Answer:
A.) 2000N
B.) 0
C.) 1414.2 N
Step-by-step explanation:
Given that the force on the rope = 1000N
A.) If the two students pull in the same direction, the resultant force will be addition of the two forces. That is
1000 + 1000 = 2000 N
B.) If the two students pull in the opposite direction, the resultant force will be sum of the two forces equal to zero. That is,
F1 + F2 = 0
F1 = positive 1000N
F2 = negative 1000N
Therefore, 1000 - 1000 = 0
The resultant force of the two forces is zero.
C.) If the two forces are at right angles, south and east to each other, the resultant force R will be achieved by using pythagorean theorem.
R = sqrt( 1000^2 + 1000^2 )
R = sqrt( 2000000 )
R = 1414.2 N
The resultant force of the two forces will be 1414.2N
Geometry, Inverse Trigonometry Find the measure of the indicated angle to the nearest degree
Answer:
? = 44 degrees
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp side/ adjacent side
tan ? = 46/48
Take the inverse tan of each side
tan ^-1 ( tan ?) = tan ^ -1 ( 46/48)
? = 43.78112476
To the nearest degree
? = 44 degrees
Show that 3 · 4^n + 51 is divisible by 3 and 9 for all positive integers n.
Answer:
To prove that 3·4ⁿ + 51 is divisible by 3 and 9, we have;
3·4ⁿ is divisible by 3 and 51 is divisible by 3
Where we have;
[tex]S_{(n)}[/tex] = 3·4ⁿ + 51
[tex]S_{(n+1)}[/tex] = 3·4ⁿ⁺¹ + 51
[tex]S_{(n+1)}[/tex] - [tex]S_{(n)}[/tex] = 3·4ⁿ⁺¹ + 51 - (3·4ⁿ + 51) = 3·4ⁿ⁺¹ - 3·4ⁿ
[tex]S_{(n+1)}[/tex] - [tex]S_{(n)}[/tex] = 3( 4ⁿ⁺¹ - 4ⁿ) = 3×4ⁿ×(4 - 1) = 9×4ⁿ
∴ [tex]S_{(n+1)}[/tex] - [tex]S_{(n)}[/tex] is divisible by 9
Given that we have for S₀ = 3×4⁰ + 51 = 63 = 9×7
∴ S₀ is divisible by 9
Since [tex]S_{(n+1)}[/tex] - [tex]S_{(n)}[/tex] is divisible by 9, we have;
[tex]S_{(0+1)}[/tex] - [tex]S_{(0)}[/tex] = [tex]S_{(1)}[/tex] - [tex]S_{(0)}[/tex] is divisible by 9
Therefore [tex]S_{(1)}[/tex] is divisible by 9 and [tex]S_{(n)}[/tex] is divisible by 9 for all positive integers n
Step-by-step explanation:
Find the number of rectangles in 6×6 chessboard.
Answer:
36
Step-by-step explanation:
quick maths
Answer:
36 rectangles
Step-by-step explanation:
Assuming that all you are asking for is the individual number of squares (not the number of squares and rectangles that can be made when combining the individual ones), the answer is 36.
We get this by multiplying the six squares on one side by the six on the other side. This allows us to calculate the total number! You can do this on a calculator or by hand.
However, if you would like the TOTAL number of rectangles that includes combining the individual ones, this chessboard would have 91 squares and 441 rectangles.
Represent 1/3 and 5/2 on the same number line.
Step-by-step explanation:
1/3 and 5/2 can be shown as:
1/3= 3/6 5/2= 15/6points with 1/6 interval on the number line:
0, 1/6, 2/6, 3/6, 4/6, ..., 15/6
Simplify the midpoint of QS.
Q (2b, 2c)
R (2a+2b, 2c)
Pl(0,0)
S (2a, 0)
Enter the value that
belongs in the green box. (a + [?], []).
Answer:
[(a + b), c]
Step-by-step explanation:
Midpoint of a segment with extreme ends represented by ordered pairs [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex],
Midpoint = [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
It is given that extreme ends of the segment QS are Q(2b, 2c) and S(2a, 0)
Coordinates of the midpoint of QS will be,
= [tex](\frac{2a+2b}{2},\frac{2c+0}{2} )[/tex]
= [(a + b), c]
Therefore, ordered pair representing the midpoint of QS will be [(a + b), c].
Answer:
(a+b, c)
Step-by-step explanation:
CORRECT FOR ACELLUS
Find the sum or difference.
81-3
3
Answer:
48
Step-by-step explanation:
81 - 33 = 48
Answer:
48
Step-by-step explanation:
81 - 33 = 48
Do 81 - 30 first = 51
Then do 51 - 3 = 48
The value of x must be greater than
B
12
0
O 1
А
15
O 3
O 7
Answer:
x > 3
Step-by-step explanation:
Given 2 sides of a triangle then the third side x will be
difference of sides < x < sum of sides , that is
15 - 12 < x < 15 + 12, so
3 < x < 27
Thus x > 3
Answer:
C. 3
Step-by-step explanation:
x > 3
Ed 2020
Please please help me!!
Answer:
The submarine is 307.8 yards below sea level.
Step-by-step explanation:
Since the 500 yards are the hypotenuse of the right angle triangle, the acute angle opposite the side of the triangle we need to find is known ([tex]38^o[/tex]), we can use the sine function to solve the problem:
[tex]sin(\theta)=\frac{opposite}{hypotenuse} \\sin(38^o)=\frac{x}{500} \\500\,*\,sin(38^o)=x\\x = 307.8307\,\,yards[/tex]
which rounded to the nearest tenth is : 307.8 yards
I need help I’m very confused with this question
Answer:
Option 1
Step-by-step explanation:
=> [tex]x^2-4x+2 = 10[/tex]
Adding 2 to both sides to complete the square
=> [tex]x^2-4x+4 = 12[/tex]
Completing the square
=> [tex](x-2)^2= 12[/tex]
Answer:
Step-by-step explanation:
exact form:
x=+2\sqrt(3+2)
decimal form:
x=5.46410161
what is the term to term rule for the sequence: 5 10 20 40 80 PLEASE HELP ITS URGENT
In the sequence 5,10,20,40,80.. I can see that it is doubled each time.
Doubling 5 is 10, doubling 10 is 20, doubling 20 is 40, and doubling 40 is 80.
Good luck! Stay safe!
- Eli <3
Question: Sara started her homework at 5:30 p.M. And finished it at 9:15 p.M. How much time did she take to finish her homework? [ 3 marks] Show your answer in 24 hour clock system. [ 2 marks]
Step-by-step explanation:
530pm = 17:50 in 24hr/military time
915pm = 21:15 in 24hr/military time
therefore..
24hr/military time. 21:15 - 17:50 = 3.65hr
our time. 3hr 45min
It took Sarah 3 hours and 45 minutes to finish her homework
The answer in 24 hour clock system is 3:45
The calculation can be done as follows
Sarah started her home work at 5:30 pm
She finished at 9:15pm
The time range here is 3 hours, 45 minutes
Please see the link below for more information
https://brainly.com/question/24991186?referrer=searchResults
What is the total surface area of the square pyramid below?
10 14 10 plz help:(
Answer: 380[tex]cm^{2}[/tex]
Step-by-step explanation:
Area of triangle= 14 x 10 = 140
140/2 = 70
4 triangles= 70 x 4 = 280
Area of the square= 10 x 10 = 100
Total surface area= 280 + 100 = 380[tex]cm^{2}[/tex]
hello fellow army :)
Find the slope and y-intercept of the line. 18x + 4y = 112 A)-9/2; 1/28 B)-2/9 ; 28 C)18; 112 D)-9/2; 28
Answer:
The slope is -9/2 and the y intercept is 28
Step-by-step explanation:
We want to put this in slope intercept form
y = mx+b where m is the slope and b is the y intercept
18x + 4y = 112
Subtract 18x from each side
18x+4y-18x = -18x+112
4y = -18x+112
Divide each side by 4
4y/4 = -18x/4 +112/4
y = -9/2x + 28
The slope is -9/2 and the y intercept is 28
Answer: D)-9/2; 28
Step-by-step explanation:
Match the question with the answer (e.G. 1 + C) 26 x 5 161 2. 25 x 6 130 3. 22 x 6 168 4. 21 x 8 150 5. 23 x 7 132 Answers: 1 + 2 + 3 + 4 + 5 +
Answer:
1+B,2+D,3+E,4+C and 5+A
Step-by-step explanation:
(A)161 (B)130 (C)168 (D)150 (E)132
1. 26 x 5=130
This is Option B, therefore we have the match:1+B
2. 25 x 6=150
This is Option D, therefore we have the match:2+D
3. 22 x 6=132
This is Option E, therefore we have the match: 3+E
4. 21 x 8=168
This is Option C, therefore we have the match: 4+C
5. 23 x 7=161
This is Option A, therefore we have the match:5+A
7x -5 (x +6) simplify this algebraic expression completely
Answer:
2x-30
Step-by-step explanation:
Expand: 7x-5x-30
=2x-30
its for 100 points Solve the chart save the picture and solve it please it going to save my life --- its first difference
The first column is found by plugging in the x values to get corresponding y values. For instance, if x = -5, then y is...
y = x^2+3x-18
y = (-5)^2+3(-5)-18
y = 25-15-18
y = 10-18
y = -8
So that explains how they got -8 in the second column, next to x = -5.
--------------
The column of first differences is found by subtracting the adjacent terms in the y column. The distance from y = -8 to y = -14 is 6 units, so we'll write 6 in the first row of the "first differences" column. The rest of the values of this column are filled out in a similar fashion. This means that you'll need to completely fill out the y column before you can move onto the "first differences" column.
--------------
The second differences is found by subtracting the adjacent first differences. You should find the results of this column are all the same value. This is true of any quadratic function.
Mrs. E buys a pair of jeans and receives a 35% discount. If the original price of the jeans was $55, how much does Mrs. E pay before taxes?
Answer:
40.39
Step-by-step explanation:
35% discount off 55 is 19.25
$35.75 is the answer
to calculate the tax its 13% rate in your area or what ever
1.13 x 35.75 = 40.39
solve the equation x^2+4x-7=0 by completing the square. Give your answer to 2 decimal places
Answer:
x ≈ - 5.32 , x ≈ 1.32
Step-by-step explanation:
Given
x² + 4x - 7 = 0 ( add 7 to both sides )
x² + 4x = 7
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(2)x + 4 = 7 + 4, that is
(x + 2)² = 11 ( take the square root of both sides )
x + 2 = ± [tex]\sqrt{11}[/tex] ( subtract 2 from both sides )
x = - 2 ± [tex]\sqrt{11}[/tex]
Thus
x = - 2 - [tex]\sqrt{11}[/tex] ≈ - 5.32 ( to 2 dec. places )
x = - 2 + [tex]\sqrt{11}[/tex] ≈ 1.32 ( to 2 dec. places )
Answer:
x=-5.32 or x=1.32
The equation of a circle is given below. ( x + 7 ) 2 + ( y + 8 ) 2 = 4 9 (x+7) 2 +(y+8) 2 = 9 4 left parenthesis, x, plus, 7, right parenthesis, squared, plus, left parenthesis, y, plus, 8, right parenthesis, squared, equals, start fraction, 4, divided by, 9, end fraction What is its center? ( (left parenthesis , ,comma ) )right parenthesis What is its radius? If necessary, round your answer to two decimal places. units
Answer:
The center is (-7,-8) and the radius is sqrt (2/3)
Step-by-step explanation:
( x + 7 )^ 2 + ( y + 8 ) ^2 = 4 /6
The equation of a circle can be written as
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
Rewriting
( x - -7 )^ 2 + ( y - -8 )^ 2 = (sqrt(2/3)^2
The center is (-7,-8) and the radius is sqrt (2/3)
Answer:
center: (-7,-8) radius: 2/3
Step-by-step explanation:
i got this from wegnerkolmp2741o. thank you wegnerkolmp2741o!!!!!
also got this correct on khan academy
Which of the following decimals is equivalent to 6%? A. 600 B. 6 C. 0.6 D. 0.06
Answer:
D
Step-by-step explanation:
Can someone please help me I really need help please help me
Answer:
≈ 18.87 cm²
Step-by-step explanation:
The shaded area is the difference between the area of the trapezium and the semicircle.
The area (A) of the trapezium is calculated as
A = [tex]\frac{1}{2}[/tex] h( a + b)
where h is the height and a, b the parallel bases
Here h = 4 ( radius of circle), a = 14 and b = 4 + 4 = 8, thus
A = [tex]\frac{1}{2}[/tex] × 4 × (14 + 8) = 2 × 22 = 44 cm²
area of semicircle = [tex]\frac{1}{2}[/tex]πr² = [tex]\frac{1}{2}[/tex]π × 4² = 8π cm²
Shaded area = 44 - 8π ≈ 18.87 cm² ( to 2 dec. places )
Answer:≈ 18.87 cm²
Step-by-step explanation:
Answer:
≈ 18.87 cm²
Step-by-step explanation:
The shaded area is the difference between the area of the trapezium and the semicircle.
The area (A) of the trapezium is calculated as
A = h( a + b)
where h is the height and a, b the parallel bases
Here h = 4 ( radius of circle), a = 14 and b = 4 + 4 = 8, thus
A = × 4 × (14 + 8) = 2 × 22 = 44 cm²
area of semicircle = πr² = π × 4² = 8π cm²
Shaded area = 44 - 8π ≈ 18.87 cm² ( to 2 dec. places
Can someone help me solve this?
Thank you!
Answer:b=-43.38
Step-by-step explanation:
Which function increases at the fastest rate between x = 0 and x = 8? A 2-column table with 5 rows titled Linear Function with the equation f of x = 2 x + 2. The first column is labeled x with entries 0, 2, 4, 6, 8. The second column is labeled f of x with entries 2, 6, 10, 14, 18. A 2-column table with 5 rows titled Exponential Function with the equation f of x = 2 Superscript x Baseline + 2. The first column is labeled x with entries 0, 2, 4, 6, 8. The second column is labeled f of x with entries 3, 6, 18, 66, 258. A 2-column table with 5 rows titled Quadratic Function with the equation f of x = 2 x squared + 2. The first column is labeled x with entries 0, 2, 4, 6, 8. The second column is labeled f of x with entries 2, 10, 34, 74, 130. A 2-column table with 5 rows titled Linear Function with the equation f of x = 3 x + 2. The first column is labeled x with entries 0, 2, 4, 6, 8. The second column is labeled f of x with entries 2, 8, 14, 20, 26.
Answer:
The correct option is;
Exponential function 2ˣ + 2
x = 0, 2, 4, 6, 8
f(x) = 3, 6, 18, 66, 258
Step-by-step explanation:
The given functions are;
f(x) = 2x + 2
x = 0, 2, 4, 6, 8
f(x) = 2, 6, 10, 14, 18
f(x) = 2ˣ + 2
x = 0, 2, 4, 6, 8
f(x) = 3, 6, 18, 66, 258
f(x) = 2·x² + 2
x = 0, 2, 4, 6, 8
f(x) = 2, 10, 34, 74, 130
f(x) = 3·x + 2
x = 0, 2, 4, 6, 8
f(x) = 2, 8, 14, 20, 26
By comparison, the function that increases at the fastest rate between x = 0 and x = 8 is Exponential function 2ˣ + 2
Answer: The answer is B on edg
Step-by-step explanation:
Anita plans to cover a solid cone with construction paper for a science project. The cone has a diameter of 11 inches and
a slant height of 28.5 inches. How many square inches of paper will she need to cover the entire cone?
492.20 in.
587.18 in.
982.82 in.
984.39 in.
Answer:
587.18 square inches
Step-by-step explanation:
We would find the Total surface area of the cone
Diameter of the cone = 11 inches
Radius = Diameter ÷ 2 = 11 / 2 = 5.5 inches
Slant height ( l ) = 28.5 inches
Let's take π = 3.14
Total Surface Area of a cone = πrl + πr²
= πr(l + r)
= 3.14 × 5.5( 28.5 + 5.5)
= π × 5.5(34)
= 587.18 square inches
There the square inches of paper will she need to cover the entire cone is 587.18 square inches
A catering company uses different functions to estimate the itemized costs for a party. The table below represents the included tip for wait staff as a function of the number of guests served. A table showing Catering Cost for Wait Staff Gratuity with two columns and 6 rows. The first column has, Number of Guests, and has the entries, 10, 20, 30, 40, 50. The second column, Wait Staff Tip, has the entries, $18, $36, $54, $72, $90. If the tip varies directly with the number of guests, which equation represents the relationship between the tip, t, and the number of guests, g?
Answer:
Step-by-step explanation:
If the tip varies directly with the number of guests, it means that an increase in the amount of tip would be as a result of an increase in the number of guests and a decrease in the amount of tip would be as a result of an decrease in the number of guests.
If we introduce a constant of proportionality, k , the relationship would be
t = kg
Given that
When t = 18, g = 10, then
18 = k × 10
k = 18/10 = 1.8
Therefore, the equation representing the relationship is
t = 1.8g
Answer:
answer is a
Step-by-step explanation:
What is the value of x in the equation 1/5x – 2/3y = 30, when y = 15?
Answer:
x = 200
Step-by-step explanation:
1/5x – 2/3y = 30
substitute in y
1/5x - 2/3(15) = 30
multiply
1/5x - 10 = 30
isolate the variable
1/5x = 40
multiply each side by 5
x = 200
Answer:
x = 200
Step-by-step explanation:
1/5x - 2/3y = 30
Put y as 15 and evaluate.
1/5x - 2/3(15) = 30
1/5x - 30/3 = 30
1/5x - 10 = 30
Add 10 on both sides.
1/5x = 40
Multiply both sides by 5.
x = 200
What is the answer to (-9c)-4=-25
Answer:
c= 7/3
Step-by-step explanation:
To solve for c:
Simplify the equation by moving all numbers to one side and variables to the other
-9c-4=-25
-9c= -25+4
-9c=-21
Now isolate c by dividing both sides by its coefficient (-9)
c= -21/-9
Since the (-) cancel out, this simplifies to:
c= 21/9
Now reduce the fraction by dividing the right hand side by a common value of 3:
c= 7/3
Given: DB= DB and EB & CB
Prove: D=A
We have proven that ∠D ≅ ∠A as shown below
Proof of anglesFrom the question, we are to complete the proof
Statements Reasons
AB ≅ DB 1. Given
1. EB ≅ CB
2. ∠ ABC ≅ ∠DBE 2. Congruent postulate
3. ΔABC ~ ΔDBE 3. Side-angle-side postulate
4. ∠D ≅ ∠A 4. CPCTC (Corresponding parts of
congruent triangles are congruent.)
Hence, we have proven that ∠D ≅ ∠A
Learn more on Proof of angles here: https://brainly.com/question/11673033
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I need an asnwer Tutor and the answer to this question
Answer:
[tex] \dfrac{1}{a^6} [/tex]
Step-by-step explanation:
[tex] a^{-6}x^0 = [/tex]
[tex] = \dfrac{1}{a^6} \times 1 [/tex]
[tex] = \dfrac{1}{a^6} [/tex]
The histogram shows the number of miles drive by a sample of automobiles in New York City. Which is a reasonable explanation for the large gap in the histogram?
Answer:
The gap in the histogram simply means that: out of all the automobiles sampled, there were none with number of miles driven between 17,500 miles and 32,500 miles.
Step-by-step explanation:
The histogram in question is missing from the question. It was obtained online and is attached to this solution.
A histogram is a chart that represents numerical data using bars. The dataset is split into intervals, each interval is represented by a bar, and the number of variables in each interval makes up the frequency for that interval.
If the bars are of equal width, the height of each bar corresponds to the frequency of the interval represented by that bar. If not, the frequency is given by the area of each bar (this is the major difference between a Bar chart and a histogram).
For this question, the histogram shows the number of miles driven by a sample of automobiles in New York City, the frequency of automobiles in each interval of miles driven is presented on the y or vertical axis and the miles driven is shown on the x-axis.
It is clear that 50 automobiles are in this sample and the class width of each interval of miles driven is 5000 miles.
So, the gap in between this histogram between the interval just after 17500 miles driven and just before 32500 miles driven simply means that none of the automobiles sampled had number of miles driven within this range.
Hope this Helps!!!