Use algebraic rules of equations to predict the solution type to the system of equations
Answers
The solution type to the system is one solution or consistent system
How to predict the solution type to the system?From the question, we have the following parameters that can be used in our computation:
f(x) = [x + y = 4
[y = 2x - 1
Substitute y = 2x - 1 in the equation x + y= 4
So, we have the following representation
x + 2x - 1 = 4
Evaluate the like terms
3x = 5
So, we have
x = 5/3
Substitute x = 5/3 in y = 2x - 1
So, we have the following representation
y = 2 * 5/3 - 1
Evaluate
y = 2.33
Because x and y have real values
Then, the solution type is a consistent system
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Related Questions
Find the absolute maximum and minimum values of f on the set D. f(x, y) = x4 + y4 − 4xy + 2, D = {(x, y) | 0 ≤ x ≤ 3, 0 ≤ y ≤ 2}
Answers
Answer:
Absolute maximum at (3,0)
Absolute minimum at (1,1)
Step-by-step explanation:
Given - f(x, y) = x⁴ + y⁴ − 4xy + 2, D = {(x, y) | 0 ≤ x ≤ 3, 0 ≤ y ≤ 2}
To find - Find the absolute maximum and minimum values of f on the set D.
Proof -
Given that, f(x, y) = x⁴ + y⁴ − 4xy + 2
Now,
Differentiate f(x,y) with respect to x and y , we get
[tex]f_{x}(x,y)[/tex] = 4x³ - 4y
[tex]f_{y}(x,y)[/tex] = 4y³ - 4x
Now,
For the critical point, put [tex]f_{x}(x,y)[/tex] , [tex]f_{y}(x,y)[/tex] = 0
we get
4x³ - 4x = 0
⇒x = 0, -1, 1
but given the range of x is 0 ≤x ≤ 3
⇒x = 0, 1
⇒y = 0, 1
∴ we get
2 critical points (x,y) = (0,0) , (1,1)
Now,
Put the values of x and y in f(x,y), we get
f(0,0) = 0 + 0 - 0 + 2 = 2
f(1,1) = 1 + 1 - 4 + 2 = 0
Now,
for the max and min values, finding the critical value is not enought, we have to find the values in the domain also.
Given domain is 0 ≤ x ≤ 3, 0 ≤ y ≤ 2
So, we have to check the values at the rectangle that have the coordinates
(0,0), (0,2), (3,2), (3,0)
Now,
f(0,0) = 0 + 0 - 0 + 2 = 2
f(0,2) = 0 + 16 - 0 + 2 = 18
f(3,2) = 81 + 16 - 24 + 2 = 75
f(3,0) = 81 + 0 - 0 + 2 = 83
∴ we get
Absolute maximum at (3,0)
Absolute minimum at (1,1)
Tommy took one of his friends out to dinner. The dinner cost $100 and he paid 3% sales tax. If Tommy left an 18% tip on the $100, how much in total did he pay?
Answers
Answer:
121
Step-by-step explanation:
3% of 100 = 3
18% of 100 = 18
100+3+18=121
To solve the equation 5sin(2x)=3cosx, you should rewrite it as___.
Answers
Answer:
A
Step-by-step explanation:
We want to solve the equation:
[tex]5\sin(2x)=3\cos(x)[/tex]
To do so, we can rewrite the equation.
Recall the double-angle identity for sine:
[tex]\sin(2x)=2\sin(x)\cos(x)[/tex]
By substitution:
[tex]5\left(2\sin(x)\cos(x)\right)=3\cos(x)[/tex]
Distribute:
[tex]10\sin(x)\cos(x)=3\cos(x)[/tex]
We can subtract 3cos(x) from both sides:
[tex]10\sin(x)\cos(x)-3\cos(x)=0[/tex]
And factor:
[tex]\cos(x)\left(10\sin(x)-3\right)=0[/tex]
Hence, our answer is A.
*It is important to note that we should not divide both sides by cos(x) to acquire 10sin(x) = 3. This is because we need to find the values of x, and one or more may result in cos(x) = 0 and we cannot divide by 0. Hence, we should subtract and then factor.
Answer:
A. cosx(10sinx-3)=0
Step-by-step explanation:
5(2sinxcosx)=3cosx
10sinxcosx-3cosx=0
cosx(10sinx-3)=0
Which option identifies the systematic error in the following scenario?
Mary is measuring the weight of an object using a scale. The scale reads 2 lbs. too high for the first measurement she takes. When she takes the measurement again using the same steps, the scale again reads 2 lbs. too high.
A.) The error cannot be predicted to occur.
B.) The error can be reproduced.
C.) The error in measurement is estimated.
D.) The error amount fluctuates.
Answers
Answer:
B the error can be reproduced
In a bag of red and green Holiday M&M’s there are 40 red M&Ms for every 100 M&Ms. How many red M&M’s are in the bag if there are 300 M&M’s total?
Answers
Answer:
if there are 300 m&m's there will be 120 red
I have nothing to do
Answers
Answer:
ok cool, bro'
Step-by-step explanation:
amazing
Answer:
paint
clean your room
call some friends
find a new hobby
bake/cook
re-do your room
make a wishlist
do some skincare
start learning a new language
start a new netflix series
bike ride/skate/drive
Can some explain how to do algebra and what's the easiest way to do it
Please explain on the best possible
Answers
Answer: The most important aspect in doing algebra is having a pen/pencil and paper in hand. It'll give you a better understanding of the question being posed.
There are 13 flavors at the soda machine, and anyone can choose 6. A sign says we are only allowed to use one of each flavor. You decide to grab a cup and fill it up with your favorite flavors at random (it’s all going to the same place, right?). How many possible soda mixtures can you make?
Answers
Answer:
1716 soda mixtures
A person can choose in 1716 different ways.
What is combination?A combination is a way of selecting items from a collection where the order of selection does not matter.
Given that there 13 flavors at a soda station, a person has to choose 6 out of this,
We need to find how many possible soda mixtures can you make,
So, using here the concept of combination,
ⁿCₓ = n! / x!(n-x)!
Here, n = 13 and x = 6,
So,
¹³C₆ = 13! / 6!(13-6)!
= 13! / 6! × 7!
= 13 × 12 × 11 × 10 × 9 × 8 × 7! / 6! × 7!
= 13 × 12 × 11 × 10 × 9 × 8 / 6!
= 13 × 12 × 11 × 10 × 9 × 8 / 720
= 1716
Hence a person can choose in 1716 different ways.
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HELP ASAP WILL GIVE BRAINLIEST PLS!!!!
How can you use probability to understand why events happen or do not happen?
Answers
ANSWER:
By determining the number of possible outcomes, we have to examine many reasons behind the events. When examining the reasons behind these events we will eventually find a pattern. This pattern is what tells us how often something may or may not happen. By knowing how often something may or may not happen we can determine when it will reoccur in the future.
Step-by-step explanation:
Marty has 1 dozen eggs. He needs 4 eggs to bake a cake.How many cakes can he bake.
If you see this your lucky.
You will get 80 points if you answer this.
This is easy
Answers
Answer:
3
Step-by-step explanation:
12 didved by 4 is 3
Answer:
3 cakes
Step-by-step explanation:
3 cakes can be bake with dozen if eggs
Minnie shovels driveways to earn money. She can shovel 6 driveways in 4 hours. She earns $19.00 for each driveway. Minnie is saving up to buy a new phone that costs $1 567.50. How many hours does Minnie need to work to earn enough money to purchase the phone? s incorrect. Change your answer and try again! 2 3 4 5 6 7 00
Answers
9514 1404 393
Answer:
55 hours
Step-by-step explanation:
The number of hours will be ...
($1567.50) ÷ ($19/driveway) ÷ (6 driveways)/(4 h)
= (1567.50×4)/(19×6) h = 55 h
Minnie needs to shovel driveways for 55 hours to hear enough for the new phone.
Answer:
about 55.275 hours. You may have to round it to the nearest tenth or whole number, whatever the question tells you to do, but this is the approximate answer. PLEASE VOTE BRAINLIEST!
Step-by-step explanation:
What we know:
6 driveways in 4 hours
$19 per driveway
needs $1,567.50
first, find amount of hours for one drive way by setting up a proportion.
6/4 =1/x
x= about 0.67 hours, or about 40.2 minutes.
now think: how many driveways does it take to make 1,567.50?
1,567.50/19= 82.5
This means it will take her 83 driveways to earn all of her money.
The final step is to multiply this by the amount of minutes, and then you will have your answer! 82.5*40.2= 3316.5
Divide by 60 to convert to hours.
Answer: 55.275
Suppose the lifetime of a cell phone battery is normally distributed with a mean of 36 months and a standard deviation of 2 months. If the company wants to replace no more than 2% of all batteries, for how many months should they guarantee the lifetime of their batteries
Answers
Answer:
They should guarantee the lifetime of their batteries for 32 months.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 36 months and a standard deviation of 2 months.
This means that [tex]\mu = 36, \sigma = 2[/tex]
If the company wants to replace no more than 2% of all batteries, for how many months should they guarantee the lifetime of their batteries?
The guarantee should be the 2th percentile of lengths, which is X when Z has a pvalue of 0.02. So X when Z = -2.054.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-2.054 = \frac{X - 36}{2}[/tex]
[tex]X - 36 = -2.054*2[/tex]
[tex]X = 31.89[/tex]
Rounding to the closest month, 32.
They should guarantee the lifetime of their batteries for 32 months.
15 - a = 17 what is a?
Answers
Answer:
a = -2
Step-by-step explanation:
15-a =17
a=15 - 17
a=-2
Answer:
hi
Step-by-step explanation:
-a=17-15
-a=2
have a nice day
Find the volume of the
rectangular prism.
3 cm
9 cm
7 cm
V = [?]
Answers
Answer:
Step-by-step explanation:
V = L * W * D
V = 9 * 7 * 3
V = 189 cm^3
Answer: 189
Step-by-step explanation: 3*9*7
NEED HELP IN FINDING AREA
Answers
Answer:
492 yd^2
Step-by-step explanation:
Way 1: 250 + 242 = 492
Way 2: 800 - 132 - 176 = 492
Write the new equation if the graph of f(x)= 4x^2 + 3 is
translated up 4 units.
Answers
Some one help please
Answers
Answer:
subtracting 14 from sides of the number sentence
Step-by-step explanation:
14 + n = 84
Since 14 is being added to n, you need to subtract 14 from both sides to solve for n.
Answer: subtracting 14 from sides of the number sentence
Evelyn is going to invest $3,500 and leave it in an account for 16 years. Assuming the interest is compounded quarterly, what interest rate, to the nearest tenth of a percent, would be required in order for Evelyn to end up with $6,200?
Answers
Answer:
Quarterly interest rate= 0.8974%
Step-by-step explanation:
Giving the following formula:
Initial investment (PV)= $3,500
Future Value (FV)= $6,200
Number of periods (n)= 16*4= 64 quarters
It is almost impossible to calculate the interest rate using a formula. To determine the interest rate, we need to use a financial calculator:
Function: CMPD
n= 64
I%= SOLVE= 0.8974
PV= 3,500
FV= -6,200
Quarterly interest rate= 0.8974%
Answer:
3.6%
Step-by-step explanation:
Solve for x and round to the nearest tenth
Answers
9514 1404 393
Answer:
88.9
Step-by-step explanation:
The relevant trig relation is ...
Cos = Adjacent/Hypotenuse
cos(77°) = 20/x
x = 20/cos(77°)
x ≈ 88.9
At a particular fast food restaurant, tacos cost $1.29 and
burritos cost $2.19. Michael spent a total of $42.93 at the
restaurant to buy food for a party. If he purchased half as
many burritos as tacos, how many tacos did he buy?
Answers
Answer:
9 burritos and 18 tacos
Step-by-step explanation:
We can start this problem by assigning a variable to our unknowns.
Let's name x the number of burritos he buys.
The question states he buys half as many burritos as tacos.
Therefore, the number of tacos he bought is 2x.
Let's set up an equation.
(Cost of burrito)(number of burritos)+(Cost of taco)(number of tacos)=Total Cost
2.19x+1.29(2x)=42.93
Simplify
2.19x+2.58x=42.93
4.77x=42.93
x=9
Michael bought 9 burritos.
2*9=18
Michael bought 18 tacos.
Answer:
[tex] \displaystyle 18[/tex]
Step-by-step explanation:
we are given that,
tacos cost $1.29 burritos cost $2.19Michael spent a total of $42.93he purchased half as many burritos as tacoslet the number of tacos and burritos be t and b respectively
according to the 3rd condition we get:
[tex] \displaystyle 1.29t + 2.19b = 42.93[/tex]
according to the 4th condition we obtain:
[tex] \displaystyle t = 2b[/tex]
therefore our system of linear equation is
[tex]\begin{cases}\displaystyle t=2b \\ \displaystyle 1.29t + 2.19b = 42.93\end{cases}[/tex]
so now we end up with a system of linear equation in order to solve the equation we can consider substitution method
so substitute the value of t which yields:
[tex] \displaystyle 1.29 \cdot 2b+ 2.19b = 42.93[/tex]
simplify multiplication:
[tex] \displaystyle 2.58b+ 2.19b = 42.93[/tex]
since we have same variable we can consider the like terms:
[tex] \displaystyle 4.77b = 42.93[/tex]
divide both sides by 4.77:
[tex] \displaystyle \frac{4.77b }{4.77}= \frac{ 42.93}{4.77}[/tex]
reduce fraction:
[tex] \displaystyle \bcancel{ \frac{4.77b }{4.77}}= \cancel \frac{ \stackrel{ \large9}{ 42.93}}{4.77}[/tex]
[tex] \displaystyle b = 9[/tex]
now substitute the value of b:
[tex] \displaystyle t = 2.9[/tex]
simplify multiplication:
[tex] \displaystyle t =18[/tex]
hence,
he bought 18 tacos
Use the models above to explain why a 5×2/3 equals 10×1/3
Answers
Answer:
I kind of need the models to help with this one
5 grams = centigigrams
Answers
Answer:
500
Step-by-step explanation:
I’ll give brainliest and 100 points
Answers
Answer:
Step-by-step explanation:
I first added 13 and 8 to get 21
After that I do 7.5*21 to get 157.5
Then I multiplied 2.5 by 8 to get 20. But it is a triangle so I have to divide by 2 to get 10
I add 10+10+157.5=20+157.5=177.5
177.5 units²
Answer:
I need 1 Brainliest before I can become Virtuoso
Step-by-step explanation:
PLEASE HELP QUICK I NEED IT TO PASS
Answers
Answer:
Its 81
Step-by-step explanation:
How many more students arrive by school bus than by car?
Answers
Answer:
125 more students arrive buy school bus than by car
Step-by-step explanation:
20% + 25% + 15% = 60%
Bus
100 - 60 = 40% ( bus = 40%)
40% = 0.4
0.4 × 500 = 200 (200 students get to school by the school bus)
Car
15% = 0.15
0.15 × 500 =
car = 75 (75 students get to school by car)
difference
200 - 75 = 125 students (125 more students get to school on the school bus then by a car)
2. Triangle ABC is similar to triangle PQR. Which statement is not always true?
1) ZA-ZP 2) ZR-ZC 3) 2B-ZR 4) 2C-ZR
Answers
helppppppppppppppppppppp meeeeeeeeeeeeeeeeeeeeee itssss urgentttttttttttttttttttttttttttttttttttttttttt
Answers
Answer:
the surface area S of the red solid is 90m^2
Step-by-step explanation:
The computation of the surface area of the red solid is shown below:
First find the scale factor i.e.
= 6 ÷ 4
= 1.5
Now the surface area of the red solid is
= 40 × 1.5 × 1.5
= 90m^2
Hence, the surface area S of the red solid is 90m^2
The same would be considered
Which expression can you substitute in the indicated equation to solve 3x − y = 5, x + 2y = 4 ?
A 2y − 4 for x in 3x − y = 5
B 3x − 5 for y in x + 2y = 4
C 3x − 5 for y in 3x − y = 5
D 4 − x for y in 3x − y = 5
Answers
Answer:
3x−y=5;x+2y=4
x=2 and y=1
Step-by-step explanation:
1. Graph the function on the coordinate plane.
(a) What are the x-intercepts?
(b) What is the y-intercept?
(c) What is the maximum or minimum value?
Answers
Answer and step-by-step explanation:
On the graph, it shows no kind of function, all it shows is the coordinate plane. That means that it has no x-intercept, no y-intercept, and has no minimum/maximum. Otherwise, there is not enough information to graph it.
Consider the equation:
y=-x+4
Identify the slope and y-interce