System of Graph per 2
Answers
To solve the given system, we have to graph each equation.
\(y=-2x\)Let's find the points when x = 1, x = 2.
\(\begin{gathered} y=-2\cdot1=-2 \\ y=-2\cdot2=-4 \end{gathered}\)The points for the first line are (1, -2) and (2, -4). Now, let's plot these points and draw the line
Now, let's repeat the process for the second equation.
\(y=3x+5\)For x = 0, and x = 1, we have
\(\begin{gathered} y=3\cdot0+5=5 \\ y=3\cdot1+5=3+5=8 \end{gathered}\)The points are (0, 5) and (1, 8). Let's graph the second line
As you can observe in the image above, the lines intersect at (-1, 2).
Hence, the solution to the system is (-1,2).
Related Questions
if a party has food to sustain 200 people for 4 days,how many days will the food sustain 160 people
WILL MARK AS BRAINLIEST
Answers
Proportionately, if a party has food to sustain 200 people for 4 days, the food will sustain 160 people for 5 days.
What is proportion?The proportion refers to the ratio that one quantity, value, or expression has in comparison with another.
Proportion is a fractional value that is depicted using decimals, fractions, and percentages.
The number of people sustained by the food for 4 days = 200
The number of days the food sustained 200 people = 4 days
Proportionately, the food will sustain 200 for 5 days (200/160 x 4)
Thus, the food that sustains 200 people for 4 days will sustain 160 people for 5 days, based on the principle of proportional relationships.
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Suppose you invest $140 at the end of each month for 5 years into an account earning 9% annual interest compounded monthly. After 5 years, you leave the money, without making additional deposits, in the account for another 22 years. How much will you have in the end?
Answers
Answer:
$75,915.92
Step-by-step explanation:
You want the value of an annuity of $140 per month for 5 years at 9% compounded monthly, after it has accumulated interest for 22 more years.
AnnuityThe formula for the future value of an ordinary annuity is ...
A = P(n/r)((1 +r/n)^(nt) -1)
where P is the periodic payment made n times per year for t years and the account earns annual interest rate r.
The value of $140 monthly payments after 5 years is ...
A = $140·(12/0.09)((1 +0.09/12)^(12·5) -1) = $140(1.0075^60 -1)/0.0075
A ≈ $10559.38
Compound interestThat annuity balance will then earn interest compounded monthly for another 22 years. Its value will become ...
A = ($10559.38)(1.0075^(22·12)) ≈ $75,915.92
You will have about $75,915.92 in the end.
__
Additional comment
An actual account would have the interest amount rounded monthly, so the final value would be slightly different from the values calculated here. Usually the difference is on the order of a dollar or so.
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3(4x + 5y) what is it
Answers
Answer: 12x+15y
Step-by-step explanation:
Answer:
12x + 15y
Step-by-step explanation:
You take the three and multiply 3 x 4 and then 3 x 5 for your answer.
a tunnel is constructed with a semielliptical arch. the width of the tunnel is 60 feet, and the maximum height at the center of the tunnel is 25 feet. what is the height of the tunnel 5 feet from the edge? round your answer to the hundredths place.
Answers
As a result, the tunnel is 13.83 feet high, 5 feet from the edge.
An ellipse is an oval curve on a plane that contains two fixed points called foci. The sum of the distances between the two foci from each point on the ellipse is constant at all points.
Since the tunnel has an arch that is semi-elliptical, we can put the ellipse's center at the center of its 60-foot width.
What is an ellipse?
An ellipse is a two-dimensional shape that is defined by its axes in geometry. When a plane intersects a cone at an angle to its base, it creates an ellipse. It focuses on two things. For each point in the curve, the sum of the two distances to the focal point remains constant.
What are an ellipse and an example?
An ellipse is the locus of points whose sum of their distances from its two foci is constant and has an eccentricity of less than one. The two-dimensional egg shape and the running tracking in a sports stadium are simple examples of the ellipse in our everyday lives.
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determine the open t-intervals on which the curve is concave downward or concave upward. x = 5 3t2, y = 3t2 t3
Answers
The curve is concave downward for t < -1, and concave upward for t > -1
The concavity of the curve defined by the parametric equations x = 5t² and y = 3t² + t³, we need to analyze the second derivatives with respect to t.
First, we find the first derivatives:
dx/dt = 10t
dy/dt = 6t + 3t²
Next, we find the second derivatives:
d²x/dt² = 10
d²y/dt² = 6 + 6t
To determine the concavity, we examine the sign of the second derivative.
When d²y/dt² > 0, the curve is concave upward.
When d²y/dt² < 0, the curve is concave downward.
Now, let's find the values of t for which the curve changes concavity:
d²y/dt² > 0:
6 + 6t > 0
t > -1
d²y/dt² < 0:
6 + 6t < 0
t < -1
So, the curve is concave upward for t > -1, and concave downward for t < -1.
To determine the open t-intervals on which the curve is concave downward or concave upward, we need to find the interval for t where the concavity changes.
Since t < -1 is the only value for which the concavity changes, the open t-interval on which the curve is concave downward is (-∞, -1), and the open t-interval on which the curve is concave upward is (-1, ∞).
Therefore, the curve is concave downward for t < -1, and concave upward for t > -1.
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Pls help me quick with this question ( will give brainy for correct )
Answers
The inequality solved for y is:
y ≥ 21/25
How to solve the ienquality for y?To solve an inequality for one variable, we need to isolate that variable.
Here we have:
(8/7)y -1 ≥ (3/7)y - 2/5
Move the terms with y to the left side and the others to the right side.
(8/7)y - (3/7)y ≥ -2/5 + 1
(5/7)y ≥ (3/5)
Now multiply both sides by 7/5, we will get:
y ≥ (3/5)*(7/5)
y ≥ 21/25
That is the solution simplfied.
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HOW FO I SOLVE THIS? ASAP!
Answers
Applying the centroid theorem, the measures in the triangle are:
x ≈ 4.1; AC = 9.1; AE = 13.5; CE = 4.4
How to Apply the Centroid Theorem?Since point C is the centroid of triangle ADF, the centroid theorem states that:
Length of AC = 2/3(length of AE)
Given the following:
AC = x + 5
AE = 5x - 7
Plug in the values:
x + 5 = 2/3(5x - 7)
Multiply both sides by 3
3(x + 5) = 3 * 2/3(5x - 7)
3x + 15 = 2(5x - 7)
3x + 15 = 10x - 14
Combine like terms:
3x - 10x = -15 - 14
-7x = -29
x ≈ 4.1
AC = x + 5 = 4.1 + 5 = 9.1
AE = 5x - 7 = 5(4.1) - 7 = 13.5
CE = AE - AC = 13.5 - 9.1 = 4.4
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After heating up in a teapot, a cup of hot water is poured at a temperature of 210°F. The cup sits to cool in a room at a temperature of 70° F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between the temperature of the water and the temperature of the room, as given by the formula below: T = T. + (To - Tale To = the temperature surrounding the object To = the initial temperature of the object t = the time in minutes T= the temperature of the object after t minutes k = decay constant The cup of water reaches the temperature of 197°F after 1.5 minutes. Using this information, find the value of k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 4 minutes. Enter only the final temperature into the input box.
Answers
Newton's Law of Cooling:
\(T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}\)
\(T(t) =\) Temperature given at a time
\(t =\) Time
\(T_{s} =\) Surrounding temperature
\(T_{o}=\) Initial temperature
\(e =\) Constant (Euler's number) ≈ 2.72
\(k =\) Constant
Using this information, find the value of \(k\), to the nearest thousandth, then use the resulting equation to determine the temperature of the water cup after 4 minutes.
First, plug in the given values in the equation and solve for \(k\):
\(T(t) =\) 197°, \(t =\) 1.5 minutes, \(T_{s} =\) 70° and \(T_{o}=\) 210°
\(T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}\\197=70+(210-70)e^{-1.5k} \\197 -70 = (140)e^{-1.5k} \\127 =(140)e^{-1.5k}\\\frac{127}{140}=e^{-1.5k} \\ln(\frac{127}{140})=-1.5k\\-0.097=-1.5k\\0.0649 = k\)
\(k\) ≈ \(0.065\)
Let the temperature of the water cup after \(t = 4\) minutes be \(T(t) = x\)
Now, let's plug the new time and \(k\) constant in the equation and solve for \(x\):
\(T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}\\\\\x=70+(210-70})e^{-0.065*4}\\\\x=70+(140})e^{-0.26}, -0.26=-\frac{26}{100}=-\frac{13}{50} \\\)
\(x=70+(140})e^{-\frac{13}{50}}\\\\\)
\(x=70+(140})e^{\frac{1}{\frac{13}{50}}\\\\\\\)
\(x=70+e^{\frac{140}{\frac{13}{50}}\\\\\\\)
\(x=70+{\frac{140}{\sqrt[50]{e^{13}}}\\\)
\(x = 70 +\frac{140}{1.3} \\x=70+107.947\\\)
\(x=177.95\) ≈ \(178\)
Temperature of water after 4 minutes is 178°
sorry if there's any misspelling or wrong step but I hope my answer is correct ':3
What is the area of the triangle?
Enter your answer in the box.
in²
Right triangle with sides forming the right traingle labeled 25 inches and 60 inches and the side across from the right angle labeled 65 inches.
Answers
Using it's formula, the area of the right triangle is of 750 inches squared.
What is the area of a right triangle?The area of a right triangle is given by half the multiplication of the two legs, which are the two smaller sides.
In this problem, the two legs are 25 inches and 60 inches, hence the area of the triangle is:
A = 0.5 x 25 x 60 = 750 inches².
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Question 7 of 10 these tables represent a quadratic function with a vertex at (0, -1). what is the average rate of change for the interval from x = 7 to x =8 a. -65 b-2 c. - 5 d. -50
Answers
The average rate of change for the interval from x = 7 to x = 8 is 3. To find the average rate of change for the interval from x = 7 to x = 8, we need to calculate the slope of the line passing through the points (7, f(7)) and (8, f(8)), where f(x) is the quadratic function with a vertex at (0, -1).
Since the vertex is at (0, -1), we know that the equation of the quadratic function is in the form f(x) = a(x - 0)^2 - 1, where a is a constant. To find the value of a, we can use one of the other points on the graph. Let's use the point (1, 2), which is given in the problem. Substituting these values into the equation, we get:
2 = a(1 - 0)^2 - 1
3 = a
So the equation of the quadratic function is f(x) = 3x^2 - 1. Now we can calculate the slope of the line passing through (7, f(7)) and (8, f(8)):
slope = (f(8) - f(7))/(8 - 7)
= (3(8)^2 - 1 - (3(7)^2 - 1))/(8 - 7)
= (191 - 188)/(8 - 7)
= 3
Therefore, the average rate of change for the interval from x = 7 to x = 8 is 3. None of the answer choices provided match this result, so we cannot select an answer from the options given.
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a. Seven prizes are to be given to seven different people in a group of 9. In how many ways can a first prize, a second prize, two third prizes, and three fourth prizes be awarded?b. If an urn has 5 white balls, 10 red balls, and 6 green balls, what is the probability that 4 randomly selected balls are all green?
Answers
The number of ways prizes can be distributed is 30240. The probability of getting a all four green balls is 0.0038
a. Seven prizes are distributed to a group of 9 people. So the total number of combinations will be
ₙCr = n!/ r!(n-r)!
₉C₇ =9!/ 7! (9-7)1 = 36
Total permutations between the chosen 7. Each will get either first, second, third or fourth. So the total permutation can be
nPr = n!/(n-r)!
₇P₄ = 7!/(7-4)! = 840
So the total ways the prize can be distributed = 36× 840 = 30240
b. Number of white balls = 5
Number of red balls = 10
Number of green balls = 6
Total number of balls = 5+10+6 =19
The combination of choosing 4 balls from 19 = ₁₉C₄ = 3876
The combination for all four balls to be green = ₆C₄ = 15.
Probability = number of likely events/ Total number of events = 15/3876 = 0.0038
So the answer for question a is 30240 and for b is 0.0038.
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Solve the system of linear equations by graphing.
- 6x - y = -8
1/2Y = 4-3x
Answers
Answer:
\(x=\frac{-8+y}{6}\)
Step-by-step explanation:
Let us evaluate this problem.
First, add Y to both sides
\(-6x-y+y=-8+y\)
Always remember to simplify.
\(-6x=-8+y\)
Divide both sides by -6
\(\frac{-6x}{6} =\frac{8}{-6} +\frac{y}{-6}\)
Simplify one more time.
\(x=\frac{-8+y}{6}\)
Your final answer is:
\(x=\frac{-8+y}{6}\)
Is this table a function or not a function
Answers
Answer:
it is a function
Step-by-step explanation:
Answer:
NO It isn't a function
Step-by-step explanation:
To first find out if something is a function or not, you see is the any of the x values given are the same ans if they are, its automatically not a function. There are also other ways to find out if it is or isn't.
how to acquire 401k step by step pls!!!
Answers
Decide how much to contribute.
Get a 401(k) match.
Consider a Roth 401(k).
Scrutinize autopilot settings.
Pick diversified 401(k) investments.
Keep 401(k) costs low.
Balance retirement saving with other expenses.
Roll over your 401(k) when you change jobs.
8.65 percent compounded monthly. (Round answer to 2 decimal places, e.g. 15.25%.) Effective annual rate \%
Answers
The effective annual rate for a 8.65% interest compounded monthly is 9.14%.
To calculate the effective annual rate, we need to take into account the compounding frequency. In this case, the interest is compounded monthly.
We can use the formula for compound interest to calculate the effective annual rate:
Effective Annual Rate = (1 + (interest rate / compounding frequency))^compounding frequency - 1
Plugging in the given values:
Effective Annual Rate = (1 + (8.65% / 12))^12 - 1
= (1 + 0.0072083)^12 - 1
= 1.0072083^12 - 1
≈ 0.0914 or 9.14%
Therefore, the effective annual rate for a 8.65% interest compounded monthly is approximately 9.14%.
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Given f(x) = 2x - 5 and g(x) = 3x - 4, find g(f(6))
Answers
Answer:
\(g(f(6))= 17\)
Step-by-step explanation:
\(g(f(6))= 3(2(6) - 5) - 4\)
\(3(12 - 5) - 4\)
\(3(7) - 4\)
\(21-4\)
\(g(f(6))= 17\)
Answer:
g(f(6)) = 17
Step-by-step explanation:
f(x) = 2x - 5
g(x) = 3x - 4,
g(f(6))
First find f(6) = 2*6 -5 = 12-5 = 7
Then find g(7) = 3*7 -4 = 21-4 = 17
g(f(6)) = 17
What percent of newborn African lions weigh less than 3 pounds? b. What percent of newborn African lions weigh more than 3.8 pounds?
Answers
The weight distribution of newborn African lions may not necessarily follow a normal distribution, and the actual percentages can vary based on the specific data available.
To determine the percentage of newborn African lions that weigh less than 3 pounds and the percentage that weigh more than 3.8 pounds, we would need statistical data on the weight distribution of newborn African lions. Since we don't have that information, we cannot provide the exact percentages.
However, if we assume that the weights of newborn African lions follow a normal distribution, we can use the properties of the standard normal distribution to make an estimation.
For the percentage of newborn African lions weighing less than 3 pounds:
We would need to know the mean and standard deviation of the weight distribution to calculate the Z-score for a weight of 3 pounds and then find the corresponding percentage using a standard normal distribution table. Without this information, we cannot provide an accurate estimation.
For the percentage of newborn African lions weighing more than 3.8 pounds:
Similarly, we would need the mean and standard deviation of the weight distribution to calculate the Z-score for a weight of 3.8 pounds and find the corresponding percentage using a standard normal distribution table. Without the required information, we cannot provide a specific estimation.
Please note that the weight distribution of newborn African lions may not necessarily follow a normal distribution, and the actual percentages can vary based on the specific data available.
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The number $m$ is a three-digit positive integer and is the product of the three distinct prime factors $x$, $y$ and $10x y$, where $x$ and $y$ are each less than 10. What is the largest possible value of $m$
Answers
largest possible value of $m$ is x=5, y =3, 10*5+3=53: 3 x 5 x 53 =795
What is prime factors ?A prime factor is a natural number, other than 1, whose only factors are 1 and itself. The first few prime numbers are actually 2, 3, 5, 7, 11, and so on.The simplest algorithm to find the prime factors of a number is to keep on dividing the original number by prime factors until we get the remainder equal to 1. For example, prime factorizing the number 30 we get, 30/2 = 15, 15/3 = 5, 5/5 = 1. Since we received the remainder, it cannot be further factorizedPrime factorisation is a method to find the prime factors of a given number, say a composite number. These factors are nothing but the prime numbers. A prime number is a number which has only two factors, i.e. 1 and the number itself.For example, 2 is a prime number which has two factors, 2 × 1. Whereas a composite number has more than two factors present in it. For example, 4 has three factors such as 1 × 2 ×To learn more about prime factors refers to:
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What kind of Slope goes up and to the right? What kind of Slope goes down to the right? What kind of Slope is flat?
Answers
Answer:
A positive slope goes up and to the right
A negative slope goes down and to the right
A slope of zero creates a flat line
Step-by-step explanation:
A positive slope goes up and to the right, because that means the graph is increasing.
A negative slope goes down and to the right, because that means the graph is decreasing.
A slope of zero creates a flat line, such as a horizontal line that never increases in the y value.
at old oak farm, there are chicken and horses. there are 120 legs and 48 heads altogether. how many horses and how many chickens are there?
Answers
Answer:
Step-by-step explanation:
We must use system of equations:
horses = h chickens = c
horses have 4 legs & chickens have 2 and there are 120 legs total so to set up the first part of the equation...
4h + 2c = 120
They both have only 1 head each and there are 48 heads total so to set up the second part of the equation...
h + c = 48
Now we combine the equations and solve:
4h + 2c = 120
h + c = 48
Now we solve...
4h + 2c = 120
h = 48 - c (subtract c on both sides to single out h)
--------------------
4(48 - c) + 2c = 120
192 - 4c + 2c = 120
-192 -192
----------------------------
-2c = -72 (divide both sides by -2)
c = 36
Now we go back and find the value of h...
h = 48 - c
h = 48 - 36
h = 12
So there are 36 chickens & 12 horses!
1
(n+2)
п+2) + 4 = 3n — 5
2
Answers
Answer:
2.4 that what I got
Step-by-step explanation:
Answer:
n=29
Step-by-step explanation:
Given h(x) = –3x – 5, solve for x when h(x) = –2.
Answers
= 6 - 5
= 1
Answer:
1
Step-by-step explanation:
h(-2)=-3(-2)-5
h(-2)=6-5
h(-2)=1
h(-2)=1
x=-2, but i'm assuming you want h(x)
Write the equation y- 6 = _5(x + 1) in
slope-intercept form.
Answers
Answer:
y = -5x + 1
Step-by-step explanation:
y - 6 = -5 (x + 1)
distribute -5 (x + 1) by multiplying
y - 6 = -5x - 5
than add 6 to both sides
y = -5x + 1
Ben uses a compass and a straightedige to bisect angle PQR, as shown below.
B
Wie statement beste wy Ben uses the cate with to draw Som there?
Answers
Answer:
The answer is <AQS = BQS when AS=BQ and AQ=BQ
Step-by-step explanation:
Which of these is true?
a) Some ordered pairs of real numbers are not points in the Cartesian coordinate system.
b)Only integer ordered pairs are allowed in the coordinate system.
c)There is no point in the coordinate system with the ordered pair (T, Tt)
d)all of the above are false
Answers
9514 1404 393
Answer:
d) all of the above are false
Step-by-step explanation:
Every ordered pair of real numbers is a point in the Cartesian coordinate system.
The various statement saying otherwise are all false.
Calculate the reliability of the following system:
0.90 0.90
0.90 0.90 0.85
0.85 0.85 0.92
Answers
The reliability of the given system is 0.4033.
To calculate the reliability of a system, we need to multiply the reliability values of all the components in the system. In this case, we have a system composed of three components with the following reliability values:
Component 1: 0.90
Component 2: 0.90 0.90 0.85
Component 3: 0.85 0.85 0.92
To find the overall system reliability, we multiply these values together:
System reliability = Component 1 reliability x Component 2 reliability x Component 3 reliability
System reliability = 0.90 x (0.90 x 0.90 x 0.85) x (0.85 x 0.85 *x 0.92)
System reliability ≈ 0.90 x 0.6831 x 0.6528 ≈ 0.4033
Therefore, the reliability of the given system is 0.4033.
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-1 1/4 × -4/5+1/4÷3
5/9×1/11+5/9×4/11-5/9×14/11
Answers
Answer:/11-5/9×14/11
Step-by-step explanation:
-4/5+1/4÷3
Helppp againnn... please-
Answers
Answer:
Its 16/81
Step-by-step explanation:
Mira and Vernon are simplifying the expression 5(x-2)-3(x-2).
Who's process is correct, Mira, Vernon, or both?
Explain your reasoning inc1 to 2 sentences
Answers
Answer:
The answer with 2x-4
Step-by-step explanation:
You haven't provided with the process followed by Mira and Vernon.
So, take the following as reference and figure it out yourself,
5(x-2)-3(x-2) or,
(5-3)(x-2) 5x-10-3x+6
2(x-2) 2x-4
2x-4
Gail averages 153 points per bowling game with a standard deviation of 14.5 points. Suppose Gail's points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(153, 14.5). z-score when x=108 is _____. The mean is 153. The z-score tell you that x=108 is _____ standard deviations to the left of the mean.
Answers
The z-score when x=108 is 3.1034. The z-score tells you that x=108 is 3.1034 standard deviations to the left of the mean.
Z-score is used in statistics to compare a score to a normal distribution. The z-score is a measure of how far away from the mean a value is in standard deviation units.
To find the z-score when x = 108, we use the formula:
z = (x - μ) / σ
where x = 108, μ = 153, and σ = 14.5.
Substituting these values, we get:
z = (108 - 153) / 14.5 = -3.1034
So the z-score when x = 108 is -3.1034.
The z-score tells us how many standard deviations away from the mean a particular value is. In this case, since the z-score is negative, we know that x = 108 is to the left of the mean.
The absolute value of the z-score tells us how many standard deviations away from the mean the value is. In this case, the absolute value of the z-score is approximately 3.1034, which means that x = 108 is approximately 3.1034 standard deviations to the left of the mean.
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