x + y = 5 2x - y = 1 substitution method
Answers
[tex]x+y = 5~~...(i)\\\\2x-y = 1~~...(ii)\\\\\text{From (i):}\\\\x+y = 5\\\\\implies x = 5-y~~~.....(iii)\\\\\text{Substitute equation (iii) in equation (ii):}\\ \\2(5-y)-y = 1\\\\\implies 10 - 2y -y = 1\\\\\implies 3y = 9\\\\\implies y = \dfrac 93 = 3\\\\\text{Substitute y= 3 in equation (iii):}\\\\x= 5-3 = 2\\\\\text{Hence,}~ (x,y) = (2,3)[/tex]
Answer:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form:
(2,3)
Equation Form:
x = 2, y = 3
Step-by-step explanation:
Related Questions
cual es el máximo común divisor de 72, 90 y 36?
Answers
Answer:
6
Step-by-step explanation:
6 x 6 = 36
6 x 12 = 72
6 x 15 = 90
During a phone call about the system of equations {5x + 2y = 8 , 8x + 4y = 8}, Dylan told Max, “It’s easy, just set them equal to each other.” But Max replied, “That doesn’t help — I get −2y = 3x. What good is that?” Help these two students solve the problem.
Answers
Answer:
x = 4
y = -6
Step-by-step explanation:
5x + 2y = 8
8x + 4y = 8
-2(5x + 2y) = -2(8)
8x + 4y = 8
-10x -4y = -16
8x + 4y = 8
-10x -4y + 8x + 4y = -16 + 8
-2x = -8
x = 4
plug 4 into x so y = -6
Find the rule to complete the pyramid.
Answers
i think this should work good luck
The large rectangle below represents one whole.
What percent is represented by the shaded area?
%
Answers
Answer:
40%
Step-by-step explanation:
2/5 is shaded
100 divided by 5 is 20
2x20=40
So, each part = 1/5
Part that is shaded = 2/5
Percentage = (2/5)*100
= 2* 20
= 40%
Jimmy just left the movies. The
movie ended at 4:47 p.m. The
movie was two hours long.
What time did the movie start?
?
Answers
Reflect the point (3,0) across the x axis.
Reflect the point (3,0) across the y axis.
Answers
Answer:
(3,0) reflection on x axis (3,0)
(3,0) reflection on y axis (-3,0)
Name any two timber plans found in the Terai region of Nepal? Where is Red panda found? Why is it called an endangered bird?
Answers
Step-by-step explanation:
red Panda is found in langtang national park and makalu-barun national park in Nepal .
timber planks for in the religion of Nepal sal, sissoo& Khair.
I'm injured birds are any bird fishing that is at risk of extinction because of a sudden rapid increase in population or a loss of its critical habitat .
Can someone help me please
Answers
Answer:
[tex]6x^2+8x[/tex]
Step-by-step explanation:
Hey there!
In order to find the answer to this question, what you need to do is first find the area of the whole grey box as a whole (including the white box to)
The dimensions for this is 3x+2 and 4x
Now we know that to find area, we need to multiply length by height
So (3x+2)(4x) is what we have to solve to get the area
Now we simplify:
1. Distribute
2. [tex]12x^2+8x[/tex]
So now we know that the total area is [tex]12x^2+8x[/tex]
Now what we do is take out the area of the white box from the area of the grey box
Lets find the area of the white box:
l=3x (l - length)
h=2x (h - height)
[tex]3x*2x=6x^2[/tex]
Now we have the area of both shapes
Since we have all the information we need to find the final answer, the following steps below will be using the information we found to find the final answer:
In order to find the final answer which is the area of the shaded region, we take out the area of the white region from the total area of the grey region (including the white region)
So now we can formulate this new equation:
[tex]12x^2+8x-6x^2= ta[/tex]
(ta= total area)
Now we simplify:
[tex]6x^2+8x\\[/tex] is going to be our final answer
So our final answer is [tex]6x^2+8x[/tex]
: Customers arrive at a shopping mart randomly at a rate of 7 per hour.
a) Find the probability that during any 90 minutes’ period, the number of customers arriving at the shopping mart is exactly 8
b) If a customer arrives at 11. 30 am, find the probability that the next patient arrives before
11. 45 am
Answers
Using the Poisson distribution, it is found that the probabilities are given by:
a) 0.1009 = 10.09%.
b) 0.8262 = 82.62%.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.Item a:
The mean is of 7 customers for 60 minutes, hence, for 90 minutes = 1.5 x 60 minutes, the mean is given by:
[tex]\mu = 1.5 \times 7 = 10.5[/tex]
The probability of exactly 8 customers is of P(X = 8), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 8) = \frac{e^{-10.5}10.5^{8}}{(8)!} = 0.1009[/tex]
Item b:
Probability of at least one patient in 15 minutes, hence:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
For 15 minutes, the mean is given by:
[tex]\mu = 0.25 \times 7 = 1.75[/tex]
Then:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 8) = \frac{e^{-1.75}1.75^{0}}{(0)!} = 0.1738[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1738 = 0.8262[/tex]
More can be learned about the Poisson distribution at https://brainly.com/question/13971530
A long solenoid with radius r = 7 cm and n = 3,170 turns/m carries a current i = 6. 7 a. What is the magnitude of the magnetic field in the central area inside the solenoid, in t?
Answers
The magnitude of the magnetic field in the central area inside the solenoid, in T is 0.0267 T
Magnetic field inside solenoidThe magnetic field inside the central area of the solenoid is given by B = μ₀ni where
μ₀ = permeability of free space = 4π × 10⁻⁷ Tm/A, n = number of turns per unit length = 3,170 turns/m and i = current in solenoid = 6.7 ASince B = μ₀ni
Substituting the values of the variables into the equation, we have
B = μ₀ni
B = 4π × 10⁻⁷ Tm/A × 3,170 turns/m × 6.7 A
B = 4π × 10⁻⁷ Tm/A × 21239 A-turns/m
B = 84956π × 10⁻⁷ T
B = 266897.15 × 10⁻⁷ T
B = 0.026689715 T
B ≅ 0.0267 T
So, the magnitude of the magnetic field in the central area inside the solenoid, in T is 0.0267 T
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The magnitude of the magnetic field in the central area inside the considered solenoid (assuming in vaccum), is approx 2.67 × 10^{-2} T
What is the measurement of the magnetic field inside a long solenoid?Magnetic field = permeability constant x relative permeability x turn density x current
B = [tex]k\mu_0nI = \mu nI[/tex]
where turn density is calculated as:
n = N/L
Where N represents the number of turns of the wire and
L represents the length of the solenoid.
Assuming that the solenoid is placed in vaccum, we have:
[tex]\mu = k\mu_0 = \mu_0 = 4\pi \times 10^{-7} \: \rm T m/A[/tex]
And it is given that:
n = 3174 turns/mI = 6.7 amperesThus, we get:
[tex]B = \mu n I = 4\pi \times 10^{-7} \times 3170 \times 6.7 \approx 2.67 \times 10^5 \times 10^{-7} \\\\B = 2.67 \times 10^{5 + (-7)}B = 2.67 \times 10^{-2} \: \tm T[/tex]
Thus, the magnitude of the magnetic field in the central area inside the considered solenoid (assuming in vaccum), is approx 2.67 × 10^{-2} T
Learn more about magnetic fields here:
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Solve the initial value problem d y d x = 2 x 1 , y ( 0 ) = 2
Answers
Using separation of variables, it is found that the solution to the initial value problem is of y(x) = x² + 2.
What is separation of variables?In separation of variables, we place all the factors of y on one side of the equation with dy, all the factors of x on the other side with dx, and integrate both sides.
In this problem, the differential equation is given by:
[tex]\frac{dy}{dx} = 2x[/tex]
Then, applying separation of variables:
[tex]dy = 2x dx[/tex]
[tex]\int dy = \int 2x dx[/tex]
[tex]y = x^2 + K[/tex]
Since y(0) = 2, we have that the constant of integration is K = 2, and the solution is:
y(x) = x² + 2.
More can be learned about separation of variables at https://brainly.com/question/14318343
The differential equation is y(x) = x² + 2.
What is the differential equation?Differential Equations In Mathematics, a differential equation is an equation that contains one or more functions with their derivatives.
The given equation is;
[tex]\rm \dfrac{dy}{dx}=2x[/tex]
Applying the variable separation method;
[tex]\rm \dfrac{dy}{dx}=2x\\\\\int\limits \, dy=\int\limits\, 2x. dx\\\\y = 2 \times \dfrac{x^{1+1}}{1+1} +c\\\\y = 2 \times \dfrac{x^{2}}{2} +c\\\\y = x^2+c[/tex]
The value of c when y( 0 ) = 2 is c =2.
Hence, the required differential equation is y(x) = x² + 2.
More can be learned about the differential equation at;
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Write the expression as a product.
25-(a + 7)^2
pls help
Answers
Answer:
-(12+a)(a+2)
Step-by-step explanation:
this is to ez
The expression as a product is (a+12)(-a-2)
What is an expression?An expression in math is a statement having minimum of two numbers, or variables, or both and an operator connecting them.
Given that, is an expression, 25-(a+7)², we need to write it in product form, 25-(a+7)²
= 25 - (a²+49+14a)
= 25-a²-49-14a
= -a²-14a-24
Factorizing,
= -a²-12a-2a-24
= -a(a+12)-2(a+12)
= (a+12)(-a-2)
Hence, the expression as a product is (a+12)(-a-2)
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When you multiply the grouping by the exponent, what is the answer?
5+4 - (8 x 3 – 22)* x 4
Answers
Answer:
1
Step-by-step explanation:
5 + 4 - (8 x 3 – 22)* x 4
5 + 4 - (24 - 22) x 4
5 + 4 - 2 x 4
5 + 4 - 8
1
Answer:
16
Step-by-step explanation:
5+4- (8x3-22) ↑4 x4
16
5+4 - (24-22) ↑4 x4
5+4- (2) ↑4 x4
2x2x2x2=16
hope that helps:)
When plotting an ordered pair, X comes before Y
Answers
Answer:
True
Step-by-step explanation:
I always remember it, over then up
The graphs of the functions (f) and (g) are shown where..
[tex]f(x) = 4.5 \sqrt{x} [/tex]
[tex]g(x) = \frac{1}{9} {x}^{2} [/tex]
Select the TWO closest approximations for solutions to the equations f(x) - g(x) = 0
A.x=0
B.x=5.0
C.x=11.7
D.x=13.5
E.x=20.0
Answers
Answer:
[tex]\red{ \rule{10pt}{999999pt}} \pink{ \rule{10pt}{999999pt}} \blue{ \rule{10pt}{999999pt}} \purple{ \rule{10pt}{999999pt}} \\ \red{ \rule{10pt}{999999pt}} \pink{ \rule{10pt}{999999pt}} \blue{ \rule{10pt}{999999pt}} \purple{ \rule{10pt}{999999pt}} \\ \red{ \rule{10pt}{999999pt}} \pink{ \rule{10pt}{999999pt}} \blue{ \rule{10pt}{999999pt}} \purple{ \rule{10pt}{999999pt}}[/tex]
\orange{ \rule{100pt}{999999pt}} < /p > < p > [tex]at < /p > < p > at</p><p>[tex]at</p><p>
Step-by-step explanation:
f(x) - g(x) = 0
f(x) = g(x)
4.5√x = ⅑ x²
4.5 × 9 = x√x
40.5 = x√x
square it on both side
1640.25= x².x
1640.25 =x³
x=11.7
What is the least common multiple? 46 and 12?
Answers
Answer:
2
Step-by-step explanation:
multiples of 12: 1, 2, 3, 4, 6, 12 (we don't use 1 in LCM)
Start with 2: 46/2 = 23, so the least common multiple is 2
A political candidate feels that she performed particularly well in the most recent debate against her opponent. Her
campaign manager polled a random sample of 400 likely voters before the debate and a random sample of 500
likely voters after the debate. The 95% confidence interval for the true difference (post-debate minus pre-debate) in
proportions of likely voters who would vote for this candidate was (-0.014, 0.064). What was the difference (pre-
debate minus post-debate) in the sample proportions of likely voters who said they will vote for this candidate?
0.064 +-0.014)
= 0.025
0.064-(-0.014)
= 0.039
0 0.064 + (-0.014) = 0.050
0.064 - (-0.014) = 0.078
N
Answers
Considering the confidence interval given, the likely difference is given by:
[tex]\frac{0.064 + (-0.014)}{2} = 0.025[/tex]
What is the point estimate of a confidence interval?Given an interval (a,b), the point estimate is the mean of the bounds, that is:
p = (a + b)/2.
In this problem, the interval is (-0.014, 0.064), hence the expression for the likely difference is given by:
[tex]\frac{0.064 + (-0.014)}{2} = 0.025[/tex]
More can be learned about confidence intervals at https://brainly.com/question/25890103
BRAINLIEST FOR CORRECT ANSWER: What is the area of this figure?
Answers
Answer:
A = 253 sq ft
Step-by-step explanation:
see image. Section off the shape into rectangles. Sometimes you have to add to find the lengths of the sides. Sometimes you have to subtract. Area is length×width. see image.
Write an equation in slope-intercept form for the line that passes through (6,6) and is
perpendicular to the line described
Answers
Answer:
Step-by-step explanation:
Solution :
Hello:
an equation for the line is : y =mx +b (m: is a slope )
perpendicular to the line described by : y = 2/3 x -2
So : product for two slopes = -1 means : m×2/3=-1
m = -3/2
now : y = -3/2 x+b
but this line :
through the point (6,6) : 6 =(-3/2)(6)+b....... b=15
conclusion :
the equation is : y = -3/2x +15
What is the value of y in the solution to the system of equations?
1 x + 2 y = 1
2x – 3y = -30
0-8
0-3
03
O 8
Answers
Answer: y = 32/7
Step-by-step explanation:
Solve the first equation for x by subtracting the 2y from the left side and getting: x = 1 - 2y.
Plug this in to the second equation: 2(1 - 2y) - 3y = -30 → 2 - 4y - 3y = -30 →
-7y = -32 → y = 32/7. Hope this helps!
¿Cuántos enteros divisibles por 9 hay entre 95 y 450?
Answers
Answer:
s so you're going to divide when you going to divide 95 why you take it to the other side it will become 95 * 450 equals to 42750 / 9 when we divide 42750 / 9 to give you 4750 that is your answe
I will mark brainliest for the first person to answer my question
Answers
Answer:
A. Line
<------------->
B. Angle
⦟
C. Line Segment
.___________.
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
Find an explicit formula for the geometric sequence 2, 6, 18, 54, ....
Note: the first term should be b(1).
b(n)=
Answers
The geometric sequence can be represented explicitly or as recursions
The explicit formula of the geometric sequence is b(n) = 2 * 3^(n-1)
How to determine the explicit formula?The sequence is given as:
2, 6, 18, 54, ....
Start by calculating the common ratio (r)
r = b2/b1
This gives
r = 6/2
Evaluate the quotient
r = 3
A geometric sequence is represented as:
b(n) = b1 * r^(n-1)
This gives
b(n) = 2 * 3^(n-1)
Hence, the explicit formula of the geometric sequence is b(n) = 2 * 3^(n-1)
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1. Find the length of the arc shown in red:
2. Find the area of the circle:
Answers
Answer:
Step-by-step explanation:
What are the solution(s) for the quadratic equation?
Y=5x^2-9x+4
Show work
Answers
Let's see
[tex]\\ \rm\rightarrowtail 5x^2-9x+4=0[/tex]
[tex]\\ \rm\rightarrowtail 5x^2-5x-4x+4=0[/tex]
[tex]\\ \rm\rightarrowtail 5x(x-1)-4(x-1)=0[/tex]
[tex]\\ \rm\rightarrowtail (5x-4)(x-1)=0[/tex]
[tex]\\ \rm\rightarrowtail x=4/5,1[/tex]
Solve each equation by finding square roots. If the equation has no real-number solution, write no solution. N^2 = 81
Answers
Answer:
N = 9
Step-by-step explanation:
N^2 = 81
NxN = 81
N = 9 because 81/9 = 9 and if you don't trust me use a calculator
what do you call the statements that are assumed to be true and do not need proof?
Answers
Answer:
A postulate :)
Step-by-step explanation:
This is because a postulate is a statement that is assumed true without proof, while a theorem is a true statement that can be proven.
Hope this helps!
simplify the following expression 4√72
Answers
Answer:
Hope this helps it is in the file below.
If you were writing a two-column proof proving that ANQP APON, which of the following statements would have
"reflexive property of congruence" as its reason?
A. ON ON
B. OP=OP
C. OP=OP
D. NP NP
Answers
Answer:
NP NP
Step-by-step explanation:
this is the only solution that works for the question
what is the solution of the system of equations 4x+2y=-1 and 3x+4y=3
Answers
Answer:
7x+6y=2
Step-by-step explanation:
All you have to do is add both of the equations together.