We will see the how we can manipulate interioir angles in terms of variables and measure their degree of angle mathematically.
We are given the following statements.
An angle LMN is bisected by a ray ( MO ). This statement can be read as that we have an unknown large angle < LMN which is divided into two halves ( bisected ) by a ray with common vertex at M originating from point O.
We can represent the above statement in a graphical form for better understanding as follows:
We see that the angle < LMN which unknown can be given a symbol as follows:
\(\angle LMN\text{ = }\theta\)The ray MO divided the above angle in to two halves. The two created constituent angles are marked and named as follows:
\(\angle LMO\text{ \& }\angle NMO\)Since the larger angle is halved then the two consituent angles must be equal with each other and:
\(\angle LMO\text{ = }\angle NMO\text{ = }\frac{\theta}{2}\)Each of the created constituent angles are expressed in terms of variable ( x ) as follows:
\(\begin{gathered} \angle LMO\text{ = 8x - 24} \\ \angle NMO\text{ = 3x + 31} \end{gathered}\)We can use the angle bisection relation that we wrote above and equate the two equally halved angled as follows:
\(\begin{gathered} \angle LMO\text{ = }\angle NMO \\ 8x\text{ - 24 = 3x + 31} \end{gathered}\)Now we can solve the above equation for the variable ( x ) as follows:
\(\begin{gathered} 5x\text{ = 55} \\ \textcolor{#FF7968}{x=}\text{\textcolor{#FF7968}{ 11 degrees}} \end{gathered}\)Using the value of ( x ) we can now evaluate the anlge measures of constituent angles as follows:
\(\begin{gathered} \angle LMO\text{ = 8}\cdot(11)\text{ - 24 = 88 - 24 = 64 degrees} \\ \angle NMO\text{ = 3}\cdot(11)\text{ + 31 }=\text{ 33 + 11 = 64 degrees} \end{gathered}\)Now again we can use the anlge bisection relationship to determine the measure of the larger angle LMN as follows:
\(\begin{gathered} \angle LMN\text{ = 2}\cdot\angle LMO\text{ = 2}\cdot\angle NMO \\ \angle LMN\text{ = 2}\cdot64 \\ \textcolor{#FF7968}{\angle LMN}\text{\textcolor{#FF7968}{ = }}\textcolor{#FF7968}{128}\text{\textcolor{#FF7968}{ degrees}} \end{gathered}\)Hence, the answers are:
\(\begin{gathered} \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 11 degrees}} \\ \textcolor{#FF7968}{m\angle}\text{\textcolor{#FF7968}{LMN = 128 degrees}} \end{gathered}\)
List five vectors in Span {v_1, v_2}. Do not make a sketch. v_1 = [8 2 -7], v_2 = [-6 4 0] List five vectors in Span {v_1, v_2} (Use the matrix template in the math palette. Use a comma to separate vectors as needed. Type an integer or a simplified fraction for each vector element.)
The integer for vector 1 {2,6,-7}, integer for vector 2 is 10,8,-14}, integer for vector 3 is {4,12,-14}, integer for vector 4 is {14,-2,-7} and integer for vector 5 is {22,0,-14}. (all these vectors are in span {V1 and V2})
List five vectors in Span {v_1, v_2}?
1) V1+v2={8,2,-7 }+{-6,4,0 }
={2,6,-7}
2) 2v1+v2={16,4,-14}+{-6,4,0}
={10,8,-14}
3)2v1+2v2={16,4,-14}+{-12,8,0}
={4,12,-14}
4)V1-v2={8,2,-7}-{-6,4,0}
={14,-2,-7}
5)2v1-v2={16,4,-14}-{-6,4,0}
={22,0,-14}
All of these vectors are contained within the span.
{v1,v2}={av1+bv2:ab∈r}
A matrix is a rectangular variety of ordered numbers (real or complex) or functions .Assume we want to express the following information about Ram and his two friends Rohan and Yash's possession of pens and pencils:
Ram has 20 pens and 7 pencils,
Rohan has 15 pens and 5 pencils,
Yash has 12 pens and 3 pencils
Now, this could be arranged in tabular form as follows,
⎢20 7⎢
⎢15 5⎢
⎢12 3⎢
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Determine the approximate minor arc length of CD.
Step-by-step explanation:
CB is the Hypotenuse of the right-angled triangle CDB.
Pythagoras :
CB² = 20² + 21² = 400 + 441 = 841
CB = sqrt(841) = 29
=> radius = 29/2 = 14.5
the total circumference of the circle (360 degrees) is
2×pi×r = 29×pi
but here we need only the part of the circumference for 180-70= 110 degrees.
CD arc = 29×pi × 110 / 360 = 29×pi×11/36 =
= 27.83800157 ≈ 27.84 cm
-Will give brainliest
What additional dimension(s) does Lisa need to know in order to find the area of the tabletop?
A diagram of a custom tabletop is shown. The tabletop is a composite figure that consists of a rectangle and a parallelogram. Lisa needs to calculate the cost of the tabletop.
The total surface area of the figure that will enable Lisa to find the total cost per square is: 42 ft²
How to find the total surface area?To find the total surface area of the figure that will enable Lisa to find the total cost per square area, we need to find both areas of rectangle and parallelogram and add up. Thus:
Area of rectangle = Length * Width
Area = 5 * 6
Area = 30 ft²
The formula for the area of the parallelogram is:
Area = Base * perpendicular height
Area = 3 * √(5² - 3²)
Area = 3 * 4
Area = 12 ft²
Total surface area = 30 + 12
Total surface area = 42 ft²
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PLEASE HELP LOOK AT THE PHOTO FOR THE QUESTION
Answer:
3 x 10^6 or option 3
Step-by-step explanation:
(6x10^11) = 600000000000
(2x10^5) = 200000
3000000
Count the zeros - the number of zeros there are will be the exponent of 10 3 is the first digit in 3000000
3 x 10^6
6/2=3
11-5=6
Keep the 10 as is
(3 x 10^6) or option 3
Pls help it due ASAP.
Please show workings
It due in a hour....
Answer:
C. \(\frac{4}{5}\)
Step-by-step explanation:
In order to find the slope knowing two points, use the slope formula \(\frac{y_2 - y_1}{x_2-x_1}\). \(x_1\) and \(y_1\) represent the x and y values of one point the line intersects, and \(x_2\) and \(y_2\) represent the x and y values of another point the line intersects.
Knowing this, use the points (-4, -4) and (6, 4) for the formula. Substitute -4 for \(x_1\), -4 for \(y_1\), 6 for \(x_2\), and 4 for \(y_2\). Then, simplify:
\(\frac{(4) - (-4)}{(6) - (-4)} \\= \frac{4+4}{6+4} \\= \frac{8}{10} \\= \frac{4}{5}\)
Thus, \(\frac{4}{5}\) is the slope of the line.
Investigate the equilibria of ˙x = a − x2 , ˙y = x − y. Show that the system has a saddle and a stable node for a > 0, but no equilibrium points if a < 0. This system is said to undergo a bifurcation as a increases through a = 0. This bifurcation is an example of a saddle-node bifurcation. Draw the phase diagrams for a = 1 and a = −1.
The phase diagrams provide a visual representation of the system's behavior by plotting the vector field and trajectories in the x-y plane.
The given system of differential equations is described by:
\(˙x = a - x^2˙y = x - y\)
To find the equilibria, we set ˙x and ˙y equal to zero:
\(a - x^2 = 0 -- > x^2 = a -- > x = ±√ax - y = 0 -- > y = x\)
So, the equilibria are (±√a, ±√a).
Now let's analyze the behavior of the system for different values of 'a'.
For a > 0:
In this case, there are two real equilibria, (√a, √a) and (-√a, -√a). We can observe that (√a, √a) is a stable node, as the eigenvalues of the linearized system around this point have negative real parts. On the other hand, (-√a, -√a) is a saddle point, as the eigenvalues have opposite signs (one positive and one negative).
For a < 0:
In this case, there are no real equilibria since √a and -√a are imaginary. Therefore, the system has no equilibrium points.
To visualize the phase diagrams for a = 1 and a = -1:
For a = 1:
The system has two real equilibria, (1, 1) and (-1, -1). The point (1, 1) is a stable node, and (-1, -1) is a saddle point. The phase diagram would show trajectories converging towards (1, 1).
For a = -1:
Since a < 0, there are no equilibrium points, and thus the phase diagram would show no fixed points or trajectories.
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What is 0.29 km in mm? Report your answer with two significant figures
29000 mm
290000 mm.
2900000 mm
0.29 km is equal to 290,000 mm when rounded to two significant figures.
Convert kilometers to millimeters, you need to multiply the given value by a conversion factor. In this case, since there are 1,000 meters in a kilometer and 1,000 millimeters in a meter, the conversion factor is 1,000,000 (1,000 x 1,000).
Step 1: Multiply 0.29 km by the conversion factor:
0.29 km x 1,000,000 = 290,000,000 mm
Step 2: Round the result to two significant figures:
Since the original value, 0.29 km, has two significant figures, we round the result to match.
290,000,000 mm becomes 290,000 mm.
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The sum of 9 times a number and 7 is 6
Given statement solution is :- The value of the number is -1/9.
Let's solve the problem step by step.
Let's assume the number we're looking for is represented by the variable "x".
The problem states that the sum of 9 times the number (9x) and 7 is equal to 6. We can write this as an equation:
9x + 7 = 6
To isolate the variable "x," we need to move the constant term (7) to the other side of the equation. We can do this by subtracting 7 from both sides:
9x + 7 - 7 = 6 - 7
This simplifies to:
9x = -1
Finally, to solve for "x," we divide both sides of the equation by 9:
9x/9 = -1/9
This simplifies to:
x = -1/9
So, the value of the number is -1/9.
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Use elimination to solve each system of equations.
1. x - y = 1
x + y = 3
2. x + y = 1
x + y = 11
3. x + 4y = 11
x - 6y = 11
4. -3 + 3y = 6
x + 3y = 18
The solutions to the systems of linear equations by elimination method are listed below:
Point (x, y) = (2, 1) is a solution of the system of equations. The system of linear equations has no solution. Point (x, y) = (0, 11) is a solution of the system of equations. Point (x, y) = (3, 5) is a solution of the system of equations.How to solve a system of linear of equations by eliminationIn this problem we find four cases of two linear equations with two variables. There are different methods to solve the system, herein we must use elimination method to find the solution to each system of linear equations, which takes advantage of adding / subtracting linear equations and multiplying linear equations by scalars in order to get every solution set.
Case 1
x - y = 1
x + y = 3
First, add the two equations:
(x - y) + (x + y) = 1 + 3
2 · x = 4
x = 2
Second, determine the variable y:
y = 3 - x
y = 3 - 2
y = 1
Point (x, y) = (2, 1) is a solution of the system of equations.
Case 2
x + y = 1
x + y = 11
Subtract the second equation from the first one:
(x + y) - (x + y) = 1 - 11
0 = - 10 (CRASH!)
The system of linear equations has no solution.
Case 3
x + 4 · y = 11
x - 6 · y = 11
First, subtract the second equation from the first equation:
(x + 4 · y) - (x - 6 · y) = 11 - 11
10 · y = 0
y = 0
Second, determine the variable y:
x = 11 + 6 · y
x = 11 + 6 · 0
x = 11 + 0
x = 11
Point (x, y) = (0, 11) is a solution of the system of equations.
Case 4
- 3 · x + 3 · y = 6
x + 3 · y = 18
First, subtract the second equation from the first equation:
(- 3 · x + 3 · y) - (x + 3 · y) = 6 - 18
- 4 · x = - 12
x = 3
Second, determine the variable y:
3 · y = 18 - x
3 · y = 18 - 3
3 · y = 15
y = 5
Point (x, y) = (3, 5) is a solution of the system of equations.
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plz help will give brainliest!!
Answer:
66 R30
Step-by-step explanation:
:) :) :/ probably wrong
Answer:
66.4918032787
Step-by-step explanation:
I'm afraid that my answer isn't an answer choice you have, but if I were you, I'd go with 66, as it's the closest.
As for how I got my answer, you can just use a calculator.
Heidi and Dan signed up for a cell phone plan with a brand new company called Bolt.
The price for 30 gigabytes of data and unlimited talk and text is $55.
Each phone costs $19 per month.
Taxes are $9.50 per month.
What is the cost for their current plan?
The cost for their current plan is $83.5
How to write and solve the cost for their current plan?The given parameters are
Price for 30 gigabytes of data and unlimited talk and text = $55.
Phone costs = $19 per month.
Taxes = $9.50 per month.
The equation of the cost for their current plan is represented as:
Total cost = Price for 30 gigabytes of data and unlimited talk and text + Phone costs + Taxes
So, we have
Total cost = 55 + 19 + 9.50
Evaluate the sum
Total cost = 83.5
Hence, the cost for their current plan is $83.5
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what is the answer to -2x- x +8
Answer:
\(x=\frac{8}{3}\)
Step-by-step explanation:
I don't know if this has an =0 at the end, but I assume it does.
This is how you would work it out:
\(-2x-x+8=0\\-3x=-8\\x=\frac{-8}{-3} \\x=\frac{8}{3}\)
what is the answer to 5g/8-1/2=-3
plssss help
Answer:
g = -4
Step-by-step explanation:
Hope this helps :)
I NEED HELP ASAP PLEASE
Answer:
<A= 92
<C=88
<H= 92
Step-by-step explanation:
Angle <E is equal to <H because they are vertical angles.
Angle <E is equal to <A because they are corresponding angles.
Angle <E and <C are supplementary because they are interior angles on the same side of a transversal, 180-92=88
The length of each square on the grid represents 1 cm. The scale
from an actual rectangle to the drawing is 24 in. to 1 cm. Make a
new scale drawing where each centimeter represents 16 in.
Label the length and width of your drawing in centimeters.
Answer:
40.64 cm x 40.64 cm
Step-by-step explanation:
The directions say that 1 centimeter = 16 inches.
1 inch = 2.54 centimeters
Multiply by 16.
16 inches = 40.64 centimeters
We know each length of the square is 1 cm or 16 inches, according to the above.
(btw problem says rectangle, a square can be a rectangle.)
The data show the bug chirps per minute at different temperatures. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute. Use a significance level of 0.05. What is wrong with this predicted value?
Answer:
This predicted value is that it is unrealistically high
Step-by-step explanation:
According to the data given in order to calculate the predicted value we would have to make the following calculation of the predicted value and then conclude.
predicted value=26.693 + 0.055*3000
predicted value=191.693
By having the result of the predicted value we can conclude that what is wrong about this predicted value is that it is unrealistically high.
Find the value of (1/5)^-3
Answer:
125
Step-by-step explanation:
using the rule of exponents
\((\frac{a}{b}) ^{-n}\) = \((\frac{b}{a}) ^{n}\)
then
\((\frac{1}{5}) ^{-3}\)
= \((\frac{5}{1}) ^{3}\)
= 5³
= 125
Practice Final Apex Unit 4 Linear Equations
How many solutions does 5 - 3x = 4 + x + 2 -4x
One solution
Two solutions
No solution
Infinitely many solutions
This is a contradiction, which means that there is no solution for the given equation. Therefore, the correct answer is option C, "No solution".
There is only one solution for the given equation.
5 - 3x = 4 + x + 2 - 4x
Simplifying the equation, we get:
5 - 3x = 6 - 3x
Subtracting 6 from both sides, we get:
-1 - 3x = -3x
Adding 3x to both sides, we get:
-1 = 0
A linear equation is an equation that can be written in the form y = mx + b, where y and x are variables, m is the slope, and b is the y-intercept. It represents a straight line on a graph. Linear equations can be used to model a variety of real-world situations, such as the relationship between temperature and time, or the cost of producing a certain quantity of goods.
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We can see that both sides are equal, which means that the equation has infinitely many solutions.
Therefore, the answer is: D. Infinitely many solutions is correct.
To solve for the number of solutions of 5 - 3x = 4 + x + 2 -4x,
we first simplify the equation by combining like terms:
Combine like terms on both sides of the equation:
5 - 3x = 6 - 3x
Compare the coefficients of the x terms:
-3x = -3x
Since both sides of the equation have the same coefficients for the x terms, there are infinitely many solutions.
Therefore, the answer is: D. Infinitely many solutions is correct.
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please help thank you very much i very much appreciate it
The probability, when the two six-sided dice is rolled can be found to be:
P( not 4) - 11/12P ( not 11 ) - 17/18How to find the probabilities ?P(not 4):
There are 3 combinations that result in a sum of 4: (1, 3), (2, 2), and (3, 1). Thus, there are 36 - 3 = 33 outcomes that do not result in a sum of 4.
P(not 4) = 33 / 36
P(not 4) = 33 / 36 = 11 / 12
P(not 11):
There are 2 combinations that result in a sum of 11: (5, 6) and (6, 5). Thus, there are 36 - 2 = 34 outcomes that do not result in a sum of 11.
P(not 11) = 34 / 36
P(not 11) = 34 / 36 = 17 / 18
So, the probability of not rolling a sum of 4 is 11/12, and the probability of not rolling a sum of 11 is 17/18.
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Which of the following describes the solution to this system of equations?
The solution to this system of equations is dependent.
Understanding Dependent matrixDependent matrix is a matrix where one or more rows can be expressed as a linear combination of the other rows. This means that the rows are not linearly independent, and there is redundancy in the information they provide.
A dependent matrix has less than full rank, which means that the rank of the matrix is less than the number of rows or columns. In a dependent matrix, one or more variables can be expressed in terms of the other variables, and the system of equations represented by the matrix has infinitely many solutions.
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Find the value of x.
A. 8
B. 40
C. 10
D. 26
Answer:
ok well i need a image and or the full question x could = anything unless i can get the question the full question
Step-by-step explanation:
Use the given scale factor and the side lengths of the scale drawing to
determine the side lengths of the real object.
18 in
Scale factor 6:1
21 in
Scale drawing
b
a
Real object
OA. Side a is 3.5 inches long and side bis 3 inches long.
OB. Side a is 126 inches long and side bis 108 inches long.
OC. Side a is 15 inches long and side bis 12 inches long.
OD. Side a is 27 inches long and side bis 24 inches long.
Help me
The answers for real objects are OA: Side a = 3.5 inches, OB: Side a = 126 inches, OC: Side a = 3 inches, and OD: Side a = 108 inches.
To determine the side lengths of the real object using the given scale factor and the side lengths of the scale drawing, we need to multiply the corresponding lengths of the scale drawing by the scale factor.
Let's apply this approach to each case:
OA:
Scale factor: 6:1
Scale drawing:
b
a
21 in
Real object:
3.5 in
To find the length of side a in the real object, we multiply the length of side a in the scale drawing (21 in) by the scale factor:
Side a = 21 in * (1/6) = 3.5 in
OB:
Scale factor: 6:1
Scale drawing:
b
a
21 in
Real object:
126 in
Using the same approach, we can find the length of side a in the real object:
Side a = 21 in * (6/1) = 126 in
OC:
Scale factor: 6:1
Scale drawing:
b
a
18 in
Real object:
12 in
Applying the formula, we calculate the length of side a:
Side a = 18 in * (1/6) = 3 in
OD:
Scale factor: 6:1
Scale drawing:
b
a
18 in
Real object:
24 in
Similarly, we multiply the length of side a in the scale drawing by the scale factor to find the length in the real object:
Side a = 18 in * (6/1) = 108 in
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Some one plz help meh I need to understand and I dont
Answer:
It's asking you to find the inputs of the function.
Step-by-step explanation:
Basically, when you input something, you replace "x" in the equation with the number you want to input. For example, if I had the equation: 5x/6+5, then I wanted to input "5", then 5 would replace x in the equation, making 5(5)/6+5. The output they are giving you is simply evaluating the equation that you used to input x, so basically in the case I gave you, the output would be 5(5)/6+5, or 25/6+5, and 55/6. Using the outputs, they want you to find the inputs.
what does it mean to say a system has a ∆g equal to zero?
a. the reaction is spontaneous at standard conditions
b. the reaction is nonspontaneous at standard conditions
c. the system is at equilibrium at standard conditions
d, the reaction is both non spontaneous and at equilibrium
e. the reaction is both spontaneous and at equilibrium
A system having ΔG equal to zero means that the system is at equilibrium at standard conditions. This is option c. In a chemical reaction, ΔG represents the change in Gibbs free energy, which is a measure of the energy available to do work.
When ΔG is equal to zero, it indicates that the system is balanced, with the forward and reverse reactions occurring at the same rate. At equilibrium, the concentrations of reactants and products remain constant over time. For example, consider the reaction A ⇌ B. Initially, if we have more A than B, the forward reaction will be favored until equilibrium is reached. At equilibrium, the rate of the forward reaction equals the rate of the reverse reaction, and the concentrations of A and B remain constant. In this case, ΔG is zero.
It is important to note that while a ΔG of zero indicates equilibrium, it does not provide information about whether the reaction is spontaneous or nonspontaneous. The spontaneity of a reaction is determined by the sign of ΔG. If ΔG is negative, the reaction is spontaneous, while a positive ΔG indicates a nonspontaneous reaction.
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Select the correct statement about the function represented by the table.
Plz help!
Answer:
I believe that it is B
If (n+1)!=90×(n-1)!,find n.
\(\displaystyle\bf\\(n+1)!=90\times (n-1)!\\\\(n-1)!\times n\times(n+1)=90\times (n-1)!~~~\Big|~:(n-1)!\\\\n(n+1)=90\\\\n(n+1)=9\times10\\\\n(n+1)=9(9+1)\\\\\implies~~\boxed{\bf n=9}\)
(a) We would like to know if Intel's stock and Southwest Airlines' stock have similar rates of return. To find out, we take a random sample of 50 days, and record Intel's and Southwest's stock on those same days.
Thus, to determine whether Intel's stock and Southwest Airlines' stock have similar rates of return, we can use a statistical analysis of the daily rate of return for each stock over a 50-day period. However, the small sample size means that we must be cautious when interpreting the results.
To determine whether Intel's stock and Southwest Airlines' stock have similar rates of return, we can conduct a statistical analysis using the sample data collected. The sample size of 50 days is relatively small, so we must be cautious when interpreting the results.
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Is 25 a prime number?
No, 25 is not a prime number. It can be divided by 5 without a remainder, so it has factors other than 1 and itself.
A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, a prime number can only be divided evenly by 1 and by itself. They are considered to be the "building blocks" of the natural numbers, and are important in number theory and other branches of mathematics.
The factors of 25 are 1, 5 and 25. Prime numbers are numbers that are divisible by only 1 and themselves. So 25 is not a prime number.
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Happy Paws charges $22.00 plus $2.50 per hour to keep a dog during the day. Woof Watchers charges
$11.00 plus $3.75 per hour. Complete the equation and solve it to find for how many hours the total cost
of the services is equal. Use the variable h to represent the number of hours.
Answer:
Step-by-step explanation:
22 +2.50x = 11 +3.75x
11+ 2.50x = 3.75x
11+2.5x=3.75x
2.5x+11=3.75x
2.5x+11−3.75x=3.75x−3.75x
−1.25x+11=0
−1.25x+11−11=0−11
−1.25x=−11
−1.25x/1.25 = 11/1.25
x=8.8
Please answer correctly !!!!!! Will mark brainliest answer !!!!!!!!!!!!!!
Answer:
(up) by 6
left by 7
Step-by-step explanation: