Answers
Answer:
x= -3, y= -5
or x= 5, y=3
Step-by-step explanation:
① Label the 2 equations
x² +y²= 34 -----(1)
3x -3y= 6 -----(2)
From (2):
x -y= 2 -----(3)
Notice that (x-y)²= x² -2xy +y²
Thus, (equation 3)²= (equation 1) -2xy
Squaring (3):
(x -y)²= 2²
(x -y)²= 4
Expand terms in bracket:
x² -2xy +y²= 4
x² +y² -2xy= 4 -----(4)
subst. (1) into (4):
34 -2xy= 4
2xy= 34 -4 (bring constant to 1 side)
2xy= 30 (simplify)
xy= 30 ÷2 (÷2 throughout)
xy= 15 -----(5)
From (3):
x= y +2 -----(6)
I'll rewrite 2 of the equations.
x= y +2 -----(6)
xy= 15 -----(5)
Subst. (6) into (5):
y(y+2)= 15
y² +2y= 15
y² +2y -15= 0
(y +5)(y -3)=0
y+5= 0 or y-3=0
y= -5 or y= 3
Subst. into (6):
x= -5 +2 or x= 3 +2
x= -3 or x= 5
Answer:
y=-5, y=3
x=-3., x=5
Step-by-step explanation:
x^2+y^2=34
3x-3y=6
isolate x in te equation
3x-3y=6
x=3/3 y+6/3
x=y+2
plug the y+2 in the equation:
x^2+y^2=34
(y+2)^2+y^2=34
y^2+4y+4+y^2=34
2y^2+4y=34-4
2y^2+4y=30 divide by 2
y^2+2x-15=0 factorize
(y+5)(y-3)=0 eiter y+5=0 ten y=-5 or y-3=0 then y=3
now plug the solution in the equation
3x-3y=6
3x-3(-5)=6
3x=6-15
x=-9/3=-3
for y=3
3x-3y=6
3x-9=6
3x=15
x=5
Related Questions
Please help me.What type of polygon would a peice of an icosahedron at a vertex create? Explain why.
Answers
Answer:
Regular Pentagon
Step-by-step explanation:
A regular icosahedron is a twenty-faced polyhedron, each face being an equiangular triangle. Each vertex is joined together by 5 faces, therefore the polygon formed at each vertex is a regular pentagon.
We can also figure out the number of faces at each vertex using Euler's formula
F+V=E+2
F=number of faces = 20
E=number of edges = number of triangular faces * edges/triangle /2
(since each edge is shared between two faces)
= 20*3/2
=30
Number of vertices
= E+2-F = 30+2-20 = 12
So number of edges meeting at each vertex
= 30 / (12/2) = 30/6 = 5
(12/2 because each edge joins two vertices).
See attached figure, courtesy of Wikipedia.
if jonny has 3 × 6 amounts of dish soap, how much dish soap does he have?!
a(I dont know)
b(18)
c(12)
d(6)
look up a skit called what's 6×3 before answering.
Answers
Answer: 18 (b)
Step-by-step explanation:
3x6=18
Answer:
18
Step-by-step explanation:
you can use a visual for a short answer or organize 3 dots in six groups, count in total
Use ￢, →, ∧ and ∨ to express the following declarative sentences in propositional logic; in each case state what your respective propositional atoms p, q, etc. a) If interest rates go up, share prices go down. b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. c) Today it will rain or shine, but not both. d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park. e) My sister wants a black and white cat.
Answers
Answer:
a) If interest rates go up, share prices go down : this will be assigned p→q
b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. P → (q∨￢r)
c) Today it will rain or shine, but not both:(p∨q) ∨ ￢(p∧q)
d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park. P → (q∨r)
e) My sister wants a black and white cat. p∧q
Step-by-step explanation:
A statement is said to be propositionally logical if the statement that can be assigned either true or false.
∧and
∨or
¬not
→implies
a) If interest rates go up, share prices go down : this will be assigned p→q implies because the occurrence of event (share prices go down) depends on the possibility of the other event happening.
b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. P → (q∨￢r) : either of the two of the other events (i.e. he has sold his car or he has not paid his mortgage ) can only occur if the first event occur
c) Today it will rain or shine, but not both:(p∨q) ∨ ￢(p∧q) : either of the events can occur but not both i.e. they are mutually exclusive
d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park. P → (q∨r) either of the two of the other events (i.e. they had a cup of coffee together or they took a walk in the park ) can only occur if the first event (Sam met Jane yesterday) occur
e) My sister wants a black and white cat. p∧q : both events can only occur together
Given that (0,0) is on the graph of f(x), find the
corresponding point for the function
f(x) – 5.
Answers
Answer:
(0, -5)
Step-by-step explanation:
You have (x, f(x)) = (0, 0) and you want (x, f(x) -5).
That would be ...
(x, f(x) -5) = (0, 0 -5) = (0, -5)
The mean monthly car payment for 123 residents of the local apartment complex is $624. What is the best point estimate for the mean monthly car payment for all residents of the local apartment complex?
Answers
Answer:
The best point estimate for the mean monthly car payment for all residents of the local apartment complex is $624.
Step-by-step explanation:
The Central Limit Theorem estabilishes 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].
In this question:
We apply the inverse Central Limit Theorem.
The mean monthy car payment for 123 residents of the local apartment complex is $624.
So, for all residents of the local apartment complex, the best point estimate for the mean monthly car payment is $624.
In the DBE 122 class, there are 350 possible points. These points come from 5 homework sets that are worth 10 points each and 3 tests that are worth 100 points each. A student has received homework scores of 7, 8, 7, 5, and 8 and the first two test scores are 81 and 80. Assuming that grades are assigned according to the standard scale, where if the grade percentage is 0.9 or higher the student will get an A, and if the grade percentage is between 0.8 and 0.9 the student will get a B, and there are no weights assigned to any of the grades, is it possible for the student to receive an A in the class? What is the minimum score on the third test that will give an A? What about a B?
Answers
Answer:
hey mate how r u I am good I am new to this app
I got the answer but I really don’t know if it’s correct or not, please help this is due today
Answers
Explanation: 180-52 = 128
So we have an equation:
2^3x+1=128 ( cuz they are in the same position)
Now we need to find what number that 2 raise to the power of that number is 128
And the answer is 2^7=128
Let’s go back to our equation:
2^3x+1=128
And we know that 2^7=128
Now we just have to make 3x+1=7:
3x+1=7
x=(7-1)/3
x=2
And there you have it x=2
Which of the following represents a coefficient from the expression given?
9x – 20 + x2
Answers
Answer:
1 or 9.
Step-by-step explanation:
A coefficient is "a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 4 in 4xy)".
So, in this case, the coefficient of 9x would be 9.
The coefficient of x^2 would be 1.
Hope this helps!
In the given quadratic expression 9x - 20 + x, 1, 9, and -20 are the coefficients.
What are coefficients in a quadratic expression?In a quadratic expression of the standard form ax² + bx + c, x is the variable and a, b, and c are the numeric coefficients.
How to solve the given question?In the question, we are asked to identify the coefficients from the given quadratic expression 9x - 20 + x².
First, we try to express the given quadratic expression, 9x - 20 + x², in the standard form of a quadratic expression, ax² + bx + c.
Therefore, 9x - 20 + x² = x² + 9x - 20.
Comparing the expression x² + 9x - 20 with the standard form of a quadratic expression ax² + bx + c, we get a = 1, b = 9, c = -20.
We know that in a quadratic expression ax² + bx + c, x is the variable and a, b, and c are the numeric coefficients.
Thus, we can say that in the given quadratic expression 9x - 20 + x², 1, 9, and -20 are the coefficients.
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20% of city employees ride the bus to work. This is up 10% from last year. What percent of employees rode the bus to work last year?
Answers
Answer:
18.18% of employees rode the bus to work last year
Step-by-step explanation:
This question can be solved using a rule of three.
Last year, a proportion of x employees riding the bus was 100% = 1.
This year, 20% = 0.2 ride the bus, which is 100 + 10 = 110% = 1.1 of last year.
So
0.2 - 1.1
x - 1
[tex]1.1x = 0.2[/tex]
[tex]x = \frac{0.2}{1.1}[/tex]
[tex]x = 0.1818[/tex]
0.1818*100 = 18.18%
18.18% of employees rode the bus to work last year
While the Pareto distributions are continuous, they tend to be used to model discrete data in humanities and actuarial sciences. Moreover, with its roots in power functions, Pareto distributions may be used in the growing popularity of the studies of networks. The probability density function (PDF) for a Pareto distribution is
Answers
Answer:
Step-by-step explanation:
While the pareto distributions are continuous in nature, they are sometimes used to model discrete data in fields such as Social Sciences, Humanities, Geophysics, and Actuarial Sciences.
The Pareto Distribution is a power-law probability distribution used in studies of observable phenomena.
The probability density function (PDF) for a Pareto Distribution is:
Xn = 1
for various Alpha levels
Where Xn is the probability value of X
As Alpha tends to infinity, the pareto distribution tends to ¶ [X-Xn]
Where ¶ is the Dirac Delta function.
How to solve the exponential equation for 3^k2 • 3^-k+2 = 81
Answers
Answer:
k=2
Step-by-step explanation:
3^k*2 * 3^-k+2 = 81
Factor out 81 to be : 3^4
Rewrite the equation:
k*2 - k+2 = 4
k^2 - 2k = 4
Simplify : k+2 = 4
- 2 - 2
k = 2
Duran Manufacturing uses a process costing system and manufactures its product in three departments. Which of the following is NOT a way in which Duran can use the cost per unit of each process? A) Duran can look for ways to cut the costs when actual process costs are more than planned process costs. B) Duran needs to set the selling price to cover the costs of making the product and provide a profit. C) Duran can only use the cost per unit of each process if all units are fully completed at the end of the accounting period. D) Duran needs to know the ending balances in the following accounts: Work-In-Process Inventory, Finished Goods Inventory, and Cost of Goods Sold.
Answers
Answer:
C) Duran can only use the cost per unit of each process if all units are fully completed at the end of the accounting period.
Step-by-step explanation:
Duran uses cost accounting technique to identify cost per unit for its products. The costing techniques allows us to identify the cost of unit that are not completely finished. It is not necessary that all unit must be completed in order to find out the cost per unit of the product. The process costing is the best method to identify cost per unit for products that are in process.
Complete the square to rewrite y = x2 - 6x + 16 in vertex form. Then state
whether the vertex is a maximum or minimum and give its coordinates.
Answers
Answer:
y = x² + 6x + 16
= (x² + 6x + 9) - 9 + 16
= (x + 3)² + 7 ← vertex form
Therefore, vertex is (-3, 7) and since the coefficient of (x + 3)² is positive the vertex is a minimum.
Answer:
minimum (3,7)
Step-by-step explanation:
HELP PLEASE!!What method can you use to find the area of the composite figure. Check ALL that apply.
Answers
Answer:
C
Step-by-step explanation:
The reason we can use this method is because we are given a composite figure with a house shape with one triangle on top. We can use the guidance of the dotted lines to make out that a rectangle can be used to find the figure. We can see that apart from the figure, there are two congruent triangles. To find the area we would do -
First find the missing height of the smaller triangles. We would use the pythagorean theorem to find that the missing height is√5
We could do 8(4) = 32 to find the area of the rectangle.
Then, we could do 2√5/2 to find one missing triangle. We could then add the triangles to find the measures of the combined triangles as 2√5. Then, we could do 32 - 2√5 to find the area as 27.5.
Hope this helps :)
Answer:
it is A,B,D
Step-by-step explanation:
i got it right on edge
In a Classroom, 1/6 of the students are wearing blue shirts, and 2/3 are wearing white shirts. There are 12 students in the classroom. How many students are wearing shirt other than blue shirts or white shirts?
Answers
Answer:
2
Step-by-step explanation:
firstly...you have to find the number of students wearing blue and white shirt and subtract from the total number of students to get the number if students that neither wears blue or white shirt as follows :
no wearing blue = 1/6 × 12 = 2
no.wearing white = 2/3 × 12 = 8
total number wearing blue and white = 8+2 =10
number of students not putting on either of the two colours include...= 12-10 = 2
.....
.....
.....
MARK BRAINLIEST will be appreciated please...thanks in advance
If (a+1) and (a-1)= 35 what is a?? Helpppppppppp
Answers
Answer:
There is no real number that can satisfy this equation
Step-by-step explanation:
a+1=35 and a-1=35 ⇒ a+1=a-1⇒ a-a = -1-1⇒ 0= -2 That's absurd so a has no real solutionLet x=−1−5i and y=5−i. Find x⋅y.
Answers
Answer:
-10 -24i
Step-by-step explanation:
Note : i=√-1 (imaginary number)
i² = -1
xy
= (−1−5i)(5−i)
= -5 +i -25i +5i²
=-5 +i -25i + 5(-1)
= -5 +i -25i -5
= -5 -5 +i -25i
= -10 -24i
A complex number is a number system that extends the real numbers with a particular element labelled "i" known as the imaginary unit. The value of x·y is (−10 −24i).
What is a complex number?A complex number is a number system that extends the real numbers with a particular element labelled "i" known as the imaginary unit, and satisfies the equation i² = -1; every complex number may be represented as a + bi, where a and b are real numbers.
Given that x=−1−5i and y=5−i. Therefore, the value of x·y is,
x·y = (−1 −5i)(5-i)
= −5 + i −25i +5i²
= −5 −24i − 5
= −10 −24i
Hence, the value of x·y is (−10 −24i).
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What is the complete factorization of x^2+4x-45?
Answers
Answer:(x-5)(x+9)
Step-by-step explanation:
You want two numbers that can give you -45 in multiplication and two numbers that can add to 4 and that is -5 and 9.
Answer: (x - 5)(x + 9)
If you have to solve, x=5 or x= -9
Step-by-step explanation: You need two numbers that multiply to be 45.
(could be 3 × 15 or 5 × 9) . The difference between the two factors needs to be 4, the coefficient of the middle term.
9 - 5 =4, so use those. -45 has a negative sign, so one of the factors must be + and the other - Since the 4 has the + sign, the larger factor has to be + so the difference will be positive.
So (x -5)(x + 9) are your factors. You can FOIL to be sure
x × x += x² . x × 9 = 9x . -5 × x = -5x . -5 × 9 = -45 .
Combine the x terms: 9x -5x = +4x
Simple linear equations
Check Whether the value given in the brackets is the root of the given equation or not (nessessary steps is needed)
a) 4x = -4 [x=-1]
b) 2(x-3) =-12 [x=3]
c) 8x - 4x = 24 [x = 1/2]
d) 9x - 4x = 24 [x=18]
Answers
Answer: Evaluate the Function, right?
Hello!
~~~~~~~~~~~~~~~~~~
A) 4x = -4 [x=-1] =
4x = -4 =
x = -1 = x = -1
( The steps : Substitute the given value into the function and evaluate.)
B) 2(x-3) =-12 [x=3] =
2 ( x - 3) = -12 = x = -3
x = 3 = x = 3
( The steps : Substitute the given value into the function and evaluate.)
C) 8x - 4x = 24 [x = 1/2] =
8x - 4x = 24 = x = 6
x = 1/2 = x = 1/2
( The steps : Substitute the given value into the function and evaluate.)
D) 9x - 4x = 24 [x=18] =
9x - 4x = 24 = x = 24/5
x = 18 = x = 18
( The steps : Substitute the given value into the function and evaluate.)
~~~~~~~~~~~~~~~~~~
Step-by-step explanation: All the steps are the same. Substitute the given value into the function and evaluate.
Hope this helped you!
1. A circus elephant is being led up a 12-foot-long ramp to a trailer that is 4 feet above
the ground.
4ft
12 ft
Which equation could be used to find the angle between the ramp and the ground?
Answers
Help please!!
What quadrant does the terminal side of this angle lie in?
Answers
Answer:
QIII
Step-by-step explanation:
Find the midpoint of the line segment joining the points (-5, 2) and (3. -8).
Answers
Hey there! :)
Answer:
(-1, -3)
Step-by-step explanation:
Use the midpoint formula to derive the coordinates of the midpoint:
[tex](x_{m} ,y_{m} ) = (\frac{x_{1} +x_{2} }{2}, \frac{y_{1}+ y_{2} }{2} )[/tex]
Plug in the coordinates given:
[tex](\frac{-5+3 }{2}, \frac{2-8 }{2} )[/tex]
Simplify:
[tex](\frac{-2 }{2}, \frac{-6 }{2} )[/tex]
(-1, -3) are the coordinates of the midpoint.
Answer:
[tex]\boxed{Midpoint = (-1,-3)}[/tex]
Step-by-step explanation:
The coordinates are (-5,2) and (3,-8)
M(x,y) = [tex](\frac{x1+x2}{2} , \frac{y1+y2}{2} )[/tex]
M(x,y) = [tex](\frac{-5+3}{2} , \frac{2-8}{2} )[/tex]
M(x,y) = [tex](\frac{-2}{2} , \frac{-6}{2} )[/tex]
M(x,y) = (-1,-3)
Each side of a square is increasing at a rate of 3 cm/s. At what rate is the area of the square increasing when the area of the square is 36 cm2?
Answers
Each side of the square would have to be 6 cm to have an area of 36 cm^2. However, as a side can never be 0, and you never gave a starting size for the square, the question is unanswerable.
Peter is buying office supplies. He is able to buy 3 packages of paper and 4 staplers for $40, or he is able to buy 5 packages of paper and 6 staplers for $62. How much does a package of paper cost? How much does a stapler cost?
Answers
Answer:
paper = $4 and stapler = $7
Step-by-step explanation:
let p represent paper and s represent stapler, then
3p + 4s = 40 → (1)
5p + 6s = 62 → (2)
Multiplying (1) by 5 and (2) by - 3 and adding will eliminate p
15p + 20s = 200 → (3)
- 15p - 18s = - 186 → (4)
Add (3) and (4) term by term to eliminate p
2s = 14 ( divide both sides by 2 )
s = 7
Substitute s = 7 into either of the 2 equations and evaluate for p
Substituting into (1)
3p + 4(7) = 40
3p + 28 = 40 ( subtract 28 from both sides )
3p = 12 ( divide both sides by 3 )
p = 4
Thus package of paper costs $4 and stapler costs $7
show that 7 1/2 - 4 2/3 = 2 5/6
Answers
Since the end fraction has a denominator of 6 try and multiply both of the ones on the LHS to get 6 as a denominator.
First though convert the improper fractions into fractions solely.
7 1/2 goes to 15/2
While
4 2/3 goes to 14/3
Now
15/2 multiply both numerator and denominator by 3 gives you 45/6
14/3 multiply both numerator and denominator by 2 gives you 28/6
Subtract 45/6 by 28/6= 17/6
Highest multiple of 6 in 17 is 12
12/6 + 5/6 = 2 5/6
Equation is [tex]7\frac{1}{2} -4\frac{2}{3}=2\frac{5}{6}[/tex] is true.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is [tex]7\frac{1}{2} -4\frac{2}{3}=2\frac{5}{6}[/tex]
We need to check whether the left hand side is equal to right hand side.
These are in the form pf mixed fraction we can convert them to the improper fraction.
[tex]7\frac{1}{2}=15/2[/tex]
[tex]4\frac{2}{3}=\frac{14}{3}[/tex]
So Let us subtract 24/3 from 15/2
15/2-14/3
LCM of 2 and 3 is 6
45-28/6
17/6
This can be written as mixed fraction [tex]2\frac{5}{6}[/tex]
Hence, equation is [tex]7\frac{1}{2} -4\frac{2}{3}=2\frac{5}{6}[/tex] is true.
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The two triangles are similar. What is the value of x? Enter your answer in the box. x =
Answers
Answer:
the value of x=12
Step-by-step explanation:
d) the answer is d on edg.
Find the domain of the graphed function.
10
-10
10
10
O A. -45x39
B. -43x8
C. X2-4
0
D. x is all real numbers.
Answers
An election ballot asks voters to select six city commissioners from a group of 24 candidates in how many ways can this be done? Six city commissioners can be selected from a group of 24 candidates in blank different ways
Answers
Answer:
134,596 diffrent ways.
Step-by-step explanation:
Combination has to do with selection. When n object is to be selected from n objects, this can be achieved using the combination formula as shown; \
nCr = n!/(n-r)!r!
If an election ballot asks voters to select six city commissioners from a group of 24 candidates, then the selection can be done in 24C6 different ways.
Applying the formula above:
24C6 = 24!/(24-6)!6!
24C6 = 24!/18!6!
24C6 = 24*23*22*21*20*19*18!/18!*6*5*4*3*2
24C6 = 24*23*22*21*20*19/24*30
24C6 = 23*22*21*20*19/30
24C6 = 134,596 different ways.
Hence, Six city commissioners can be selected from a group of 24 candidates in 134,596 different ways
a dense fog advisory means visibility is less than 1/8 of a mile
-true
-false
Answers
Good luck
if p+4/p-4, what is the value of p
Answers
Answer:
p = 2
Step-by-step explanation:
p + 4/p - 4
multiplying through by p,
p×p + 4/p ×p - 4×p
p² + 4 - 4p = 0
p² - 4p + 4 = 0
factorizing,
p(p - 2) -2(p - 2) =0
(p -2)(p -2) =0
p-2 =0
p=2