To find the point Q that partitions the line segment LM in a given ratio, we can use the formula for the coordinates of the point that divides a line segment in a given ratio.
Let's say we want to divide the line segment LM in the ratio r:s. The coordinates of the point Q can be found using the following formula:
Q = ((s * Lx) + (r * Mx)) / (r + s), ((s * Ly) + (r * My)) / (r + s)
In this case, we want to find the point Q that partitions LM in a given ratio. Let's assume the ratio is r:s.
Given:
L(-2, 5) and M(2, -3)
Let's say the ratio r:s is given as 2:3.
Substituting the values into the formula:
Qx = ((3 * (-2)) + (2 * 2)) / (2 + 3) = (-6 + 4) / 5 = -2 / 5
Qy = ((3 * 5) + (2 * (-3))) / (2 + 3) = (15 - 6) / 5 = 9 / 5
Therefore, the point Q(6/5, -7/5) partitions the line segment LM in the ratio 2:3.
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Please help!!! Find the equation of the line, use exact numbers:
y=__x+__
(__ means to fill in)
i do not know how to get the solutions
Answer: this is the solutions
An arborist examined trees in an orchard to see if they were infected with a virus. 324
out of 540 trees were infected with the virus. What percentage of the trees were infected?
Write your answer using a percent sign (%).
Answer:
60%
Step-by-step explanation:
324/540 x100=60%
Np!
HELP!! Which of the following represents the graph of the equation y = 1/2 x +1
ANSWER - The first seems more accurate according to my view it's A
A solid oblique pyramid has a square base with edges measuring x cm. the height of the pyramid is (x 2) cm.
The volume of a solid oblique pyramid with a square base with edges measuring x cm and height (x + 2) cm is (x³ + 2x²)/3 cm³
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The base of the pyramid is x cm while the height is x + 2, hence:
Volume of pyramid = (1/3) * area of square base * height = (1/3) * x * x * (x + 2) = (x³ + 2x²)/3 cm³
The volume of a solid oblique pyramid with a square base with edges measuring x cm and height (x + 2) cm is (x³ + 2x²)/3 cm³
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What is the length of a diagonal of a rectangle with a length of 8 meters and a width of 6 meters
Answer:
10 m
Step-by-step explanation:
If we draw the diagonal of the rectangle, we form a right triangle where the diagonal is the hypotenuse and the legs are 6 and 8.
This is a well-known Pythagorean triple, which gives the diagonal to be 10 m.
Why is it important to be able to express a clear and coherent argument visually or in writing? Think: where would you use this in the “real-world?”
It is important to be able to express a clear and coherent argument visually or in writing because without establishing coherence, your reader will not be able to know or understand the key points that you are trying to express or show.
Why is it important to have coherence in one's writing?Coherence is known to be a key quality for kind of good academic write up.
Note that in the area of academic writing, the ways that ideas flows is very important and as such, it need to be smooth and logical.
Therefore without coherent argument , the reader cannot understand the key points that a person is trying to show and thus hinders the readability of your work.
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30) A student has not been to class and must pass a 20 question true/false exam to continue in the course. The student will guess on every question and must get at least 14 correct to pass the test. What is the probability that the student will pass the test
The probability that the student will pass the test is 0.057
In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli,[1] is the discrete probability distribution of a random variable which takes the value 1 with probability [tex]p[/tex] and the value 0 with probability [tex]{\displaystyle q=1-p}[/tex]. Less formally, it can be thought of as a model for the set of possible outcomes of any single experiment that asks a yes–no question. Such questions lead to outcomes that are boolean-valued: a single bit whose value is success/yes/true/one with probability p and failure/no/false/zero with probability q.
The student will pass if he at least answers 14 questions correctly .
This can be written as a Bernoulli distribution function [tex]P(Q=i)= 20C_{i} (\frac{1}{2} )^i(1-\frac{1}{2} )^(20-i)[/tex]
P(Q≥ 14) = P(Q=14) + P(Q=15) + P(Q=16) +P(Q=17) + P(Q=18)+ P(Q=19) + P(Q=20)
P(Q=14) = 20[tex]C_{14}[/tex][tex](1/2)^{20}[/tex]
P(Q=15) = 20[tex]C_{15}[/tex][tex](1/2)^{20}[/tex]
P(Q=16) = 20[tex]C_{16}[/tex][tex](1/2)^{20}[/tex]
P(Q=17) = 20[tex]C_{17}[/tex][tex](1/2)^{20}[/tex]
P(Q=18) = 20[tex]C_{18}[/tex][tex](1/2)^{20}[/tex]
P(Q=19) = 20[tex]C_{19}[/tex][tex](1/2)^{20}[/tex]
P(Q=20) = [tex]20C_{20}(1/2)^{20}[/tex]
On summing up all we get,
P(Q≥ 14) = (38760 + 15504 + 4845+ 1140 + 190 + 20 + 1)/2^(20)
= 15115/262144=0.057
Thus the probability that the student will pass the test is 0.057
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The table shows how far a distance runner has traveled since the race began. what is her average rate of change, in miles per hour, during the interval 0.75 to 1.00 hours?
The average rate of change will be 5 miles per hour from 0.75 to 1 hour.
The average rate of change is the ratio of change in the y-value or the function value by the change in the x-value.
So according to the question,
the interval between 0.75 to 1 hour is =1-0.75=0.25 hour.
At 0.75 hours elapsed, the distance traveled is 3.5 miles
at 1 hour elapsed, the distance traveled is 4.75miles.
during the interval, 0.75 hours to 1-hour distance travelled=4.75-3.5=1.25 miles.
the average rate of change will be = change in distance traveled during the interval/interval time.
=(4.75-3.5)/(1-0.75)=1.25/0.25=5 miles per hour
Therefore the average rate of change will be 5 miles per hour from 0.75 to 1 hour.
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Answer:
B
Step-by-step explanation:
If you don’t want to read
A recipe requires 150 grams of sugar to make 6 serves of a special desert how much sugar will be needed to make 15 serves of this desert?
Answer:
150g for 6 servings
x grams for 15 servings
150/6 = 25
15 x 25 = 375
375g of sugar will be required to make 15 servings.
Give the equation of the circle that has a diameter with endpoints G(-6, — 3) and
R(-6,-8).
Generally, the equation of a circle is organized like this: [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is the centre and r is the radius.
Solving the QuestionWe're given the endpoints of the diameter: [tex](-6,-3)[/tex] and [tex](-6,-8)[/tex].
First, we can find the centre of the circle by finding the midpoint of these two endpoints.
[tex]midpoint=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]
Plug in the points:
[tex]midpoint=(\dfrac{-6+-6}{2},\dfrac{-3+-8}{2})\\\\midpoint=(-6,\dfrac{-11}{2})[/tex]
Therefore, the centre of the circle is [tex](-6,\dfrac{-11}{2})[/tex]. Plug this into the general equation:
[tex](x-h)^2+(y-k)^2=r^2\\\\(x-(-6))^2+(y-(-\dfrac{11}{2}))^2=r^2\\\\(x+6)^2+(y+\dfrac{11}{2})^2=r^2[/tex]
To find the radius of the circle, we can calculate the distance between the centre and one of the given endpoints:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
Plug in the centre and one of the endpoints:
[tex]d=\sqrt{(-6-x_1)^2+(\dfrac{-11}{2}-y_1)^2}\\d=\sqrt{(-6-(-6))^2+(\dfrac{-11}{2}-(-3))^2}\\d=\sqrt{(-6+6)^2+(\dfrac{-11}{2}+3)^2}\\\\d=\sqrt{(0)^2+(-5.5+3)^2}\\\\d=\sqrt{(0)^2+(-2.5)^2}\\\\d=\sqrt{(0)^2+(-\dfrac{5}{2})^2}\\\\d=\sqrt{0+\dfrac{25}{4}}\\d=\sqrt{\dfrac{25}{4}}\\\\d=\dfrac{5}{2}[/tex]
Therefore, the radius of the circle is [tex]\dfrac{5}{2}[/tex]. Plug this into the general equation:
[tex](x+6)^2+(y+\dfrac{11}{2})^2=r^2\\\\(x+6)^2+(y+\dfrac{11}{2})^2=(\dfrac{5}{2})^2\\\\(x+6)^2+(y+\dfrac{11}{2})^2=\dfrac{25}{4}[/tex]
Answer[tex](x+6)^2+(y+\dfrac{11}{2})^2=\dfrac{25}{4}[/tex]
can someone help me with this thanks
The length of the brace required is 4.3m
What is sine rule?
In a ΔABC a, b and c are the sides and A, B and C are angles then,
[tex]\frac{a}{SinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]
We can find the length, l as shown below:
Let AB=3m, BC=2m and AC=l
Let ∠A=25°
So, in ΔABC
[tex]\frac{BC}{sinA}=\frac{AB}{sinC}=\frac{AC}{SinB}[/tex]
[tex]\frac{BC}{sinA}=\frac{AB}{sinC}[/tex]
[tex]\frac{2}{sin25}=\frac{3}{sinC}[/tex]
[tex]\angle{C}=sin^{-1}(\frac{3\times sin25}{2} )[/tex]
∠C=39.34°
∠A+∠B+∠C=180°
∠B=180°-25°-39.34°
∠B=115.66°
[tex]\frac{BC}{sinA}=\frac{AC}{SinB}[/tex]
[tex]\frac{2}{sin25}=\frac{l}{sin(115.66)}[/tex]
[tex]l=\frac{2\times sin(115.66)}{sin25}[/tex]
l=4.2659
Rounding to nearest tenth of meter.
l=4.3m
Hence, the length of the brace required is 4.3m
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Find the area of the shape. ( image of 3/4 circle with the radius of 6 ) Answer in exact terms of pi or use 3.14 as pi and enter as a decimal.
The area of the shape is 84.78 square units
Area of a circleThe formula for calculating the area of a circle is expressed as:
A = πr²
where
r is the radius of a circle
Given the following
r = 6 units
pi = 3.14
Substitute
A = 3.14 * 6²
A = 113.04 square units
If the figure is 3/4 of a circle, the area of the shape will be:
A = 3/4 * 113.04
A = 84.78 square units
Hence the area of the shape is 84.78 square units
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There are 4 reb balls, 6 white balls, and 3 green balls in a bag. If one ball is drawn the bag at random, what is the probability that it is not white?
Answer:
7/13
Step-by-step explanation:
in all there are 13 balls and the number of balls that aren't white are 7
Answer:
7/13
Step-by-step explanation:
To find the probability that it is not white
P( not white) = number of balls that are not white / total balls
The balls that are not white are red and green = 4+3
= (4+3)/ ( 4+6+3)
= 7/13
Dad has 15 oak and maple boards from the lumber yard. each oak board is 6 centimetres thick. each maple board is 9 centimetres thick. when my dad stacks the boards, the stack is 96 centimetres thick. how many of each type of board does he have?
Answer:
He has 2 maple boards and 13 oak boards.
Step-by-step explanation:
Assuming all boards are oak : 6*15=90
Maple minus oak = 3
96-90=6 6/3=2 maple boards
Verification : 2*9+6*13 = 96
Answer:
13 oak, 2 maple
Step-by-step explanation:
o = oak
m = maple
o + m = 15
6o + 9m = 96
o + m = 15
o = 15 - m
6o + 9m = 96
6(15 - m) + 9m = 96
90 - 6m + 9m = 96
90 + 3m = 96
3m = 6
m = 2
o + 2 = 15
o = 13
6(13) + 9(2) = 96 (Yes, correct!)
Brainliest, please :)
Explain and demonstrate the multiplication of complex conjugates using 2+3i and its complex conjugate. Be sure to discuss all steps of the process, including the solution and to which number set it belongs.
The product of a complex number and its conjugate is (a + i b) · (a - i b), where a and b are real numbers, and the result for the complex number 2 + i 3 is 13.
What is the multiplication of a complex number and its conjugateLet be a complex number a + i b, whose conjugate is a - i b. Where a and b are real numbers. The product of these two numbers is:
(a + i b) · (a - i b)
Then, we proceed to obtain the result by some algebraic handling:
a · (a + i b) + (- i b) · (a + i b)
a² + i a · b - i a · b - i² b²
a² - i² b²
a² + b²
If we know that a = 2 and b = 3, then the product of the complex number and its conjugate is:
[tex]z\cdot \bar z = 2^{2} + 3^{2}[/tex]
[tex]z\cdot \bar z = 13[/tex]
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solve using substitution:
4x- 2y = 6 and x + y = 6
solve using elimination:
4x- 2y = 6 and x + y = 6
Answer:
Step-by-step explanation:
Substitution is a method that rewrites one of the equations in terms of one variable, and substitutes that in the other equations.
We can easily rewrite x + y = 6 by subtracting y from both sides, giving us
[tex]x = -y+6[/tex]
By putting this equation in place of x in the first equation, we can solve for y:
[tex]4(-y+6)-2y=6[/tex]
[tex]-4y+24-2y=6[/tex] [Distributing 4 into the parentheses]
[tex]-6y+24=6[/tex] [Combining like terms]
[tex]-6y = -18[/tex] [Subtracting 24 from both sides]
[tex]y=3[/tex] [Dividing both sides by -6]
Since we solved for y, we can again substitute by putting it into the second equation.
[tex]x+3=6[/tex]
[tex]x=3[/tex] [Subtracting 3 from both sides]
The solution for this system of equations is (3,3).
Elimination is another method of solving systems of equations. In this method, we multiply one equation such that when both equations are combined, only one variable is left.
We can first multiply both sides of the second equation by 2.
[tex]2x+2y=12[/tex]
Now, let's add both equations to cancel out y.
[tex]4x-2y=6[/tex]
[tex]2x+2y=12[/tex]
[tex]6x=18[/tex]
Now, we can divide 6 from both sides to get the value of x.
[tex]\frac{6x}{6} = \frac{18}{6}[/tex]
[tex]x=3[/tex]
We can now substitute this value into one of the equations to get the value of y. Here, I used the second equation.
[tex]3+y=6[/tex]
[tex]y=3[/tex]
The solution to our system of equations is (3,3).
Barack is travelling to dubai. he wants to bring $350 cad with him. the conversion rate from cad to uae dirham is 2.94. how much money, in dirham, will barack be able to bring with him?
Barack be able to bring 1029 dirham with him.
What is currency conversion rate?The amount of one currency needed to buy items in another is shown by conversion rates.
Currency rates and spot prices on the foreign exchange market are comparable to conversion rates.
In relation to supply and demand, conversion rates are impacted.
Governments and central banks implement policies in response to supply and demand dynamics that affect the conversion rate.
According to the question,
The conversion rate from cad to uae dirham is 2.94
Money, in dirham, Barack would be able to bring with him,
=(350*2.94) dirham
=1029 dirham
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What is a Venn Diagram?
Answer:A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things. Circles that overlap have a commonality while circles that do not overlap do not share those traits. Venn diagrams help to visually represent the similarities and differences between two concepts
Step-by-step explanation:
Answer:
uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items
Step-by-step explanation:
looks like circles that meet and overlap and
the middle part explains the relationship of both circles
example
if the left circle says water & right circle says freezing the middle part would say ice
mathworldwolfram
OUICK PLEASE
Find the equation of the line
Answer:
y = 2x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = ( 0, 4) ← 2 points on the line
m = [tex]\frac{4-0}{0-(-2)}[/tex] = [tex]\frac{4}{0+2}[/tex] = [tex]\frac{4}{2}[/tex] = 2
the line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = 2x + 4 ← equation of line
help is needed please!
1. A force of 50 N acts on an object of mass 250 kg which is initially at rest, for 10 s. find the distance travelled and the velocity gained at the end of this time.
The distance travelled is 10 m
The velocity gained at the end of the time is 2 m/s
MotionFrom the question, we are to determine distance travelled and the velocity gained
From one of the equations of motion for linear motion, we have that
S = ut + 1/2at²
Where S is the distance
u is the initial velocity
t is the time taken
and a is the acceleration
First, we will calculate the acceleration
Using the formula,
F = ma
Where F is the force
m is the mass
and a is the acceleration
∴ a = F/m
Where F is the force
and a is the acceleration
From the given information,
F = 50 N
m = 250 kg
Putting the parameters into the equation,
a = 50/250
a = 0.2 m/s²
Thus,
From the information,
u = 0 m/s (Since the object was initially at rest)
t = 10 s
S = 0(t) + 1/2(0.2)(10)²
S = 10 m
Hence, the distance travelled is 10 m
For the velocity
Using the formula,
v = u + at
Where v is the velocity
v = 0 + 0.2×10
v = 2 m/s
Hence, the velocity gained at the end of the time is 2 m/s
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The spinner of the compass is two congruent isosceles triangles connected by their bases as shown in the diagram. The base of each of these triangles is 2 centimeters and the legs are 5 centimeters.
2 congruent isosceles triangles are connected by their bases. A circle is drawn around the triangles.
If the metal used to construct the spinner costs $13.25 per square centimeter, how much will it cost to make this part of the compass? Round to the nearest cent.
Cost = $
Applying the area of a rectangle, the cost to make the part of the compass is: $129.85.
What is the Area of a Triangle?Area of a triangle = 1/2(base)(height).
Find the height of the triangle using the Pythagorean theorem:
Height = √(5² - 1²) ≈ 4.9 cm.
Base = 2 cm
Area of the two triangles = 2[1/2(base)(height)]
Area of the two triangles = 2[1/2(2)(4.9)] = 9.8 cm².
Cost to to make this part of the compass = 9.8 × $13.25 = $129.85.
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Answer: 129.82
Step-by-step explanation: its on edge I got it right :)
"What is the y-intercept of the line that has a slope of- 4 and passes through the point (A)- 10 (B)-6 (C) 8 (D) 10
The y-intercept which is the point at which x = 0 is; A: -10
How to find the y-intercept?The general form of an equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
We are given the slope;
m = -4
Now, the line passes through the point 0, -10. Thus;
(y - y1)/(x - x1) = -4
(y + 10)/(x - 0) = -4
y + 10 = -4x
y = -4x - 10
Thus, the y-intercept which is the point at which x = 0 is; y = -10
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Write an equation of a line that passes through (3, -1) and is parallel and perpendicular to y = 6x - 4
Here,
y=mx+c
the slope of the line 6x+4y= -16 is -20.
if the two lines are perpendicular, the slope of 1st line * slope of second line=-1
the slope of the 2nd line is -1/2
y-y1=m(x-x1)
y-13=-1/2(x- -18)
when you solve, you get the equation of the line as 2y+x=50
In basic geometry, if two geometry objects intersect at right angles (90 degrees or π / 2 radians), they are vertical.
If two lines intersect at right angles, the line is perpendicular to another line. Explicitly (1) if two lines intersect, the first line is perpendicular to the second line. (2) At the intersection, the straight line angle on one side of the first line is cut by the second line into two congruent angles. Verticality can be shown as symmetric. That is, if the first line is perpendicular to the second line, then the second line is also perpendicular to the first line. Therefore, two straight lines can be said to be perpendicular (to each other) without specifying the order.
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Two sets of data both have a mean of 76. however, the first set has a standard deviation of 1.4 and the second set has a standard deviation of 5.7. what must be true about the two sets?
1) it is not possible to have two sets with the same mean and different standard deviations.
2) the first set of data has values that are closer to the mean because the standard deviation is lower.
3) the first set of data has values that are farther from the mean because the standard deviation is lower.
4) the second set has more data values than the first.
Option 2) the first set of data has values that are closer to the mean because the standard deviation is lower is correct
If two samples have the same mean, then it means that the two values in the two samples are centered around the same value. However, this does not mean that the data values in the samples vary equally around this center and thus the standard deviations may also differ.
It depends what the standard deviations are. The standard deviation is a measure of how close the results are to the mean, a low standard deviation means that the measurements are accurate, so close to the mean. A high standard deviation means that the measurements are more spread out.
We need to find that if two sets of data both have a mean of 76. however, the first set has a standard deviation of 1.4 and the second set has a standard deviation of 5.7. what must be true about the two sets
The first set of data has values that are closer to the mean because the standard deviation is lower because in first set standard deviation is 1.4 and in second set standard deviation is 5.7
The one with smaller standard deviation are least spead from the mean
Hence the first set of data has values that are closer to the mean because the standard deviation is lower.
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find the mod points of line AB where point A and B have coordinate (2,3) and (4,5)
Answer:
( 3 , 4 )
Step-by-step explanation:
Midpoint Formula: ( (x1+x2)/2 , (y1+y2)/2 )
Distance Formula: d = √[(x1-x2)^2 + (y1-y2)^2]
Gradient (Slope) Formula: (y2-y1) / (x2-x1)
Midpoint Formula:
( (x1+x2)/2 , (y1+y2)/2 )
(2,3) and (4,5)
( (2+4)/2 , (3+5)/2 )
( (6)/2 , (8)/2 )
( 3 , 4 )
wyzant sean w
Please help me!! due today. Find the volume of the right triangular prism !:)
Answer: 115.5 cubic m
Step-by-step explanation:
[tex]V=\frac{1}{2}(7)(11)(3)=115.5[/tex]
If the parabola of the form y = a(x – h)2 + k is always shifted horizontally h units and vertically k units, then its vertex is always
(–h, –k)
(h, k)
(–h, k)
(h, –k)
The vertex of the transformed parabola with the equation [tex]y=a(x-h)^2+k[/tex] is (h, k).
What are the transformation rules for horizontal and vertical shifts?The transformation rules are:
Translation: (x, y) → (x + a, y) or (x, y) → (x - a, y) (Horizontal shift)
Translation: (x, y) → (x , y + b) or (x, y) → (x , y - b) (Vertical shift)
Calculation:It is given that, the transformed parabola is [tex]y=a(x-h)^2+k[/tex]
This parabola has vertex at (h, k).
Since this equation is obtained by shifting h units horizontally and k units vertically.
So, the original vertex is at (h - h, k - k) = (0, 0)
Thus, the equation of the actual parabola is [tex]y=ax^2[/tex]
Therefore, the given transformed equation of parabola has vertex (h, k).
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Answer:
B] (h,k)
The next answer is Vertex (-5, -4)
☆
EDGE2022; Good luck :3!!!!
A farmer has a piece of land with an area of 4 square yards. If a cow can graze grass at a rate of 2 square feet per hour, how long will it take 3 cows to graze the entire piece of land
Answer:
2 hours
Step-by-step explanation:
4 square yards to feet: 4*3 = 12ft
3 cows grazing grass at 2 ft per hour: 2*2 = 6 square ft per hour
Time taken: 12ft/6ft per hour = 2 hours
The Drury Lane Theater has 10 seats in the first row and 38 rows in all. Each successive row contains one additional seat. How many seats are in the theater?
[tex]{anyone \: is \: here \: }[/tex]
Answer:
1083 seats
Step-by-step explanation:
i just answered that.
arithmetic sequence
a1 = 10
an = an-1 + 1 = a1 + (n-1)×1 = 10 + (n-1) = 9 + n
a38 = 9 + 38 = 47 seats
the sum of such an arithmetic sequence
n×(a1 + an)/2
in our case
38×(10 + 47)/2 = 19×57 = 1083 seats