9x² + 8x) - (2x²+ 3x)
9x² + 8x - 2x²+ 3x
= 7x² + 8x - 3x
= 7x² + 5x
Simplifying we get ,
taking x common,
= x( 7x + 5) .
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find a solution of the quadratic equation.6x squared + 7x + 2 =0
Given the equation:
[tex]6x^2+7x+2=0[/tex]We will use the following rule to find the solution to the equation:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]From the given equation: a = 6, b = 7, c = 2
So,
[tex]\begin{gathered} x=\frac{-7\pm\sqrt[]{7^2-4\cdot6\cdot2}}{2\cdot6}=\frac{-7\pm\sqrt[]{1}}{12}=\frac{-7\pm1}{12} \\ x=\frac{-7-1}{12}=-\frac{8}{12}=-\frac{2}{3} \\ or,x=\frac{-7+1}{12}=-\frac{6}{12}=-\frac{1}{2} \end{gathered}[/tex]So, the answer will be option B) x = -1/2, -2/3
Determine which set of side measurements could be used to form a triangle. 12, 23, 7 10, 7, 2 8, 3, 11 5, 11, 8
Based on the triangle inequality theorem, the set of side measurements that could be used to form a triangle is: D. 5, 11, 8.
What is the Triangle Inequality Theorem?The triangle inequality theorem states that three set of side measurements, a, b, and c would form a triangle if a + b > c, that is, the sum of any of two sides should be greater than the third side.
The set of side of measurements 5, 11, 8 will form a triangle because:
5 + 11 > 8 ⇒ 16 > 8
5 + 8 > 11 ⇒ 13 > 11
8 + 11 > 5 ⇒ 19 > 8
The other set of side of measurements do not conform to this criterion set by the triangle inequality theorem, therefore, the only set of side measurements that will form a triangle is: D. 5, 11, 8.
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Answer:
D.
5, 11, 8
Step-by-step explanation:
Match the equivalent fractions
5
13
choose the correct description of the graph of the compound inequality1: A number line with an open circle on 0 shading to the left and a closed circle on 2 shading to the right2: A number line with a closed circle on 0, shading to the left, and an open circle on 2 shading to the right3: A number line with a closed circle on 2, and shading in between 4: A number line with an open circle on 2, and shading in between
Answer:
Step-by-step explanation:
0.18 times 7 Show the work to get the answer pls
1.26
1) We can calculate that by writing out this algorithm:
We proceed normally as if we had two whole numbers. Multiplying 7 by each number.
Note that since there are two decimal places in the factor 0.18 we count two decimal places from the left to the right in the product.
2) Thus the answer is 1.26
Please help with this question
Answer:
A is correct. √11 and √14 are both between 3 and 4.
which set could not represent the lengths of the slides of a triangle?
hello
to solve this question, we asume it's a right angled triangle and we use pythagorean theorem
pythagorean thorem states that the square of the longest side which is the hypothenus of a triangles is equal to the sum of the square of the two other sides which are the opposite and adjacent
according to pythagorean
[tex]x^2=y^2+z^2[/tex]now we go through the options
from the first option (3, 4, 5)
the longest side here is 5
let's check if this is true
[tex]\begin{gathered} x^2=y^2+z^2 \\ 5^2=4^2+3^2 \\ 25=16+9 \\ 25=25 \end{gathered}[/tex]option 1 is represents a triangle
let's check option 2
(2, 5, 9)
longest side = 9
[tex]\begin{gathered} 9^2=2^2+5^2 \\ 81=4+25 \\ 81\ne29 \end{gathered}[/tex]option 2 does not represents a triangle and it's the right option here
Sherry has 40% as much money as Anna. Anna has $80?
Sherry has $112.
bo
Answer: Sherry has $112
A bell rings every 20 minutes. A horn blows every 30 minutes. If Htel Htel heard the two sounds at 8:00AM, at what time will be hear the sounds together again.
Answer:
Htel Htel will hear the sounds again at 9:00 AM
Compute the complement rate where the trade discount rate is 15%.
The Complement rate where Trade discount rate is 15% = 100 - 15 = 85%.
Thanks
GEOMETRY! PLEASE HELLPPP
Answer: It would be Figure L
Step-by-step explanation:
It is supposed to be reflected off the y-axis and the only shape in that same box across is Figure L. So there, have a nice and blessed day!
Answer:
Figure L
Explanation:
It's reflected across the y-axis. The y-axis is a vertical line
Michael bought 1/2 pound of Swiss cheese. He used 1/4 pound for
a sandwich. How much was left?
Answer:
1/4
Step-by-step explanation:
1/2 - 1/4 = 2/4 - 2/4 = 1/4
Solve for b, then solve for each angle in the triangle
We know that the sum of the interior angles of a triangle equals 180, then,in this case we have the following equation:
[tex]b+2b+(b+16)=180[/tex]then, solving for b, we get:
[tex]\begin{gathered} b+2b+(b+16)=180 \\ \Rightarrow4b+16=180 \\ \Rightarrow4b=180-16=164 \\ \Rightarrow b=\frac{164}{4}=41 \\ b=41 \end{gathered}[/tex]now that we have that b = 41, we can find the measure of each angle:
[tex]\begin{gathered} b=41 \\ 2b=2(41)=82 \\ b+16=41+16=57 \end{gathered}[/tex]how do you start square roots in mathmaticals?
Answer:
a square root is basically any number multiplied by itself to get another number. there are 2 types, perfect and non perfect, perfect is when the number being multiplied by itself is an a whole number, while the non perfect is when the number that is being multiplied by itself is a decimal or fraction
Step-by-step explanation:
I dint know the answers to this and its SUPER important I get it right.
A. The corresponding angles of triangles are coungrent (YES)
B. The triangles have the same shape (YES)
C. The triangles have the same size (YES)
D. The corresponding sides of the triangles are congruent (YES)
PLEASE HURRY
What is the value of the expression −34 − 17 − (−22)?
Answer:
-29
Step-by-step explanation:
subtracting the negative 22 from the -17 made it positive until you subtract the 34 which made it -29
A country's population in 1993 was 204 million.In 2000 it was 208 million. Estimatethe population in 2015 using the exponentialgrowth formula. Round your answer to thenearest million.burP = AektEnter the correct answer.DONE?DOO
Here, we want to use the exponential growth formula to estimate the 2015 population
In order to use the exponential growth formula, we have to get some of the needed points like the growth rate or constant represented by K
At any point in time, A represents the initial popultaion, which is the population in 1993, given as 204 million
P represents the population at that point in time
k is what we want to calculate
t is the difference in the number of years
Thus, for between 1993 and 2015, we have ;
[tex]undefined[/tex]Question 6 is the target pls helo
Answer:
80°Step-by-step explanation:
the angles in a triangle add up to 180
2x + 3x + 4x = 180
(combine like terms)
9x = 180
(divide both sides by 9 to find out what x is)
x = 20
so now we know
(2x)° = 40°
(3x)° = 60°
(4x)° = 80°
What is the measure of the largest angle in the triangle shown above?
80°How do I solve this, and how do I know if I need to add or subtract at the beginning
Let's solve the system of equations using elimination:
4x + 5y = 14
-4x -2y = -8
First, we need to get rid of one variable.
Sometimes we multiply them by some factors to have the same number on one variable, but in this case, we can subtract the x variable
4x +5y =14
-4x-2y = -8
----------------------
4x-4x =0, 5y -2y = 3y and 14-8=6
------------------------------
0+3y = 6
Solve the equation for y
Divide by 3 into both sides
3y/3 = 6/3
y = 2
Then, replace this variable on one equation, whichever you want:
4x + 5y = 14
4x +5(2) = 14
4x +10 = 14
and solve the equation for x
4x +10 = 14
Subtract 10 on both sides
4x +10-10 = 14-10
4x = 4
Divide by 4 into both sides
4x/4 = 4/4
x = 1
You can replace both variables to confirm the results:
4x +5y =14
4(1) +5(2) = 14
4 +10 = 14
14 = 14
---------------------------------
-4x -2y = -8
-4(1) -2(2) = -8
-4-4 = -8
-8 = -8
The result is correct, so my ordered pair is (x,y) = (1,2)
all you need is in the photo put only the answer Don't do step by step please answer fast pleaseeeeegkg
Substitute the values of the constant in the equation to obtain the value of x.
[tex]undefined[/tex]For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.A. yes; y=2xB. yes; y=3xC. yes; y=4xD. no; y does not vary directly with x.
We are given a table with values of "x" and associated values of "y". Let's remember that direct variation implies that each value of "y" will be related with its corresponding value of "x" according to the following relationship:
[tex]y=kx[/tex]Where "k" is the constant of proportionality. If the table shown has direct variation the same constant should apply for each value. Let's take the first value of the table, that is, x = 3 and y = 6. Substituting we get:
[tex]6=k(3)[/tex]Dividing both sides by 3 we get:
[tex]\frac{6}{3}=k[/tex]Solving the operations:
[tex]2=k[/tex]Now we substitute in the relationship:
[tex]y=2x[/tex]Now, for the second value of "x", that is x = 6:
[tex]\begin{gathered} y=2(6) \\ y=12 \end{gathered}[/tex]Since we did not get the corresponding value of "y" in the table, this means that the constant of proportionality doesn't work for this value, and therefore, "y" does not vary directly with "x".
What's 9 + 10? ______________________________________________________
Answer:
Hmm, that's a tough one. I think it's 19. I'm not sure though.
Answer:
19
Step-by-step explanation:
The time to complete a standardized exam is approximately normal with a mean of 70 minutes and a standard
deviation of 10 minutes. How much time should be given to complete the exam so that 80% of the students will complete the exam in the time given?
(A) 61.6 minutes
(B) 78.4 minutes
(C) 79.8 minutes
(D) 80.4 minutes
which candy is better to buy $4.12 for 4 bars of 7.14 for 7 bars?
4 candy bars for 4.12=1.03
7 candy bars for 7.14=1.02
so 7 candy bars for 7.14
Answer: The one for 7 candy bars for $7.14.
Step-by-step explanation:
If x
2 = 25 , where x ε z then x =
The value of the quadratic equation given as x^2 = 25 is 5
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to solve the quadratic equation?The quadratic equation is given as
x2 = 25
Rewrite the equation properly
So, we have
x^2 = 25
Take the square roots of both sides
x = 5
Hence, the solution of the equation is 5
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determine the inverse function of f(x) = x² + x - 6, x> - 1/2, if it exists. Then, state its domain and range.
Since the domain is restricted to one side of the axis of symmetry of the full graph of f(x), an inverse does exist.
Letting [tex]f(x)=y[/tex],
[tex]x=y^2 +y-6\\\\x=\left(y+\frac{1}{2} \right)^2 -\frac{25}{4}\\\\x+\frac{25}{4}=\left(y+\frac{1}{2} \right)^2[/tex]
Since the domain is restricted to the right hand side of the axis of symmetry, and since the range of the inverse is the same as the domain of the original function, we take the positive square root.
[tex]\sqrt{x+\frac{25}{4}}=y+\frac{1}{2}\\\\y=f^{-1}(x)=\sqrt{x+\frac{25}{4}}-\frac{1}{2}[/tex]
The domain of the inverse is the range of the original function, which is [tex]\left[-\frac{25}{4}, \infty \right)[/tex].
The range of the inverse is the domain of the original function, which is [tex]\left[-\frac{1}{2}, \infty)[/tex],