Answer:
x = (12-k)/2, y = k, z = (k-6)/4Step-by-step explanation:
Given the system of equation
x + y - 2z = 9 ... 1
3x + y + 2z = 15 ...2
x - 5y + 22z = -27... 3
First let us reduce the system of equation into two with two unknowns.
Subtracting 1 from 3
y-(-5y) + (-2z-22z) = 9-(-27)
y+5y + (-24z) = 9+27
6y-24z = 36 ... 4
Multiplying equation 1 by 3 and subtracting from equation 2
3x + 3y - 6z = 27
3x + y + 2z = 15
On subtracting both;
(3y-y)+(-6z-2z) = 27-15
2y-8z = 12 ... 5
Equating 4 and 5
6y-24z = 36 ... 4
2y-8z = 12 ... 5
Multiplying equation 5 by 3 the equation becomes;
6y-24z = 36 ... 6
6y-24z = 36 ... 7
We can see that equation 6 and 7 are the same;
let y = k
6k - 24z = 36
k - 4z = 6
4z = k-6
z = k-6/4
Substituting y = k and z = k-6/4 into equation 1 to get x
From 1; x + y - 2z = 9 ... 1
x + k -2( k-6/4) = 9
x + k - (k-6)/2 = 9
x = 9+(k-6)/2-k
x = {18+(k-6)-2k}/2
x = (12-k)/2
The solutions to the system of equations are x = (12-k)/2, y = k, z = (k-6)/4 where k is any constant. This shows that the system of equation has infinite solutions.
There are 100 people in a wedding house, including children, men and women, and there are 100 pappadas to give with Sadya Te.
5 pappadam for males
3 pappadams for women
1/2 pappadam for children
Then there are how many children there are, how many men, how many women
Answer:
Two possible sets of answers.
5 men, 11 women and 42 children, or
10 men, 2 women and 88 children
Selamat Sadhya!
Step-by-step explanation:
M = number of men
W = number of women
100-M-W = number of children
Total number of pappadas
5M+3W+(100-M-W)/2 = 100
Solve for W
W = (100-9M)/5 .......................(1)
Examine equation (1).
In order to have W as a whole number, M must be multiple of 5
Therefore M = 5 or 10
If M = 5, W = (100-45)/5 = 11 and children = 100-5-11 = 84
If M = 10, W = (100-90)/5 = 2 and children = 100-10-2 = 88
what is 1.8÷0.004? using long division
Answer:
Hi! Answer will be below.
Step-by-step explanation:
The answer is 450.
If you divide 1.8 and 0.004 the answer you should get is 450.
Below I attached a picture of how to do long division...the picture is an example.
Hope this helps!:)
⭐️Have a wonderful day!⭐️
Use an appropriate series to find Taylor series of the given function centered at the indicated value of a. Write your answer in summation notation.
sinx, a= 2π
Answer:
The Taylor series is [tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]
Step-by-step explanation:
From the question we are told that
The function is [tex]f(x) = sin (x)[/tex]
This is centered at
[tex]a = 2 \pi[/tex]
Now the next step is to represent the function sin (x) in it Maclaurin series form which is
[tex]sin (x) = \frac{x^3}{3! } + \frac{x^5}{5!} - \frac{x^7}{7 !} +***[/tex]
=> [tex]sin (x) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]
Now since the function is centered at [tex]a = 2 \pi[/tex]
We have that
[tex]sin (x - 2 \pi ) = (x-2 \pi ) - \frac{(x - 2 \pi)^3 }{3 \ !} + \frac{(x - 2 \pi)^5 }{5 \ !} - \frac{(x - 2 \pi)^7 }{7 \ !} + ***[/tex]
This above equation is generated because the function is not centered at the origin but at [tex]a = 2 \pi[/tex]
[tex]sin (x-2 \pi ) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x - 2 \pi)^{2n+1}][/tex]
Now due to the fact that [tex]sin (x- 2 \pi) = sin (x)[/tex]
This because [tex]2 \pi[/tex] is a constant
Then it implies that the Taylor series of the function centered at [tex]a = 2 \pi[/tex] is
[tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]
(SAT Prep) In the given figure, a║b. What is the value of x? A. 70° B. 45° C. 80° D. 65° I NEED THIS FAST PLZZZZZZ!!!!!!!!!!!!
Answer:
70
Step-by-step explanation:
You have to find the vertical of x. To the right of the vertical, we see that there is an angle of 25 (since the 25 up top corresponds to that blank angle). Once you add 25 + 85 + x = 180 (since this is a straight line), we see that x is 70, and its vertical is also 70.
Solve.
1/3-6<24
{s | s<6}
O {S | s < 10}
O {S | s < 54}
O {S | s < 90}
Answer:
The answer is:
The fourth option,
{s | s <90}
Step-by-step explanation:
yes
Answer:
[tex]\boxed{s|s<90}[/tex]
Step-by-step explanation:
1/3s-6<24
Add 6 on both sides.
1/3s<30
Multiply both sides by 3.
s<90
A bag contains two red marbles, four green ones, one lavender one, four yellows, and six orange marbles. HINT [See Example 7.] How many sets of four marbles include one of each color other than lavender
Answer:
192
Step-by-step explanation:
There are a total of 15 marbles . When the lavender is left out 14 remain.
Using combinations we find that each of the four color marbles can be chosen in the following way.
2C1*4C1*4C1*6C1= 2*4*4*6= 192
We select one of the two red marbles , one of the four green marbles, one of the four yellow marbles, one of the 6 orange marbles leaving the lavender out.. We apply combinations and then multiply to get the answer.
Could anyone help me with this? T+S+U=130 T=3(U) S= T+10 U= ?? I need to decipher the value of T,S and U.
Answer:
U = 17 1/7
T = 51 3/7
S = 61 3/7
Step-by-step explanation:
Given
T+S+U=130\
T=3(U)
S= T+10 we have to find value of u
First step:
find S and T in terms of U
T is given
T = 3U
S = T +10 , using T = 3U
S = 3U+10
Using the above value in T+S+U=130
3U + 3U+10 + U = 130
=> 7U = 130-10 = 120
=> U = 120/7 = 17 1/7
T = 3U = 3*120/7 = 360/7 = 51 3/7
S = T+10 = 360/7 + 10 = (360+70)/7 = 430/7 = 61 3/7
Thus,
U = 17 1/7
T = 51 3/7
S = 61 3/7
Which equation represents an exponential function with an intitial value of 500? f(x) = 100(5)^x, f(x) = 100(x)^5, f(x) = 500(2)^x, f(x) = 500(x)^2
Answer:
f(x) = 500(2)^x
Step-by-step explanation:
Let's assume the initial x value is 0
500(0)^2 = 0
100(0)^5 = 0
500(2)^0 = 500
500(0)^2 = 0
Answer:
C
Step-by-step explanation:
Edge
HELP WILL GIVE BRAINLIEST FOR ANSWER QUICKLY PLEASE HELP
Answer:
We have sinθ = 12/13
The method here is to figure out the value of θ
Using a calculator sin^(-1)(12/13) =67.38°
67.38° is in quadrant 1 so we must substract 67.38° from 180° wich is π
180-67.38= 112.61° ⇒ θ= 112.61°Now time to calculate cos2θ and cosθ using a calculator
cosθ = -5/13 cos2θ = -0.7The values we got make sense since θ is in quadrant 2 and 2θ in quadrant 3
Determine the value of X....... Please
Answer:
x is approximately 53°
Answer:52.64°
Step-by-step explanation:
opp=31
hyp=39
sin x° =[tex]\frac{opp}{hyp}[/tex]
sin x°=31/39
sin x°=0.7949
x=[tex]sin^{-1} (0.7949)\\[/tex]
x=52.64
i give you brailenst
Answer:
The answer is #3 which is 24%.
Step-by-step explanation:
6 × 100
25
25 into 100 is 4, then 6×4 = 24%
I really hope this helps :)
Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 18 of the 52 boxes on the shelf have the secret decoder ring. The other 34 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have the secret decoder ring?
Answer:
3/26
Step-by-step explanation:
Probability of the first box to have the secret decoder ring is 18 out of 52:
18/52= 9/26Probability of the second box to have the ring is 17 out of 51, because one box with the ring already selected and not counted:
17/51= 1/3Probability that both of them have the secret decoder ring:
9/26*1/3= 3/26So the answer is 3/26
Given: ∠N ≅ ∠S, line ℓ bisects at Q. Prove: ∆NQT ≅ ∆SQR Which reason justifies Step 2 in the proof? If two lines are parallel, then the corresponding angles formed are congruent. If two lines are parallel, then the alternate interior angles formed are congruent. Vertical angles are congruent. If two lines are parallel, then the same-side interior angles formed are congruent.
Answer:
Vertical angles are congruent.
Step-by-step explanation:
Vertical angles are opposite angles formed by intersecting lines, and are always congruent.
7987.1569 to the nearest thousandth
Answer:
7987.1569 to the nearest thousandths is 7987.157
Step-by-step explanation:
Two hundred undergraduate students were randomly selected from a university that has 47,000 students in total. Systolic blood pressure was tested on the 200 students. The sample mean is 118.0 mmHg and the sample standard deviation is 11.0 mmHg. Please construct a 95% confidence interval for the population mean of students' systolic blood pressure. Which one of the following results is the closest to your answer? (Hint: use 1.96 as the critical z-value)
a. [110.5, 125.5]
b. [112.5, 123.5]
c. [114.5, 121.5]
d. [116.5, 119.5]
Answer:
The correct option is d
Step-by-step explanation:
From the question we are told that
The population size is [tex]N = 47000[/tex]
The sample size is [tex]n = 200[/tex]
The sample mean is [tex]\= x = 118.0 \ mmHg[/tex]
The standard deviation is [tex]\sigma = 11.0 \ mmHg[/tex]
Given that the confidence level is 95% then the level of significance can be calculated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from z-table , the value is [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05 }{2} } = 1.96[/tex]
The reason we are obtaining critical value of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because
[tex]\alpha[/tex] represents the area under the normal curve where the confidence level interval ( [tex]1-\alpha[/tex]) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the margin of error .
NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } *\frac{\sigma }{ \sqrt{n} }[/tex]
substituting values
[tex]E = 1.96 *\frac{11.0 }{ \sqrt{200} }[/tex]
[tex]E = 1.5245[/tex]
The 95% confidence level interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]118.0 - 1.5245 < \mu < 118.0 + 1.5245[/tex]
[tex]116.5< \mu < 119.5[/tex]
[tex][116.5 , 119.5][/tex]
5-(m-4)= 2m+ 3 (m-1)
Answer: m= 2
Step-by-step explanation: First Expand the brackets! 5-m+4=2m+3m-3
Then Do the addition and subtraction in both sides!
9-m=5m-3
Then bring m to one side and the constants the other!
6m=12
Then solve for m where m=2
If you want you can check your answer bu substituting m as 2. 5-(2-4)=7 and 2(2) + 3(2-1) which also = 7.
Help ASAP!!!
Identify the correct trigonometry formula to use to solve for x.
Answer:
The answer is option 2.
Step-by-step explanation:
You have to apply Cosine Rule, cosθ = adjacent/hypotenuse. Then, you have to substitute the values into the formula :
[tex]cos(θ) = \frac{adj.}{hypo.} [/tex]
[tex]let \: θ = 55[/tex]
[tex]let \: adj. = 11[/tex]
[tex]let \: hypo. = x[/tex]
[tex]cos(55) = \frac{11}{x} [/tex]
The correct trigonometry formula to use to solve for x is [tex]\frac{11}{x}[/tex] . Thus option 1 is correct.
According to the question, we have
base = 11
hypotenuse = x
here for [tex]cos Ф[/tex]Ф, it is not required to find the value of perpendicular,
we know that in a right-angle triangle using trigonometric ratio, we get
[tex]cos Ф[/tex] Ф = [tex]\frac{base }{hypotenuse}[/tex]
[tex]cos Ф[/tex] Ф = [tex]\frac{11}{x}[/tex]
here Ф = [tex]55 ^0[/tex]
[tex]cos 55^o = \frac{11}{x}[/tex]
Thus, the value of the trigonometry formula to use to solve for x is [tex]\frac{11}{x}[/tex].
Thus option 1 is correct.
Learn more about Trigonometry here :
https://brainly.com/question/22986150
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the result of two forces acting on a body has a magnitude of 80 pounds. The angles between the resultant and the forces are 20 degrees and 52 degrees. find the magnitude of the large force
Answer:
Larger force= 66.28 pounds
Step-by-step explanation:
The angle of the resultant force 80 pounds = 180-(52+20)
The angle of the resultant force 80 pounds = 180-72
The angle of the resultant force 80 pounds = 108°
The larger force is the force with 52°
Let the larger force be x
Magnitude of the larger force
x/sin52 = 80/sin108
X= sin52 *(80/sin 108)
X= 0.7880*(80/0.9511)
X = 0.7780*(84.1131)
X = 66.28 pounds
rewrite(6+3)9using the distributive property of multiplication over Addition
Find the area of the shaded region.
Answer:
The answer would be 27π
Step-by-step explanation:
the area is 36pi and the shaded region is 3/4 of the circle, as a 90 degree angle is 1/4 of a 360 degree circle. 3/4 of 36pi is 27pi
Answer:
27π
Step-by-step explanation:
Imagine that this circle was complete. As you can see, only 3 / 4th of the circle remains, with respect to this whole circle. This is not an assumption, though it does appear so. The portion missing forms a right angle with the radii, and thus by definition, that portion is a quarter of a circle.
________
The simplest approach is to assume this circle to be complete, and solve for that area - provided the radii being 6 inches. Afterward we can take 3 / 4th of this area, solving for the area of the shaded region. After all, this circle is 3 / 4ths of our " complete circle. "
Area of an Imaginary " Complete Circle " = π[tex]r^2[/tex] = π[tex](6)^2[/tex] = 36π,
Area of Shaded Region ( 3 / 4th of the " Complete Circle " ) = [tex]\frac{3}{4}[/tex]( 36π ) = 27π
27π is the exact area of the shaded region. If you want an approximated area, take π as 3.14, or a similar quantity to that.
The perimeter of the rectangle below is 132 units.
Answer:
The answer is 29 unit.
Step-by-step explanation:
Here,
given that,
DC (l) =4z+1
CD (b)=5z+2
perimeter (p)= 132
now,
perimeter of rectangle (p) is= 2(l+b)
or, 132 = 2×{(4z+1)+(5z+2)}
or, 132= 2×(9z+3)
or, 132= 18z+6
or, 18z=132-6
or, z=126/18
or, z= 7.
therefore, 4z+1=4×7+1=29
5z+2= 5×7+2=37.
As our question is about to find AB,
DC = AB. (as opposite side of rectangle is equal).
so, the valueof AB is 29unit.
Hope it helps...
helpppppppppppppppppppppp pleaseeeeeeeeeeeeeeeeeeeeeee
Answer:
0.29
Step-by-step explanation:
There are 29 squares shaded in. In all, there are 100 squares in the 10 × 10 square, so there are 29 shaded squares out of 100 squares in all. That is basically:
[tex]\frac{29}{100}[/tex]
[tex]\frac{29}{100}[/tex] can be converted to 0.29.
Answer:
0.29
Step-by-step explanation:
Since the grid is a 10x10, it means there are 100 total 'blocks' in the grid. So, since there are 29 shaded in out of the 100 'blocks total, the decimal would be .29, since the decimal means 29 hundredths, and it also means that there is 29 hundredths of the total grid shaded in.
Question 15: (5 points)
Find one possibie missing coordinate so that the point becomes a solution to the given inequality.
(x, 7) is a solution to 2 x - 3<y.
=
In a few sentences, please explain how you arrived at your answer
Answer:
[tex](4,7)[/tex]
Step-by-step explanation:
Given
[tex]2x - 3 < y[/tex]
[tex](x,7)[/tex]
Required
Find one possible value of x
From the given parameters;
[tex](x,7)[/tex] is a possible solution of [tex]2x - 3 < y[/tex] where y= 7
Substitute 7 for y
[tex]2x - 3 < 7[/tex]
Add 3 to both sides
[tex]2x - 3 + 3 < 7 + 3[/tex]
[tex]2x < 10[/tex]
Divide both sides by 2
[tex]2x/2 < 10/2[/tex]
[tex]x < 5[/tex]
The result of the inequality implies that x is less than 5; So, the possible values of x is all real numbers less than 5;
Having said that;
[tex](4,7)[/tex] is one possible coordinate of [tex]2x - 3 < y[/tex]
Help ASAP!!!!
Find the cos(A). Reduce the ratio if necessary.
Answer:
[tex]\boxed{Cos A = 3/5}[/tex]
Step-by-step explanation:
Cos A = Adjacent/Hypotenuse
Where Adjacent = 30 and Hypotenuse = 50
Cos A = 30/50
Cos A = 3/5
Answer:
[tex]\boxed{\mathrm{cos(A) = \frac{3}{5} }}[/tex]
Step-by-step explanation:
[tex]\displaystyle \mathrm{cos(\theta) = \frac{adjacent}{hypotenuse} }[/tex]
The adjacent side to angle A is 30 units. The length of the hypotenuse of the triangle is 50 units.
[tex]\displaystyle \mathrm{cos(A) = \frac{30}{50} }[/tex]
The fraction can be simplified.
On an uphill hike Ted climbs at 3mph. Going back down, he runs at 5mph. If it takes him forty minutes longer to climb up than run down, then what is the length of the hike?
Answer:
10 miles
Step-by-step explanation:
3 mi/1 hr x (h hours + 2/3 hr) = 5 mi/1 hr x h hours
3h + 2 = 5h
2 = 2h
h = 1 hour
3mi/hr x 1 2/3 hr = 5 miles
5 mi/hr x 1 hr = 5 miles
He hiked 10 miles. (
Which of the following is 18x2/6x simplified?
3x
9x
4x
x/3
Answer:
3x
Step-by-step explanation:
18 x^2 / 6x
Divide the numbers
18/6 =3
Then divide the variables
x^2 /x = x
The result is 3x
Answer:
3x
Step-by-step explanation:
18x^2/6x
x^2 / x is x
18x/6
18/6 is 3
it all simplifies into 3x
help!! I have problem to solve this question
Answer:
Step-by-step explanation:
[tex]\frac{x-1}{2} =t\\\frac{y-2}{3} =t\\\frac{z-3}{4} =t\\so~eq.~of~line~L_{1}~is\\\frac{x-1}{2} =\frac{y-2}{3} =\frac{z-3}{4} \\its~d.r's~are~2,3,4\\again~\frac{x-2}{1} =s\\\frac{y-4}{2} =s\\\frac{z+1}{-4} =s\\so~eq. ~of~line~L_{2}~is\\\frac{x-2}{1} =\frac{y-4}{2} =\frac{z+1}{-4} \\its~d.r's ~are~1,2,-4\\let ~the ~d.r's~of~line~perpendicular~to~both~L_{1}~and~L_{2}~be~a,b,c,~then~\\2a+3b+4c=0\\1a+2b-4c=0\\solving\\\frac{a}{3*-4-4*2} =\frac{b}{4*1-2*-4} =\frac{c}{2*2-3*1} \\[/tex]
[tex]\frac{a}{-20} =\frac{b}{-4} =\frac{c}{1} \\d.r's~of ~reqd~line~is~-20,-4,1~or~20,4,-1[/tex]
now you find the point of intersection.
then calculate the angle.
What is the total amount of 2/5+5/3+9/3 and the lowest common denominator?
The lowest common denominator is lcm(5, 3), which is 15.
The sum of 2/5 + 5/3 + 9/3 is 6/15 + 25/15 + 45/15, which is 76/15 or [tex]5\frac{1}{15}[/tex].
what is the answer. plz heelp 5h+2(11-h)= -5
Answer:
h = -9
Step-by-step explanation:
5h+2(11-h)= -5
Distribute
5h +22 -2h = -5
Combine like terms
3h +22 = -5
Subtract 22 from each side
3h +22-22 = -5-22
3h = -27
Divide by 3
3h/3 = -27/3
h = -9
Determine whether the following problem involves a permutation or a combination and explain your answer. How many different -letter passwords can be formed from the letters , , , , , , and if no repetition of letters is allowed? Choose the correct answer below. A. The problem involves a permutation because the order in which the letters are selected does matter. B. The problem involves a combination because the order in which the letters are selected does not matter. C. The problem involves a combination because the order in which the letters are selected does matter. D. The problem involves a permutation because the order in which the letters are selected does not matter.
Answer:
B. The problem involves a combination because the order in which the letters are selected does not matter.
Step-by-step explanation:
Computation technique is a method of statistics to find possible ways of combination. In computation technique it is assumed that order does not matter and letters will be selected at random. Permutation is a statistics technique to find possible ways of combination when the order does matter. Permutation technique cannot be used when order does not matter.