A system of 3 equations can have 0, 1, 2, or infinitely many solutions.
It is possible for a system of 3 equations to have no solutions if the equations are incompatible, meaning that there is no combination of values for the variables that can satisfy all of the equations simultaneously. It is possible for a system of 3 equations to have exactly one solution if the equations are dependent, meaning that one of the equations can be derived from the other two. It is possible for a system of 3 equations to have exactly two solutions if the equations are independent, meaning that the equations are not related to each other and cannot be derived from each other. Finally, it is possible for a system of 3 equations to have infinitely many solutions if the equations are consistent and the variables are linearly dependent.
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Marcia and Becky shared some money
in the ratio 1:4
Marcia gets £18 less than Becky. How
much does Marcia receive?
The money received by Marcia = £ 6
According to the given information
The money is shared between Marcia and Becky in the ratio = 1 : 4
Let the money got by Becky = £ x
Marcia got £ 18 less than Beck = x - 18
So
Taking the ratio
[tex]\frac{1}{4}=\frac{x-18}{x}[/tex]
Cross multiply both the fractions
x = 4(x - 18)
x = 4x - 72
-3x = -72
x = 24
Money got by Beck = £ 24
Money received by Marcia = 24 - 18
= £ 6
Hence
The money received by Marcia = £ 6
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What is the smallest number divisible by 3?
The smallest number that is divisible by 3 is 3 itself. Every integer that is divisible by 3 is called a multiple of 3.
For example, some of the multiples of 3 are 6, 9, 12, 15, 18, 21, etc. All of these numbers can be obtained by multiplying 3 by an integer.
What does "divisible" mean in math?If a number evenly divides (leaves no residue) into another number, it can be divided. For instance, 34 may be divided by 2 equally, making it a divisible number. However, because doing so would result in a leftover, 34 cannot be divided by 3.
How are three divided?According to the law of three's divisibility, a number is completely divisible by three if the sum of its digits is also divisible by three. Take 308 as an example. To determine whether or not 308 is divisible by 3, add the digits together and find the sum (3+0+8=11).
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How do you work out 13X13?
Therefore , the solution of the given problem of squaring comes out to be square of the 13 is 169.
What does it mean to square a number?A resultant is referred to as a "Square Number" when a number or integer (not a fraction) is multiplied by itself. For instance, 3 x 3 is 32 when multiplied by itself three times. In essence, the exponential form of multiplying an integer or number by itself is referred to as a square number.
Here,
Try to add up the four stages here.
Multiplication of two-digit numbers using a math shortcut trick
shortcuts: 13 times 13 equals
13X13 = 169 is the answer when a two-digit number is multiplied.
Therefore , the solution of the given problem of squaring comes out to be square of the 13 is 169.
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Find the first 5 terms of the sequence.
The first five terms of the expression are -7,-3,1,5, and 9.
What is arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that , F(1) = -3 and F(n) = F(n-1) + 4. Calculate the first term of the sequence,
F(1) = F(1-1) + 4
-3 = F(0) + 4
F(0) = -7
The common difference is calculated as,
d = -3 - 7
d = 4
The third term will be, -3 + 4 = 1
The fourth term will be, 1 + 4 = 5
The fifth term will be, 5 + 4 = 9
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How do you identify congruent in SAS?
-15+23r+9r^2-16r+10
A 9r^-10-7r
B 16r^2-5
C 9r^2-7r^-5
D 9r^2+tr-5
Answer:
9r^2+7r-5
Step-by-step explanation:
-15+23r+9r^2-16r+10
=-15 + 9r^2 + 7r +10
= 9r^2 + 7r - 5
Answer:
[tex]9r^2+tr-5[/tex]
The given expression is a polynomial in the variable r. The correct answer among the options provided is D, which has the same terms as the given expression, in the same order, but with an additional term (tr) at the end. The other options do not match the given expression.
Please give a step by step explanation
The evaluation of the composite figure comprising of a square and an equilateral triangle is as follows;
9 (a) ∠ABD = 90°
(b) ∠BCD = 60°
(c) ∠ADC = 105°
What is a composite figure?A composite figure is a figure comprising of two or more regular geometric figures.
9. The shape of the quadrilateral ABDE = A square
The kind of triangle specified for the triangle ΔBCD = Equilateral triangle
The sides of the square ABDE are congruent by the definition of a square
Therefore; AB = BD = DE = AE by the definition of congruency
(a) Angle ∠ABD is a corner of the square ABDE, therefore;
The size of angle ∠ABD = 90° (properties of the interior angle of a square)
∠ABD = 90°(b) The size of angle ∠BCD = 60° (Interior angle of an equilateral triangle)
∠BCD = 60°(c) The size of angle ∠ADC is found as follows;
Triangles ΔAED and triangle ΔABD formed by the diagonal AD are congruent by Side-Side-Side, SSS congruency postulate
∠DAB ≅ ∠ADB (base angles of isosceles triangle ΔABD)
∠DAB = ∠ADB (Definition of isosceles triangles)
∠ABD + ∠DAB + ∠ADB = 180° (Angle sum properties of a triangle)
90° + 2 × ∠ADB = 180° (substitution property)
∠ADB = (180° - 90°) ÷ 2 = 45°
∠BDC = 60° (Interior angle of an equilateral triangle)
∠ADC = ∠ADB + ∠BDC (Angle addition postulate)
Therefore, ∠ADC = 45° + 60° = 105°
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How do I follow up on SSS sickness benefit application?
The follow up on SSS loan sickness benefit application are as follows :
Sickness Benefit Application (SBA) FormAny legitimate primary ID card or document, such as an SS ID or UMID, as follows:- Driver’s License
- Passport
- Voter’s ID Card
- National Bureau of Investigation (NBI) Clearance
- Postal Identity Card
- Any other government-issued (secondary) ID cards/documents
supporting medical records, if any, for extended illness or incarceration :- Laboratory, X-ray, ECG, and other diagnostic results
- Operating room/clinical record that will support the diagnosis
For illnesses or injuries that occurred abroad, the issuing nation's official documentation must include an English translation and be properly authenticated by the Philippine Embassy or Consulate Office or properly certified by a notary public of the receiving nation.
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How many solutions can 2 linear equations have?
The number of solutions that a system of 2 linear equations in 2 variables can have is explained below.
In the question ,
it is given that ,
the system of 2 linear equations in 2 variables .
we know that the linear equations represent a line .
(i) the two linear equations will have No Solution / Zero Solution if the two lines are parallel .
(ii) the two linear equations will have One Solution/Unique Solution if the two line intersect at a point .
(iii) the two linear equations will have infinitely many solution if the lines overlap on each other .
Therefore , the number of solutions of linear equation is explained above .
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Need help as quick as possible due tmrw
The height of the tree is 61.92 feet.
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.
Given that,
Distance of Tamara from tree = 30 feet.
Angle of elevation = 62°.
And the height of Tamara from the ground = 5.5 feet.
To find the height of the tree,
Use trigonometric formula,
tan θ = height / distance
tan 62 = x / 30
1.88 = x / 30
x = 56.42 feet
The total height of tree = x + 5.5 = 56.42 + 5.5 = 61.92 feet
The height of the tree is 61.92 feet.
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What is the width of the rectangular area?
The width of a rectangle is the smaller side length that situated vertically. Width of rectangular area = Area of rectangle/ length of rectangle
or width of rectangular area = (perimeter of rectangle /2) - length of rectangle
what is the perimeter of a shape?The perimeter is the line that goes continuously along the boundary of a geometrical shape.
How can we find the width of rectangle?the width of rectangle can be found from the area of rectangle formula or area of perimeter formula when the value of length, area and perimeter is known to us.
area = length × width
perimeter = 2(length × width)
hence, the width of a rectangle is the smaller side length along the vertical axis.
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A one-pound pack of wall putty costs $3. A 10-pound pack costs $24. What is the percent savings If you buy the 10-pound pack? 2096 24% 25% 60%
Answer:
20%
Step-by-step explanation:
let x = percent savings
$3/lb (cost per lb of a 1 lb pack)
$24/10lb = $2.40/lb (cost per lb for a 10 lb pack)
$3 - $3x = $2.40
-3x = -0.60
x = -0.60/3 = 0.20
0.20 x 100 = 20%
What is the quotient?
Help :D
1065 ÷ 33
Enter your answer as a mixed number in simplest form in the box.
Answer:
32 3/11
Step-by-step explanation:
Happy Holidays!
7. Explain in your own words why √-4 is not possible.
Answer:
There is no real square root of -4 because it is impossible to square any real number and get a negative answer.
You might think -2 could work. However, a negative times a negative is positive → -2(-2) = +4, so the problem would have to be written as [tex]\sqrt4[/tex] instead of [tex]\sqrt{-4}[/tex]. Hence, there is no real square root of -4.
Note the word real, as it is possible to find a non-real answer to [tex]\sqrt{-4}[/tex] using the imaginary number [tex]i[/tex], which represents [tex]\sqrt{-1}[/tex].
The perez family and the smyth family are each taking road trips. The perez family travels at an average rate of 65 miles per hour and the smyth family travels at an average rate of 50 miles per hour. How far does each family travel after 6 hours?.
Answer:
90 miles.
Step-by-step explanation:
65 - 50 = 15
In each hour they have a difference of 15 miles.
In six hours:
6 * 15 = 90 miles
Yoezer bought 25 shares that had a face value of Nu 100 but were selling at a discount of 5%. A 15% dividend rate was paid at the end of one year. He then sold the stock at a 5% premium.
i. Find the amount of his investment.
ii.Calculate his total profit.
2375 is the amount of his investment and 625 is his total profit
The discount on the shares is 5%, so the price of each share is 100 - (5/100)100 = 95.
The total price Yoezer paid for the shares is 2595 = 2375.
To calculate Yoezer's total profit, we need to find the total dividend he received and the price he sold the shares for.
The dividend rate is 15%, so Yoezer received a dividend of (15/100)100 = 15 on each share.
The total dividend he received is 1525 = 375.
The price Yoezer sold the shares for was increased by a premium of 5%, so the selling price was 100 + (5/100)100 = 105.
The total selling price for the shares is 10525 = 2625.
Yoezer's total profit is the selling price minus the price he paid for the shares plus the dividends he received. This is 2625 - 2375 + 375 = 625.
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HELP PLEASE PLEASE A recipe uses 5 cups of milk to make 25 servings. If the same amount of milk is used for each serving, how many servings can be made from one gallon?
The solution is 80 servings
The number of servings that can be made from 1 gallon is 80 servings
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 number of servings from 1 gallon be = A
Now , the equation will be
The number of cups of milk = 5 cups
The number of servings from 5 cups of milk = 25 servings
So ,
The number of servings from 1 cup of milk = number of servings from 5 cups of milk / 5 cups
Substituting the values in the equation , we get
The number of servings from 1 cup of milk = 25 / 5
The number of servings from 1 cup of milk = 5 servings
Now , 1 gallon = 4 quarts
1 quarts = 2 pints
1 pint = 2 cups
So , 1 gallon = 16 cups
And , number of servings from 1 gallon = number of servings from 16 cups
So ,
The number of servings from 16 cups = number of servings from 1 cup of milk x 16
Substituting the values in the equation , we get
Number of servings from 1 gallon = 5 x 16
Number of servings from 1 gallon = 80 servings
Therefore , the value of A is 80 servings
Hence ,
The number of servings is 80 servings
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What is the median of 1 2 3 4 5 6 7 8?
5.5 is is the median of the set of numbers .
What are the mean, median, and example?
The most frequent number, or the one that happens the most frequently, is known as the mode.
Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.
Since the number of observations is even, the median is the average of
= (n/2) th and (n/2 +1)th observation.
The average of 5th and 6th observations = (5+6)/2 = 11/2 = 5.5.
Hence, the median of the given set of numbers is 5.5.
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How do you find the mean of a set?
Mean mode formula - Mean = {Sum of Observation} ÷ {Total numbers of Observations}
What does the mode mean?
By summing all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined.
A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently.
What are the mean, median, and example?
The most frequent number, or the one that happens the most frequently, is known as the mode. Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.
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What will be the nature of the roots of 2x2 4x 7?
Answer: Roots of given quadratic equation are real and distinct.
If a quadratic equation is given by ,then nature of its roots can be find by it's discriminate (D).
Roots are real and distinct, if D>0
Roots are real and equal, if D=0
Roots are imaginary (no real root exists), if D<0
Step 1:
Write coefficients of x², x and constant term.
Compare the given equation with standard quadratic equation.
Thus,
Roots of given quadratic equation are real and distinct.
Learn more:
1) Find the nature of roots of quadratic equation 2x sq. + 3x - 7=0
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2) Find the nature of the roots of the following quadratic equations. If real roots exist, find them:
(i) 2x² – 3x + 5 = 0 ...
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Step-by-step explanation:
Todd drives 2,365 miles in a month. His average mpg is 20. How much will he pay in gas if gas is $3. 12 per gallon?.
Answer:
He pays:
$368.94
Step-by-step explanation:
20 miles ⇒ 1 gallon
2365 miles ⇒ A gallons
A = 2365 miles * 1 gallon / 20 miles
A = 118,25 gallons
Then:
$3.12 ⇒ 1 gallon
$B ⇒ 118.25 gallons
B = 118.25 gallons * $3.12 / 1 gallon
B = $368,94
How many terms does 3xy have?
3xy has two terms, 3 and xy. The term 3 is a constant and the term xy is a product of two variables.
3xy is a multiplication of three individual components. It consists of three distinct parts, namely 3, x, and y. Each of these components is considered a distinct term, so 3xy has three terms in total. The 3 represents a numerical value, while the x and y are variables that can be assigned any numerical value. When multiplied together, the three terms form a single expression, 3xy, which can then be evaluated for a resulting value.
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Is Cos 2x continuous?
What is 4 1/2÷(−2 2/3)?
Write the answer as a mixed number in simplest form.
help plssss
Answer:
Step-by-step explanation:
you cant divide fractions so you multiply the reciprocal so your answer would be
1 11/16
A circle has center (0,4) and radius 5. Which of the following is an equation of the circle
Answer:
Given that a circle has a center (0,4) and the radius 5. 5. So the standard equation of the given circle is x2+(y−4)2=25.
Step-by-step explanation:
The equation s=100−5m represents the relationship between the total score on Mr. Totten's algebra quiz, s, and the number of questions a student missed, m. Which statement describes the slope in this equation?
The statement that describes the slope in this equation is that the score of each question is 5
How to determine the statement that describes the slope in this equation?From the question, we have the following parameters that can be used in our computation:
Equation: s = 100 - 5m
Also from the question, we have:
s = The total score
m = the number of questions a student missed
Recall that
s = 100 - 5m
A linear equation is represented as
y = mx + c
Where m = slope
By comparing the equations, we have
m = -5
This means that the slope is -5
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The volume of a rectangular prism is 6x3 + 19x2 + 2x - 3
and the height is x + 3. What is the area of the base of the prism?
To find the area of the base of the rectangular prism, we need to find the expression for the area of a rectangle with dimensions equal to the dimensions of the base of the prism.
The volume of a rectangular prism is given by the formula:
Volume = length * width * height
Substituting the given expressions for the volume and the height into this formula, we get:
6x3 + 19x2 + 2x - 3 = (length * width) * (x + 3)
Expanding the right-hand side of the equation, we get:
6x3 + 19x2 + 2x - 3 = length * width * x + length * width * 3
Matching the terms on the left-hand side of the equation with the corresponding terms on the right-hand side, we can see that the expression for the area of the base of the rectangular prism is:
length * width = 6x3 + 19x2 + 2x - 3 - length * width * 3
Simplifying this expression, we get:
length * width = -3x3 - 17x2 - 2x + 3
Therefore, the area of the base of the rectangular prism is given by the expression -3x3 - 17x2 - 2x + 3.
The probability of an unfavorable outcome plus the probability of a favorable outcome equals 1.
O True
O False
Your answer is False
A direct variation includes the points (5,10) and (1,n). Find n.
Write and solve a direct variation equation to find the answer.
A(n) ____ is a numerical summary of a sample.
A statistic is a numerical summary of a sample.
A sample statistic is explained as any number computed from a sample of data.
Examples include the sample average, median, sample standard deviation, and percentiles. A statistic is a random variable because it is based on data obtained by sampling technique in which each sample has an equal probability of being chosen.
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