There are several methods for finding the solution to a system of equations, which include:
1. Graphing: This method involves plotting the equations on a coordinate plane and finding the point(s) of intersection. This method is useful when the system has a small number of variables and the equations are in the form of y = mx + b.
2. Substitution: This method involves solving one of the equations for one variable and then substituting that expression into the other equation. This method is useful when one equation is easier to solve than the other or when one equation is a simpler form than the other.
3. Elimination: This method involves adding or subtracting the equations to eliminate one of the variables. This method is useful when the variables are in similar forms and the coefficients are easy to add or subtract.
4. Matrix method: This method involves solving the system of equations in matrix form using matrix algebra techniques such as Gaussian elimination, Gauss-Jordan elimination and Cramer's rule. This method is useful when the system of equations have a large number of variables and when you want to solve system of equations in a more efficient and less time-consuming way.
5. Numerical methods: This method involves using numerical techniques such as Newton-Raphson method, Iterative methods to approximate the solution of a system of equations.
It is important to note that in some cases, a system may have no solution or infinitely many solutions. A system has no solution when the equations are inconsistent, meaning they cannot be true at the same time. A system has infinitely many solutions when the equations are dependent, meaning one equation can be derived from the other equation
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Two step equation that equals 13
Following are the different equations, for which the value of equals 13.
There are numerous mathematical formulae that could all equal 13. The following phrases all equal 13.
9+ 4 = 13
15-2 = 13
1 × 13 = 13
Let's think about some intriguing expressions right now.
x³ - x² + x + 7
The equation will equal 13 if the value of x is 2.
A word puzzle states that Shiya has 10 balls and Riya has 3 more than Tom. How many balls does Ria possess?
Let x represent the quantity of Balls Shiya owns.
Shiya has 10 Balls, thus x is equal to 10, and Ry has x+3 Balls.
As a result, Riya has = x + 3 = 10 + 3 = 13 Balls.
Therefore, Riya has 13 Balls total.
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What is a product of a fraction?.
The product of fractions is a fraction or an integer.
We know that the fraction is used to represent the portion or part of the whole thing.
The fraction has two parts: numerator and denominator.
The top part of fraction is numerator and the bottom part is denominator.
consider a fraction 1/8.
Here, numerator is 1, denominator is 8
When certain thing is divided into 8 equal parts then each part of is represented by fraction1/8
The multiplication of fractions is defined as the product of a fraction with a fraction or the product of a fraction with an integer or the product of a fraction with the variables.
The steps to multiply two fraction are:
First multiply the numerator with numerator
Then Multiply the denominator with the denominator
And lastly simplify the fractions, if required
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For each scatter plot, determine if the relationship shown is linear and positive, linear and negative or nonlinear.
Linear and Positive
Linear and Negative
Nonlinear
For the scatter plots shown;
a) Non linear
b) Linear positive
c) Non linear
d) Linear negative
What is the scatter plot?We know that the scatter plot is used to show the relationship between variables. The variable that is plotted on the vertical axis is the dependent variable while the variable that is plotted on the horizontal is the independent variable.
The points that we have on the scatter plot can help us to be able to know whether or not the relationship between the variables is linear.
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Rewrite $r\left(t\right)=\left(0. 88\right)^{4t}$ in the form $y=a\left(1r\right)^t$ or $y=a\left(1-r\right)^t$ to determine whether it repreent exponential growth or exponential decay. Round $a$ and $r$ to the nearet hundredth if neceary
We have exponential decay of roughly 40% per time unit.
We have to y=(0.88)^4t in the form y=a(1+r)^t or y=a(1−r)^t to determine whether it represents exponential growth or exponential decay. Round a and r to the nearest hundredth if necessary.
y=(0.88)^4t
y=1( (0.88)^4 )^t
y=1( 0.59969536 )^t
Set 0.59969536 equal to 1-r and solve for r
1-r = 0.59969536
-r = 0.59969536-1
-r = -0.40030464
r = 0.40030464
r = 0.40
This means we have,
y=a( 1 - r )^t
y=1( 1 - 0.40 )^t
which means a = 1 and r = 0.40 approximately
We have exponential decay of roughly 40% per time unit.
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A vector in standard position has its terminal point at (7, –4). what is the magnitude of the vector? startroot 3 endroot 3 startroot 65 endroot 65
Answer:
(c) √65
Step-by-step explanation:
You want to know the magnitude of the vector (7, -4).
Vector magnitudeThe magnitude of a vector is the root of the sum of the squares of its components.
|(7, -4)| = √(7² +(-4)²) = √(49 +16) = √65
The magnitude of the vector is √65.
Answer:
√65
Step-by-step explanation:
Students in Mrs. Barnes’s class determined the probability that she will check homework on a randomly chosen day is 0.42. They also determined the probability that she will give a pop quiz when she checks homework is 0.6, and the probability that she will give a pop quiz when she does not check homework is 0.9. The probabilities are displayed in the tree diagram.
A tree diagram. Random day goes to checks homework and does not check homework. The arrow to checks homework is 0.42, and does not check homework is 0.58. Checks homework to pop quiz, 0.60; checks homework to no pop quiz, 0.40. Does not check homework to pop quiz, 0.90; does not check homework to no pop quiz, 0.10.
What is the probability that Mrs. Barnes checks homework if the students take a pop quiz?
0.25
0.33
0.67
0.77
The probability that Mrs. Barnes checks homework if the students take a pop quiz is 0.77, the correct option is D.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
Given;
Mrs. Barnes’s class determined the probability that she will check homework on a randomly chosen day is 0.42;
They also determined the probability that she will give a pop quiz when she checks homework is 0.6, and the probability that she will give a pop quiz when she does not check homework is 0.9;
Then the probability that Mrs. Barnes does not check homework if the students take a pop quiz;
P= 0.42*0.60 + 0.58*0.90
P = 0.252 + 0.522
P = 0.774
P ≈ 0.77
Therefore, the probability will be 0.77
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Determine whether the two expreion are equivalent. 1) 3a 6 5a and 8a 6
2) 5c - 4c c and 3c
3) 8x 8 - 4x - 3 and 16% - 7
The process of multiplying a number or expression by itself a certain number of times, known as its exponent.
1) 3a + 6 = 5a
3a + 6 - 5a = 0
-2a = 0
a = 0
2) 5c - 4c = c
5c - 4c - c = 0
c = 0
3) 8x8 - 4x - 3 = 16% - 7
8x8 - 4x - 3 - 16% + 7 = 0
64x - 3 - 16% = 0
64x - 3 - 16/100 = 0
64x - 0.16 = 0
64x = 0.16
x = 0.0025
Exponents are a way to represent repeated multiplication of a number by itself. To solve an equation with an exponent, we must simplify the expression by breaking down the exponent into its component parts, and then simplify the equation by solving for the variable. We can then solve for the exponent by substituting the value of the variable into the equation. For example, if we had an equation of 3a + 6 = 5a, we would first subtract 5a from both sides to get -2a = 0. We can then substitute that value into the equation to get a = 0. Exponents can be a useful tool to quickly solve equations, but can also be tricky to solve if you don't know the basics of algebra.
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Mira ha breakfat at a retaurant. She leave a 20\%20%20, percent tip of \$1. 80$1. 80dollar ign, 1, point, 80
Therefore, the price of the complete meal is $9.00 before tax.
Percentage:
A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
As per the data given in the above question are as bellow,
The details provided are as follow,
Provided that 20% of the expense of breakfast is $1.8.
To calculate the total cost of the breakfast before the tip, we may apply proportions.
Set x as the price of a full breakfast:
Therefore 0.2 = 1.8
So, 1.0 = x
0.2x = 1.8 x 1.0
x = 1.8/0.2
x = 9
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Note: The correct question is as bellow,
Mira has breakfast at a restaurant. She leaves a 20%, percent tip of $1.80. What is the price of Mira's breakfast, before tip?
Answer this functions question
Answer:
x=0
Step-by-step explanation:
You want the value of x that cannot be in the domains of either f(x) = 2/x or g(x) = (x+1)/x.
DomainThe domain of a function is the set of input values for which the function is defined.
These functions f(x) and g(x) are "undefined" when x=0, because that would cause division by zero.
x cannot be zero
Which of the following expressions is equivalent to 2 exponent -4
Answer:
Step-by-step explanation:
2^-4=0.0625
we can divide by any number to to make an equivalent expression. (Note it is more easier when it is not a repeating decimal.)
we can do 0.0625/2= 0.03125 with this answer we can make an equivalent expression
1(0.03125+0.03125)=0.0625
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{2^{-4}}[/tex]
[tex]\mathsf{= \dfrac{1}{4 \times 4 \times 4 \times 4}}[/tex]
[tex]\mathsf{= \dfrac{1}{2^4}}[/tex]
[tex]\mathsf{= \dfrac{1}{2 \times 2 \times 2 \times 2}}[/tex]
[tex]\mathsf{= \dfrac{1}{4 \times 4}}[/tex]
[tex]\mathsf{= \dfrac{1}{16}}[/tex]
[tex]\huge\text{Therefore, your answer could possibly be: }[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{1}{16}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Finding the final amount given the original amount and a...
Last year, Deandre opened an investment account with $7600. At the end of the year, the amount in the account had decreased by
21.5%. How much is this decrease in dollars? How much money was in his account at the end of last year?
Answer:
The decrease in dollars is $1634
Deandre has $5966 in his bank account at the end of the year
Step-by-step explanation:
7600 times 0.215 = 1634
7600 - 1634 = 5966
Margaret i purchaing a new cell phone. The phone he want to buy cot $275. If he ha a coupon for the phone tore for 15% off and another coupon for $20 off, which hould he ue?
Coupon 1 will provide more discount and hence he will use coupon 1.
Describe percent discount:Percent discount is a way to express a reduction in price as a percentage of the original price. It is commonly used in sales and promotions. For example, a 20% discount on a $100 item would reduce the price to $80.
In order to check which coupon provides more discount to the Margaret we need to check for both coupon value and the coupon whose value is greater that one we will use
coupon 1 is 15 percent of initial cost.
Coupon 1 value = (15/100) * 275
=> $0.15*275
=> $41.25
Coupon 2 value = $20
so Coupon 1 will provide more discount .
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95 divided by 2?? Please help!
Answer:
47.5
Step-by-step explanation:
95 divided by 2 is equal to 47 with a remainder of 1.
To divide 95 by 2, you need to perform long division.
Here's the step-by-step process:
Write the dividend (95) inside the division bracket, and the divisor (2) outside the bracket.
Place the quotient above the division bracket.
__
2 | 95
Start with the leftmost digit of the dividend (9) and divide it by the divisor (2). Since 9 is smaller than 2, we move to the next digit.
__
2 | 95
4
Bring down the next digit of the dividend (5) to the right of the remainder
(1) obtained from the previous step.
__
2 | 95
4 1
Divide 15 by 2. The quotient is 7, and the remainder is 1.
__
2 | 95
47 1
Since there are no more digits in the dividend, we have completed the division.
The quotient is 47, and the remainder is 1.
Therefore, 95 divided by 2 is equal to 47 with a remainder of 1.
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100 POINTS AND BRAINIEST
Laisha rides a bike 8 miles in 40 minutes. Jefford rides a bike 5 miles in 30 minutes.
Who will bike the farthest in 1 hour?
2nd question. How much farther?
Step-by-step explanation:
laisha bike farthest in 1 hour
which information is not sufficient to prove that a parallelogram is a square
a. The diagonals are both congruent and perpendicular.
b. The diagonals are perpendicular and one pair of adjacent sides are congruent.
c. The diagonals are congruent and one pair of adjacent sides are congruent.
d. The diagonals are perpendicular and one pair of adjacent sides are perpendicular.
The statement B. "The diagonals are perpendicular and one pair of adjacent sides are congruent." is not sufficient to prove that a parallelogram is a square.
A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. It has opposite angles equal in measure. The diagonals of a parallelogram bisect each other.
A square is a type of rectangle and a type of parallelogram. It is a four-sided polygon with all sides of equal length and all angles right angles. The opposite sides of a square are parallel and congruent, and opposite angles are congruent as well. The diagonals of a square are congruent and bisect each other. Additionally, the diagonals of a square are also perpendicular to each other.
Note that a rhombus also has congruent adjacent sides and perpendicular diagonals, but it's not a square.
Therefore, if the diagonals are perpendicular and one pair of adjacent sides are congruent, the parallelogram is not necessarily a square.
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How many solutions does equation x1 x2 x3 11 have where x1 x2 and x3 are non negative integers?.
The number of solutions to an equation x₁ + x₂ + x₃ = 11 are 55
Consider given equation x₁ + x₂ + x₃ = 11,
wherex₁, x₂, and x₃ are non-negative integers.
We can oberve that x₁ is the number of ones before the first zero, x₂ the number of ones between the first and the second zero, x₃ is the number of ones after the second zero.
So, we can say that there is a one to one correspondence between the solutions and reorderings of 11 ones and 2 zeros.
So, the number of solutions to given equation would be,
n = ¹¹C₂
Using combination formula [tex]^nC_r=\frac{n!}{r!\times(n-r)!}[/tex],
¹¹C₂ = 11! / (2! × (11 - 2)!)
¹¹C₂ = 55
So, n = 55
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The complete question is:
How many solutions does equation x₁ + x₂ + x₃ = 11 have where x₁, x₂, and x₃ are non negative integers?.
Jamar is ordering a taxi from an online taxi service. The taxi charges $3.50 just for the pickup and then an additional $2 per mile driven. How much Would a taxi ride cost if Jamar is riding for 7 miles? How much would a taxi ride cost that is m miles long?
Answer:
Step-by-step explanation: Hello! (Don't read this if you are taking a test, please!)
You know that the taxi will already charge $3.50. Write that down. You know that Jamar is riding for 7 miles. You know that each mile costs $2. Multiply the cost of a single mile by the amount of miles, 7. Then you will get your answer. I hope I helped you out!
What is the height H of the roof?.
Answer:
Step-by-step explanation:
Per ASCE 7, the Mean Roof Height (h) is defined as the average of the roof eave height and the height to the highest point on the roof surface, except that, for roof angles of less than or equal to 10°, the mean roof height is permitted to be taken as the roof eave height
i hope it helps
What is the area of equilateral ∆ having side 12 cm?.
To find the area of an equilateral triangle with side 12 cm, we can use the formula:
Area = (√3/4) * (side length)^2
Substituting the value of the side length, we get:
Area = (√3/4) * 12^2
Area = (√3/4) * 144
Area = (√3/4) * 1212
Area = (√3/4) * 1212 = (√3/4)144 = (√3)12(12/4) = (√3)123 = 1212*√3 cm^2
So, the area of the equilateral triangle is 1212√3 cm^2.
please answer this it is urgent and due tomorrow morning
Answer: a) 190cm³
b) 76cm³
(refer to the image to see all the steps and workings I did related to these diagrams)
what number is equivalent to 49 ÷ 9
The value of the equation is A = 5.44
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = 49 ÷ 9 be equation (1)
On simplifying the equation , we get
A = 5.44
Therefore , the value of A is 5.44
Hence , the equation is A = 5.44
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Questions 4,5,6, please.
Hope it helps. To know the values of all trigonometric ratios, see the table.
If you have any query, feel free to ask.
Chris is at the deli and is trying to figure out how much total cheese he has bought. He knows that he bought ½ pound of American cheese and two packs of 2/3 pound Mozzarella cheese. How much total cheese did he buy?
Answer: 7/6 or 1 1/6
Step-by-step explanation:
1/2+2/3= 7/6 or 1 1/6
2x2 and 3x2 which is 4/6 (multiply with 2)
1x3 and 2x3 which is 3/6 (multiply with 3)
4/6+3/6= 7/6 or 1 1/6
What is the name of Σ?.
The Greek letter Sigma (Σ) is a mathematical symbol used to represent the sum of a series. It is also used to denote standard deviation and other statistical terms, and is the eighteenth letter of the Greek alphabet.
The symbol is written as a capital letter Σ, and is used to indicate the summation of a set of numbers, with a subscript indicating the range. For example, Σ1-10 would indicate the sum of numbers from one to ten.
Sigma can also be used to represent a group of numbers' standard deviation. To do this, the sigma symbol is written with a subscript indicating the range, and the square root of the variance of the set is calculated.
In summary, the sigma symbol is used to represent the sum of a series, as well as to denote standard deviation and other statistical terms. It is written as the capital letter Σ, and is usually followed by a subscript to indicate the range of the summation or standard deviation.
Complete answer:
What is the name of Σ?
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here is an equation.
a+b=c
that given: a,b and c are different single-digit numbers
a,b=c are all even,
a,b=c are all positive,
a=6.
find the numbers b and c to make the equation true.
The numbers of a, b and c that make the equation true are given as follows:
a = 6, b = 2, c = 8.
How to obtain the values of a, b and c?The equation for this problem is defined as follows:
a + b = c.
The value of a is given as follows:
a = 6.
Hence:
6 + b = c.
b and c are single-digit even numbers, hence they can be obtained by trial and error as follows:
b = 0 -> c = 6, not possible as it would be equals to a.b = 2 -> c = 8, correct option.b = 4 -> c = 10, not possible as c would be a two digit number.More can be learned about equations at https://brainly.com/question/24808124
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What is y =- 4 on a graph?.
It is a horizontal line which crosses the y axis at -4
The y-intercept is the point at which the graph crosses the y-axis. The most important step in graphing any function with the formula y = f(x) is finding the intercepts. The x-intercept and the y-intercept are the two possible forms of an intercept for a function. The point on the axis where a function's graph intersects it is known as the intercept.
In this equation, y=-4 which means y-intercept is -4 (i.e., c= -4) and the slope of the line is 0.
Thus, it will be a horizontal line cutting the y-axis at -4
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Shawnece is solving the equation x/7 − 4 = −6. One of her steps is to multiply both sides of the equation by 7. Why?
Multiplying both sides by 7 undoes the division of x by 7 in the original problem
The negative sign in −6 must be changed to positive.
Multiplying both sides by 7 undoes the subtraction in the original problem.
Multiplying both sides by 7 undoes the addition in the original problem.
Multiplying both sides by 7 undoes the division of x by 7 in the original problem. Therefore, option A is the correct answer.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is x/7 -4=-6
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Multiplying both sides of equation by 7, we get
x-28=-42
Add both sides of equation by 28, we get
x=-42+28
x=-42
Therefore, option A is the correct answer.
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stefanie has 18 grams of 20% sugar syrup, and john has 30 grams of 25% sugar syrup. how many grams of sugar are in john's syrup?
John syrup contains 11.1 grams of sugar
How to calculate the number of grams in john's syrup?Stefanie has 18 grams of 20% syrup
John has 30 grams of 25%
Therefore the number of grams of sugar in John's syrup can be calculated as follows
18× 20/100 + 30 × 25/100
= 18×0.2 + 30×0.25
= 3.6 + 7.5
= 11.1
Hence there are 11.1 grams of sugar in John's syrup
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What is the base of 2?.
The base of 2 is a binary number. This means it is comprised of only 0's and 1's.
A binary number is a number represented in the base-2 numeral system or binary numeral system, a method of a mathematical term which uses only two symbols: typically "0" (zero) and "1" (one).
A binary number system is one of the types of the number system. In computer applications, where only two symbols or digits represent binary numbers, i.e. 0 (zero) and 1(one). The binary numbers here are represented in the base-2 numeral system. For example, (101)₂ is a binary number. Each digit in this system is stated to be a bit.
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Whitney drink 1,500 mL of water each day troy drink 1. 8 L of water each day
Who drink more water?
By how much water?
The person who drink more water is Troy and he drinks 0.3 L more than Whitney
What is unit conversion?It is the transformation of a value expressed in one unit of measurement into an equivalent value expressed in another unit of measurement of the same nature.
To solve this problem, we have to do the conversion of units with the given information:
Information about the problem:
Whitney = 1500 mLTroy = 1.8 L1 L is equal to 1000 mLBy converting the unit from mL to L, we have:
1500 mL * (1 L / 1000 mL ) = 1.5 L
Comparing the volume of water that Whitney and Troy drink we have:
1.8 L > 1.5 L
Troy > Whitney
Troy drinks more water than Whitney
Calculating how much water Troy drinks more, we get:
Volume difference = Troy - Whitney
Volume difference = 1.8 L - 1.5 L
Volume difference = 0.3 L
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