The proof that if if a, b, and c are real numbers such that A^2 + B^2 + C^2 = 0, then A = B = C = 0 is made by contradiction in this problem.
What is a proof by contradiction?Proof by contradiction is different of traditional proof because it accepts a single example showing that a statement is false, instead of having the need to derive a general relationship for all input values.
For this problem, we must assume the case in which at least one of the terms is non-zero, hence we assume that A is non-zero, hence the expression would be given as follows:
A² + B² + C² = 0
A² = -(B² + C²)
This means that the square of A would be negative. However, the square of a number is always a non-negative number, hence this equation above is a contradiction.
This contradiction was used to prove that if a, b, and c are real numbers such that A^2 + B^2 + C^2 = 0, then A = B = C = 0.
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which fractions, when converted, result in a repeating decimal? select all that apply 1/8 1/6 3/12 8/9 2 and 4/5 4 and 3/11
Answer:
B. 1/6
D. 3/12
F. 4 3/11
PLEASE MARK BRAINLIEST
What is the unit rate for 4543.08 km in 52.4 h?
The unit rate for 4543.08 km in 52.4 hours is 86.7 km.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
4543.08 km = 52.4 hours
Divide 52.4 into both sides.
86.7 km = 1 hour
Thus,
The unit rate is 86.7 km.
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Question 2(Multiple Choice Worth 5 points)
(Two-Step Linear Inequalities MC)
Find c for the inequality three fifths times c plus 7 is less than or equal to two fifths.
c ≤ −11
c ≥ −11
c ≤ −5
c ≥ −5
The value of c obtained from the linear inequality (3/5)·c + 7 ≤ 2/5 is the option;
c ≤ -11
What is an inequality?An inequality is a (non equal) comparison between two expressions that have different values.
The specified inequality can be expressed as follows;
[tex]\dfrac{3}{5} \times c + 7 \leq \dfrac{2}{5}[/tex]
Simplifying the above inequality by subtracting 7 from both sides, we get;
[tex]\dfrac{3}{5} \times c + 7 - 7 \leq \dfrac{2}{5} - 7[/tex]
Evaluating and simplifying the right hand side into a fraction, we get;
[tex]\dfrac{3}{5} \times c + 0 \leq \dfrac{2}{5} - 7 = \dfrac{2 - 35}{5} = \dfrac{-33}{5}[/tex]
[tex]\dfrac{3}{5} \times c \leq \dfrac{-33}{5}[/tex]
Multiplying both sides by 5, we get;
[tex]5\times \dfrac{3}{5} \times c \leq 5 \times \dfrac{-33}{5}[/tex]
[tex]\dfrac{5}{5} = 1[/tex], therefore;
3·c ≤ -33
Dividing both sides of the above inequality by 3, we get;
3·c ÷ 3 ≤ -33 ÷ 3
c ≤ -11
The correct option is; c ≤ -11
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a baker has 85 cups (c) of flour to make bread.she uses 6 1/4 c of flour for each loaf of bread
The baker can make 13 loafs of bread using 85 cups of flour using 6 1/4 c of flour for each loaf of bread.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, A baker has 85 cups (c) of flour to make bread she uses 6 1/4 c of flour for each loaf of bread.
Now, The fraction 6 1/4 can be written as 25/4.
Therefore, The number of bread loaf the baker can make is,
= (85/25/4).
= 85×(4/25).
= (17×4)/5.
= 68/5.
= 65/5 + 3/5.
= 13 + 3/5.
So, he can make 13 bread loafs.
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Select each equation that the number 10^3 makes true.
6.01 x
= 601
O 0.305 x
= 305
0.54 x
= 540
O 0.097 x
970
0.97 x
= 97
All of the equations which the number 10³ makes true include the following:
B. 0.305 × __ = 305
C. 0.54 × __ = 540
How to determine the true equations?In this exercise, you are required to determine the equations which the number 10³ makes true. This ultimately implies that, we would substitute the number 10³ into each of the given equations as follows;
6.01 × 10³ = 601
By expanding the exponent, we have the following equation:
6.01 × 1,000 = 601
6010 = 601 (False).
0.305 × 10³ = 305
By expanding the exponent, we have the following equation:
0.305 × 1,000 = 305
305 = 305 (True).
0.54 × 10³ = 540
By expanding the exponent, we have the following equation:
0.54 × 1,000 = 540
540 = 540 (True).
0.097 × 10³ = 970
By expanding the exponent, we have the following equation:
0.097 × 1,000 = 970
97 = 970 (False).
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I need help with problem eight.
Forty points for whoever answers this problem
Answer:
1
Step-by-step explanation:
1/1260 = 0.00079365079
0.00079365079 * 1260 = 1
Calculate the perimeter of a square with side 12cm
Answer: 48 cm
Step-by-step explanation:
12 + 12 + 12 + 12 = 48
-50 POINTS- only answer if you know. NOT (4,7) OR (5,2).
Answer:
(8, -2)
Step-by-step explanation:
Given:
[tex]\textsf{If P = (8, 2), Find $\sf R_{x-axis}(P)$}[/tex]
[tex]\sf R_{x-axis}(P)[/tex] means to reflect the given point P in the x-axis.
When a point is reflected in the x-axis, the x-value is unchanged, but the y-value becomes negative:
(x, y) → (x, -y)Therefore:
[tex]\sf R_{x-axis}(P)=(8,-2)[/tex]
Philip is twice as old as Annie. Paul is 4 years older than Phillip and Chris is 2 years younger than Annie. Which represents the order of the children by age, from oldest to youngest? A. Paul, Phillip, Annie, Chris B. Chris, Paul, Annie, Phillip C. Annie, Phillip, Paul, Chris D. Paul, Phillip, Chris, Annie
Option -A is correct that is the order of the children by age, from oldest to youngest is Paul, Phillip, Annie, Chris.
Given that,
There are 4 children's. The names of the children's are Philip, Annie, Paul and Chris.
Philip is twice as old as Annie. Paul is 4 years older than Phillip and Chris is 2 years younger than Annie.
We have to find which represents the order of the children by age, from oldest to youngest.
We know that,
Lets us take the ages if the children's as a,b,c,d of Philip, Annie, Paul and Chris.
Philip is twice as old as Annie.
That means a = 2b
Paul is 4 years older than Phillip and
That mean c =4+a
Chris is 2 years younger than Annie.
That means d=b-2
So,
If we take the age of Philips as 20
Then Annie is 10, Paul is 24 and Chris is 8.
Therefore, Option -A is correct that is the order of the children by age, from oldest to youngest is Paul, Phillip, Annie, Chris .
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1. Convert the following improper fractions to mixed numbers; a. 55
2
b. 43 3
2. Convert the following mixed numbers to improper fractions; a. 72
5
b. 121 2
[1]
[1]
[1]
7½
7×2+1/2
14+1/2
15/2
212½
12×2+1/2
24+1/2
25/2
the slope to (9, -10), (0, 8) with the work shown please.
Answer:
-2
Step-by-step explanation:
To find the slope, subtract y1 - y2, then divide by x1-x2
The y numbers in this set is -10 & 8
The x numbers in this set is 9 & 0
-10-8= -18
9-0 = 9
-18/9 = -2
The slope would be -2
The density of a certain material is such that it weighs 6900 grams for every 4.5 quarts of volume. Express this density in pounds per cubic foot. Round your answer to the nearest whole number.
The density in terms of pounds per cubic foot is 101.2 pounds/ft³
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here; 6900 g for every 4.05 quarts thus expressing in terms of pounds per cubic foot we get = 15.22/0.15039
= 101.2
Hence, The density in terms of pounds per cubic foot is 101.2 pounds/ft³
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If Nayesha pumps 9.4 gallons of gas in her gas tank and each gallon costs $2.98, how much money will she spend? QUCIKLY
Answer:
28.012
Step-by-step explanation:
9.4*2.98 = 28.012
What is the slope of the line that passes through the points (-6, -6) and
(-9, -5)? Write your answer in simplest form.
So basically what I do is find the formula for slope.
M= y2-y1/x2-x1
So I got
-5-(-6)/-9-(-6) = 1/3
answer = 1/3
:)
Please help will mark Brainly
Answer:
y < 1/2x +6
Step-by-step explanation:
You want the inequality graphed in the given figure.
Line and shadingThe line is dashed, and the shading is below it, so the inequality will have the form ...
y < ...
This is because the boundary line is not included, and the y-values in the solution are less than those on the boundary line.
Boundary lineThe y-intercept is at +6, where the line crosses the y-axis.
The line goes 2 units to the right for each 1 unit up, so its slope is ...
m = rise/run = 1/2
The slope-intercept equation for the boundary line is ...
y = mx +b . . . . . . slope m; y-intercept b
y = 1/2x +6 . . . . . equation of the boundary line in the graph
InequalityPutting the boundary line expression into the inequality form gives the inequality that describes the graph:
y < 1/2x +6
am is paying off his eight-year, $15,360 loan in semiannual installments. The loan has an interest rate of 9.58%, compounded semiannually, and a service charge of $1,294.64. Once the loan has been fully paid off, what percentage of the total finance charge will the service charge be? Round all dollar values to the nearest cent.
a.
5.48%
b.
8.43%
c.
18.55%
d.
15.65%
Please select the best answer from the choices provided
A
B
C
D
The percentage of the total finance charge on the loan that the service charge will be is about 15.65%. Option D is correct.
D. 15.56%
What is a loan?A loan is an item borrowed for a charged amount, such as an amount borrowed to be repaid with a specified interest fee.
The compound interest formula for the semiannual interest rate is presented as follows;
A = P·[1 + R/n]^(n·t)
Where;
P = The initial amount borrowed on loan = $15,360
t = The interest rate on the loan = 9.58% = 0.0958
n = The number of periods in a year = 2 for semiannual interest rate
t = The duration of the loan = 8 years
The equal semi annual installment (ESI) formula is presented as follows;
[tex]ESI = P\times \dfrac{\dfrac{r}{2} \times\left(1 + \dfrac{r}{2} \right)^n }{\left(1+\dfrac{r}{2} \right)^n-1}[/tex]
Therefore;
ESI = 15360 × ((0.0958/2)×(1 + 0.0958/2)¹⁶)/((1 + 0.0958/2)¹⁶-1) ≈ 1396.16
The total amount Sam pays = 16 × 1396.16 ≈ 22338.6
The finance charge ≈ 22338.6 - 15360 = 6978.6
The percentage of the finance charge represented the service charge is therefore;
(1294.64/(6978.6 + 1294.64))×100 ≈ 15.65%
The percentage of the total finance charge represented by the service charge is therefore about 15.65%
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A 38 ounce box of cat food costs $1.69 and a 24 ounce box costs $1.29. How much can be saved per ounce by guiding the larger box
The amount of money that can be saved per ounce by guiding the larger box is $0.009.
What is equation modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.
Given is that a 38 ounce box of cat food costs $1.69 and a 24 ounce box costs $1.29.
For the larger box -
38 ounce box of cat food costs $1.69
1 ounce of this box will cost $(1.69/38) = $0.045
For the smaller box -
24 ounce box of cat food costs $1.29
1 ounce of this box will cost $(1.29/24) = $0.054
Money that can be saved per ounce by guiding the larger box -
0.054 - 0.045
0.009
Therefore, the amount of money that can be saved per ounce by guiding the larger box is $0.009.
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on Monday the solar panels on a house produced 37.124 units of energy. On Tuesday, the solar panels produced 2,846 fewer units of energy than on Monday. What is the total number of units of energy in two days.
The total number of units of energy produced in the two days is 71,402.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Monday:
Energy = 37,124
Tuesday:
Energy = 37,124 - 2846 = 34278
The total energy produced.
= 37124 + 34278
= 71402
Thus,
The total number of energy in two days is 71,402.
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what would be themissing side length
The missing side length is 5.7.
What would be themissing side length?The missing side length AB, can be calculated using the Pythagorean Theorem.The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the two sides adjacent to the right angle (A and B) is equal to the square of the length of the hypotenuse (C).In other words, AB^2 + BC^2 = AC^2.In this case, AB^2 = AC^2 - BC^2, or AB^2 = 6.7^2 - 3^2, which simplifies to AB^2 = 44.89.Taking the square root of both sides yields AB = 6.7.Therefore, the missing side length, AB, is 6.7.The missing side length of a triangle with sides of lengths a, b, and c is calculated by using the Pythagorean theorem, which states that a^2 + b^2 = c^2. In this case, we are given that side c is 3, and side a is 6.7.Using the Pythagorean theorem, we can solve for side b by rearranging the equation to read b^2 = c^2 - a^2. Plugging in our known values, we get b^2 = 9 - 44.89, or b^2 = -35.89.Since the square root of a negative number is not a real number, this implies that there is no real number solution for b, and therefore the missing side length of the triangle is not possible.
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Canvas Reproductions, Inc has RM4,500 researching a new project. The project requires RM20,000 worth of new machinery which would cost RM3,000 to install. The company would realize RM4,500 in after tax proceeds from the sale of the old machinery. If Canvas’s working capital is unaffected by this project, what is the initial investment amount for this project?
Hi. This is an informal letter .
The body of letter goes like this
Hi friend hope u are enjoying ur life and luck find u in best state of mind. My exam have been over and wanted to share my experience with my near and dear one so I was planning to come to ur place to enjoy my vacationHi. This is an informal letter .
The body of letter goes like this
Hi friend hope u are enjoying ur life and luck find u in best state of mind. My exam have been over and wanted to share my experience with my near and dear one so I was planning to come to ur place to enjoy my vacationHi. This is an informal letter .
The body of letter goes like this
Hi friend hope u are enjoying ur life and luck find u in best state of mind. My exam have been over and wanted to share my experience with my near and dear one so I was planning to come to ur place to enjoy my vacationHi. This is an informal letter .
The body of letter goes like this
Hi friend hope u are enjoying ur life and luck find u in best state of mind. My exam have been over and wanted to share my experience with my near and dear one so I was planning to come to ur place to enjoy my vacation
The function f(x)= -3x^3 + x^2 +2x rises as x grows very small.
A. True
B. False
False, the function f(x)=[tex]-3x^3 + x^2 +2x[/tex] does not rises as x grows very small.
How to determine the statementFirst, we need to know that functions are described as laws, expressions or rules that are used to show the relationship between two variables in an equation.
These variables are known as;
The independent variableThe dependent variableThe function f(x) =[tex]-3x^3 + x^2 + 2x[/tex] does not rise as x grows very small. When x approaches negative infinity, the dominant term is [tex]-3x^3[/tex], which becomes increasingly negative.
Therefore, the function decreases as x grows very small in the negative direction.
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At the end of an interview you are offered a job. You would start at 7.50 an hour and work an average of 45 hours a week. At the end of six months with a positive evaluation, your hourly pay would increase to 8. The job pays overtime at a time and a half rate, based on 37 1/2 hour regular work week. What total earrings could you expect to make by working a full year
By working a full year, you may expect to earn a total of $19,646.25 in earrings.
Explain about the expression?This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. The following is the structure of an expression: Expression: (Number/Variable, Math Operator, Math Operator)
An expression, also known as an algebraic expression, is any mathematical statement that consists of numbers, variables, and an arithmetic operation between them. For example, the mathematical sign + separates the phrases 4m and 5 from the variable m in the phrase 4m + 5.
Combining numbers, variables, and operators to represent something's value is known as a mathematical expression. Setting two expressions equal to one another creates an equation, a mathematical statement.
= Total overtime pay of $2,193.75 (first 6 months)
Add the regular and overtime pay after that:
= $7,312.50 + $2,193.75
= $9,506,25 in total income (first 6 months)
$7,800.00totalregularpay(last6months)
Overtime pay:(26weeks in a half year) \=$8\times
7.57.5\times1.51.5\times
$ 26
= Total overtime pay of $2,340.00 (last 6 months)
Add the regular and overtime pay after that:
= $7,800.00 + $2,340.00
= $10,140.00 in total income (last 6 months)
In the end, add the combined earnings from the two half years:
= $9,506.25 + $10,140.00
= Total annual profits of $19,646.25 (expected)
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3a²b and 3ab² are like terms true or false
Step-by-step explanation:
false.
3a²b≠3ab².
If a is 3 and b is3 it is not equal
if x=1−sin a and y= 1+cos a, Express y in terms of x and a only
Answer:
Step-by-step explanation:
Given
[tex]x=1-sin(a)\\y=1+cos(a)[/tex]
Solve for [tex]a[/tex] in the second equation.
[tex]y=1+cos(a)[/tex]
[tex]y-1=cos(a)[/tex]
[tex]a=cos^{-1}( y-1)[/tex]
Insert our answer for [tex]a[/tex] into the first equation.
[tex]x=1-sin(a)[/tex]
[tex]x=1-sin(cos^{-1}( y-1))[/tex]
[tex]cos^{-1}=arccos[/tex]
[tex]x=1-sin(arccos( y-1))[/tex]
Lets simplify [tex]1-sin(arccos( y-1))[/tex]
A piece of graph paper would be helpful in my opinion.
Here is how I would go about doing so
Draw a triangle in the plane with vertices [tex](y-1,\sqrt{1^2-(y-1)^2}),(y-1,0)[/tex] and the origin.
[tex]arccos(y-1)[/tex] is is the angle between the positive x-axis and the ray beginning at the origin and passing through [tex](y-1,\sqrt{1^2-(y-1)^2})[/tex]. Therefore [tex]sin(arccos(y-1))[/tex] is [tex]\sqrt{1-(y-1)^2}[/tex]
Now we have
[tex]x-1-\sqrt{1-(y-1)^2}\\a=arccos(y-1)[/tex]
We can write [tex]1[/tex] as [tex]1^2[/tex]. Since both terms are now perfect squares, we can factor using the difference of squares formula.
[tex]a^2-b^2=(a+b)(a-b)[/tex] where [tex]a=1[/tex] and [tex]b=y-1[/tex]
[tex]x=1-\sqrt{(1+y-1)(1-(y-1))}[/tex]
After simplifying we get
[tex]x=-\sqrt{y(-y+2)}+1[/tex]
[tex]x=-\sqrt{y(-y+2)}+1[/tex]
[tex]a=arccos(y-1)[/tex]
I think this is what your question was. If not let me know.
Solve on the interval [0, 2pi): 4csc x +6=-2
By solving the interval : [0,2pi] 4 csc x +6=-2 is 7pi/6 , 11pi/6
What are Trigonometric identities?Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence. These are identities that, geometrically speaking, involve certain functions of one or more angles. defining sine and cosine in terms of tangent, cotangent, secant, and cosecant interactions. The sine and cosine formula according to Pythagoras. This trig identity is arguably the most significant.[tex]& 4 \csc x+6=-2 \\[/tex]
[tex]& 4 \csc x=-8 \\[/tex]
Simplifying,
[tex]& \csc x=-2 \\[/tex]
[tex]& \frac{1}{\sin x}=-2 \\[/tex]
[tex]& \sin x=-\frac{1}{2} \\[/tex]
We get,
[tex]& x=\frac{7 \pi}{6}, \frac{11 \pi}{6}[/tex]
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Segment
B
D
‾
BD
bisects
∠
A
B
C
∠ABC. Solve for
x
x. Round to the nearest tenth, if necessary. (Image not necessarily to scale.)
The value of x on the line segment and the triangle is 17.3 units
How to determine the value of xFrom the question, we have the following parameters that can be used in our computation:
A triangle (see attachment for the triangle)
Also from the question, we understand that:
BD bisects ∠ABC
Using the bisector theorem, we have
x/13 = 20/15
Multiply both sides of the equation by 13
So, we have the following representation
13 * x/13 = 20/15 * 13
Evaluate the products
So, we have the following representation
x = 20/15 * 13
Evaluate the other products
So, we have the following representation
x = 52/3
This gives
x = 17.3
Hence, the length x is 17.3 units
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Chen tosses a number cube 19 fewer times than Jayden. Chen tosses a number cube 38 times. How many times does Jayden toss a number cube?
Find three consecutive integers such that 4 times the first decreased by the second is 12 more than twice the third
The three consecutive number are 17 , 18 and 19 respectively
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
Let the first number be = x
Let the second number be = ( x + 1 )
Let the third number be = ( x + 2 )
Now ,
A = 4 times the first decreased by the second is 12 more than twice the third
Substituting the values in the equation , we get
4x - ( x + 1 ) = 12 + 2 ( x + 2 )
On simplifying the equation , we get
4x - x - 1 = 12 + 2x + 4
3x - 1 = 16 + 2x
Subtracting 2x on both sides of the equation , we get
x - 1 = 16
Adding 1 on both sides of the equation , we get
x = 17
Therefore , the value of x is 17
Hence , the consecutive numbers are 17 , 18 and 19
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? Question
Drag the tiles to the correct boxes to complete the pairs.
Solve each equation using the square root property. Then, match the solutions to the equatio
Tiles
Help please
The solutions for the given equations are x = 9i , -9i , x = 2i,-2i ,
x = [tex]\sqrt{13}[/tex] , - [tex]\sqrt{13}[/tex] , x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i .
Given equations ,
[tex]x^{2}[/tex] + 81 = 0 ,[tex]x^{2}[/tex]-22 = -26 , 3[tex]x^{2}[/tex]-18=21 ,2[tex]x^{2}[/tex] +15 = -13
What is Quadratic equation ?
quadratic equation can be defined as the equation which is in the form of a[tex]x^{2}[/tex]+bx + c = 0 .
where a,b,c are constants .
By solving we get ,
[tex]x^{2}[/tex] +81 = 0
[tex]x^{2}[/tex] = -81
x = 9i , -9i
[tex]x^{2}[/tex] - 22 = -26
[tex]x^{2}[/tex] = -26 + 22
[tex]x^{2}[/tex] = -4
x = 2i,-2i
3[tex]x^{2}[/tex] - 18 = 21
3[tex]x^{2}[/tex] = 18+21
3[tex]x^{2}[/tex] = 39
[tex]x^{2}[/tex] = 13
x = [tex]\sqrt{13}[/tex] , - [tex]\sqrt{13}[/tex]
2[tex]x^{2}[/tex] +15 = -13
2[tex]x^{2}[/tex] = -13-15
2[tex]x^{2}[/tex] = -28
[tex]x^{2}[/tex] = -14
x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i
Hence the solutions for the given equations are x = 9i , -9i , x = 2i,-2i ,
x = [tex]\sqrt{13}[/tex] , - [tex]\sqrt{13}[/tex] , x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i .
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Q.
The surface area of a cube is
37.5 cm². What is the area of
each side of the cube?
The total surface area of the cube will be 37.5 cm²
What is the surface area of a cube?A three-dimensional shape's surface area is the sum of all of its faces. Finding the area of each face and adding them together gives us the surface area of a shape.Surface area analysis refers to the measurement of a particle's available surface. It is important because it is the means by which a solid interacts with its surroundings, whether they are gases, liquid, or other solids.Here the edge of the cube is given
Edge = 2.5 cm
We have to find out the total surface area of the cube
Total surface area of cube = 6a², where a is the edge of the cube
= 6 × 2.5 × 2.5
= 37.5 cm²
Hence, the total surface area of the cube will be 37.5 cm²
The complete question is,
Find the surface area of a cube of Edge 2.5 CM
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