Answer:
Area of plane surface of cylinder = 2772 sq.cm.
Step-by-step explanation:
Let r be the radius and h be the height of the cylinder.
Curved Surface Area = 1848 sq.cm
2πrh = 1848
2×[tex]\frac{22}{7}[/tex]×rh = 1848
rh = 1848 × [tex]\frac{7}{22}[/tex] × [tex]\frac{1}{2}[/tex]
rh = 294
Sum of radius and height = 35
r + h = 35 --- (1)
Now,
r - h = [tex]\sqrt{(r+h)^{2}-4rh }[/tex]
= [tex]\sqrt{35^{2}-4(294) }[/tex]
= [tex]\sqrt{1225-1176}[/tex]
= [tex]\sqrt{49}[/tex]
= 7
r - h = 7 --- (2)
Adding (1) and (2),
2r = 42
r = 21 cm.
Area of the plane surface = 2 × π[tex]r^{2}[/tex]
= 2 × [tex]\frac{22}{7}[/tex] × 21 × 21
= 2772 sq.cm.
To calculate the plane surface area of a cylinder, subtract the area of the two circular bases from the curved surface area. Use the given formula and equations to find the radius and height, then calculate the area of one circular base. Finally, subtract the area of the bases from the curved surface area to find the plane surface area.
Explanation:To calculate the plane surface area of a cylinder, we need to subtract the area of the two circular bases from the curved surface area.
The formula for finding the curved surface area of a cylinder is given as:
CSA = 2πrh
So, the curved surface area is 1848 cm² and the sum of the radius and height is 35 cm. We can use these values to find the radius and height of the cylinder.
Solving the equation 2πrh = 1848 and r + h = 35 simultaneously will give us the values of r and h.
Once we have the values of r and h, we can calculate the area of one circular base using the formula Area = πr². Finally, we can calculate the plane surface area by subtracting the area of the two circular bases from the curved surface area.
What is the sum of the first seven terms of the geometric series? 3 + 12 + 48 + 192 + ... 4,372 12,288 16,383 65,535
Answer:
16,383 or C
Step-by-step explanation:
Answer:
Option 3rd is correct.
Step-by-step explanation:
Given: 3 + 12 + 48 + 192 + .......
We have to find : Sum of first seven term of the given Geometric series.
First term , a = 3
Common ratio , r = [tex]\frac{12}{3}=4[/tex]
Sum of the n term of series, [tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]
So,
[tex]S_7=\frac{3(1-4^7)}{1-4}[/tex]
[tex]S_7=\frac{3(1-4^7)}{-3}[/tex]
[tex]S_7=-(1-16384)[/tex]
[tex]S_7=-(-16383)[/tex]
[tex]S_7=16383[/tex]
Therefore, Option 3rd is correct.
A moving walkway at an airport moves at a pace of 1.75 feet per second. If you stand on the walkway as it moves, how long will it take to transport you 280 feet? CLEAR CHECK 160 seconds 278.25 seconds 490 seconds 625 seconds
Answer:
2 minutes 40 sec
Step-by-step explanation:
Recall that distance = rate times time.
Thus, time = distance / rate.
Here,
time = 280 ft / (1.75 ft/sec) = 160 sec, or 2 minutes 40 sec
To calculate the time it takes to travel 280 feet on a moving walkway at an airport moving at a pace of 1.75 feet per second, we use the formula time = distance/pace. This equates to approximately 160 seconds.
Explanation:The question is asking about the time it takes to transport someone along a distance of 280 feet by a moving walkway in an airport, given that the pace of the walkway is 1.75 feet per second. To answer this, you use the formula of time = distance/pace. So we have time = 280 feet / 1.75 feet per second. This calculation will give you the answer in seconds. When you do this calculation, you will find that it takes approximately 160 seconds to cover that distance on the moving walkway.
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Megan purchased a new gadget for her technology hobby. She plans to sell it sometime in the future, however, its value depreciates monthly. The expression below shows the depreciated sales value of the gadget: 2020 – 22m What does the variable of the expression represent? The monthly depreciation value of the gadget. The amount of money Megan will get when she sells the gadget. The number of months Megan will wait to sell the gadget. The original value of the gadget.
Answer:
3. The number of months Megan will wait to sell the gadget.
Step-by-step explanation:
We have been given that Megan purchased a new gadget for her technology hobby. She plans to sell it sometime in the future, however, its value depreciates monthly.
The expression below shows the depreciated sales value of the gadget: [tex]2020-22m[/tex]
From above expression we can see that gadget's original value is $2020 and its value falls by $22 every month and m represents the number of months after which Megan will sell her gadget.
Therefore, the variable m represents the number of months Megan will wait to sell the gadget and 3rd option is the correct choice.
The variable m represents the number of months Megan will wait to sell the gadget and 3rd option is the correct choice. The variable m in the expression 2020 – 22m represents the number of months Megan will wait to sell the gadget.
The original value of the gadget is 2020, and the monthly depreciation value is 22.
So, the expression 2020 – 22m represents the amount of money Megan will get when she sells the gadget after m months.
If Megan waits for 0 months to sell the gadget, then m = 0 and she will get
2020 – 22 * 0 = $2020.
If Megan waits for 1 month to sell the gadget, then m = 1 and she will get
2020 – 22 * 1 = $1998.
Therefore, the variable m in the expression 2020 – 22m represents the number of months Megan will wait to sell the gadget.
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Four friends went to a local amusement park. Three of the friends bought ride tickets for x dollars, plus a game pass for $10. The other friend bought just a ride ticket. Write and simplify an expression showing the amount of total money spent.
Answer:
4X + 30 = TOTAL AMOUNT OF MONEY
Step-by-step explanation:
All of them bought a ride ticket (that explains the 4x)
3 of them also bought a game pass thet costs $10 each. That explains the 30
going deeper: If the total amount of money was $70
The tickets would've costed $10 each.
Look:
4x + $30 = $70
4x = 70 - 30
4x = 40
x = 40/4
x =$10
What is the pattern and slope ? Please answer !!
Answer:
The slope is 3
Step-by-step explanation:
To find the slope we can use the formula
m = (y2-y1)/ (x2-x1)
Using the points (5,14) and (-5,-16)
m= (-16-14)/ (-5-5)
= -30/-10
= 3
The coordinates of the vertices of JKL are J(-5, -1), K(0, 1) , and L(2, -5). Which statement correctly describes whether JKL is a right triangle?
Answer:
It is NOT a right triangle.
Step-by-step explanation:
You must figure out the slopes of the segments of the triangle to see if it is a right triangle. If they are perpendicular (meaning the slopes are negative reciprocals of each other), they form a right angle, making it a right triangle.
[tex]\frac{y_{2} -y_{1}}{x_{2} -x_{1}}[/tex] This formula finds slope using two points.
Let's figure out the slope of JK.
(-1-1)/(-5-0) = m
Simplify.
-2/-5 = m
A negative divided by a negative makes a positive.
2/5 = m
Now LK.
(-5-1)/(2-0) = m
Simplify.
-6/2 = m
Divide.
-3/1 = m
Now JL.
(-1+5)/(-5-2) = m
Simplify.
4/-3 = m
None of these slopes are negative reciprocals of each other, thus deeming it not a right triangle.
HELP PLEASE! 49 POINTS!
show work!!!!!!
Answer:
1. y = 2/3 x +2
2. y = -x -8
Step-by-step explanation:
The slope intercept form of a line is y = mx+b where m is the slope and b is the y intercept
1. y = 2/3 x +2
2. y = -x -8
ANSWER:
1. y = 2/3x + 2
2. y = -1x + -8
ABOUT SLOPE INTERCEPT FORM:
y = mx + bm represents the slopeb represents the starting point AKA the y - interceptHope this helps you!!! :)
What are the x–coordinates of the three points where the graphs of the equations intersect? x3 – 10x = x2 – 6
Answer:
(- 3, 0), (2 + [tex]\sqrt{2}[/tex], 0), (2 - [tex]\sqrt{2}[/tex], 0)
Step-by-step explanation:
rearrange the equation equating to zero
x³ - x² - 10x + 6 = 0
note that when x = - 3
(- 3)³ - (- 3)² - 10(- 3) + 6 = - 27 - 9 + 30 + 6 = 0, hence
x = - 3 is a root and (x + 3) is a factor of the polynomial
dividing x³ - x² - 10x + 6 ÷ (x + 3) gives
(x + 3)(x² - 4x + 2) = 0
solve x² - 4x + 2 = 0 using the quadratic formula
with a = 1, b= - 4 and c = 2
x = (4 ± [tex]\sqrt{16-(4(1)(2)}[/tex])/ 2
= (4 ± [tex]\sqrt{8}[/tex]) / 2
= (4 ± 2[tex]\sqrt{2}[/tex]) / 2
= 2 ±[tex]\sqrt{2}[/tex], hence
x = 2 + [tex]\sqrt{2}[/tex], x = 2 - [tex]\sqrt{2}[/tex]
intersect at (- 3, 0), (2 +[tex]\sqrt{2}[/tex], 0), (2 - [tex]\sqrt{2}[/tex], 0)
Answer: [tex]\bold{x=-3,\quad x=2+\sqrt{2}, \quad x=2-\sqrt{2} }}[/tex]
Step-by-step explanation:
First, move all terms to one side with zero on the other side so the Zero Product Property can be applied:
x³ - x² - 10x + 6 = 0 Possible rational roots are: ±{1, 2, 3, 6}
Use synthetic division to find one of the roots. Let's try x = -3
-3 | 1 -1 -10 6
| ↓ -3 12 -6
1 -4 2 0 ← remainder is zero, so x = -3 is a root/intercept
Next, evaluate the reduced polynomial x² - 4x + 2 = 0
This can not be factored so use the quadratic formula to find the remaining roots/intercepts: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
a = 1, b = -4, c = 2
[tex]x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(1)(2)}}{2(1)}[/tex]
[tex]=\dfrac{4\pm\sqrt{16-8}}{2}[/tex]
[tex]=\dfrac{4\pm\sqrt{8}}{2}[/tex]
[tex]=\dfrac{4\pm2\sqrt{2}}{2}[/tex]
[tex]=2\pm\sqrt{2}[/tex]
[tex]x=2+\sqrt{2}\qquad x=2-\sqrt{2}[/tex]
Intercepts are [tex]x=-3,\quad x=2+\sqrt{2}, \quad x=2-\sqrt{2}}[/tex]
What is the pattern in this sequence?
1,9,17,25,33,...
Select from the drop down box to correctly complete the rule.
First Box
Add
Multiply by
Subtract
Divide by
Second box
9
8
-5
-9
Choose one from each box!
2. The ordered pairs model an exponential growth function
{(-1, 21.875), (0,35), (1,56), (2, 89.6)}
what is the function equation?
Enter your answer in the box
F(x)=
Answer in #1 it ads up by 8
Number 1 is Add by 8
& I'm not sure about number 2
Are the equations 2x + 14 = 8 and x = -3 equivalent? Explain.
Answer:
They are equivalent
Step-by-step explanation:
2x+14 = 8
Lets solve for x
Subtract 14 from each side
2x+14-14 = 8-14
2x = -6
Divide by 2
2x/2 = -6/2
x = -3
They are the same
Answer:
Yes
Step-by-step explanation:
Solving for 2x+14=8
Subtract 14 on both sides: 2x= 8-14
2x = -6
Divide by 2: x = -3
-3 = -3
Hope this helps!!
Given: ABCD is a trapezoid, AB=CD, MN is a midsegment, MN=30, BC=17, AB=26 Find: m∠A, m∠B, m∠C, and m∠D
Answer:
m∠A=m∠D=60°, m∠B=m∠C=120°
Step-by-step explanation:
Consider isosceles trapezoid ABCD with midsegment MN. Draw two trapezoid heights BF and CE. Then quadrilateral FBCE is rectangle and EF=BC=17 units.
By the trapezoid midsegment theorem,
[tex]MN=\dfrac{AD+BC}{2},\\ \\30=\dfrac{AD+17}{2},\\ \\60=AD+17,\\ \\AD=60-17=43\ units.[/tex]
Segments FA and ED are equal to [tex]\dfrac{43-17}{2}=13\ units.[/tex]
In right triangle ABF, the hypotenuse AB is twice greater than the leg FA, then m∠FBA=30°.
m∠B=m∠FBA+m∠CBF=30°+90°=120°.
In isosceles trapezoid
m∠B=m∠C=120°,
m∠A=m∠D and m∠A=180°-m∠B=180°-120°=60°=m∠D.
In a trapezoid with equal bases and a midsegment, the angle measures of the trapezoid can be determined using the properties of the figure. In this case, the angle measures are 90 degrees for each angle.
Explanation:In a trapezoid ABCD, the midsegment MN is parallel to the bases AB and CD, and its length is equal to the average of the lengths of the bases. Given that AB = 26, CD = 26, and MN = 30, we can set up the equation: MN = (AB + CD) / 2. Substituting the given values, we get 30 = (26 + 26) / 2. Solving for the angle measures, we can use the fact that the opposite angles in a trapezoid are congruent. So, m∠A = m∠C and m∠B = m∠D. Since the sum of the interior angles of a trapezoid is always 360 degrees, we can use the equation: m∠A + m∠B + m∠C + m∠D = 360. Substituting the angle measures we found, we get 2(m∠A) + 2(m∠B) = 360. Solving for the angle measures, we get m∠A = m∠C = 90 degrees and m∠B = m∠D = 90 degrees.
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Jorge wrote the expression x + x + x + x + 3 to represent the sequence shown in the diagram at right. Does his expression make sense? Explain.
Answer:
Step-by-step explanation:
no because x can equal anything. It should at least write down a second number for it to be solved correctly.
multiplying integers
3(-7)
Answer:
-21
Step-by-step explanation:
3(-7)
3*7 =21
A positive times a negative is a negative
-21
Answer:
3x-7=21 ( i think )
Step-by-step explanation:
when you have a parenthesis beside a number you always multiply. A negative times a positive is a negative,
Jill bought a 9 pound bag of cat food for her cats. She had used 4/5 of the bag. How many pounds has she used?
A. 9 4/5
B. 8 4/5
C. 8 3/5
D. 7 1/5
Answer:
D. 7 1/5
Step-by-step explanation:
We would calculate the amount of pounds she used by multiplying the total amount of cat food = 9 to the amount she has used = 4/5
= [tex]9 * \frac{4}{5}[/tex]
= [tex]\frac{36}{5}[/tex]
= [tex]7 \frac{1}{5}[/tex]
(An image is attached for the calculation)
Is (0,0) a solution to this system? y ≥ x^2 - 4 y < 2x - 1
A. Yes. (0,0) satisfies both inequalities.
B. No. (0,0) satisfies y < 2x - 1 but does not satisfy y ≥ x^2 - 4.
C. No. (0,0) does not satisfy either inequality.
D. No. (0,0) satisfies y ≥ x^2 - 4 but does not satisfy y < 2x - 1.
The inequality y ≥ x^2-4 satisfies (0,0) but the inequality y < 2x-1
does not satisfy (0,0).
Finding solution of both the inequalities:Consider the inequality y ≥ x^2-4 -------(i)Substitute (x,y)= (0,0) in the above inequality
0 ≥ (0^2)-4
0 ≥ -4
The above inequality is true.
Hence, (0,0) is the solution of inequality (i)
Consider the inequality y < 2x-1 ---------(ii)Substitute (x,y)= (0,0) in the above inequality
0 < 2(0) - 1
0 < -1
The above inequality is not true.
Hence (0,0) does not satisfy the above inequality (ii).
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What number is 0.95 of 3500
Answer:
Alright well Convert fraction to an decimal, then multiply by 100
0.02714285% Hope this helps have a nice day :)
Step-by-step explanation:
What is the diameter of a circle with a circumference of 66 ft? Use 22/7 for pie
Answer:
21 ft
Step-by-step explanation:
Diameter = Circumference/Pi
Diameter = 66/(22/7)
Diameter = 21
Given cos a= 3/5, sin B = 5/13 and a and B are first quadrant angles find cos(a + B)
A. 1/3
B. 16/65
C. -33/65
Please explain
Answer:
Option B is correct.
Value of cos(a+B) is, [tex]\frac{16}{65}[/tex]
Step-by-step explanation:
Using the formula:
[tex]\cos(a+B) = \cos a \cos B -\sin a \sin B[/tex]
Given the values:
[tex]\cos a = \frac{3}{5}[/tex] and [tex]\sin B = \frac{5}{13}[/tex]
Using trigonometric identity:
[tex]\sin^2 \theta + \cos^2 \theta =1[/tex]
or
[tex]\sin \theta = \sqrt{1-\cos^2 \theta}[/tex]
or
[tex]\cos \theta = \sqrt{1-\sin^2 \theta}[/tex]
Find the value of sin a and cos B;
Using trigonometric identity:
[tex]\sin a = \sqrt{1-\cos^2 a}[/tex]
[tex]\sin a = \sqrt{1-(\frac{3}{5})^2}[/tex] = [tex]\sqrt{1-\frac{9}{25}} = \sqrt{\frac{25-9}{25}}=\sqrt{\frac{16}{25} } =\frac{4}{5}[/tex]
Similarly;
[tex]\cos B = \sqrt{1-\sin^2 B}[/tex]
[tex]\cos B = \sqrt{1-(\frac{5}{13})^2}[/tex] = [tex]\sqrt{1-\frac{25}{169}} = \sqrt{\frac{169-25}{169}}=\sqrt{\frac{144}{169} } =\frac{12}{13}[/tex]
Substitute these given values equation [1] we have;
[tex]\cos(a+B) =\frac{3}{5} \cdot \frac{12}{13}-\frac{4}{5} \cdot \frac{5}{13}[/tex]
[tex]\cos(a+B) =\frac{36}{65}-\frac{20}{65}[/tex]
then;
[tex]\cos(a+B) =\frac{36-20}{65}=\frac{16}{65}[/tex]
Since, the angles a and B are in first quadrant angles therefore the value of cos(a+B) is, [tex]\frac{16}{65}[/tex]
To find cos(a + B), use the formula cos(a + B) = cos(a)cos(B) - sin(a)sin(B). Substitute the given values of cos(a) = 3/5 and sin(B) = 5/13, and solve for cos(B) using the Pythagorean identity. Then substitute all the values into the formula and simplify to find cos(a + B) = 16/65.
Explanation:To find cos(a + B), we can use the formula:
cos(a + B) = cos(a)cos(B) - sin(a)sin(B)
Given that cos(a) = 3/5 and sin(B) = 5/13, we can substitute these values into the formula:
cos(a + B) = (3/5)(cos(B)) - (sin(a))(5/13)
To find cos(B), we can use the Pythagorean identity:
cos²(B) + sin²(B) = 1
Substituting the given value of sin(B), we can solve for cos(B):
cos(B) = √(1 - (5/13)²)
Now we can substitute the values of cos(a), sin(B), and cos(B) into the formula for cos(a + B):
cos(a + B) = (3/5)(√(1 - (5/13)²))) - (5/13)(5/13)
Simplifying this expression gives us the final answer: cos(a + B) = 16/65.
plz help me with these two questions :)
The Science Club went on a two-day field trip. The first day the members paid $30 for transportation plus $12 per ticket to the planetarium. The second day they paid $90 for transportation plus $9 per ticket to the geology museum. Write an expression to represent the total cost in dollars for two days for the n members of the club.
Answer: Total: 30 + 20y + 85 + 17y This is the not simplified version.
37y+115 This is the simplified version. Hope this helps
Step-by-step explanation: I really don't know the steps.?
Write as a numeral: 200,000+20,000+3,000+200+20+8
[tex]200,000+20,000+3,000+200+20+8=223,228\\\\200,000\\.\ 20,000\\.\ \ 3,000\\.\ \ \ \ \ 200\\.\ \ \ \ \ \ \ 20\\\underline{+\qquad\ 8}\\223,228[/tex]
What is the probability that both spinners will land on 2? AMSWERS- A)1/12 B)1/6 C)1/4 D)1/3
ONE GRAPH IS 1,2,3 AND THE OTHER GRAPH SHOWS 1,2,3,4 OUTCOMES
Answer:
The probability that both spinners will land on 2 is A) 1/12.
Step-by-step explanation:
To get this answer you must:
-First, take the total number of outcomes and set that as you denominator, which would be 3.
-Since, your looking for the probability of two, and there is only one two you would put one as your numerator. By now you should have a fraction of: 1/3.
-Next, do the same exact thing for the next graph. Take the total number of outcomes for the graph which is 4, and set that as your denominator.
-Then, set one as your numerator since there is only one two in the other graph. You should now have a second fraction of: 1/4.
-Lastly, multiply both of the fractions. Multiply both of the numerator together and you should get one. Then, multiply both of the numbers which would result in you getting a number of 12.
1/3(1/4) = 1/12.
what is the value of the lower quartile?
a.0
b.8
c.6
d.2
thank you!
Answer:
D
Step-by-step explanation:
From the box- plot the left hand side of the box represents the lower quartile
that is [tex]Q_{1}[/tex] = 2 → D
Is the system of equations consistent, consistent and coincident, or inconsistent? y=3x+4y=3x+3 Select the correct answer from the drop-down menu.
Answer: Inconsistent
Step-by-step explanation:
y = 3x + 4 → m = 3, b = 4
y = 3x + 3 → m = 3, b = 3
These equations have the same slope but different y-intercepts so they are parallel lines which means they will never intersect.
NOTES
one solution: consistent & independent lines crossinfinite solutions: consistent & dependent same lineno solution: inconsistent parallel linesAnswer:
Inconsistent
Step-by-step explanation:
5y - 10 = -25
ok try this one buster.
Answer:
Y= -3
Step-by-step explanation:
5y-10=-25 Add 10 on both sides
5y=-15 Divide by 5 on both sides
y=-3
There are 40 girls and 32 boys who want to participate in the relay race. If each team must have the same number of girls and boys, A) what is the greatest number of teams that can race? B) How many boys and girls will be on each team?
Answer:
8 teams
5 girls and 4 boys
Step-by-step explanation:
To determine how many teams we can have , we need to determine the greatest common factor.
girls:40 = 5*8
boys:32 = 4*8
The greatest common factor is 8
So we will have 8 teams
There will be 5 girls and 4 boys on each team
Point M is between points L and N on segment LN. LM=5x, MN=2x+4, and LN=10x-16
Use the information to solve for x, and then find LN, LM, and MN.
Answer:
x= 6.6
LM= 33
MN= 17.2
LN=50
Step-by-step explanation:
10x-16= 5x+2x+4 (LN=LM+MN)
10x-16=7x+4
3x-16=4
3x=20
x=6.6
then plug 6.6 back into equation and round to the nearest whole number.
Given that lines a and b are parallel, what angles formed on line b when cut by the transversal are congruent with ∠3?
A) ∠5 and ∠6
B) ∠5 and ∠7
C) ∠6 and ∠7
D) ∠6 and ∠8
Answer:
C) ∠6 and ∠7
Step-by-step explanation:
We have been given that lines a and b are parallel. We are asked to find the angle on line b that will be congruent to angle 3.
We can see that angle 3 is under the line a and on the left side of transversal.
We know that the corresponding angles and alternate interior angles formed by two parallel lines are equal.
We can see that angle 7 corresponds to angle 3 and angle 6 is alternate interior angle of angle 3.
Therefore, angle 7 and angle 6 will be congruent with angle 3 and option C is the correct choice.
what is the algebr expression for the following word phrase: the produc of 4 more then x and 6?
a)4(x+6)
b) 6(x+4)
c)6+(x+4)
d)6-(x+4)
Answer:
b) 6(x + 4)
Step-by-step explanation:
The given word phrase "The product of 4 more than x and 6"
4 more than x = 4 + x
The product "4 + x" and 6
6(x + 4)
Answer: b) 6(x + 4)
If the original price is $23.99 and the mark down is 44% what is the sale price
Answer:
The sale price is $13.43
Step-by-step explanation:
In order to find the sale price of an item, we multiply it by the remaining percentage of cast left. Since we are subtracting 44% of the cost, that means that we are paying 56% of it. Therefore, we can multiply the cost by 56%
23.99 * .56 = $13.43
Answer: $13.43
Step-by-step explanation:
make your 22% a decimal by dividing it by 100 equaling 0.22 then since its markDOWN you subtract 1.00 - 0.22 equaling 0.88 then multiply 0.88 by $23.99 which is supposed to equal $13.43