The required solution of given equation is x = 5, y = 1.
What is substitution method to equation?The effective use of substitution relies upon two things: first, given a circumstance in which factors happen, a replacement is just a difference in factor; second, it is just successful if the difference in factor improves on the circumstance and, ideally, empowers one to take care of the worked on issue.
According to question:We have,
4x+3y=23---------()1
And
x-5y=0 ⇒ x = 5y
Put the value of x in equation(1)
4(5y) + 3y = 23
20y + 3y = 23
23y = 23
y = 1
Then x = 5y = 5(1) = 5
Thus, solution of equation x = 5, y = 1
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Why is 3.14 called pi?
It was first called "pi" in 1706 by William Jones, because pi is the first letter in the Greek word perimitros, which means "perimeter."
question 21 options: suppose the american kennel club estimates that 38% of households in u.s. have a pembroke welsh corgi. a random sample of 400 households is taken. round probability answers to 4 decimal places, i.e. .xxxx do not include leading or ending zeros. what is the probability the sample proportion is more than 40%?
The probability that the sample proportion is more than 40% is approximately .0001.
What is Probability?
Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.
To find the probability that the sample proportion is more than 40%, we need to use the normal distribution and the central limit theorem.
The central limit theorem states that the distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.
To find the probability that the sample proportion is more than 40%, we need to first calculate the mean and standard deviation of the sample proportion. The mean of the sample proportion is equal to the population proportion (38%), and the standard deviation of the sample proportion is equal to:
[tex]standard\ deviation = sqrt((population\ proportion * (1 - population\ proportion)) / sample\ size)\\\\= \sqrt{((.38 * .62) / 400)}\\\\= .048[/tex]
Next, we need to standardize the sample proportion of 40% by subtracting the mean and dividing by the standard deviation:
z = (40% - 38%) / .048 = 4.17
The probability that it is less than or equal to 40% is approximately .9999.
The probability that the sample proportion is more than 40% is then equal to 1 - .9999 = .0001.
So, The probability that the sample proportion is more than 40% is approximately .0001.
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The graph represents a quadratic function. Write an equation of the function in standard form.
Answer:
Below
Step-by-step explanation:
From the graph, the zeroes are at -4 and - 0.5 so the equation starts like this:
a (x+4)(x+.5) = 0 now ya need to sub in a point to calculate 'a'
...... point 0,4 results in this:
a (0+4)(0+.5) = 4
2a = 4
a = 2
so the equation becomes 2 ( x+4)(x+.5) = 0
2 ( x^2 + 4.5x +2) = 0
2 x^2 + 9x + 4 =0
A certain state uses the following progressive tax rate for calculating individual income tax: Income Progressive Range ($) Tax Rate 0 - 10,000 3% 10,001 - 50,000 5% 50,001 - 100,000 5.5% Calculate the state income tax owed on a $40,000 per year salary. tax = $[?] Round your answer to the nearest whole dollar amount. Enter
The state income tax owed on the $40,000 salary should be $1,800.
What is Income Tax?An income tax is a tax levied on persons or companies based on their earnings or profits. In most cases, income tax is calculated as the result of a tax rate multiplied by the taxable income. Taxation rates may differ depending on the taxpayer's attributes and the source of income.
Given:
Income Progressive Range ($) Tax Rate
0- 10,000 3%
10-001- 50000 5 %
50001- 100000 5.5%
The calculation of the state income tax owed on $40,000 salary
= 3% of $10,000 + 5% of $30,000
= $300 + $1,500
= $1,800
Hence, the state income tax owed is $1,800.
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What are all of the solutions to the equation 2x2 = 100?
O +5√2
O +10
O +50
O +√2
The solutions to the equation 2x^2 = 100 is [tex]x=\pm 5 \sqrt{2}[/tex].
How do you find all solutions of a quadratic equation?
The solutions of a quadratic equation ax2 + bx + c = 0 are given by the quadratic formula x = [-b ± √(b² - 4ac)] / (2a). So to solve a quadratic equation using quadratic formula, just get the equation into standard form ax2 + bx + c = 0, and apply the quadratic formula.
[tex]$$2 x^2=100$$[/tex]
Divide both sides by 2
[tex]\frac{2 x^2}{2}=\frac{100}{2}$$[/tex]
Simplify
[tex]x^2=50$$[/tex]
For [tex]$x^2=f(a)$[/tex] the solutions are [tex]$x=\sqrt{f(a)},-\sqrt{f(a)}$[/tex]
[tex]$$x=\sqrt{50}, x=-\sqrt{50}$$[/tex]
[tex]$$\begin{aligned}& \sqrt{50}=5 \sqrt{2} \\& -\sqrt{50}=-5 \sqrt{2} \\& x=5 \sqrt{2}, x=-5 \sqrt{2}\end{aligned}$$[/tex]
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Square: if AC =26, find BC
BC is equal to 24cm.Now, by applying the Pythagoras theorem i.e. in a right-angled triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides, we can find BC.
Find BC ?
So, we can apply the Pythagoras theorem here, if it is right-angled at C then the side opposite to C will be the hypotenuse of the triangle that is AB = 25 cm, and the other two sides are AC = 7 cm and BC.
AB = 25 cm, AC = 7 cm and BC =?
In triangle ACB, By Pythagoras theorem, (Hypotenuse)2 = (Perpendicular)2 + (Base)2
AB)2 = (AC)2 + (BC)2
(25)2 = (7)2 + (BC)2
625 = 49 + (BC)2
(BC)2 = 625 – 49
(BC)2 = 576
BC = 24 cm
Thus, BC is equal to 24cm
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The boeing 747-8 intercontinental jet can carry approximately 63,500 gallons of jet fuel, making it possible for the jet to travel 14,430 kilometers before needing to refuel. use a linear model to predict the amount of jet fuel that is present on the jet after it has been in flight for 18 hours without stopping to refuel. in two or more complete sentences, explain your answer.
The initial amount at the start of the flight, which was 63,500 gallons, indicating that the jet would need to refuel soon after the 18 hours of flight.
The linear model that can be used to predict the amount of jet fuel present on the Boeing 747-8 Intercontinental jet after 18 hours of flight without refueling is given by the equation
F = 63,500 - (800 x 18),
where F is the amount of jet fuel in gallons and 18 is the number of hours of flight. This equation indicates that after 18 hours of flight, the jet would have an estimated amount of jet fuel of 42,400 gallons remaining. This amount is significantly lower than the initial amount at the start of the flight, which was 63,500 gallons, indicating that the jet would need to refuel soon after the 18 hours of flight.
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Is 1 A All real number?
No, 1 is not a real number.
What is real number?Real numbers are numbers that can be used to measure or describe anything, such as a quantity or distance. Real numbers can be either rational (e.g. fractions, decimals, and integers) or irrational (e.g. roots and pi). Real numbers are usually represented on a number line, where points to the right of 0 represent positive numbers and points to the left of 0 represent negative numbers.
Real numbers include all the rational and irrational numbers. They can be integers, fractions, decimals, and even imaginary numbers. 1 is an integer, so it is not considered a real number. Real numbers are those that have a decimal representation, which 1 does not.
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How many nickels are there in $22? Solve the equation 22 ÷ 0.05 to help you.
25
44
225
440
Answer:440
Step-by-step explanation:
Answer:
To find the number of nickels in $22, we need to first convert the amount of money from dollars to cents and then divide this number by the value of a nickel in cents. Since 1 dollar is equal to 100 cents, we can convert $22 to 2200 cents.
Next, we need to find the value of a nickel in cents. Since a nickel is worth 5 cents, the value of a nickel in cents is 0.05 * 100 = 5 cents.
Finally, we can divide the total number of cents by the value of a nickel in cents to find the number of nickels:
2200 cents / 5 cents/nickel = 440 nickels
Therefore, there are 440 nickels in $22. Solving the equation 22 ÷ 0.05 gives the same result.
Is a straight vertical line a function?
A vertical straight line is not a function. It is a relation, but not a function as it does not follow the condition to be a function.
A condition for a function is that a unique input gives a unique output, that is a unique output can trace back to only one unique input.
In the case of a vertical straight line, it is of the form x = a, where a is a constant. That is for x = a, there is infinitely many values for y, therefore it does not follow the condition of a function and hence a vertical straight line is not a function.
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Why is 2 a prime number?
2 is a prime number because it has only two factors (1 x 2).
What are prime number?A natural number greater than one that is not the product of two smaller natural numbers is referred to as a prime number. A composite number is a natural number greater than 1 that is not prime.
Numerical tables, which were typically printed before calculators and computers, were used to record all primes or prime factorizations up to a certain limit. The Sieve of Eratosthenes is the most well-known method for making a list of prime numbers.
Given why 2 is prime,
The natural numbers greater than 1 with exactly two factors, i.e. 1, and the number itself, are known as prime numbers.
so 2 has only two multiple
1 and 2,
Hence 2 is a prime number.
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What is the answer to -( 7 4x )= 9?
The answer to the expression -( 7 4x )= 9 is -7, since subtracting 7 from both sides of the equation leaves us with 4x = 2, and then dividing both sides of the equation by 4 gives us x = -7.
The expression -( 7 4x ) = 9 can be solved by using basic algebraic operations. First, we subtract 7 from both sides of the equation to obtain -4x = 2. This is because when subtracting a number from both sides of an equation, we are essentially adding the opposite of that number to both sides. Then, we divide both sides of the equation by 4 to obtain x = -7. This is because when dividing both sides of the equation by a number, we are essentially multiplying both sides by the inverse of that number. Therefore, the answer to the expression is -7.
-(7 4x ) = 9
-7 - 4x = 9
-4x = 2
x = -7
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A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror. The pipe is located 9 inches from the vertex of the mirror. Write an equation of the parabola that models the cross section of the mirror. Assume that the parabola opens upward.
An equation of the parabola that models the cross section of the mirror is, y = [tex]\frac{x^{2} }{36}[/tex]
Given that,
A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror.
Define Parabola:A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.
The pipe is located 9 inches from the vertex of the mirror.
The parabola is open upwards . the vertex of the parabola is (0,0)
and pipe is located 9 inches from the vertex (0,0)
9 inches is the focus of the mirror
The distance between the vertex and the focus = 9
Since parabola is upwards and vertex is (0,0) we use formula,
[tex]4py = x^{2}[/tex]
Where,
p is the distance between the vertex and focus p = 9
Now,
[tex]4*9*y = x^{2}[/tex]
[tex]36y =x^{2}[/tex]
Now isolate y by dividing 36 on both sides, we get
y = [tex]\frac{x^{2} }{36}[/tex]
Therefore,
An equation of the parabola that models the cross section of the mirror is, y = [tex]\frac{x^{2} }{36}[/tex]
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What is the nature of the roots of the quadratic equation 2x² 5 √ 3x 6 0?
The roots of the quadratic equation 2x² + 5√3x - 6 = 0 are imaginary.
To solve this equation, we can use the Quadratic Formula. The Quadratic Formula is:
x = [ -b ± Â√(b2 - 4ac) ] / 2a
In this equation, a = 2, b = 5√3, and c = -6.
Plugging these values into the formula, we get:
x = [ -(5√3) ± Â√((5√3)2 - 4(2)(-6)) ] / (2(2))
Simplifying, we get:
x = [ -(5√3) ± Â√(25*3 + 24) ] / 4
Simplifying further, we get:
x = [ -(5√3) ± Â√(75) ] / 4
Since √75 is an irrational number, the roots of the equation are imaginary.
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The question is in the picture below :)
Answer:
Number of international passengers increased then decreased whereas the number of domestic passengers constantly increased
Step-by-step explanation:
What is the value of polynomial 5 x minus 4 x square 3 at x is equal to zero?
The value of polynomial 5x - 4x² + 3 at x=0 is equal to 3
Given that,
The polynomial is 5x - 4x² + 3
To find : The value of polynomial 5x - 4x² + 3 at x=0
A combination of more than two algebraic expressions, particularly when they each contain a distinct power of the same variable (s).Polynomials are algebraic expressions made up of coefficients and variables. Occasionally, variables are referred to as indeterminates. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all possible; however, division by variable is not. x2+x-12 is an illustration of a single-variable polynomial. Three terms are involved in this example: x2, x, and -12.
Given : x = 0
→ 5x - 4x² + 3
→ 5 ( 0 ) - 4 ( 0) ² + 3
→ 0 - 0 + 3 ( ∵ here + 0 - 0 cancels )
→ 3
Therefore, The value of polynomial 5x - 4x² + 3 at x=0 is 3.
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What is the domain of F x all real numbers?
On solving the provided question we can say that - The answer to the question is that all real numbers or domain (−∞,∞)
What is Domain?The range of values that may be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set. Let y = f(x) be a function where x and y are the independent and dependent variables. If a function f offers a means of successfully generating a single value y while employing a value for x to that end, then the selected x-value is said to belong to the domain of f.
The answer to the question is that all real numbers or (−∞,∞)
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What is the nature of the roots 5x² 3x 2 0?
The Nature of roots of the quadratic equation "5x² -3x +2 = 0" is imaginary and conjugate .
To find the Nature Of Roots of the Quadratic Equation ax² + bx + c = 0 , we find the discriminant(D) by the formula ; D = b² - 4ac .
the quadratic equation is given as 5x² -3x +2 = 0 ;
On comparing , we get , a = 5 , b = -3 and c = 2 .
Substituting the values in the Discriminant formula mentioned above , we get
D = (-3)² - 4×5×2
= 9 - 40
= -36 .
Since the value of the discriminant is less than 0 ,
Therefore , the roots will be imaginary and conjugate .
The given question is incomplete , the complete question is
What is the nature of the roots of the equation 5x² -3x +2 = 0 ?
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6. A shop keeper has 56 pens. He
soid them for 280 dollars. How
much did the shopkeeper charge
for each pen?
The cost of each pen would be 5 dollars.
What is a unit value?
When the expenditures or value of production of an item is divided by the quantity, the result is known as a unit value. Context: The unit value of a set of homogeneous products is the total value of the purchases/sales divided by the sum of the quantities
The shopkeeper has 56 pens. and he sold them for 280 dollars
Cost of each pen = total amount/ number of pens
= 280/56
=10/2
= 5
Hence, the cost of each pen would be 5 dollars.
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What is domain and range of a function examples?
Domain is the input of a function and range is the output of a function, for f(x) = sin(x), domain will be (-inf, +inf) and range will be [0,1].
What is a function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).
What is domain and range of a function?Domain is the input of a function and range is the output of a function.
Examples:
f(x) = sin(x), domain = (-inf, +inf) and range = [0,1].
f(x) = cos(x), domain = (-inf, +inf) and range = [0,1].
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What is the formula for 3 consecutive integers?
The formula for 3 consecutive integers (X) , (X + 1) , (X + 2) if the first number is supposed to be x.
What are consecutive numbers ?
Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.
Let us find three consecutive integers whose sum is 399. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 399. Therefore, you can write the equation as follows:
(X) + (X + 1) + (X + 2) = 399
To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:
X + X + 1 + X + 2 = 399
3X + 3 = 399
3X + 3 - 3 = 399 - 3
3X = 396
3X/3 = 396/3
X = 132
Which means that the first number is 132, the second number is 132 + 1 and the third number is 132 + 2. Therefore, three consecutive integers that add up to 399 are 132, 133, and 134.
Hence , The formula for 3 consecutive integers (X) , (X + 1) , (X + 2) if the first number is supposed to be x.
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What is the mode of 1 2 3 4 5 6 7 8 9 10?
The mode of a set of numbers is the number that appears most often in the set. In the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, there is no number that appears more often than any other, so the mode of this set is not defined.
How does math work out the mode?The mode can be calculated quite easily. After sorting the numbers in a set according to their order—lowest to highest or highest to lowest—count how many times each number appears in the group. The mode is the one that is most prevalent.
With an example, what is the mode formula?The value that appears most frequently in a set of values is referred to as the mode. It is the value that shows up the most frequently. Example: Since the number 5 appears twice in the provided data set of 2, 4, 5, 6, and 7, it is the mode of the data set. 2
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Which equation represents a linear Function
Xy=5
y=x²-3
y= 2/x + 7
3x + 2y = 6
Answer:
3x + 2y = 6
Step-by-step explanation:
When you solve for y in this equation, it is in the same format as the slope-intercept equation.
3x + 2y = 6
2y = -3x + 6
y = -3/2 x + 3
The slope intercept equation is ...
y = mx + b
(m can be any number)
The slope-intercept equation is for linear functions!
If liters of water are enough to water of the plants in the house, how much
water is necessary to water all the plants in the house?
Write a multiplication equation and a division equation for the situation. (
Answer the question. Explain or show your reasoning and be sure to reduce all
fractions, if necessary.
According to the calculation used to compute it, [tex]3\frac{1}{3}[/tex] liters of water are required to water all the indoor plants.
What are mathematical operations?
The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. An expression in mathematics is a combination of digits and operations. A mathematical expression that performs an operation has the following components: Operations and Operands
The amount of water needed to water all the indoor plants is 1/3 liter, according to the calculation used to determine this.
[tex]= 4/3 / 2/5\\ = 4/3 X 5/2\\ = 3\frac{1}{3}[/tex]
Consequently, 3 1/3 liters are needed.
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What are the 3 steps when finding vertical asymptote?
Identify the denominator of the function and set it equal to zero. Solve the equation to find the x-values of the asymptote. Substitute the x-values found in step two into the original equation to determine if the vertical asymptote is a true asymptote.
The first step when finding vertical asymptotes is to identify the
denominator of the function and set it equal to zero. This creates an equation which can then be solved to find the x-values of the asymptote. The second step is to solve the equation, using methods such as factoring or completing the square, to find the x-values of the asymptote. The final step is to substitute the x-values found in step two into the original equation and determine if the vertical asymptote is a true asymptote. If the limit of the function as x approaches the x-value found in step two is either positive or negative infinity, then the vertical asymptote is a true asymptote. If, however, the limit of the function as x approaches the x-value found in step two is not infinity, then the vertical asymptote is not a true asymptote. This process of finding vertical asymptotes can be used to find the vertical asymptotes of any function.
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Let A be a 4X5 matrix. If a1,a2,a4 are linearly independent and a3=a1+2a2 a5=2a1-a2+3a4 determine the reduced row echelon form of A.
As per the given 4 x 5 matrix, the reduced row echelon form of A is [tex]\left[\begin{array}{ccc}1&2&0\\0&0&1\\0&0&0\end{array}\right][/tex]
The term matrix in math refers a set of numbers arranged in rows and columns so as to form a rectangular array.
Here we have the 4 x 5 matrix.
And here we also know that a1,a2,a4 are linearly independent and the value of a3=a1+2a² and a5=2a1-a²+3a⁴.
Now, we have to apply the value of
a1 = 1, a2 = 0, a3 = 0, a4 = 0, a5 = 1, a6 = 0, a7 = 0, a8 = 0, and a9 = 1.
Then we get the matrix of 3 x 3 looks like the following,
[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex]
Now, we have to do the following steps in order to get the reduced row echelon form of A,
The first and foremost steps is to take the non-zero number in the first row is the number 1.
Then we have to place any non-zero rows are placed at the bottom of the matrix.
This steps are repeated until the final row becomes zero.
Then we get the resulting matrix as [tex]\left[\begin{array}{ccc}1&2&0\\0&0&1\\0&0&0\end{array}\right][/tex]
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5. Which of the following are vertical angles?
2 3
A. 1 and 6
8
7
6
B. 4 and 7
C. 1 and 5
D. 3 and 8
Answer:
Option C
1 and 5
Step-by-step explanation:
Vertical angle;Each of the pairs of opposite angles made by two intersecting lines.ORVertical angles are angles opposite each other where two lines cross.So,
as you can see here,
1 and 52 and 63 and 74 and 8are the vertical angles.
Latanya had math and reading homework tonight. Latanya can solve each math problem in 1.5 minutes she can read each page in two minutes. The number of math problems Latanya had is 4 more than the number of pages she read and it took her 48 minutes to complete all of her homework. graphically solve a system of equations in order to determine the number of math problems Latanya solved, X, and the number of pages she read, y.
The system of equations obtained from the given information are 1.5x +2 y = 48 and x = 4 + y respectively.
What exactly is a math equation?equation: a statement that two expressions having variable- and/or number-filled expressions are equivalent. Since equations are essentially questions, the search for a way to respond to them has spurred the development of mathematics.
Here,
Given data:
Time taken by Latanya to solve a problem = 1.5 minute.
Time to read one page = 2 minutes.
Number of problems completed = x problems.
Total time used for reading = y minutes.
Using the data to consider:
Let x be the the number of math problems that Latanya solved.
Let y be the number of pages that Latanya read.
thus,
1.5x +2 y = 48
and
x = 4 + y
Thus, we can conclude the the system of equations obtained from the given information are 1.5x +2 y = 48 and x = 4 + y respectively.
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Answer number 2 or number 3 thank you
Answer:
2.) the answer is D, because 12 hours is the closest number between 10 and 15
How do you write an equation of a line in slope intercept form?
The equation of the line that passes through the points (0,3) and (2,7) in slope intercept form is y = 2x + 3 .
The Slope Intercept form of the line is written as y = mx + c ; where c is the y intercept and m is the slope of the line .
to find the equation , we first need to find the slope ,
So , slope (m) = (7-3)/(2-0) = 4/2 = 2 ;
next we need to find the y intercept ;
So , putting the values , we get ;
3 = 2(0) + c
c = 3 .
putting the values of y intercept and slope in the equation ,
we get ;
the equation as ; y = 2x + 3 .
Therefore , the equation of the line is y = 2x + 3 .
The given question is incomplete , the complete question is
How do you write an equation of a line that passes through the points (0,3) and (2,7) in slope intercept form ?
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