Each block on the grid is 1 unit by 1 unit. We wish to walk from A to B via 7 unit path but we have to stay on the grid. How many different paths can we take?
Answers
Answer:
The number of path we can take to walk from A to B via a 7 unit path while staying on the grid is 35 paths
Step-by-step explanation:
Given that we are to walk via a 7 unit path, we have;
Path to walk = Right or Left from start point A
Total number of rights and left to get to point B from A must be 7
3 of the turns have to be in the left direction while 4 of the turns are right
Therefore, in 7 turns we have 4 in the right direction and 3 in the left direction which gives;
Number of ways for the first turn = 7, the next turn has 6 ways after that 5 and so on so we have;
7 × 6 × 5 × 4 × 3 × 2 × 1 out of which four are in the right direction in 4 × 3 × 2 × 1 ways and 3 are in the left direction in 3 × 2 × 1 ways, which gives the number of ways as follows;
[tex]Number \, of \, ways = \dfrac{7\times 6\times 5\times 4\times 3\times 2\times 1}{4\times 3\times 2\times 1 \times 3\times 2\times 1 } =\dfrac{5040}{144} = 35[/tex]
Therefore, there are 35 paths we can take to walk from A to B via a 7 unit path while staying on the grid.
Related Questions
What is a unit rate?
Answers
Answer:
a unit rate is a rate with 1 in the denominator! if you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.
1) sqrt x^+6x+9 if x≥3
2) sqrt x^2+6x+9 if −3≤x<3
3) sqrt x^2−6x+9 if x<−3
will give brainliest
Answers
Answer:
Step-by-step explanation:
first one:
[tex]x^{2}+6x+9={(x+3)}^{2} \\\sqrt{{(x+3)}^{2} }=x+3[/tex]
second one:
[tex]x^{2}+6x+9=(x+3)^{2} \\\sqrt{(x+3)^{2} } = x+3[/tex]
third one:
[tex]x^{2} -6x+9=(x-3)^{2} \\\sqrt{(x-3)^{2} } =|x-3| \ \ (because \ x<-3)[/tex]
From the figure, if y = 400 then find the value of x .
Answers
Answer:
70°Solution,
y=40°
now,
[tex]2x + y = 180( \: sum \: of \: angle \: in \: straight \: line) \\ or \: 2x + 40 = 180 \\ or \: 2x = 180 - 40 \\ or \: 2x = 140 \\ or \: x = \frac{140}{2} \\ x = 70 \: degree[/tex]
Hope this helps...
Good luck on your assignment...
y=40
180 (angles in a straight line)
180-40=140
140 / 2
=70
PLEASE SOLVE! FIST CORRECT ANSWER GETS BRAINLIEST! Simplify using the distributive property: -0.1·(100a+10b-c)
Answers
Answer:
-10a - b + 0.1c
Step-by-step explanation:
We can distribute the -0.1 to 100a, 10b and -c.
-10a - b + 0.1c
That's all!
Hope this helps
Answer: -10a - b + 0.1c
Step-by-step explanation:
simplify 0.1 * 10b * -c
10a - b - 0.1 * -c
regroup terms.
-10a - b - ( - 0.1 * c )
remove parentheses
-10a - b + 0.1 * c
Two workers finished a job in 12 days. How long would it take each worker to do the job by himself if one of the workers needs 10 more days to finish the job than the other worker?
Answers
Answer:
20 days
Step-by-step explanation:
t = time required by one worker to complete the job alone
(t+8) = time required by the other worker
So:
7.5/ t + 7.5/ (t + 8) = 1
Solve for t.
...
t = 12 days, the first guy working alone
The other worker would finish the job in 20 days.
Answer:
7 days and 17 days
Step-by-step explanation:
We can write an equation to solve this. An equation could be: ½x + ½y = 12. x - y = 10. Variables that solve this equation are x=7 and y=17. 7 + 17 = 24÷2 (since there are 2 workers) =12. Also, ½(7) + ½17 = 3.5 + 8.5 = 12. So, we know that the faster worker will take 7 days and the slower worker will take 17 days.
Hope this helps! Plz give me brainliest, it will help me achieve my next rank.
When working with whole numbers, which of the following functions will not always result in the answer being a whole number?
A. Addition
B. Multiplication
C. Subtraction
D. Division
Answers
Lines L and M are parallel.
4
3
5
L
2
1/6
38° 7.
- M
Find : m24
Enter the number that
belongs in the green box.
?]
Enter
Answers
Answer:
38°solution,
<2=38°( being corresponding angles)
<4=<2( being vertically opposite angles)
=38°
About corresponding angles:
Please look the first one picture.
There,
<b is an exterior and <d is an interior angle lying to the same side of transversal and they are not adjacent to each other.They are called corresponding angle.A pair of corresponding angles made by a transversal with parallel lines is always equal.
About vertically opposite angles
please look the second one picture.
there,
<AOC and <BOD are formed by intersected line segments and they lie to the opposite side of common vertex.They are called vertically opposite angles.<AOD and <BOC are another pairs of vertically opposite angles.Vertically opposite angles are always equal.
<AOC=<BOD
<AOD=<BOC
Hope this helps...
Good luck on your assignment..
What is the slope of the line that contains the point (-2, 7) and (2, 3)? A. -1 B. -4 C. 1 D. 4
Answers
Answer:
A. -1
Step-by-step explanation:
Slope = (y2 - y1) / (X2 - X1)
= (3 - 7) / (2 +2)
= - 4/ 4
= - 1
Hope this helps.. Good Luck!
Answer:
The slope is -1.
Step-by-step explanation:
Plug it into the formula.
Find the volume of a pyramid with a square base, where the perimeter of the base is
12.8 m and the height of the pyramid is 12.5 m. Round your answer to the nearest.
tenth of a cubic meter.
Answers
Answer:
42.7 cm ^2
Step-by-step explanation:
I need helpppppppppppppo
Answers
Answer:
25%, -2x + 3
Step-by-step explanation:
8/24 = 1/4 =.25 = .25%
plug in numbers
PLEASE MARK ME BRAINIEST
Which of the following shows the graph of y = 2 l n x On a coordinate plane, a curve starts at (0, negative 2) in quadrant 4 and then increases into quadrant 1 and approaches y = 3. On a coordinate plane, a curve starts in quadrant 4 and then curves up into quadrant 1 and approaches y = 5. It crosses the x-axis at (1, 0). On a coordinate plane, a curve approaches the y-axis in quadrant 2 and then increases into quadrant 1. It crosses the y-axis at (0, 1). On a coordinate plane, a curve approaches the y-axis in quadrant 2 and then increases into quadrant 1. It crosses the y-axis at (0, 2).
Answers
Answer:
The answer to this question can be defined as follows:
Step-by-step explanation:
Given:
[tex]f(x)= 2^{-x}=\frac{1}{2^x}[/tex]
In the above choices it is clearly defined from the above equation that output rises in the first quadrant, the value of f(x) tends to be zero and increases into another second quadrant. For x = 0, y, once again, has become 1, that is the function passes the y platform at (0,1). Therefore an exponential function reaches y = 0 in quadrant 1 on a coordinate plane and rises into quadrant 2. (0,1) stage is the temperature at which the y-axis intersects.The graph of y = 2ln(x) is (b) on a coordinate plane, a curve starts in quadrant 4 and then curves up into quadrant 1 and approaches y = 5. It crosses the x-axis at (1, 0).
How to determine the graph of the equation?The equation of the graph is given as:
[tex]y = 2\ln(x)[/tex]
Start by plotting the graph of [tex]y = 2\ln(x)[/tex] .
From the graph (see attachment), we have the following highlights
The curve of the graph starts at the 4th quadrantIt moves up to the 1st quadrantIt crosses the x-axis at x = 1, and it approaches y = 5From the list of given options, only option (b) describes the above highlights
Hence, the graph of y = 2ln(x) is (b)
Read more about graphs and functions at:
https://brainly.com/question/3939432
The graph of f(x) shown below resembles the graph of g(x)=x^3, but it has been vertically stretched. Which of the following could be the equation of f(x)?
Answers
Answer: it’s b
Step-by-step explanation:
(-2,-11);slope=4 write the equation of the line
Answers
Answer: y = 4x-3
slope = 4, y intercept = -3
=================================================
m = 4 is the slope
[tex](x_1,y_1) = (-2,-11)[/tex] is the point the line goes through
Using point slope form, we can say,
[tex]y - y_1 = m(x - x_1)\\\\y - (-11) = 4(x - (-2))\\\\y + 11 = 4(x + 2)\\\\y + 11 = 4x + 8\\\\y + 11-11 = 4x + 8-11\\\\y = 4x - 3\\\\[/tex]
The equation is in slope intercept form y = mx+b
m = 4 = slope
b = -3 = y intercept
------------------------
As an alternative, you can use y = mx+b to get the same answer. We'll plug in m = 4 and (x,y) = (-2,-11) to solve for b
y = mx+b
-11 = 4(-2)+b
-11 = -8+b
-11+8 = -8+b+8
-3 = b
b = -3 we get the same y intercept value as above
------------------------
To check the answer, plug x = -2 into the equation. We should get y = -11
y = 4x-3
y = 4(-2)-3
y = -8-3
y = -11 we get the proper y value. The answer is confirmed.
Answer:
y = 4x-3
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b
The slope is 4
y = 4x+b
Substitute the point into the equation
-11 = 4(-2)+b
-11 = -8+b
Add 8 to each side
-11+8 = b
-3 = b
y = 4x-3
If a triangle’s original dimensions are 24 cm by 40 cm, which triangle would be an enlargement of the original by a scale factor of 2.2? A triangle with a base of 18.18 centimeters and a height of 10.9 centimeters. A triangle with a base of 42.2 centimeters and a height of 26.2 centimeters. A triangle with a base of 88 centimeters and a height of 52.8 centimeters. A triangle with a base of 200 centimeters and a height of 120 centimeters.
Answers
Answer: C) 52.8 and 88
Step-by-step explanation:
Simply multiply both dimensions(24 and 40) by 2.2 to get 52.8 and 88. Thus the answer is C.
Hope it helps <3
Answer:
Third Choice 52.8 cm by 88 cm
Step-by-step explanation:
Multiply each dimension by the scale factor.
24 cm * 2.2 = 52.8 cm
40 cm * 2.2 = 88 cm
Answer:
Given O O below, the arcs GĦ and JK must be congruent.
G
#
A. True
70"
B. False
125
K
SUBM
Answers
Answer:
False.
Step-by-step explanation:
Just look at them. They aren't even similar.
A circle is a curve sketched out by a point moving in a plane. The given statement "Given circle O below, the arcs GH and JK must be congruent." is false.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
For the given two arcs in the circle, the given statement "Given circle O below, the arcs GH and JK must be congruent." is false. This is because the measure of the central angle of the both arcs is not equal. Therefore, it can be concluded that the length of the two arcs is not equal.
Hence, the given statement is false.
Learn more about Circle:
https://brainly.com/question/11833983
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3m^2+4mn-5n^2+(-m^2)-6mn+2n^2+3mn-n^2+3m^2+mn+4n^2
Answers
Answer:
5m^2 + 2mn
Step-by-step explanation:
Answer:
[tex]5 {m}^{2} + 2mn[/tex]solution,
[tex]3 {m}^{2} + 4mn - 5 {n}^{2} + {( - m)}^{2} - 6mn + 2 {n}^{2} + 3mn - {n}^{2} + 3 {m}^{2} + mn + 4 {n}^{2} \\ = 3 {m}^{2} + 4mn - 5 {n}^{2} - {m}^{2} - 6mn + 2 {n}^{2} + 3mn - {n}^{2} + 3 {m}^{2} + mn + 4 {n}^{2} \\ [/tex]
Collect like terms:
[tex]3 {m}^{2} - {m}^{2} + 3 {m}^{2} - 5 {n}^{2} + 2 {n}^{2} - {n}^{2} + 4 {n}^{2} + 4mn - 6mn + 3mn + mn \\ [/tex]
Simplify:
[tex] = 5 {m}^{2} - 4 {n}^{2} + 4 {n}^{2} + mn + mn \\ = 5 {m}^{2} + 2mn[/tex]
Hope this helps..
Good luck on your assignment..
What property do rectangles and parallelograms always share? 4 right angles 4 sides of equal length 2 pairs of parallel sides 2 acute angles (1 answer choice)
Answers
Answer:
A property that rectangles and parallelograms always share is that they both have two pairs of parallel sides.
Step-by-step explanation:
A rectangle is a shape that has two pairs of parallel sides and has 4 right angles.
A parallelogram is a shape that has two pairs of parallel sides and has 2 pairs of congruent sides.
The only thing these shapes have in common is that they both have two pairs of parallel sides.
Answer:
C: 2 pairs of parallel side
Step-by-step explanation:
I got it correct in a quiz I did that had this question.
A student can get paid $12 per hour to run a three-hour economics tutoring session, or he can take a five-hour shift helping at his mom’s store that pays $15 per hour. What is the opportunity cost of working at the store? $12 $75 $36 $45 $60
Answers
Answer: C. $36
Step-by-step explanation:
Opportunity cost refers to the best economic alternative so in this case, it would be referring to the student tutoring for three hours. $12x3=$36
30 POINTS!!! Heather is collecting dimes. She saves one dime on the first day, two dimes on second day, and three dimes on third day. If this pattern continues, hom much money will heather have saved at the end of 30 days? Please Explain!
Answers
Answer:
hope dis help ;_;
Step-by-step explanation:
It's easy to see the manual solution: 1(.1) + 2(.1) + 3(.1) +......+ 30(.1).
But nobody wants to do that repetitive computation. If we factor out the (.1),
we see (.1) * (1+2+3+4...+30). Still somewhat repetitive, but not bad for just 30.
We really need a formula for big numbers though. The short cut for adding a series
of numbers is to find the average of the first and last numbers and multiply by how
many there are in the list:
(first + last)(the quantity of numbers) / 2 = (1 + 30)(30) / 2 = 465
465(.1) = $46.50
The money that Heather will save at the end of 30 days will be 465.
What is arithmetic progression?
Arithmetic progression is a sequence of numbers with a common difference. It is given by,
aₙ = a₁ + (n - 1)d
Where,
aₙ = the nᵗʰ term in the sequence
d = common difference
a₁ = first term
Now,
We have,
Heather saves one dime on the first day, two dimes on the second day, and three dimes on the third day and continues for 30 days.
So,
Money saved on the first day = 1
And,
Money save on 30 day = 30
So,
Using the sum of Arithmetic progression formula,
Sₙ = n/2 [ a + l ]
where,
n = 30
a = first term = 1
l = last term = 30
Now,
Sₙ = n/2 [ a + l ]
Sₙ = 30/2 [ 1 + 30]
Sₙ =15 × 31
Sₙ = 465
So, money saved at the end of 30 days = 465
Hence we can say that the money that Heather will save at the end of 30 days will be 465.
To learn more about arithmetic progression click here,
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solve this systems of linear equations.separate the x- and y-values with a comma 18x+7y=-89 9x-9y=18
Answers
Answer:
Step-by-step explanation:
18x+7y=-89 equation1
9x-9y=18 equation2
multiplying equation 2 by 2
2(9x-9y=18) 18x-18y=36 equation 3
subtacting equation 1 and 3
18x-18x+7y+18y=-89-36
25y=125
y=5
putting the values of y in equation1
18x+7(5)=-89
18x+35=-89
18x=-89-35
18x=-124
x=-6.8
What is Negative 2 (3 x + 12 y minus 5 minus 17 x minus 16 y + 4) simplified?
Answers
Answer:
28x+8y+2
Step-by-step explanation:
Write out the equation first: -2 (3x+12y-5-17x-16y+4)
Simplify within parentheses : -2 (-14x-4y-1)
Multiply by -2: 28x+8y+2
PLS ANSWER NOW i'm desperate
Answers
Answer:
1.6 < x < 9.6
Step-by-step explanation:
The smallest the third side can be is greater than the difference of the other two sides
x > 5.6 -4
x > 1.6
The largest the third side can be is less than the sum of the other two sides
x < 5.6 +4
x < 9.6
1.6 < x < 9.6
(-3ab - 8a + 8) - (-5ab +2)
Answers
Answer:
2ab - 8a + 6
Step-by-step explanation:
(-3ab - 8a + 8) - (-5ab +2)
(-3ab - 8a + 8) -1(-5ab +2)
Distribute -1 to the brackets.
(-3ab - 8a + 8) + 5ab - 2
Remove the brackets.
-3ab - 8a + 8 + 5ab - 2
Rearrange.
5ab - 3ab - 8a + 8 - 2
Combine like terms.
2ab - 8a + 6
What is the common ratio of the following sequence?
-5, -20, -80,-
0-4
0 1
NI
04
NEYT OLIESTION
Answers
Answer:
4
Step-by-step explanation:
Given
-5, -20, -80, .....
Required
Determine the common ratio
The common ratio of a sequence is determined by dividing a term by its immediate previous term;
Let the term be represented with [tex]T_1, T_2, T_3[/tex] and the common ratio with r
From the analysis above;
[tex]r = \frac{T_2}{T_1}\ or\ r = \frac{T_3}{T_2}[/tex]
Substitute -5 for [tex]T_1[/tex]; -20 for [tex]T_2[/tex]; -80 for [tex]T_3[/tex]
[tex]r = \frac{-20}{-5}\ or\ r = \frac{-80}{-20}[/tex]
[tex]r = 4\ or\ r = 4[/tex]
Both values of r are the same;
Hence, the common ratio of the sequence is 4
A rectangular prism has a length of 3 feet, a height of 7 feet, and a width of 14 feet.
What is its volume, in cubic feet?
Answers
Answer:
294 cubic ft.
Step-by-step explanation:
All you do is just multiply the length, width, and height!
3 × 14 × 7 = 294
hopefully this helped :3
Answer:
294 cubic feet
Step-by-step explanation:
PLZZ ANSWER AND ANSWER STEP BY STEP PLZZZ I NEED HELP!
Elaine earns $9.50 for the first 10 1/2 hours she works and $10.30 for every hour after that.If Elaine worked 20 1/4 hours,how much would she earn.
Answers
Answer: B
Step-by-step explanation:
I had this question on EDG
Which statement is the most appropriate comparison of the spreads?
Answers
Answer:
D The IQR for town A is less than the IQR for town B
Step-by-step explanation:
A small IQR indicates that the points are closer together, while a larger IQR means that the points are scattered and that the plot is skewed in a certain direction. As you can see, town A's plot looks fairly balanced, while town B's plot is skewing to the left. Hope this helps :)
which solution can be used to fill in both blanks in the table
Answers
Answer:
(5, 2)
Step-by-step explanation:
As 8x = 40
x = 40÷8
x = 5
This is the first solution
Then 4x + 4y = 28
We know that x = 5 as above
So let's substitute it:
4x + 4y = 28
(4 × 5) + 4y = 28
20 + 4y = 28
Let's get the 20 to other side
20 - 20 + 4y = 28 - 20
4y = 8
y = 8 ÷ 4
y = 2
Hence we get these two solutions
(5,2)
:-)
Consider the line - 8x-5y = -7.
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
Answers
Answer:
See below
Step-by-step explanation:
First, you need to find the slope of the given line. You can do this by rearranging the equation so that it is in slope-intercept form (y = mx + b).
-8x - 5y = -7
-5y = 8x - 7
y = -8/5x + 7/5
The slope of this line is -8/5.
The slope of a line that is perpendicular will be the negative reciprocal. You have to change the sign, and basically flip the numerator upside down. The slope of the perpendicular line will be 5/8
-8/5 = 8/5 = 5/8
The slope of a line that is parallel will be equal. This means that the slope will be -8/5.
A point a is graphed at (0,5). Complete the coordinates of a shape that can be rotated around the y axis to create a cylinder provide an explanation for your answer to receive full credit.
Answers
Answer:
The coordinates of the shape (rectangle), that can be rotated around the y axis to create a cylinder are;
A = (0, 5)
B = (2, 5)
C = (2, 0)
D = (0, 0)
Step-by-step explanation:
A shape that can be rotated around the y axis to create a cylinder is a rectangle ABCD
Given that the rectangle is to be rotated about the y-axis to form a cylinder, the vertical sides of the rectangle are to be parallel to the y-axis such that the x coordinates at the top and bottom will be equal in the opposite vertical segments as follows;
The complete coordinates of the rectangle, ABCD that can be rotated around the y axis to create a cylinder are therefore presented as follows
A = (0, 5)
B = (2, 5)
C = (2, 0)
D = (0, 0).