Answer:
x=-4 and y=2 Those 2 equations when graphed give a vertical line and a horizontal line that intersect at the point (-4,2)
x+4=0 and y-2=0 are the same two lines.
or if you want more complicated systems of equations, with the same solution:
x+y=-2 and x-y=-6
in standard form, that's y=-x-2 and y=x+6 Graph those two lines and they intersect at (-4,2)
Those 2 lines are with slopes of -1 and +1. Those 2 equations are a system of equations
whose solution is x=-4 and y=2.
Rotate two perpendicular lines around the point (-4,2) and you get more systems of
equations with the same solution.
They don't have to be perpendicular though. x+y=-2 and x=-4 are two lines forming
a 45 degree angle, with the same solution (-4,2)
They don't have to be linear either. Take a parabola with the vertex (-4,2) and the line x=-4.
They intersect at the point (-4,2). That parabola could be the simple y=x2 shifted up and
to the left, to y-2 = (x+4)2 or y=x2+8x+18 or it could be any one of a family of parabolas with
the same vertex.
You could have 2 circles tangent at the point (-4,2) Endless circles could have that point
as a tangent and their equations having that same solution (-4,2)
Step-by-step explanation:
Hope this helps <3
What are the zeros of the quadratic function f(x)
128² - 10x - 3?
Answer:
When 2x^2 - 10x - 3 is plugged into the quadratic equation, the resulting zeroes are x = (5 + sqrt(31))/2 and (5 - sqrt(31))/2. Hope this helps!
Step-by-step explanation:
If my answer is incorrect, please correct me! If you like my answer and explanation, mark me as brainliest!
What is the length of the hypotenuse of the triangle?
Answer:
[tex]\sqrt{58}[/tex]
Step-by-step explanation:
To find the hypotenuse, we need to use the pythagorean theorem which is [tex]a^2+b^2=c^2[/tex]
[tex]3^2+7^2=c^2[/tex]
[tex]9+49=c^2[/tex]
[tex]58=c^2[/tex]
[tex]\sqrt{58} =c^2[/tex]
Hope this helps
Answer:
Step-by-step explanation:
√58
Evaluate the following integral on the region R in xy-plane
An obvious substitution would be to take u = x - y and v = x + 2y, so that 0 < u < 1 (which follows from y = x ==> x - y = 0 and y = x - 1 ==> x - y = 1), and 0 < v < 1.
Solve for x and y in terms of u and v :
u - v = (x - y) - (x + 2y) = -3y ==> y = (v - u)/3
2u + v = 2 (x - y) + (x + 2y) = 3x ==> x = (2u + v)/3
Compute the Jacobian and its determinant:
[tex]J=\begin{bmatrix}D_ux&D_vx\\D_uy&D_vy\end{bmatrix}=\begin{bmatrix}\dfrac23&\dfrac13\\\\-\dfrac13&\dfrac13\end{bmatrix} \implies |\det(J)|=\dfrac13[/tex]
Now in the integral, we have
[tex]\displaystyle\iint_R\frac{x+2y}{\cos(x-y)}\,\mathrm dx\,\mathrm dy = \frac13\int_0^1\int_0^1\frac{v}{\cos(u)}\,\mathrm du\,\mathrm dv \\\\ \displaystyle= \frac13\left(\int_0^1v\,\mathrm dv\right)\left(\int_0^1\sec(u)\,\mathrm du\right) \\\\ \displaystyle= \frac13\bigg(\frac{v^2}2\bigg)\bigg|_0^1\bigg(\ln|\sec(u)+\tan(u)|\bigg)\bigg|_0^1 \\\\ \displaystyle= \boxed{\frac16\ln(\sec(1)+\tan(1))}[/tex]
Given the triangle below, what is the length of the third side, rounded to the
nearest whole number?
B
18
A
12
620
Triangle not drawn to scale
A. 18
B. 14
C. 16
D. 20
Answer:
Option C
Step-by-step explanation:
In this question measure of two sides and and the angle between these sides of a triangle is given.
We have to calculate the measure of third side.
By applying cosine rule in the given triangle.
BC² = AB² + AC² - 2(AB)(AC)cos(A)
BC² = (18)² + (12)² - 2(18)(12)cos(62°)
BC² = 324 + 144 - 202.81
BC² = 265.19
BC = 16.28
BC ≈ 16 units
Therefore, Option C will be the correct option.
I NEED HELP PLEASE!!!
Answer:
Step-by-step explanation:
1.
[tex]-\frac{5 \pi }{6} +2\pi =\frac{-5\pi +12 \pi }{6} =\frac{7\pi }{6}[/tex]
2.
405-360=45°
I NEED HELP! You throw a ball from an initial height of 6 feet and with an initial velocity of 46 feet per second. Write an equation that gives the height of the ball (in feet) as a function of the time (in seconds) since it left your hand, then find the time it takes for the ball to hit the ground.
Answer:
t = 0.77930
t = 1.2832
Step-by-step explanation:
if the bookstore pays $60 to the publisher what will be the selling price?
Answer:
This means that, when the price of a book from a publisher is $60, the bookstore will sell it for $88 to the students.
To find the percentage, what I did was that I divided 55 and 163 and the answer I got was 33%. However, my answer was incorrect. Because my answer was incorrect, how do I go about this problem?
Answer:
200
Step-by-step explanation:
You were right to divide 55 by 163. The problem, however, asks for the answer to be rounded to the nearest tenth.
Therefore, 55 / 163 = 0.3374 = 33.7%
Hope this helps!
Will mark brainlest!!!
Step-by-step explanation:
We have,
[tex]g(x)=x^3+x^2-x-2[/tex]
To find g(-1), put -1 in place of x i.e.
[tex]g(-1)=(-1)^3+(-1)^2-(-1)-2\\\\=-1[/tex]
To find g(1), put 1 in place of x i.e.
[tex]g(1)=1^3+1^2-1-2\\\\=-1[/tex]
To find g(2), put 2 in place of x i.e.
[tex]g(2)=2^3+2^2-2-2\\\\=8[/tex]
g(2) + g(1) = 8+(-1)
= 7
Hence, this is the required solution.
Answer:7
Step-by-step explanation: mark brainliest pls lol
Clara, Dean and Elaine were candidate in an election in which 1000 people voted.elaine won the election receiving 95 more votes than Dean,and 186 more than Clara. how many votes did dean receive?
Answer:
E = 427 votes
Step-by-step explanation:
Let Elaine's vote be ELet Dean's vote be DLet Clara's vote be C.Translating the word problem into an algebraic expression, we have;
E = D + 95
E = C + 186
Equating the two equations, we have;
D + 95 = C + 186
D = C + 186 - 95
D = C + 91
Also, the sum of all the votes is equal to 1000.
E + D + C = 1000
Substituting the value of "D" we have;
E + (C + 91) + C = 1000
E + C + 91 + C = 1000
E + 2C + 91 = 1000
E + 2C = 1000 - 91
E + 2C = 909
But, E = C + 186
Substituting the value of "E" we have;
(C + 186) + 2C = 909
C + 186 + 2C = 909
3C + 186 = 909
3C = 909 - 186
3C = 723
C = 723/3
C = 241 votes
Next, we would find Elaine's vote;
E = C + 186
E = 241 + 186
E = 427 votes
Lastly, we would find Dean's vote;
E = D + 95
427 = D + 95
D = 427 - 95
D = 332 votes
Check:
E + D + C = 1000
427 + 332 + 241 = 1000
1000 = 1000
Please help with this question ive been asking for half an hourrrr
answer asap pls
Ill mark brainlist
f(n) = 10(1.02)n
Part A: When the scientist concluded his study, the height of the plant was approximately 11.04 cm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(n) represent? (2 points)
Part C: What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent? (4 points)
Answer:
Step-by-step explanation:
11.04 = 10(1.02)^n
1.104 = 1.02^n
ln 1.104 = ln 1.02^n
ln 1.104 = n ln 1.02
n = ln 1.104/ ln 1.02
n = 4.99630409516
4.99 can be rounded to 5.
So a reasonable domain would be 0 ≤ x < 5
PART B)
f(0) = 10(1.02)^0
f(0) = 10(1)
f(0) = 10
The y-intercept represents the height of the plant when they began the experiment.
f(1) = 10(1.02)^1
f(1) = 10(1.02)
f(1) = 10.2
(1, 10.2)
f(5) = 10(1.02)^5
f(5) = 10(1.1040808)
f(5) = 11.040808
f(1)=10(1.02)^1
f(1)=10.2
Average rate= (fn2-fn1)/(n2-n1)
=11.04-10.2/(5-1)
=0.22
the average rate of change of the function f(n) from n = 1 to n = 5 is 0.22.
pila ka adlaw ang 288 ka oras
Answer:
anu po yan salamat po sa point
What is the other number to this math equation?
Answer:
You need to ask yourself what times 20 gives you 600. Then ask yourself what times 20 gives you 160. Then that will give you your answer.
Step-by-step explanation:
What is the volume of the solid figure?
help pls
Answer:
B, 4x6x7 and 1x3x3.
Step-by-step explanation:
First, remember the formula: V=LWH (Volume equals length times width times height). Lastly, find the equations that match that formula, therefor B, 4x6x7 and 1x3x3 matches the formula, so B is your correct answer.
i need help
can someone help me
ty
a.
Answer:
1170cm^3
Step-by-step explanation:
Break it into two prisms. 5 x 9 x 15 and 11 x 3 x 15. Find the volume of each and add.
(5 x 9 x 15) + (11 x 3 x 15)
675 + 495
1170cm^3
b.
Answer:
846cm^2
Step-by-step explanation:
Add each side's area together.
(9x15) + (5x15) + (6x15) + (3x15) + (12x15) + (11x15) + (5x9) + (5x9) + (11x3) + (11x3)
135 + 75 + 90 + 45 + 180 + 165 + 45 + 45 + 33 + 33
846 cm^2
Answer:
(a)1170 cm^3
(b)846 cm^2
Step-by-step explanation:
(a) Rectangle #1= 11 x 3 = 33 cm^2
Rectangle #2 = 5 x 9 = 45 cm^2
Volume = 45 + 33 = 78 x 15 = 1170 cm^3
(b) First find the surface are of all 8 faces in the prism and then add them all.
1st face = (11 x 3) + (5 x 9 ) = 33 + 45 = 78 cm^2
2nd face = (11 x 3) + (5 x 9 ) = 33 + 45 = 78 cm^2
3rd face = 15 x 3 = 45 cm^2
4th face = 15 x 6 = 90 cm^2
5th face = 15 x 9 = 135 cm^2
6th face = 15 x 5 = 75 cm^2
7th face = 15 x 12 = 180 cm^2
8th face = 15 x 11 = 165 cm^2
1st + 2nd + 3rd +4th + 5th+ 6th + 7th + 8th = 846 cm^2
Hope this helps!
Is -40/8 positive or negative?
Answer:
Negative. The answer gives - 5
Answer:
Negative
Step-by-step explanation:
-40/8 is equivalent to -5. Since -5 or "negative five" is negative (as it states), the equation is negative.
Please anybody? Line intergal
Parameterize the path by
r (x) = (x, x + 2)
with 0 ≤ x ≤ 2. Then
r' (x) = (1, 1) ==> ||r' (x)|| = √(1² + 1²) = √2
and the line integral is
[tex]\displaystyle\int_Lxy\,\mathrm ds=\sqrt2\int_0^2x(x+2)\,\mathrm dx=\boxed{\frac{20\sqrt2}3}[/tex]
Can I have help I am stuck on this problem It would mean the world if u helped me and tysm!! =-)
Answer:
Step-by-step explanation:
Wage = rate / hr * the number of hours worked.
Wage = ?
rate = 15.45
time = 29.25 hours
Wage = 15.45 * 29.25
Wage = 451.91
can someone give me the anwser please?
Answer:
5/6 + 11/6 = 16/ 6
Step-by-step explanation:
Distance between any Teo labeled tick marks =
(1 - 2/3) / 2 = 1/3 ÷ 2 = 1/3 * 1/2 = 1/6
From the left :
2/3 + 1/6 = 5/6
5/3 + 1/6 = 11/6
5/6 + 11/6 = (5 + 11) / 6 = 16/6
5/6 + 11/6 = 16/ 6
Prove that if a and b are positive integers,then there exists a unique integers q and r such that a=bq+r where 0≤r<b
Step-by-step explanation:
Correct option is
C
0≤r<b
If r must satisfy0≤r<b
Proof,
..,a−3b,a−2b,a−b,a,a+b,a+2b,a+3b,..
clearly it is an arithmetic progression with common difference b and it extends infinitely in both directions.
Let r be the smallest non-negative term of this arithmetic progression.Then,there exists a non-negative integer q such that,
a−bq=r
=>a=bq+r
As,r is the smallest non-negative integer satisfying the result.Therefore, 0≤r≤b
Thus, we have
a=bq1+r1, 0≤r1≤b
A rectangle has vertices (−5, 6), (−1, 6), (−1, 3), and (−5, 3). It is first dilated by the rule (x, y)→(7x, 7y) and then translated 10 units down. What are the coordinates of the image?
A(−35, 32), (−7, 32), (−7, 11), (−35, 11)
B(−45, 42), (−17, 42), (−17, 21), (−45, 21)
C(−105, 42), (−77, 42), (−77, 21), (−105, 21)
D(−35,−28), (−7,−28), (−7,−49), (−35,−49)
Evaluate the integral.
∫ 17/ (x^3 − 27) dx
Answer:
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Which is correct?????????????
Answer:
It discusses the role of the God in influencing our decisions
Answer:
I believe it is choice D
Step-by-step explanation:
in the excerpt it talks about how sight gives us the ability to observe and experience. it also states "we prefer sight to almost everything else." hope I'm right! ☺️
What is the correct written expression for the variable expression: (3 - x)/7
3 divided by the difference of 7 and x
or
the difference of 3 divided by 7 and x
Answer:
3 divided by 7 and x=-1.5*x
Step-by-step explanation:
I need help help help
Answer:
use app Gauthmath its will give you the answer
A machine fills boxes at a constant rate.At the end of 35 minutes it has filled 5 boxes. Which table represents the relationship between the number of minutes the machine fills boxes and the number of boxes it has filled?
Answer:
7
Step-by-step explanation:
5 x 7 = 35 or 35/5 = 7 [ correct me if i'm wrong ]
PLEASE HELP!! will give brainliest!!
Suppose cos(x) = 1/sqrt5 and sin(x) > 0. What is the value of tan(2x)?
-4/3
For your question: Suppose cos(x) =1/(sqrt(5)) and sin(x) >0. What is the value of tan(2x)?
The value of tan(2x) is equal to -4/3
giving brainliest to whomever answers correctly!
Answer:
B: A systematic random sample
Step-by-step explanation:
Systematic sampling is a type of probability sampling in which members of a larger population are chosen at random from a larger population but at a fixed, periodic interval. This interval, also known as the sampling interval, is calculated by dividing the population size by the sample size desired. Despite the fact that the sample population is chosen in advance, systematic sampling is still considered random if the periodic interval is set in advance and the starting point is chosen at random.
Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?
Hai vòi nước cùng chảy vào một bể. Vòi thứ nhất chảy trong 8 giờ thì đầy bể, vòi thứ hai chảy trong vòng 10 giờ thì đầy bể. Hỏi:
a, cả hai vòi cùng chảy thì sau bao lâu sẽ đầy bể
b, Nếu có một một vòi thứ ba Thảo nước ra trong 16 giờ thì sẽ cạn hết bể đầy nước thì khi mở cả 3 vòi cùng một lúc sau bao nhiêu lâu sẽ đầy bể(lúc đầu bể đầy nước)
Answer:
Please say in English
Step-by-step explanation:
I don't understand, Sorry
What is the probability of rolling a number greater than 0 on a six-sided die? Someone pls help it’s urgent!!
Answer:
6/6=1
Step-by-step explanation:
There are six sides on a die and you have six total outcomes. Hope this helps! :)