Answer:
AB = 21
Step-by-step explanation:
Tales' theorem
\(\frac{12}{14} =\frac{18}{AB}\)
\(AB=\frac{(14)(18)}{12}\)
\(AB=21\)
Hope this helps
(i)Given that:
AE || BD
AB = ? [Let AB be x]
BC = 3
ED = 12
DC = 4
We know that
By Basic Proportionality Theorem,
AB/BC = ED/DC
On substituting these values in the above formula
⇛ AB / 3 = 12 / 4
On applying cross multiplication then
⇛ x(4) = (12)3
⇛ 4x = 36
Shift the number 4 from LHS to RHS.
⇛ x = 36÷4
⇛ x = 36/4
Therefore, AB = 9
Answer: The value of AB for the given problem is 9.
Similarly,
(ii) Given that:
EB || DC
AE = 14
ED = 12
AB = ? [Let AB be X]
BC = 18
We know that
By Basic Proportionality Theorem,
AE / ED = AB / BC
On substituting these values in the above formula
⇛ 14 / 12 = x / 18
On applying cross multiplication then
⇛ 14(18) = (12)x
⇛ 252 = 12x
Shift the number 252 from LHS to RHS.
⇛ X = 256÷12
⇛ X = 21
Therefore, AB = 21
Answer: The value of AB for the given problem is 21
Additional comment:
Basic Proportionality Theorem
" A line drawn parallel to the one side of a triangle intersecting other two sides at two different points, then the line divides the other two sides in the same ratio".also read similar questions: In the given figure QR ∥AB, RP∥ BD,CQ=x+2,QA=x,CP=5x+4,PD=3x.The value of x is..
https://brainly.com/question/18679712?referrer
https://brainly.com/question/18679661?referrer
What is the rectangular form of 12(cos(π) + i sin(π))?
12
-12
12 + i
–12 + i
Answer:
12-12-12+i-12+i =0-i
.
.
.
,
a room has the shape of a rectangle with a right triangle taken from one of its corners as shown at left. the rectangle has a length of 22 2222 feet ( ft ) (ft)(, start text, f, t, end text, )and a width of 19 ft 19 ft 19, start text, f, t, end text. both sides next to the removed corner have a length of 10ft 10 ft 10, start text, f, t, end text. what is the perimeter of the room in feet?
Perimeter of the room left after removing the corner, using the Pythagoras theorem = 76ft.
What is Pythagoras Theorem?According to the Pythagoras theorem, the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. Imagine that BC² = AB² + AC² exists in the ABC triangle.
In this equation, AB stands for the base, AC for the altitude, and BC for the hypotenuse. It should be remembered that a right-angled triangle's hypotenuse is its longest side.
Now here, sides of the rectangle are, l = 22ft and b = 19ft.
A right triangle is removed from the corner.
The dimension of the triangle becomes height =12ft and base = 9ft.
As it's a right triangle, the hypotenuse using the Pythagoras theorem =
√ (12² + 9²)
=√ 225
= 15ft.
Now, the perimeter of the shape left after removing the triangle =
22ft + 19ft + 10ft + 15ft + 10ft
= 76ft.
Therefore, the perimeter of the room =76feet.
To know more about Pythagoras Theorem, visit:
https://brainly.com/question/343682
#SPJ1
Which of the given is the set of zeroes of the polynomial p(x)=2x3+x2-5x+2
Answer:
x = 1, \(\frac{1}{2}\), -2Step-by-step explanation:
To find the roots (zeros), replace y with 0 and solve for x .
Hope this helped. A brainliest would be very much appreciated. (I need 5 brainliest so I can level up) :)
The city of London, England, has an
elevation of 11 meters.
Which of these describes the elevation
of London?
below sea level
at sea level
above sea level
Answer:
above sea level
Step-by-step explanation:
Find an equation for the perpendicular bisector of the line segment whose endpoints
are (1,3) and (-9,7).
I need help :(
This is the same as y = 2.5x+10 since 5/2 = 2.5
============================================
Explanation:
Let's find the slope of the line through those given points
m = (y2-y1)/(x2-x1)
m = (7-3)/(-9-1)
m = 4/(-10)
m = -2/5
To find the perpendicular slope, we flip the fraction and flip the sign
flip the fraction: -2/5 turns into -5/2
flip the sign: -5/2 turns into 5/2
The perpendicular slope is 5/2
Side note: The original slope (-2/5) and the perpendicular slope (5/2) multiply to -1.
-------------------------
Now find the midpoint
We add the x coordinates of the original points to get 1+(-9) = -8, which cuts in half to -8/2 = -4. This is the x coordinate of the midpoint.
Do the same for the y coordinates. First add: 3+7 = 10, then cut in half: 10/2 = 5. The y coordinate of the midpoint is 5.
The midpoint is (-4,5)
-------------------------
The perpendicular bisector will go through this midpoint. It has a slope of m = 5/2
Turn to point slope form to find the equation we need
y - y1 = m(x - x1)
y - 5 = (5/2)(x - (-4))
y - 5 = (5/2)(x + 4)
y - 5 = (5/2)x + (5/2)*4
y - 5 = (5/2)x + 10
y = (5/2)x + 10 + 5
y = (5/2)x + 15
y = 2.5x + 15 ... since 5/2 = 2.5
Missing angles/math please help guys
Answer:
Step-by-step explanation:
FILL IN THE BLANK a/an ____________________________ diagram can be used to show how the tables in a database are defined and related..
A/an database schema diagram can be used to show how the tables in a database are defined and related.
This type of diagram provides a visual representation of the structure and organization of the database. It illustrates the tables ,and their attributes, and the relationships between them.
The database schema diagram helps in the understanding the logical design of the database, including primary keys, for foreign keys, and the connections between different tables. It allows developers, database administrators, and stakeholders to visualize the database structure and serves it as a reference for in designing, modifying, and querying the database effectively.
To learn more about database click here:
brainly.com/question/31664263
#SPJ11
the hurwicz criterion is a compromise between the minimax and maximin criteria. a. true b. false
True. In game theory and decision theory, the Hurwicz criterion is a decision-making rule between the minimax and maximin criteria.
The Hurwicz criterion is a hybrid of the minimax and maximin criterion. The minimax criterion is concerned with minimising the most potential loss, whereas the maximin criterion is concerned with maximising the least possible gain. The Hurwicz criterion is expressed as a weighted average of the greatest and worst outcomes:
Decision value = α(best payoff) + (1-α)(worst payoff)
where alpha is coefficient representing the decision-maker's optimism or pessimism. The Hurwicz criterion provides a more versatile decision-making tool than the minimax or maximin criteria alone, allowing for a balance between risk-taking and risk-aversion.
To know more about Hurwicz criterion, visit,
https://brainly.com/question/29103554
#SPJ4
a. Write 64√2 in the form 2^n
We get the expression 64√2 in the form 2ⁿ as 2⁶°⁵.
An expression is a way in which numbers are written.
It can be variables, constants or a combination of both.
We are given an expression:
64 √2
We know that:
64 = 2 × 2 × 2 × 2 × 2 × 2
64 = 2⁶
Also, we can write √2 as
√2 = 2⁰°⁵
We get that:
2⁶ × 2⁰°⁵
simplifying the expression, we get that:
= 2⁶⁺⁰°⁵
= 2⁶°⁵
Therefore, we get the expression 64√2 in the form 2ⁿ as 2⁶°⁵.
Learn more about expression here:
https://brainly.com/question/723406
#SPJ9
Given the parent function f(x)=1x , match each transformed function with it transformation.
Answer:
4858576
Step-by-step explanation:
so what do you 5th and I
Considering the middle 95% of the data, determine the margin of error, to the nearest hundredth, for the simulated results. In the given context, explain what this value represents.
The 95% margin of error simony states that there is a 95% probability that the confidence interval contains the true population mean.
What is a margin of error?It should be noted that the margin of error simply means a measurement that accounts for the difference between the actual result and the projected result in a survey sample.
In this case, the 95% margin of error simply states that there is a 95% probability that the confidence interval contains the true population mean. This is the radius of the 95% confidence interval.
Learn more about margin of error on:
brainly.com/question/27909412
#SPJ1
Question 3
The figure below is a rectangular shipping bax Name two different pla
b
C
d
plane FBC, plane ADC
plane ADE, plane FBC
plane ADC, plane CGH
plane ADE, plane CGH
DH
The answer is d. plane ADE, plane CGH.
Using the elimination method, what is the solution to the system of equations? 6x + 6y = 12 6x - 5y = 12
Answer: x = 2, y = 0
Step-by-step explanation:
11y = 0
y = 0
6x + 6(0) = 12
6x = 12
x = 2
A ketchup Company purchased eight shipments of tomatoes, they were 900 tomatoes in each shipment how many did the company purchased in all
Answer:
7200 tomatoes
Step-by-step explanation:
8 shipments of tomatoes at 900 tomatos per shipment add up to 7200 tomatoes. That';s the product of 8 shipments and 900 tomatoes per shipment.
The concentration of copper(II) sulfate in one brand of soluble plant fertilizer is 0.0700% by weight. A 16.0 g sample of this fertilizer is dissolved in 2.00 Lof solution 4th attempt til See Periodic Table See Hint Calculate the number of moles of Cu2in the 16.0 g sample. 333 mol X 10
The number of moles of Cu2+ in the 16.0 g sample of the soluble plant fertilizer can be calculated as follows:
First, we need to determine the mass of Cu2+ in the sample. Since the concentration of Cu2+ in the fertilizer is given as a percentage by weight, we can simply multiply the mass of the sample by the concentration to obtain the mass of Cu2+ in the sample:
Mass of Cu2+ = 16.0 g x 0.0700% = 0.0112 g
Next, we need to convert the mass of Cu2+ to moles. The molar mass of Cu2+ is 63.55 g/mol. Therefore, the number of moles of Cu2+ in the sample is:
Moles of Cu2+ = Mass of Cu2+ / Molar mass of Cu2+ = 0.0112 g / 63.55 g/mol = 0.0001767 mol
Thus, the number of moles of Cu2+ in the 16.0 g sample of the soluble plant fertilizer is 0.0001767 mol.
Learn more about fertilizer here
https://brainly.com/question/30624208
#SPJ11
CAN SOMEONE PLS HELP ?! a piece of land resembles a trapezoid with bases 250 yards and 330 yards and a height of 20 yards. Estimate the area of the land by finding the area of the trapezoid.
Answer:
5800 yd²
Step-by-step explanation:
Area of trapezoid = area of the land = ½(a + b)×h
Where,
a = 250 yds
b = 330 yds
h = 20 yds
Thus,
Area = ½(250 + 330) × 20
Area = 5800 yd²
Carol spends 11 hours in a 4-week period practicing her culinary skills. How many hours does she practice in 5 weeks?
Answer:
13.75 hours
Step-by-step explanation:
If she spends 11 hours in a 4 week practice
then she pends X hours in 5 weeks
11 hours = 4 weeks
X hours = 5 weeks
11 x 5 =4x X
55=4X
X = 55/4
X =13.75 hours
Write the equation of the line that passes through the point (4,−1) that is parallel to the line 2x−3y=9
First we find the slope of the line 2x−3y+8=0 by placing it into slope intercept form:
2x−3y+8=0
⇒−3y=−2x−8
⇒3y=2x+8
⇒y=
3
2
x+
3
8
Therefore, the slope of the line is m=
3
2
.
Now since the equation of the line with slope m passing through a point (x
1
,y
1
) is
y−y
1
=m(x−x
1
)
Here the point is (2,3) and slope is m=
3
2
, therefore, the equation of the line is:
y−3=
3
2
(x−2)
⇒3(y−3)=2(x−2)
⇒3y−9=2x−4
⇒2x−3y=−9+4
⇒2x−3y=−5
Hence, the equation of the line is 2x−3y=−5.
Answer:
y=2/3x-11/3
Step-by-step explanation:
Hi there!
We are given the equation 2x-3y=9 and we want to write an equation that is parallel to it and that passes through (4,-1)
Parallel lines have the same slopes
So we need to first find the slope of 2x-3y=9
We can do this by converting the equation of the line from standard form (ax+by=c where a, b, and c are integers) to slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)
To do this, we need to isolate y on one side
2x-3y=9
subtract 2x from both sides
-3y=-2x+9
divide both sides by -3
y=2/3x-3
as 2/3 is in the place where m is, 2/3 is the slope of the line
It's also the slope of the line parallel to it that passes through (4,-1).
Here's the equation of that line so far:
y=2/3x+b
now we need to find b
as the line will pass through the point (4,-1), we can 4 as x and -1 as y in order to solve for b
-1=2/3(4)+b
multiply
-1=8/3+b
subtract 8/3 to both sides
-11/3=b
Substitute -11/3 as b into the equation
y=2/3x-11/3
There's the equation
Hope this helps!
Needddd Helpp Asap!!!!!!
Answer:
the answer will be D because it looks like it would be d
Answer: The first one
Step-by-step explanation:
find the length of the loop of the given curve. x = 9t − 3t3, y = 9t2
The length of the loop for the given curve x=9t-3t³, y=9t² is 36√3
What is meant by length?The distance measured from one end to the other of an object's longer or longest side. additionally: any measured distance. the state or trait of being long. the duration of something duration of a visit. The length of something is defined as its measurement or extent from end to end. In other terms, it is the biggest of two or the highest of three geometrical forms or objects' dimensions.
Given,
x=9t-3t³, y=9t²
The loop starts from x=0 and with x=0
Therefore, x=0
9t-3t³=0
3t(3-t²)=0
3-t²=0
t=±√3
dx/dt=9-9t²
dy/dt=18t
Hence length of a loop of a curve,
By using the integration,
=\(\int\limits^a_b\)√(dx/dt)²+(dy/dt)²
Here a=√3, b= -√3
=\(\int\limits^a_b\)√(9-9t²)²+(18t)²dt
=\(\int\limits^a_b\)√(1-t²)²+4t²dt
=\(\int\limits^a_b\)√1-t⁴-2t²+4t²dt
=\(\int\limits^a_b\)√1+t⁴+2t²
=\(\int\limits^a_b\)√(1+t²)dt
=9(t+t²/3)
=36√3
Therefore, the length of the loop is given by 36√3.
To know more about length, visit:
https://brainly.com/question/13194650
#SPJ1
The coordinates of the points A and B are ( 0 , -2 ) and ( 3 , 0 ) respectively.
(a) What is the y - intercept of the line AB?
(b) What is the gradient of the line AB?
(c) What is the length of the line AB?
Answer: The y-intercept is -2
The gradient is 2/3
and the length is 13
Step-by-step explanation:
what statistics are robust to outliers
There are several statistics that are robust to outliers: Median, Interquartile range, Winsorized mean and Trimmed mean.
How we find that what statistics are robust to outliers?These statistics are more suitable for datasets that contain outliers as they are less influenced by the extreme values and provide more accurate information about the central tendency and variability of the data.
Median: The median is less sensitive to extreme values in a dataset as it only considers the middle value, regardless of how large or small the other values are.Interquartile range (IQR): IQR is the difference between the third quartile (75th percentile) and the first quartile (25th percentile) of a dataset. It is calculated using the middle 50% of the data and is not influenced by the extreme values.Winsorized mean: The Winsorized mean is calculated by first replacing a fixed percentage (for example, 5%) of the largest and smallest values in a dataset with the nearest remaining value, and then calculating the mean. This method reduces the impact of extreme values on the mean.Trimmed mean: The trimmed mean involves removing a fixed percentage of the smallest and largest values in a dataset and then calculating the mean of the remaining values. This approach is similar to the Winsorized mean and also reduces the influence of extreme values on the mean.Learn more about Statistics are robust to outliers
brainly.com/question/28589666
#SPJ11
A company employs three analysts, two programmers and one salesperson.
- The analysts are paid a combined total of $264K.
- The third analyst makes 50% less than the first two analysts combined.
- The first analyst makes 20% more than the second analyst.
- The first programmer makes $30K more than the second.
- The salesperson makes $20K less than the second programmer.
- The company spends a total of $505K on salaries.
Determine the salary (in $K) of each employee
First analyst: x1 = 110.06 K Second analyst: x2 = 91.72 K Third analyst: x3 = 101.89 K First programmer: x4 = 121.72 K Second programmer: x5 = 71.72 K Salesperson: x6 = 66.89 K (x6 is found by subtracting total salaries of the other employees from total salary)Note: The salaries are in thousands. Therefore, each salary is followed by a 'K' which represents thousand.
Let’s begin by defining variables for each employee and start forming the equations which will help us to solve the system of linear equations.Let x1 be the salary of the first analyst.x2 be the salary of the second analyst.x3 be the salary of the third analyst.x4 be the salary of the first programmer.x5 be the salary of the second programmer.x6 be the salary of the salesperson.So we have, x1 + x2 + x3 = 264 ............(1)(The analysts are paid a combined total of $264K.)x3 = 0.5(x1 + x2) ...........................(2)(The third analyst makes 50% less than the first two analysts combined.)x1 = 1.2x2.........................................(3)(The first analyst makes 20% more than the second analyst.)x4 = x2 + 30.................................(4)(The first programmer makes $30K more than the second.)x5 = x4 - 20...................................(5)(The salesperson makes $20K less than the second programmer.)Adding all these equations, we get;x1 + x2 + 0.5(x1 + x2) + x2 + 1.2x2 + x2 + 30 + x4 - 20 = 5052.7x1 + 5.2x2 + x4 = 495............(6)Now using equations 1, 2 and 3;x1 + x2 + 0.5(x1 + x2) = 264
Substituting x3 from equation 2, we get;x1 + x2 + 0.5(x3) = 264Substituting the value of x3 from equation 2, we get;x1 + x2 + 0.5(x1 + x2) = 264x1 + x2 + 0.5x1 + 0.5x2 = 2641.5x1 + 1.5x2 = 264Substituting the value of x1 from equation 3;x1 = 1.2x21.2x2 + x2 + 0.5(1.2x2 + x2) = 2642.9x2 = 264x2 = 91.72Putting the value of x2 in equation 3x1 = 1.2(91.72)x1 = 110.06Putting the value of x2 in equation 4x4 = 91.72 + 30x4 = 121.72Putting the value of x2 in equation 5x5 = 91.72 - 20x5 = 71.72
Therefore, the salary (in $K) of each employee is:First analyst: x1 = 110.06 KSecond analyst: x2 = 91.72 KThird analyst: x3 = 101.89 KFirst programmer: x4 = 121.72 KSecond programmer: x5 = 71.72 KSalesperson: x6 = 66.89 K (x6 is found by subtracting total salaries of the other employees from total salary)Note: The salaries are in thousands. Therefore, each salary is followed by a 'K' which represents thousand.
Learn more about Value here,
https://brainly.com/question/30390056
#SPJ11
Really easy! PLEASE HELP, I Will mark Brainliest
Answer:
(x,y)=(-5,5)
Step-by-step explanation:
Acceleration versus time graph for four objects are shown below. All axes have the same scale. Which object had the greatest change in velocity during the interval ?
The slope of a velocity graph represents the acceleration of the object.
Why does slope make things go faster?
Gravity is what causes the change in speed on a slope. Objects accelerate (move faster) when traveling downhill, and decelerate (move slower) when moving uphill (slow down).
They will then continue moving at the same pace on a level surface, presuming there is little friction.
= area of graph is 1/2 t₀a₀.
= area is less than 1/2 t₀a₀.
= area is more than 1/2 t₀a₀.
So in option (d) change in velocity is greatest.
Learn more about The slope of a velocity
brainly.com/question/28357012
#SPJ4
write the equation of the line that passes through the point (-5,5) and is parallel to the line y=-3x+3
Graph 2x+y<1Y>1/2x+2
We need to graph the next given inequalities:
\(\begin{gathered} 2x+y<1 \\ \text{and} \\ y>1/2x+2 \end{gathered}\)For 2x+y<1.
We need to find the x-intercept and y-intercept
To find the y-intercept, set x=0
\(\begin{gathered} 2(0)+y<1 \\ \text{Then} \\ y<1 \\ \text{The y-intercept is the point (0,1)} \end{gathered}\)To find the x-intercept, set y=0
\(\begin{gathered} 2x+0<1 \\ \text{solve for x} \\ x<\frac{1}{2} \end{gathered}\)The symbol "<" means less than, so we get the next graph:
For the second inequality y>1/2x+2
To find the y-intercept, set x=0
what is the value of x?
At the movie theatre, child admission is $6.40 and adult admission is $9.50. On Sunday, 165 tickets were sold for a total sales of $1266.80. How many adult tickets were sold that day?
Answer:
68Step-by-step explanation:
1. Define unknowns:
x - number of adult tickets ($9.50 each)y - number of child tickets ($6.40 each)2. Make system of equations:
\(x+y=165\) \(9.5x+6.4y=1266.8\)3. Multiply both sides of first equation by 6.4:
\(6.4x+6.4y=1056\) \(9.5x+6.4y=1266.8\)4. Subtract first equation from second one:
\((9.5x-6.4x)+(6.4y-6.4y)=1266.8-1056\) \(3.1x=210.8\) \(x=68\)Please someone help me out with my math homework .
Answer:
you see that Square on the corner of B use that unit box and trace it and then go to E and Trace two unit boxes at the top