2x=x+30
-x -x
x=30
The value of x is 30
Identify the surface area of the composite figure in terms of π. HELP PLEASE!!
Answer:
S = 264π m²
Step-by-step explanation:
Left cone
= π(6)(8)
= 48π m²
Central cylinder
= 2π(6)(14)
= 168π m²
Right cone
π(6)(8)
= 48π m²
Surface area = 48π + 168π + 48π = 264π m²
The surface area of the composite figure is 264π [tex]m^{2}[/tex]
How to find the surface area of a composite figure?r = 6m
h = 14m
l = 8m
The curved surface area of the cylinder = 2πrh
= 2*[tex]\pi[/tex]*6*14
=168π [tex]m^{2}[/tex]
The curved surface area of the cone = πrl
=π*6*8
=48π [tex]m^{2}[/tex]
The total surface area of the composite figure
= CSA of cylinder + 2( CSA of cone )
= 168π + 2*48π
=168π + 96π
= 264π [tex]m^{2}[/tex]
Therefore, option S = 264π [tex]m^{2}[/tex] is the correct answer
To learn more about composite figure, refer:
https://brainly.com/question/21135654
#SPJ2
If the walls are 9' high, how much paint would I need to buy to paint the walls of all three bedrooms?
Answer:
The required paint for a total of [tex]1.404\ ft^{2}[/tex] is approximate 6 gallons
Step-by-step explanation:
we know that
To find how much paint would I need to buy to paint the walls of all three bedrooms, calculate the area of all three bedrooms
Master Bedroom
The area is equal to
[tex]A1=(16+16+12+2+18)*9=576\ ft^{2}[/tex]
2 Bedroom
The area is equal to
[tex]A2=(12+14+10+10)*9=414\ ft^{2}[/tex]
3 Bedroom
The area is equal to
[tex]A3=(10+10+14+10+2)*9=414\ ft^{2}[/tex]
The total area is equal to
A=A1+A2+A3
[tex]A=576+414+414=1.404\ ft^{2}[/tex]
Approximate one gallon of paint covers 250 square feet
so
[tex]1.404/250=5.6\ gal[/tex]
The figure below is rotated 270° clockwise about the origin .List the coordinates of the image.
A ( , )
B( , )
C( , )
D( , )
Answer:
A (-4, -4), B (-2, 6), C (-1, 1), D(-3, -5)
Step-by-step explanation:
Before the rotation:
A (-4, 4), B (6, 2), C (1, 1), D(-5, 3)
270° rotation clockwise is the same as 90° counterclockwise. To do that transformation:
(x, y) → (-y, x)
Therefore, the coordinates of the rotated figure are:
A (-4, -4), B (-2, 6), C (-1, 1), D(-3, -5)
The coordinates of the image are:
A'(-4,-4)B'(-2,6)C'(-1,1)D(-3,-5)---------------------------
This question is solved applying a 270° clockwise about the origin, which has the following rule:
[tex](x,y) = (-y,x)[/tex]
---------------------------
Coordinate A:
At the Figure, coordinate A is A(-4,4). Applying the rule:
[tex](-4,4) = (-4, -4)[/tex]
So the image of A is A'(-4,-4).
---------------------------
Coordinate B:
At the Figure, coordinate B is B(6,2). Applying the rule:
[tex](6,2) = (-2, 6)[/tex]
So the image of B is B'(-2,6).
---------------------------
Coordinate C:
At the Figure, coordinate C is C(1,1). Applying the rule:
[tex](1,1) = (-1, 1)[/tex]
So the image of C is C'(-1,1).
---------------------------
Coordinate D:
At the Figure, coordinate C is D(-5,3). Applying the rule:
[tex](-5,3) = (-3,-5)[/tex]
So the image of D is D'(-3,-5).
A similar question is given at https://brainly.com/question/3382538
30 POINTS PLEASE HELP!
Which division problem does the model represent?
Answer:
first 1
Step-by-step explanation:
first 1
Answer:
7/4 ÷ 1/2= 3 1/2
Step-by-step explanation:
This is the answer hope it help's :)
Use substitution to solve the system of equations x= -3y-13 2x+2y=-6
For this case we have a system of two equations with two unknowns:
[tex]x = -3y-13\\2x + 2y = -6[/tex]
To solve we follow the steps below:
We substitute the first equation in the second:
[tex]2 (-3y-13) + 2y = -6[/tex]
We apply distributive property to the terms of parentheses:
[tex]-6y-26 + 2y = -6[/tex]
We add 26 to both sides of the equation:
[tex]-6y + 2y = -6 + 26\\-4y = 20\\y = \frac {20} {- 4}\\y = -5[/tex]
We find the value of x:
[tex]x = -3 (-5) -13\\x = 15-13\\x = 2[/tex]
Answer:
[tex](x, y) :( 2, -5)[/tex]
Help please! (See image.)
FED is 5/4 times bigger than CBA. So, 44×1.25 is 55. 40×1.25 is 50. The perimeter is 125
A television manufacturer decides to increase its production by 25% per month to meet increasing customer demand. The company currently produces 2,000 television sets a month.
Which of the following graphs shows the total number of television sets, y, manufactured by the company in x months?
Answer:
The last graph
Step-by-step explanation:
The problem presented here is similar to a compound interest problem since we have an initial value, a growth constant and the aspect of time.
We can consider the number of television sets currently produced by the company to be our Principal amount;
P = 2000
The rate of increase in production per month can be considered as our interest rate earned;
r = 25% = 0.25
The total number of television sets y will be our Accumulated amount;
A = y
The duration x becomes our time n.
The compound interest formula is given as;
[tex]A=P(1+r)^{n}[/tex]
We simply substitute the given information into the formula;
[tex]y=2000(1.25)^{x}[/tex]
This is an exponential growth function since the base of the exponent x is greater than 1.
A graph of the function will be an exponential curve passing through ( 0, 2000) since 2000 is our initial value
Answer: the last ones
Step-by-step explanation: I put it and got it right:)
In the straightedge and compass construction of the equilateral triangle below, how do you know that AB ≈ AC?
Answer:
C
Step-by-step explanation:
C: AB is the radius of both circles.
Answer:
C. line segment AB is the radius of both circles.
Step-by-step explanation:
If point A is the center of the first circle and point B is the center of the second circle (in the figure), therefore Line segment AB is the radius of both circles and we write.
Line segment AB = line segment AC (radius of first circle ) and
line segment AB = line segment BC (radius of second circle).
Hence line segment AB is the radius of both circle is the correct option for AB =AC.
The equation that models the current water temperature t of the swimming pool is t -6=78 which best describes the error made when solving for the current temperature
Answer:
The same number was not added to both sides.
Step-by-step explanation:
The same number was not added to both sides.
In line 2, 6 was added to the left side and 78 was added to the right side.
The best that describes the error made when solving for the current temperature is that the same number was not added to both sides of the equation.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given equation can be solved as shown below.
t - 6 = 78
t - 6 + 6 = 78 + 6
t = 84
Now, if we compare it with the given equation, we can find that the error made when solving for the current temperature is that the same number was not added to both sides of the equation.
Hence, the best that describes the error made when solving for the current temperature is that the same number was not added to both sides of the equation.
Learn more about Equation here:
https://brainly.com/question/14686792
#SPJ6
Which of the following steps were applied to ABCD to obtain A'B'C'D?
A. shifted 3 units left and 3 units up
B. shifted 4 units left and 4 units up
C. shifted 4 units left and 3 units up
D. shifted 3 units left and 4 units up
C. shifted 4 units left and 3 units up
If you compare the graphs (ABCD=Blue; A’B’C’D’=Red), you see that ABCD was moved left 4 and up 3 to become A’B’C’D’.
A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position. The correct option is A.
What are coordinates?A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
To know the steps that were applied to ABCD to obtain A'B'C'D, we need to observe the coordinates of any one point of the polygon given.
Now, if we look at the coordinates of the points D and D', then it can be observed that point D is shifted 3 units left and 3 units up to form A'B'C'D.
Learn more about Coordinates:
https://brainly.com/question/23450276
#SPJ2
Rearrange the formula a2 + b2 = c2 for a. A) a = (c2 − b2)2 B) a = (c2 + b2)2 C) a = c2 − b2 D) a = c2 + b2
Answer:
C2 + a2 +2 = b
Would be the new formula
Answer:
the correct answer is:
a = √ c^2 − b^2
Step-by-step explanation:
a^2 + b^2 = c^2
Explanation:
a^2 + b^2 = c^2
a^2 = c^2 − b^2
a = √ c^2 − b^2
Which choice is equivalent to the quotient below shown here when x>0?
Answer:
Choice B is correct
Step-by-step explanation:
The given radical division can be expressed in the following form;
[tex]\frac{\sqrt{16x^{3} } }{\sqrt{8x} }[/tex]
Using the properties of radical division, the expression can be expressed in the following form;
[tex]\sqrt{\frac{16x^{3} }{8x} }=\sqrt{2x^{2} }[/tex]
Simplifying further yields;
[tex]\sqrt{2x^{2} }=\sqrt{2}*\sqrt{x^{2} }=x\sqrt{2}[/tex]
Choice B is thus the correct alternative
For this case we must simplify the following expression:
[tex]\frac {\sqrt {16x ^ 3}} {\sqrt {8x}} =[/tex]
Join the terms in a single radical:
\[tex]\sqrt {\frac {16x ^ 3} {8x}} =\\\sqrt {\frac {8 * (2x ^ 3)} {8x}} =\\\sqrt {\frac {2x ^ 3} {8x}} =\\\sqrt {2x ^ 2} =\\\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So:
[tex]\sqrt {2x ^ 2} =\\x \sqrt {2}[/tex]
Answer:
Option B
Solve for x.
A. 6
B. 7
C. 4
D. 5
Answer:
D
Step-by-step explanation:
[tex]\frac{5x}{20} =\frac{45}{36}[/tex]
Cross multiply:
(5x)(36)=(20)(45)
180x = 900
divide by 180.
x=5
The value of x is 5.
How to find the value of x?Δ ACE ≅ Δ BCD (by AAA property)
Therefore
[tex]\frac{CD}{CE} = \frac{CB}{CA}[/tex] ( Similar triangle property)
[tex]\frac{20}{36} = \frac{5x}{45}[/tex]
5x = [tex]\frac{20 * 45}{36}[/tex]
5x = 25
x = 5
Therefore, option D. 5 is the correct answer
To learn more about similar triangles, refer:
https://brainly.com/question/14285697
#SPJ2
Find an equation in standard form for the ellipse with the vertical major axis of length 18 and minor axis of length 6.
a)x squared divided by 81 plus y squared divided by 9 = 1
b)x squared divided by 9 plus y squared divided by 3 = 1
c)x squared divided by 9 plus y squared divided by 81 = 1
d)x squared divided by 3 plus y squared divided by 9 = 1
C seem reasonable to me
A room contains three urns: u1, u2, u3. u1 contains 3 red and 2 yellow marbles. u2 contains 3 red and 7 yellow marbles. u3 contains 1 red and 4 yellow marbles. 66) referring to urns we enter the room and select an urn, but we are not sure which, and then we randomly remove a marble from the urn. find the probability that the marble is red.
Answer:
[tex]\dfrac{11}{30}[/tex]
Step-by-step explanation:
Urn U1: 3 red and 2 yellow marbles, in total 5 marbles.
The probability to select red marble is [tex]\dfrac{3}{5}=0.6.[/tex]
Urn U2: 3 red and 7 yellow marbles, in total 10 marbles.
The probability to select red marble is [tex]\dfrac{3}{10}=0.3.[/tex]
Urn U1: 1 red and 4 yellow marbles, in total 5 marbles.
The probability to select red marble is [tex]\dfrac{1}{5}=0.2.[/tex]
The probability to choose each urn is the same and is equal to [tex]\frac{1}{3}.[/tex]
Thus, the probability that the marble is red is
[tex]\dfrac{1}{3}\cdot 0.6+\dfrac{1}{3}\cdot 0.3+\dfrac{1}{3}\cdot 0.2=\dfrac{1.1}{3}=\dfrac{11}{30}.[/tex]
the equation of a line is given below.
4x + 3y = -24
find the x-intercept and the y-intercept.
then use them to graph the line.
x-intercept: ?
y-intercept: ?
Answer:
See below.
Step-by-step explanation:
4x + 3y = -24
We convert to slope/intercept form ( y = mx + b):
3y = - 4x - 24
Divide through by 3:
y = (-4/3)x - 8
Comparing this with y = mx + b:
we see that b ( the y-intercept) is -8.
To find the x -intercept solve (-4/3)x - 8 = 0
(-4/3)x = 8
Multiplying through by -3/4:
x = 8 * -3/4 = -6 = x-intercept.
To draw the graph draw a line through the points (-6,0) and (0, -8).
Answer:
-3/4 y-6
Step-by-step explanation:
The depth of a lake is 100 centimeters less than 1401 meters what is the depth in kilometers
The depth of the lake is 1.4 kilometers after converting the result to kilometers.
To find the depth of the lake in kilometers when it is 100 centimeters less than 1401 meters, first convert the depth difference to meters.
Since 100 centimeters is equivalent to 1 meter, the actual depth of the lake in meters is 1400 meters (which is 1401 meters - 1 meter).
To convert this depth into kilometers, we divide by 1000, since there are 1000 meters in one kilometer.
Hence, the depth is 1.4 kilometers.
Which relationships hold true for the sum of the magnitudes of vectors u and v, which are perpendicular? Select all correct answers.
[tex]||u+v||=||u||+||v||\\||u+v||=\sqrt{||u||^2+||v||^2}\\||u+v||\ \textless \ \sqrt{||u||^2+||v||^2}\\||u+v||\ \textless \ ||u||+||v||[/tex]
Answer:
the correct answers are marked in green below
Step-by-step explanation:
As with any right triangle, the length of the hypotenuse is equal to the root of the sum of the squares of the legs. That root is less than the sum of the leg lengths and greater than the longest leg (for non-zero leg lengths).
_____
Comment on the choices
The relationship is actually ...
║u+v║ ≤ ║u║ + ║v║
That makes the first selection possibly correct. It will only be correct if ║u║ or ║v║ is zero. The problem statement does not rule out that case.
Answer:
As with any right triangle, the length of the hypotenuse is equal to the root of the sum of the squares of the legs. That root is less than the sum of the leg lengths and greater than the longest leg (for non-zero leg lengths).
_____
Comment on the choices
The relationship is actually ...
║u+v║ ≤ ║u║ + ║v║
That makes the first selection possibly correct. It will only be correct if ║u║ or ║v║ is zero. The problem statement does not rule out that case.
Step-by-step explanation:
Please help with this question. I don't understand!
Answer:
6135.9m^3
Step-by-step explanation:
V=3.14r^2 h/3
step by step
1. the radius is half so half of 25 is 12.5 that's the r in your equation
2.the height in your equation is 3 times more then the radius and your radius is 12.5X3 =37.5 for your height
3. plug everything in back into the equation v=3.14(12.5)^2(37.5/3)= 6135.923 when rounded it is 6135.9m^3
If a jelly bean machine contains 16 pink jelly beans, 34 blue jelly beans, 24 black jelly beans and 26 purple jelly beans, what is the probability that a jelly bean chosen at random will be blue?
A. 13/50
B. 6/25
C. 4/25
D. 17/50
Answer:
The correct answer option is D. 17/50.
Step-by-step explanation:
We are given that a jelly bean machine has 16 pink jelly beans, 34 blue jelly beans, 24 black jelly beans and 26 purple jelly beans.
We are to find the probability of getting a blue jelly bean chosen at random.
Total number of jelly beans = 16 + 34 + 24 + 26 = 100
Number of blue jelly beans = 34
P (getting a blue jelly bean) = 34/100 = 17/50
The manager of cups R' Us handed out 125 coupons to his customers on Monday, c coupons on Tuesday, and 220 coupons on the Wednesday. Write an expression for the total number of coupons the manager handed out. Then simplify the expression.
Answer:125+220+c
if c= 20 then it would be 125+220+20=365
Step-by-step explanation:
IXL question
I don't understand this one and I need more than 0 points :/
[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\[2em] \begin{array}{ccccllll} &\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\ \cline{2-4}&\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}\\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \cfrac{\textit{small cylinder}}{\textit{large cylinder}}\qquad \stackrel{\stackrel{\textit{ratio of the }}{\textit{sides}}}{\cfrac{3}{6}}= \stackrel{\stackrel{\textit{ratio of the }}{\textit{volumes}}}{\cfrac{\sqrt[3]{V}}{\sqrt[3]{V}}}\implies \cfrac{3}{6}=\sqrt[3]{\cfrac{1000}{V}}\implies \left( \cfrac{3}{6} \right)^3=\cfrac{1000}{V} \\\\\\ \left( \cfrac{1}{2} \right)^3=\cfrac{1000}{V}\implies \cfrac{1^3}{2^3}=\cfrac{1000}{V}\implies \cfrac{1}{8}=\cfrac{1000}{V}\implies V=8000[/tex]
Find the maximum and minimum values of the function.
y=7cosx
Answer:
B
Step-by-step explanation:
If a sinusoidal function is given in the form y = B Sin x or y = B Cos x, then,
B is called the amplitude of the function. It will define minimum and maximum.
The minimum & maximum of this form of a cos function is B and -B.
The function given is y = 7 Cos x, so the Maximum is 7 and Minimum is -7
Correct answer is B.
For a normally distributed random variable x with m = 75 and s = 4, find the probability that 69 < x < 79 Use the table to help find the answer.
10-14-19-12-14-18-10-15-15
The graph of the function, f(x) = 3^2 + x + 2, opens(down or up) and has a (minimum or maximum) value.
1. The parabola opens upward.
2. It has a minimum value
Step-by-step explanation:The explanation is shown below. Also, the graph of this function is shown below including the vertex.
If g=27 and F=54° find h. Round to the nearest tenth
(picture provided)
For this case we have to:
[tex]cos (F) = \frac {h} {27}[/tex]
That is, the cosine of the angle F, will be equal to the adjacent leg on the hypotenuse.
So, by clearing h we have:
[tex]h = 27 * cos (54)\\h = 27 * 0.58778525\\h = 15.87020175[/tex]
Rounding out the value of h we have:
[tex]h = 15.9[/tex]
Answer:
Option B
Answer:
The correct answer is option b. 15.9
Step-by-step explanation:
Points to remember:-
Trigonometric ratio
Cos θ = adjacent side/Hypotenuse
From the figure we can see a right triangle triangle FGH.
To find the value of h
It is given that, g=27 and F=54°
Cos F = adjacent side/Hypotenuse
Cos 54 = adjacent side/Hypotenuse
= FG/FH = h/g
h = g * Cos F = 27 * Cos 54 = 27 * 0.5878 = 15.87 ≈ 15.9
Therefore the correct answer is option b. 15.9
2) If events A and B are DEPENDENT, then A) A and B must occur together. B) A and B cannot occur together. C) A's occurrence can affect the probability of B's occurrence. D) A's occurrence cannot affect the probability of B's occurrence.
Answer:
by 5
Step-by-step explanation: because tgey wou;d nred help
Answer:
C.) If events A and B are DEPENDENT, then A's occurrence can affect the probability of B's occurrence. For example, when two cards are chosen from a deck without replacement, the possibilities change for the second card.
Evaluate.
9!/7!
A.) 63
B.) 72
C.) 81
ANSWER
B.) 72
EXPLANATION
Recall the expansion for the factorial notation:
[tex]n! = n \times (n - 1) \times (n - 2) \times ...3 \times 2 \times 1[/tex]
We want to simplify
[tex] \frac{9!}{7!} [/tex]
Let us expand the numerator up to 7! while maintaining the denominator.
[tex] \implies \: \frac{9 \times 8 \times 7!}{7!} [/tex]
When we cancel out the common factors,we obtain:
[tex]\implies \: \frac{9 \times 8 \times 1}{1} [/tex]
This simplifies to
[tex]\implies \: \frac{72}{1} = 72[/tex]
The correct answer is B.
A Store is having two sales on popcorn. The original price of the popcorn is $10 for 10 oz. Sale A offers you 33% more popcorn for free. Sale B offers you the same amount of popcorn, but at 33% off of the original price. What is the better deal? Why?
Answer:
33% off is the better deal
Step-by-step explanation:
1.33 times as much popcorn for the same price is equivalent to 1/1.33 ≈ 0.75 times the price for the original amount of popcorn. That price is equivalent to a sale of 1 - 0.75 = 0.25 = 25% off.
The sale price of 33% off is a better deal (if you don't want the extra popcorn).
What are the period and amplitude of the function?
ANSWER
Period: 2π , amplitude: 4
EXPLANATION
The graphed function is
[tex]y = 4\cos(x) [/tex]
The amplitude of this function is
[tex] |4| = 4[/tex]
The period is 2π because there is no phase shift hence the period is still equal to the parent function.
Period: 2π , amplitude: 4
Answer:
The correct option is 3.
Step-by-step explanation:
The general form of a cosine function is
[tex]f(x)=A\cos (Bx+C)+D[/tex]
where, A is amplitude, 2π/B is period, C is phase sift and D is midline.
[tex]A=midline=\frac{Maximum-Minimum}{2}[/tex]
[tex]A=midline=\frac{4-(-4)}{2}[/tex]
[tex]A=midline=4[/tex]
The amplitude of the function is 4.
The given graph complete a cycle in the interval [0,2π], therefore the period of the graph is 2π.
Therefore the correct option is 3.