Point A is at (-2, 4) and point C is at (4, 7). Find the coordinates of point B on AC such that the ratio of AB to AC is 1: 3. B =
Answers
the coordinates of point B are \((2, 6.25).\)
What are the coordinates?To find the coordinates of point B, we can use the fact that the position of a point dividing a line segment in a given ratio can be found using the section formula.
Let's first find the coordinates of point B using the section formula. Let the coordinates of point B be (x, y). Then the ratio of AB to AC is 1:3, which means that the distance between A and B is one-fourth of the distance between A and C. We can express this mathematically as:
\(AB/AC = 1/3\)
\(= > AB = (1/4) * AC\)
Using the distance formula, we can find the length of AC:
AC = \(\sqrt\)\((4 - (-2))^2 + (7 - 4)^2]\)
\(\sqrt6^2 + 3^2]\)
\(\sqrt 45\)
So, we have:
\(AB = (1/4) \times \sqrt45\)
Now, using the section formula, we can find the coordinates of point B. The section formula states that the coordinates of the point dividing the line segment joining two points \((x1, y1)\) and \((x2, y2)\) in the ratio m:n are given by:
\(x = (nx2 + mx1)/(m + n)\)
\(y = (ny2 + my1)/(m + n)\)
In our case, the coordinates of point A are \((-2, 4)\), the coordinates of point C are \((4, 7)\) , and the ratio of AB to AC is \(1:3.\) So, we have:
\(m:n = 1:3\)
Substituting the values, we get:
\(x = (34 + 1(-2))/(1 + 3) = 2\)
\(y = (37 + 14)/(1 + 3) = 6.25\)
Therefore, the coordinates of point B are \((2, 6.25)\) .
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Related Questions
eight less than the product of a number n and 1/5 is no more than 98
Answers
Answer:
8<n+1/5<98
Step-by-step explanation:
if the dilation of K(-2,4) equals K'(1,-2), the scale factor used for the dilation is
Answers
Answer:
-1/2
Step-by-step explanation:
We know
The dilation of K(-2,4) equals K'(1,-2)
To get from -2 to 1, we time -1/2
To get from 4 to -2, we time -1/2
So, the scale factor used for the dilation is -1/2
What is the volume of the pyramid? Show all work.
6 m
8 m
4 m
Answers
192/3 = 64
Volume = 64m^3
What is 4/6÷4/12?!?!
Answers
Answer:2
Step-by-step explanation:
Keep, Change, Flip...4/6 divided by 4/12 = 4/6 * 12/4 which equals 48/24 which when simplified equals 2.
4/6÷4/12 the answer is 2
The county fair charges $1.00 per rode and an additional $3.00 to get in the fair. Write an equation to represent the total cost of attending the fair.
First identify the independent and dependent variables.
Answers
Answer:
Step-by-step explanation:
It's independent
Find a formula for the linear function passing through the points (-1,14) and (2,-10)
Answers
A(-1;14), x=-1, y=14
B(2;-10), x=2, y=-10
General equation for linear function is \(y=mx+b\)
Let's solve system of equations
\(\displaystyle\\\left \{ {{14=-1m+b} \atop {-10=2m+b}} \right. \\\\\left \{ {{b=14+m} \atop {2m+b=-10}} \right. \\\\2m+(14+m)=-10\\3m=-24\\m=-8=>b=14+(-8)=6\\\text{Answer}: y=-8m+6\)
help meeee again ¾÷⅕ =
Answers
Answer:
decimal: 2.25
fraction: 9/4
Step-by-step explanation:
Answer:
Fraction: 15/4
Decimal: 3.75
The formula for the area of a trapezoid is A= 1/2h(b1+b2), Where h is the height and b1 and b2 are the two bases. Rewrite the formula to solve for b1 in terms of A, h, and b2.
Answers
Answer:
Correct choice: B
Step-by-step explanation:
Equation Solving
The area of a trapezoid with height h and bases b1 and b2 is given by:
We must solve this formula for h.
First, multiply by 2 to eliminate denominators:
Now, divide by b1+b2:
Swapping sides:
Correct choice: B
Need help ASAP have 30 minutes
Answers
Explanation: divide 14.50 by 2
Answer:
1 box of paper will cost $7.25.
Step-by-step explanation:
14.50 divided by 2 is 7.25, therefore one box of paper will be 7.25
whoever answers gets brainliest and 100 points help
Answers
Answer:
12
the power of two are increased and become 12
answer is 2 power 12
CAN I GET BRAINLIEST NOW
Answer:
The answer would be 12 I hope this helps.
Write a inequality please help.
a number is at least -43
Answers
Answer:
x≥ -43
Step-by-step explanation:
at least means greater than or equal to
Let x be the unknown number
x≥ -43
I can't figure this one out| geometry Classifying and Solving for Side/Angles in Triangles
Answers
Answer:
use Pythagorean theorem (a^2 + b^2 = c^2)
Step-by-step explanation:
Round 0.00359 to the nearest ten-thousandth.
Answers
Answer:
0.0036 !
Step-by-step explanation:
Give brainliest please :)
0.00359, when rounded to nearest thousandth results in 0.0036.
What is Rounding Off?Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc. Rounding off numbers is done to preserve the significant figures.
Given, value to be rounded is : 0.00359
Since, 1 ten thousands = 10000 (104). So, 1 ten thousandth = 0.0001 (10-4)
Therefore, while rounding to nearest ten thousandth, we round the fractional part(or decimal part) upto 4 digits.
Here, In 0.00359, the digit after ten thousandth place is 9, which is (equal to or greater) than 5. So, 5 can be rounded to 6.
Hence, finally, 0.00359, when rounded to nearest thousandth results in 0.0036
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how much money will she have left after she pays back the money she borrowed from the bank
Answers
Step-by-step explanation:
whatever amount her bank account balance is at the same time frame when paying off her loan as only her bank knows
when you refer to the meer-kitty survey feedback tab, you are pleased to find that the available data is aligned to the business objective. however, you do some research about confidence level for this type of survey and learn that you need at least 120 unique responses for the survey results to be useful. therefore, the dataset has two limitations: first, there are only 40 responses; second, a meer-kitty superfan, user 588, completed the survey 11 times. as the survey has too few responses and numerous duplicates that are skewing results, you should remove the duplicates and continue analyzing the remaining 29 responses.
Answers
The meer-kitty survey feedback tab has limitations in its data. The survey results must have at least 120 unique responses to be considered useful and aligned with the business objective. The current data, however, only has 40 total responses, with 11 of them coming from one user. This skews the results and makes it difficult to accurately analyze the feedback.
To address these limitations, it is recommended to remove the duplicates, in this case the 11 responses from one user, and focus on the remaining 29 unique responses. This will provide a clearer picture of the survey results and a more accurate representation of the feedback. By doing so, the analysis of the data will be better aligned with the original business objective and provide more valuable insights.
It is important to consider the limitations of the data when conducting any type of analysis, especially when it comes to surveys and feedback. By taking the necessary steps to ensure the data is as accurate and reliable as possible, the results of the analysis will be more meaningful and relevant to the business.
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Use differences to find a pattern in the sequence.
3,8,15,28,51,88,143
Assuming that the pattern continues, the eighth term should be
Answers
Answer:
220
Step-by-step explanation:
You want to use differences to find the pattern and the next term in the sequence 3, 8, 15, 28, 51, 88, 143.
First differencesSubtracting each term from the next, we find the sequence of first differences to be ...
5, 7, 13, 23, 37, 55
Second differencesThe first differences are not constant, so we know the sequence is not linear. They are not in an arithmetic progression, so we know the sequence is not quadratic. They do not have a common ratio, so we know the sequence is not exponential.
The second differences are the differences of the sequence of first differences. They are ...
2, 6, 10, 14, 18
Third differencesThe differences of the terms of the 2nd-difference sequence are constant: 4.
4, 4, 4, 4, 4
Constant 3rd differences mean the original sequence can be described by a 3rd degree polynomial. The coefficients found by a calculator are shown in the attachment.
Next termSince we know the third differences are constant, we can work our way back up the chain of differences to find the next term of the original sequence.
next 2nd difference = 18 +4 = 22
next 1st difference = 55 +22 = 77
next sequence term = 143 +77 = 220
The eighth term should be 220.
__
Additional comment
The n-th term is ...
f(n) = 2/3n^3 -3n^2 +28/3n -4
If a polygon is a kite, then it is a quadrilateral. Write the inverse of the conditional statement and determine whether it is true or false. A) If a polygon is a quadrilateral, then it is a kite. TRUE B) If a polygon is a quadrilateral, then it is a kite. FALSE C) If a polygon is not a kite, then it is not a quadrilateral. TRUE D) If a polygon is not a kite, then it is not a quadrilateral. FALSE
Answers
The correct answer is D) If a polygon is not a kite, then it is not a quadrilateral. FALSE
Explanation:
The statement "If a polygon is a kite, then it is a quadrilateral" as other statements is composed of two parts: the if statement or hypothesis and the conclusion. Additionally, to create the inverse of this statement it is necessary to negate both statements, this means the inverse is "If a polygon is not a kite, then it is not a quadrilateral" because this negates the hypothesis and the conclusion. Besides this, it can be concluded this inverse statement is false because the word "quadrilateral" describes all shapes with four sides, which include not only kites but squares, rectangles, trapezoids, etc. Therefore, a polygon can be quadrilateral without being a kite.
HELPPPPP
Find the value for x that makes m
ll n?
m
n
(3x + 47)°
(x + 7)
x 7
Answers
Answer:
x = 31.5
Step-by-step explanation:
(3x + 47)° + (x + 7)° = 180° (same side interior angles theorem)
\( 3x + 47 + x + 7 = 180 \)
Collect like terms
\( 4x + 54 = 180 \)
Subtract 54 from both sides
\( 4x = 180 - 54 \)
\( 4x = 126 \)
Divide both sides by 4
\( x = \frac{126}{4} \)
\( x = 31.5 \)
22. Which table shows the x- and y coordinates of points on the liney - "2x?
A
B
X
y
X
у
2
4
2
4
2
1
1
2.
.
4
8
4
"8
D
X
y
у
X
-2
4
2
4
0
0
2
2
1
-2
2.
1
20
Done
Next
Previous
1
3
7 8 9 10 11 12 13 14 15 16 17 18
25 26 27 28 29 30
21 22 23
2022 Voyager Sopris Learning, Inc. All Rights Reserved. PRIVACY POLICY | Terms of Use Terms of Selo
Answers
Answer:
A
Step-by-step explanation:
The easiest way to solve this is by plugging in the values for x into the given equation. So first try plugging -2 into -2x, you get +4 as your value for y since the equation is really "y= -2x". Do this for the rest of your x-values and you'll see that A is correct.
Blank - 3/10 = 1/5 What is the blank number
Answers
Answer:
1/2
Step-by-step explanation:
Let's consider the number we want is x
x-3/10=1/5
On both sides of the equation, if we substract (or add) a certain number, say 3/10, the equality relation still exists.
That is x-3/10+3/10=1/5+3/10
Then x=1/5+3/10
You see 1/5+3/10=2/10+3/10=1/2
So x=1/2
Complete the missing value in the solution
2x+3y=12
Answers
Answer:
x= 1 and y= 3
Step-by-step explanation:
2*1+3*3=12.
Write the standard form of the line that has a slope of −3/4 and y-intercept of −2. Include your work in your final answer.
Answers
Y=Mx+b —-> Y=-3/4x-2
Then we can put it in standard form
Ax+By=C
We move the x to the other side
3/4x+y=-2
And that’ll be your answer :)
*if Ax it’s not positive you will have to multiply by -1*
HURRY PLZ I WILL MARK BRAINLIEST
Which point is located in Quadrant II?
A coordinate plane.
(–4, 5)
(–4, –5)
(4, –5)
(4, 5)
Answers
(-4,5)
Step-by-step explanation:
I took this math a bit ago, just trust me
Answer:
A
Step-by-step explanation:
"8% of a number is 20."
Answers
Answer: 250
Step-by-step explanation:
EXPLORE ACTIVITY 2
TEKS 7.13.8
Analyzing a Family Budget
One way to present a budget is in a circle graph. You can see at a glance which
categories take the greatest part of the family's resources. You can also work
backward from a circle graph to figure out exactly how much money is in each
category.
Use the circle graph to complete
the table for the Baker family's
monthly budget. Their net
monthly income is $4,000.
STEP 1)
STEP 2
STEP 3
STEP 4
STEP 5
432 Unit 7
Enter the income in the table.
Enter the percent or amount of money for each
category from the circle graph in the table.
Calculate the amount of money or the percent
for each category in the table.
Determine which expenses are fixed and
which are variable. Place X's in the appropriate
columns.
Complete the Amount Available column.
Item
Net monthly income
means how much
income the family
has after taxes.
Net monthly
Income
Housing cost
Food
Savings
Entertainment
Clothing
Medical
Transportation
Emergency
fund
Amount
($)
Percent
(%)
Baker Family's Monthly Budget
Emergency fund
Transportation
(car expense,
bus passes)
$400
Medical
(insurance
and
additional
expenses)
$600
Clothing
8%
Entertainment
Savings
$320
Fixed
Variable
Amount
Expense Expense Available
($)
Housing
cost (house
payment and
Insurance!
$1,400
Food
15%
Answers
Note that the table of budget is attached accordingly, and steps 1-4 have been completed. See the table.
What happened during emergency repair of $305?4) Since the emergency fund for that month was $200, it means that they are in the short for $105. They can only affod it if they take from their savings.
5) they had a balance of $800 for the month. This is miscellaneous funds. They can make use of this for the trip to NASA. This way, they won't have to touch the savings or entertainment.
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Full Question:
See attached image.
Reflect
4. Analyze Relationships One month, the family must make an
emergency car repair for $305. Are they able to pay for it out of the
fixed emergency fund for that month? If not, how can they afford it?
5. The family wants to make a trip to Houston to visit the NASA Space
Center. What are some ways they can save without using all of the
allotted $160 for entertainment
como resolver:
"los ceros son 0, -1, 1, 3/2, P(-3) = 300"
Answers
The polynomial with the given zeros is:;
P(x) = (300/108)*x*(x + 1)*(x - 1)*(x - 3/2)
How to find the polynomial?Remember that if a polynomial has the zeros a, b, c, and d, then we can write it as:
P(x) = K*(x - a)*(x - b)*(x - c)*(x - d)
Where K is a coefficient.
Here the zeros are 0, -1, 1, 3/2
Then we can write:
P(x) =K*(x - 0)*(x + 1)*(x - 1)*(x - 3/2)
P(x) =K*x*(x + 1)*(x - 1)*(x - 3/2)
We also know that when x = -3, P(x) = 300
Then we can write:
300 = K*(-3)*(-3 + 1)*(-3 - 1)*(-3 - 3/2)
300 = K*(-3)*(-2)*(-4)*(-9/2)
300 = K*108
300/108 = K
Then the polynomial is:
P(x) = (300/108)*x*(x + 1)*(x - 1)*(x - 3/2)
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What is the M.A.D. (mean absolute deviation) of the following data set?
8 9 9 7 8 6 9 8
Answers
The mean absolute deviation is 0.75
How to determine the mean absolute deviationTo calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set
From the information given, we have that the data set is;
8 9 9 7 8 6 9 8
Let's calculate the mean, we get;
Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8
Mean = 64 / 8
Divide the values
Mean = 8
Let's determine the absolute difference, we get;
Absolute differences=
|8 - 8| = 0
|9 - 8| = 1
|9 - 8| = 1
|7 - 8| = 1
|8 - 8| = 0
|6 - 8| = 2
|9 - 8| = 1
|8 - 8| = 0
Find the mean of the absolute differences:
Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8
Absolute difference = 6 / 8 = 0.75
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1. 18x^3-2x^2+4x-1
1.1 How many terms are in 18x^3-2x^2+4x-1
Answers
The polynomial 18x³ - 2x² + 4x - 1 consists of four terms.
The number of terms in a polynomial helps when performing operations like simplification, factoring, or evaluating expressions.
The polynomial 18x³ - 2x² + 4x - 1 consists of four terms.
In order to determine the number of terms in a polynomial, we count the number of distinct algebraic expressions separated by addition or subtraction operations.
In this polynomial, we have:
Term 1: 18x³ (This is the term with the highest degree, which is 3 in this case, and it includes the coefficient 18.)
Term 2: -2x² (This term has a degree of 2 and a coefficient of -2.)
Term 3: 4x (This term has a degree of 1 and a coefficient of 4.)
Term 4: -1 (This is a constant term with a degree of 0.)
We can see that there are four distinct terms separated by addition and subtraction operations:
18x³, -2x², 4x, and -1.
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Please help fast!!!!!!!
Answers
Answer: 156.38 m
Step-by-step explanation:
Using the arc length formula, the answer is \(2\pi(8^2) \cdot \frac{140}{360} \approx 156.38\)
Question 2 (1 point)
What are the multiplicative and additive inverses of -7?
a
multiplicative inverse 1/7; additive inverse -7
b
multiplicative inverse 1/7; additive inverse 7
c
multiplicative inverse -1/7; additive inverse -7
d
multiplicative inverse -1/7; additive inverse 7
Answers
answer is option D ,The multiplicative inverse of a number is the reciprocal of that number such that when you multiply them together, you get one. The multiplicative inverse of -7 is -1/7.
what is multiplicative inverse ?
The multiplicative inverse of a number is also known as its reciprocal. It is the number that, when multiplied by the original number, results in a product of 1. In other words, if the original number is a, then its multiplicative inverse
In the given question,
The additive inverse of a number is the opposite of that number such that when you add them together, you get zero. The additive inverse of -7 is 7.
The multiplicative inverse of a number is the reciprocal of that number such that when you multiply them together, you get one. The multiplicative inverse of -7 is -1/7.
Therefore, the correct answer is (c) multiplicative inverse -1/7; additive inverse -7.
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