well, tis noteworthy that whenever we have an absolute value equation is really a piece-wise function in disguise, namely the absolute expression is really two in disguise.
[tex]8x=2|6x-2|\implies \cfrac{8x}{2}=|6x-2|\implies 4x=|6x-2|\implies \begin{cases} 4x=+(6x-2)\\ 4x=-(6x-2) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 4x=+(6x-2)\implies 4x=6x-2\implies 0=2x-2 \\\\\\ 2=2x\implies \cfrac{2}{2}=x\implies \boxed{1=x} \\\\[-0.35em] ~\dotfill\\\\ 4x=-(6x-2)\implies 4x=-6x+2\implies 10x=2\implies x=\cfrac{2}{10}\implies \boxed{x=\cfrac{1}{5}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill x= \begin{cases} 1\\[1em] \frac{1}{5} \end{cases}~\hfill[/tex]
An activity on a pert network has these time estimates: optimistic = 2, most likely = 5, and pessimistic = 10. what is its expected activity time?
The expected activity time for the given statement is = 5.33
What time is the PERT network expected to be active?The average amount of time required for an activity when it is repeatedly performed is known as the expected time. The weighted average of the three estimated times, i.e., the optimistic time, the most probable time, and the pessimistic time, is used in project management analysis to determine the expected time of activity.
The PERT system:A network model called the Program Evaluation and Review Technique (PERT) allows for randomness in the timing of activity completion. PERT was created in the late 1950s again for a massively labor-intensive Polaris project for the US Navy. It might shorten a lot of time and cost needed to finish a project.
According to the given information:optimistic = 2
most likely = 5
pessimistic = 10.
We will use the following formula to calculate the anticipated time for each activity in order to solve this problem:
Expected Time = (Optimistic Time + (4 x Most likely) + Pessimistic Time) / 6
Putting the values into formula:
= (2 + (4 x 5) + 10)/ 6
= (2 + 20 + 10) / 6
= 5.33
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Someone know this? The graph of g(x)is the graph of f(x)=x2 shifted 4 units left, vertically stretched by a factor of 3, then shifted 5 units up. What is the function rule for g(x)?
The function g(x) is given as: g(x) = 3 ( x + 4 )^2 + 5
Given data
f(x)=x2
shifted 4 units left
stretched by a factor of 3
shifted 5 units up
How to find the function rule for g(x)The function g(x) is formed from the function f(x) by the following moves:
Shifting 4 units to left
To shift the graph 4 units to the left is given by
f(x) = x^2
f(x) = ( x + 4 )^2
Stretching by a factor of 3
to stretch by a factor of 3 means multiplying by 3
f(x) = 3 * ( x + 4 )^2
f(x) = 3 ( x + 4 )^2
Shifting 5 units up
This movement is shows in the y axis and is represented as follows
f(x) = 3 ( x + 4 )^2 + 5
At this stage the function rule for g(x) is completed hence
f(x) = 3 ( x + 4 )^2 + 5 = g(x)
and
g(x) = 3 ( x + 4 )^2 + 5
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I don't understand, help would be appreciated.
Answer:
Ok so "X" will ALWAYS be the first number in a ordered pair so in this case 3 WILL be the "X" value 5 will be the "Y" value. "X" is the Horizontal line on the graph you will always start with "X" so you will go over 3 times and up 5 I'm making this complicated but pretty much all you need to know is that "X" is 3
Note: I hope you have a good day and I hoped this helped! :))
WILL MARK BRAINLIST !!
Find the value of xº from the given figure applying the activity.
Answer:
total inner angle of quadrilateral is 360 so
66 is remaining angle.
Please mark me as brainlist answer.
You has promised. Don't broke promise that you will give brainlist answer.
Answer:
The sum of the interior angle of a quadrilateral is given by the formula
(n-2)×180°
n represent the number of sides
(4-2)×180°
2×180°
=360°
then equate the angle to 360°
What must be added to x² - 2xa to make it a perfect square?
Answer:
we need to add [tex]a^{2}[/tex] to make it a perfect square.
Step-by-step explanation:
since we know
[tex]a^{2}+b^{2}-2ab=(a-b)^{2}[/tex]
then after compairing it with x² - 2xa
we have;
missing term as [tex]a^{2}[/tex]
hence we need to add [tex]a^{2}[/tex] to make it a perfect square.
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15. If the endpoints of a diameter of a circle are (2, -1) and (4, 0), what is the y
coordinate of the center of the circle?
Y = -0.5
The center point of a straight line can be located using the midpoint formula. You may occasionally need to determine the difference between two specific numbers. For that, you find the average of the two numbers. In a similar way, we obtain the halfway number (or point) between two coordinates using the midpoint formula in coordinate geometry
Let the midpoint of (x₁ ,x₂ ) and (y₁ , y₂) is (x ,y)
x,y = ( x₁ + x₂)/2 , (y₁ +y₂)/2
Since radius is half of the diameter, we need to find the findthe midpoint of the diameter
Using midpoint formula,
y = (y₁ + y₂)/2
= (0 + (-1))/2
= -0.5
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16^((3)/(8))* 16^((1)/(8))
solve the equation for the given variable. justify each step.
9x + 2y = 5; y
1/15s - 2/3t = -2; s
Answer: y=[tex]\frac{5-9x}{2}[/tex]
s=-30+10t
Step-by-step explanation:
9x + 2y = 5; y
9x-9x+2y = 5-9x
2y=5-9x
y=[tex]\frac{5-9x}{2}[/tex]
1/15s - 2/3t = -2; s
(1/15s - 2/3t = -2)*15 ==> Get rid of fraction by multiplying both sides by 15
s - 30/3 t=-30
s-10t=-30
s=-30+10t
Sam's plumbing service charges a $50 diagnostic fee and then $20 per hour. How much money does he earn, m, when he shows up to your house to do a job that takes h hours?
Answer:
50 + 20h
Step-by-step explanation:
a fishing boat accidentally spills 15 barrels of diesel oil into the ocean. each barrel contains 42 gallons. if the oil film on the ocean is 2.5×102nm thick, how many square meters will the oil slick cover?
The square meters of the area the oil slick will cover is 9.6 × 10⁶ m².
What is meant by volume?Volume is defined as the amount of three-dimensional space enclosed by a closed surface.
The liter (L) is the metric system's base volume unit, with several extended volume units also available. There are also many metric volume units based on the a cubic length dimension, including such cubic meters or cubic centimeters. Gallons and ounces are examples of imperial volume units.Now, as per the given question;
First, we determine the entire volume of oil in gallons by multiplying the volume per barrel even by total number of barrels:
15×42 gal = 630 gal
This volume must be converted to square meters:
V = 630 gal × (0.00379 m³/ gal
V = 2.4 m³
The thickness (height) of a oil film in meters is required:
h = 250 nm × (m/10⁻⁹nm)
h = 2.5 × 10⁻⁷m
The surface area of a oil film is calculated by dividing the oil volume by height of the oil film.
A = V/h
A = 2.4 m³/2.5 × 10⁻⁷m
A = 9.6 × 10⁶ m²
Therefore, the area of the oil slick cover is found to be 9.6 × 10⁶ m².
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if i walked 4 miles for 180 days how much miles would i have walked
Answer:
720
Step-by-step explanation:
4x180=720 u have to multiply because 4 miled in 180 days is the same as 4x180
An explanation needed, thx
The points (-4,2) and (4,2) are two vertices of a square. State all other order pairs that could be the other two vertices of the square.
Find the midpoint of the given line segment with the given endpoints
(-3, 8) and (2, -4)
The midpoint of the given line segment with the given endpoints
(-3, 8) and (2, -4) is (-0.5, 2)
Midpoint of coordinatesThe formula for calculating the midpoint of coordinate is expressed as;
M(x, y) = (x₁+x₂/2, y₁+y₋/2 )
Given the coordinate points( -3, 8) and (2, -4)
Substitute
M(x, y) = (-3+2/2, 8-4/2)
M(x, y)= (-1/2, 4/2)
M(x, y) =(-0.5, 2)
Hence the midpoint of the given line segment with the given endpoints
(-3, 8) and (2, -4) is (-0.5, 2)
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If a person with an hourly pay of $9.50 per hour gets a 20% raise, what is the hourly pay?
Which expression is equivalent to 9(15)?
9(10+5)
9 left parentheses 10 plus 5 right parentheses
9(10+50)
9 left parentheses 10 plus 50 right parentheses
9(1+5)
9 left parentheses 1 plus 5 right parentheses
9(1+50)
Answer:
9(10+5)
Step-by-step explanation:
because 10+5 is fifteen so then when you as them together you get the same expression as before
Answer:
9(10+5)
Step-by-step explanation:
because 10+5=15 and it's 9(15)
If the parents of a family already have two boys, what is the probability that the next two offspring will both be girls?
The probability that the next two offspring will both be girls is 1/3.
To find P both children are girls
A: Event that both children are girls
A: {MM} and B: {MF, FM, MM} →→ P (A ∩∩ B) = {MM}
Probability that both are males, if we know one is a female =P(A/B)=P(A∩B)/P(B)
(P(A∩B)P(B))
Given S = {MM, MF, FM, FF}, we can see that: P (A) = 1414; P (B) = 3434; P (A ∩∩ B) = 1414
Therefore,
P(B/A)=P(A∩B)/P(A) = (1/4)/(3/4)=1/3.
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PLEASE HELP ME ASAP PLEASE.
Answer:
See below
Step-by-step explanation:
g (h(6)) :
h (6) = 3 ( 6^2) + 2 = 110
then g (110) = sqrt (110)
h (g(5))
g(5) = sqrt 5
then h( sqrt5) = 3 ( sqrt5)^2 + 2 = 17
a² + b²
______
a-b
if a = 3 and b = 4
Please help!
Answer:
Step-by-step explanation:
3^2+4^ / 3-4 = -25
Find an equation in cylindrical coordinates for the equation given in rectangular coordinates. 25x2=25y2=6x
25r(cos^2Ф-sin^2Ф)-6cosФ=0
The equation in rectangular coordinates is 25x2=25y2=6x, we need to write in cylindrical coordinates
What is rectangular coordinate system?The rectangular coordinate system consists of two real number lines that intersect at a right angle
In cylindrical coordinate, x=rcosФ
y=rsinФ
z=z
25(rcosФ)^2=25(rsinФ)^2=6rcosФ
25r^2cos^2Ф-25r^2sin^2Ф=6rcosФ
25r^2(cos^2Ф-sin^2Ф)=6rcosФ
25r(cos^2Ф-sin^2Ф)-6cosФ=0
25r(cos^2Ф-sin^2Ф)-6cosФ=0 is the required equation in cylindrical coordinates.
Therefore 25r(cos^2Ф-sin^2Ф)-6cosФ=0 is the required cylindrical equation
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Cylinder A has radius 3 cm and
height 10 cm
Cylinder B has radius 6 cm and
height 8 cm
10 cm
Cylinder A
8 cm
Cylinder B
6 cm
Cylinder A is half full of water.
Work out the volume of water in
Cylinder A.
Give your answer in terms of Pie
The volume of the water filled in the cylinder A is 141.77 cm³.
How do you describe a cylinder?A cylinder is a 3 solid that contains two parallel bases connected at a fixed distance by a curved surface.
These bases are typically circular in shape (such as a circle), with the center of a two bases connected by a line segment known as the axis.A cylinder does have two flat ends shaped like circles. A curved face which resembles a tube connects these two faces. A flat net for just a cylinder resembles a rectangle with such a circle connected at each end.The formula for the volume of the cylinder is;
Volume = πr²h
Where, π = 3.14,
radius r = 3 cm.
height h = 10 cm.
Put the values and obtain the volume.
Volume = (3.14)(3)²(10)
Volume = 282.74 cm³.
As, the cylinder is half filled with water;
Water volume = 282.74/2 cm³
Water volume = 141.77 cm³
Thus, the volume of water filled in cylinder A is 141.77 cm³.
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The correct question is-
Cylinder A has radius 3 cm and height 10 cm. Cylinder A is half full of water.
Work out the volume of water in Cylinder A.
f(x)= [[x]] is the "greatest integer" function. The range of f(x) = x-[[x]] is:
Deondra is 1.35 meters tall. At 10 a.m., she measures the length of a tree's shadow to
be 35.25 meters. She stands 31.2 meters away from the tree, so that the tip of her
shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest
hundredth of a meter.
Answer:
If the length of a tree's shadow is 35.25 meters. The height of the tree to the nearest hundredth of a meter will be : 11.74m
Given:
Denora height=1.35 meters
Length =35.25 meters
Width =31.2 meters
Height of the tree=x
Proportion:
1.35 : 35.25 :: x : 31.2
Now let's determine the height of the tree:
35.25 - 31.2 / 1.35 = 35.25 / x
4.05 / 1.35 = 35.25 / x
Cross multiply
4.05x = 35.25 × 1.35
4.05x = 47.58
Divide both sides
x = 47.58 / 4.05
x = 11.74
In conclusion, if the length of a tree's shadow is 35.25 meters. The height of the tree to the nearest hundredth of a meter will be: 11.74m
A bee flies at 20 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 17 minutes, and then flies directly back to the hive at 12 feet per second. It is away from the hive for a total of 19
minutes.
In linear equation, the distance of the flowerbed from the hive is 2250 feet.
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.Let , the distance of the flowerbed from the hive is feet.
The bee flies 20 feet per second directly to a flowerbed from its hive and flies directly back to the hive at 12 feet per second.
time = distance / speed
So, the time taken by the bee to reach the flowerbed x/20 seconds and the time taken to fly back to the hive = x/12 seconds.
The bee stays at the flowerbed for 15 minutes or (15×60)seconds or 900 seconds and it is away from the hive for a total of 20 minutes or (20×60)seconds or 1200 seconds.
So, the equation will be
x/20 + x/12 + 900 = 1200
3x + 5x / 60 = 300
8x = 300 * 60
x = 2250
Thus, the distance of the flowerbed from the hive is 2250 feet.
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there are 126 students.
2/9 of them are taking geometry. 3/7
of the students taking
geometry are male.
how many female students are taking geometry?
Out of 126, 2/9 of them are taking geometry , 3/7 of the students are males ,number of female students taking geometry are 16.
As given in the question,
Total number of students = 126
Number of Students taking geometry = (2/9) × 126
= 28
Number of male students taking geometry= (3/7) × 28
= 12
Number of female students taking geometry= 28 - 12
= 16
Therefore, out of 126, 2/9 are taking geometry , 3/7 are males ,number of female students taking geometry are 16.
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Please Help fast
What does The function decrease by as well
Answer:
Step-by-step explanation:
the given graph is montonous so no decreasing or increasing
please mark me
Answer:
the graph decreases from -infinity to -3 and 3 to positive infinity and increase from -3 to +3
Step-by-step explanation:
Find the sum of the whole numbers from 1 to 680.
The sum of the whole numbers from 1 to 680 is 231540.
What is the sum of the whole numbers from 1 to 680?Arithmetic sequence is a list of numbers where each number is equal to the previous number, plus a constant called the common difference.
The formula for sum of first n numbers can be expressed as;
Sₙ = (n/2)( a₁ + aₙ )
Where n is the number of terms, a₁ is the first term and aₙ is the nth term.
Given that,
The numbers are whole numbers from 1 to 680
Number of terms n = 680First term a₁ = 1680th term a₆₈₀ = 680Sum S₆₈₀ = ?Plug the given values into the equation above.
Sₙ = (n/2)( a₁ + aₙ )
S₆₈₀ = (680/2)( 1 + 680 )
S₆₈₀ = 340( 681 )
S₆₈₀ = 231540
Therefore, the sum of the whole numbers from 1 to 680 is 231540.
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What does the pair of equations y = 1, z = 8 represent? in other words, describe the set of points (x, y, z) such that y = 1 and z = 8. a plane
The set of points (x , 1 , 8) describe a line that has constant value of y and z coordinates, i.e., is parallel to x-axis in the plane.
What is the equation of a line in a plane?The equation of a plane in R has the generic form: ax + by + cz + d = 0, where a, b, and c are the elements of the normal vector n = (a, b, c) that is perpendicular to the plane or any vector parallel to the plane.
Given: Equations of the lines:
y = 1z = 8To find: description of the points (x, y, z) in the plane.
Finding:
According to the given conditions, the lines y = 1 and z = 8 describe two lines with constant values of y and z coordinates respectively in the plane.
The set of points (x , 1 , 8) describe a line that has constant value of y and z coordinates, i.e., is parallel to x-axis and can have infinitely many values of x in the plane.
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A diagram shows a 5 cm* 5 cm* 5 cm cube.Calculate the length of the diagonal AB. Give your answer correct to 1 decimal place
The length of the diagonal AB of the given square is 8.660
Given that a diagram of a cube having dimensions 5×5×5 and asked to find out the length of diagonal AB(which is a body diagonal of the cube).
To calculate the body diagonal 1st we need to calculate the face diagonal via the Pythagorean theorem
Let's assume the length of the face diagonal is x
By Pythagorean theorem
[tex]x^{2} =5^{2} + 5^{2}[/tex]
[tex]x^{2} =50[/tex]
[tex]x=5\sqrt{2}[/tex]
Therefore, the length of the face diagonal is [tex]5\sqrt{2}[/tex]
Let's assume the body diagonal is y
By Pythagorean theorem
[tex]y^{2} =5^{2} +(5\sqrt{2} )^{2}[/tex]
[tex]y=\sqrt{125}[/tex]
y=[tex]5\sqrt{3}[/tex]=8.660
Therefore, The length of the diagonal AB of the given square is 8.660
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6 minus a number minus 11
Answer:
In equation form it should be: (6-x) -11
Step-by-step explanation:
BOOM!!! Your Welcome
The data set represents the heights, in centimeters, of ten model bridges made for
an engineering competition.
13
14
14
16
16
16
16
18
19
What is the MAD?
According to the given information the mean(MAD) of the data is = 16.
What is the mean mathematical term?The mean is the average of a set of variables in mathematics and statistics. The mean can be calculated in a variety of ways, such as the simple arithmetic mean (add the numbers and divide the sum by the number of observations), geometric mean, and harmonic mean.
According to the given data:(13 ,14 ,14, 16, 16, 16, 16, 18, 18, 19)
adding the numbers together.
(13 + 14 + 14 + 16 + 16 + 16 + 16 + 18 + 18 + 19)
= 160.
Then divide it by the amount of numbers. Which is ten.
160 divided by 10 = 16.
—MAD—
Subtract each value from the mean.
(|13-16| + |14-16| + |14-16| + |16-16| + |16-16| +|16-16| + |16-16| + |18-16| + |18-16| + |19-16|)
Negative numbers are unimportant; everything should be positive.
(3 + 2 + 2 + 0 + 0 + 0 + 0 + 2 + 2 + 3)
= 16.
16 divided by 16 (amount of numbers).
MAD = 1
–IQR—
Separate both sides in half.
(|13 14 14 16 16| ,|16 16 18 18 19|)
Take the middle value of each group.
Group1.
|13 14 (14) 16 16|
This one is 14.
Group 2:
|16 16 (18) 18 19|
This one is 18.
Subtract (number from group 2) 18 from (number from group 1) 14.
18 - 14 = 4
IQR = 4.
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