A trapezoid will appear smaller than the original trapezoid if it is dilated with a scale factor between 0 and 1.
What shape is a trapezoid?An open, flat shape with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium. A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel.
What are a trapezoid's three characteristics?What three characteristics do trapezoids have? An isosceles trapezoid has equal base angles and diagonals. The midpoints of the two opposing sides are parallel to the point where the diagonals intersect. An isosceles trapezoid has opposite sides that are congruent to one another or have the same length.
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Zasha spent $6 on packages of gum. How many more packages of gum that cost $1.20 each can she buy if she has a $20 bill?
Answer: Zasha spent $6 on packages of gum, which means that she bought 6 / $1.20 = 5 packages of gum.
If she has a $20 bill, she has $20 - $6 = $14 left to spend on gum.
Zasha can buy an additional 14 / $1.20 = 11.6666666666666666666666667 packages of gum with this money.
Rounded down, Zasha can buy an additional 11 packages of gum.
Therefore, Zasha can buy a total of 5 + 11 = 16 packages of gum.
Step-by-step explanation:
What is the product of - 2 1/2 and - 3 1/3
What number should be added to the polynomial 2x³ − 3x² − 8x so that the resulting polynomial leaves the remainder 12 when divided by 2x 1?
The number that should be added to the polynomial 2x³ - 3x² - 8x is 12x
When a polynomial is divided by a linear factor, the remainder is equal to the constant term of the polynomial multiplied by the reciprocal of the linear factor.
In this case, the polynomial is 2x³ - 3x² - 8x, and the linear factor is 2x-1.
To find the remainder when this polynomial is divided by 2x-1, we need to multiply the constant term of the polynomial, which is -8, by the reciprocal of 2x-1, which is 1/(2x-1).
So the remainder should be -8*(1/(2x-1)) = -8/(2x-1) = -4/(x-0.5)
To make the remainder 12, we will add 12x to the polynomial so that the new constant term is 12.
The polynomial 2x³ - 3x² - 8x + 12x will have a remainder of 12 when divided by 2x-1.
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Which is greater, 1 2cup or 1 3cup? How much greater *fractions*
Answer:
Step-by-step explanation:
A half of a cup is greater than 1/3 of a cup. This is because if you convert the fractions to the nearest common denominator (6) you can see that 1/2 = 3/6 and 1/3 = 2/6, so 1/2 of a cup is greater.
I hoped this helped!!
what is k if 1 1/3k=1/3
Answer: k = 11
Step-by-step explanation:
[tex]\frac{11}{3k} = \frac{1}{3} \\\\[/tex]
Cross multiply:
[tex]11 * 3 = 1*3k[/tex]
[tex]33 = 3k[/tex]
[tex]k = 11[/tex]
Claire keeps track of the miles per gallon her car gets per week. She has accumulated the following data: (1, 22.42), (2, 22.84), (3, 23.26), (4, 23.68) What is the common difference or ratio
The common difference is 0.42. The comparison of each ratio's successive values over time for a single firm.
Now, According to the question:
What is meant by ratio?
When expressed in numbers or amounts, a ratio is a relationship between two things. For example, if a room contains ten boys and thirty girls, the boy-to-girl ratio is 1:3, or one to three.A ratio, or getting rationed, on the occurs when replies to a tweet vastly outnumber likes or retweets. This means that people are reacting negatively to the tweet's content.It usually means that your comment has received more replies than likes. This implies that there are more people who disagree with your comment than agree with it.Therefore, simplifying the equation then we get,
if you take the ranges (y) and subtract one from the other you get 0.42.
(22.84 - 22.42)/(2 - 1) = 0.42/1 = 0.42
(23.26 - 22.84)/(3 - 2) = 0.42
(23.68 - 23.26)/(4 - 3) = 0.42
Hence, The common difference is 0.42
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The magnolia trees purchased for planting at the school are 3 feel tall. Research shows that these types of trees grow at a average of 3/4 per year.
I made a equation y=3/4x+3
Please help me determine the hight of the tree in 3 years!
Using the linear function given, the tree will have a height of 5.25 feet in 3 years
What is Linear FunctionLinear functions are mathematical functions where the output values are in direct proportion to the input values. A linear function has the form
y = mx + c, where m is the slope of the line and c is the y-intercept.
In this problem, the function given already models y = mx + c
Since y = 3/4x + 3;
The height of the tree in 3 years can be solved as;
y = 3/4(3) + 3
y = 9/4 + 3
y = 5.25
The height of the tree in 3 years is 5.25 feet
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a company spent 762500 to make a movie that will be shown in theaters for 8 weeks. If the movie makes 1250000 in its first week how much money does the movie need to earn in the next 7 weeks to make profit of atleast 2,000,000
The movie need to earn $ 1,512,500 in the next 7 weeks.
What is Unitary Method?The unitary technique involves first determining the value of a single unit,
followed by the value of the necessary number of units.
For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
A company spent 762500 to make a movie.
The total movie will be earned
= 762500 + 2000000
= 2,762,500
First week the movie earned 1, 250,000.
So, in 7 weeks the movie needs to earned
= 2,762,500 - 1, 250,000
= 1,512,500
Hence, the movie earn 1,512,500 more.
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Suppose that ƒ(−1)=10 and ƒ'(x)≥−3 for all values of x. What is the least possible value of ƒ(3)?
Using the mean value theorem, the least possible value of f(3) is - 2
What is the mean value theorem?The mean value theorem states that for a function f(x) on the interval (a, b), there exists a value c such that
f'(c) = f(b) - f(a)/(b - a)
How to find the least possible value for f(3)?Since ƒ(−1) = 10 and ƒ'(x) ≥−3 for all values of x, we require the least possible value of f(3).
Using the mean value theorem where
b = 3, a = -1 and f'(c) ≥ 3.We choose f'(c) = 3 since f'(x) = 3 is the minimum value of f'(x).
So, substituting the values of the variables into the equation, we have that
f'(c) = f(b) - f(a)/(b - a)
f'(x) = f(3) - f(-1)/(3 - (-1))
f'(x) = f(3) - f(-1)/(3 + 1)
f'(x) = f(3) - f(-1)/4
So, making f(3) subject of the formula, we have that
f(3) = f(-1) + 4f'(x)
Since
f'(x) = 3 and f(-1) = 10,Substituting the values of the variables into the equation, we have that
f(3) = f(-1) + 4f'(x)
f(3) = 10 + 4(-3)
f(3) = 10 - 12
f(3) = - 2
So, the least possible value is - 2
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What is the difference between an undecidable problem and an intractable problem?
Therefore , the solution of the given problem of tractable problem comes out to be Undecidable troubles are those for which there will never be a computer solution.
What does a tractable problem actually mean?a technique that completes a manageable task in a polynomial period of time. Utilizing the polynomial upper bound is advantageous. A problem is said to be intractable if it cannot be solved in a polynomial amount of time. The bound has a minimum that is exponential.
Here,
Intractable problems would be those in which there is significant proof that, while they can be solved by a desktop, they cannot be solved quickly enough to be actually useful in practice.
Undecidable troubles are those for which there will never be a computer solution, whereas undecidable difficulties are those for which there will never be a computer solution.
Therefore , the solution of the given problem of tractable problem comes out to be Undecidable troubles are those for which there will never be a computer solution.
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On a coordinate plane, a line is drawn from point L to point M. Point L is at (negative 4, 8) and point M is at (4, 8).
The rule DO,0.25 (x, y) → (0.25x, 0.25y) is applied to the segment LM to make an image of segment L'M', not shown.
The coordinates of L' in the image are
.
The coordinates of M' in the image are
.
The length, L'M', is
.
The slope of the original segment and dilated segment are
.
Answer:
L' = (-1,2)
M' = (1,2)
L'M' = 2
The slope of the original segment and dilated segment are both zero
Step-by-step explanation: just did it on edge!
What is the value of a if 2 is a zero of the polynomial 4x² 2x 5a?
The value of a is [tex]-\frac{12}{5}[/tex] if 2 is a zero of the polynomial [tex]$4 x^2-2 x+5 a$[/tex].
As per the given data, the polynomial is p(x) = [tex]$4 x^2-2 x+5 a$[/tex]
The polynomial is zero polynomial if x is 2
The places where a polynomial becomes zero overall are known as the zeros of the polynomial. The term "zero polynomial" refers to a polynomial with a value of zero (0).
Replace x with 2 we get
Therefore [tex]4(2)^2-2(2)+5 \mathrm{a}=0[/tex]
[tex]\Rightarrow[/tex] 4 (4) - 2 (2)+5 (a) = 0
[tex]& \Rightarrow[/tex] 16 - 4 + 5 (a) = 0
[tex]& \Rightarrow[/tex] 12 + 5 (a) = 0
Add -12 on both sides we get
12 + 5 (a) - 12 = 0 - 12
5 (a) = -12
Divided by 5 into both sides we get
a = [tex]-\frac{12}{5}[/tex]
Therefore the value of a is [tex]-\frac{12}{5}[/tex]
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f(n) = 2n-1 find the arithmetic sequence ?
An arithmetic sequence is a sequence of numbers in which the difference between any two successive members of the sequence is a constant value. The general form of an arithmetic sequence is:
a, a + d, a + 2d, a + 3d, ...
where "a" is the first term of the sequence, and "d" is the common difference between successive terms.
Given the function f(n) = 2n - 1, we can see that the function outputs a sequence of integers, with a common difference of 2. So f(n) is not an arithmetic sequence.
Arithmetic sequence is a list of numbers in which each number is the sum of the previous number and a constant number.
Example: 1,3,5,7,9 is an arithmetic sequence because the constant difference is 2.
If you have any other question feel free to ask.
What is the smallest positive integer that is both a multiple of $7$ and a multiple of $4$?
The smallest positive integer that is both a multiple of 7 and a multiple of 4, is 28 .
How to find the smallest positive integer ?To find the smallest positive integer that is both a multiple of 7 and a multiple of 4, first find the multiples of both 4 and 7 to see which multiples are common between them and which are the lowest.
The multiples of 4 and 7 are:
Multiples of 4 :
4, 8, 12, 26, 20, 24, 28, 32, 36, 40,
Multiples of 7 :
7 , 14 , 21 , 28 , 35 , 42 , 49
The smallest positive integer that is both a multiple of 7 and a multiple of 4 is therefore 28.
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What should be added in the polynomial x³ 6x² 11x 8 so that it is completely divisible by X² 3x 2?
The number that should be added in the polynomial [tex]x^{3}-6x^{2} +11x+8[/tex] , so that it is completely divisible by [tex]x^{2} -3x+2[/tex] is -14 .
What are Polynomials ?
A polynomial is defined as a type of algebraic expression where the exponents of all the variables is a whole number.
The exponents of the variables in any polynomial is a non-negative integer. A polynomial consists of constants and variables.
the polynomial expression is ⇒ [tex]x^{2} -3x+2[/tex], which can be written in factor form as : [tex](x-1)(x-2)[/tex] ,
that means the polynomial is divisible by both x = 1 and x = 2 ;
So , on substituting [tex]x=1[/tex] in the polynomial [tex]x^{3}-6x^{2} +11x+8[/tex] ,
we get , [tex]1^{3}-6\times1^{2} +11\times 1+8[/tex] = 14 ;
on substituting [tex]x=2[/tex] in the polynomial [tex]x^{3}-6x^{2} +11x+8[/tex] ,
we get , [tex]2^{3}-6\times2^{2} +11\times 2+8[/tex] = 14 ;
So , the remainder is 14 .
Therefore , -14 should be added in the given polynomial .
The given question is incomplete , the complete question is
What should be added in the polynomial x³ -6x² +11x +8 so that it is completely divisible by x² -3x +2 ?
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A line pae through the origin and through point A(−2, b í 14) and B(14 í b, 72). What i the greatet poible value of b?
The greatest poible value of b is (72-14)/(14-(-2))×(x+2)+14.
What is possible value?Possible value is the potential for something to have a particular outcome, result, or consequence. It is the amount of beneficial or desirable result that can be achieved, given the available resources. Possible value is often determined by assessing various factors such as cost, risk, and time. It is an important concept in economics, finance, and business, as it helps to identify the most beneficial course of action.
The greatest possible value of b is found by solving the equation of the line through A and B, which is y = (72-14)/(14-(-2))×(x+2)+14.
Setting the y-value to 0 and solving for x gives x = -14, which means b = 14. Therefore, the greatest possible value of b is 14.
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Why is it called revolution?
The term "revolution" is often used to refer to a dramatic and sudden change in a situation, especially number of a political situation. It is derived from the Latin word revolutio, which means "a turn around". The term was first used in the 1500s to describe a political movement of overthrowing a government or social system and replacing it with another.
Revolution is a term used to refer to a dramatic and sudden change in a situation, especially a political situation. It is derived from the Latin word revolutio, which means "a turn around". The term was first used in the 1500s to describe a political movement of overthrowing a government or social system and replacing it with another, thus making it a revolution.
The term "revolution" is often used to refer to a dramatic and sudden change in a situation, especially number of a political situation. It is derived from the Latin word revolutio, which means "a turn around". The term was first used in the 1500s to describe a political movement of overthrowing a government or social system and replacing it with another.
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What is the slope of the line that passes through the points (-5, 8)(−5,8) and (-5, 4)(−5,4)?
The slope of the line that passes through the points (-5, 8)and (−5,4) is undefined.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Given:
A line that passes through the points (-5, 8)and (−5,4).
If a line passes through two points (x₁ ,y₁) and (x₂, y₂),
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
m = (4-8) / (-5 + 5)
m = -4/0
The slope is undefined.
Therefore, the slope is undefined.
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Ella stacks two boards under a table to make it level. One board is inch thick. The
other board is inch thick. Which equation most closely estimates the thickness of
the two boards?
"Thickness of two boards = Thickness of first board + Thickness of second board" would be the closely estimated equation.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, separated by the 'equal' sign.
Define quadratic equation.x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
The thickness of the two boards together can be represented by the sum of the thickness of each individual board. Therefore, the equation that most closely estimates the thickness of the two boards stacked together is:
Thickness of two boards = Thickness of first board + Thickness of second board
So in this case, the equation would be:
Thickness of two boards = inch + inch
This equation gives the total thickness of two boards stacked together and it's the closest estimation.
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(I NEED THIS RIGHT AWAY!) (PLS HELP) Lynette earns $5 by delivering newspapers. She saves $3 and she spends the rest. If she saved $27 one month, how much did she spend?
Answer:
$18
Step-by-step explanation:
To find how many times she has saved money, you would do 27/3=9. This means that she worked 9 times. Since she worked 9 times, she earned $45 in total. To find how much she saved you would do 45-27=$18
F(x) = 3x -4 find each value of F(0)
Answer:
Step-by-step explanation:
Rewrite the function as an equation.
y
=
3
x
−
4
Use the slope-intercept form to find the slope and y-intercept.
Tap for fewer steps...
The slope-intercept form is
y
=
m
x
+
b
, where
m
is the slope and
b
is the y-intercept.
y
=
m
x
+
b
Find the values of
m
and
b
using the form
y
=
m
x
+
b
.
m
=
3
b
=
−
4
The slope of the line is the value of
m
, and the y-intercept is the value of
b
.
Slope:
3
y-intercept:
(
0
,
−
4
)
Write an equation for the parabola that passes through (-2,7), (1, 10), and (2,27)
An equation for the parabola is y=.
Answer: To find an equation for a parabola that passes through three specific points, we can use the method of algebraic manipulation.
Since the parabola is symmetric about the y-axis, the equation of the parabola will have the form y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.
Given three points (-2,7), (1, 10), and (2,27), we can use the vertex form of the equation and substitute the x, y values of the three points to find the values of a, h and k
y = a(x-h)^2 + k
Since it is passing through (-2,7), we can substitute the values of x and y in the equation and get
7 = a(-2 - h)^2 + k
It passing through (1, 10), we can substitute the values of x and y in the equation and get
10 = a(1 - h)^2 + k
It passing through (2,27), we can substitute the values of x and y in the equation and get
27 = a(2 - h)^2 + k
Now we have three equations with three variables, we can solve it using any of the techniques such as substitution, elimination or matrix. But the final equation will be in the form of y= a(x-h)^2 + k
Here, x= (-2, 1, 2) and y = (7, 10, 27) . Therefore it has a unique parabola passing through these points.
Step-by-step explanation:
The mean and median of the five Numbers are the same 4 6 x y 10
The value of x is 7 and value of y is 8
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given data set is {4, 6, x, y, 10}
The mean and the median are the same value.
The median is the middle value, which is x, and the mean is:
M = (4 + 6 + x + y + 10)/5
Then we have that:
(4 + 6 + x + y + 10)/5 = x
Now let's solve this:
(4 + 6 + x + y + 10) = 5x
20 + x + y = 5x
20 + y = 4x
And x and y are whole numbers. Then we can take x = 7 to get:
20 + y = 4*7
y = 28 - 20 = 8
Then we have x = 7 and y = 8.
Hence, the value of x is 7 and value of y is 8 in the data set 4 6 x y 10
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(Car Sales) Of the cars sold during the month of July, 85 had air conditioning, 102 had automatic transmission, and 54 had power steering. 8 cars had all three of these extras. 24 cars had none of these extras. 25 cars had only air conditioning, 56 cars had only automatic transmissions, and 26 cars had only power steering. 11 cars had both automatic transmission and power steering. How many cars had exactly two of the given options
24 cars lacked power steering but did have air conditioning and an automatic gearbox.
According to the question,
No. of cars with Air conditioning = 88
No. of cars with Automatic transmission = 96
No. of cars with power steering = 76
All three = 4
None of these extras = 19
Only air conditioning = 23
Only automatic transmissions = 61
Only power steering = 28
Power steering and automatic transmission both = 11
The calculation for missing values:
11 - 4 = 7
96-61-4-7 = 24
88-24-4-23=37
It is obvious that 24 cars lacked power steering but did have air conditioning and an automatic gearbox.
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Evaluating Linear Functions
The value of linear equations are f(x) = -17 and f(x) = -73 .
What is linear equation ?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).
Equation with two variables of degree one is referred to as a linear equation with two variables. Formal expression: ax+by+c=0, where a, b, c R & a, b 0.
A)
f(x) = -2x + 7 when x = -12f (x) = -2*12 + 7
= -24 + 7
= -17
f(x) = 5x - 13 when x = -14f(x) = 5*-14 - 13
= -60 -13
= -73
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How do you graph the transformation of an absolute value function?
By translating, stretching and contracting, or reflecting, two functions from the same function family can become one another. Any function from a function family can be obtained by applying one or more transformations to a parent function.
By altering the graph of the parent absolute value function, many other absolute value functions can be created. The resulting absolute value functions take the following form:
[tex]y = |x-h| + k[/tex], where h and k are real numbers.
Absolute value functions can be created using the same kinds of operations that produce new linear functions. They also have a similar impact on absolute value functions. The transformations may, however, appear differently graphically due to some important discrepancies between linear functions and absolute value functions.
Here are some of the transformations:
Vertical Transformations
Translation up k units, k > 0; [tex]y = |x|+k[/tex]Translation down k units, k < 0; [tex]y = |x| + k[/tex]Horizontal Transformations
Translation to the right h units, h > 0; [tex]y = |x - h|[/tex]Translation to the left h units, h < 0; [tex]y = |x - h|[/tex]This is how we graph the transformation of an absolute value function.
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Find the radius of convergence R of the series. [infinity] n bn (x − a)n, b > 0 n = 1
R= ____
Find the interval of convergence of the series.
The radius of convergence R = 1/b
The radius of convergence for a power series is given by the formula:
1/R = lim sup |bn|^(1/n)
In this case, the radius of convergence is given by:
1/R = lim sup |bn|^(1/n) = lim sup b^(1/n) = b^(1/n) as b > 0.
So R = 1/b
As for the interval of convergence, it is the set of values of x for which the series converges. The series converges when |x-a| < R, and diverges when |x-a| > R. So the interval of convergence is (a-R, a+R) which is (a-1/b, a+1/b)
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Shay and Nadine solve this problem in two different ways.
Mark has $25 in his bank account.
He makes $7 per hour babysitting.
How many hours must he babysit to have a total of $165 in his account?.
Use the drop-down menus to complete the sentences below.
Shay's
Assignment
25+7h-165
25-25 7h-165-25
7h-140
7h-140
7h 7h
A-20
Nadine's
Assignment
166-25-140
You need to make
$140 babysitting
140
-20
You need to babysit
for 20 hours
Please Help!
On solving the provided proportionality question we got that, U = 7.72, is rounded off nearest to tenth digit.
What is proportionality?When two quantities or variables are linearly related in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable decreases in proportion to the other when it falls to 1/100th of its previous value.We must determine the ratio of the two quantities for each value supplied in order to determine if two quantities are proportionate. The proportionate link between them is evident if their proportions are equal. Their connection is not proportionate if all the ratios are out of balance.
Here,
U/5 = 17/11
U = 17/11 X 5
U = 7.72
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the question in the picture below
Answer:
answer is option A
Step-by-step explanation:
2x+6≤10or2x+8>20
2x≤10-6 or 2x>12
x≤4/2 or x>2/12
x≤2 or x>6
PLS HELP
using factorisation solve
E=(a+1)(a-1)-3(a+1)²
Answer:
Step-by-step explanation:
factoring
e =
(a+1)(a-1-3(a+1))
= (a+1)(a-1-3a-3)
= (a+1)(-2a-4)
= -2(a+1)(a+2)