On multiplying by [3], the slope becomes 3 times the original slope and
y - intercept becomes 3 times of the original value.
What is the general equation of a Straight line?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
We have the following problem -
f(x) = ax + b, where [a] and [b] are nonzero real numbers. Now, the function f(x) is multiplied by 3.
The given straight line is -
y = f(x) = ax + b
After multiplied by [3], we get -
y' = 3f(x) = 3(ax + b) = (3a)x + (3b)
Therefore, on multiplying by [3], the slope becomes 3 times the original slope and y - intercept becomes 3 times of the original value.
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[Complete question - Given f(x) = ax + b, where a and b are nonzero real numbers, which of the following describes the differences between the graph of f and the graph of the output of f multiplied by 3 ]
what equation is parallel to y=1/3x that goes through (6,0)
Considering the definition of parallel line, the equation y= 1/3x - 2 is parallel to y=1/3x and it goes through (6,0).
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Parallel lineParallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.
Two lines are parallel if they have the same slope and different y-intercepts.
Equation of parallel line in this caseIn this case, the line is y=1/3x
where:
m= 1/3b= 0If two lines are parallel if they have the same slope, the parallel line has a slope of 1/3 and has a form of: y= 1/3x + b
The line passes through the point (6, 0). Replacing in the expression for parallel line:
0= 1/3× 6 + b
0= 2 + b
0 -2 = b
-2= b
Finally, the equation of parallel line is y= 1/3x - 2.
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A penguin walks south. it completes the first 1/3 mile in 1/5 hour and continues walking at the same rate. what is the penguin's speed in miles per hour?
In distance, the penguin speed in mi/hr is 1.67mi/hr.
What is distance in math?
A measurement of the distance between two places along a line or line segment.the length or width between two objects, points, lines, etc. remoteness is the state or fact of something or someone being physically distant from another. A straight line in space It would take too long to walk seven miles in one hour. a distance; a space: The ship was encircled by a sizable body of water.Distance = 1/3 mile
Time = 1/5 hour
Speed of the penguin = Distance/Time taken
Substitute the given data into the speed formula;
Speed = (1/3)/(1/5)
Speed = 1/3 * 5/1
Speed = 5/3
Speed = 1.67miles/hour
Hence the penguin speed in mi/hr is 1.67mi/hr
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A credit card bill for $559 was due on September 14. Purchases of $286 were made on September 19, and $15 was charged on September 28. A payment of $250 was made on
September 25. The annual interest on the average daily balance is 19.5%. Find the finance charge due (in dollars) on the October 14 bill. (Use 365 for the number of days in a year.
Round your answer to the nearest cent.)
With 19.5% annual interest on a daily basis, the finance charge due on October 14 will be $623.
What is interest?In the fields of finance and economics, interest is the payment made at a set rate by a borrower or deposit-taking financial institution to a lender or depositor in excess of the principal amount (the amount borrowed). It is not the same as a fee that the borrower might pay to the lender or another party. It also differs from a dividend, which is money given to shareholders (owners) by a company from its profit or reserve but not at a set rate predetermined in advance, but rather on a pro-rata basis as a share of the reward received by risk-taking businesspeople when revenue is earned that exceeds all costs.So, the finance charge due:
(+) $ 559 due on sep 14, $ 559 * (19.5*31) / (100 * 365) = $ 9.20(+) purchase $ 289 on Sep 19, $ 289 * (19.5*26 ) / (100 * 365) = $ 2.42(+) finance charge on sep 28, $ 18 *(19.5*17 ) / (100 * 365) = $ 0.17(-) Repayment on 25 sep , $ 250 * (19.5*20 ) / (100 * 365) = (2.745)Finance charges from 14 sep to 14 oct = $ 9.7= appr. 10Amount due on 14 October = $559+$289+$15+$11.855- $250= $ 623Therefore, with 19.5% annual interest on a daily basis, the finance charge due on October 14 will be $623.
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a woman's boxing match consists of four 2-minute rounds, there is a 1-minute rest interval between each round. what information do you know that will help you find how long a boxing match lasts?
The total time for the boxing match will be 9 minutes.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
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 a woman's boxing match consists of four 2-minute rounds, there is a 1-minute rest interval between each round.
The time of the match will be calculated as:-
Time = 2 x Total rounds + 1
Time = ( 2 x 4 ) + 1
Time = 8 + 1 = 9 minutes
Therefore, the total time for the boxing match will be 9 minutes.
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if A = 32 degrees, a = 17, and b =11 find the measure of angle B
round to the nearest tenth
The 32° measure of A and the length of side a which is 17, and side B with length 11, using the law of sines, gives;
The value of angle B is approximately 20.1°What is the law of sines?The law of sines can be stated as follows;
The ratio of the sine of an interior angle in an oblique triangle to the length of the side opposite the given angle, is a constant for the angles and their opposite sides of the triangle.
Mathematically, we have;
[tex] \frac{sin( A) }{a} = \frac{sin( B )}{b} =\frac{sin( C )}{c} [/tex]
Where;
Angle A is the angle opposite to side a
Angle B is the angle opposite to side b
Angle C is the angle opposite to side c
The given measure of angle A = 32°
The length of segment, a = 17
The length of segment, b = 11
Taking the given dimensions as the measurements of parts of a triangle, using sine rule, we have;
[tex] \frac{sin( A)}{s } = \frac{sin( B )}{b} [/tex]From the question, we have;
A = 32°
a = 17
b = 11
Which gives;
[tex] \frac{17}{sin( 32^{ \circ} ) } = \frac{11}{sin( B )} [/tex]
Therefore;
[tex] sin( B ) = \frac{11 \times sin( 32^{ \circ} ) }{17} [/tex]
Which gives;
[tex] \displaystyle{ B = arcsin \left( \frac{11 \times sin( 32^{ \circ} ) }{17} \right) \approx 20.1 ^{ \circ} }[/tex]
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Dentro de 65 años tendré 6 veces la edad que tenía hace 10 años ¿qué edad tengo?
Based on the calculations, the age of this person is equal to 25 years.
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
In order to solve this word problem, we would assign a variable to the age of this person and then translate the word problem into algebraic equation as follows:
Let x represent the age.
Translating the word problem into an algebraic equation, we have;
x + 65 = 6(x - 10)
Opening the bracket, we have:
x + 65 = 6x - 60
Re-arranging the equation, we have:
6x - x = 60 + 65
5x = 125
Dividing both sides by 5, we have:
x = 125/5
x = 25 years.
In conclusion, we can reasonably infer and logically state that this person's age was 25 years ten (10) years ago.
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Complete Question:
In 65 years I will be 6 times as old as I was 10 years ago. How old am I?
It took a plane 2 hours to fly from Dallas to New York with the head wind and 1.5 hours to return with the tailwind. If the speed of the wind was 30 mph, how far apart are the 2 cities? Giving brainliest to correct answer
Answer:
The distance between the two cities is 360 miles.
Step-by-step explanation:
Let value "a" equal the airspeed of the plane in still air, and let value "d" be the distance between the two cities. Then:
d/a+30=1.5
d=1.5a+45
and
d/a-30=2
d=2a-60
So
2a-60=1.5a+45
.5a=105
a=210
d/210-30=2
d=360
The distance between the two cities is 360 miles.
Factor 63a–35. Write your answer as a product with a whole number greater than 1.
The expression 63a–35 factored as a product with a whole number greater than 1 is 7(9a - 5)
What are algebraic expressions?Algebraic expressions are defined as expressions made up of variables, terms, coefficient, constants, and factors.
The are also made up of arithmetic or mathematical operations which includes;
SubtractionMultiplicationParenthesesAdditionBracketDivision, etcWhat is factorization?Factorization can be defined as the mathematical method of breaking a number down into similar and smaller numbers which are the products of the original number.
Given the expression;
63a–35
To factor expression, we need to find a common product of the values
We have;
7(9a - 5)
This cannot be further factorized
Hence, the factored form is 7(9a - 5)
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service call has just come in, but the type of malfunction is unknown. it is p.m. and service technicians usually get off at p.m. what is the probability the service technician will have to work overtime to fix the machine today?
(a) The probability distribution table is provided in the attachment.
(b) The probability distribution of X is discrete.
Let X = number of hours a service calls take.
(a)The probability of an event E is:
P(E)=n(E)/N
Here,
n (E) = number of favorable outcomes
N = total number of outcomes.
The probability distribution table is provided in the attachment.
(b)For a discrete probability distribution:
f(x) >= 0
summation f(x)= 1
Check that the probability distribution of X is discrete as follows:
The value of f (x) for all values of x is greater than 0.
The sum of all f (x) is 1.
Thus, the probability distribution of X is discrete.
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twice the sum of -17 and a number is -14
After thoroughly calculating we have come to find that, a number twice the sum of -17 and -14 is −62
How to find sum of two numbers?To sum and complete mathematical operations, numerical values are needed. Numbers are used to represent numerical values, and they can also be used to represent them alphabetically. For instance, the number 22 can be expressed in writing or by using the alphabet 22. One more example is the number 3, which can be written as 3.
Numbers can take many different forms. Examples of opposites include odd and even, fraction and integer, rational and irrational, natural and whole, and many more. A few of the operations include arithmetic, algebra, and trigonometry.
Twice the sum of -17 and -14 is
2((-17) + (-14))
⇒ 2(-17 -14)
⇒ 2 × (-31)
⇒ −62
So, a number twice the sum of -17 and -14 is −62.
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what fraction of one minute is 7 seconds
Factorise 5x^2-28x+23=0
[tex]5 {x}^{2} - 28x + 23 = 0 \\ \\ 5 {x}^{2} - 23x - 5x + 23 = 0 \\ (5 {x}^{2} - 23x) - (5x - 23) = 0 \\ x(5x - 23) - (5x - 23) = 0 \\ (x - 1)(5x - 23) = 0 \\ \\ x - 1 = 0 \\ \\ or \\ \\ 5x - 23 = 0 \\ \\ \\ x = 1 \\ \\ or \\ \\ x = \frac{23}{5} [/tex]
ATTACHED IS THE SOLUTION
John buys some boxes of pencils and some packets of pens for people to use at a conference.
There are 40 pencils in a box.
There are 15 pens in a packet.
John gives one pencil and one pen to each person at the conference.
He has no pencils left.
He has no pens left.
What is the smallest number of boxes of pencils and smallest number of packets of pens that John bought?
In linear equation, He 3 boxes of pencils and 8 boxes of pens.
What are instances of linear equations?
Ax+By=C represents a two-variable linear equation in its standard form. A standard form linear equation is, for instance, 2x+3y=5.Finding both intercepts of an equation in this form is rather simple (x and y).When resolving systems of two linear equations, this form is also incredibly helpful.A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.He bought 3 boxes of pencils and 8 boxes of pens.
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120
Mulitples of 40: 40, 80, 120
This means that there are 120 people at the conference, and that he bought 3 boxes of pencils (40x3=120) and 8 boxes of pens (15x8=120)
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How do division properties help you evaluate expressions?
Drag a word or number to the box to correctly complete the statement.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
When the area of a fraction is equal to −1 and the numerator is nonzero, the value of the fraction is equal to the .
Options: numerator, opposite of the numerator, denominator, opposite of the denominator, 0
The division property of equality informs us quite simply that if we divide both sides of an equation by the same number, then the resulting equation is unaltered. This is known as the distributive property of equality.
How can we make sense of this information?It is important to keep in mind that the value of a fraction is always equivalent to the numerator of the fraction if the denominator of the fraction is 1 and the numerator of the fraction is anything other than zero.
To speak in terms of fractions is to refer to numbers that are not whole.
The value of the numerator in a fraction is determined by whether or not the numerator is nonzero and whether or not the denominator is 1.
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Which expressions are equivalent to 25? Choose ALL that apply.
6-6-6-6-6-6
2-6
12-12
2-2-2-2-2-2
4-16
8-8
None of the given expressions are equivalent to 25.
What is an expression?
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers (operands), variable, operations, units, brackets, punctuation, and groups can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's sequence of operations and other features.
Many writers make a distinction between an expression and a formula, with the former designating a mathematical object and the latter a claim about such objects. However, in contemporary mathematics, and particularly in computer algebra, formulae are seen as expressions that, depending on the values supplied to the variables present in the expressions, can be evaluated to true or false.
The expressions are solved as follows
6-6-6-6-6-6 = -24
2-6 = -4
12-12 = 0
2-2-2-2-2-2 = -8
4-16 = -12
8-8 = 0
Hence, none of the expressions are equivalent to 25.
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Solve the absolute value by re writing it as an equaulant compound in
| 3x - 1 > 11
The solution of the inequality will be;
⇒ x > 4 or x < -10/3
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is;
|3x - 1| > 11
Now, The inequality is solved as;
|3x - 1| > 11
⇒ 3x - 1 > 11 or 3x - 1 < -11
Solve the inequality as;
⇒ 3x - 1 > 11
Add 1 we get;
⇒ 3x - 1 + 1 > 11 + 1
⇒ 3x > 12
Divide by 3;
⇒ x > 4
And, Solve the inequality as;
⇒ 3x - 1 < - 11
Add 1 we get;
⇒ 3x - 1 + 1 < - 11 + 1
⇒ 3x < -10
Divide by 3;
⇒ x < -10/3
Thus, Solution of the inequality will be;
⇒ x > 4 or x < -10/3
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This question is not from a test. This is an extra credit MATHS assignment. Please help me if you can. If you do, thank you! :)
we have the equation
[tex]y=31sin5x+32[/tex]Find out the first derivative
[tex]\begin{gathered} y^{\prime}=(5)(31)c0s5x \\ y^{\prime}=155cos5x \end{gathered}[/tex]equate to zero the derivative, to find out the critical points
[tex]\begin{gathered} 155cos5x=0 \\ cos5x=0 \end{gathered}[/tex]The value of cosine is zero when the angle is 90, 270 degrees (pi/2 and 3pi/2)
so
[tex]\begin{gathered} 5x=\frac{\pi}{2} \\ \\ x=\frac{\pi}{10} \end{gathered}[/tex][tex]\begin{gathered} 5x=\frac{3\pi}{2} \\ \\ x=\frac{3\pi}{10} \end{gathered}[/tex]For x=pi/10
Find out the y-coordinate
[tex]\begin{gathered} y=31s\imaginaryI n\frac{5\pi}{10}+32 \\ \\ y=31sin\frac{\pi}{2}+32 \\ \\ y=31+32=63\text{ ft} \end{gathered}[/tex]Verify for x=3pi/10
[tex]\begin{gathered} y=31s\imaginaryI n5(\frac{3\pi}{10})+32 \\ \\ y=31s\imaginaryI n(\frac{3\pi}{2})+32 \\ y=-31+32=1\text{ ft} \end{gathered}[/tex]The maximum height is 63 ftTranslate the triangle 4 units right and 3 units down
Answer:
L'(0,-2)
K' (3, -2)
J' (0,3)
Step-by-step explanation:
Please help for 100 points.
By using matrix operations, the resulting matrix is [tex]4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] - \left[\begin{array}{cc}1&2\\4&5\end{array}\right][/tex] is [tex]\left[\begin{array}{cc}3&6\\12&15\end{array}\right][/tex].
How to simplify a combination of matrices
In this problem we must simplify a combination of two matrices, this can be done by using properly the fundamental operations for matrices. Matrices are algebraic constructions characterized by a number of row and a number of columns. For instance, there is a matrix with two rows and three columns:
[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\end{array}\right][/tex]
There are two fundamental operations for matrices:
Sum - The respective elements of the same row and the same column of the matrix are summed:
[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] + \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] = \left[\begin{array}{ccc}2&4&6\\8&10&12\\14&16&18\end{array}\right][/tex]
Where C(i, j) = A(i, j) + B(i, j), i is the row index and j is the column index.
Scalar mutiplication - Every element of the matrix is multiplied by a scalar:
[tex]2 \cdot \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] = \left[\begin{array}{ccc}2&4&6\\8&10&12\\14&16&18\end{array}\right][/tex]
Where B(i, j) = k · A(i, j), k is the scalar.
Now we show the complete procedure to find the simplified expression:
[tex]4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] - \left[\begin{array}{cc}1&2\\4&5\end{array}\right][/tex] Given
[tex]4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] + (- 1) \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right][/tex] Definition of subtraction
[tex]\left[\begin{array}{cc}4&8\\16&20\end{array}\right] + \left[\begin{array}{cc}- 1&- 2\\- 4&- 5\end{array}\right][/tex] Scalar multiplication
[tex]\left[\begin{array}{cc}3&6\\12&15\end{array}\right][/tex] Sum of matrices / Result
The simplifed form of the matrix is [tex]4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] - \left[\begin{array}{cc}1&2\\4&5\end{array}\right][/tex] is [tex]\left[\begin{array}{cc}3&6\\12&15\end{array}\right][/tex].
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please help asap! i dont understand this
Answer:
y = -2x + 11
Step-by-step explanation:
When two lines are parallel, their gradients are the same. So the gradient of the line parallel to this equation will be -2 as well.
Now we substitute values from this point to find the rest of the equation :
y = -2x + c
3 = -2(4) + c
3 = -8 + c
c = 11
So the equation of the line parallel will be y = -2x + 11
Hope this helped and have a good day
-8n-4+n+7 where like terms need to be simplified
Answer:
- 8n -4 +n+7
like terms (-8n, n) and (-4, 7)
so; -8n+n-4+7
= -7n+3
Answer:
-7n + 3
Step-by-step explanation:
Simplify:Like terms are terms that have same variable with same power.
-8n and n are like terms. subtract or add the coefficient of the like terms.
(-8) and 1. So, subtract and it is -7n
(-4) and 7 are like terms(constants).
-8n - 4 + n + 7 = -8n + n - 4 + 7
= -7n + 3
What is the pressure when 650N is applied over 40m2?
Answer:
16.25 pascal
Step-by-step explanation:
pressure=force/area
pressure=650/40
pressure=16.25 pascal
The Distributive Property Use the Distributive Property to rewrite each expression without parenthesis. 1. 6(x + 3) 2. 5( y - 4 ) 3. -7( m - 1 )
Answer:
1. 6x+18 2. 5y-20 3. -7m+7
Step-by-step explanation:
1. 6(x+3) 2. 5(y-4) 3. -7(m-1)
6x+24. 5y-20. -7m+7 <--- - times - = +
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
If you have a right triangle, then you have 2 legs and 1 hypotenuse. The hypotenuse is the longest side across from the 90 degree angle. Pythagoras came up with the theorem for right triangles that states that the sum of the squares of the 2 legs is equal to the hypotenuse squared.
Write an algebraic equation for the following problem and then solve it.
The population of a country in 2015 was estimated to be 321.4 million people. This was an increase of 17% from the population in 1990. What was the population of the country in 1990?
The algebraic equation is _=321.4
The population of the country in 1990 will be 274.7 million.
How to illustrate the information?From the information given, the population of a country in 2015 was estimated to be 321.4 million people and this was an increase of 17% from the population in 1990.
Therefore,since let the population on 1990 be x. Therefore, this will be illustrated as:
x + (17% × x) = 321.4
x + 0.17x = 321.4
1.17x = 321.4
Divide
x = 321.4 / 1.17
x = 274.7
The population is 274.7 million.
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Under his cell phone plan, Julian pays a flat cost of $52 per month and $3 per gigabyte. He wants to keep his bill at $58 per month. Which tape diagram could be used to represent the context if gg represents the number of gigabytes of data Julian can use while staying within his budget?
The tape diagram to represent the context regarding the number of gigabytes of data Julian can use while staying within his budget is Tape D.
What is a tape diagram?A tape diagram simply has to do with a diagram that's used to illustrate the relationship between the numbers that are given.
In this case, Julian pays a flat cost of $52 per month and $3 per gigabyte and she wants to keep his bill at $58 per month.
This will be illustrated as:
let g = the number of gigabytes of data.
The expression will be:
52 + 3g = 58
The appropriate tape diagram is D.
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( Please help + Will mark brainliest )
Answer the question in photo.
Answer:
length of I'J'= 4 units
length of IJ= 16 units
scale factor = 16/4 = 4
plssssss marks as brainliest
Last night, Bruce completed all 5 levels of his favorite video game, Extreme Treasure Hunter. In the game, you can earn points by collecting gemstones or finding pieces of the treasure map. Bruce collected 10 gemstones in each level, earning x points per gemstone. He also earned 30 points in each level by finding pieces of the treasure map! Pick all the expressions that represent Bruce's score at the end of the game.
The expressions that represent Bruce's score at the end of the game will be 5(10x) + 30(5) = 150 + 50x.
How to illustrate the expression?From the information, Bruce completed all 5 levels of his favorite video game, Extreme Treasure Hunter and in the game, you can earn points by collecting gemstones or finding pieces of the treasure map.
The expression to illustrate the number of points will be:
= 5(10x) + 30(5)
where c = number of points per gemstone
= 50x + 150
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Estimate the quotient of 56.6 ÷ 7.21.
6
7
8
9
Answer:
56.6 estimated= 56
7.21 estimated=7
56/7= 8
pls mark as brainliest
Answer:
56.6 estimated= 56
7.21 estimated=7
56/7= 8
Step-by-step explanation:
Choose the expression that is equivalent to a fraction with nine raised to the negative third power in the numerator and the quantity three raised to the negative second power times nine squared end quantity in the denominator and the entire fraction is cubed.
The expression that is equivalent to a fraction with nine raised to the negative third power in the numerator and the quantity three raised to the negative second power times nine squared end quantity in the denominator and the entire fraction is cubed is [tex]\frac{3^{6} }{9^{15} }[/tex]
Nine raised to the negative third power = [tex]9^{-3}[/tex]
Three raised to the negative second power times nine squared = [tex](3x^{-2})(9^{2} )[/tex]
The expression is [tex](\frac{9^{-3} }{(3^{-2})(9^{2} ) } )^{3}[/tex]
=[tex]\frac{9^{(-3)(3)} }{(3^{(-2)(3)})(9^{(2)(3)} }[/tex]
=[tex]\frac{9^{-9} }{(3^{-6})(9^{6}) }[/tex]
= [tex]\frac{3^{6} }{(9^{9})(9^{6}) }[/tex]
= [tex]\frac{3^{6} }{9^{15} }[/tex]
Hence, the expression that is equivalent to a fraction with nine raised to the negative third power in the numerator and the quantity three raised to the negative second power times nine squared end quantity in the denominator and the entire fraction is cubed is [tex]\frac{3^{6} }{9^{15} }[/tex]
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