The correct answer is option d) \( 1+\tan x \), since \( \sec x=1+\tan x \).
The correct answer for the given expression \( \tan x \cdot \sin x+\cos x=? \) is option d) \( 1+\tan x \).
Step-by-step explanation:
We can start by using the identity \( \tan x = \frac{\sin x}{\cos x} \) to rewrite the expression:
\( \frac{\sin x}{\cos x} \cdot \sin x+\cos x=? \)
Next, we can simplify the expression by multiplying the numerator and denominator by \( \cos x \):
\( \frac{\sin^2 x+\cos^2 x}{\cos x}=? \)
Now, we can use the identity \( \sin^2 x+\cos^2 x=1 \) to further simplify the expression:
\( \frac{1}{\cos x}=? \)
Finally, we can use the identity \( \frac{1}{\cos x}=\sec x \) to rewrite the expression in terms of \( \sec x \):
\( \sec x=? \)
Therefore, the correct answer is option d) \( 1+\tan x \), since \( \sec x=1+\tan x \).
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whats the answer? I have to finish this quiz since I missed it
Answer:
Step-by-step explanation:
For this triangle, we can find the angle adjacent to side length 4 using trig:
tan(theta) = 7/4
theta = tan^-1(7/4)
theta = 60.26
Now we use sine to find x:
sin(60.26) = 7/x
x = 7/sin(60.26)
x = 8.06
I don't know how far you need to round, so it can either be this or 8.1
Hope this helps!
Find the measure of the central angle indicated. Lines that appear to be diameters, are diameters.
The measure of the central angle indicated is 60°.
Define central angle?The central angle of a circle is the angle that an arc takes up in the centre. The radius vectors are what make up the angle's arms.
The formula for calculating a central angle is: Central Angle = Arc length (AB) / Radius (OA) = (s 360°) / 2r, where "s" stands for arc length and "r" for circle radius.
Now here in the given diagram,
Let x equal the desired angle.
The central angle that we need to find is:
Now x = 360-120-(90+90)
⇒ x = 360-300
⇒ x = 60°
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Question 5 If \( A \) and \( B \) are \( 3 \times 3 \) matrices satisfying \( \operatorname{det} A=12 \) and \( \operatorname{det} B=3 \), then \( \operatorname{det}\left(2 A^{-1} B^{2}\right)= \) A 1
\( \operatorname{det}\left(2 A^{-1} B^{2}\right) = \frac{18}{12} = \frac{3}{2} \)Explanation: We are given that \( \operatorname{det} A=12 \) and \( \operatorname{det} B=3 \). We need to find the determinant of \( 2 A^{-1} B^{2} \). We can use the properties of determinants to simplify the expression. Recall that \( \operatorname{det}(cA) = c^n \operatorname{det}(A) \) for an \( n \times n \) matrix \( A \) and a scalar \( c \), and that \( \operatorname{det}(AB) = \operatorname{det}(A)\operatorname{det}(B) \). Using these properties, we can write:\( \operatorname{det}\left(2 A^{-1} B^{2}\right) = \operatorname{det}(2) \operatorname{det}(A^{-1}) \operatorname{det}(B^{2}) \)\( = 2^3 \operatorname{det}(A^{-1}) \operatorname{det}(B)^2 \)\( = 8 \cdot \frac{1}{\operatorname{det}(A)} \cdot (\operatorname{det}(B))^2 \)\( = 8 \cdot \frac{1}{12} \cdot (3)^2 \)\( = \frac{18}{12} = \frac{3}{2} \)Therefore, \( \operatorname{det}\left(2 A^{-1} B^{2}\right) = \frac{3}{2} \).
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If M<1 = 140 what is M <4
Answer:
I think its 560
Step-by-step explanation:
Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume the variable is positive.)
The properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms ln(√z) = (1/2)ln(z)
What is the logarithms?
Logarithms are mathematical functions that help to solve exponential equations. They are used to express very large or very small numbers in a more convenient and manageable way.
We can use the property of logarithms that states:
logb (a∙c) = logb a + logb c
to expand the expression as a sum of logarithms:
ln(√z) = ln(z^(1/2))
Using the power rule of logarithms, we can simplify this as:
ln(z^(1/2)) = (1/2)ln(z)
Hence, we can write:
ln(√z) = (1/2)ln(z)
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Failures have occurred at the following cumulative test times (Type II testing): 28, 146, 258, 426, 521, 1027, 1273 hours.
A) Fit the AMSAA growth model and estimate the MTTF at the conclusion of the test cycle.
B) On the basis of (A), how many more hours of test time will be necessary to achieve and MTTF of 3000 hours?
C) Assume that growth testing has resulted in achieving the desired MTTF of 3,000 hours. How many items must now be placed on test to obtain another 10 failures with 5,000 hours of test time available? (Assume a constant failure rate)
D) If the testing in (c) continues for only 600 more hours, what is the expected number
of failures?
AMSAA growth model
The MTTF at the conclusion of the test cycle is 232.59 hours. 22423.54 more hours of test time will be necessary to achieve and MTTF of 3000 hours. 52.15 items must now be placed on test to obtain another 10 failures with 5,000 hours of test time available. If the testing continues for only 600 more hours, 1.75 is the expected number of failures.
A) To fit the AMSAA growth model, we first need to calculate the cumulative number of failures (C) and the logarithm of the test time (lnT).
| Test Time (T) | C | lnT |
|---------------|---|-----|
| 28 | 1 | 3.33|
| 146 | 2 | 4.98|
| 258 | 3 | 5.55|
| 426 | 4 | 6.05|
| 521 | 5 | 6.26|
| 1027 | 6 | 6.93|
| 1273 | 7 | 7.15|
Next, we can use linear regression to estimate the parameters of the AMSAA model, β and η:
C = βlnT - η
Using linear regression, we get β = 1.11 and η = 3.82.
To estimate the MTTF at the conclusion of the test cycle, we can use the formula:
MTTF = (T/C)^(1/β)
Plugging in the values for T (1273), C (7), and β (1.11), we get:
MTTF = (1273/7)^(1/1.11) = 232.59 hours
B) To achieve an MTTF of 3000 hours, we need to solve for T in the equation: 3000 = (T/C)^(1/β)
Plugging in the values for C (7), β (1.11), and rearranging the equation, we get:
T = 3000^(β) * C = 3000^(1.11) * 7 = 23696.54 hours
Since we have already tested for 1273 hours, we need an additional 23696.54 - 1273 = 22423.54 hours of test time to achieve an MTTF of 3000 hours.
C) To obtain another 10 failures with 5000 hours of test time available, we can use the formula:
C = βlnT - η
Plugging in the values for C (10), β (1.11), η (3.82), and T (5000), and rearranging the equation, we get:
10 = 1.11ln(5000) - 3.82
ln(5000) = (10 + 3.82)/1.11 = 12.47
5000 = e^(12.47) = 260753.13
Therefore, we need to place 260753.13/5000 = 52.15 items on test to obtain another 10 failures with 5000 hours of test time available.
D) If the testing in (c) continues for only 600 more hours, we can use the formula:
C = βlnT - η
Plugging in the values for β (1.11), η (3.82), and T (600), and rearranging the equation, we get:
C = 1.11ln(600) - 3.82 = 1.75
Therefore, the expected number of failures in 600 more hours of testing is 1.75.
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I need help with these maths questions
Answer:
see explanation
Step-by-step explanation:
(a)
• the opposite sides of a rectangle are congruent
then
4x + 1 = 2x + 12
(b)
solving
4x + 1 = 2x + 12 ( subtract 2x from both sides )
2x + 1 = 12 ( subtract 1 from both sides )
2x = 11 ( divide both sides by 2 )
x = 5.5
(c)
the perimeter (P) is the sum of the 4 sides of the rectangle , that is
P = 4x + 1 + x + 2x + 12 + x ( collect like terms )
= 8x + 13 ( substitute x = 5.5 )
= 8(5.5) + 13
= 44 + 13
= 57
Answer:
a) Because two opposite sides of the rectangle have the same sizes
B)
[tex]x = \frac{11}{2} [/tex]
c)
[tex]57[/tex]
Step-by-step explanation:
b)
[tex]4x + 1 = 2x + 12 \\ 4x - 2x = 12 - 1 \\ 2x = 11 \\ \frac{2x}{2} = \frac{11}{2} \\ x = \frac{11}{2} [/tex]
c) Perimeter
[tex]p = 2(x + y) \\ 2( \frac{11}{2} + 23) \\ 2( \frac{57}{2} ) \\ 57[/tex]
23 comes from
[tex]2x + 12 \\ x = \frac{11}{2} \\ 2( \frac{11}{2} ) + 12 \\ 11 + 12 \\ \\ 23[/tex]
Point W(-6, 7) is rotated 90° clockwise where is W
Check the picture below.
pls help me
Let f(t) = 10 and g(t) = 65t. The distance, in miles, that a car is from a city can be modeled by f(t) + g(t), where t represents time, in hours. Riordan claims that the car is 150 miles from the city after 2 hours of driving, since (10 + 65) = 75(2) = 150. Decide if Riordan is correct. If he is correct, enter 150 below. If he is incorrect, enter the correct distance. miles
Answer: Using the given functions, we can model the distance, d(t), that the car is from the city as:
d(t) = f(t) + g(t) = 10 + 65t
So, after 2 hours of driving, the distance that the car has traveled from the city is:
d(2) = 10 + 65(2) = 10 + 130 = 140 miles
Therefore, Riordan is incorrect, and the correct distance the car is from the city after 2 hours of driving is 140 miles.
Step-by-step explanation:
Chose all the asswer that describe the quadrilateral ABCD if AB // CD, AB=9 CD=9
In the quadrilateral ABCD if AB ||CD and AB=9 as well as are CD=9. Then, quadrilateral ABCD is both parallelogram and trapezium.
Explain about the features of trapezium and parallelogram? A trapezium is still a two-dimensional quadrilateral with two parallel opposed sides that is made up of four straight lines. The base and legs of the trapezium are the opposing parallel sides, which are referred as the base and indeed the non-parallel sides, respectively. It has four sides plus four corners and is a closed plane shape.Parallelogram's characteristics
The different sides are distributed uniformly and parallel.Angles on either side are equal.The following or neighboring angles are supplemental.All of the angles will end up being right angles when any of them is a right angle.In the quadrilateral ABCD:
AB ||CD AB = CD = 9.Thus, the quadrilateral ABCD is both parallelogram and trapezium.
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College Algebua - „,1 Modellng with Quadratles Mahemet Koothall Thrun - Cine caact atswens, the and the fanctian ta ibcin your animen. - Show all necinary calnulations - Wrice par answis in ceptreste itriansich. reresest? 2. What a theytipenret' What dors it repericnt? Hha happris? ia at 10 irst be isurn wa fer be isle ta catis thin forchile College Algebra - 3.1 Modeling with QuadraticsMahomes Football Throw At a Kansas City Chiefs football practice, Patrick Mahomes is practicing his throws. He stands at one end of the football field and throws the ball. The ball's height, (in feet) as a function of horizontal distance,x(in feet), from Mahomes can be described by the following function:f(x)=−1201(x−88)2+151058- Give exact answers. Use only the function to obtain your answers. - Show all necessary calculations. - Write your answers in complete sentences. 1. What is the positivex-intercept? What does it represent? 2. What is they-intercept? What does it represent? 3. What is the maximum height that the foothall reaches?. What is the horizontal distance from Mahomes when this happens? 4. Travis Kelce is standing along the path of the football 160 feet from Patrick Mahomes. Travis can catch a ball that is at 10 feet or lower. Will he be able to catch this football? 5. What is the horizontal distance of the football from Patrick Mahomes when it first reaches a height of 40 feet?
1. The positive x-intercept of the function f(x)= -1201(x-88)^2 + 151058 is 88 feet.
2. The y-intercept of the function f(x) = -1201(x-88)^2 + 151058 is 151058 feet.
3. The maximum height that the football reaches is 151058 feet, and the horizontal distance from Patrick Mahomes when this happens is 88 feet.
4. Yes, Travis Kelce will be able to catch the football, since it reaches a height of 10 feet or lower at the horizontal distance of 160 feet from Patrick Mahomes.
5. The horizontal distance of the football from Patrick Mahomes when it first reaches a height of 40 feet is 176 feet.
1. The positive x-intercept represents the horizontal distance from Patrick Mahomes at which the football is initially released.
2. The y-intercept of the function represents the height of the football when it is released from Patrick Mahomes.
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#4:
Victoria is solving the equation x-3-4. Some
of her steps are shown below.
• equation 1: x-3=4 5
21
• equation 2:
2
3
X-3=
5
2
• equation 3: x-3+3=¹+3
21
5
Which statement correctly explains whether equation 3
in Victoria's work is valid in solving the equation?
It is not valid because because Victoria should subtract 3
instead of adding 3.
It is valid because -3+3=0.
It is not valid because Victoria did not also add 3 to
It is valid because because Victoria added the same amount
to each side of the equation.
The statement "It is valid because Victoria added the same amount to each side of the equation" correctly explains whether equation 3 in Victoria's work is valid in solving the equation.
What explanation is suitable?In equation 3, Victoria added 3 to both sides of the equation x-3=4/21. This operation is valid because she added the same amount (3) to both sides, which maintains the equality between the two sides of the equation. The resulting equation is x-3+3=4/21+3, which simplifies to x=4/21+63/21 or x=67/21.
Therefore, equation 3 is a valid step in solving the equation x-3=4/21.
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please help me for 20 poins!!
Answer: C, 2 2/8
Step-by-step explanation: To turn a mixed number into an improper fraction, multiply the whole number by the denominator. Then, add the numerator. So in this example it would be:
4 3/8 = 35/8
2 1/8 = 17/8
Now, since the denominators are equivalent, all we need to do is subtract the numerators.
35/8 - 17/8 = 18/8
The answer needs to be changed back to a mixed number. For this problem, there is an easy way to do this.
18/8 = 8/8 + 8/8 +2/8, which as a mixed number would be 2 2/8.
So the correct choice would be (C).
How to find the Zeros, Multiplicity, and Effect?
f(x)=-8x^(3)-20x^(2)
The Zeros of the equation would be x = -5/2.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given the equation as;
[tex]f(x)=-8x^3-20x^2[/tex]
We can factor;
4x^2 ( 2x+5)
Using the zero product property
2x = 0
2x + 5 = 0
x = -5/2
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A middle school basketball player makes a free throw with a probability of 0.6. Assuming each free throw is an independent event, what is the probability the player makes zero of their next three free throws? (A) 0.064 (B) 0.216 (C) 0.784 (D) 0.936 (E) None of these
A middle school basketball player makes a free throw with a probability of 0.6. Assuming each free throw is an independent event,the probability the player makes zero of their next three free throws is 0.064. The correct answer is A.
The probability that a middle school basketball player makes zero of their next three free throws can be calculated using the formula P(A) = P(A')ⁿ, where P(A) is the probability of the event occurring, P(A') is the probability of the event not occurring, and n is the number of trials.
In this case, P(A) is the probability of the player making zero free throws, P(A') is the probability of the player missing a free throw (1 - 0.6 = 0.4), and n is the number of free throws (3).
Using the formula, we can calculate the probability of the player making zero free throws as follows:
P(A) = P(A')ⁿ
P(A) = (0.4)³
P(A) = 0.064
Therefore, the correct answer is (A) 0.064.
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Keegan was asked to graph (R90•D2)(Triangle ABC). Explain Keegan’s error.
Keegan's error is that he did not provide enough information to fully determine the result of the given composition of transformations, namely (R90•D2)(Triangle ABC).
To be able to graph the image of Triangle ABC under the composition of R90 (a 90-degree counterclockwise rotation) and D2 (a dilation with center the origin and scale factor 2), we need to know the center of rotation for the rotation R90.
The reason for this is that the composition of a rotation and a dilation is not commutative, meaning that the order of the transformations matters. Specifically, the result of the composition depends on whether the dilation is applied before or after the rotation. If the dilation is applied before the rotation, then the center of dilation becomes the center of rotation for the rotation. If the rotation is applied before the dilation, then the center of dilation is not affected by the rotation.
Therefore, without knowing the center of rotation for the rotation R90, we cannot determine the exact result of the composition (R90•D2)(Triangle ABC), and thus we cannot graph it accurately.
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Concepts to make sure are (re)-discussed: Isolating the radical Checking for extraneous solutions Solving rational exponents in equations- more than one solution Sample problems: 1. V4x + 1 - Vx+ 10 = 2. V2x+30 = (x+3)
To solve the given equations, we need to follow these steps:
1. Isolate the radical on one side of the equation.
2. Square both sides of the equation to eliminate the radical.
3. Solve the resulting equation for the variable.
4. Check for extraneous solutions by plugging the solution back into the original equation.
5. If there are rational exponents, use the same steps but raise both sides of the equation to the reciprocal of the exponent.
Let's apply these steps to the sample problems:
1. V4x + 1 - Vx+ 10 = 2
First, isolate the radical on one side:
V4x + 1 = Vx+ 10 + 2
V4x + 1 = Vx+ 12
Next, square both sides to eliminate the radical:
(4x + 1) = (x+ 12)^2
4x + 1 = x^2 + 24x + 144
Solve for x:
0 = x^2 + 20x + 143
Using the quadratic formula:
x = (-20 ± √(20^2 - 4(1)(143)))/(2(1))
x = (-20 ± √(400 - 572))/2
x = (-20 ± √(-172))/2
x = (-20 ± √172i)/2
There are no real solutions for this equation.
2. V2x+30 = (x+3)
Isolate the radical:
V2x+30 = x+3
Square both sides:
2x + 30 = (x+3)^2
2x + 30 = x^2 + 6x + 9
Solve for x:
0 = x^2 + 4x - 21
Using the quadratic formula:
x = (-4 ± √(4^2 - 4(1)(-21)))/(2(1))
x = (-4 ± √(16 + 84))/2
x = (-4 ± √100)/2
x = (-4 ± 10)/2
x = 3 or x = -7
Check for extraneous solutions by plugging the solutions back into the original equation:
V2(3)+30 = (3+3)
V36 = 6
6 = 6 (True)
V2(-7)+30 = (-7+3)
V16 = -4
4 = -4 (False)
Therefore, the only solution is x = 3.
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There are 12 boys and 13 girls in my 3rd period class. How many pairs can I make if I choose
one boy and one girl?
A pack of 8 collectable cards contains 1 rare card, 3 uncommon cards, and 4 common cards. If Javier has 45 packs of cards, how many more uncommon cards does he have than rare cards?
Javier has 90 more uncommon cards than rare cards.
To find out how many more uncommon cards Javier has than rare cards, we need to multiply the number of packs he has by the number of each type of card in a pack, and then subtract the number of rare cards from the number of uncommon cards. We can do this with the following equation:
Uncommon cards - Rare cards = Difference
First, we'll multiply the number of packs by the number of each type of card:
45 packs × 3 uncommon cards = 135 uncommon cards
45 packs × 1 rare card = 45 rare cards
Now we'll subtract the number of rare cards from the number of uncommon cards to find the difference:
135 uncommon cards - 45 rare cards = 90
So, the number of uncommon cards is 90 more than the rare cards.
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Fifth order linear ODE with one real root r and two complex
roots a ± bi and c ± di. From the given information, determine its
general solution.
The general solution of a fifth order linear ODE with one real root r and two complex roots a ± bi and c ± di can be determined by using the fact that the general solution of a linear ODE is the sum of the solutions corresponding to each of the roots.
For the real root r, the solution is given by:
y1 = C1 * e^(r*x)
For the complex roots a ± bi, the solution is given by:
y2 = C2 * e^(a*x) * cos(b*x) + C3 * e^(a*x) * sin(b*x)
For the complex roots c ± di, the solution is given by:
y3 = C4 * e^(c*x) * cos(d*x) + C5 * e^(c*x) * sin(d*x)
The general solution of the fifth order linear ODE is the sum of these solutions:
y = y1 + y2 + y3
= C1 * e^(r*x) + C2 * e^(a*x) * cos(b*x) + C3 * e^(a*x) * sin(b*x) + C4 * e^(c*x) * cos(d*x) + C5 * e^(c*x) * sin(d*x)
This is the general solution of the fifth order linear ODE with one real root r and two complex roots a ± bi and c ± di.
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write these number in standard form seventeen thousand
Answer:
17,000
Step-by-step explanation:
17000 in words is written as Seventeen-thousand. The number 17000 represents a value equivalent to it.
need help with 7 A & B? “Quadratic Functions” algebra 1
The required solutions are as follows,
(a) The parabola will open downwards and have a maximum.
(b) The axis of symmetry for this function is t = 15.
A parabola is a cross-section cut out of the cone and represented by an equation shown in the question.
Here,
(a) The function C(t) is a quadratic function with a coefficient of -0.2 in front of the t² term. Since this coefficient is negative, the parabola will open downwards and have a maximum.
(b) The axis of symmetry of a quadratic function in the form of f(x) = ax² + bx + c is given by the formula x = -b/2a.
In this case, the function is C(t) = -0.2t² + 6t + 28.5, so a = -0.2 and b = 6. Thus, the axis of symmetry is:
t = -b/2a = -6/(2*(-0.2)) = 15
Therefore, the axis of symmetry for this function is t = 15.
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How to find the least common denominator of 1/6x + 3/8?
Answer:
Step-by-step explanation:
The least common denominator for 1/6 + 3/8 is 24
first find the multiples of 6 and 8
6= 6, 12, 18, 24, 30
8 = 8, 16, 24, 32
Next circle the number that appear in both
That number will be 24 which is the least common denominator.
A social media survey found that 75% of parents are "friends" with their children on a certain online networking site. A random sample of 160 parents was selected.
a. Calculate the standard error of the proportion.
b. What is the probability that 125 or more parents from this sample are "friends" with their children on this online networking site?
c. What is the probability that between 120 and 128 patents
The formula for standard error of proportion is √(pq/n) where p is the sample proportion, q = 1-p, and n is the sample size. Here, the sample proportion is 0.75, q is 0.25, and n is 160. Therefore, the standard error of proportion is √(0.75*0.25/160) = 0.035
The probability that between 120 and 128 patents (inclusive) are friends with their children can be calculated using the z-score formula:
z = (x - np)/√(npq)
where x is the number of parents between 120 and 128 who are friends with their children,
np = 160*0.75 = 120, and pq = 160*0.25 = 40.
Therefore,√(npq) = √(120*40) = 24.49
z = (120 - 120)/24.49 = 0
z = (121 - 120)/24.49 = 0.04
z = (122 - 120)/24.49 = 0.08
z = (123 - 120)/24.49 = 0.12
z = (124 - 120)/24.49 = 0.16
z = (125 - 120)/24.49 = 0.2
z = (126 - 120)/24.49 = 0.24
z = (127 - 120)/24.49 = 0.29
z = (128 - 120)/24.49 = 0.33
Using a z-table or a calculator, the probability that z is between 0 and 0.33 is 0.1292. Therefore, the probability that between 120 and 128 parents are friends with their children is 0.1292.
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Find the measurements of X
pt 3
Answer:
180 p
Step-by-step explanation:your welcome
Find the volume of the composite figure below.
Show work.
Answer:
1278in^3
Step-by-step explanation:
21×8=168
168×6=1008in^3
5×9=45
45×6=270in^3
1008+270=1278in^3
What is the volume of a cylinder with a radius of 3 feet and a height of 4 feet? Use 3.14 for pi. Round to the nearest hundredth.
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=4 \end{cases}\implies V=\pi (3)^2(4)\implies \stackrel{ \pi =3.14 }{V=113.04}[/tex]
In this caee there are no restricoions onb1b2, andbnso the zystern has the uniquex1=−40b1+16b2+9bj,x1=1b1−5b2−3b3+x1=5b2−2b2−bjfor all values ofb1,b2, andb3. Exercise set 1,6 7.−1x1+5x1=band using Theorm i.6. 2x1+2x2=b11.xk+x2=25x3+6x2=9 2. 4x1−5x3=−12x1−5x2=9the bri natue ike aviten 3.x1+3x2+x1=42x1+2x4+x1=−12x5+2x1+x4=4.4x3+3x2+2r5a 4 asind matrar fa tindu3xx+3xz+2xy=2xz+xn=5Q.x1−4x1=4x1+2x2+x2+x1L.B4=t1by=is.x+y+z=5 6. −x−2y−3z=0x+y−4z=10(y+x+4y+4z=7−4x+y+8=04.3x+7y+9z=4−ay−2x−4y−4tan 14. −x1+4x1+f1=x1+9x2+2x1=dx1+2r1=1r11b3=a1d2=1. Thue Iatsa Eneriaes.
It seems like the question is asking about a system of equations with no restrictions on the variables b1, b2, and b3. However, the question is filled with typos and formatting errors that make it difficult to understand the exact problem and provide an accurate answer. It would be best to ask the student to clarify the question and provide a properly formatted version of the problem before attempting to answer.
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Sides of three square rooms measure 13 feet each, and sides of two square rooms measure 15 feet each. Which expression shows the total area of these five rooms?
An expression that shows the total area of five rooms is (3 × 13²) + (2 × 15²)
The correct answer is an option (A)
Let 'a' represents the side length of the square rooms measuring 13 ft each and 'b' represents the side length of the square rooms measuring 15 ft each.
We know that the formula for the area of a square is A = s²
where 's' is the side of a square.
Sides of three square rooms measure 13 feet each.
So, the area of the three rooms would be:
A₁ = 3 × a²
A₁ = 3 × 13²
And sides of two square rooms measure 15 feet each.,
So, the area of the two rooms would be:
A₂ = 2 × b²
A₂ = 2 × 15²
Total area of the five rooms A = A₁ + A₂
So, we get an expression:
A = 3 × 13² + 2 × 15²
A = 3 × 169 + 2 × 225
A = 957 ft²
Therefore the total area of the five rooms be 957 ft².
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The complete question is:
Sides of three square rooms measure 13 feet each, and sides of two square rooms measure 15 feet each. Which expression shows the total area of these five rooms?
a.(3 × 13^2) + (2 × 15^2)
b.(2 × 13^3) + (2 × 15^2)
c.(3 × 15^2) + (2 × 13^2)
d.(3 × 13^2) × (2 × 15^2)
(2)
Solve the inequality 2r - 5 ≤ 9 and present your answer in interval
notation.
The solution to the inequality 2r - 5 ≤ 9 in interval notation is (-∞, 7].
To solve the inequality 2r - 5 ≤ 9, we need to isolate the variable r on one side of the inequality. Here are the steps to do so:
Step 1: Add 5 to both sides of the inequality to eliminate the -5 on the left side. This gives us: 2r ≤ 14Step 2: Divide both sides of the inequality by 2 to isolate the variable r. This gives us: r ≤ 7Now, we can present our answer in interval notation. Interval notation is a way to represent an interval on the number line. It is written in the form of [a, b], where a and b are the endpoints of the interval. The square brackets mean that the endpoints are included in the interval.
Since our inequality is r ≤ 7, our interval notation would be (-∞, 7], where -∞ represents negative infinity and 7 is the endpoint. The square bracket on the 7 means that 7 is included in the interval.
Therefore, the solution to the inequality 2r - 5 ≤ 9 in interval notation is (-∞, 7].
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