Answer:
D. 1.25
Step-by-step explanation:
The values of the correlation coefficient must be between -1 and 1 (they can include -1 and 1)
The only value outside that range is 1.25
1.25 is not a possible correlation coefficient
Help plz. Ignore the orange color around the choices.
Hello There!
Your answers would be #1 and #3
If Earl jogged 5 yards forward and then jogs 9 yards back, we are subtracting 9 from 5 and we get a difference of -4. This is because he jogged backward from his position after 5 yards.
If Clarissa had $49 in her checking account, we subtract $53 because she bought a pair of shoes so we get a difference of also -4
Answer:
the first one was the answer
justin ran 800 meters in track meet today. How many yards did he run? Round your asnwer to the nearest tenth.
874.890 i think, sorry if im wrong
Which of the following are solutions to the equation 3x2 + 7x + 4 = 0
Select all that apply
O x=-1
O x=-4/3
x=3/4
x=1
For this case we have the following quadratic equation:
[tex]3x ^ 2 + 7x + 4 = 0[/tex]
Where:
[tex]a = 3\\b = 7\\c = 4[/tex]
According to the quadratic formula we have:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]
Substituting:
[tex]x = \frac {-7 \pm \sqrt {7 ^ 2-4 (3) (4)}} {2 (3)}\\x = \frac {-7 \pm \sqrt {49-48}} {6}\\x = \frac {-7 \pm \sqrt {1}} {6}\\x = \frac {-7 \pm1} {6}[/tex]
We have two roots:
[tex]x_ {1} = \frac {-7 + 1} {6} = \frac {-6} {6} = - 1\\x_ {2} = \frac {-7-1} {6} = \frac {-8} {6} = - \frac {4} {3}[/tex]
Answer:
[tex]x_ {1} = - 1\\x_ {2} = - \frac {4} {3}[/tex]
Answer:
x = -4/3 x=-1
Step-by-step explanation:
3x^2 + 7x + 4 = 0
Factor the equation
(3x+4) (x+1) = 0
Using the zero product property
3x+4 =0 x+1 =0
3x+4-4=0-4 x+1-1=0-1
3x=-4 x=-1
3x/3 = -4/3
x = -4/3 x=-1
What is the base of expression 9^12
Answer:
the answer is 9
Step-by-step explanation:
What is the answer to this question
Answer: about 34.6
Step-by-step explanation: 11 is the radius, but you need the diameter which is 22. multiply 22 by pi and divide that number by 2 since it is half a circle.
For the following geometric sequence, find the explicit formula.
{1, -3, 9, ...}
Answer:
the explicit formula for given geometric sequence {1,-3,9,..} is [tex]a_{n}= (-3)^{n-1}[/tex]
Step-by-step explanation:
We are given the series
1,-3,9,...
the common ratio is:
-3/1 = -3
9/-3 = -3
So, the common ratio in the series is -3
a₁ = 1
The formula used for geometric series is:
[tex]a_{n}= a_{1}(r)^{n-1}[/tex]
Putting values of a₁ and r
[tex]a_{n}= 1(-3)^{n-1}[/tex]
[tex]a_{n}= (-3)^{n-1}[/tex]
So, the explicit formula for given geometric sequence {1,-3,9,..} is [tex]a_{n}= (-3)^{n-1}[/tex]
Solve for x in the equation y^2 + 2x + 1 = 17.
Answer:
x = −1 ± √17
Hope this helps and have a nice day! :)
Answer:
B
Step-by-step explanation:
So your equation is actually x^2+2x+1=17
Left hand side is already set for rewriting it as a perfect square
So you have actually that (x+1)^2=17
Now you just take square root of both sides
x+1=(pm) sqrt(17) (pm) means plus or minus
x=-1 (pm) sqrt(17) I subtracted 1 on both sides
B
What is 270° converted to radians?
A.) pi/6
B.) 3/2
C.) 3pi/2
D.) 3
Answer:
the answer C) 3pi/2 semoga membantu
Jada created the two-way table below to describe the performance of her basketball team this season.
Which statements are supported by the data in the table? Check all that apply.
The team is twice as likely to win a home game as they are an away game.
The team wins 3/5 of their home games.
The team wins 1/2 of their games.
The team played a total of 27 games.
The team won a total of 6 games.
The team lost more home games than away games.
...........................WIN..........LOSS
HOME GAMES ... 6 ..........10
AWAY GAMES .....3.............8
Answer:
The correct option is 1, 4 and 6.
Step-by-step explanation:
The given two-way table is
WIN LOSS TOTAL
HOME GAMES 6 10 16
AWAY GAMES 3 8 11
TOTAL 9 18 27
Total number of home games won by team is 6 and total number of away games won by team is 3. It means the team is twice as likely to win a home game as they are an away game.
The correct option is 1.
Total number of home games = 16.
Home game won by team is
[tex]\frac{6}{16}=\frac{3}{8}[/tex]
Option 2 is incorrect.
Total games = 27
Total games won by the team = 9
Total part of games won by team is
[tex]\frac{9}{27}=\frac{1}{3}[/tex]
Option 3 is incorrect.
The team played a total of 27 games.
Option 4 is correct.
The team won a total of 9 games.
Option 5 is incorrect.
Total home games loose by team = 10
Total away games loose by team = 8
The team lost more home games than away games.
Option 6 is correct.
Therefore the correct option is 1, 4 and 6.
Answer:
4 and 6
Step-by-step explanation:
took quiz
which graph shows the solution set for 2x+3>-9.
Answer:
x > -6
The solution above is graphed correctly in the last option choice.
Step-by-step explanation:
We have been given the equation 2x + 3> -9
In order to graph the solution, we must find the value of x
2x + 3 > -9
Subtract three from both sides
-9 - 3 = -12
2x > -12
Divide both sides by 2
x > -6
To determine how to graph the solution, look at the inequality symbol. If the symbol is "greater than" then you would graph the line going left. If it was "less than" than you would graph the line going right.
In our problem, we have the "greater than" symbol which means we will be graphing our line going to the right, and since we start our line from -6 we know the last option is the correct answer.
A beach resort is offering two weekend specials. One includes a two night stay with 3 meals and costs $195. The other includes a three night stay with 5 meals and costs $300. How much is the cost of a one night stay?
Answer: $75 per night and $15 per meal
Step-by-step explanation:
a 1 night cost $15
What's the equation defining?
Mathematics written statement indicating the equality of 2 expressions. this consists of the sequence of symbols that are split in the left or right sides joined by the equal sign. e.g, 2 + 4 + 5 = 11 is an equation.
Do equations always contain terms?
When equality holds, the total weight on the each side is the same. Equations often contain terms other than a unknowns. These other terms, which are assumed to known, is usually known as constants, coefficients and parameters
Step-by-step explanation:
offer 1 : (1) 2*night+3*meal=195
(2) night=(195-3*meal)/2
offer 2: (3) 3*night+5*meal=300
if we replace eq (2) in eq (3)
3*(195-3*meal)/2+5*meal=300
292.5+0.5meal=300
meal=$15
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Connie has to solve the following problem
5 boxes of cereal costs $12.50. How much will 18 boxes cost
Choose EVERY proportion Connie could use to solve this problem
Answer:
$45
Step-by-step explanation:
$12.50÷5=$2.50
$2.50×18=$45
or
12.50/5=n/18
Answer: Cost of 18 boxes is $45.
Step-by-step explanation:
Since we know that
Cost of 5 boxes of cereal = $12.50
We will use "Unitary method":
Cost of 1 box of cereal is given by
[tex]\dfrac{12.50}{5}\\\\=\$2.5[/tex]
So, Cost of 18 boxes would be
[tex]\$2.5\times 18\\\\=\$45[/tex]
Hence, cost of 18 boxes is $45.
:
Malik received a $300 gift card from his grandparents and is using it only to pay for his karate lessons, which cost $30 per month.
Determine what amount, in dollars, remains on the card after 8 months.
Answer:
60$ will be left
Step-by-step explanation: 30x8 = 240. subtract 300-240 and you get 60
Answer:
60
Step-by-step explanation:
30*8=240
300-240=60
A 12-ounce Pepsi contains 54 mg of caffeine. A can of Red Bull (8.2 oz) has 80 mg of caffeine.
a. What is the average caffeine content per ounce of Pepsi? Round your answer to the nearest tenth, if needed.
Answer:
4.5 mg per ounce
Step-by-step explanation:
To find the average caffeine content per ounce of Pepsi, take the caffeine and divide by the ounces
54 mg/12 ounces
4.5 mg per ounce
Answer:
The average caffeine content per ounce of Pepsi is 4.5 gm
Step-by-step explanation:
Given :A 12-ounce Pepsi contains 54 mg of caffeine
To Find : What is the average caffeine content per ounce of Pepsi? Round your answer to the nearest tenth, if needed.
Solution :
A 12-ounce Pepsi contains 54 mg of caffeine.
We are supposed to find the average caffeine content per ounce of Pepsi
Amount of caffeine in 12 ounces of Pepsi = 54 mg
Amount of caffeine in 1 ounce of Pepsi = [tex]\frac{54}{12}[/tex]
= [tex]4.5[/tex]
Hence the average caffeine content per ounce of Pepsi is 4.5 gm
A bag contains 10 green , 10 orange, 10 pink , and 10 purple chips each numbered 1 through 10. a chip is chosen at random.
What is the probability that the chip is purple, given that the card is a 4?
Answer: [tex]\bold{a.\quad \dfrac{1}{4}}[/tex]
Step-by-step explanation:
Since it is already given that the number is a 4 and each of the four colors only has one 4, then the probability for green is:
[tex]P=\dfrac{\text{number of green 4's}}{\text{total number of 4's}}=\dfrac{1}{4}[/tex]
If you wanted to find the probability that it is a four and it is green then you would calculate the probability as:
[tex]P=\dfrac{\text{number of 4's}}{\text{total number of numbers}}\times \dfrac{\text{number of greens}}{\text{total number of colors}}\\\\\\.\ =\dfrac{4}{40}\times\dfrac{1}{4}\\\\\\.\ =\dfrac{1}{40}[/tex]
17x - 6 + 3x - 5 = x + 11 + 4x
Answer:
x = 22/15
Step-by-step explanation:
17x - 6 + 3x - 5 = x + 11 + 4x
Combine like terms on each side.
20x - 11 = 5x + 11
Add 11 to both sides. Subtract 5x from both sides.
15x = 22
Divide both sides by 15.
x = 22/15
Answer: 20x-11=5x+11
Step-by-step explanation:
if alpha and beta are the roots of a quadratic polynomial 3x^2-6x-1 find the values of (Alpha-beta)
Answer:
Either [tex]-4\sqrt{6}[/tex] or [tex]4\sqrt{6}[/tex], depending on whether [tex]\alpha[/tex] is larger than [tex]\beta[/tex].
Step-by-step explanation:
The two roots (might necessarily be distinct or real) of the quadratic equation
[tex]ax^{2} + bx + c = 0[/tex], where [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are constants and [tex]a\ne 0[/tex] are
[tex]\displaystyle x_1 = \frac{-b+\sqrt{\text{b^{2} - 4ac}}}{2a}[/tex], and[tex]\displaystyle x_2 = \frac{-b-\sqrt{\text{b^{2} - 4ac}}}{2a}[/tex].The difference between the two will be either:
[tex]x_1 - x_2 = 2\sqrt{b^{2} - 4ac}[/tex] or
[tex]x_2 - x_1 = -2\sqrt{b^{2} - 4ac}[/tex].
For this question,
[tex]a = 3[/tex], [tex]b = -6[/tex], and[tex]c = -1[/tex].[tex]x_1 - x_2 = 2\sqrt{(-6)^{2} - 4\times 3\times (-1)} = 4\sqrt{6}[/tex], or
[tex]x_1 - x_2 = -2\sqrt{(-6)^{2} - 4\times 3\times (-1)} = -4\sqrt{6}[/tex].
What is the result of 2 divided by 4/10
Answer:
5
Step-by-step explanation:
When you are dividing fractions you must flip the second digit and the sign should be changed to multiplication sign.
So in this equation it will be
2 / 4/10 =
2 * 10/4=
20/4=
5
Hope you found this answer helpful
Jimmy is selling used books at a yard sale. A customer buys 9 books at a cost of $0.75 each and pays with a $20.00 bill. Jimmy must determine c, the amount of change in dollars he should give the customer. Which equation represents c?
20-0.75C=9
20-0.75-9c
0.75(9)+c+20
0.75+9+20
Answer:
it is C
Step-by-step explanation:
on edge
Which of the following will give you the incorrect slope? (1 point)
the quantity y subscript two minus y subscript one over the quantity x subscript two minus x subscript one.
the quantity y subscript two minus y subscript one over the quantity x subscript one minus x subscript two.
the quantity y subscript one minus y subscript two over the quantity x subscript one minus x subscript two.
rise over run
Answer:
2nd one
Step-by-step explanation:
No mixing order so the second one.
You can do either
(y2-y1)/(x2-x1) or (y1-y2)/(x1-x2) which will give you rise/run in either situation
Answer:
2nd one
Step-by-step explanation:
got it right on the test and got 100%
hope this helps :)
Help me now..
Which cell organelle is primarily responsible for ATP synthesis
Answer:
Mitochondria
Step-by-step explanation:
Mitochondria is the cell organelle responsible for ATP synthesis.
Hope this helps!
Feel free to ask if you have anymore questions!
Answer: the mitochondria
Step-by-step explanation: it’s the power source of the cell. Hope this helps! :)
Find a1, for the given geometric series. Round to the nearest hundredth if necessary.
Sn= 88,560, r= 2.2, n= 6
a. 8,765.73
b. 2,477.6
c. 945.65
d. 14,754.5
Answer:
* The value of a1 = 945.65 ⇒ answer c
Step-by-step explanation:
* Lets revise the geometric series
- There is a constant ratio between each two consecutive numbers
- Ex:
# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)
# 5000 , 1000 , 200 , 40 , …………………………(÷5)
* General term (nth term) of a Geometric Progression:
- U1 = a , U2 = ar , U3 = ar² , U4 = ar³ , U5 = ar^4
- Un = ar^n-1, where a is the first term , r is the constant ratio
between each two consecutive terms, n is the position
of the term
- The sum of first n terms of a Geometric series is calculate
from Sn = [a1 (1 - r^n)]/(1 - r) , where a1 is the first term, r is the
common ratio and n is the number of the terms
* Lets solve the problem
∵ Sn = 88,560
∵ r = 2.2
∵ n = 6
∵ Sn = [a1 (1 - r^n)]/(1 - r)
∴ 88,560 = [a1 (1 - 2.2^6)]/(1 - 2.2) ⇒ simplify up and down
∴ 88,560 = [a1 (-112.379904)]/(-1.2) ⇒ simplify the fraction
∴ 88,560 = a1 (93.64992) ⇒ divide both sides by 93.64992
∴ a1 = 945.6494998 ≅ 945.65
* The value of a1 = 945.65
Identify the similar triangles and find x. Then find the measures of the indicated sides.
Answer:
The similar triangles are Δ KMJ and Δ NML
The value of x is 3
KM = 6 and NM = 3
Step-by-step explanation:
* Lets revise the cases of similarity
1) AAA similarity : two triangles are similar if all three angles in the first
triangle equal the corresponding angle in the second triangle
- Example : In ΔABC and ΔDEF, m∠A = m∠D, m∠B = m∠E and
m∠C= m∠F then ΔABC ≈ ΔDEF by AAA
2) AA similarity : If two angles of one triangle are equal to the
corresponding angles of the other triangle, then the two triangles
are similar.
- Example : In ΔPQR and ΔDEF, m∠P = m∠D, m∠R = m∠F then
ΔPQR ≈ ΔDEF by AA
3) SSS similarity : If the corresponding sides of two triangles are
proportional, then the two triangles are similar.
- Example : In ΔXYZ and ΔLMN, if
then the two triangles are similar by SSS
4) SAS similarity : In two triangles, if two sets of corresponding sides
are proportional and the included angles are equal then the two
triangles are similar.
- Example : In triangle ABC and DEF, if m∠A = m∠D and
then the two triangles are similar by SAS
* Now lets solve the problem
- ∠KMJ is a aright angle and M is on JL
∴ m∠JML = 180° ⇒ straight angle
∵ m∠JMK + m∠LMN = m∠JML
∴ 90° + m∠NML = 180° ⇒ subtract 90° from both sides
∴ m∠NML = 90°
- In Δ KMJ and ΔNML
∵ m∠KMJ = m∠NML ⇒ proved
∵ m∠KJM = m∠NLM ⇒ given
- By using the second case above (AA similarity)
∴ Δ KMJ ≈ Δ NML
* The similar triangles are Δ KMJ and Δ NML
- From similarity
∴ Their sides are proportion
∴ [tex]\frac{KM}{NM}=\frac{MJ}{ML}=\frac{KJ}{NL}[/tex]
∵ KJ = 10 and NL = 5
∵ KM = 3 + x and NM = x
- Substitute these values in the proportion relation
∵ [tex]\frac{KM}{NM}=\frac{KJ}{NL}[/tex]
∴ [tex]\frac{3+x}{x}=\frac{10}{5}[/tex]
- By using cross multiplication
∴ 5(3 + x) = 10(x) ⇒ simplify
∴ 5(3) + 5(x) = 10x
∴ 15 + 5x = 10x ⇒ subtract 5x from both sides
∴ 15 = 5x ⇒ divide both sides by 5
∴ 3 = x
* The value of x is 3
∵ KM = 3 + x
∵ x = 3
∴ KM = 3 + 3 = 6
∵ NM = x
∴ NM = 3
* KM = 6 and NM = 3
- Check the ratio
∵ KM/NM = 6/3 = 2
∵ KJ/NL = 10/5 = 2
∴ The sides are proportion
Answer:
Triangle JMK is similar to triangle LMN.
[tex]x = 3[/tex].
[tex]\rm \overline{KM}= 6[/tex].
[tex]\rm \overline{NM} = 3[/tex].
Step-by-step explanation:
The angle [tex]\rm N\hat{M}L[/tex] is a right angle for it is complementary with another right angle, [tex]\rm K\hat{M}J[/tex].
The diagram also indicates that angle [tex]\rm \hat{J}[/tex] is equal to angle [tex]\rm \hat{L}[/tex]. As a result, [tex]\rm \triangle JMK \sim \triangle LMN[/tex] for two of their angles are equal.
Consequently,
[tex]\displaystyle \rm \frac{(\overline{MN})}{(\overline{MK})} = \frac{(\overline{LN})}{(\overline{JK})}[/tex].
Let [tex]x[/tex] be the length of segment [tex]\rm MN[/tex].
[tex]\displaystyle \frac{x}{3+x} = \frac{5}{10}[/tex].
Cross multiply. In other words, multiply both sides by [tex]10(3 + x)[/tex].
[tex]10x = 5(3 + x)[/tex].
[tex]x = 3[/tex].
[tex]\rm \overline{KM} = 3 + \mathnormal{x} = 6[/tex].
[tex]\rm \overline{MN} = \mathnormal{x} = 3[/tex].
Which best explains if quadrilateral WXYZ can be a parallelogram? WXYZ is a parallelogram because diagonal XZ is bisected. WXYZ is not necessarily a parallelogram because it is unknown if CZ = CY. WXYZ is a parallelogram because ZC + CX = ZX. WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.
Answer:
D. WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.
Step-by-step explanation:
edge2021
The statement which best explains that the quadrilateral WXYZ can be a parallelogram is D. WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.
What is Parallelogram?Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.
Opposite sides are parallel, and the opposite sides and opposite angles are equal.
In order to find this, we have to know the properties of the diagonals of a parallelogram.
Here given a parallelogram WXYZ.
The diagonals of a parallelogram bisect each other.
That is, if WXYZ is a parallelogram,
WC = CY and ZC = CX
But it is unknown that these are equal.
Hence the correct option is D.
Learn more about Parallelograms here :
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100 Points last one i promise! helpp!
Answer:
$40.35
Step-by-step explanation:
First, solve for the sales price. Change the percentage into a decimal:
60% = 60/100 = 0.60
Next, multiply 0.60 with the original price, 97:
97 x 0.60 = 58.2
Subtract 58.2 from the original price:
97 - 58.2 = 38.8
Now, change the tax percentage into a decimal.
4% = 4/100 = 0.04
Multiply 0.04 with the sales price:
38.8 x 0.04 = 1.552
Add the sales price (rounded to nearest hundredth) to the sales price:
1.55 + 38.8 = 40.35
$40.35 is your answer.
~
Answer:
40.35
Step-by-step explanation:
First find the discount
97 * 60%
97 *.6 = 58.2
Subtract the discount to find the new price
97-58.20 =38.80
Next find the tax
38.80 * 4%
38.80 * .04
1.55
We add the tax to the sales price
38.8+1.55
40.35
Plzzz helppp me!!! And thank
Answer:
A. The slope is 4.
B. The y-intercept is 8.
C. The equation is y = 4x + 8
Step-by-step explanation:
We know that there is a flat $8 cost in addition to $4 per ride. We can express this by using:
y = 8 + 4x.
y is the total cost
x is the number of rides
The question wants the equation in slope-intercept form.
Slope-intercept form of a line: y = mx + b
m = slope
b = y-intercept
y = 8 + 4x ➵ y = 4x + 8
Now that we have the slope-intercept form of the line, we can answer the problems.
A. The slope is 4.
B. The y-intercept is 8.
C. The equation is y = 4x + 8
What is the value of x and the length of segment DE?
10x + 15 = 9(9)
x =
Length of =
units
Answer:
Part 1) [tex]x=6.6\ units[/tex]
Part 2) [tex]DE=16.2\ units[/tex]
Step-by-step explanation:
Part 1) Find the value of x
we know that
Triangles CDF and FDE are similar
therefore
The ratio of its corresponding sides is proportional and its corresponding angles are congruent
so
[tex]CD/FD=FD/DE[/tex]
[tex]\frac{5}{9}=\frac{9}{2x+3} \\ \\5*(2x+3)=9*9\\ \\10x+15=81\\ \\10x= 81-15\\ \\10x=66\\ \\ x=6.6\ units[/tex]
Part 2) Find the length of DE
[tex]DE=2x+3[/tex]
substitute the value of x
[tex]DE=2(6.6)+3=16.2\ units[/tex]
Answer:
x = 6.6
Length of = 16.2 units
Which of the following is a correct equation for the line passing through the
point (-3,2) and having slope m = 2/3?
Check all that apply.
A. V-2 ={(x+3)
c. "=3x+4
D. 21 – 3y = - 12
Answer:
[tex]2x-3y=-12[/tex]
Step-by-step explanation:
We can use the point-slope formula given by:
[tex]y-y_1=m(x-x_1)[/tex]
The given line passes through the
point (-3,2) and having slope [tex]m=\frac{2}{3}[/tex].
We substitute the given point and slope to get:
[tex]y-2=\frac{2}{3}(x--3)[/tex]
[tex]y-2=\frac{2}{3}(x+3)[/tex]
we clear the fraction to get;
[tex]3y-6=2(x+3)[/tex]
[tex]3y-6=2x+6[/tex]
[tex]3y-2x=6+6[/tex]
[tex]3y-2x=12[/tex]
Or in standard form:
[tex]2x-3y=-12[/tex]
The correct equation for a line passing through the point (-3,2) with a slope of 2/3 is y = 2/3x + 4, which corresponds to option C in the provided choices.
To find a correct equation for a line passing through a specific point with a given slope, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is the point through which the line passes.
In this problem, we have the point (-3, 2) and a slope of 2/3. Substituting these values into the point-slope form gives us:
y - 2 = 2/3(x + 3).
After multiplying both sides by 3 to eliminate the fraction, the equation becomes:
3(y - 2) = 2(x + 3).
Expanding and simplifying this equation further, we end up with:
3y - 6 = 2x + 6,
or
y = 2/3x + 4, which matches option C.
Therefore, the correct equation for the line passing through the point (-3, 2) with a slope of 2/3 is y = 2/3x + 4.
In the diagram, C and D are located such that AB is divided into three equal parts. What are the coordinates of C and D?
Step-by-step Answer:
Topic: Points of division
There are scary looking formulas that can be used, but it is much easier to calculate by reasoning.
Given : A(-3,6), B(6,-3)
Solution:
The idea is to subdivide the DIFFERENCE in coordinates into thirds, and add onto that of A. We choose A as the starting point, but method works equally well if we chose B.
Difference in coordinates (delta) between A & B is then
delta(Bx-Ax, By-Ay)
=(6-(-3), -3-6)
=delta(9, -9)
One third of difference (for point C)
=delta/3 = (3,-3)
So coordinates of point C
= A(-3,6)+(3,-3)
= C(0,3)
Two thirds of difference (for point D)
= (2/3)delta = (6, -6)
Coordinates for point D
= A(-3,6)+(6,-6)
= D(3,0)
If you prefer to use formulas, it would be
New coordinates = (Xa+(Xb-Xa)*k, Ya+(Yb-Ya)*k)
where
Xa,Xb = x-coordinates of points A & B respectively.
Ya,Yb = y-coordinates of points A & B respectively.
k=ratio (usually less than 1)
Here
k for point C = 1/3
k for point D = 2/3
Coordinate of C is: (0,3)
and Coordinate of D is: (3,0)
Step-by-step explanation:We know that if a point C(x,y) divides the given line segment A(a,b)B(c,d) into ratio of m:n
then the coordinates of points C are:
[tex]x=\dfrac{m\times c+n\times a}{m+n},\ y=\dfrac{m\times d+n\times b}{m+n}[/tex]
Point C cuts the line segment AB in the ratio 1:2.Here A(a,b)=A(-3,6)
and B(c,d)=B(6,-3)
This means that the coordinate of Point C are:
[tex]x=\dfrac{1\times 6+2\times (-3)}{1+2},\ y=\dfrac{1\times (-3)+2\times 6}{1+2}\\\\i.e.\\\\x=\dfrac{6-6}{3},\ y=\dfrac{-3+12}{3}\\\\i.e.\\\\x=0,\ y=\dfrac{9}{3}\\\\i.e.\\\\x=0,\ y=3[/tex]
Hence, the coordinates of Point C are: (0,3)
Similarly Point D cuts the line AB in the ratio 2:1Hence, the coordinates of point D is calculated by:
[tex]x=\dfrac{2\times (6)+1\times (-3)}{1+2},\ y=\dfrac{2\times (-3)+1\times 6}{1+2}\\\\i.e.\\\\x=\dfrac{12-3}{3},\ and\ y=\dfrac{-6+6}{3}\\\\i.e.\\\\x=\dfrac{9}{3},\ y=\dfrac{0}{3}\\\\i.e.\\\\x=3,\ y=0[/tex]
Hence, the coordinate of Point D is: (3,0)
Will someone help me plz
Answer:
Associative property of addition
Step-by-step explanation:
The order of the addition doesn't matter. That is what the brackets show.
Answer:
Associative Property of AdditionStep-by-step explanation:
[tex]\bold{Commutative\ Property\ of\ Addition:}\ a+b=b+a\\\\\bold{Inverse\ Property\ of\ Addition:}\ a+(-a)=0\\\\\bold{Commutative\ Property\ of\ Multiplication:}\ a\cdot b=b\cdot a\\\\\bold{Associative\ Property\ of\ Addition:}\ a+(b+c)=(a+b)+c\\\\\text{We have}\ 7+(4+4)=(7+4)+4\\\\\text{It's Associative Property of Addition.}[/tex]