The term "if and only if" makes the sentence bi-conditional. A triangle is equilateral if and only if it has three congruent sides.
A conditional statement with its opposite expressed in the form of "if and only if," collectively known as a bi-conditional statement. Bi-conditional logic is the theory behind bi-conditional assertions.
This can be compared to the conditional sentence, "if this, then that." Due to the lack of a "if and only if," it is not bi-conditional. The reversal of a conditional statement's ability to produce a bi-conditional depends on whether it is also true.
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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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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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( 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
Translate the triangle 4 units right and 3 units down
Answer:
L'(0,-2)
K' (3, -2)
J' (0,3)
Step-by-step explanation:
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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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 ftA 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 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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Find the slope of the line passing through the points (4,9) and (-6,9)
Answer:
Slope = 0
Step-by-step explanation:
[tex]\text{Slope} = m = \dfrac {(y_{2} - y_{1})} {(x_{2} - x_{1})}[/tex]
where (x1, y1) and (x2, y2) are any two points on the line
Given he two points (4, 9) and (-6, 9)
m = (9 - 9)/(-6 - 4) = 0/-10 = 0
Lucy wants to drink 2L of water.
She has poured this amount into a jug. Between breakfast and lunch she pours 2 glasses of water each measuring 250ml.
Between lunch and her dinner she pours 3 glasses also measuring 250 ml.
How much water does she need to drink before going to bed?
The amount of water that Lucy should drink more is 750 ml.
How to calculate the value?From the information, Lucy between breakfast and lunch she pours 2 glasses of water each measuring 250ml. This will be:
= 250ml × 2
= 500ml
Between lunch and her dinner she pours 3 glasses also measuring 250 ml. This will be:
= 3 × 250ml
= 750 ml
Since Lucy wants to drink 2L of water, the amount needed to drink more will be:
= 2L - (750 + 500)
= 2000ml - 1250ml
= 750ml
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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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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:
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
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.
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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Show all work. Round all percentages to the nearest tenth of a percent. Mr. McCullough paid 80 people to say they were his friends. After he paid them, 26 of them still did not claim to be his friend. What percent of the people he paid claimed to be his friends?
The percent of the people he paid claimed to be his friends is 67.5%
Given,
Mr. McCullough paid 80 people to say they were his friends.
and, After he paid them, 26 of them still did not claim to be his friend.
To find the percent of the people he paid claimed to be his friends
Now, According to the question:
Based on the given condition,
Formulate :
(80- 26) ÷ 80
Calculate:
(80- 26) / 80
= 54/80
Simplify
= 27/40
=0.675
Convert to percentage;
Multiply a number to both the numerator and the denominator
0.675 × 100/100
Calculate
67.5 / 100
= 67.5%
Hence, The percent of the people he paid claimed to be his friends is 67.5%.
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need to show my work and find the surface area
4) The surface area of the square pyramid is; 145 ft²
5) The surface area of the rectangular prism is; 948 ft²
How to find the surface area of regular shapes?
4) For the square pyramid, we see that the faces have been broken down into 4 equal rectangles and one square base.
We know that;
Area of triangle = 1/2 * base * height
Thus
Area of 4 triangles = 4(1/2 * 5 * 12) = 120 ft²
Area of square = 5 * 5 = 25 ft²
Total surface area = 120 + 25 = 145 ft²
5) The surface area of a rectangular prism is;
A = 2(wl + hl + hw)
Thus, Area = 2((20 * 3) + (20 * 18) + (18 * 3))
Area = 2(474)
Surface area = 948 ft²
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Find the inverse function in slope-intercept form f(x)=x-5
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:f{}^{-1}(x) = x +5 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
We need to find the inverse of given function; f(x) = x - 5
[tex]\qquad \tt \rightarrow \: y = x - 5[/tex]
here, write x in terms of y.
[tex]\qquad \tt \rightarrow \: x = y + 5[/tex]
replace x with [tex]{\tt{{f}^{-1} (x)} } [/tex] and y with x, you will get your required inverse function.
[tex]\qquad \tt \rightarrow \: f {}^{ - 1} (x) = x + 5[/tex]
And it's already in slope intercept form
[tex]\qquad \tt \rightarrow \: y = mx + c[/tex]
where, slope (m) = 1 and y intercept (c) = 5
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
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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what fraction of one minute is 7 seconds
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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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
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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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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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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please help asap! i dont know what to do
rise over run to find the slope
y = mx+b
we rose 1 and went over by 2
which means the equation is 1/2 x or 0.5x
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.
3/4 divided by 2/x simplified
Answer:3
Step-by-step explanation:
(-3/4)/(-2/8)=(-3/4)(-8/2)=(-3/4)(-4)=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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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