We need to add 81 as the constant term to the binomial (n² - 18n) so that the resulting trinomial is a perfect square, and factorization of that resulting trinomial will be (n - 9).
As per the question statement, we are provided with a binomial (n² - 18n),
And we are required to add a proper constant to the above mentioned binomial so that the resulting trinomial is a perfect square, and then factorise the resulting trinomial.
To answer question, first we need to know the standard form of expanding a perfect square into a trinomial, which goes as,
[(a - b)² = {(a)² + (b)² - (2 * a * b)]
Here, if we compare our concerned binomial (n² - 18n), or, [(n)² - (2 * n * 9)], with the above mentioned standard expansion of a perfect square into a trinomial, we get, (a = n) and (b = 9), and the (b²) term is missing.
Adding [(b²) = (9²) = 81] which is a constant term, to our concerned binomial (n² - 18n), we get, (n² - 18n + 81),
Or, [(n)² + (9)² + (2 * n * 9)],
Which is a trinomial and matches with the standard expansion of a perfect square into a trinomial, and hence,
[(n² - 18n + 81) = (n - 9)²]
That is, we need to add 81 as the constant term to the binomial (n² - 18n) so that the resulting trinomial is a perfect square, and factorization of that resulting trinomial will be (n - 9).
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Jane received a $70 gift card for a coffee store. She used it in buying some coffee that cost $8.39 per pound. After buying the coffee, she had $28.05 left on her card. How many pounds of coffee did she buy?
Answer:
85 ggoooofffffyyy
Step-by-step explanation:
Which value of y makes the two matrices inverses of each other?
[6 14]. [-1 -7/2]
[-2-4] [y. 3/2]
-1/2
-5/14
1/2
2
The value of y that makes the two matrices inverse of each other is 1/2
The inverse of a square matrix A, denoted by A⁻¹.
The formula is [tex]\frac{1}{|A|}.adj(A)[/tex]
The product of A and A⁻¹ should be the identity matrix. The identity matrix that results will be the same size as matrix A.
Inverse of given first matrix is
[tex]\left[\begin{array}{cc}6&14\\-2&-4\end{array}\right][/tex]
Determinant = |A| = 6(-4) - (14)(-2)
= -24 + 28
= 4
Adjoint of matrix = [tex]\left[\begin{array}{cc}-4&-14\\2&6\end{array}\right][/tex]
Inverse of matrix = [tex]\frac{1}{|A|}.adj(A)[/tex]
Therefore , Inverse = [tex]\frac{1}{4}.\left[\begin{array}{cc}-4&-14\\2&6\end{array}\right][/tex]
= [tex]\left[\begin{array}{cc}-4/4&-14/4\\2/4&6/4\end{array}\right][/tex]
A⁻¹ = [tex]\left[\begin{array}{cc}-1&-7/2\\1/2&3/2\end{array}\right][/tex]
Is required inverse
If we compare the inverse with second matrix
y = 1 / 2
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Answer:
third option: 1/2
Step-by-step explanation:
What is the vertex of f(x)= 3x^2+12x-8? A (2, 28) B (-2, -20) C (4,88) D (-4,-8)
Answer:
B (-2,-20)
Step-by-Step Explanation:
f(x)=3x^2 + 12x - 8
a=3 b=12
x=-12/2*3
x=-2
f(x)=3(-2)^2 + 12x - 8 , x=-2
f(-2) = -20
solution (-2,-20)
Does-4y-3=1/3(12y-9)-8y
Blank 1 options
(Blank 1)
have one solution, no solution, or infinitely many solutions?
Answer:
infinite solution
Step-by-step explanation:
Since 0 = 0 for any value of y, the system of equations has infinite solutions.
I WILL MARK BRANLIEST FOR CORRECT ANSWER! The two-way frequency table contains data about how students access courses.
Traditional Online Row totals
Computer 28 62 90
Mobile device 46 64 110
Column totals 74 126 200
What is the joint relative frequency of students who use a mobile device in a traditional class?
23%
37%
46%
72%
The joint relative frequency is 23%. So option (1) is correct.
Joint relative frequency is defined as the ratio of a frequency that is not in the total row or column to the total number of values or observations. The marginal frequency in a two-way frequency table is the entry in the "total" for the column and the "total" for the row.
Given data:
Traditional Online Row totals
Computer: 28 62 90
Mobile device: 46 64 110
Column totals: 74 126 200
The joint relative frequency can be found by the formula:
= (Number of students using a mobile device in traditional class / Total Number of students) x 100%
Number of students using mobile devices in traditional class = 46
Total number of students = 200
= (46 / 200) x 100%
= 0.23 x 100%
= 23 %
Therefore the joint relative frequency of students in traditional classes using a mobile device is 23%.
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Which of the following is a line that is parallel to the line defined by the equation 4x+7y=49−2x+4y?
a
3y+40=3x+10
b
y=20x+15
c
4y=10x+15
d
y=4x−2
e
2y+x=40−3x
A line parallel to the line 4x + 7y = 49 - 2x + 4y must have a slope of - 2.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given a line that is 4x + 7y = 49 - 2x + 4y.
7y - 4y = - 2x - 4x + 49.
3y = - 6x + 49.
y = - 2x + 49/3.
Now, lines parallel to each other have the same slope.
Now if we simply the given options none of the lines have a slope of - 2 so none of the given lines are parallel to the line 4x + 7y = 49 - 2x + 4y.
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-2/5 + -2/5 i just need this thank you
Answer:
The answer would be -4/5
Step-by-step explanation:
When you add a negative to a negative, you first take out the plus sign and rewrite it as: -2/5 - 2/5.
Now you just simply subtract 2/5 from -2/5 to get -4/5.
Hope this helps.
Please give brainliest
The sides of a triangle are in the ratio of 3:4:5. A man jogged around it 5 times and cover a distance of 3000m What are the sides of the triangle?
The sides of the triangle are 150m, 200m and 250m.
What is distance?
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.
Given: The sides of a triangle are in the ratio of 3:4:5. A man jogged around it 5 times and cover a distance of 3000m.
As man jogged around triangle 5 times and cover a distance of 3000m.
So, the distance for one round is 3000/5 = 600m.
The covered distance is nothing but the perimeter of the triangle.
So, the perimeter of the triangle is 600m.
Let, 3x, 4x, 5x are the sides of the triangle.
⇒ 3x + 4x + 5x = 600
12 x = 600
x = 50
Therefore,
3x = 3(50) = 150
4x = 4(50) = 200
5x = 5(50) = 250
Hence, the sides of the triangle are, 150m, 200m and 250m.
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Given mn, find the value of x.
+
(8x-4)°
(6x-12)°
Answer:
The value of the equation will be 14
Please help now !!!!!!
Answer:
The tablet costs more than the smartphone
Step-by-step explanation:
1 year tablet = $1.50
1 year smartphone = $0.02x12months = $0.24
what is 112/200 as a percentage
Answer:
56%
Step-by-step explanation:
112/200 as a percentage
112/200 = 0.56
0.56 as a percentage:
0.56 * 100 = 56%
Answer::
To do percentages with fractions,
divide the numerator by denominator to get a decimal,
so for example, your question, 112/200
112/200 is 0.56 decimal, and then to make it percent,
we multiply by 100,
how does that work?
you move two places to the right because 100 has two zeros
so 0.56 would be 56,
therefore the percent of 112/200 would be 56%
Have a good day! <3
Cube root of 426 give your answer to the nearest integer
Answer:
3
Step-by-step explanation:
Question 2(Multiple Choice Worth 1 points)
(02.05 MC)
Choose the table that represents g(x) = -2xf(x) when f(x) = x + 4.
The correct table is :
x g(x)
1 -10
2 -12
3 -14
Given, f(x) = x+4
and g(x) = -2.f(x)
we check for x = 1
f(x) = 1+4
= 5
now g(x) = -2.f(x)
= -2(5)
= -10
for x=2
f(x) = 2+4
= 6
now g(x) = -2.f(x)
= -2(6)
= -12
for x=3
f(x) = 3+4
= 7
now g(x) = -2.f(x)
= -2(7)
= -14
Hence we get the required values.
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Answer:
C
Step-by-step explanation:
see the other dudes answer im jus making it easier to see and select for kids who have to hide the fact that they're cheating on their FLVS
Gaste el 30% de lo que no gaste, si hubiera gastado el 40% de lo que no hubiera gastado, entonces ahora tendría 30 dólares menos de los que tengo
Veremos que originalmente tenias $300, y el valor de la compra fue de $90
¿Cuanto dinero tenía originalmente?Definamos X como la cantidad original de dinero. Ahora trabajaremos con porcentajes.
Sabemos que tu gastaste 30% de esto, entonces lo que te sobra es:
0.7*X
Sabemso qe si hubieras gastado el 40% (en este caso te sobra 0.6*X), te sobrarian 30 dolares menos, entonces podemos escribir:
0.7*X = 0.6*X + $30
Resolviendo para X
0.7*X - 0.6*X = $30
0.1*X = $30
X = $30/0.1 = $300
Originalmente tenias $300 dolares, y gastaste:
$300*0.3 = $90
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the per capita consumption of meat by people in the united states in a recent year was normally distributed with a mean of 218.4 pounds and standard deviation of 42 pounds. a random selection of 30 people was taken. what is the probability that the sample mean is less than 200 pounds? (notice i used the words sample mean!)
The probability that the sample mean is less than 200 pounds is 33% or 0.33
Given that,
The average annual meat consumption in the United States was 218.4 pounds, with a standard deviation of 42 pounds, and was normally distributed. A random sample of 30 individuals was chosen.
Mean (μ) = 218.4
Standard deviation (σ) =42
Probability = P(X< 200) = P[(X-μ ) / σ < (200-218.4) /42 ]
= P(z <-0.44 )
Using z table
=0.3300
Probability=0.3300
Therefore, 33% or 0.33 of the time, the sample mean will weigh less than 200 pounds.
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a) Work out the gradient of the line y=5x-3 (1)
Gradient = (Answer here)
b) Work out the gradient of the line 3y-12x+7=0 (1)
Gradient = (Answer here)
Answer:
5 and 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the gradient and c the y- intercept )
(a)
y = 5x - 3 ← is in slope- intercept form
with gradient m = 5
(b)
3y - 12x + 7 = 0 ( add 12x to both sides )
3y + 7 = 12x ( subtract 7 from both sides )
3y = 12x - 7 ( divide through by 3 )
y = 4x - [tex]\frac{7}{3}[/tex] ← in slope- intercept form
with gradient m = 4
Which value is the best approximation for the range in ages for the oldest 25% of viewers?
4
6
15
20
The best estimation for the range of the oldest 25% is 20, so the correct option is the last one.
Which value approximates the range for the oldest 25%?The graph is separated in four parts, each part represents a 25% of the population.
The oldest 25% would be the last segment (the line in the right of the graph).
The range is defined as the difference between the largest value and the smallest value.
The segment starts at:
a = 35
And ends at:
b = 55
Then the range is something like:
55 - 35 = 20
The correct option is the last one.
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PLEASE HELP! I WILL NAME YOU THE BRAINLIEST!
THE THING IS IN THE PHOTO!
Work does not need to be shown.
Answer: The correct answer is Option D: h=2A/(b1+b2)
Step-by-step explanation:
Solve for h:
a=(1/2h)(b1+b2)
Step 1: Flip the equation
1/2b^2h+1/2b1h=a
Step 2: Factor out variable h
h((b2+b1)/2)=a
Step 3: Divide both sides by (b^2+b1)/2
h((b2+b1/2))/(b2+b1/2)=(a/(b2+b1)/2)
h=2a/(b2+b1)
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Starting at the beginning of the year, Kianna was able to save $215 each month. However
for the last 3 months, she increases her saving to $305 each month, and she plans to
continue saving the same amount of money for 2 more months (until end of the year).
What will be the amount of money Kianna save this year?
By using addition and multiplication, the result obtained is
Kianna saves $3020 this year
What is addition and multiplication?
Suppose there are many numbers. To get the sum total of all the numbers, addition is used
Repeated addition is called multiplication
Addition and multiplication will be used here
Amount of money Kianna saves each month for the first 7 months = $215
Total amount of money Kianna saved in the first 7 months = $215 [tex]\times[/tex] 7
= $1505
Amount of money she saves each month for the last 5 months = $305
Amount of money she saves in the last 5 months = $305 [tex]\times[/tex] 5 = $1515
Total amount of money Kianna saves this year = $(1505 + 1515)
= $3020
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At the gym on Saturday, Reese ran 5 miles in the treadmill and then the completed 1 mile in the elliptical machine and burned 725 calories. On Sunday she ran 3 miles on the treadmill and completed 1 mile in the elliptical, and burned 505 calories. Write and solve a linear system to find the number of calories Reese burns on the machine
Answer:The equations are 5t + e = 725 and 3t + e = 505
Step-by-step explanation:Subtract equation (2) from equation (1) and you arrive at;
2t = 220
Divide both sides of the equation by 2
t = 110
Having calculated the value of t, substitute for the value of t into equation (1)
5t + e = 725
5(110) + e = 725
550 + e = 725
Subtract 550 from both sides of the equation
e = 175
The above calculations shows that the calories burned on each gym equipment are;
Treadmill = 110 per hour
Elliptical = 175 per hour
Find the total area for the shape!!
Answer:
56cm²
Step-by-step explanation:
Because this is an irregular shape, you have to split it into two shapes and find the area of each one. Then you can add those two areas together to find the total area of the figure. There are many ways you can split it but the way I did it left me with the equation (12·3)+(4·5). Then all you have to do is multiply and add which will give you a total of 56cm².
7. The perpendicular bisectors of
AEFG meet at point H. Find HJ.
The distance of the intersection of 3 perpendicular bisectors of a triangle to the 3 vertices are equal.
In other words, HF = HE = HG.
Therefore, we see that 3 isosceles triangles are identified : HFE, HFG, HGF.
We're given HF = 15, therefore HE = 15.
Since HJ is the perpendicular bisector of line EG, JE = JG.
Therefore, JE = 12.
Now, we use the Pythagorean theorem in the right triangle HJE :
[tex]HE^{2} = HJ^{2} + JE^{2} - > HJ = \sqrt{15^{2} - 12^{2} } =\sqrt{81} = 9.[/tex]
Can anyone state the vertex of the graph?
The graph has no vertex
The transformations from the parent function are
Vertical shift down 2Horizontal shift left 4How to determine the vertex?The graph represents the given parameter
As a general rule, the maximum or the minimum of a graph is the vertex
However, the graph has no maximum or minimum
This means that there is absence of a vertex in the graph
The transformationHere, we have:
The graph is translated 4 units to the left of the origin The graph is translated 2 units below the originThis transformation can be represented as (x - 4, y - 2)
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Factor the expression (72a9b3 − 18a7b5) completely.
The factor of the expression 72[tex]a^{9} b^{3}[/tex] - 18[tex]a^{7} b^{5}[/tex] is 18[tex]a^{7} b^{3}[/tex](4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]).
Given expression:
= 72[tex]a^{9} b^{3}[/tex] - 18[tex]a^{7} b^{5}[/tex]
divide by 18 .
= 4[tex]a^{9} b^{3}[/tex] - [tex]a^{7} b^{5}[/tex]
divide by [tex]a^{7}[/tex]
= 4[tex]a^{2}b^{3}[/tex] - [tex]b^{5}[/tex]
divide by [tex]b^{3}[/tex]
= 4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]
= 18[tex]a^{7} b^{3}[/tex](4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]).
Therefore the factor of the expression 72[tex]a^{9} b^{3}[/tex] - 18[tex]a^{7} b^{5}[/tex] is 18[tex]a^{7} b^{3}[/tex](4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]).
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Question content area top
Part 1
The dot plot shows predictions for the winning time in the 200-meter sprint. The winner finished the race in 22.4 seconds. What is the greatest percent error among the predictions?
The greatest percent error among the predictions is of:
2.23%.
How to obtain the percent error of a measure?The percent error of a measure is obtained by the division of the difference between the actual value and the estimated value by the actual value, and multiplied by 100%, hence the equation is:
Percent error = |Actual - Estimate|/Actual x 100%.
From the given dot plot, we have that the farthest measure from 22.4 seconds is of 22.9 seconds.
The difference between the actual time and the estimate time is of:
22.9 seconds - 22.4 seconds = 0.5 seconds.
Applying the presented division, the percent error is given as follows:
Percent error = 0.5/22.4 x 100% = 2.23%.
Missing InformationThe dot plot is given by the image at the end of the answer.
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Linda' chool play tarted at 9:05 AM. It lated 1 hour and 45 minute. What time did the play end?
In given word problem ending time of the play is 10.50 AM.
What is word problem?
A comprehensive list of math word problems focuses on addition, subtraction, multiplication, division and more specific operations. life scenario. This means that children must be familiar with vocabulary associated with familiar mathematical symbols in order to understand word problems.
Here starting time of play = 9:05 AM
It took 1 hour 45 minutes to end the play. Then ,
=> 9 hour 05 minutes
1 hour 45 minutes +
=> 10 hour 50 minutes.
Hence ending time of the play is 10.50 AM.
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A triangle has sides with lengths of 26 inches, 36 inches, and 46 inches. Is it a right triangle?
yes or no
Answer:
no
Step-by-step explanation:
You want to know if side lengths 26 in, 36 in, 46 in form a right triangle.
Pythagorean tripleThe integer side lengths will form a right triangle if they are a Pythagorean triple, or a multiple of one.
We notice that these side lengths have a common difference of 10 in. That makes them an arithmetic sequence. The only Pythagorean triples that are an arithmetic sequence are {3, 4, 5} and its multiples. The shortest side is 3 times the common difference.
The lengths {26, 36, 46} cannot form a right triangle. The attachment shows the triangle is an obtuse triangle.
No, the triangle is not a right triangle.
__
Additional comment
The side lengths will form a right triangle if and only if they satisfy the relation a² +b² = c², where a, b are the two short sides.
26² +36² = 1972 ≠ 2116 = 46²
16 divided by the sum of 2 and 6
Answer:
Step-by-step explanation:
16/(2+6)
16/8=2
−0.25 + 316 + 2112? what is the answer to this and how did i solve it?
Answer:
Step-by-step explanation:
2427
2x² - 9 = 3x
A. {3,-1.5}
B. (-3,-1.5}
C. {-3, 1.5}
D. {3, 1.5}
The roots for the given quadratic equation 2x² - 9 = 3x is {3, -1.5}.
What is a quadratic equation?
The Quadratic equations are second-order polynomial equations such as ax² + bx +c = 0 for x, where a ≠ 0.
It has at least one solution that could be real or complex.
The given equation is 2x² - 9 = 3x.
Now expressing in the form of ax² + bx + c = 0, we get
2x² - 3x - 9 = 0,
a = 2, b = -3, c = -9, Now solving the above equation, we get
2x² - 6x + 3x - 9 =0
2x(x - 3) + 3(x - 3) = 0
(x - 3)(2x + 3) = 0
x - 3 = 0 (or) 2x + 3 = 0
x = 3 (or) x = -1.5
Hence, the roots of the equation are {3, -1.5}.
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