Therefore , the solution to the given problem is the equation of the midline is: y = M+m /2 .
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
Here,
The midline equation is y = M+m /2
when a function has: o a max M AND a min m or o (if it does not have extrema) a bound above M and a bound below m, where M is the minimum bound above and m is the maximum bound below.
When one of the following conditions is true for a function, even though it has a bound below, there is no midline (even if it has a bound above)
It is solely constrained from above (or below)
Any line is midline if a function has the values (-∞, +∞)
Therefore , the solution to the given problem is the equation of the midline is: y = M+m /2 .
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2) 45+ 17 = 62
3) X + 5/6 = 7/16
4) Y + 1/7 = 5/8
9514 1404 393
Answer:
2) true
3) X = -19/48
4) Y = 27/56
Step-by-step explanation:
3) Subtract 5/6 from both sides
X = 7/16 -5/6 = (7·6 -16·5)/(16·6) = (42 -80)/96
X = -19/48
__
4) Subtract 1/7 from both sides
Y = 5/8 -1/7 = (5·7 -8·1)/(8·7)
Y = 27/56
In the following problems the values of sin(θ)and cos(θ)are given. Determine the value of tan(θ).
a. sin(θ)=0.1 and cos(θ)=0.995
tan(θ)=
b. sin(θ)=−0.158 and cos(θ)=−0.987
tan(θ)=
c. sin(θ)=−0.631and cos(θ)=0.776
tan(θ)=
Answer:
a) ≈ 0.1
b) ≈ 0.2
c) ≈ 0.9
Step-by-step explanation:
GIVEN :-
Values of sinθ & cosθTO FIND :-
Value of tanθFACTS TO KNOW BEFORE SOLVING :-
[tex]\tan \theta = \frac{\sin \theta}{\cos \theta}[/tex]SOLUTION :-
a) [tex]\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{0.1}{0.995}[/tex] ≈ 0.1
b) [tex]\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{-0.158}{-0.987} = 0.16 (appx)[/tex] ≈ 0.2
c) [tex]\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{0.631}{0.776} = 0.81 (appx)[/tex] ≈ 0.9
is 9.307 greater than 9.37
Answer:
No because 9.307 is less than due the facts that the seven in 9.307 is in the thousandth while the seven in 9.37 is in the hundredths
how do you get 3/8 from 13/8
You can get 3/8 from 13/8 by subtraction. The solution is 10 / 8
How to get 3/8 from 13/8In order to get 3/8 from 13/8 we would have to carry out a subtraction of fractions.
That is we would have: 13/8 - 3/8
take the lcm of the denominator
[tex]\frac{13 - 3}{8}[/tex]
= 10 / 8
Hence when we take 3 / 8 from 13 / 8, the solution that we would have would be from subtraction. This is 10 / 8
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Mary can make a quilt in 3 days and Eva can make
a quilt in 5 days. In how many days can they make
quilt working together?
Answer: in explanation
Step-by-step explanation
Sandi can perform 1/9 of the task in a day
Eva can perform 1/5 of the task in a day
Working together, they can perform
1/9 + 1/5 of the task per day
= 5/45 + 9/45 = 14/45 of the task in a day
or 45/14 days in the task = 3.2 days
So
It would take about 3.2 days to complete the task working togethe
I just need help appreciate it and have a great day
On solving the provided question, we can say that - by doing the fraction we have 3/12 = 1/4
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
balloons is 12
blew up is 1/3
friend blew up is 5
1/3*12 = 4
4+5 = 9
3/12 = 1/4
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The perimeter of a rectangular field is 74 yards. The length of the field is 27 yards. What is the width in yard of the field
Answer:
width = 10 yds
Step-by-step explanation:
perimeter = 2L + 2W
74 = 2(27) + 2W
74 = 54 + 2W
subtract 54 from both sides of the equation:
2W = 20
divide both sides by 2:
W = 10
The width of the yard whose length is 27 yards and perimeter is 74 yards is evaluated to be 10 yards
How to find the perimeter of a rectangle?For a rectangle with length and width L and W units, we get:
Perimeter of the rectangle = [tex]2(L + W) \: \rm units[/tex]
For this case, let we assume that:
The width of the considered rectangular field = W yards
Then, as we're provided that:
Perimeter of the rectangular field = 74 yardsLength of the rectangular field = 27 yards.Putting these in the formula for perimeter of a rectangle, we get;
[tex]Perimeter = 2( L + W)\\74 = 2(27 + W)\\\\\text{Dividing both the sides by 2}\\\\\dfrac{74}{2} = \dfrac{2(27+W)}{2}\\\\37 = 27 + W\\\\\text{Subtracting 27 from both the sides}\\\\37 - 27 = W\\W = 10 \: \rm yards[/tex]
Thus, the width of the yard whose length is 27 yards and perimeter is 74 yards is evaluated to be 10 yards
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The Science Club went on a two-day field trip. On the first day, the members paid $60 for transportation plus $15 per ticket to the planetarium. On the second day, they paid $95 for transportation plus $12 per ticket to the geology museum.
Write an expression to represent the total cost for two days for the ₙ members of the club.
Answer: Let n be the number of members in the Science Club.
On the first day, the total cost for transportation plus the cost of tickets is 60 + (15n) dollars.
On the second day, the total cost for transportation plus the cost of tickets is 95 + (12n) dollars.
So, the total cost for both days is (60 + 15n) + (95 + 12n) = 155 + 27n dollars.
The expression to represent the total cost for two days for the n members of the club is 155 + 27n dollars.
This equation represents the total cost for the transportation, planetarium and geology museum for 2 days for the n members in the club.
It should be noted that this is the monetary representation and it might vary depending on other factors, such as group discounts.
Step-by-step explanation:
Answer:
(n x 27)+155
Step-by-step explanation:
15 +12 = 27
Each member pays $27 for the tickets so we multiply it by the number of members.
95 + 60 = 155
The members pay $155 in total for transportation.
Multiply: (–4 + i)(2 – 3i)
a. –5 – 10i
b. –8 + 11i
c. –5 + 14i
d. –11 + 14i
The result of the product of the given complex numbers as required to be determined is; Choice C; -5 + 14i.
What is the product of the given complex numbers?It follows from the task content that the result of the product of the given complex numbers is to be determined.
On this note, since the required product to be evaluated is; (–4 + i) (2 – 3i).
We can therefore multiply as follows;
-8 + 12i + 2i - 3i².
However, it is noteworthy to know that; i² = -1.
Hence, we have that;
-8 + 14i + 3
= -5 + 14i
On this note, it follows that the result of the product of complex numbers as required is; -5 + 14i.
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You stand 25 m from the base of a tree and the angle of elevation from the ground to the top of the tree is 48 degrees. How tall is the tree?
Answer:
ffyftxrrxrrxcvcmuvcyztzxvujgyh
Step-by-step explanation:
✋☝☝✊✋❤❤❤
Suppose that $20,000 is invested at 9% interest, compounded annually. After time t, in years, it grows to the amount A given by the function A(t) = $20,000(1.09)
a) Find the amount of time after which there will be $200,000 in the account.
b) Find the doubling time.
After what amount of time will there be $200,000 in the account?
Answer:
Years = {log(total) -log(Principal)} ÷ log(1 + rate)
Years = [log (200,000) -log (20,000)] / log (1.09)
Years = [5.3010299957 -4.3010299957] / 0.037426497941
Years = 1 / 0.037426497941
Years = 26.7190374471
*************************************************
Finding Doubling Time : (We'll calculate $100 becoming $200)
Years = {log(total) -log(Principal)} ÷ log(1 + rate)
Years = log (200) -log (100) / log(1.09)
Years = (2.3010299957 -2) / 0.037426497941
Years = .3010299957 / 0.037426497941
Years 8.0432317278
It takes 8.0432317278 years for money to double at 9% per year.
Source:
http://www.1728.org/compint2.htm
Step-by-step explanation:
Answers are
(-1,3)
(0,2)
(1,2)
(2,-1)
(2,2)
HELP ME !!
PLEASE ANSWER !! ILL GIVE BRAINLIEST !!
50 POINTS !!
FAKE ANSWERS WILL GET REPORTED .
Answer:
<1=62
<2=83
<3=35 this is the answer of this question
In this figure question attached
Answer:
x = 20°
Step-by-step explanation:
x = 180 - (70 + 90)
x = 180 - 160
x = 20°
Hope this helps!
Consider the following. 12, 7, 18, 23, 24, 27 Compute the population standard deviation of the numbers. (Round your answer to two decimal place.) (a) Double each of your original numbers and compute the standard deviation of this new population. (Round your answer to two decimal place.) (b) Use the results of part (a) and inductive reasoning to state what happens to the standard deviation of a population when each data item is multiplied by a positive constant k.
Answer:
(a) [tex]\sigma = 7.04[/tex]
(b) [tex]\sigma = 14.1[/tex]
(c) The population standard deviation is multiplied by k
Step-by-step explanation:
Given
[tex]Dataset: 12, 7, 18, 23, 24, 27[/tex]
Solving (a): The population standard deviation
Start by calculating the mean
[tex]\mu = \frac{\sum x}{n}[/tex]
[tex]\mu = \frac{12+7+18+23+24+27}{6}[/tex]
[tex]\mu = \frac{111}{6}[/tex]
[tex]\mu = 18.5[/tex]
The population standard deviation is:
[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}[/tex]
This gives:
[tex]\sigma = \sqrt{\frac{(12-18.5)^2 + (7 - 18.5)^2 + (18-18.5)^2 + (23-18.5)^2 + (24 - 18.5)^2 + (27 - 18.5)^2}{6}}[/tex]
[tex]\sigma = \sqrt{\frac{297.5}{6}}[/tex]
[tex]\sigma = \sqrt{49.5833}[/tex]
[tex]\sigma = 7.04[/tex]
Solving (b): Double the dataset and calculate the new population standard deviation
The new dataset is:
[tex]Dataset: 24, 14, 36, 46, 48, 54[/tex]
Start by calculating the mean
[tex]\mu = \frac{\sum x}{n}[/tex]
[tex]\mu = \frac{24+ 14+ 36+ 46+ 48+ 54}{6}[/tex]
[tex]\mu = \frac{222}{6}[/tex]
[tex]\mu = 37[/tex]
The population standard deviation is:
[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}[/tex]
This gives:
[tex]\sigma = \sqrt{\frac{(24-37)^2 +(14-37)^2 +(36-37)^2 +(46-37)^2 +(48-37)^2 +(54-37)^2}{6}}[/tex]
[tex]\sigma = \sqrt{\frac{1190}{6}}[/tex]
[tex]\sigma = \sqrt{198.33}[/tex]
[tex]\sigma = 14.1[/tex]
Solving (c): What happens when the dataset is multiplied by k
In (a), we have:
[tex]\sigma = 7.04[/tex]
In (b), when the dataset is doubled,
[tex]\sigma = 14.1[/tex]
This implies that when the dataset is multiplied by k, the population standard deviation will be multiplied by the same factor:
i.e.
[tex]New \sigma = k * \sigma[/tex]
Given that the polynomial x² - 10x + 14 leaves the same remainder when divided by x + 2b orx + 2c where 3b - 2c = 0 and b # c . Find the values of b and c.
Step-by-step explanation:
please refer to the 3 pages of sketch for details
What IS the approximate length of arc s on the circle below? Use 3.14 for T Round your answer to the nearest
tenth.
Answer:
14.1 inches
Step-by-step explanation:
The formula to be used to find the arc length is Ф = s(arc length) / r(radius)
First we rearrange the formula to find the arc length which would be s = Ф * r
This formula only works in radians so the first step is converting 135° to radians so we would do 135° * π radians/180° which would give us 3π/4
We would then multiply 3π/4 * 6 and get 18π/4, plugging that value into a calculator returns us a value of ≈ 14.137
We then round to the nearest tenth and get an answer of 14.1 inches for the arc length of the circle below
Irregular polygons has sides that are not equal lenght and angles that are not equal?
TRUE OR FALSE?
Answer:
yeah it's true
Step-by-step explanation:
regular polygon have all equal side and all equal angleIRREGULAR polygon have atleast one unequal side and one unequal angle............THANKS.........
How do you write 0.0912 in scientific notation?
Therefore , the solution of the problem of expression comes out to be
9.12 x 10 ^-2.
How does one select expression?An algebraic expression must be checked via replacing each variable with a number and performing arithmetic operations. In the example above, the answer variable is comparable to 6, since 6 + 6 equal 12. If we know the values of the variables, we can replace them with those values and evaluate the expression.
Here,
Given : 0.0912 in scientific notation
=> 9.12 /100
By using scientific notation
=> 9.12 × 10^-2
=> 9.12 x 10 ^-2
So, we get 9.12 x 10 ^-2 as the scientific notation for the given expression
Therefore , the solution of the problem of expression comes out to be
9.12 x 10 ^-2.
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A biologist tags ducks living at a pond for her research. She uses 14 blue tags, 19 red tags, 27 white tags, and 6 yellow tags on individual ducks before releasing them back into the wild. When the biologist returns to the pond to continue the study, she is more likely to find a duck with a blue tag than a duck with a ...
A red tag
B white tag
C yellow tag
D yellow or red tag
What are the solutions of the equation (5x –
- 2)(x + 6) = 0?
9514 1404 393
Answer:
-2/5, -6
Step-by-step explanation:
We assume you're asking for solutions to ...
(5x -(-2))(x +6) = 0
This can be simplified to ...
(5x +2)(x +6) = 0
__
The solutions are the values of x that make the factors zero. (The product can only be zero if a factor is zero.) Here, we'll find the zeros of the factors one at a time.
5x +2 = 0
5x = -2 . . . . . subtract the constant
x = -2/5 . . . . divide by the x-coefficient
__
x +6 = 0
x = -6 . . . . . .subtract the constant
The solutions of the equation are x = -2/5 or -6.
__
The graph shows the x-values that make the product zero.
Help?
Describe how to translate the graph of y= x to obtain the graph of y = x – 15.
Answer:
Shift down 15 units
Step-by-step explanation:
the number on the right is the one that determines where the line intersects through the y axis
Two of the statements are true; one is a lie.
Select the one that is a lie.
Then explain your reasoning.
∠GAF ≌ ∠TAE.
∠TAE and ∠FAH are complementary.
∠TAF is obtuse.
Answer: Choice A
angle GAF = angle TAE is the lie (aka false statement)
========================================================
Explanation:
Let's go through each answer choice to see which is true or which is false.
-----------------------------
Choice A
The markers for angles GAF and TAE are different. Both would need to have a single angle marker, or a double angle marker. The differing markers indicates the angles aren't the same.
Also, note that angle TAG isn't a 180 degree angle, or that point G isn't on line TA. We need this to be the the case, so that two vertical angles form. However, such a thing doesn't happen.
So that's why angles TAE and GAF aren't the same measure.
Choice A is the answer. You can stop here if you wanted.
-------------------------------
Choice B
Let
x = measure of angle TAE
y = measure of angle TAH
z = measure of angle HAF
We can see that x+y+z = 180, since angle EAF is a straight angle. The diagram gives y = 90 and z = 50, so,
x+y+z = 180
x+90+50 = 180
x+140 = 180
x = 180-140
x = 40
Angle TAE is 40 degrees. It adds with angle FAH to get 40+50 = 90, showing that the two angles are indeed complementary.
Choice B is a true statement, so we can rule it out.
-------------------------------
Choice C
Angle TAF is composed of angles TAH and HAF
Adding the two angles gets us 90+50 = 140, which is larger than 90.
Therefore angle TAF is obtuse.
Choice C is a true statement, and it can be ruled out as well.
Technically you could have stopped at choice A once you found the lie, but I figured to show why choices B and C could be ruled out.
If the dimensions of the following cylinder are doubled, what factor will the surface area change by? 8 in 0.5 ft answers 2 8 4 6
Question: If the dimensions of the following cylinder are doubled, what factor will the surface area change by?
8
6
4
2
Answer: i think it is 8 but i will update it if not i am on the test
If the dimensions of the cylinder are doubled, then by 4 factor the surface area changed
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface.
The radius of cylinder is r=8 inches
Height is 0.5 feet.
Surface area of cylinder=2πr(r+h)
We know that 0.5feet=6 inches
Suface area of original cylinder=2πr(r+h)
=2×π×8(8+6)
=224π
Now the dimensions are doubled ,so r=16 inches , h=12 inches
Suface area of changed cylinder=2πr(r+h)
=2π×16(16+12)
=32π×(28)
=896π
=4(224π)
Hence by 4 factor the surface area is changed.
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Below is a dot plot showing how much time customers spent in a store, rounded to the nearest five minutes. Which of the following is a representative sample of this population?
NEED THIS BAD PLEASE HELP ME!!!!!!!
Answer:
D
Step-by-step explanation:
i did a test with the same question
The representative sample of the population displayed by the dot plot is: dot plot D.
What is a Representative Sample of a Population?The representative sample of a population can be described as a subset of a particular population which displays or exhibit similar characteristics of the larger population group.
From the image given, the dot plot that reflects the characteristics of the dot plot of the population is the dot plot in option D.
Dot plot D is a representative sample.
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HAVE A NICE DAY
WILL GIVE BRAINLST :)
Answer:
1. A
2. C
Step-by-step explanation:
What angle would it be?
Answer:
A cute
Step-by-step explanation:
NEED HELP ASAP DUE TMR
1. The length of the altitude is 15 units.
2. The perimeter of trapezoid ABCD is 132 units.
Perimeter of a trapezoid.An altitude is the vertical height of a given object from the sea level. This is majorly a height reached by an object to the sea level as a reference.
The perimeter of a trapezoid is the sum of all its sides.
From the question;
1. To determine AE,
DE = (DG - EF)/ 2
= (22 - 6)/ 2 (since AB = EF = 6)
= 8
DE = 8 units
The altitude AE can be determined by applying the Pythagorean theorem to triangle ADE. So that;
/hyp/^2 = /opp/^2 + /adj/^2
AD^2 = DE^" + AE^2
17^2 = 8^2 + AE^2
289 = 64 + AE^2
AE^2 = 225
AE = 15
Thus the length of the altitude is 15 units.
2. To determine the perimeter of the trapezoid, we have;
AE = (AD - EF)/ 2
= (58 - 16)/ 2 (since BC = EF = 16)
= 21
AE = 21 units
So that from triangle ABE, applying the Pythagorean theorem to determine the value of AB, we have;
/hyp/^2 = /opp/^2 + /adj/^2
AB^2 = BE^2 + AE^2
= 20^2 + 21^2
AB = 841^1/2
AB = 29
Perimeter of the trapezoid = 29 + 16 + 29 + 58
= 132 units
Thus, the perimeter of the trapezoid is 132 units.
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I just need help with question A
Suppose your cousin missed class and asks you, “Why do we plug in 0 for x to find y-intercepts and 0 for y to find x-intercepts? That doesn’t make sense to me.” Explain to your cousin WHY this process works. Use the line
5x+4y=14 as an example.
A) A description in words why this works
The reason why the cousin's procedure for getting the x and y intercepts work is because they represent the definition of those points on a graph.
How to find the x and y intercepts?The x-intercept of a graph or function simply refers to the point at which the graph crosses the graph crosses the x-axis or the point at which y = 0. In a similar manner, the y-intercept simply refers to the point at which the graph crosses the y-axis or simply the point at which x = 0.
Now, we are given the equation of the line as;
5x + 4y = 14
The general form of equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Rewriting the equation of the line in slope intercept form is;
y = -⁵/₄x + ⁷/₂
Now, the reason why we plug in 0 for x to get the y-intercept is because when x = 0, that is only where we can get the y-intercept as the corresponding value of x will be traced to 0.
Similarly, the reason why we plug in 0 for y to get the x-intercept is because when y = 0, that is only where we can get the x-intercept as the corresponding value of y will be traced to 0.
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Factorise 2(x-y)-a(y-x)
Answer:
( a + 2 ) ( x - y )
Step-by-step explanation:
2 ( x - y ) - a ( y - x )
= 2 ( x - y ) + a ( x - y )
= ( 2 + a ) ( x - y )
= ( a + 2 ) ( x - y )
Hence factorised.