Find the point on the line 6x + y = 8 that is closest to the point
(−5, 2).
(x, y) =
9514 1404 393
Answer:
(x, y) = (31/37, 2 36/37) ≈ (0.8378, 2.9730)
Step-by-step explanation:
There are several ways we can go at this.
Method 1
Find the point of intersection with the perpendicular line through (-5, 2).
The perpendicular line will have the x- and y-coefficients swapped, one of them negated, and a new constant consistent with the given point.
x -6y = (-5) -6(2) = -17
So, we're looking for the solution of the system of equations ...
6x +y = 8x -6y = -17Using Cramer's Rule, we can find the solution to be ...
x = ((1)(-17) -(-6)(8))/((1)(1) -(-6)(6)) = 31/37 ≈ 0.837_837*
y = ((8)(1)-(-17)(6))/37 = 110/37 ≈ 2.972_972
The closest point is (x, y) = (31/37, 2 36/37).
__
Method 2
We can write the given line in parametric form, then find the point on it such that the direction along the line is perpendicular to the direction to the given point.
Solving the given equation for y, we have ...
y = 8 -6x
So, the parametric form of the given line can be written as ...
(x, y) = (0, 8) +t(1, -6) . . . . for some parameter t
The direction to the given point from (x, y) is then ...
(-5, 2) -(x, y) = (-5, 2) -((0, 8) +t(1, -6)) = (-5-0-t, 2-8+6t) = (-t-5, 6t-6)
The dot-product of this direction vector with the direction vector of the original line will be zero for the value of the parameter at the closest point.
(1, -6) · (-t-5, 6t-6) = 0 = (1)(-t -5) +(-6)(6t -6)
0 = -t -5 -36t +36 = -37t +31
31/37 = t
So, filling this value into the parametric equation gives the closest point as ...
(0, 8) +(31/37)(1, -6) = (31/37, 2 36/37) = (x, y)
__
Method 3
Find the point of tangency of the given line with a circle centered at (-5, 2).
The equation of a circle centered at (-5, 2) is ...
(x +5)^2 +(y -2)^2 = r^2
The given line will meet the circle at a point that satisfies this equation and the equation of the circle. Writing an expression for y using the given line, we can substitute into the circle equation to get ...
(x +5)^ +((8 -6x) -2)^2 = r^2
x^2 +10x +25 +36 -72x +36x^2 = r^2
37x^2 -62x + (some constant) = 0
This will have one solution when the constant is chosen to make the left-side expression a perfect square. That perfect square will be ...
37(x -31/37)^2 = 0
which is to say the tangent point of the line and the circle will have x-coordinate x = 31/37. The y-coordinate is 8 -6(31/37) = 2 36/37.
The closest point is (x, y) = (31/37, 2 36/37).
_____
* repeated decimal fractions are signified in typeset text with an overbar over the repeating digits. In plain text, we sometimes use a preceding underscore to identify the repeating digits.
Assume that it is equally likely for a child to be born a boy or a girl, and that the Lin family is planning on having three children. List the elements of the event that the Lins have at least one girl. (Use B to represent boy, and G to represent girl. For example, if there are three girls born, it would be represented as GGG).
Answer:
[tex]List = \{GBB; BGB; BBG; GGB; BGG; GBG; GGG\}[/tex]
Step-by-step explanation:
Given
[tex]Children = 3[/tex]
Required
List all cases of having at least 1 girl
We have:
[tex]B = Boy[/tex]
[tex]G = Girl[/tex]
For 1 girl, we have:
GBB; BGB; BBG
For 2 girls, we have:
GGB; BGG; GBG
For 3 girls, we have:
GGG
Hence, the list is:
[tex]List = \{GBB; BGB; BBG; GGB; BGG; GBG; GGG\}[/tex]
Antwon gathered data on the ages of 15 randomly-chosen parents of students in his sche
He recorded the data in the table below.
36
32
51
31
30
42
56
32
43
54
26
43
38
43
28
Which is the best prediction that Antwon can make about the ages of the parents of all of the
students at his school?
A
There are not any parents older than 54.
B
Most parents are about 43 years old.
с
The mean age is about 39.
D
At least half the parents are more than 45 years old.
Answer:
You can easily rule out A and D, and the mean is 39 which essentially makes B irrelevant. The answer is C.
Number rule
equation to fit the pattern x 24 32 40 48 and y 6 8 10 12
Answer:
y = 1/4(x)
Step-by-step explanation:
Given the equation:
x 24 32 40 48
y 6 8 10 12
The slope = (y2 - y1) / (x2 - x1)
Slope = (12 - 6) / (48 - 24)
Slope = 6 / 24
Slope = 1 / 4
The slope intercept relation is expressed thus :
y = mx + c
m = slope ; c = intercept
Picking a point :
x = 32, y = 8
8 = 1/4(32) + c
8 = 8 + c
c = 0
Hence, the fit pattern for the equation is :
y = 1/4(x)
your friend finds the area of the triangle..
is you friend correct?
yes or no
explain your reasoning
!NO LINKS, NO FILES!
please :)
HE 5 2. Jimmie bought 7/8 pound of candy. He ate 3/8 pound. How much of the candy is left?
Answer:
4/8
Step-by-step explanation:
7/8 - 3/8 = 4/8
What is the value of x in this octagon?
Enter your answer in the box.
Answer: 166 degrees
Step-by-step explanation:
An octagon has 1080 degrees in it. So just subtract all of the angles out of 1080.
1080-104-126-163-130-131-107-153= 166
ANSWER: 166 degrees
Answer:
166 degrees
Step-by-step explanation:
in an octagon, there are a total of 1080 degrees,
so we take all of the degrees we do know, and subtract them from 1,080 degrees! --- (1080-104-126-163-130-131-107-153= 166)
we end up with 166 degrees! :)
hope this helped!
16. Kim spends 10 minutes washing her car. Denzel spends 3 times as many minutes (d)
washing his car as Kim spends.
Part A
Which equation can be used to find how many minutes Denzel spends washing
his car?
A.
10 + 3 = d
B.
10 3 = d
C.
10- 3 = d
D. 10 = 3 = d
Answer:
B
Step-by-step explanation:
10x3= 30
because kim spends 10 min washing her car, and Denzel spends 3 x as a many washing his car.
so you do 10 x 3 = 30
The equation that represents the time Denzel spends is d = 10×3.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Given, Kim spends 10 minutes washing her car and Denzel spends 3 times as many minutes (d) washing his car as Kim spends.
∴ The equation that represents the time Denzel spends is d = 10×3.
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2x=6 how do I answer this?
Find x.
2x/2=x 6/2=3
x=3
Answer:
x=3
Step-by-step explanation:
you have to leave the x alone you do divide so it will be like this x=6/2 since you can reduse them it will be x=3
7 students have 5 blocks each. Which helps you find the total number of blocks? 7 - 5 7 ÷ 5 7 × 5 7 + 5
Answer:
7 X 5
You use multiplacation to find the total number of blocks
Pls help this is timing me!!!!!
Answer:
D
Step-by-step explanation:
Grafting, the uniting of the stem of one plant with the stem or root of another, is widely used commercially to grow the stem of one variety that produces fine fruit on the root system of another variety with a hardy root system. For example, most sweet oranges grow on trees grafted to the root of a sour orange variety. Suppose each graft fails independently withprobability 0.3. Five grafts are scheduled to be performed nextweek. Let X deonte the number of graftes that will fail nextweek.
a. The random variable x is (choose one): binomial, hypergeometric, negative binomial, poisson.
b. Give the sample space and pmf of x.
c. give the expected value and variance of x.
d. Suppose that the cost of each failed graft is $9.00. Find:
i. The probability that the cost from failed grafts will exceed $20.00.
ii. The expected and the variance of the cost from failed grafts.
Step-by-step explanation:
a. The random variable is a binomial distribution.
b. the sample space, X = {0, 1, 2, 3, 4, 5}
the pmf
we solve for this using
nCx * P^x * (1-p)^n-x
n = 5
p = 0.3
for x = 0
5C0 * 0.3⁰(1-0.3)^5-0
= 1 * 1* 0.7⁵
= 0.16807
for x = 1
5C1*0.3¹(1-0.3)^5-1
= 5*0.3(0.7)⁴
= 5x0.3x0.2401
= 0.36015
for x = 2
5C2 * 0.3² * (1-0.3) ^5-2
= 0.30870
for x = 3
5C3 * 0.3³ * (1-0.3) ^ 5-3
= 10 * 0.027 * 0.7²
= 0.1323
for x = 4
5C4 * 0.3⁴ (1-0.3) ^ 5-4
= 5 * 0.0081 * 0.7
= 0.02835
for x = 5
5C5 *0.3⁵ (1- 0.3) ^5-5
= 1*0.00243*0,7⁰
= 0.00243
c. E[X] = N*p = 5*0.3 = 1.5
var[X] = np(1-p) = 5*0.3*0.7 = 1.05
d. 20/9 = 2.222
so we have that if x is greater than or equal to 3, cost will exceed 20
p(x=3) + p(x=4) + p(x=5)
= 0.1323 + 0.02835 + 0.00243
probability = 0.16308
E[C] = 1.5 * 9 = 13.5
VAR[C] = 1.05 * 9 = 9.45
Please help this is due today.
Answer:
[tex]b = 90[/tex]
[tex]c=80[/tex]
[tex]d =100[/tex]
Step-by-step explanation:
Given
See attachment
Required
Find b, c and d
First, we solve for b using:
[tex]b + 10 + b - 10 = 180[/tex] --- base angles of a parallelogram
Collect like terms
[tex]b + b =180+10-10[/tex]
[tex]2b = 180[/tex]
Solve for b
[tex]b = 180/2[/tex]
[tex]b = 90[/tex]
Then, we have:
[tex]d =b + 10[/tex]
[tex]c = b - 10[/tex] --- opposite angles
So, we have:
[tex]d =90 + 10[/tex]
[tex]d =100[/tex]
[tex]c = 90 - 10[/tex]
[tex]c=80[/tex]
Simplify the following expression.
-20 + (-15)
O A 5
OB. -35
O C.
-5
OD. 35
Reset
Submit
Answer:
B) -35
Step-by-step explanation:
-20+(-15)
as taught when there is a minus and plus sign together it becomes a minus sign automatically (+ -)= -
Therefore -20+(-15)
will be -20-15 which gives you -35
How many 3/4 cup servings are in 1/2 cup of yougurt? Simplest fraction form
Answer:
2/3 serving
Step-by-step explanation:
(1/2)/(3/4) = 1/2 x 4/3 = 4/6 = 2/3 serving
What is a number c decreased by 15?
(Only people who are going to answer the question truly are only allowed to comment)
Answer:
C - 15
Step-by-step explanation:
"Decreased by" means subtraction. We are subtracting 15 from C so the answer is C - 15. Hope this helpssss
A classroom floor has a perimeter of 132 feet. What is the perimeter in
yards?
Answer:
44 yards
Step-by-step explanation:
Formula :
divide the length value by 3
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Please help this assignment is over due and I don't get it thx;)
Answer: m=6
Step-by-step explanation:
Divide both sides by 3.4
3.4m/3.4 and 20.4/3.4
124 oz =
Ib
I need help
Answer:
7.75
Step-by-step explanation:
Remember, 1 ounce equals 0.0625 pounds.
Multiply 124 x 0.0625 to get you answer.
Hope this helps,If you have any questions revolving around this topic,feel free to ask me,Good luck!
In 60 words or fewer, write what you think the term economy means.
Answer:
the structure or conditions of economic life in a country, area, or period also : an economic system.
Step-by-step explanation:
Given that NO ML and ML JK, which postulate or theorem can be used to show that all 3 center triangles in the
Antigua and Barbuda flag are similar?
A. ASA similarity theorem
B. SSS similarity theorem
C. SAS similarity theorem
D. AA similarity postulate
Answer:
A
Step-by-step explanation:
Source:
Trust me bro
The theorem used to prove the three triangles are similar is the ASA similarity theorem. The correct option is A.
What is the similarity?If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and the side included between the angles of the second triangle.
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the following data points represent the number of spots on each giraffe that lives in the Curran plains find the median 174,226,236,231,203,185,194,221,197 find the median
The required median number of spots on giraffes in the Curran plains is 203.
What is Median?A data set's median value is the place where 50% of the data points have values that are lower or equal to it, and 50% of the data points have values that are higher or equal to it. To organize the data points in increasing order for a small data set, count the number of data points (n).
According to question:To find the median, we need to first sort the data points in ascending order:
174, 185, 194, 197, 203, 221, 226, 231, 236
Since there are an odd number of data points, the median is the middle value, which in this case is 203.
Therefore, the median number of spots on giraffes in the Curran plains is 203
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Kerry puts pennies into a jar every day. On the first day, she puts 2 pennies into the jar. On the second day, she adds double the number of pennies she put into the jar on the first day. On the third day, she adds double the number of pennies she put into the jar on the second day. This pattern follows for a week.
Answer:
By the end of the week she will have 254 pennies and she will put 128 pennies for the last day
Hurry plz don't be bots The scale on a map shows that 10 kilometers is represented by 4 centimeters. Which proportion can be used to find
the actual distance, x, represented by 20 centimeters on the map?
10 x
0
4 20
10 20
x
리 8 8
Answer:
10/4=20
Step-by-step explanation:
x=50
Step-by-step explanation:
10/4=x/20
this will give you x=50
A cylindrical storage tank has a depth of 5 ft and a radius measuring 3 ft. The tank needs to be painted. If 1 pint of paint covers 50 ft2 and you can only purchase full pints of paint, how many pints must be purchased to paint the exterior of the storage tank? (Use your calculator value of . Round your answer up to the nearest whole number.)
Answer:
4 pints
Step-by-step explanation:
Well to figure this one out we need the surface area of the cylinder
The formula is : SA=2πrh+2πr^2
Don't worry about memorizing most of these formula's except the basic ones for Surface area and Volume in a test the formula's will be given but I do recommend practicing them
Any way lets keep going
Depth of 5ft basically means 5ft in height (to let you know)
2*pi*3*5+2*pi*3^2
SA=150.796447372 ft^2 rounded is basically 151
any way we know one pint paints 50 ft^2
so 151/50 is 3 remainder 1 so you will need 4 pints except you will barley use 1 pint
T
100. The number of ash trees on a tree farm is 5
times the number of pine trees. Choose one
expression from each column to creae an
equation that compares the number of ash trees
(a) and pine trees (p),
Answer :-
a = 5p
Option 3 from 1st column and option 2 from 2nd column
My Someone please explain why G is 125 and H is 62!
guaranteed brainliest to the first correct answer!
PLEASE HELP ME WITH THIS
Opposite angles inscribed in a cyclic quadrilateral are supplementary, so:
[tex]m\angle R+m\angle T=180^{\circ}\\\\m\angle R+47^{\circ}=180^{\circ}\\\\m\angle R=\boxed{133^{\circ}}[/tex]
I WILL MARK BRAINLIEST
Answer:
-6, -5, -4, -3, and -2
n≥-6
Step-by-step explanation:
Multiply both sides by 2
n≥-6
so the values that make this true are -6, -5, -4, -3, and -2
It takes 2 workers 6 hours to paint a school hall.
How long would it take 4 workers to paint the same hall
Answer:
it will take 3 hour to paint the wall
Answer:
3 hours
Step-by-step explanation:
because we know that 2 x 3 = 6 and 4 x 3 = 12 basically your finding the median. if the number of values is an even number, the median will be the average of the two middle numbers
Sentence: It will take 3 hours for 4 workers to paint the same wall.