Simple
They are 64 ,0,32Sum of all three
64+0+32=96Sum of first two
64+0=64Divide by
64/322Yes Verified
Two points have the coordinates P (6, -3,9) and Q (3, -6, -3). A point R divides line PQ internally in the ratio 1:2. The position vectors of P, Q and Rare p, q and r respectively.
(a) Express the position vector of p and q.
i. In terms of p and q.
ii. In terms of i, j and k
(b) Hence state the coordinates of R.
Answer:
p = 6i -3j +9k
q = 3i -6j -3k
r = 2p +q
r = 5i -4j +5k
R(5, -4, 5)
Step-by-step explanation:
Given points P(6, -3, 9) and Q(3, -6, -3) and R that divides PQ in the ratio 1:2, you want ...
position vectors p and qr in terms of p and qr in terms i, j, and kthe coordinates of RPosition vectorThe vector from the origin to a point (x, y, z) will be ...
xi +yj +zk
where i, j, k are unit vectors in the direction of the x, y, and z axes, respectively.
Using this pattern, we find the position vectors p and q to points P and Q to be ...
p = 6i -3j +9k . . . . . . . . . . . . . position vector p
q = 3i -6j -3k . . . . . . . . . . . . . position vector q
DivisionPoint R divides PQ in the ratio 1:2, so its position vector will be the weighted sum of p and q:
r = (2p +q)/3 . . . . . . . . . . . . . . . . r in terms of p and q
Using the values of p and q from above, we find r to be ...
r = (2(6i -3j +9k) +(3i -6j -3k))/3 = ((2·6+3)i +(2(-3)-6)j +(2·9-3)k)/3
r = 5i -4j +5k . . . . . . . . . . r in terms of i, j, k
CoordinatesThe coordinates of R are the coordinates of the head of position vector r:
R(5, -4, 5) . . . . . . . . . . . . . coordinates of R
$10.14 is what percent of $8.45?
Write your answer using a percent sign (%). For example, 0.5%, 12.7%, or 56%.
Answer:
120%
Step-by-step explanation:
10.14 is more than all of 8.45.
8.45 is 100% of 8.45.
So 10.14 will be more than 100%.
10.14 ÷ 8.45 = 1.2
This is the decimal value.
To change to %, multiply by 100.
1.2 × 100 = 120
10.14 is 120% of 8.45
How many solutions does the following equation have? -1/3x2=5/6+1/3y2 5y2=25/2-5x2
The system of equations have 2 solutions
How to determine the number of solutions?The system of equations is given as:
-1/3x² = 5/6 + 1/3y²
5y² = 25/2 - 5x²
Next, we plot the graph of the system of equations.
From the attached graph, the equations intersect at two points
Hence, the system of equations have 2 solutions
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Find the solutions to the equation below.
Check all that apply.
2x² +9x+4=0
A. x = -4
B. X= 4
C. X=-3
D. X= 7
0 E. x= -1/2
F. X=2
SUBMIT
Answer-
-1/2, -4
Step-by-step explanation:
A, E
Did the math to find the solution earlier, got right xoxo :)
18
Select the correct answer.
Exponential function fis represented by the table.
X
f(x)
=
-2
-46
OA
O B.
OC.
O D.
-1
-22
0
-10
1
-4
Function g is represented by the equation.
g(x)
- 18(3)² + 2
Which statement correctly compares the two functions on the interval [-1, 2]?
2
-1
ہے
Only function fis increasing, and only function fis negative.
Only function fis increasing, but both functions are negative.
Both functions are increasing, but function g increases at a faster average rate.
Both functions are increasing, but function fincreases at a faster average rate.
A statement which correctly compares the two functions on the given interval [-1, 2] is: C. Both functions are increasing, but function g increases at a faster average rate.
How to compares the two functions?First of all, we would determine the values of function g(x) on the given interval [-1, 2] as follows:
g(x) = -18(⅓)^x + 2
At x = -1, we have:
g(-1) = -18(⅓)^(-1) + 2
g(-1) = -52.
At x = 0, we have:
g(0) = -18(⅓)^(0) + 2
g(0) = -16.
At x = 1, we have:
g(1) = -18(⅓)^(1) + 2
g(1) = -4.
At x = 2, we have:
g(2) = -18(⅓)^(0) + 2
g(2) = 0.
By critically observing the values of each functions, we can logically deduce that both functions are increasing but function g(x) increases at a faster average rate because it started with a lower value and ended with a higher value.
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A toy rocket is launched from a 1.4 m high platform in such a way that its height, h (in meters), after t seconds is given by the equation
h= -4.9t² +9.1t+1.4. How long will it take for the rocket to hit the ground?
The rocket will take 2 seconds for the rocket to hit the ground.
We have,
To find the time it takes for the rocket to hit the ground, we need to determine when the height, h, becomes zero (since the ground is at height zero).
Given the equation for the height of the rocket at time t:
h = -4.9t² + 9.1t + 1.4, we can set h to zero and solve for t:
0 = -4.9t² + 9.1t + 1.4
This is a quadratic equation in the form of at² + bt + c = 0,
where a = -4.9, b = 9.1, and c = 1.4.
To solve for t, we can use the quadratic formula:
t = (-b ± √(b² - 4ac)) / 2a
Substituting the values:
t = (-(9.1) ± √((9.1)² - 4(-4.9)(1.4))) / 2(-4.9)
t = (-9.1 ± √(82.81 + 27.44)) / (-9.8)
t = (-9.1 ± √110.25) / (-9.8)
Now, we have two possible solutions for t:
t₁ = (-9.1 + √110.25) / (-9.8)
t₂ = (-9.1 - √110.25) / (-9.8)
Calculating these values:
t₁ ≈ -0.143
t₂ ≈ 2
Since time cannot be negative, the only meaningful solution is t₂ ≈ 2 seconds.
Thus,
The rocket will take 2 seconds for the rocket to hit the ground.
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Solve for x.
3(x + 5)-2(x+2)=20
1
9
13
Answer:
the answer is 9
Step-by-step explanation:
if you use distributive property you'll find your answer
x = 9
Step-by-step explanation:
3(x+5)-2(x+2)=20
3x +15 - 2x - 4 = 20
3x - 2x = 20 + 4 - 15
x = 24 - 15
x = 9
The mass of the dust particle can be written in the form ax 100 kg, where a = ₁ and b =
The mass of the comet can be written in the form of a × 10b kg, where a =
and b
D
Submit
DELL
The dust particle is seen to have 400 times more mass than the pollen particle
How to use rule of exponents?We will use the scientific notation.
For example, 0, 002 can be written as:
2 × 10³
Where;
3 is the number of times the comma (,) must be run to the right to convert the quantity 0, 002 to 2.
0, 002
0| 0 0 2
0 0| 02 -----------1
0 0 0|2------------2
0 0 0 2| ----------3
Thus, for the given expression:
Powder particle 0.000000778 g
It can be written as: 0.0000008 g = 8 × 10⁻⁷
b = -7
In the same way
Pollen grain of 0.00000000155 g
It can be written as:
0.000000002 g = 2 × 10⁻⁹
To know how big the mass of the dust particle is with respect to the pollen, we have;
(8 × 10⁻⁷)/(2 × 10⁻⁹) = 400
Complete question is;
The table below shows the approximate masses of a dust particle and a grain of pollen.
Dust Particle 0.000000778 g
Grain of Pollen 0.00000000155 g
The mass of a dust particle can be estimated and written in the form a × 10^b, where a = 8 and b =
The mass of a grain of pollen can be estimated and written in the form a × 10^b, where a = 2 and b =
Based on the estimates, the mass of a dust particle is approximately BLANK
times larger than the mass of a grain of pollen.
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At the flower store they told her that the vase should be filled for the flowers to last the longest. her cylinder vase has a radius of 3in and a height of 8in. how much water should mary pour into the vase?
Mary should pour around 3.7 liters or 226.08 in³ volume of water in the vase.
Given Information and Formula Used
Radius of the cylindrical vase, r = 3 inches
Height of the cylindrical vase, h = 8 inches
The formula for the volume, V of a cylinder is given as,
V = πr²h
Here, r is the radius of the cylinder and h is the height of the cylinder.
Calculating the Volume
Substituting the given values of r and h in the formula for the volume of cylinder, we get
Volume, V = π(3)²(8)
Using π = 3.14, we have,
V = 3.14(9)(8)
V = 226.08 cubic inches
Volume in Liters
Since, 1 Liter = 61.0237 cubic inches,
1 cubic inch = 1/61.0237 liters
⇒ 226.08 cubic inches = 226.08/61.0237 liters
⇒ 226.08 cubic inches ≈ 3.07 liters
Thus, Mary needs to pour approximately 3.07 liters volume of water in the vase.
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25/3 ÷ x = 7/3 ÷8.1
I don't get it, what's the answer??
Answer:
x=28.93(rounded) x=28.929(not rounded)
Step-by-step explanation:
Step-by-step explanation:
25/3÷x=7/3÷8.1
25/3×8.1=7/3×x
135/2=7/3×x
x=135/2×3/7
x=405/14=28.929
Please help!! T-T Overdue~~~
Answer:
5√3
Step-by-step explanation:
An equilateral triangle is a triangle that has all same 3 measurements of 60°, and since all measurements are same, all sides are also equal too.
Hence, there'll be 3 sides that are 10 units. Since the base is divided into half, each will be 5 for base.
Then apply Pythagoras Theorem where states that:
[tex]\displaystyle{c=\sqrt{a^2+b^2}}[/tex] or [tex]\displaystyle{c^2=a^2+b^2}[/tex]
where c is hypotenuse, a and b can be defined either adjacent or opposite.
We know that our adjacent is 5 units, opposite is h unit(s) and hypotenuse is 10 units. Apply the theorem:
[tex]\displaystyle{10^2=h^2+5^2}[/tex]
Solve the equation for h-term:
[tex]\displaystyle{100=h^2+25}\\\\\displaystyle{100-25=h^2}\\\\\displaystyle{75=h^2}\\\\\displaystyle{h=5\sqrt{3} }[/tex]
Therefore, the height or value of h is 5√3
The picture is attached for visual reference regarding sides of triangle. If you have any questions, please let me know in the comment!
To make a small vase, elisa uses no more than 4.5 ounces of clay. to make a large vase, she uses at least 12 ounces of clay. which compound inequality represents the number of ounces of clay, c, that elisa uses to make one vase of either size?
The compound inequality which represents the number of ounces of clay is c≤4.5 or c≥12.
Given ELISA uses no more than 4.5 ounces of clay and to make a large vase, she uses at least 12 ounces of clay.
Let c denote the wide variety of oz of clay that Elisa makes use of to make one vase of both length.
The words "no more than" implies "much less than or equals to".
So, for a small vase c must be less than or equal to 4.5 ounce, which gives
c≤4.5 ...(1)
And to make a huge vase, she makes use of as a minimum 12 oz of clay.
The word "at least" implies "extra than or equals to"
So, for a large vase c must be more than or equal to 12 ounce, which gives
c≥12 ...(2)
By combining equations (1) and (2), we get
c ≤ 4.5 or c ≥ 12
Hence, the compound inequality represents the number of ounces of clay, c, that ELISA uses to make one vase of either size is c≤4.5 or c≥12.
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Answer:
D. c ≤ 4.5 or c ≥ 12
Step-by-step explanation:
Water freezes at 0^\circ0
∘
0, degrees Celsius.
Manoj's water is 3^\circ3
∘
3, degrees Celsius.
Leo's water is 7^\circ7
∘
7, degrees Celsius.
Whose water matches each description?
Manoj's water
Leo's water
Is at a greater temperature
Is closer to freezing
\quad
Leo's water is at a greater temperature. And Manoj's water is closer to freezing.
What is the temperature?The temperature refers to the degree of hotness ant coldness of the substance.
Water freezes at 0 °C.
Manoj's water is 3 °C.
Leo's water is 7 °C.
Leo's water is at a greater temperature.
Manoj's water is closer to freezing.
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Consider the following situations: (a) A survey of 18,87518,875 people aged 1818 to 2525 reported that 55.1U.1% drank alcohol in the past month. (b) In a study of work stress, 250250 restaurant workers were asked about the impact of work stress on their personal lives. (c) In a study of Monarch butterflies, 5555 milkweed plants in a Yosemite Valley were randomly sampled. The average number of Monarch eggs per plant was 0.73.was 0.73. Identify the population and sample for each of the situations.
1. 18.875 people age 18 to 25 2. All people aged 18 to 25 3. Proportion of 55.1% 4. All restaurant workers 5. 250 restaurant workers 6. 55 milkweed plants 7. All milkweed plants in Yosemite Valley 8. Average of 0.73
a. Population b. Sample
First statement shows sample ,second shows population, third shows sample, fourth shows population, fifth shows sample, sixth shows sample, seventh shows population, eight shows sample.
Given eight statements which shows the variables in research of alcholic consumption.
Population is anentire group about which we want to find the conclusions.
Sample is a part of population for which the conclusions are drawn. The size of sample may varry with the effectiveness and the confidence level needed.
First statement is a sample because it defines a number of people.
Second statement is a population as it shows all the people fro age 18 to 25.
Third statement is a sample as it defines a percentage of people.
Fourth statement is a population as it contains all the workers.
Fifth statement is a sample because it shows number of restaurant workers.
Sixth statement is a sample because it shows a definite number.
Seventh statement is a population as it includes all the milkweed plants.
Eight statement is a sample as it contains a definite percentage.
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There are 12 sweets in a bag. The
probability of choosing a strawberry sweet
5
1
is 12, a cola sweet is and a raspberry
sweet is. What is the probability of
3
choosing either a raspberry or a
strawberry sweet? Give your answer in its
simplest form.
The probability of choosing either a raspberry or a strawberry sweet is 17/60.
Probability of choosing either a raspberry or a strawberry sweetLet the probability of choosing a strawberry sweet P(s) = 1/5Let the probability of choosing a cola sweet and a raspberry = 1/12
P(s) ∩ P(c) = P(s) x P(c) = 1/12
where;
P(s) is the probability of choosing a strawberry sweet P(c) is the probability of choosing a cola sweet1/12 = P(s) x P(c)
1/12 = 1/5 x P(c)
P(c) = 5/12
P(s) ∪ P(c) = 1/5 + 5/12 = 17/60
Thus, the probability of choosing either a raspberry or a strawberry sweet is 17/60.
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Please Help Me Ill Appreciate Your Help Please And Thank You!
The student has to plug y=2x+4 into 3x+y=9 to solve for the system of equations
Answer:
Step-by-step explanation:
The friend solved
Calculator
Bookwork code: Q86 allowed
Second chance! Review your workings and see if you can correct your mistake.
Bethany rolled a six-sided dice a number of times and recorded the outcomes in
the table below.
< Back to task
Work out the relative frequency of landing on
a) the number 4.
b) a prime number.
Give your answers as decimals.
Outcome
1
2
3
4
5
Frequency
12
6
8
14
3
Watch video
7
Answer >
1) The frequency of landing 4 is 14.
2) The frequency for prime numbers is 8 and 3.
What is probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given:
Outcome Frequency
1 12
2 6
3 8
4 14
5 3
1) The frequency of landing 4 is 14.
2) The frequency for prime numbers is 8 and 3.
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2 six-sided dice, one green and one red, are released. What is the probability that : The number on the red die is 3
Which of the following is NOT a solution to the system of inequalities? Please help
A) (1, 5)
B) (2, 1)
C) (1, 2)
D) (0, 4)
Answer:
B (It isn't in the shaded region)
Triangles J K L and M N R are shown.
In the diagram, KL ≅ NR and JL ≅ MR. What additional information is needed to show ΔJKL ≅ ΔMNR by SAS?
∠J ≅ ∠M
∠L ≅ ∠R
∠K ≅ ∠N
∠R ≅ ∠K
The correct answer is option B which is we need ∠L ≅ ∠R to prove congruency.
What is congruency?The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.
According to the SAS theorem which means Side Angle Side, The angle which is included between the two sides must be congruent.
Here we are given that
KL = NR
JL = MR
Now in the figure, we can clearly see that the angle included between JL & KL is L & the angle included between NR & MR is R.
So for the triangles to be congruent by SAS, angle L must be congruent to angle R.
∠L=∠R
Therefore the correct answer is option B which is we need ∠L ≅ ∠R to prove congruency.
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Answer: option b
Step-by-step explanation:
The list below gives the location of friends who are scuba diving together.
Mallory is exploring at an elevation of -25 feet.
Jacob is standing on the boat, at an elevation of 15 feet.
Eva just jumped in and is 5 feet below the surface of the water.
Which inequality correctly compares the distance of the scuba divers from the surface of the water?
Eva > Mallory
Mallory < Jacob
Jacob < Eva
Mallory > Eva
According to the information, it can be inferred that the correct inequality is Mallory > Eva (option D).
How to identify who is closer to the surface of the water?To identify who is closer to the surface of the water we must read the distance that each of the characters is.
In this case, the person closest to the surface is Eva, who is 5 feet from the surface.
Now we must identify which inequality corresponds to reality. In this case the inequality that is correct is:
Mallory > EvaThis inequality is correct because Mallory is further from the surface than Eva.
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In the following exercises, multiply the binomials. Use any method.
243. (y − 6)(y − 2)
Answer:
Hence the expression. [tex](y-6)(y-2)=y^{2} -8x-12[/tex]
Step-by-step explanation:
The given expression is (y-6)(y-2).We have to multiply the given expression.Multiply the (y-6) by -2, multiply the (y-6) by y then add like terms.[tex]$$\begin{array}{r}y-6 \\\times \quad \underline{y-2} \\-2 y-12 \\\underline{y^{2}-6 y} \\y^{2}-8 y-12\end{array}$$[/tex]
According to the synthetic division below, which of the following statements
are true?
Check all that apply.
54 -17 -15
20 15
3 0
4
A. (4x2-17x-15) - (x + 5) = (4x + 3)
B. The number 5 is a root of F(x) = 4x² - 17x - 15.
OC. (4x2-17x-15) - (x - 5) = (4x + 3)
D. (x+5) is a factor of 4x2-17x-15.
E. The number -5 is a root of F(x) = 4x²-17x-15.
OF. (x-5) is a factor of 4x2 - 17x-15.
The correct statements about the synthetic division are C, D, F.
How to illustrate the information?It should be noted that 4x² - 17x - 15 will be:
= 4x² - 20x - 3x - 15
= (x - 5)(4x + 3)
The roots of the polynomial will be:
= f(x) = 0
(x - 5) = 0
x = 5
4x + 3 = 0
x = -3/4
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Expand. (n^2 -3n +1)(2n + 3) =
Answer:
[tex]2n^3-3n^2-7n+3[/tex]
Step-by-step explanation:
[tex](n^2 -3n +1)(2n + 3) =\\n^2(2n) - (3n)(2n) + (1)2n + (n^2)(3) + (-3n)(3) + (1)(3)=\\2n^3 - 6n^2 + 2n + 3n^2 -9n + 3 =\\[/tex]
Collecting like terms and simplifying yields
[tex]2n^3-3n^2-7n+3[/tex]
Need some help please?
The value of the unknown length is 24
How to determine the unknown length?Represent the unknown length with x.
So, we have the following equivalent ratio:
30 : 30 + x = 25 : 45
Express as fraction
30/30 + x = 25/45
Simplify the fraction
30/30 + x = 5/9
Cross multiply
150 + 5x = 270
Evaluate the like terms
5x = 120
Divide by 5
x = 24
Hence, the value of the unknown length is 24
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As bria's distance from her house increases from 80 yards to 190 yards, her distance from the bus stop varies from ______ yards to ________ yards.
Answer:
This really needs more information to answer correctly. What is bria's movement relative to the bus stop? Is she moving towards it, away, or to the side?
Step-by-step explanation:
Lacking this information, I can only say that as Bria's distance increases as she moves away from the bus stop (an assumption of direction). Let's say the bus stop is x yards distant in the other direction. Bria's distance from the bus stop varies from x+80 yards to x+190 yards. The signs would change if she were moving towards the bus stop. And they'd be something entirely different if a different angle were involved.
a is directly proportional to the cube root of c.
w is inversely proportional to the square root of a
When c = 2, a = 48
When a = 9, w = 2400
Find the value of w when c = 6
The value of w is 38400 when the value of c is 6 as per the concept of a proportional relationship.
Given:
a is directly proportional to the cube root of c.w is inversely proportional to the square root of a.When c = 2, a = 48When a = 9, w = 2400We have to find the value of w at c = 6.
If c = 6, then the value of a becomes a = 48 times (6 divided by 3)
Therefore, the value of a can be evaluated as,
a = 48 x 6/3
a = 48 x 3
a = 144
To find the value of w, rearrange the value of 'a' in the multiple of 9.
For that, divide 144 by 9.
144/9 = 16.
Now, multiply 16 by 2400.
The final value of w = 2400 x 16
w = 38400
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The Marcos family consists of 2 adults and 4 children. They spent a total of $40 on circus tickets. Let x represent the cost of an adult ticket, and let y represent the cost of a child’s ticket. Which graph represents the possible costs of the tickets?
On a coordinate plane, a line goes through points (0, 10) and (20, 0).
On a coordinate plane, a line goes through points (0, 20) and (10, 0).
On a coordinate plane, a line goes through points (negative 10, 0) and (0, 20).
On a coordinate plane, a line goes through points (negative 20, 0) and (0, 10).
Answer:
First Option
Step-by-step explanation:
First, we will find the equation for the total cost of the tickets.
Given x = Cost of 1 adult ticket
y = Cost of 1 Child ticket
Total Cost of tickets at $40:
2x + 4y = 40
To find which graph represent the cost of the tickets,
we can substitute x = 0 to find y and vice-versa.
If x = 0 ,
[tex]2(0) + 4y = 40\\4y = 40\\y = \frac{40}{4} \\= 10[/tex]
So when x = 0 , y = 10 which gives the coordinates (0,10).
Now if y = 0,
[tex]2x+4(0) = 40\\2x = 40\\x = \frac{40}{2} \\= 20[/tex]
So when y = 0 , x = 20 which gives the coordinates (20,0)
This shows that this particular line passes through these 2 points and therefore the answer is the first option.
Answer: A i just took the test
Step-by-step explanation:
Please help! If the current in a circuit is 3 + j2 amps and the resistance is 4 - j3 ohms, what is the voltage?
The value of the voltage is 18 - j volts if the current in a circuit is 3 + j2 amps and the resistance is 4 - j3 ohms option (c) is correct.
What is a complex number?
It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have:
The current in a circuit is 3 + j2 amps and the resistance is 4 - j3 ohms.
As we know,
V = IR
V = (3 + j2)(4 - j3)
[tex]\rm V=\left(3\cdot \:4-2\left(-3\right)\right)+\left(3\left(-3\right)+2\cdot \:4\right)j[/tex]
j² = -1 (complex part)
After simplification:
V = 18 - j volts
Thus, the value of the voltage is 18 - j volts if the current in a circuit is 3 + j2 amps and the resistance is 4 - j3 ohms option (c) is correct.
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These trapezoids are similar. Which of the following is the correct similarity statement?
Answer:
ABCD-DEFG
Mark as brainlist pls!