From the given table which represents the two system of linear function is given by y = -4x +10 and y = -3x +2 , the solution of the system of linear function is (x, y) = (8 , -22).
As given in the question,
Table which represents the system of linear function are as follow:
table 1:
x: -4 -2 0 2
y: 26 18 10 2
table 2:
x: -4 -2 0 2
y: 14 8 2 -4
For table1 :
System of linear function:
(x₁ , y₁) = (0,10)
(x₂ , y₂) = (2, 2)
Equation of linear function:
(y -y₁)/ (x-x₁) =(y₂ -y₁)/(x₂ -x₁)
⇒(y -10)/ (x-0) =(2-10)/(2-0)
⇒y-10 =-4(x)
⇒ y = -4x +10 __(1)
For table2 :
System of linear function:
(x₁ , y₁) = (0,2)
(x₂ , y₂) = (2, -4)
Equation of linear function:
(y -y₁)/ (x-x₁) =(y₂ -y₁)/(x₂ -x₁)
⇒(y -2)/ (x-0) =(-4-2)/(2-0)
⇒y-2 =-3(x)
⇒ y = -3x +2 __(2)
Solve system of linear function (1) and (2) we get,
-4x +10 = -3x +2
⇒4x -3x =10 -2
⇒x =8
⇒y = -4(8) +10
= -22
(x, y) = (8 ,-22)
Therefore, from the given table which represents the two system of linear function is given by y = -4x +10 and y = -3x +2 , the solution of the system of linear function is (x, y) = (8 , -22).
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Answer:
D
Step-by-step explanation:
trust
resolver por método de Cramer
1/2x+2/3y=6
-4x+3/5y=8
ayuda
The points (2, -4), (x, y), A, and B all lie on the line.
Find an equation relating x and y. (Lesson 2-11)
An equation relating x and y is given by y = 3x/4 - 11/2.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
For the slope of this line using point AB, we have:
Slope of AB = (2 - (-1))/10 - 6)
Slope of AB = (2 + 1)/4
Slope of AB = 3/4
Since point AB and points (2, -4), (x, y) all lie on the same straight line, they would all of the same slope. Therefore, an equation relating x and y can be calculated as follows:
3/4 = (y + 4)/(x - 2)
3(x - 2) = 4(y + 4)
3x - 6 = 4y + 16
4y = 3x - 6 - 16
4y = 3x - 22
y = 3x/4 - 22/4
y = 3x/4 - 11/2
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its an algebra problem i need help soon
perp. is perpendicular
The slope-intercept form of the equation of the line is y = 2/3(x) - 4
How to determine the slope-intercept form of the equation of the line?Given that: the unknown line passes through (0, -4) and it is perpendicular to y= -3/2(x) + 1
The slope-intercept form of a straight line is:
y = mx + c,
where m is the slope and c is the y-intercept
When the two lines are perpendicular, the product of their slope is -1 i.e.
m₁ × m₂ = -1
where m₁ and m₂ represent the slope of the lines
Let the slope of the given line be m₁ and the slope of the unknown line be m₂
Line1(given):
y = -3/2(x) + 1 and m₁ = -3/2
m₁ × m₂ = -1
-3/2 × m₂= -1
m₂ = 2/3
Line 2(unknown) with the point (0, -4):
y = mx + c (x = 0 and y = -4)
-4 = 3/2(0) + c
c = -4
y = 2/3(x) - 4
Therefore, the slope-intercept form of the equation of the line that passes through (0, -4) and is perpendicular to y= -3/2(x) + 1 is y = 2/3(x) - 4
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the distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. a sample size of 40 is drawn randomly. find the probability that the sum of the 40 values is greater than 7,450. (round your answer to four decimal places.)
The probability that the sum of the 40 values is greater than 7,450 is 0.0239
Define Normal Distribution.
A normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable.Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.Formula of Normal Distribution isZ = (x - μ ) / (σ / √n )
We have given following info,
mean μ = 180
Standard deviation σ = 20
n = 40
σ(mean of x) = σ / √ n
= 20 / √40
= 3.16
Sample average (mean of x) = 7450 / 40
= 186.25
P(x > 186.25) = 1 - P(x < 186.25)
= 1 - P( (x - μ ) / σ(mean of x) ) < ( [186.25 - 180] / 3.16) )
= 1 - P( Z < 1.98)
Using Normal distribution table,
= 1 - 0.9761
P(x > 186.25) = 0.0239
Therefore,the probability that the sum of the 40 values is greater than 7,450 is 0.0239
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386666666667/100000000000 simplest fraction
Answer: ___________________________________________
58/15
a recipe calls for 15oz of flour every 8oz of milk, if you use 150z of milk how much flour should you use
The required weight of the flour is 28.125 ounces.
A recipe calls for 15 ounces of flour for every 8 ounces of milk. It is given that we use 15 ounces of milk. Then we need to calculate the weight of flour we need to use.
The ratios of the ingredients must remain in equal proportions. The fraction of one divided by the other is referred to as the ratio. A proportion is an equation that equates two ratios. We will use the unitary method. Let the weight of the flour required be denoted by the variable "w". A variable is a quantity that can change in a mathematical problem or experiment.
w = (15/8)*15
w = 28.125
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john wanted a pressure washer for a flat fee of $50 plus $9 per hour how many hours did he rent the pressure washer if the total bill was $86?
He rented the pressure washer for 4 hours, given that the total bill was $86.
An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.
Let x = total number of hours he rented the pressure washer
The total bill, which was $86, includes the flat fee of $50 plus $9 per hour of use.
Hence, the equation will be 50 + 9x = 86.
Solve for x.
50 + 9x = 86
9x = 86 - 50
9x = 36
x = 4
total number of hours he rented the pressure washer = 4
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in a one-period binomial model of an option value, the probabilities of an up-move and a down-move are:
In a one-period binomial model of an option value, the probabilities of an up-move and a down-move are "calculated from the model inputs."
What is binomial model?The number of survivors, x, in n independent tests is described by a binomial model. The number of tests must be predetermined, the results—success or failure—must be statistically independent for each test, and the survival probability—p—must be constant throughout the tests. When a process is repeated a certain number of times (for example, in a set of patients), the result for each patient can either be a success or a failure, the binomial distribution model enables us to calculate the probability of observing a specified number of "successes."
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What is the ordered pair for the reflection of the point (2,-1) over the x~axis
Answer:
(2,1)
Step-by-step explanation:
The x-value stays the same since we are only moving up/down and the y-value becomes the opposite
(x,y)--> (x,-y)
So the point becomes (2,1)
Answer:
(2,-1) hope this helps you understand
Graph the function f(x) = -5(x - 8)² - 2.
Plot the vertex. Then plot another point on the parabola. If you make a mistake, you can
erase your parabola by selecting the second point and placing it on top of the first.
The vertex is at (8, -2).The point (10, -22) is also on the parabola.
Step-by-step explanation:
Here is the graph of the function:
The vertex is at (8, -2).
To plot another point on the parabola, we can choose any x-value and plug it into the equation to solve for y.
For example, if we choose x = 10, then we have:
f(x) = -5(x - 8)² - 2
f(10) = -5(10 - 8)² - 2
f(10) = -5(2)² - 2
f(10) = -5(4) - 2
f(10) = -20 - 2
f(10) = -22
So, the point (10, -22) is also on the parabola.
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Cant get the right answer
The expression equates to R = 926.19
What is a equation?
An equation is a relation equating two mathematical expressions. For example -
2x + 4 = 5x + 7
We have -
R = 21000([0.052/4]/[1+0.052/4]²⁰ - 1]
We have the following equation -
R = 21000([0.052/4]/[1+0.052/4]²⁰ - 1]
R = 21000([0.013/(1.013)²⁰ - 1)
R = 21000([0.013/(1.29475890663 - 1)]
R = 21000(0.0441038411650727)
R = 926.1806644665257
R = 926.19
Therefore, the expression equates to R = 926.19
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Tank B is 60% full of water. It requires an additional 2800 litres of water to be full. How many litres of water fills tank B?
a sum of money was shareed between aziz and ahmad in the ratio of 4:7. aziz reeceived 21 dollars less than ahmad. find the total sum of money shareed by both of them
The total sum of money is 77 dollars .
Let the total sum of money be x .
⇒ Aziz's share = 4x / 11
Ahmad's share = 7x / 11
Given : Aziz received 21 dollars less than Ahmad
⇒ 4x / 11 = ( 7x / 11 ) - 21
Solving the above linear equation in one variable ,
( 7x - 4x ) / 11 = 21 ( taking like terms together )
3x = 21 * 11
x = 7 * 11
x = 77
Aziz's share = ( 4 / 11 ) * 77 = 28
Ahmad's share = ( 7 / 11 ) * 77 = 49
Total Sum of money = 28 + 49 = 77 dollars .
Hence , the total sum of money = 77 dollars .
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23% of $52 is $???? Answer needs a decimal
Answer:
$11.96
Step-by-step explanation:
Now we have to,
→ find 23 percent of $52.
Let's solve the problem,
→ 23% of $52
→ (52/100) × 23
→ 0.52 × 23
→ $11.96
Hence, answer is $11.96.
You have $8.50 and you need to make copies of a flyer at a store that charges
$0.35 per copy. Find the inequality that represents the number of copies you can
make. Use x as the variable.
What is the maximum number of copies you can afford to make?
copies
The required number maximum number of copies can be afforded x < 24.28.
Given that,
We have $8.50 and you need to make copies of a flyer at a store that charges $0.35 per copy.
Inequality can be defined as the relation of an equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Let the number of copies be x,
According to the question,
0.35x < 8.50
x < 8.50 / 0.35
x < 24.28
Thus, the required number maximum number of copies can be afforded x < 24.28.
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Bill wants to save for his son’s college expenses. He knows what tuition will cost in 18 years and knows the interest rate on the bank account. What he doesn’t know is how much to deposit each month to save enough for his son’s college expenses. Which Excel formula would you use?
The Excel formula that Bill would use is PMT.
How to illustrate the information?From Bill's situation, he has the following information:
time = NPER = number of periods = 18 years
RATE of the bank
FV = future value = cost of tuition
PMT, is a financial function, computes the loan payment based on constant payments and a constant interest rate. The Excel PMT function is a financial function that computes loan payments based on a fixed interest rate, the number of periods, and the loan amount. The function's name is derived from the acronym "PMT," which stands for "payment."
In conclusion, the correct option is PMT.
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Complete question
Bill wants to save for his son’s college expenses. He knows what tuition will cost in 18 years and knows the interest rate on the bank account. What he doesn’t know is how much to deposit each month to save enough for his son’s college expenses. Which Excel formula would you use? Choose from FV, PV, PMT, NPER, or RATE.
what is the 5th letter of the alphabet
The 5th letter of the alphabet is E.
What is an alphabet?An alphabet is a standardized collection of basic written symbols or graphemes that represent the phonemes of different spoken languages.
The letter a begins the English alphabet and ends with the letter z. The alphabet is always written in the same order: a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-p-q-r-s-t-u-v-w-x-y-z. A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z. This is known as "alphabetical order."
The set of 26 symbols represents sounds used in speech and writing. Each character in a syllabary, for example, represents a syllable, whereas characters in logographic systems represent words, morphemes, or other semantic units. In this case, E is the 5th letter.
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I need help like asap !!!
only numbers and decimal points
Answer: 30 in.
Step-by-step explanation:
So when you look at the right triangle closely, you can see that the c is the same length as the 30 in. That's why I think it is 30 in. (May be wrong)
Andy needs to solve
3/5
A. No, because and are not equivalent.
3
OD. Yes, because
3. In order to do this, he multiplies. Will Andy's method work?
OB. Yes, because dividing by a fraction is the same as multiplying by the reciprocal of the fraction.
OC. No, because one strategy involves division and the other involves multiplication.
3/6
and are equivalent
What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = [tex]\frac{1}{5}[/tex] x - 5
Step-by-step explanation:
y = mx +b You have to find the slope and the y intercept
slope:
I used the two points on the graph (0,-5) and (5,-4) The slope is the change in y over the change in x. An ordered pair is given in the form (x,y)
[tex]\frac{- 4 - - 5}{5-0}[/tex] = [tex]\frac{-4 + 5}5}[/tex] = [tex]\frac{1}{5}[/tex]
or you could just look at the two points. If you start at (0,-5) and go straight up one and the then go right 5 spaces, you will be at the point (5,-4) [tex]\frac{1}{5}[/tex]
The y intercept for the b is where the line crosses the x axis. It crosses at the point (0,-5) The -5 is the b part.
A 850 kg car is moving with a speed of 10 m/s. Which of the following would cause the largest change in momentum?
a. Double the velocity and mass
b. Double the velocity and cut the mass in half
c. Keep the velocity the same and triple the mass
d. Cut the mass and velocity in half
The largest change in momentum will happen when the velocity and mass of the object are doubled( option A)
What is momentum?The momentum of a body is the product of the mass of the body and it's velocity. Momentum is measured in kg/ms^-1. It is a vector quantity. it is represented by p
Momentum of a body is expressed as p= m× v
where m is the mass of the body and v is it's velocity. This means that the higher the mass and velocity of the body the higher it's momentum.
The initial momentum of the body of mass 850kg and velocity 10ms^-1 = 850kgms^-1
When the velocity and mass are doubled , then the new momentum will be 1700× 20= 34000kgms^-1
Therefore the largest change in momentum will be obtained when both mass and velocity are doubled.
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A bake sale committee wants to raise $162 for a donation to a local charity. They set aside $12 of their profit at the end of each day. How many days will it take them to raise enough money for the whole donation
Answer:
It would take them 13.5 days to raise enough money.
Step-by-step explanation:
In order to find the answer, you just have to take the amount of money they want to raise, which is $162, and divide it by the amount of money they save each day, or $12. In this case that would be dividing 162/12 giving you an answer of 13.5 days.
if you conduct a hypothesis test (for example, a z test), and find a p-value of .30, what is the meaning of the p-value?
The value for p is 30.
Hypothesis.Though there is not so much information, but the fact that $700 is an average. We can work with two hypothesis at first, he first Hypothesis before the downturn the rent are over $700. And the second one, the bedroom rent are under $700.Graphically, the shaded area before the downturn, represents the set of values for Rents greater than $700. So, rent (y) > 700) Graphically, the shaded area after the downturn, represents the set of values for Rents lesser than $700. So, rent 700 <y<0A hypothesis is an educated prediction regarding the solution to a scientific question that is supported by sound reasoning. It is the expected result of the experiment, however it is not proof in an experiment.Depending on the information received, it might be supported or might not be supported at all.learn more about hypothesis click here:
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plssss help me . i’ll give brainliest .
Jamie has a table top that he wants to cover in contact paper. The table top has the following dimensions. Length: 3.5 ft. Width: 3.5 ft. Height: 0.25 ft. How many square feet of contact paper does he need to cover the entire table top?
The area of the contact paper required to cover the entire tabletop is 12.25 square feet.
Jamie has a tabletop that he wants to cover with contact paper. The length, width, and height of the tabletop are 3.5 feet, 3.5 feet, and 0.25 feet, respectively. We need to calculate the area of the contact paper required to cover the entire tabletop.
Let the area of the tabletop be represented by the variable "A". We need to calculate the area of only the top surface of the table. The table is rectangular in shape. The area of the tabletop must be the product of the length and the width of the table.
A = 3.5×3.5
A = 12.25
Hence, the area of the tabletop is 12.25 square feet.
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simplify by using order of operations 22 - (8 x 1) divided by (6 - 4) - 2
The value of the expression 22 - (8 x 1) divided by (6 - 4) - 2 is 0.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
The expression given is:
22 - (8 x 1) divided by (6 - 4) - 2
= 22 - (8 x 1) ÷ (6 - 4) - 2
= [22 - 8] ÷ [2 - 2]
= 14 ÷ 0
= 0
The value is 0.
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choose the correct order
Answer:
6CO2 + 6H2O → C6H12O6 + 6O2.
Step-by-step explanation:
That's the equation for photosynthesis. let me know if you have any questions.
some airlines have restrictions on the size of items of luggage that passengers are allowed to take with them. suppose that one has a rule that the sum of the length, width and height of any piece of luggage must be less than or equal to 234 cm. a passenger wants to take a box of the maximum allowable volume. if the length and width are to be equal, what should the dimensions be?
The length, breadth and height will be 78 cm, 78cm, 78cm each.
let consider the length = l
breadth = b
height = h
we are provided that
l + b + h = 234cm .......(1)
Also we have to maximize the volume , provided length is equal to breadth
∴ eqn (1) becomes
2b + h = 234
h = 234 - 2b
also ,
volume(v) = lbh
v = b²(234 - 2b)
v = b²234 - 2b³
now to maximize the volume we take the first derivative of the volume wrt 'b' and place it equal to zero. ( lagrange method )
i.e. d( v)/db = 0
∴ 468b - 6b² = 0
6b² - 468b = 0
6b( b - 78 ) = 0
∴ b = 78 cm
now as length = breadth
l = b = 78 cm
also putting this value in eqn (1)
h = 234 - 2b
h = 78 cm
So , the dimensions will be equal and will be 78cm , 78cm, 78cm each .
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PLEASE HELPPPP FAST!!!!!
Simplify the imaginary number...
help meeeeeeeeeeeeeee pleaseee
The table of solutions for the given equation (y = -2x²) include the following:
x y_
-2 -8
-1 -2
0 -0
1 -2
2 -8
Also, a graph of the solution of this equation (y = -2x²) has been plotted in the image attached below.
How to determine the solution?In order to determine the valid and true solutions to the given quadratic equation, we would have to substitute the values of contained in the table into the quadratic equations as follows;
At x = -2, the value of point y is as follows:
y = -2x²
y = -2(-2)²
y = -2 × 4
y = -8
At x = -1, the value of point y is as follows:
y = -2x²
y = -2(-1)²
y = -2 × 1
y = -2
At x = 0, the value of point y is as follows:
y = -2x²
y = -2(0)²
y = -2 × 0
y = 0
At x = 1, the value of point y is as follows:
y = -2x²
y = -2(1)²
y = -2 × 1
y = -2
At x = 2, the value of point y is as follows:
y = -2x²
y = -2(2)²
y = -2 × 4
y = -8
In conclusion, we can logically deduce that the graph of this quadratic equation forms a downward parabola.
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