Find the intersection of the two planes. Do this by solving for z in terms of x and y ; then solve for y in terms of x ; then again for z but only in terms of x.
-4x + 2y - z = 1 ==> z = -4x + 2y - 1
3x - 2y + 2z = 1 ==> z = (1 - 3x + 2y)/2
==> -4x + 2y - 1 = (1 - 3x + 2y)/2
==> -8x + 4y - 2 = 1 - 3x + 2y
==> -5x + 2y = 3
==> y = (3 + 5x)/2
==> z = -4x + 2 (3 + 5x)/2 - 1 = x + 2
So if we take x = t, the line of intersection is parameterized by
r(t) = ⟨t, (3 + 5t )/2, 2 + t⟩
Just to not have to work with fractions, scale this by a factor of 2, so that
r(t) = ⟨2t, 3 + 5t, 4 + 2t⟩
(a) The tangent vector to r(t) is parallel to this line, so you can use
v = dr/dt = d/dt ⟨2t, 3 + 5t, 4 + 2t⟩ = ⟨2, 5, 2⟩
or any scalar multiple of this.
(b) (-1, -1, 1) indeed lies in both planes. Plug in x = -1, y = 1, and z = 1 to both plane equations to see this for yourself. We already found the parameterization for the intersection,
r(t) = ⟨2t, 3 + 5t, 4 + 2t⟩
Write the sentence as an inequality. The cost of a ticket t will be no more than $52.
Answer:
t is less than or equal to $52, or t <= $52
Step-by-step explanation:
If you can't have more than $52, then use less than symbol (<). The sentence doesn't state that a ticket shouldn't cost $52, so it's safe to assume that you can have exactly $52.
A road crew must repave a road that is 2/3 miles long. They can repave 1/12 miles each hour. How long will it take the crew to repave the road?
Write your answer in simplest form.
The value of the expression 23 +32–3x4–52-5+(7x4) is
Answer:
24
Explanation:
(23+32)-(3×4)-(52-5)+(7×4)
(55)-(12)-(47)+(28)
55-12=43-47+28= -1943-19=24Evaluate −a2+c2 when c=−4.
Answer:
[tex]a = 4, -4[/tex]
Step-by-step explanation:
Step 1: Plug in -4 for c
[tex]-a^{2} + c^{2}[/tex]
[tex]-a^{2} + (-4)^{2}[/tex]
[tex]-a^{2} + 16[/tex]
Step 2: Solve for a
[tex]-a^{2}+16-16=0-16[/tex]
[tex]-a^{2}/-1 = -16/-1[/tex]
[tex]a^{2} = 16[/tex]
[tex]\sqrt{a^{2}} = \sqrt{16}[/tex]
[tex]a = 4, -4[/tex]
Answer: [tex]a = 4, -4[/tex]
MIN-
Bill is measuring a piece of material for some curtains.
It is 215 cm wide, how many mm is this?
There are 10 mm in 1 cm.
mm
Answer:
2,150 mm
Step-by-step explanation:
If every cm is 10 mm you multiply 215 by 10. I hope this helped!
How do u determine the equation of the line through each pair of points in slope-intercept form (y=mx+b). (3,0) and (2,4) (-6,3) and (2,-2)
Answer:
Y =-4X +12
Y =-0.625X -0.75
Step-by-step explanation:
(3,0) and (2,4)....
x1 y1 x2 y2
3 0 2 4
(Y2-Y1) (4)-(0)= 4 ΔY 4
(X2-X1) (2)-(3)= -1 ΔX -1
slope= -4
B= 12
Y =-4X +12
~~~~~~~~~~~~~~~~~
(-6,3) and (2,-2)
x1 y1 x2 y2
-6 3 2 -2
(Y2-Y1) (-2)-(3)= -5 ΔY -5
(X2-X1) (2)-(-6)= 8 ΔX 8
slope= - 5/8
B= - 3/4
Y =-0.625X -0.75
(a). Find the value of log 216.
Answer:
2.334453751
Step-by-step explanation:
Press log on your Casio calculator (if you have one) and plug in 216, then close the parentheses!
PLEASE ANSWER I WILL GIVE BRAINLIEST FAST
Answer:
E &F
Step-by-step explanation:
The rules of a 30-60-90 Triangle is E, and F is just a different value of numbers (but the same ratio).
Find the perimeter and area of a square with sides 6 inches in length.
Which of the following is NOT equivalent to 22/7?
a) 2 + 8/7
b) 1 + 15/7
c) 3 (7/1) + 1/7
d) 3 (7/7) + 1/7
Answer:
the option c is the answer for this question
What is the squad root of 81
Answer:
[tex]9[/tex]
Step-by-step explanation:
Step 1: Find the square root of 81
[tex]\sqrt{81}[/tex]
[tex]\sqrt{9*9}[/tex]
[tex]\sqrt{9^{2}}[/tex]
[tex]9[/tex]
Answer: [tex]9[/tex]
Answer:
the square root of 81 is 9
The angles in a triangle are 89, 1, and 90 degrees. Classify the triangle by its angles and sides.
A. Right isosceles
B. Right Scalene
C. Obtuse scalene
D. Acute isosceles
E. Acute scalene
F. Obtuse isosceles
Answer: B. Right Scalene
Step-by-step explanation: Right because one of the degrees is 90 and scalene because no of the sides of the triangle are the same length.
Answer:
b
Step-by-step explanation:
A pyramid art installation has a surface area of 24 m2. An artist creates replicas with scale factors of 1/8, 1/10, and 1/12. What is the surface area of each replica?
Answer:
The replicas will have a surface area of 3 m2, 2.4 m2 and 2 m2 respectively.
Step-by-step explanation:
Given that a pyramid art installation has a surface area of 24 m2, and an artist creates replicas with scale factors of 1/8, 1/10, and 1/12, to determine what is the surface area of each replica, the following calculation has to be done:
24 x 1/8 = 3
24 x 1/10 = 2.4
24 x 1/12 = 2
Therefore, the replicas will have a surface area of 3 m2, 2.4 m2 and 2 m2 respectively.
Answer:
1/8 = 0.38 m^2
1/10= 0.24 m^2
1/12= 0.17 m^2
Step-by-step explanation:
A sign on the gas pumps of a chain of gasoline stations encourages customers to have their oil checked with the claim that one out of four cars needs to have oil added. If this is true, what is the probability of the following events?
a. One out of the next four cars needs oil.
b. Two out of the next eight cars needs oil.
c.Three out of the next 12 cars need oil.
Answer:
a) 0.4219 = 42.19% probability that one out of the next four cars needs oil.
b) 0.3115 = 31.15% probability that two out of the next eight cars needs oil.
c) 0.2581 = 25.81% probability that three out of the next 12 cars need oil.
Step-by-step explanation:
For each car, there are only two possible outcomes. Either they need oil, or they do not need it. The probability of a car needing oil is independent of any other car, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
One out of four cars needs to have oil added.
This means that [tex]p = \frac{1}{4} = 0.25[/tex]
a. One out of the next four cars needs oil.
This is P(X = 1) when n = 4. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{4,1}.(0.25)^{1}.(0.75)^{3} = 0.4219[/tex]
0.4219 = 42.19% probability that one out of the next four cars needs oil.
b. Two out of the next eight cars needs oil.
This is P(X = 2) when n = 8. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{8,2}.(0.25)^{2}.(0.75)^{6} = 0.3115[/tex]
0.3115 = 31.15% probability that two out of the next eight cars needs oil.
c.Three out of the next 12 cars need oil.
This is P(X = 3) when n = 12. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{12,3}.(0.25)^{3}.(0.75)^{9} = 0.2581[/tex]
0.2581 = 25.81% probability that three out of the next 12 cars need oil.
At the beginning of an experiment, a scientist has 120 grams of radioactive goo. After 135 minutes, her sample has decayed to 3.75 grams. Find an exponential formula for G ( t ) G(t) , the amount of goo remaining at time t t .
Answer:
[tex]G(t) = 120e^{-0.0257t}[/tex]
Step-by-step explanation:
Amount of substance:
The amount of the substance after t minutes is given by:
[tex]G(t) = G(0)e^{-kt}[/tex]
In which G(0) is the initial amount and k is the decay rate.
At the beginning of an experiment, a scientist has 120 grams of radioactive goo.
This means that [tex]G(0) = 120[/tex], so:
[tex]G(t) = G(0)e^{-kt}[/tex]
[tex]G(t) = 120e^{-kt}[/tex]
After 135 minutes, her sample has decayed to 3.75 grams.
This means that [tex]G(135) = 3.75[/tex].
We use this to find k. So
[tex]G(t) = 120e^{-kt}[/tex]
[tex]3.75 = 120e^{-135k}[/tex]
[tex]e^{-135k} = \frac{3.75}{120}[/tex]
[tex]\ln{e^{-135k}} = \ln{\frac{3.75}{120}}[/tex]
[tex]-135k = \ln{\frac{3.75}{120}}[/tex]
[tex]k = -\frac{\ln{\frac{3.75}{120}}}{135}[/tex]
[tex]k = 0.0257[/tex]
So
[tex]G(t) = 120e^{-0.0257t}[/tex]
Someone help me?????
Step-by-step explanation:
4. b 612 (72/100) x 850)
5. c. 275 (33/100) x 835
6. b. 39% (3.24 - 2.85) x100%)
What is the slope formula?
Answer:
D is your answer
Step-by-step explanation:
Answer:
Here the slope formula m = ( y 2 − y 1 )/( x 2 -x 1 ) = Δy/Δx
Step-by-step explanation:
Which graph represents the function f (x) = StartFraction 5 minus 5 x squared Over x squared EndFraction? On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens up and to the left in quadrant 2. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens up and to the left in quadrants 2 and 3. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 2, and the other curve opens up and to the left in quadrant 3. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrants 3 and 4.
9514 1404 393
Answer:
2. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens up and to the left in quadrants 2 and 3
Step-by-step explanation:
Technically, the curve is not a hyperbola. A hyperbola is of the form 1/x; this one is of the form 1/x².
The function can be simplified to ...
f(x) = 5/x² -5
which is a "hyperbola" with a vertical asymptote at x=0 and a vertical translation of -5 units to bring parts of it into the 3rd and 4th quadrants.
Avi uses 11 toothpicks to form a row of 5 attached triangles, as shown. Suppose he continues this pattern, using 89 toothpicks in all. What is the total number of triangles formed? (sorry the picture wasn't uplodaing)
Answer:
44
Step-by-step explanation:
Given that Avi used 11 toothpicks to form a row of 5 attached triangles.
Total number of toothpicks used = 89
Let the total number of triangles formed be represented by x, so that:
11 toothpicks = 5 triangles
It would be observed that only the first triangle starting the pattern has 3 toothpicks. So that;
the average number of toothpicks for 1 triangle = [tex]\frac{11}{5}[/tex]
= 2.2
The number of toothpicks per triangle = 2.0
Thus,
x = [tex]\frac{89}{2.0}[/tex]
= 44.5
x = 44
The total number of triangles formed is 44.
Didi invested a total of $16125 in two accounts paying 8.5% and 4% simple interest. If her total return at the end of 2 years was 1740 , how much did she invest in each account?
Answer:
5000 ;
11125
Step-by-step explanation:
Given :
Total principal = 16125
Rates = 8.5% and 4%
Period, t = 2 years
Total interest = 1740
Let :
Principal amount invested at 8.5% = x
Principal amount invested at 4% = 16125 - x
Interest formula :
Interest = principal * rate * time
Hence, mathematically ;
(x * 8.5% * 2) + [(16125 - x) * 4% * 2] = 1740
(0.17x + 1290 - 0.08x ) = 1740
0.09x + 1290 = 1740
0.09x = 1740 - 1290
0.09x = 450
x = 450 / 0.09
x = 5000
Amount invested at 4% :
16125 - 5000 = 11125
Annual income: The mean annual income for people in a certain city (in thousands of dollars) is 41, with a standard deviation of 28. A pollster draws a sample of 92
people to interview.
Answer:
By the Central Limit Theorem, the distribution of the sample means is approximately normal with mean 41 and standard deviation 2.92, in thousands of dollars.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 41, standard deviation of 28:
This means that [tex]\mu = 41, \sigma = 28[/tex]
Sample of 92:
This means that [tex]n = 92, s = \frac{28}{\sqrt{92}} = 2.92[/tex]
Distribution of the sample means:
By the Central Limit Theorem, the distribution of the sample means is approximately normal with mean 41 and standard deviation 2.92, in thousands of dollars.
For this exercise assume that the matrices are all nn. The statement in this exercise is an implication of the form "If "statement 1", then "statement 2"." Mark an implication as True if the truth of "statement 2" always follows whenever "statement 1" happens to be true. Mark the implication as False if "statement 2" is false but "statement 1" is true. Justify your answer.
If there is an n x n matrix D such that Ax =0, then there is also an nxn matrix C such that CAI.
a. True
b. False
Answer:
A) True
Hope this helps!
What is the domain of the relation described by the set of ordered pairs (-2,8), (-1,1) (0,0) (3,5), (4,-2)?
Step-by-step explanation:
(-2,-1,0,3,4) are the domain
(x,y)=(domain,range)
simply x components are the domain whereas y components are the range
The longest leg is Select one:
a. 5√3
b. 10√3
c. 5
d. 20
Answer:
D:20
sqrt(3) is less than 2 thus 10*sqrt(3) is less than 20
Step-by-step explanation:
ms.+sanchez+bought+3+pounds+of+turkey+to+make+sandwiches+for+her+family+.+She+uses+.25+of+a+pound+for+each+sandwich+.+How+many+sandwiches+can+she+make+?
Answer:
she can make 12 sandwiches
Step-by-step explanation:
3/.25 is the solution
find the exact value of tan -75
How do you know if a radical can be simplified? Explain.
Answer:
An expression is considered simplified only if there is no radical sign in the denominator. If we do have a radical sign, we have to rationalize the denominator . This is achieved by multiplying both the numerator and denominator by the radical in the denominator.
The diameter of a circle is inches what is the area?
Answer:
Pie( r ^2)
Step-by-step explanation:
Here value of r is in inches
Answer quick please.
Answer
The Answer is A C D
Step-by-step explanation:
You need to solve a system of equations. You decide to use the elimination method. Which of these is not allowed? 2x - 3y = 12
-x + 2y = 13
O A. Multiply the left side of equation 2 by 2. Then subtract the result from equation 1.
O B. Multiply equation 1 by 2 and equation 2 by 3. Then add the new equations.
C. Multiply equation 2 by-2. Then add the result to equation 1.
Answer:
A.
Step-by-step explanation:
The Elimination Method is the method for solving a pair of linear equations which reduces one equation to one that has only a single variable.
If the coefficients of one variable are opposites, you add the equations to eliminate a variable, and then solve.
If the coefficients are not opposites, then we multiply one or both equations by a number to create opposite coefficients, and then add the equations to eliminate a variable and solve.
When multiplying the equation by a coefficient, we multiply both sides of the equation (multiplying both sides of the equation by some nonzero number does not change the solution).
So, option B is not allowed (it is not allowed to multiply only one part of the equation)
