Point A is at (2,-8) and the point C is at (-4,7). Find the coordinates of point B on AC such that the ratio of AB to BC is 2:1.
Answers
Answer:
The coordinates of point B are (-2, 2)
Step-by-step explanation:
We have two points: A and C.
The coordinates for A are (2, -8) and the coordinates for C are (-4, 7).
We have to find the coordinates of the point B, that satisfies the condition that the distance AB is 2 times the distance BC.
We also know that B is a point of the line AC.
We can calculate the line AC as a linear function y=mx+b.
The slope m is:
[tex]m=\dfrac{y_c-y_a}{x_c-x_a}=\dfrac{7-(-8)}{-4-2}=\dfrac{15}{-6}=-2.5[/tex]
Then, the y-intercept b can be calculated using the coordinates of one of the points, in this case point A:
[tex]y=-2.5x+b\\\\b=y_a+2.5x_a=-8+2.5*2=-8+5=-3[/tex]
Then, we know that B is a point of the linear function y=-2.5x-3, within the range x ∈ (-4; 2).
To have a ratio AB to BC of 2 to 1, we can divide the length of the line AC in 3 parts, and the point B will be located in the end of the segment nearer to point C.
In the picture attached, you can see the division of the segment AC in three parts and the location of point B=(x, y).
Applying the Thales theorem, we can divide the segment in the y-axis in three and calculate y, and the same for the x-axis.
Then, the coordinate y for the point B is:
[tex]y=y_c-(y_c-y_a)/3\\\\y=7-[7-(-8)]/3=7-15/3=7-5=2\\\\\\x=x_c-(x_c-x_a)/3\\\\x=-4-(-4-2)/3=-4-(-6)/3=-4+2=-2[/tex]
Then, the point B has coordinates (-2, 2).
We can verify the distances as:
[tex]AB=\sqrt{(2-(-2))^2+((-8)-2)^2}=\sqrt{16+100}=\sqrt{116}\\\\\\BC=\sqrt{((-2)-(-4))^2+(2-7)^2}=\sqrt{4+25}=\sqrt{29}\\\\\\\dfrac{AB}{BC}=\dfrac{\sqrt{116}}{\sqrt{29}}=\sqrt{\dfrac{116}{29}}=\sqrt{4}=2[/tex]
Answer: (-2,2)
Step-by-step explanation:
Related Questions
15 cm
12 cm
7 cm find area
Answers
Answer:
1260cm^2
Step-by-step explanation:
15 times 12 = 180
180 times 7 = 1260
1260cm^2
You multiply 15 with 12, it equals 180
15 • 12 = 180
Multiply 180 with 7, it equals 1260
180•7=1260
If b (middle term) is negative and c (last term is positive) then what do you know about the two factors? ex. 2x^2-7x+6
Answers
Answer:
signs of the constants in the binomial factors are negative
Step-by-step explanation:
Assuming the first term (a) is positive, the fact that c is negative means the constants in the binomial factors have the same sign. The negative b means that sign is negative.
2x^2 -7x +6 = (x -2)(2x -3)
__
Further comment
c is the product of the constants in the binomial factors so will be positive when both those constants have the same sign.
b is the sum of the constants in the binomial factors. If both factors have the same sign (c > 0), then those constants have the same sign as b.
In this analysis, "a" is assumed to be positive. If it is not, then the same analysis can be done after reversing all of the signs.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. Show your work OR give an explaination.
Answers
Answer:
5x - 1
Step-by-step explanation:
f(x) = 3x - 2
g(x) = 2x + 1
(3x - 2) + (2x + 1)
3x + 2x = 5x
-2 + 1 = -1
Answer: 5x - 1
What is the quotient when the sum of 13 and 11 is divided by the difference of 13 and 11
Answers
Answer:
12
Step-by-step explanation:
[tex]\dfrac{13+11}{13-11}=\dfrac{24}{2}=12[/tex]
Hope this helps!
Find the sum
(2x−6)+4(x−3)
ANSWER QUICKLY PLEASE!!
Answers
Answer:
6x - 18
Step-by-step explanation:
(2x - 6) + 4(x - 3) =
= (2x - 6) + 4x - 12 =
= 2x - 6 + 4x - 12 =
= 2x + 4 - 6 - 12 =
= (2x + 4x) + (-6 - 12) =
= 6x - 18
Pwease hewp me pwease shanks lob u
Answers
Answer:
a = 3
b = 12
c = 13
Step-by-step explanation:
[tex] \frac{ {2}^{5}. {8}^{4} }{16} = \frac{ {2}^{5}. { ({2}^{a}) }^{4} }{ {2}^{4} } = \frac{ {2}^{5}. { {2}^{b} } }{ {2}^{4} } = {2}^{c} \\ \\ \frac{ {2}^{5}. {8}^{4} }{16} = \frac{ {2}^{5}. { ({2}^{a}) }^{4} }{ {2}^{4} } \\ \\ \frac{ {2}^{5}. {( {2}^{3}) }^{4} }{ {2}^{4} } = \frac{ {2}^{5}. { ({2}^{a}) }^{4} }{ {2}^{4} } \\ {( {2}^{3}) }^{4} = { ({2}^{a}) }^{4} \\ {2}^{3} = {2}^{a} \\ \huge \red{ \boxed{a = 3}} \\ \\ \frac{ {2}^{5}. {8}^{4} }{16} = \frac{ {2}^{5}. { {2}^{b} } }{ {2}^{4} } \\ \frac{ {2}^{5}. { ({2}^{3} )}^{4} }{ {2}^{4} } = \frac{ {2}^{5}. { {2}^{b} } }{ {2}^{4} } \\ { ({2}^{3} )}^{4} = { {2}^{b} } \\ {2}^{12} = { {2}^{b} } \\ \huge \purple{ \boxed{b = 12}} \\ \\ \frac{ {2}^{5}. {8}^{4} }{16} = {2}^{c} \\ \frac{ 16 \times 2. {( {2}^{3}) }^{4} }{16} = {2}^{c} \\ 2 \times {2}^{12} = {2}^{c} \\ {2}^{13} = {2}^{c} \\\huge \orange{ \boxed{ c = 13}}[/tex]
a green and a red die are tossed. what is the probability that a 4 shows
on the green die and a 5 shows on the red die.
Answers
Answer:
1/36
Step-by-step explanation:
The probability of getting green is 1/6
and the probability of getting red is 1/6.
Now,we want to know the probability of getting red and green. In probability,the word 'and' means times.
So it would be;
1/6 times 1/6
= 1/36
What is the measure of the whole angle?
Answers
Answer:
130
Step-by-step explanation:
60° + 70° = x
In an equation our aim is to find the value of what we are looking for as well as keeping the equation balanced. For example if we took away 60 only from one side then the equation would change so it's an important rule to keep in mind when solving equations, that you need to keep both sides of the equation the same.
60 + 70 = x
→ Simplify
130 = x
x = 130°
write the linear function if f(0)=5 and f(2)=35
Answers
Answer: y=15x+5
Step-by-step explanation:
Looking at what we are given, we can tell that the y-intercept is 5. To ge tthe slope, you use [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]. With the slope , you get 15.
Please answer this correctly
Answers
Florida reappraises real estate every year, so the county appraiser's Web site lists the current "fair market value" of each piece of property. Property usually sells for somewhat more than the appraised market value. Here are the appraised market values and actual selling prices (in thousands of dollars) of condominium units sold in a beachfront building in a 93-month period:
Selling price 832 878 628 1067 924 792 645 854
Appraisal value 744.7 842.8 480.9 1005.2 787.9 758.3 548.9 634.3
Selling price 764 708 752 862 720 1099 1301 800
Appraisal value 641.7 514.8 552.9 747.4 475.5 756.3 1039.4 582.8
Here is part of the Minitab output for regressing selling price on appraised value:
Predictor Coef SE Coef T
Constant 227.0989 95.044 2.389
Appraisal 0.8991 0.133 6.76
S = 88.7959 R-Sq = 76.5% R-Sq (adj) = 74.9%
The equation of the least square regression line for predicting selling price from appraised value is (round your answer to at least four decimals):
price appraised value.
Answers
Answer:
The equation of the least square regression line for predicting selling price from appraised value is:
[tex]\text{Selling Price}=227.0989 + 0.8991\ \text{Appraised Value}[/tex]
Step-by-step explanation:
The general form of the least square regression line is:
[tex]y=a+bx[/tex]
Here,
y = dependent variable
x = independent variable
a = y-intercept
b = slope
The Minitab output for regressing selling price on appraised value is:
Predictor Coef SE Coef T
Constant 227.0989 95.044 2.389
Appraisal 0.8991 0.133 6.76
S = 88.7959
R-Sq = 76.5%
R-Sq (adj) = 74.9%
The constant term in the regression output represents the y-intercept and the Appraisal coefficient the slope of the regression line.
Then the equation of the least square regression line for predicting selling price from appraised value is:
[tex]\text{Selling Price}=227.0989 + 0.8991\ \text{Appraised Value}[/tex]
Human visual inspection of solder joints on printed circuit boards can be very subjective. Part of the problem stems from the numerous types of solder defects (e.g., pad non-wetting, knee visibility, voids) and even the degree to which a joint possesses one or more of these defects. Consequently, even highly trained inspectors can disagree on the disposition of a particular joint. In one batch of 10,000 joints, inspector A found742that were judged defective, inspector B found745such joints, and1145of the joints were judged defective by at least one of the inspectors. Suppose that one of the 10,000 joints is randomly selected.
(a) What is the probability that the selected joint was judged to be defective by neither of the two inspectors? (Enter your answer to four decimal places.)
(b) What is the probability that the selected joint was judged to be defective by inspector B but not by inspector A? (Enter your answer to four decimal places.)
Answers
Answer:
a
The probability that the selected joint was judged to be defective by neither of the two inspectors is [tex]P(A' n B' ) = 0.8855[/tex]
b
The probability that the selected joint was judged to be defective by inspector B but not by inspector A is [tex]P(A' n B) =0.0403[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n_s = 10000[/tex]
The number of outcome for inspector A is [tex]n__{A}} = 742[/tex]
The number of outcome for inspector B is [tex]n__{B}} = 745[/tex]
The number of joints judged defective by both inspector is [tex]n(A u B) = 1145[/tex]
The the probability that the selected joint was judged to be defective by neither of the two inspectors is mathematically represented as
[tex]P(A' n B' ) = 1 - P(A u B)[/tex]
Now
[tex]P(A\ u \ B) = \frac{n(Au B)}{n_s }[/tex]
substituting values
[tex]P(A\ u \ B) = \frac{1145}{ 10 000 }[/tex]
So
[tex]P(A' n B' ) = 1 - \frac{1145}{10 000}[/tex]
[tex]P(A' n B' ) = 0.8855[/tex]
the probability that the selected joint was judged to be defective by inspector B but not by inspector A is mathematically represented as
[tex]P(A' n B) = P(A \ u \ B) -P(A)[/tex]
Now
[tex]P(A) = \frac{n__{A}}{n_s}[/tex]
substituting values
[tex]P(A) = \frac{742}{10 000}[/tex]
So
[tex]P(A' n B) = \frac{1145}{10 000} - \frac{742}{10 000}[/tex]
[tex]P(A' n B) =0.0403[/tex]
what was disney’s reaction to seeing pixar’s first proposal of toy story?
Answers
We're in the screening room of an exotic little San Francisco Bay area production company called Pixar Animation Studios, watching the dailies of a major work-in-progress, director John Lasseter presiding. And not to get too hyperbolic here, but we're witnessing history being made before our very eyes. You've heard of Debbie Does Dallas? Call this Disney Does Digital.
Two years ago, less than a half-dozen feature films employed the use of computer graphics; this year maybe a half-dozen won't use any sort of digital enhancements. If Hollywood has suddenly embraced the computer as a significant (and cost-effective) illusion-making tool, then Disney's Toy Story is arguably the most ambitious computer-generated undertaking yet.
hope this helps!
Answer:
We're in the screening room of an exotic little San Francisco Bay area production company called Pixar Animation Studios, watching the dailies of a major work-in-progress, director John Lasseter presiding. And not to get too hyperbolic here, but we're witnessing history being made before our very eyes. You've heard of Debbie Does Dallas? Call this Disney Does Digital.
Two years ago, less than a half-dozen feature films employed the use of computer graphics; this year maybe a half-dozen won't use any sort of digital enhancements. If Hollywood has suddenly embraced the computer as a significant (and cost-effective) illusion-making tool, then Disney's Toy Story is arguably the most ambitious computer-generated undertaking yet.
Step-by-step explanation:
A man travelled 450 km on the first day and 565,000 m on the second and the third day he travel double the distance you travel on the first day on the fourth day he reached his destination which was 2500km from his starting point how far did he travel on the fourth
Answers
Answer:
1000miles
Step-by-step explanation:
A men travel 585 km on fourth day.
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that;
A man travelled 450 km on the first day and 565,000 m on the second day, the third day he travel double the distance you travel on the first day.
Here, On the fourth day he reached his destination which was 2500km from his starting point.
Let the distance he travel on the fourth day = x
So, We can formulate;
⇒ 450 km + 565,000 m + 2 × 450 km + x = 2500 km
⇒ 450 km + 565 km + 900 km + x = 2500 km
⇒ 1915 km + x = 2500 km
⇒ x = 2500 - 1915
⇒ x = 585 km
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You are given the five number summary from a set of data as follows: Minimum=5, Q1=7, Median=8, Q3=11.5 and Maximum=15. Explain how to find the difference between the Range and the Interquartile Range. Find this difference.
Answers
Answer:
a) Range =10
b) inter quartile range = 4.5
Step-by-step explanation:
Explanation:-
Given minimum =5
Median=8
upper quartile (Q3) =11.5
Lower quartile range= 7
Maximum=15
a) Range = maximum value -minimum value
= 15 -5
= 10
b) Interquartile Range = median of upper half - median of lower half
= Q₃- Q₁
= 11.5 - 7
= 4.5
Just give me the answer no expiation.
Answers
Answer:
b. 424
Step-by-step explanation:
it gives the equation N=41b+137
N=41(7)+137
N=424
What is the surface area of the rectangular pyramid? m2 18 point for how ever awncers this first
Answers
Answer:
When all side faces are same
surface area = lw + 1/2 × perimeter × slant height.
When the side faces are different
surface area = base area + lateral area
Step-by-step explanation:
The question you ask is the formula one can use to calculate the surface area of a rectangular pyramid.
The base of a rectangular pyramid is rectangular. The picture below shows how a rectangular pyramid looks like .
The surface area of the rectangular pyramid includes the area of the base and areas of all the triangular faces. This simply implies the area of the rectangular base and the area of each triangular faces. Mathematically, it can be represented below.
The base area(rectangle) = length × width = lw
Area of a triangle = 1/2 × base × height = 1/2bh
Therefore, if all the faces of the triangle are the same(regular pyramid) the total surface area will be
surface area = lw + 1/2 × perimeter × slant height.
Note the triangular faces are 4 in numbers.
If all the sides of the triangle are different the surface are will be
surface area = base area + lateral area
We have to add the triangular faces individually for an irregular pyramid.
p(x) is a polynomial p(x) divided by (x-9) has a remainder of 1. P(x) divided by (x-4) has a remainder of 7. P(x) divided by (x+4) has a remainder of 0. P(x) divided by (x+9) has a remainder of -5
P(4)=?
P(-9)=?
Answers
Answer:
[tex]P(4)=7\,,\,P(-9)=-5[/tex]
Step-by-step explanation:
Given: P(x) has a remainder 1 when divided by [tex]x-9[/tex], P(x) has a remainder 7 when divided by [tex]x-4[/tex], P(x) has a remainder 0 when divided by [tex]x+4[/tex] and P(x) has a remainder -5 when divided by [tex]x+9[/tex]
To find: [tex]P(4),P(-9)[/tex]
Solution:
According to remainder theorem, when a polynomial [tex]P(x)[/tex] is divided by a polynomial [tex]x-a[/tex], the remainder obtained is equal to [tex]P(a)[/tex].
As P(x) has a remainder 7 when divided by [tex]x-4[/tex],
[tex]P(4)=7[/tex]
As P(x) has a remainder -5 when divided by [tex]x+9[/tex],
[tex]P(-9)=-5[/tex]
What is the volume of the cone in the diagram
A. 150 pi cubic units
B. 200 pi cubic units
C. 250 pi cubic units
D. 300 pi cubic units
Answers
Answer:
A
150 pi cubic units
Step-by-step explanation:
Answer:
Substituting the values r = 5 and h = 18 in the formula V=1/3×πr^2h, you get V=1/3×π×52×18 = 150π cubic units.
Step-by-step explanation:
Given y = 4x + 3, what effect does changing the equation to y = 4x - 3 have on the y-intercept?
A)
graph becomes steeper
B)
no change to y-intercept
C)
graph moves down 3 units
D)
graph moves down 6 units
Answers
Answer:
graph moves down 6 units
Step-by-step explanation:
Y intercept of a line is point on y axis where the line crosses the y-axis.
Since the line is of the slope intercept form y = mx+ c
where m is slope of line and c is y intercept
_________________________________________________
Equation of old line : y = 4x + 3
then for equation y = 4x + 3
m: 4 and c = 3
Thus y intercept is +3 unit above the X axis
_________________________________________________
Equation of new line : y = 4x - 3
Similarly based on above explanation
m: 4 and c = -3
Thus y intercept is +3 unit below the X axis.
Thus we can see that y intercept has moved downward
Lets calculate no. of units it moved downward
Distance between them is 3 - (-3) = 6 unit
Thus graph moved 6 units downwards.
Steepness of graph depends on slope of line. The slope is 4 for both the lines and hence there is no change in steepness.
Thus correct answer is graph moves down 6 units
The number of new cars (c) a ship carries can’t exceed 975
Answers
Answer:
That may or may not be true, depending one the ship size.
Step-by-step explanation:
'Can't really give a proper answer, to somethings that's not a q. *shrug*
hus, D satisfying (ABC)DequalsI exists. Why does the expression for D found above also satisfy D(ABC)equalsI, thereby showing that ABC is invertible? Select the correct choice below and, if necessary, fill in the answer box within your choice. A. After substituting the expression for D, the product DABC simplifies to I by repeated application of the associative property and the definition of inverse matrices. B. After substituting the expression for D, left multiplying the product by nothing results in the equation IequalsABCD. C. After substituting the expression for D, taking the inverse of both sides of the equation results in the equation IequalsABCD. D. After substituting the expression for D, right multiplying the pr
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
First Question
Option A is correct
Second Question
Option C is correct
Third Question
[tex]D = A^{-1} * B^{-1} * C^{-1}[/tex]
Fourth Question
So substituting for D in (ABC) D = I
[tex](ABC) * A^{-1} * B^{-1} * C^{-1} = I[/tex]
[tex]I = I[/tex]
This proof that ABC is invertible
Step-by-step explanation:
From the question we are told that
A , B and C are invertible which means that [tex]A^{-1} , B^{-1}, C^{-1}[/tex] exist
Now
From the question
(ABC) D = I
Where I is an identity matrix
Now when we multiply both sides by [tex]A^{-1}[/tex] we have
[tex]A^{-1} A BCD = A^{-1} * I[/tex]
[tex]IBCD = A^{-1}[/tex]
Now when we multiply both sides by [tex]B^{-1}[/tex] we have
[tex]B^{-1 } *I BCD = A^{-1} * B^{-1}[/tex]
[tex]I CD = A^{-1} * B^{-1}[/tex]
Now when we multiply both sides by [tex]C^{-1}[/tex] we have
[tex]C^{-1} * I CD = A^{-1} * B^{-1} * C^{-1}[/tex]
[tex]I D = A^{-1} * B^{-1} * C^{-1}[/tex]
[tex]D = A^{-1} * B^{-1} * C^{-1}[/tex]
So substituting for D in the above equation
[tex](ABC) * A^{-1} * B^{-1} * C^{-1} = I[/tex]
[tex]I = I[/tex]
This proof that ABC is invertible
What’s the correct answer for this?
Answers
Answer:
C = 10 units²
Step-by-step explanation:
AB is 4 units long AC is 5 units long(by distance formula)
call AB and AC the base and height respectively. Multiply them, divide by 2: 4x5=20
20/2 = 10
Natalia is moving into a new house. All together, her furniture weighs 3,204 pounds. If it takes 8 trucks to carry all of Natalia's furniture, what is the average weight load on each truck? A. 640.8 pounds per truck B. 801 pounds per truck C. 1,602 pounds per truck D. 400.5 pounds per truck
Answers
Answer:
D
Step-by-step explanation:
The average can be found by dividing the number of pieces (or trucks in this case) by the total, so 3204/8=400.5 pounds, or D as our answer
Which statement is an example of the transitive property of congruence?
O A. If AKLME APQR, then APQR=ASTU.
O B. If AKLME APQR and APOR=ASTU, then AKLME ASTU.
C. AKLM: AKLM.
O D. If AKLME APOR, then APORE AKLM.
Answers
Answer:
B. If ΔKLM ≅ ΔPQR and ΔPQR ≅ ΔSTU, then ΔKLM ≅ ΔSTU
Step-by-step explanation:
The transitive property in general says ...
if a=b and b=c, then a=c
The transitive property of congruence replaces the equal sign with a congruence symbol, and replaces a, b, c with any geometric figure. Here, the geometric figures used are triangles KLM, PQR, and STU.
If ΔKLM ≅ ΔPQR and ΔPQR ≅ ΔSTU, then ΔKLM ≅ ΔSTU
ASAP PLEASE
Mike and Jhon has a large plastic cup that he is going to fill with water. The plastic cup is in the shape of a cone as shown. Mike uses the formula V = π(3)2(7) to find the volume whereas Jhon says his formula V= V = 1/3π(3)2(7) is correct to find the volume.
Who is incorrect ? and why?
Answers
Answer:
I can't really see the whole question, but for a cone the volume formula is πr2h
3
Step-by-step explanation:
Given the reaction at equilibrium:
N2(g) + O2(g) + energy +2 NO(g)
Which change will result in a decrease in the amount of NO(g) formed?
A)
decreasing the pressure
B)
decreasing the concentration of N2(g)
C)
increasing the concentration of O2(g)
D)
increasing the temperature
Answers
The amount of NO can be decreased by decreasing the concentration of N2(g).
What is equilibrium?The term equilibrium refers to the point at which the rate of the forward reaction and the rate of the reverse reaction are the same.
We have the reaction; N2(g) + O2(g) + energy ------>2 NO(g), in order to drive this reaction in the reverse direction, the concentration of N2(g) can be decreased.
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bo and Luke are driving to uncle Jesse's house their car at the generally can go nearly 208 miles on 13 gallons of gas they only have 3 gallons of gas left in the tank but they are 42 miles away from uncle Jesse's house how far can the generally go on 3 gallons of gas in its tank
Answers
Answer:
48 miles
Step-by-step explanation:
What we must do is calculate the car's performance, that is, the number of miles per gallon of gas, like this:
208/13 = 16
which means that for each gallon of gas you can travel a total of 16 miles.
They tell us they have 3 gallons of gasoline left so they can go:
16 * 3 = 48
If your goal is 42 miles away, that means you can make it and you still have 6 more miles to go.
If f(x) = 4x + 12 is graphed on a coordinate plane, what is the y-intercept of the graph?
04
08
O 12
0 16
Answers
Find the value of x in the
following parallelogram:
2x - 10
2x + 50
Answers
Answer:
the value of x = 35 ( NOT - 40 )
Step-by-step explanation:
In order to calculate the value of x in the following parallelogram: 2x - 10
2x + 50, we would have to calculate the following formula:
m<QPS+m<PQR=180°
According to the given data we have the following:
m<QPS=2x - 10
m<PQR=2x + 50
Therefore, 2x - 10+2x + 50=180
4x+40=180
x=140/4
x=35
The value of x is 35 because in a parallelogram sum of the two adjacent angles is equal to 180 degree
What is parallelogram?In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
As we know,
In a parallelogram sum of the two adjacent angles is equal to 180 degree
2x - 10 + 2x + 50 = 180
4x + 40 = 180
4x = 140
x = 35
Thus, the value of x is 35 because in a parallelogram sum of the two adjacent angles is equal to 180 degree
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