The collection of all logical values for each independent variable under consideration.
What is the difference between reasonable domain and range?The set of all independent variable values that are logical in the particular circumstance. the collection of every possible value for the dependent variable the collection of all feasible dependent variable values that are appropriate in the situation.
Let y = f(x) represent a function where x and y are independent variables. The chosen x-value is said to fall within the domain of f if a function f offers a means of successfully producing a single value y while using a value for x to that end.
The set of possible input values is referred to as the domain, and the domain of a graph is made up of all the input values displayed on the x-axis. The set of potential output values that make up the range is represented by the y-axis.
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suppose a researcher finds that the p-value of a test statistics is 0.08. which of the following significance levels gives you a chance of finding a statistically significant result? -0,01 -0,001 -0,1 -0,05
the best chance of finding a statistically significant result would be 0.1. This is because the p-value of 0.08 is less than the significance level of 0.1, but greater than the significance levels of 0.01, 0.001, and 0.05
The p-value of a test statistic is a measure of the probability of obtaining a result that is at least as extreme as the one observed, given that the null hypothesis is true. In other words, it is a measure of the strength of the evidence against the null hypothesis.
If the p-value of a test statistic is 0.08, it means that there is an 8% chance of obtaining a result at least as extreme as the one observed, given that the null hypothesis is true. This does not necessarily mean that the result is statistically significant at any particular significance level.
To determine whether a result is statistically significant, you need to compare the p-value to a predetermined significance level, also known as the alpha level. The alpha level is the probability of rejecting the null hypothesis when it is actually true (also known as a type I error).
If the p-value is less than the alpha level, then the result is considered statistically significant. For example, if the alpha level is set at 0.05, and the p-value of the test statistic is 0.03, then the result would be considered statistically significant.
In the case of the options you provided, the significance level that gives you the best chance of finding a statistically significant result would be 0.1. This is because the p-value of 0.08 is less than the significance level of 0.1, but greater than the significance levels of 0.01, 0.001, and 0.05.
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Income taxes that are withheld from employees' pay and not remitted as of the balance sheet date will constituted a ____________ to be verified by the auditors.
Income taxes that are withheld from employees' pay and not remitted as of the balance sheet date will constituted a liability to be verified by the auditors.
A tax placed on people or organizations in relation to their income or profits is known as an income tax. Tax rates multiplied by taxable income are typically used to calculate income taxes.
Tax rates might change depending on the taxpayer's attributes and source of income. As taxable income rises, the tax rate can also. Corporate tax, which is often assessed at a fixed rate, is the name given to the tax charged on businesses. Individual income is frequently subject to progressive taxation.
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Martin will receive a pay raise of 6%. He currently makes $30 per hour. What will be his new hourly rate?
Answer:
New hourly rate is $31.8-------------------
GivenCurrent rate is $30,Pay raise is 6%,SolutionNew rate is:
$30 + 6% = $30 + $30*6/100 =$30 + $1.8 = $31.8Question 1(Multiple Choice Worth 1 points)
(05 04 LC)
A survey was taken of students in math classes to find out how many hours per day students spend on social media. The survey results for the first-, second-, and third-period classes are as follows
First period: 2, 4, 3, 1, 0, 2, 1, 3, 1, 4, 9,2,4,3,0
Second period: 3, 2, 3, 1, 3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2
Third period: 4, 5, 3, 4, 2, 3, 4, 1, 8, 2, 3, 1,0, 2, 1, 3.
Which is the best measure of center for first period, and why?
O Mean, because there are no outliers that affect the center
O Median, because there is one outier that affects the center
O
Interquartile range, because there is one outier that affects the center
O Standard deviation, because there are no outliers that affect the center
Answer:uu
Step-by-step explanation:
Simplify:
O
O
O
O
(3) ²
9
4
9
(())
9
< Previous
-12
-7
9
(4)
-3
6help
The simplified form of the given expression is, [tex]((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9} )^7[/tex].
What is simplifying an expression?
To simplify an expression, create an equivalent expression without any terms that are similar. The expression will then be rewritten using the fewest terms possible.
Consider, the given expression,
[tex]((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5[/tex]
To simplify this using the exponent rule:
[tex]((a)^b)^c = a^b^.^c[/tex]
⇒
[tex]((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9})^(^-^4^*^-^3)(\frac{4}{9})^-^5\\ ((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9})^1^2(\frac{4}{9} )^-^5[/tex]
Now use the exponent rule:
[tex]a^ba^c = a^(^b^+^c^)[/tex]
⇒
[tex]((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9} )^(^1^2^-^5^)\\((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9} )^7[/tex]
Hence, the simplified form of the given expression is, [tex]((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9} )^7[/tex].
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How do you write 5 as a fraction??
Ples answer quick its grading day
Answer:
5/1
Step-by-step explanation:
I think?
Jackson has $650 in their account and uses their debit card to take out $40 cash each week. Their card has a $5 ATM fee.
Write an equation to express their balance, y, after x weeks.
What will their balance be after 8 weeks?
After 8 weeks, how much will Jackson have paid in ATM fees alone?
The word problem have the following answers:
y = $650 - $45x is an equation to express their balance, y, after x weeks$290 will their balance be after 8 weeks.After 8 weeks, Jackson would have paid $40 in ATM fees alone.Word problems in mathematicsWord problems are mathematical problems which involves the use ofordinary words, instead of mathematical symbols.
From the question, if y is the balance after x weeks, this implies Johnson took out $45 multiplied by x in total including ATM fees, and their balance will be the equation;
y = $650 - $45x
After 8weeks, their balance will be;
y = $650 - $45(8)
y = $650 - $360
y = $290
After 8 weeks, Jackson will pay in ATM fees alone;
$5 × 8 = $40
Therefore, the equation y = $650 - $45x is to express their balance, y, after x weeks and $290 will be their balance after 8 weeks. While Johnson would have paid in $40 in ATM fees alone after 8 weeks.
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standard deviation for 6,8,10,4?
Standard deviation for 6,8,10,4 will be;
⇒ 2.58
What is Standard deviation?
Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given that;
The data set is,
⇒ 6, 8, 10, 4
Now,
Since, The data set is,
⇒ 6, 8, 10, 4
Hence, Mean = 6 + 8 + 10 + 4 / 4
= 7
So, The standard deviation= √ (6 - 7)² + (8 - 7)² + (10 - 7)² + (4 - 7)² / (4 - 1)
= √20/3
= 2.58
Thus, Standard deviation for 6,8,10,4 will be;
⇒ 2.58
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PLS HEEEEEEELP For 100 Points!!!!
Ana was washing dishes at the end of her shift at a restaurant. She washed 40 plates from 7:20 to 7:30.
When she finishes washing all the plates, her shift will end.
(a) If she started washing plates at 7:10 and ended at 7:35, estimate how many plates she washed in
total. Explain your reasoning.
(b) Write an equation to represent how many plates Ana has left to wash at a particular time after her
start at 7:10. Explain your reasoning.
Answer:
If Ana started at 7:20, ended at 7:38, and she washes 6 dishes per minute, than she has 108 dishes left to wash.
Step-by-step explanation:
Answer:
Step-by-step explanation:Answer: 138 plates are to be washed by her if she started at 7:15 and ends at 7:38, and the function will be f(x)=6x.
Step-by-step explanation:
Since we have given that
She washed 30 plates from 7:30 to 7:35,
That means in 5 minutes, the number of plates get washed here = 30
We need to find the number of plates from 7:15 to 7:38
First, we count the number of minutes
In 1 minute, the number of plates gets washed by her is given by
In 23 minutes, the number of plates gets washed by her is given by
The equation to represent how many plates Ana has left to wash at a particular time after her start at 7:15 is given by
Hence, 138 plates are to be washed by her if she started at 7:15 and ends at 7:38, and the function will be f(x)=6x.
Select all true statements if n || m.
Parallel lines M and N cut by two transversals, A B and B C. Along line M, three angles are labeled 2, 3, and 4, which together form a straight angle. Transversal A B forms two angles below line N, one labeled 20 degrees and the other labeled A. Together, these angles form a straight angle. Transversal B C forms two angles below line N, one labeled C and the other labeled 60 degrees. Together, these angles form a straight angle. Angle 1 is vertical to the 60-degree angle and is an alternate interior angle to angle 4. Together, angles 1, 3, and an unlabeled angle that is vertical to the 20-degree angle form a triangle between the two parallel lines.
A. m∠2 = 60°
B. m∠3 = 100°
C. m∠2 + m∠4 = 80°
D. m∠2 + m∠3 = 80°
E. m∠2 = 20°
Answer:
Hi, the correct answer is A) m∠2 = 60°.
let me put it in this way.
Step-by-step explanation:
Since parallel lines M and N are cut by transversals A B and B C, corresponding angles are formed. Corresponding angles are pairs of angles that are formed by intersecting lines and are on opposite sides of the transversal. In this case, angles 2 and C are corresponding angles, as are angles 3 and A.
We know that angles 2 and C form a straight angle along line M, and angles C and 60 degrees form a straight angle along line N. Since corresponding angles are congruent (have the same measure), this means that angle 2 must have the same measure as the 60-degree angle
HELP?!!? You’ve been hired to help a car company with analyzing sale trends to help them with figuring out what direction development of new products should go. Due to rising fuel costs the industry is seeing a rise in people purchasing compact cars, but the kind of features and thus price people are targeting is less clear.
Based on your initial analysis the average cost of a compact car over the last 10 years has ranged from $12,000 to $28,000. Your job is to assist your team with plotting this data on a graph to help your team with visualizing potential trends in the data. The years will be on the x-axis and the cost will be on the y-axis.
(a) What is a good maximum and minimum value along the y-axis that would be a good fit for your data on this graph? Explain your reasoning.
(b) What is a good distance between the marks along the y-axis on the graph to ensure that you have appropriate resolution for your data set? Explain your reasoning. Too few means you can’t reasonably read the data, too many will make your graph too cluttered.
(c) What is a good maximum and minimum value along the x-axis which would be a good fit for your data on this graph? Explain your reasoning.
(d) What is a good distance between the marks along the x-axis on the graph to ensure that you have appropriate resolution for your data set? Explain your reasoning. Too few means you can’t reasonably read the data, too many will make your graph too cluttered.
Select the postulate that confirms each statement.
a. Angles GFH and are supplementary angles.
Linear Pair Postulate
Segment Addition Postulate
Vertical Angle Postulate
Angle Addition Postulate
The correct postulate is the Linear Pair postulate. It can be find out by the concept of supplementary angles.
What is supplementary angles?
Two angles are said to be supplementary if their sums total 180 degrees.
Linear Pair postulate: When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°.
Segment Addition Postulate: According to the segment addition postulate, if two points on a line segment, A and C, are given, a third point, B, will only be found on line segment AC if and only if the distances between the points satisfy the conditions of the equation AB + BC = AC. This option is not correct.
Vertical Angles: When two lines intersect each other then the angles made on the opposite sides of the intersection point is known as vertical angles and they give equal measurment. This option is not correct.
Addition Postulate states: The measure of an angle formed by two angles side by side is the sum of the measures of the two angles. This option is not correct.
Hence, the correction postulate is the Linear Pair postulate. It can be find out by the concept of supplementary angles.
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A train travels for 3.75 hours at 80 miles an hour. Use the formula d = r. t, where
d = distance, r = rate, and t = time, to find the distance the train traveled.
The distance traveled is
miles.
The solution is
Distance travelled is 300 miles
What is distance ?The total movement of an object, independent of direction, is its distance. The amount of space that an object has traveled, regardless of where it started or ended, is referred to as distance.
According to the given information
You know the equation: D = r × t.
where D represents the distance traveled, r is the train's speed, and t denotes the amount of time (in hours) required.
Train travels for 3.75 hours at 80 miles per hour
By putting the values in the above equation
D = 80 miles in 3.75 hours per hour
= 80 × 3.75
= 300 miles
Distance travelled is 300 miles
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An arch has the shape of a semi-ellipse (the top half of an ellipse). The arch has a height of 6 feet and a span of 22 feet. Find an equation for the ellipse. (Assume a center at (0, 0)). Use the equation to find the height of the arch at a distance of 3 feet from the center. (Round your answer to two decimal places.)
The equation of ellipse is [tex]\frac{x^2}{11^2} + \frac{y^2}{6^2} = 1[/tex] and height of arch is 5.77 feet
Assume that the center of the ellipse is at the origin.
So, The general equation for an ellipse is:
[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]
Where:
x is Horizontal distance, in feet.
y is Vertical distance, in feet.
a is Horizontal semiaxis length (half-width), in feet.
and b is Vertical semiaxis length (height), in feet.
According to the question,
x = 3 , a = 11 and b = 6
Putting all the values ,
So , the equation of ellipse will be
[tex]\frac{x^2}{11^2} + \frac{y^2}{6^2} = 1[/tex]
Putting x = 3,
[tex]\frac{3^2}{11^2} + \frac{y^2}{6^2} = 1[/tex]
Solving for y,
[tex]\frac{y^2}{36} = 1 - \frac{9}{121}[/tex]
=> [tex]y^2 = \frac{(121 - 9)36}{121}[/tex]
=> y² = 4032 / 121
=> y = √33.32
=> y = 5.77 feet
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A school is arranging a field trip to the zoo. The school spends 835.19 dollars on passes for 45 students and 2 teachers.
Answer: $17.77 per pass
Step-by-step explanation:
$835.19 / (45 + 2)
$835.19 / 47
= $17.77 price per pass
Could someone help me with my math?? Neville says, "I add because of the words
in all. The answer is 9 pencils." Anthony says,
"I multiply because there are equal groups.
The answer is 18 pencils." Who is correct?
Explain.
From the statement, Anthony is correct because 3*6=18
How to determine the number of pencils she bought?We should know that the problem is to determine the number of pencils he bought
The given parameters are that
You can draw a 3 packages of pencils with 6 pencils in each to represent t package.
Now let us do the following:
For Neville
3*6 = 18
And also,
18÷3 = 6
For Anthony
6*3 =18 and
18÷6 = 3
In conclusion, looking at the two analysis, it seems that Anthony is more correct knowing fully well that each of the multiplications and divisions give us 18 or 6
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Complete question:
Critique Reasoning Neville and Anthony are solving this problem: Barbara bought You can draw a 3 packages of pencils with 6 pencils in each to represent t package. How many pencils did she buy in all? Neville says, “I add because of the words in all. The answer is 9 pencils.” Anthony says, “I multiply because there are equal groups. The answer is 18 pencils.” Who is correct? Explain.
Solve
3 x+10=14 y
8 x-7 y=34
Answer:
x = 6, y = 2
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Write an equation for a line passing through points (-2,3) and (3,5)
Answer:
[tex]y=\frac{2}{5}x+\frac{31}{5}[/tex]
Step-by-step explanation:
The slope of the line is [tex]\frac{3-5}{-2-3}=-\frac{2}{5}[/tex].
So, the equation is:
[tex]y-5=-\frac{2}{5}(x-3) \\ \\ y-5=-\frac{2}{5}x+\frac{6}{5} \\ \\ y=\frac{2}{5}x+\frac{31}{5}[/tex]
. If F F G H text is a rhombus, find each missing value
J G=
F J=
m ∠ E F H=
m ∠H G E=
2. If J K Z If is a square, find each missing value
J L=
M A=
m ∠ R N L=
R∠ M E U=
The value of JG = 24,
FJ = 7,
∠EFH = 74°,
∠HGE = 16°
What are the properties of a diagonal of rhombus?
In a rhombus, diagonals bisect each other at right angles. Diagonals bisect the angles of a rhombus. The sum of two adjacent angles is equal to 180 degrees. You will get a rectangle when you join the midpoint of the sides.
Solution:
Given :
EJ = 24
∴ GJ = 24
∠FHG = 74°
∴ ∠EFH = 74° by alternate angle properties
Now, we know
FG² =FJ² + GJ² - 2FJ × GJ × cos(90) ------ diagonals of the rhombus are perpendicular to each other
Substitute FG = 25, GJ = 24, we get
25² = FJ² + 24² - 2FJ × GJ × cos(90)
FJ² = 49
∴FJ = 7
180 =∠GHJ +∠HGJ + ∠GJH ------ sum of all angles of a triangle is 180°
∴ ∠HGE = ∠HGJ = 180 - 90 - 74
∴ ∠HGE = 16°
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2. The value of JL = 14
ML = 7√2
∠KNL = 90°
∠MKJ = 45°
What are the properties of diagonals of a square?
The diagonals of the square bisect each other at 90°.The two diagonals of the square are equal to each other. The diagonal of the square divide it into two similar isosceles triangles.
Solution:
Given; NM = 7
We know that diagonals of the square are equal
∴ NM = NL = NK = NJ = 7
∵ JL = JN + NL
∴ JL = 7 + 7
∴JL = 14
∠KNL = 90° ----- as we know that diagonals bisect each other at 90°
For ∠MKJ
we know that KM = KN + NM = 14
KJ = JM = 7√2------- property of isosceles triangle
∠KJM = 90° ----- all angles of square are 90°
We know that diagonals of a square dissects the square into two equal isosceles triangle.
∴ ∠MKJ = JMK = ∠KJM/2
∴ ∠MKJ = 90/2
∴ ∠MKJ = 45°
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The value of JG = 24 , FJ = 7, ∠EFH = 74°, ∠HGE = 16°
What are the properties of a diagonal of rhombus?
In a rhombus, diagonals bisect each other at right angles. Diagonals bisect the angles of a rhombus. The sum of two adjacent angles is equal to 180 degrees. You will get a rectangle when you join the midpoint of the sides.
Given :
EJ = 24
∴ GJ = 24
∠FHG = 74°
∴ ∠EFH = 74° by alternate angle properties
Now, we know
FG² =FJ² + GJ² - 2FJ × GJ × cos(90) ------ diagonals of the rhombus are perpendicular to each other
Substitute FG = 25, GJ = 24, we get
25² = FJ² + 24² - 2FJ × GJ × cos(90)
FJ² = 49
∴FJ = 7
180 =∠GHJ +∠HGJ + ∠GJH ------ sum of all angles of a triangle is 180°
∴ ∠HGE = ∠HGJ = 180 - 90 - 74
∴ ∠HGE = 16°
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2. The value of JL = 14
ML = 7√2
∠KNL = 90°
∠MKJ = 45°
What are the properties of diagonals of a square?The diagonals of the square bisect each other at 90°.The two diagonals of the square are equal to each other. The diagonal of the square divide it into two similar isosceles triangles.
Given; NM = 7
We know that diagonals of the square are equal
∴ NM = NL = NK = NJ = 7
∵ JL = JN + NL
∴ JL = 7 + 7
∴JL = 14
∠KNL = 90° ----- as we know that diagonals bisect each other at 90°
For ∠MKJ
we know that KM = KN + NM = 14
KJ = JM = 7√2------- property of isosceles triangle
∠KJM = 90° ----- all angles of square are 90°
We know that diagonals of a square dissects the square into two equal isosceles triangle.
∴ ∠MKJ = JMK = ∠KJM/2
∴ ∠MKJ = 90/2
∴ ∠MKJ = 45°
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URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Answer: b. The radius is the same as a cylinder with a volume of 500(3) and the same height.
Step-by-step explanation:
The volume of a cylinder is 3 times that of a cone (assuming they have the same perpendicular height and radius).
200-8.(2x+7)=112
(2x-123):3=33
is it two questions?
if it is then.....
Is answer correct?
Factorise the following:
a) x + 3x-4
b) x - 2x - 3
c) x + 2x - 8
By Factorise the equations we get 2 points for each equation:
for a) we get (x+4),(x-1)
for b) we get (x-3),(x+1)
for c) we get (x+4),(x-2)
a) x^2 + 3x-4
for this equation we have to take factors of -4:
x^2+4x-x-4
Taking common in the equation we get:
x(x+4)-1(x-4)
After taking common, Now we get two points:(x+4,)(x-1)
b) x^2 +-2x-3
for this equation we have to take factors of -3:
x^2-3x+x-3
Taking common in the equation we get:
x(x-3)+1(x-3)
After taking common, Now we get two points:(x-3,)(x+1)
c) x^2 + 2x-8
for this equation we have to take factors of -8:
x^2+4x-2x-8
Taking common in the equation we get:
x(x+4)-2(x+4)
After taking common, Now we get two points:(x+4,)(x-2)
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"The correct question is":
Factorise the following:
a) x ^2+ 3x-4
b) x^2 - 2x - 3
c) x ^2+ 2x - 8
The Chess Club wants to raise a total of $150 for a group trip.
They earn $1.25 for each box of pies they sell. They have
already made $16.25. Which equation could be used to find
how many more boxes of pies they must sell?
Answer:
Step-by-step explanation:
The number of boxes of pies that the Chess Club must sell to reach their goal of $150 can be represented by the variable x. We can create the following equation to represent this relationship:
1.25x + 16.25 = 150
To find the number of boxes of pies that the Chess Club must sell, we can solve this equation by subtracting 16.25 from both sides and then dividing both sides by 1.25:
1.25x = 150 - 16.25
1.25x = 133.75
x = 133.75 / 1.25
x = 107.
Therefore, the Chess Club must sell 107 more boxes of pies to reach their goal of $150.
Given the equation four ninths plus h equals eleven over nine, determine the value of h. nine over seven, seven ninths, forty four over eighty one, fifteen over ninetee,n
The required value of h in the equation 4/9 + h = 11/9 is 7/9 or seven ninths.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equation is,
4/9 + h = 11/9 (1)
To determine the value of h, solve the equation,
Subtract 4/9 from both the sides,
4/9 + h - 4/9 = 11/9 - 4/9
h = 7/9
The value of h is 7/9 or seven ninths.
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Evaluate the following:
Logn(-n)2 = ?
The value of the logarithm expression logₙ (n)⁻² will be negative 2.
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ logₙ (n)⁻²
Simplify the expression, then we have
⇒ logₙ (n)⁻²
⇒ -2 logₙ (n)
⇒ - 2
The value of the logarithm expression logₙ (n)⁻² will be negative 2.
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What is 7/10 divided by 3.4
Answer: 0.20588235294 or ≈0.21
Step-by-step explanation: First, we should change the 7/10 into a fraction. (Divide numerator by the denominator) You should get .7 or 0.7. Then, when dividing, it would be 0.7 divided by 3.4 and I got 0.20588235294. I rounded it to the nearest hundredth to get ≈0.21. I hope this helped! Please, mark brainliest! (If can)
The approximate length of side XY is
units
The approximate length of side YZ
units.
The approximate length of side ZX is
v units.
The approximate perimeter of triangle XYZ is
units
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Answer:
ZX = 3√2, XY =√10, YZ = 4, Perimeter of ΔXYZ = 14√5 units
Step-by-step explanation:
1. We can see that if we were to draw an altitude from vertex X to side ZY of this triangle, the length of this altitude would be: 3 units
2. The length of ZX can be determined through Pythagorean Theorem. If this altitude were to be called XW, it would be one of the legs of a mini triangle ZXW, along with leg ZW. ZW clearly = 3, thus ZX^2 = 3^2 + 3^2 = 18, and ZX = √18 units = 3√2.
3. The same thing can be applied to another "mini" triangle YXW. This triangle would have legs XW (altitude of the triangle ZXY) and YW. Knowing XW to have a length of 3 units, and YW to have length of 1 unit ⇒ XY^2 = XW^2 + YW^2 = 3^2 + 1^2, and XY = √10.
4. YZ is visualized to have a length of 4 units.
5. Knowing that ZX = 3√2, XY =√10, and YZ = 4 ⇒ Perimeter of ΔXYZ = ZX + XY + YZ = 3√2 + √10 + 4 = 14√5 units. To simplify this, it would be that the Perimeter of ΔXYZ = 14√5 units
ZX = 3√2, XY =√10, YZ = 4, Perimeter of ΔXYZ = 14√5 units
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
1. We can see that if we were to draw an altitude from vertex X to side ZY of this triangle,
the length of this altitude would be: 3 units
2. The length of ZX can be determined through Pythagorean Theorem.
If this altitude were to be called XW, it would be one of the legs of a mini triangle ZXW, along with leg ZW.
ZW clearly = 3,
thus
[tex]ZX^2 = 3^2 + 3^2 = 18[/tex],
and ZX = √18 units = 3√2.
3. The same thing can be applied to another "mini" triangle YXW. This triangle would have legs XW (altitude of the triangle ZXY) and YW.
Knowing XW to have a length of 3 units, and YW to have a length of 1 unit [tex]= > XY^2 = XW^2 + YW^2 \\= > 3^2 + 1^2[/tex],
and XY = √10.
4. YZ is visualized to have a length of 4 units.
5. Knowing that
ZX = 3√2, XY =√10, and YZ = 4
⇒ Perimeter of ΔXYZ = ZX + XY + YZ
⇒ Perimeter of ΔXYZ = 3√2 + √10 + 4
⇒ Perimeter of ΔXYZ = 14√5 units.
To simplify this, it would be that the Perimeter of ΔXYZ = 14√5 units
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Evaluate 15/r -1 when r = 5.
The value of the expression 15/r -1 when r = 5 will be equal to 2.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 15/r -1. The value of r is 5. The value of the expression at r=5 will be calculated as,
E = 15/r - 1
E = 15 / 5- 1
E = 3 - 1
E = 2
Therefore, the value of the expression 15/r -1 when r = 5 will be equal to 2.
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what is the product to 6.5x9.5
Answer: 61.75
Step-by-step explanation:
ABCD is a square with four congruent sides and four congruent angles. triangle BAD is congruent to
ΔBAD is congruent to ΔBCD by the ASA rule.
What is the ASA congruency of triangles?
If any two angles and sides included between the angles of one triangle are equivalent to the corresponding two angles and sides included between the angles of the second triangle, then the two triangles are said to be congruent by the ASA rule.
In the given figure ABCD is a square.
In ΔBAD and ΔBCD
∠B ≅ ∠B ----Common Angle
∠A ≅ ∠A ------Each of 90° angle
Side BD ≅ Side BD ----Common Side
So we can say that ΔBAD ≅ ΔBCD -----(ASA rule)
Hence, ΔBAD is congruent to ΔBCD by the ASA rule.
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