The intersection of two planes can be found by solving the system of equations formed by the equations of the planes. In this case, the intersection is given by the equations x = (4 - 9y) / 6, y = y, and z = -3 - (23y/6), where y can be any real number.
Explanation:The intersection of two planes can be found by solving the system of equations formed by the equations of the planes.
To find the intersection, we can set the two equations equal to each other and solve for x, y, and z.
Rewrite the equations in standard form: 5x - 5 + 2y + z + 1 = 0 and x - 1 + 7y - z - 1 = 0Add the equations together: 6x + 9y = 4Solve for x in terms of y: x = (4 - 9y) / 6Substitute the value of x into one of the original equations to solve for z: 5((4 - 9y) / 6 - 1) + 2y + (z + 1) = 0Simplify and solve for z: z = -3 - (23y/6)Therefore, the intersection of the two planes is given by the equations x = (4 - 9y) / 6, y = y, and z = -3 - (23y/6), where y can be any real number.
Miss Cohan purchased a bottle of vitamins for $7.99 a bottle of aspirin for $6.49 and a bottle of mouthwash for $2.99 she gave the clerk two $10 bills how much change did she receive
what is the vertex of -3x^2 - x + 12
Find the zeros and state whether the multiplicity of each zero is even or odd. What are the zeros of f?
it is given that ln(y+1) - ln(y) = 1+3ln(x) . express y in terms of x in a form not involving logarithms
We transformed the logarithmic equation ln(y+1) - ln(y) = 1 + 3ln(x) into an algebraic expression, resulting in y = 1 / (e × [tex]x^3[/tex] - 1).
To express y in terms of x from the given equation ln(y+1) - ln(y) = 1 + 3ln(x), we can follow these steps:
Apply the logarithm property ln(a) - ln(b) = ln(a/b): ln((y+1)/y) = 1 + 3ln(x).Rewrite the right-hand side using exponentiation: ln((y+1)/y) = ln(e) + 3ln(x) = ln(e × [tex]x^3[/tex]).Since the natural logarithms are equal, set their arguments equal to get the equation without logarithms: (y+1)/y = e × [tex]x^3[/tex].Isolate y by solving the above equation: y + 1 = y × e × [tex]x^3[/tex], hence y = 1 / (e × [tex]x^3[/tex] - 1).This gives us the final expression of y in terms of x without involving logarithms.
7^18/7^5 simplifies to 7^p is the value of p 3?
can u show me common core way how to get the answer to this problem 4 1/5. ×4 3/8
Rita makes and sells necklaces. The materials to make each necklace cost $2.75. Last week she made 8 necklaces and wants to make a total profit of $78. Using the equation 8(x+2.75)=78, Rita determined that she needs to sell each necklace for $7 to make a total profit of $78. Which error did Rita make?
Answer:
Rita made a sign error.
Step-by-step explanation:
Let x be the selling price of each necklace.
We are told that the materials to make each necklace cost $2.75.
Since profit is the difference between selling price and cost.
[tex]\text{Profit}=\text{Selling price- Cost}[/tex]
So profit of Rita from selling one necklace will be:
[tex]\text{Profit of Rita from 1 necklace}=x-2.75[/tex]
To find the profit of Rita from selling 8 necklace we will multiply 8 by profit of 1 necklace.
[tex]\text{Profit of Rita from 8 necklaces}=8(x-2.75)[/tex]
As Rita wants to make a total profit of $78 from selling 8 necklaces, so we will substitute 78 as profit of 8 necklaces.
[tex]78=8(x-2.75)[/tex]
Upon comparing our equation with the given equation we can see that Rita made a sign error as she added the cost with the selling price instead of subtracting the cost from selling price.
Let us find the selling price.
[tex]78=8x-22[/tex]
[tex]78+22=8x[/tex]
[tex]100=8x[/tex]
[tex]\frac{100}{8}=x[/tex]
[tex]12.5=x[/tex]
We can see that the selling price of each necklace will be 12.5, therefore, Rita made a sign error.
The triangular shaped bases of a prism are 24 cm in length and have a height of 35 cm. Each side is 37 cm. The height of the prism is 29 cm. What is the surface area of the triangular prism? A) 2192 cm2 B) 2312 cm2 C) 3220 cm2 D) 3682 cm2
A company invests a total of $40 comma 00040,000 of surplus funds at two annual rates of interest: 55% and 66one half 1 2%. It wishes an annual yield of no less than 6one fourth 1 4%. What is the least amount of money that the company must invest at the 66one half 1 2% rate? The company should invest at least how much money
at 66one half 1 2%.
Evaluate the expression.
r = <9, -7, -1>, v = <2, 2, -2>, w = <-5, -2, 6>
v ⋅ w
A) <-18, 14, -2>
B) -26
C) 1
D) <-10, -4, -12>
the above person lied and used bots for 5 star ratings the real answer is 6.
Evaluate the expression.
r = <9, -7, -1>, v = <2, 2, -2>, w = <-5, -2, 6>
v ⋅ r (3 points)
<18, -14, 2>
You Answered -26
1
Correct Answer 6
The price of a bicycle was increased from $300 to $450. What percent of the original price is the increased price?
The percentage increase is 50% than the original price.
The price of a bicycle was increased from $300 to $450. What percent of the original price is the increased price?
Calculate the increase: $450 - $300 = $150.
Calculate the percentage increase: ($150 / $300) x 100% = 50%.
What is 8587 divided by 12
The shorter leg of a 30°-60°-90° triangle measures 3 inches. What is the length of the hypotenuse?
A. 6 inches
B. 3sqrt3 inches
C. 9 inches
D. 6sqrt3 inches
how to set the answer up
Let s and g represents the numbers of suits and gowns produced.
The number of zippers used is 2s+g.
The number of buttons used is 5s+8g.
In order to use all of the available zippers and buttons, we must have ...
2s + g = 1715s + 8g = 576Cramer's rule tells you the solution to the system
ax +by = cdx +ey = fIs given by
x = (bf-ey)/(bd-ea)y = (cd-fa)/(bd-ea)Using this rule on the equations for zippers and buttons, we have
... s = (1·576 -8·171)/(1·5 -8·2) = -792/-11 = 72
... g = (171·5 -2·576)/-11 = -297/-11 = 27
72 suits and 27 gowns can be made from available zippers and buttons.
what is 7 × (12 + 8) - 6=
Jose can spend no more than 24$ to buy oranges and apples. He will pay 3$ per pound for oranges and $4 per pound for apples. Draw a graph that represents the number of pounds of oranges as the number of pounds of apples Jose can buy.
Hint First, write an inequality. Then, find the x and y intercepts to draw your line. Consider whether you need a solid or dotted line. Do not forget to shade.
When 18 boys joined a group of why students, the ratio of boys to girls in the group became 4 : 5. Write an algebraic expression for the number of girls in terms of Y.
According to the Rational Root Theorem, which number is a potential root of f(x) = 9x8 + 9x6 – 12x + 7?
Answer:
All the potential root of f(x) are [tex]\pm 1,\pm7, \pm \frac{1}{3},\pm \frac{7}{3}, \pm \frac{1}{9},\pm \frac{7}{9}[/tex].
Step-by-step explanation:
According to the rational root theorem, all the potential root of f(x) are defined as
[tex]x=\pm\frac{p}{q}[/tex]
Where, p is factor of constant term and q is factor of leading coefficient.
The given function is
[tex]f(x)=9x^8+9x^6-12x+7[/tex]
Here, constant term is 7 and leading coefficient is 9.
Factors of 7 are ±1, ±7 and the factors of 9 are ±1, ±3, ±9.
Using rational root theorem, all the potential root of f(x) are
[tex]x=\pm 1,\pm7, \pm \frac{1}{3},\pm \frac{7}{3}, \pm \frac{1}{9},\pm \frac{7}{9}[/tex]
Therefore all the potential root of f(x) are [tex]\pm 1,\pm7, \pm \frac{1}{3},\pm \frac{7}{3}, \pm \frac{1}{9},\pm \frac{7}{9}[/tex].
There are 96 raisins and 24 cashews in each package of granola. What is the unit rate in raisins per cashew?
4
12
20
96
Prove: tan(x-y)+tan(y-z)+tan(z-x)=tan(x-y)tan(y-z)tan(z-x)
Find the expected number of pairs of different people, a and b, such that a picks b's name and b picks a's name. g
Which statement about the following argument is true?
Argument:
If it snows, the roads will get slippery.
It's snowing.
Therefore, the roads are slippery.
A:The argument is valid by the Law of Syllogism.
B: The argument is valid by the Law of Detachment.
C: The argument is invalid.
D: The argument is valid but does not follow the Law of Syllogism or the Law of Detachment.
Which is not a characteristic of an exponential parent function?
A. The range is positive real numbers (y > 0).
B. The domain is all real numbers.
C. It goes through the origin.
D. It passes through (0, 1).
Answer:C. It goes through the origin
Step-by-step explanation:
Answer:
Option C) It goes through the origin.
This is the wrong statement about the parent exponential function.
Step-by-step explanation:
We are given the following:
The characteristic of exponential parent function:
[tex]f(x) = y = b^x\\\text{where b is the base}[/tex]
A) True
The range is all positive number that is y > 0
Range can never be negative.
B) True
The domain is all real number.
C) False
It does not pass through origin.
[tex]y = f(0) = b^0 = 1[/tex]
D) True
It always passes through (0,1) as shown above.
In the figure. d=4 yd, h=6 yd, and H=8 yd. What is the approximate volume of the figure? Use 3.14 to approximate
Answer: 84yd
Step-by-step explanation:
Vcylinder=πr2h
=π(2)2(6)
=24π
≈24(3.14)
≈75.36 yd
_____________________
The height of the cone is the height of the figure minus the height of the cylinder:
8 yd−6 yd=2 yd
Vcone=13πr2h
=13π(2)22
=223π
≈223(3.14)
≈8.37 yd3
Add the volumes.
75.36 yd3+8.37 yd3=83.73 yd3
To the nearest cubic yard, the volume is 84 yd3.
For a fixed loan amount, what happens to the monthly payment as the annual rate increases? a. as the annual rate increases, the monthly payment increases c. as the annual rate increases, the monthly payment stays the same b. as the annual rate increases, the monthly payment decreases d. no correlation
Answer:
c. as the annual rate increases, the monthly payment stays the same.
Step-by-step explanation:
A loan is an amount of money given by individuals, organizations to borrower over a period of time and to repay the principal amount with interest.
A fixed loan amount means that a borrower pays the same amount through each stage of agreed payment of the loan. The amount paid installmentally should not vary or fluctuate during the life of the loan. The amount paid by the borrower every month is fixed, thereby ensures that the loan is paid off in full with interest at the end of its term. As the annual rate increases, the monthly payment stays the same but the number of years may increase.
Paul and jose are trying to measure the height of a tree. paul is standing 19m from the foot of the tree and measures the angle of elevation to the top of the tree to be 59o. jose measures it to be 43o, how far is jose from the base of the tree?
Here is a list of ingredients for making cherry scones: Makes 8 cherry scones 200 grams flour 60 grams margarine 40 grams sugar 60 grams cherries 160 ml milk Sophie has 80 grams of sugar and 300 grams of flour. She has plenty of the other ingredients. What is the greatest number of cherry scones she can make?
You are a builder and need to submit an estimate to a customer for remodeling a bathroom. Your project costs are $451.75 for labor, $332.52 for materials and $289.12 for subcontracting for plumbing. Round these amounts to whole numbers to estimate the cost of the total project.
(Will give Brainliest/5 Stars if correct answer)
Find the angle between the given vectors to the nearest tenth of a degree.
u = <8, 4>, v = <9, -9>
A) 81.6°
B) 25.8°
C) 35.8°
D) 71.6°
Answer:
71.6°
Step-by-step explanation:
arctan(4/8) - arctan(-9/9) = 26.57° - (-45°) ≈ 71.6°
How much interest is earned on $269 at 10% for five years?
The simple interest can be calculated using the formula:
[tex] I = \frac{PRT}{100} [/tex]
We are given :
Principal = $269
Rate of interest = 10%
Time = 5 years
Plugging the values in the formula:
[tex] I = \frac{269*10*5}{100} [/tex]
Interest = $134.5
The interest on the principal amount in 5 years at the rate of 5% will be equal to $134.5.
What is Simple interest?A quick and simple way to figure out interest on that money is to use the simple interest approach, which adds interest at the same rate for each daily cycle, and it is to the initial principal amount.
A way to figure out how much interest will be charged on an amount of money at a specific rate and for a specific duration of time is by using simple interest.
As per the question, the given data is,
Principle, P = $269
Rate, T = 10%
Time, T = 5 years
[tex]SI =(P*R*T)/100[/tex]
SI = (269 ×10 × 5)/100
SI = $134.5
Therefore, the interest earned in 5 years is $134.5.
To know more about Simple interest:
https://brainly.com/question/25845758
#SPJ2