The coordinate of the point L is such that ΔL K L is a scalene triangle that will be either (0,y) or (2a,y).
It is given that in ΔL K L , J has coordinates (0,0) and K has coordinates (2 a, 2 b) .
We have to find the coordinates of point L so that , ΔL K L is a scalene triangle.
What is a triangle ?
A triangle is a 3-sided shape. There are three sides and three angles in every triangle, some of which may be the same.
As per the question ;
The ΔL K L is a scalene triangle.
J has coordinates (0,0)
K has coordinates (2 a, 2 b) .
The possible coordinate of the point L will be (0,y) or (2a,y).
Let's check it.
Using the distance formula ;
JK = [tex]\sqrt{(2a-0)^2 + (2b -0)^2}[/tex]
JK = [tex]\sqrt{(4a^2 + 4b^2)}[/tex]
JK = [tex]2\sqrt{a^2 + b^2}[/tex]
Similarly ;
JL = [tex]\sqrt{0^2 + y^2}[/tex]
JL = y
And
KL = [tex]\sqrt{4a^2 + (2b - y)^2}[/tex]
The sides are all of different lengths, so , we can conclude that this is a scalene triangle.
Thus , the coordinate of the point L is such that ΔL K L is a scalene triangle that will be either (0,y) or (2a,y).
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Evaluate the sum of the finite geometric series. 3+6+12+24+48+ . . . +768
The infinite geometric series has the general form a1 + a1r + a1r² + a1r³+…, where r is the common ratio and a1 is the first term. The sum of the finite geometric series 3 + 6 + 12 + 24 + 48 + . . . + 768 is 1533.
What is geometric series?The result of an endless geometric sequence exists an infinite geometric series. There would be no conclusion to this series. There would be no conclusion to this series. The infinite geometric series has the general form a1 + a1r + a1r² + a1r³+…, where r is the common ratio and a1 is the first term.
The equation be S = a1/(1-r), where s is the total, a1 is the series's first term, and r is the common ratio, is a general formula for calculating the sum of an infinite geometric series. The formula a2/a1, where a2 is the second term in the series and a1 is the first term in the series, can be used to determine the common ratio.
Let the finite geometric series be
3 + 6 + 12 + 24 + 48 +. . . + 768
Where, the first term, a = 3
common difference, r = 6/3 = 2
n = 9
The equation be Sn = a(1 - [tex]$$r^{n}[/tex])/(1 - r)
substitute the values in the above equation, we get
S9 = 3(1 - [tex]$$2^{9}[/tex]))/(1 - 2)
simplifying the above equation, we get
= 3(1- 512)/(-1)
= 3(-511))/(-1)
= 3(511) = 1533
Therefore, the sum of the finite geometric series 3 + 6 + 12 + 24 + 48 + . . . + 768 is 1533.
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There are different methods to solving this problem. Which do you think is the best? Why? Enter your answer.
The best method to solve a problem is Brainstorming.
According to the statement
We have to find that the which method is the best for solving the problem.
So, For this purpose, we know that the
A mathematical problem is a problem that can be represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem.
From the given information:
There are different methods to solving this problem.
Then
we know that the to solve a problem there are lot of the method, but the some method are the best to solve the problem.
The method is called a brainstorming session.
It is the Brainstorming is a problem-solving activity where students build on or develop higher order thinking skills. Encourages creative thought. Brainstorming encourages students to think creatively.
And due to their special capability it is the best method.
So, The best method to solve a problem is Brainstorming.
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Help! 25 points! 5h=60. what does h equal to
Answer:
the answer is 12.
Step-by-step explanation:
to find the answer divide 60 by 5 and you'll get the answer (aka 12)
Answer:
12
Step-by-step explanation:
5h=60
h= 60÷5
=12
ans: h=12
.........................................................................................................
Answer:
256
Step-by-step explanation:
20-8=12
12+4=16
16x16=256
Answer:
256
Step-by-step explanation:
What is 2 5/11×2??????
Answer: 4 10/11
Step-by-step explanation:
Evaluate: 54.25÷6.2−3.8
Answer: 4.95
Step-by-step explanation:
54.25÷6.2−3.8=
54.25/6.2−3.8=
8.75-3.8=
8.75-3.80=
8-3+0.75-0.80=
5-0.05=4.95
Evaluate each logarithm.
log₂ 1/2
Answer:
well done ......hope it's helpful
How to factor this? Please help. Question attached
Answer:
(y+4)²
Step-by-step explanation:
[tex](a+b)^2=a^2 + 2ab+b^2[/tex]
Here, a=y and b=4.
Need answers ASAP!!!!
solve the pairs of simultaneous equation x+ 2y =7 and 4x +2y =10
Answer:
Step-by-step explanation:
Okay
x+2y=7
x+2y-2y=7-2y
x=7-2y
4x+2y=10
4x+2y-2y=10-2y
4x=10-2y
divide both sides by 4
4x/4=(10/4)-(2y/4)
x=(5-y)/2
Hope this helps! ^^
Summerfield's zoo has two elephants. The male elephant weighs 7 1/12 tons and the female elephant weighs 1 1/3 tons. How much more does the male weigh than the female?
4.313
Step-by-step explanation:
Use the given information to determine whether LM is a perpendicular bisector, median, and/or an altitude of ΔJ K L .
JM ≅KM
If JM ≅KM then M is the midpoint of ΔJKL then LM is the median of
JM ≅ KM.
What is the difference between perpendicular bisectors, medians, and altitudes of a triangle?
A perpendicular bisector is a 90° angle line that intersects and passes through the midpoint of a given segment.
The median of a triangle is a line segment that connects a vertex to the midpoint of the opposing side. Each triangle has three medians, one from each vertex, which all intersect at the triangle's centroid.
The altitude of a triangle is a line segment that runs through a vertex and is perpendicular to the baseline.
We know that JM ≅ KM then M is the midpoint of ΔJKL. Therefore, LM is the median of JM ≅ KM.
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does anybody know what 4021836 - 1987269 is?
Well, doing 4021836 - 1987269 on paper, you would get the answer of 2034567
solu. 2034272
Alternate form. 2.034272*10^2
If In triangleABC, (AB)^2 + (BC)^2 = (AC)^2, then triangleABC is a right triangle.
Determine whether this conjecture is true or false and find a counter example if it is false.
The triangle of ABC is a right-angle triangle is true.
In Triangle of ABC
⇒(AC)^2=(BC)^2+(AB)^2 ----equation (1)
given by
Pythagoras theorem,
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.
These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
The hypotenuse is the longest side in this situation because it makes an angle of 90°
⇒(hypotenuse)^2=(one side)^2+(other side)^2 ---equation (2)
comparing one (1) and (2)
we get, AC is a hypotenuse of a triangle.
⇒ hypotenuse is the longest side of a right-angled, opposite the right angle.
⇒ opposite angle of AC is ⇒∠ B.
Hence, ∠ B is a right angle of triangle ABC. so, the triangle of ABC is a right angle triangle is true.
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Find the value of x for the given values of a and b .
a+8=-4(x-b) , for a=8 and b=3
The value of x so that the equation based on a and b has a solution is x = -4/3
What are equations?An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.
Equations can be graphed, just like a function.
As we can see, we have the following equation:
a + 8 = -4(xb)
and we have the values of the coefficients a and b, and these are:
a = 8b = 3We substitute these values in the equation:
(8) + 8 = -4 [x(3)] We solve the equation
16 = -4(3x)
16 = -12x
x = 16-/12
x = 8/-6
x = 4/-3
x = -4/3
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A grocer is going to sort 13.5 pounds of candy into bags weighing 0.75 pounds each. How much candy will be left over?
3 5/8 times 21 2/3 what is the answer
Answer:
78 13/24
Step-by-step explanation:
3 5/8=29/8
21 2/3=65/3
29/8×65/3=1885/24=78 13/24
So, your answer is 78 13/24
Hey there!
3 5/8 * 21 2/3
= 3 * 8 + 5 / 8 * 21 * 3 + 2 / 3
= 24 + 5 / 8 * 63 + 2 / 3
= 29 / 8 * 65 / 2
= 29 * 65 / 8 * 2
= 1,885 / 16
= 78 13/24
Therefore, your answer should be:
78 13/24
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Find the diameter and radius of a circle with the given circumference. Round to the nearest hundredth. (Lesson 10-1) C=23cm
Answer:
radius: 3.66 Diameter: 7.32
Step-by-step explanation:
Radius = C/2π 3.6605636911136
Diameter = C/2π7.3211273822272
You swim 4 lengths of a pool and break a record by 0.72 second. The table shows your time for each length compared to the previous record holder. How much faster or slower is your third length than the previous record holder?
IfIf you swim 4 lengths of a pool and break a record by 0.72 second. The table shows your time for each length compared to the previous record holder. How much faster or slower is your third length than the previous record holder is: 0.54 seconds.
How much faster or slower is the third lengthFirst step is to calculate the different in speed between first and fourth length
Using this formula
Speed =-First length time in seconds +(- Fourth length time in seconds)
Let plug in the formula
Speed=-0.23+(-0.42)
Speed=-0.65
Second step is to calculate the third length
Speed=-0.65+0.11
Speed=-0.54 seconds
Therefore If you swim 4 lengths of a pool and break a record by 0.72 second. The table shows your time for each length compared to the previous record holder. How much faster or slower is your third length than the previous record holder is: 0.54 seconds.
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While taking a personal finance course, Lakshmi decided to create and follow a personal financial plan. To estimate her annual expenses, she kept track of everything that she spent for one month. She was surprised to discover that she spent $150 on clothing and accessories. If Lakshmi decided to cut her monthly clothing and accessories expenditure in half, how much could she save in a year?
Using proportions, it is found that she would save $900 in a year.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
She spends $150 a month on clothing and accessories, hence, if she saves half of that, the amount saved in a month is:
0.5 x 150 = $75.
In a year, this amount will add up to:
75 x 12 = $900.
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Find the geometric mean between each pair of numbers.
8 and 36
A group of products are averaged to determine central tendency using the geometric mean. The geometric mean of 8 and 36 is 6√8.
What is meant by geometric mean?
The geometric mean in mathematics is a mean or average that, by using the product of the values of the numbers, shows the center tendency or usual value of a set of numbers.
The geometric mean, sometimes known as the compounded annual growth rate, is a tool used in finance to determine average growth rates.
The Geometric Mean (GM) is the average value or mean that reveals the central tendency of a group of numbers by adding up the values of those numbers.
Formula to calculate G.M is
x = √(a × b)
Where, a = 8 and b = 36
x = √(8 × 36)
x = 6√8
Therefore, the value of x = 6√8.
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A shopkeeper packed two bags of sugar each 120 Kg into 3 Kg and 2 Kg packets respectively. There were half as many 2 Kg packets as 3 Kg packets. How many 3 Kg packets did he obtain?
Answer:
60
Step-by-step explanation:
Since both bags of sugar were 120 kg, there is a total of 240 kg of sugar to be distributed into the packs. Let x represent the number of 2 kg packets and y represent the number of 3 kg packets. We know that all the sugar was packed into these two kinds of packets, so:
[tex]2x+3y=240[/tex]
And we know that there were half as many 2 kg packets as 3 kg packets, so:
[tex]x=\frac{1}{2} y[/tex]
Now, we have a system of equations!
[tex]\left \{ {{2x+3y=240} \atop {x=\frac{1}{2}y }} \right.[/tex]
Let's put the second equation equal to y, since that removes the fraction:
[tex]x=\frac{1}{2}y\\ 2x=y[/tex]
Now substitute y into the first equation:
[tex]2x+3y=240\\2x+3(2x)=240[/tex]
Now simplify to find x:
[tex]2x+3(2x)=240\\2x+6x=240\\8x=240\\x=30\\[/tex]
There are 30 of the 2 kg packets! Now, we can use x to find y, the number of 3 kg packets!
[tex]2x=y\\2(30)=y\\60=y[/tex]
There are 60 of the 3 kg packets!
Ten times the sum of half a number and 6 is 8 in number form
The required no . is ( - 10. 4 ) .
According to ques .
10 * [ ( 1 / 2 ) x + 6 ] = 8
Solving linear equation in one variable above ,
( 1 / 2 ) x = ( 8 / 10 ) - 6
( 1 / 2 ) x = - 52 / 10
x = ( - 52 / 10 ) * 2
x = - 10 . 4
Hence , the no . is ( - 10 . 4 ) .
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Four quarter circles are cut out from a 16cm square. Work out the shaded area. Convert your answer to mm^2
the required area of shaded part is 549.3807mm^2
Four quarter circles are cut out from a 16 cm square
that is we have given that square has each side 16 cm
we know that
area of square = (side) ^2
= 16*16 cm^2
= 256 cm^2
four quarter circles are cut out from a 16 cm square
we know that
area of sector = N/360 ( pi *r^2)
= 90/360( pi* 8^2) it makes angle 90 degree and r=8cm
= 1/4( pi* 64)
therefore area of four quarter circles is given by
=4*(1/4)*(64*pi)
=64pi
now the required area of the shaded part is equal to
=area of square - area of four quarter circles
= 256 - 64pi
= 256 - 201.06193
= 54.93807 cm^2
we know that 1cm is equal to 10mm
54.93807*10 =549.3807mm^2
Hence the required area of shaded part is 549.3807mm^2
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Evaluate the following algebraic expressions when
x = -2, y = -3, z =4
Write the value of the expressions in the boxes
a) 2x+3y
b) 2(y - z)
c) 6x over 2y
This question means you need to divide the top by the value of 2y
Answer:
Solutions below
Step-by-step explanation:
This question requires the concept of substitution and order of operations (Bracket > Multiplication / Division > Addition / Subtraction).
Given x = - 2, y = - 3 and z = 4,
a) 2 x + 3 y = 2 (- 2) + 3 (- 3) = - 4 + (- 9) = - 4 - 9
= - 13
b) 2(y - z) = 2 (- 3 - 4) = 2 (- 7) = - 14
c)
[tex] \frac{6x}{2y} \\ = \frac{6( - 2)}{2( - 3)} \\ = \frac{ - 12}{ - 6} \\ = 2[/tex]
Find the distance between the two points rounding to the nearest tenth (if necessary).
(3, 1) and (5,-2)
8.06 is the distance between the two points .
What is distance in math?
The length or width between two objects, points, lines, etc. the quality or condition of being remote from something else in space; remoteness. a straight line in space It would take too long to walk seven miles in one hour. a big area.A wide body of water encircled the ship.Using their coordinates, an algebraic expression provides the distances between two places (see coordinate system). The distance formulas for points in rectangular coordinates in two- and three-dimensional Euclidean space are based on the Pythagorean theorem.distance d = [tex]\sqrt{( 5 + 3)^{2} + ( -2 + 1)^{2} }[/tex]
d = [tex]\sqrt{8^{2} + (-1)^{2} }[/tex]
d = [tex]\sqrt{64 + 1}[/tex]
d = √ 65
d = 8.06225 ≈ 8.06
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682,548-300,752=
92,730-5,472=
47,569+21,478=
741,658+32,567=
Answer:
1.381796
2.87258
3.69047
4.774225
Step-by-step explanation:
Align the numbers as an ordinary subtraction problem. Write the larger number above the smaller number. If the smaller number has fewer digits, line them up on the right, as you would in a decimal (base ten) subtraction problem.
Answer:
682,548 - 300,752 = 381,796
92,730 - 5,472 = 87,258
47,569 + 21,478 = 69,047
741,658 + 32,567 = 774,225
Step-by-step explanation:
How many different 4-digit PIN codes are there that only include the digits 2, 3, 4, 6, 7, 8 and 9
if each of those digits is only allowed to be used once?
The number of different 4-digit PIN codes if each of those digits is only allowed to be used once is 840
How to determine the number of different 4-digit PIN codes if each of those digits is only allowed to be used once?The digits are given as:
2, 3, 4, 6, 7, 8 and 9
There are 7 digits represented in the above list
If each of those digits is only allowed to be used once, then we have the following possibilities
First character: Any of the 7 digits
Second character: Any of the remaining 6 digits
Third character: Any of the remaining 5 digits
Fourth character: Any of the remaining 4 digits
The number of 4-digit PIN codes is
Number = 7 * 6 * 5 * 4
Evaluate
Number = 840
Hence, the number of different 4-digit PIN codes if each of those digits is only allowed to be used once is 840
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1. Solve 5h+34 = 17 for h.
A -17/5
B -51/5
C 51/5
D 17/5
Answer:
A. -17/5
Step-by-step explanation:
h= -17/5
Hope this helps! :)
The cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55. The cost of 3 kg of mushrooms and 4 kg of turnips is £13.10. Work out the cost of a) 1 kg of turnips. b) 1 kg of mushrooms. check image
If the cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55 and the cost of 3 kg of mushrooms and 4 kg of turnips is £13.10, then cost of 1 kg of turnips is £1.1 and cost of 1 kg of mushrooms is £2.9.
Given that the cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55 and the cost of 3 kg of mushrooms and 4 kg of turnips is £13.10.
We are required to find the cost of 1 kg of mushrooms and the cost of 1 kg of turnips.
Cost is basically the expenditure that we do in order to buy or produce a product.
Suppose the cost of 1 kg of mushrooms be x and the cost of 1 kg of turnips be y. The equations will be as under:
2x+2.5y=8.55------1
3x+4y=13.10-------2
Equation1 *3 and Equation2 *2.
6x+7.5y=25.65-----3
6x+8y=26.20-------4
Subtract 4 from 3.
6x+7.5y-6x-8y=25.65-26.20
-0.5y=-0.55
y=1.1
Put the value of y in 1.
2x+2.5*1.1=8.55
2x+2.75=8.55
2x=8.55-2.75
2x=5.80
x=2.9
Hence if the cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55 and the cost of 3 kg of mushrooms and 4 kg of turnips is £13.10, then cost of 1 kg of turnips is £1.1 and cost of 1 kg of mushrooms is £2.9.
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In the class of 2019, more than 1.6 million students took the SAT. The distribution of scores on the math section (out of 800) is
approximately normal with a mean of 528 and standard deviation of 117.
According to the given statement;
The probability of student Who scored less than 350 is 0.0643.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. The concept of probability was developed to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a certain event will occur.
According to the given value;
Population Mean,μ = 528
Population Standard Deviation,σ = 117
X follows normal distribution
I.e X ~ N ( μ = 528 ,σ = 117 )
formula for z score is
Z =
0
Subtract the mean and then divide by the standard deviation to turn x into a standard Normal z
X ≤ 350
(x-528)/117 ≤ (350-528)/117
z ≤ -1.52
Now, by using standard normal distribution table
area left of -1.52
= 0.0643
Hence,The required probability is 0.0643.
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