All of the statements are True when the expressions are evaluated using appropriate illustrations.
What are Real numbers?Real numbers are made up of both rational and irrational numbers. Real numbers include integers (-2, 0, 1), fractions (1/2, 2.5), and irrational numbers such as 3, (22/7), and so on.STATEMENT: 1
Real numbers have both rational and irrational values and can thus be manipulated using arithmetic operators like addition.
As a result, the statement is correct.
[tex]1+\frac{1}{2}=1 \frac{1}{2}[/tex]
STATEMENT: 2
Real numbers can be expressed or raised to the power of another number in a variety of ways, including being squared.
2² = 4; (1/3)² = 1/9STATEMENT: 3
All positive integers have a squared value that is greater than or equal to the value.
n = 2; n² = 2² = 44 > 2STATEMENT: 4
A sum's absolute value is always less than or equal to the sum of two numbers' absolute values.
a = 3 ; b = - 4|a + b | = |3-4| ≤ |-3|+|4||-1| ≤ 3 + 4-1 ≤ 7Therefore, all of the statements are True when the expressions are evaluated using appropriate illustrations.
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The complete question is given below:
Rewrite the following statements less formally, without using variables. Determine, as best as you can, whether the statements are true or false.
a. There are real numbers u and v with the property that u+v b. There is a real number x such that x2 c. For all positive integers n,n2≥n.
d. For all real numbers a and b,|a+b|≤|a|+|b|
Multiplying and dividing Decimals.
−6.87(−2.65).
Answer:18.2055
Step-by-step explanation:−6.87(−2.65)=−6.87*−2.65=18.2055
please help me, i have a test soon :/
Answer:
-2 <= y <= 4
Step-by-step explanation:
-3 <= 2y + 1 <= 9
-4 <= 2y <= 8
-2 <= y <= 4
Answer:
-2 <= y <= 4
Step-by-step explanation:
-3 <= 2y + 1 <= 9
-4 <= 2y <= 8
-2 <= y <= 4
on the next play, the team gained 5 yards and then lost 6 yards. what is the total change in yards? 5- blank
= 5 + blank
= blank
help me schools tomorrow
Solve for x in the diagram below.
X =
хо
100°
3x°
Answer:
20
Step-by-step explanation:
the line equals 180 degrees total.
so subtract the angle we already know from the total...
180- 100=80
then, make an equation with the last two variables since we know both of them added together should equal 80
80=x +3x
Combine like terms
80=4x
Divide by 4
20=x
3. What is an equation of the line in slope intercept form? (1 point)
A.y=2x-2
B.y=-2x-2
C.y=-2x+2
D.y=2x+2
Answer:
C. y = 2x + 2
Step-by-step explanation:
There are 2 points on the line (0,2) and (-3,-4)
from (-3,-4) to (0,2), rise over run is 6/3 so slope is 2
You can calculate it too
m = (y2-y1)/(x2-x1)
m = (-4 - 2)/(-3 - 0) = -6/-3 = 2
Using m = 2, x = 0, y = 2
y = mx + b
2 = 2(0) + b
b = 2
therefore
y = 2x + 2
(Precalc) NEED HELP 100PTS: (−2 ≤ x ≤ 2) f(x) = csc(x)
A. Find the intervals on which the graph of y = f(x) is increasing and the intervals on which the graph of y = f(x) is decreasing. Answer in interval notation.
Increasing: ___
Decreasing: ___
B. Find all relative extrema, if any, of the graph of y = f(x).
Relative min: ___
Relative max: ___
Thank youu!! <333
Answer:
Step-by-step explanation:
y=csc(x) x∈ [-2,2]
[tex]A.\\\displaystyle\\Increasing: \ [-2,-\frac{\pi }{2})U(\frac{\pi }{2},2]\\\\Decreasing:\ (-\frac{\pi }{2},0)U(0,\frac{\pi }{2} ) \\\\B.\\\\Relative\ min:\ 1\\\\Relative \ max:\ -1[/tex]
Watching the graph:
Answer:
[tex]\textsf{Increasing}:\left[-2,-\dfrac{\pi}{2}\right) \textsf{ and }\left(\dfrac{\pi}{2},2\right][/tex]
[tex]\textsf{Decreasing}:\left(-\dfrac{\pi}{2}, 0\right) \textsf{ and }\left(0, \dfrac{\pi}{2}\right)[/tex]
[tex]\textsf{Relative min}: \left(\dfrac{\pi}{2},1 \right)[/tex]
[tex]\textsf{Relative max}: \left(-\dfrac{\pi}{2},-1 \right)[/tex]
Step-by-step explanation:
Part A
Given function:
[tex]f(x)=\csc (x), \quad -2\leq x\leq 2[/tex]
[tex]\csc(x)=\dfrac{1}{\sin(x)}[/tex]
Therefore, the function f(x) is undefined when sin(x) = 0, leading to vertical asymptotes at the value of x where sin(x) = 0.
[tex]\sin(x) = 0 \textsf{ at }x = 0\pm 2 \pi n, \pi \pm 2 \pi n[/tex]
Therefore, f(x) has a vertical asymptotes at x = -2π, -π, 0, π, 2π etc.
Where the graph of the sine function increases, the graph of the cosecant function decreases.
Where the graph of the sine function decreases, the graph of the cosecant function increases.
The sine function increases on the intervals:
[tex]\left(-\dfrac{\pi}{2}\pm 2 \pi n, \dfrac{\pi}{2}\pm 2 \pi n\right)[/tex]
and decreases on the intervals:
[tex]\left(\dfrac{\pi}{2}\pm 2 \pi n, \dfrac{3\pi}{2}\pm 2 \pi n\right)[/tex]
Therefore, for the interval -2 ≤ x ≤ 2, the cosecant function f(x):
Increases on the intervals:
[tex]\left[-2,-\dfrac{\pi}{2}\right) \textsf{ and }\left(\dfrac{\pi}{2},2\right][/tex]
Decreases on the intervals:
[tex]\left(-\dfrac{\pi}{2}, 0\right) \textsf{ and }\left(0, \dfrac{\pi}{2}\right)[/tex]
Part B
The relative minimums of the graph of the sine function are the relative maximums of the graph of the cosecant function.
The relative maximums of the graph of the sine function are the relative minimums of the graph of the cosecant function.
The sine function has a range of -1 ≤ sin(x) ≤ 1.
Therefore, its minimum points are when sin(x) = -1 and its maximum points are when sin(x) = 1.
[tex]\sin(x)=-1 \implies x=\dfrac{3\pi}{2}\pm 2 \pi n \implies \textsf{Minimum points}: \left(\dfrac{3\pi}{2}\pm 2 \pi n ,-1 \right)[/tex]
[tex]\sin(x)=1 \implies x=\dfrac{\pi}{2}\pm 2 \pi n \implies \textsf{Maximum points}: \left(\dfrac{\pi}{2}\pm 2 \pi n,1 \right)[/tex]
Therefore, the minimum and maximum points of the cosecant function in the given interval -2 ≤ x ≤ 2 are:
[tex]\textsf{Relative min}: \left(\dfrac{\pi}{2},1 \right)[/tex]
[tex]\textsf{Relative max}: \left(-\dfrac{\pi}{2},-1 \right)[/tex]
Note in the attached graph:
The given interval -2 ≤ x ≤ 2 is shown shaded in green.Vertical asymptotes are shown as red dashed lines.Function f(x) is the black curve.The sine function is the blue dashed curve.Relative min/max shown as black points.What transformation would take triangle ABD to A’B’D ( translation, reflection , or rotation ) ?
Answer: Rotation
Step-by-step explanation:
write the non-teerminating decimal as fraction 0.555555555...
Answer:
111111111/200000000
11. A population of bacteria triples every week in a laboratory. The number of
bacteria is modeled by the expression 900 3*, where x is the number of weeks
after a scientist measures the population size. When x = -2, what does the value
of the expression represent?
Answer:
Step-by-step explanation:
Let x represent the number of weeks a population of the bacteria increases. Then, we have the number of bacteria is molded by the expression of 900*3^x. By, the given expression and when we assigned a value of x=2. Then we have 900*3² .
Multiply:
-2x(3x - 4)
Enter the correct answer
Answer:
- 6x² + 8x
Step-by-step explanation:
- 2x(3x - 4) ← multiply each term in the parenthesis by - 2x
= - 6x² + 8x
(write each as an algebratic expression) a cubed is equal to 31
Which scales of data measurement are associated with quantitative data? interval and ratio ratio and nominal ordinal and interval nominal and ordinal
Interval and ratio scales of data measurement are associated with quantitative data.
Data measurement:- Data measurement is the way in which data can be subcategorized to analyze the data properly. Data can be classified into two types-
Quantitative data:- The data, which can be measured with numbers is called as quantitative data. Ex: duration, speed etc. This kind of data can be again subcategorized into two types-Discrete:- The data, which is of whole number, that can't be broken. Ex: a number of items.Continuous:- The data, which can be broken. Ex: height, weight etc. This type of data can be measured using interval and ratio measurement scales.Qualitative data:- The data, which is non-numerical value and categorical is called as qualitative data. Ex: yes, no responses or eye color etc. This type of data can be measured using nominal and ordinal measurement scales.Thus we can conclude that, Interval and ratio scales of data measurement are associated with quantitative data.
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Find the median and mean of the data set below:
Median = 1
201
49, 16, 5, 3, 6
Mean =
The mean and the median value of the given data set is 12.62 and 6.
According to the statement
We have to find that the mean and the median of the following data.
So, For this purpose, we know that the
The mean is found by adding all of the numbers together and dividing by the number of items in the set.
And
The median is the middle number in a sorted, ascending or descending list of numbers
From the given information:
The data set are:
1,20,1, 49, 16, 5, 3, 6
Then
According mean definition,
Mean = 1+20+1+ 49+ 16+ 5+ 3+6/8
Mean = 101/8
Mean = 12.625
Then
The data set is 1,3,5,6,16,20,49.
Median = 8 terms /2
Median = 4th term
Median = 6.
So, The mean and the median value of the given data set is 12.62 and 6.
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The granite sample has a
mass of 24. 31 g and a volume
of 9. 35 cm3. What is the
density of the granite?
d = [?] g/cm3
HELPPPPP PLEASE. PLEASE TELL ME THE BLANKS IN ORDER.
176.912 round off to the closest integer.
Answer:
177
Step-by-step explanation:
An integer is a negative or positive whole number. any number greater or equal to 5 you round up the the nearest whole number
Hope this helps.
"decimals are not included in the set of integers." with this information you can infer that you need to round to the nearest whole number, therefore 176.912 would be round to 177 because the decimal in the tenth place is 5 or above (9) so you round UP.
11. The following describes the United States nuclear stockpile from
1944 to 1974. From 1944 to 1958, there was a gradual increase in the
number of warheads from 0 to about 5000. From 1958 to 1966, there
was a rapid increase in the number of warheads to a maximum of
about 32,000. From 1966 to 1970, there was a decrease in the number
of warheads to about 26,000. Finally, from 1970 to 1974, there was
a small increase to about 28,000 warheads. Sketch a graph of the
function.
10.
nxhudkdodisuhaiioavsbos
Find the measure of the missing angles.
55°
X
y
Answer:
x = 35° , y = 125°
Step-by-step explanation:
y and 55° lie on the straight line and sum to 180° , that is
y + 55° = 180° ( subtract 55° from both sides )
y = 55°
x and 55° form a right angle and sum to 90° , that is
x + 55° = 90° ( subtract 55° from both sides )
x = 35°
the number of questions marked incorrect on a statistics midterm, y, is dependent on the pages of notes a student wrote over the semester, x, and can be modeled by the function y(x)
The another point is (2,23) of the function y(x).
What does regression analysis mean?
Finding the variables that have an effect on an interest issue can be done with accuracy using regression analysis. You can confidently establish which elements are most important, which ones can be ignored, and how these factors interact when you do a regression.The given Regression is -
y (X) = 30 - 3. 5 x .......................(1)
now when x = 0 , y(x) = 30 ..........................(1)
thus , y- intercept = 30
one point is ( 0 , 30 )
Again taking x = 0 we get
y(x) = 30 - 3. 5 x 2 by (1)
y(X) = 23
Thus the another point is (2,23).
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Please help !!! , I have 8 mins left on the clock .
Express the relation below as a set of ordered pairs.
By critically observing the graph shown above, the set of ordered pairs include the following:
(-1, 5)(4, -3)(-5, -3)(0, 5)(-4, 5)What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
What is an ordered pair?An ordered pair can be defined as a pair of two elements that are typically written in a fixed order within parentheses as (x, y), which represents the x-axis (abscissa) and the y-axis (ordinate) on a coordinate plane.
By critically observing the graph shown above, we can logically deduce that the set of ordered pairs include the following:
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Ella's bait and tackle shop sold 128,107 live worms in april and 102,278 live worms in may to the nearest thousand how many worms did ella's bait and tackle shop sell in april and may together
Ella's bait and tackle shop sells 230,385 in April and May.
Based on the given conditions, formulate:
Bait and tackle sold in 128,278 live worms in April
Bait and tackle sold in 102,278 live worms in May
So the total number of Bait and tackles sold in April and May =
=128,107+102,278
= 230,385
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What is the value of the absolute value expression |−134| + |4| − |−35|?
Answer:
174
Step-by-step explanation:
absolute value means the distance from zero. Distance is always measured with a positive number. If you asked me how far I lived from my work, I would never say -12 miles away. If I was going or coming to work, the distance would be the same 12 miles.
134 + 4 + 35 = 174
Diferencia entre álgebra y aritmética
Which number would be found on the number line between 0 and -1
Answer: -.5 OR -.1, -.2, -.3, -.4, -.5, -.6,-.7,-.8,-.9
Step-by-step explanation: The simple answer is -.5, it is right in the middle of 0 and -1. The answer number is everything in between.
Which is an equivalent expression for 4 times d raised to the negative third power all over quantity 22 times d raised to the ninth power end quantity?
really need help pleeease
An equivalent expression for 4 times d raised to the negative third power all over quantity 22 times d raised to the ninth power is 2d⁻³/11d⁻⁹
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
What is an exponent?An exponent can be defined as a mathematical operation that is used to raise a quantity to the power of another and it is generally written as bⁿ.
Translating the word problem into an algebraic expression, we have;
4 times d raised to the negative third power = (4 × d)⁻³ = 4d⁻³
22 times d raised to the ninth power = (22 × d)⁻⁹ = 22d⁻⁹
Next, we would write the equation as a quotient:
Expression = 4d⁻³/22d⁻⁹
Expression = 2d⁻³/11d⁻⁹
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Help !!! With this please !!!
Answer: $48.17
Step-by-step explanation:$148.68-$24.32= $124.36
$124.36-$37.53= $86.83
$135 -$86.83=$48.17
So he needs forty-eight dollars and 17 cents.
a. what fraction of the total goal distance did sarah run? b. tori ran 2 −3 of the total goal distance. who ran farther – sarah or tori?
The total goal distance Sarah run is 7/8.
The distance covered by Sarah is found to be more than Tori.
What is the exponents?A number's exponent indicates what many times a number has been multiplied by itself. For instance, 2×2×2×2 can be composed as 2⁴.
If a fraction does have a negative exponent, we take its reciprocal to make this same exponent positive.
If a fraction does have a negative exponent, we take its reciprocal to create the exponent positive.
Some properties of exponents are-
Law of Product: [tex]a^m \times a^n=a^{m+n}[/tex]Law of Negative Exponent: [tex]a^{-m}=1 / a^m[/tex]Law of Power of a Power: [tex]\left(a^m\right)^n=a^{m n}[/tex]Law of Power of a Product: [tex](a b)^m=a^m b^m[/tex]Law of Quotient: [tex]a^m / a^n=a^{m-n}[/tex]Now, as pet the given question;
Tori has covered 2⁻³ of the total distance;
Thus, it can be written as;
= 1/2³
= 1/8
Lets consider the total distance covered by both of them is 1.
Then, the distance covered by Sarah will be;
= 1 - 1/8
= 7/8
Thus, the distance covered by Sarah is 7/8.
As, 7/8 > 1/8
Therefore, the distance covered by Sarah is more than Tori.
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1. solve 2r = 5s/2 - s/4 for s
2. If r =9/2, find s
1. Solve w = x/y - z solve for x
2. If w = -8 y = -5 z = 6 find x
Answer:
[tex]\textsf{1.} \quad s=\dfrac{8r}{9}[/tex]
[tex]\textsf{2.} \quad s=4[/tex]
[tex]\textsf{1.} \quad x=y(w+z)[/tex]
[tex]\textsf{2.} \quad x=10[/tex]
Step-by-step explanation:
Question 1
1. Solve for s:
[tex]\implies 2r = \dfrac{5s}{2}-\dfrac{s}{4}[/tex]
[tex]\implies 2r = s\left(\dfrac{5}{2}-\dfrac{1}{4}\right)[/tex]
[tex]\implies 2r = s\left(\dfrac{10}{4}-\dfrac{1}{4}\right)[/tex]
[tex]\implies 2r = s\left(\dfrac{9}{4}\right)[/tex]
[tex]\implies 4(2r) = 9s[/tex]
[tex]\implies 8r = 9s[/tex]
[tex]\implies s=\dfrac{8r}{9}[/tex]
2. When r = ⁹/₂ :
[tex]\implies s=\dfrac{8\left(\frac{9}{2}\right)}{9}[/tex]
[tex]\implies \dfrac{8}{9} \times \dfrac{9}{2}[/tex]
[tex]\implies \dfrac{8 \times9}{9 \times2}[/tex]
[tex]\implies s=\dfrac{72}{18}[/tex]
[tex]\implies s=4[/tex]
Question 2
1. Solve for x:
[tex]\implies w=\dfrac{x}{y}-z[/tex]
[tex]\implies w+z=\dfrac{x}{y}[/tex]
[tex]\implies y(w+z)=x[/tex]
[tex]\implies x=y(w+z)[/tex]
2. When x = -8, y = -5, z = 6:
[tex]\implies x=-5(6+(-8))[/tex]
[tex]\implies x=-5(6-8)[/tex]
[tex]\implies x=-5(-2)[/tex]
[tex]\implies x=10[/tex]
Kyle found the product of two rational expressions and identified the excluded values of the expression. However, he made a mistake in his work and included an extra number in his list of excluded values. His work is shown below.
Select the step where Kyle made his first mistake. Then select the number that should not be included in the list of excluded values.
Answer:
Step-by-step explanation:
Mistake in step 3 the (2x+1) and the (x-1) both cancel out but the other binomials (x + 3) and (x - 3) are different so don't cancel out.
Step 3 should be 3(x-3) / 4(x+3)
3 should not be an excluded value.
v/9 - 7 = -8
I'll give brainliest!! please explain
By isolating the variable, we will see that the solution of the linear equation is v = -9
How to solve the linear equation?Here we have the following linear equation:
v/9 - 7 = -8
Where we can see that the variable is v. To solve this, we need to perform operations in both sides of the linear equation in a way such that the variable is isolated in one of the sides.
Adding 7 in both sides we get:
v/9 - 7 + 7 = -8 + 7
v/9 = -1
Now we multiply both sides by 9:
(v/9)*9 = -1*9 = -9
v = -9
We conclude that the solution of the linear equation is v = -9.
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