The number of unit tiles needed to be added to the expression [tex]x^2 + 4x + 3[/tex] for making it perfect square trinomial is: Option A: 1
What is a perfect square polynomial?If a polynomial p(x) can be written as:
[tex]p(x) = [f(x)]^2[/tex]
where f(x) is also a polynomial, then p(x) is called as perfect square polynomial.
What are terms in polynomials?Terms are added or subtracted to make a polynomial. They're composed of variables and constants all in multiplication.
Example: [tex]x^2 + 3x + 4[/tex] is a polynomial consisting 3 terms as [tex]x^2 ,3x , \rm and \: 4[/tex]
If there is one term, the polynomial will be called monomial.If there are two terms, the polynomial will be called binomialIf there are three terms, the polynomial will be called trinomialThe given trinomial is [tex]x^2 + 4x + 3[/tex]
Since the tiles are added to be in unit and positive(1, 2, 3, or 4), thus, let it be denoted by z, then:
[tex]x^2 + 4x + 3 + z = (x+a)^2[/tex]
since z is added such that the specified trinomial becomes perfect square trinomial, and since its degree is 2, so it must be product of two linear polynomials, and since coefficient of x in given trinomial is 1, so we kept the coefficient of linear polynomial as 1
Now, expanding the obtained equation, and comparing the coefficients, we get:
[tex]x^2 + 4x + 3 + z = (x+a)^2\\x^2 + 4x + 3 + z = x^2 + a^2 + 2ax\\[/tex]
Thus, from comparison of coefficients of like terms and constants, we get:
[tex]2a = 4\implies a = 2\\3 + z = a^2 = 2^2 = 4\\z = 1[/tex]
Thus, the number of unit tiles needed to be added to the expression [tex]x^2 + 4x + 3[/tex] for making it perfect square trinomial is: Option A: 1
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Answer:
A.) 1
Step-by-step explanation:
Edge 2022
a bag contain 150 marbles. some are blue, and the rest are white. there are 21 blue marbles for every 4 white marbles.How many blue marbles are in the bag? Explain your resoning.
Answer:
787.5
Step-by-step explanation:
150x21÷4 sana makatolong
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS MATH QUESTION RIGHT NOOOO SCAMS PLEASE AND PLEASE EXPLAIN WHY THAT IS THE ANSWER
D.62 you can’t see it cause the picture too small but this is just another answer choice it’s not the answer
Answer:
28
Step-by-step explanation:
3p+6=90
3p=84
p=28
6) Slope = -2, y-intercept = -3
A) 2x + y = -3 B) 2x - y = 3
C) 3x + y = 3 D) x + 2y = 43
Answer:
A)
Step-by-step explanation:
Use synthetic division to solve (4 x cubed minus 3 x squared 5 x 6) divided by (x 6). What is the quotient? 4 x squared minus 27 x 167 minus StartFraction 996 Over x minus 6 EndFraction 4 x squared 21 x 131 StartFraction 792 Over x 6 EndFraction 4 x squared 21 x 131 StartFraction 792 Over x minus 6 EndFraction 4 x squared minus 27 x 167 minus StartFraction 996 Over x 6 EndFraction.
The quotient of the provided polynomial divide by the (x+6) with the help of synthetic division method is,
[tex]f(x)=4x^2-27x+167-\dfrac{996}{x+6}[/tex]
What is the factor of polynomial?The factor of a polynomial is the terms in linear form, which are when multiplied together, give the original polynomial equation as result.
The polynomial given in the problem is,
[tex]4x^3-3x^2+5x+6[/tex]
This polynomial is divided by the linear factor (x+6). Thus use -6 to for the synthetic division of polynomial as,
-6 | 4 -3 +5 6
x -24 +162 -1002
Add the numbers as,
4 -27 167 -996
Put these values, we get,
[tex]f(x)=4x^2-27x+167-\dfrac{996}{x+6}[/tex]
Hence, the quotient of the provided polynomial divide by the (x+6) with the help of synthetic division method is,
[tex]f(x)=4x^2-27x+167-\dfrac{996}{x+6}[/tex]
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Answer: D
Step-by-step explanation:
Edge 2023
Emma has 200 pages of her book left to read. In 4 minutes, she reads 6 pages.
At this rate, can she finish her book in 2 hours?
Answer:
She would finish her book in 2 hours and 16 minutes
Step-by-step explanation:
6 x 34 = 204
4 x 34 = 136
136 = 2 Hours and 16 minutes
Yes, she can finish her book in 2 hours if she reads at the same rate of 6 pages every 4 minutes.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Examples:
1 hour = 60 minutes
1 minute = 60 seconds
1 km = 1000 m
We have,
First, we need to convert 2 hours to minutes:
So,
= 2 hours × 60 minutes/hour
= 120 minutes
Now,
6 pages/4 minutes
= 1.5 pages/minute
So in 120 minutes, she can read:
= 1.5 pages/minute × 120 minutes
= 180 pages
Thus,
Since Emma has only 200 pages left to read, she can finish her book in 2 hours if she reads at the same rate of 6 pages every 4 minutes.
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#SPJ2
70.4 divided by 11 with work shown
Answer:
6.4
Step-by-step explanation:
70.4/11
= 6.4
use your calculator
Answer:
6.4
Step-by-step explanation:
66/11=6 4.4/11=0.4
Who holds the world record for memorizing the most digits of pi.
Answer:
Akira Haraguchi.
Step-by-step explanation:
Akira Haraguchi, who in 2006 recited 100,000 digits of pi from memory at a public event near Tokyo.
PLEASE HELP ASAP!!!!!!
Answer:
C.
We know that there are 100 total females and males.
So, the amounts of each type of math for both genders should add to get 100
A.
57 + 64 ≠ 100
B. 57 + 64 ≠ 100
C. 57 + 43 = 100
D. 57 + 64 ≠ 100
So, it has to be C
What other angle between O and 360 degrees has the same TAN value as 71
degrees? Just type the angle measure in the bldnk without the units.
Answer:
-289 degrees
Step-by-step explanation:
You are looking for what is called Coterminal Angles.
To find a coterminal angle between 0 and 360 you add or subtract 360.
In this case, we subtracted 360 from 7171 - 360 = -289 tan(-289) = 2.90If TAN 71 = 2.90 and TAN -289 = 2.90, you know -289 is your answer.Hope this helps!! Please mark Brainliest!!!
You want to find out the height of a tree, so you hold a square cardboard so that the edges line up with the top and bottom of the tree, as shown in the diagram below. Your friend measures the horizontal distance from you to the tree, and the vertical distance from the ground to your eye.
What is the height of the tree to the nearest tenth of a foot?
The height of the tree to the nearest tenth of foot is 20.5 ft
Right angle triangle:A right angle triangle has one of its angles as 90 degrees. The sides can be found using Pythagoras theorem.
Therefore,
The base of the big triangle can be found as follows:
c² = a² + b²
c² = 9.2² + 5.8²
c² = 84.64 + 33.64
c = √118.28
c = 10.8756608995
c = 10.88 ft
Therefore, using similar triangle ratio,
5.8 / 10.9 = 10.9 / x + 5.8
5.8x + 33.64 = 118.81
5.8x = 118.81 - 33.64
5.8x = 85.17
x = 85.17 / 5.8
x = 14.6844827586
x = 14.68
Therefore, the height of the tree = 14.7 + 5.8 = 20.5 ft
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what is the distance between 2, -4 and 9, -4
8 units
11 units
0 units
7 units
Answer:
6,13 is the right answer
What is the surface area?
6 cm
6 cm
6 cm
square centimeters
Answer:
216CM SQUARE :).......
The grouped frequency table below represents the lengths of the fingers of some
students in centimetres.
Length (x cm) Frequency (f)
8<< < 9 3
9<3 <10 11
10 < x < 11 17
11 < x < 129
Find an estimate for the mean length.
cm
Answer:
10.3
Step-by-step explanation:
When calculating the mean from a grouped frequency table, first you must estimate what the value is through finding the number halfway between the value that x is greater than and less than:
The number halfway between 8 and 9 is 8.5
The number halfway between 9 and 10 is 9.5
The number halfway between 10 and 11 is 10.5
The number halfway between 11 and 12 is 11.5
Next, you have to multiply the estimated value by its frequency:
8.5 x 3 = 25.5
9.5 x 11 = 104.5
10.5 x 17 = 178.5
11.5 x 9 = 103.5
Then, add up the values you calculated and divide them by the total frequency (all the frequencies added up).
total estimated length: 25.5 + 104.5 + 178.5 + 103.5 = 412
total frequency: 3 + 11 + 17 + 9 = 40
412/40 = 10.3
1) The sum of three numbers is 22. The second is 3 more than the first. The third is
one less than twice the first. Find the numbers.
Answer: The numbers are 5, 8, and 9
Step-by-step explanation:
x+y+z=22
y=x+3
z=2x-1
After you have those three equations, you can plug the y and z value into the first equation.
You get x+x+3+2x-1=22, so 4x+2=22
Therefore, 4x=20, so x=5
If x=8, then y=5+3, so y=8
Also, z=2(5)-1, so z=9
What could you multiply by to clear the fractions? Solve for x
x
.
23(x + 4) = 59x + 1
Answer:
x=91/36
Step-by-step explanation:
When the polynomial 3x^3+22x^2+38x+15 is divided by (x + 2), the remainder is 3. What is known about the function?
Answer:
It is known that x+2 is not a factor of the function.
Step-by-step explanation:
Whenever a remainder is present after diving a problem, the divisor is not a factor of the overall polynomial. Since this applies in this case, x+2 is not a factor.
The figure (not drawn to scale) consists of a semicircle, one large rectangle, and one small rectangle,
with dimensions as shown. The width of the small rectangle is 3 feet and its length is 3 times the width.
50 ft
The shaded region area is the amount of space covered by the shaded region
The area of the shaded region is 3.75 square feet
How to determine the shaded areaThe question is incomplete, as the figure is not given.
So, I will give a general explanation
Assume that the figure has the following properties
Big rectangle of dimension, 10 ft by 5 ftSmall rectangle of dimension 3 ft by 9ftSemicircle of a diameter of 7ftStart by calculating the area of the big rectangle
Area = 10 ft * 5 ft = 50 square ft
Calculate the area of the small rectangle
Area = 3 ft * 9 ft = 27 square ft
Calculate the area of the semicircle
Area = 0.5 * 22/7 * (3.5)^2 ft = 19.25 square ft
Assume that the shaded area is outside the semicircle and the small rectangle, the shaded area would be:
Shaded area = Big rectangle - Small rectangle - Semicircle
So, we have:
Shaded area = 50 - 27 - 19.25
Shaded area = 3.75
Using the assumed values, the area of the shaded region is 3.75 square feet
Read more about shaded area at:
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Answer:
The shaded region area is the amount of space covered by the shaded region
The area of the shaded region is 3.75 square feet
How to determine the shaded area
The question is incomplete, as the figure is not given.
So, I will give a general explanation
Assume that the figure has the following properties
Big rectangle of dimension, 10 ft by 5 ft
Small rectangle of dimension 3 ft by 9ft
Semicircle of a diameter of 7ft
Start by calculating the area of the big rectangle
Area = 10 ft * 5 ft = 50 square ft
Calculate the area of the small rectangle
Area = 3 ft * 9 ft = 27 square ft
Calculate the area of the semicircle
Area = 0.5 * 22/7 * (3.5)^2 ft = 19.25 square ft
Assume that the shaded area is outside the semicircle and the small rectangle, the shaded area would be:
Shaded area = Big rectangle - Small rectangle - Semicircle
So, we have:
Shaded area = 50 - 27 - 19.25
Shaded area = 3.75
Using the assumed values, the area of the shaded region is 3.75 square feet
Step-by-step explanation:
What happens to the standard error of m as sample size increases?.
Answer:
SEM decreases by a factor of √N
Step-by-step explanation:
The standard error of the mean (SEM) is inversely proportional to the square root of the sample size. As the sample size (N) increases, the SEM is decreased by a factor of √N.
The SEM is the population standard deviation divided by √N for a normal distribution.
The Area of Parallelogram is 32 cm² , its Base is 8 cm. Then find its Height .
Question :-
The Area of Parallelogram is 32 cm², its Base is 8 cm . Then find its Height .Answer :-
Height of Parallelogram is 4 cm .[tex] \rule {210pt} {2pt} [/tex]
Given :-
Area of Parallelogram = 32 cm²Base of Parallelogram = 8 cmTo Find :-
Height of Parallelogram = ?Solution :-
As per the provided information in the given question, we have been given that the Area of Parallelogram is 32 cm² . Base of Parallelogram is given 8 cm . And, we have been asked to calculate the Height of Parallelogram .
For calculating the Height , we will use the Formula :-
[tex] \bigstar \: \: \boxed{ \sf{ \: Area \: _{Parallelogram} \: = \: Base \: \times \: Height \: }} [/tex]
Therefore , by Substituting the given values in the above Formula :-
[tex] \longmapsto \: \: \sf{ Area \: _{Parallelogram} \: = \: Base \: \times \: Height} \\ [/tex]
[tex] \longmapsto \: \: \sf{ 32 \: = \: 8 \: \times \: Height} \\ [/tex]
[tex] \longmapsto \: \: \sf{ \dfrac{32}{8} \: = \: Height } \\ [/tex]
[tex] \longmapsto \: \: \sf{ \dfrac{4}{1} \: = \: Height } \\ [/tex]
[tex] \longmapsto \: \: \textbf {\textsf {Height = 4 cm}} [/tex]
Hence :-
Height of Parallelogram = 4 cm .[tex] \underline {\rule {210pt} {4pt}} [/tex]
Additional Information :-
[tex] \begin{gathered} \begin{gathered}\begin{gathered}\boxed{\begin{array}{c} \\ \underline{ { \textbf {\textsf \red{ \dag \: \: More \: Formulas \: \: \dag}}}} \\ \\ \\ \footnotesize \bigstar \: \bf{Area \: _{Square} = Side \times Side} \\ \\ \\ \footnotesize\bigstar \: \bf{Area \: _{Rectangle} = Lenght \times Breadth} \\ \\ \\ \footnotesize \bigstar \: \bf{Area \: _{Triangle} = \frac{1}{2} \times Base \times Height } \\ \\ \\ \footnotesize \bigstar \: \bf{Area \: _{Parallelogram} = Base \times Height} \\ \\ \\ \footnotesize \bigstar \: \bf{Area \: _{Trapezium} = \frac{1}{2} \times [ \: A + B \: ] \times Height } \\ \\ \\ \footnotesize \bigstar \: \bf {Area \: _{Rhombus} = \frac{1}{2} \times Diagonal \: 1 \times Diagonal \: 2}\end{array}}\end{gathered}\end{gathered} \end{gathered} [/tex]
Area of a parallelogram is base times it's height, here so if we assume the height to be H, then:
→ H × 8 = 32
→ H = (32/8)
→ H = 4 cm
The population of a town, y, is 15,000 people and is growing by 1.5% per year.
linear or exponential?
I believe it’s exponential and could someone help me write the equation?
Answer:
Exponential should be correct I should think.^
SONGS
CUT
Match each question you might ask yourself on the left with how you might respond on the right
Why don't like spinach?
I left my coat in the car
Why am I so cold?
It tastes bitter to me
DOO
Why was I late for school?
I forgot to set my alarm
Answer:
Step-by-step explanation:
why dont you like spinach? it tastes bitter to me
why am is so cold? i left my coat in the car
Why was i late for school? i forgot to set my alarm
Each section of toy train tracks is 13 centimeters long. If jude lays 15 section end to end, how long is his train track
Answer:
195 Cm
Step-by-step explanation:
13x15=195
what is 86% of 20?
please help
Answer:
17.2
hi, how is your day?
Answer: 17.2
Step-by-step explanation:
Which of these could be the area of circle b? Explain your reasoning
Answer:
c about 900 in²
ím not sure
The equation of a line is given below.
2x+y=-3
Find the slope and the y-intercept.
Then use them to graph the line.
Answer:
Slope = -4.000/2.000 = -2.000
y-intercept = -3/1 = -3.00000
Step-by-step explanation:
^
Answer:
-2 is slope and -3 in y-intercept
Step-by-step explanation:
Starting with 2x + y = -3
Subtract 2x from both sides to get y alone:
y = -2x -3
This is now in slope-intercept form, which is y=mx+b, where m=slope and b=y-intercept.
-2 is in the m spot, so it is the slope
-3 is in the b spot, so it is the y-intercept
See image for graph
If ∠G is supplementary to ∠H and the measure of ∠G is 65° what is the measure of ∠H?
Solution:
Given:
∠G = 65°Supplementary angles are a pair of angles that sum up to 180°.
It should be noted:
If ∠G and ∠H are a pair of supplementary angles, they both sum up to 180°.Equation formed: ∠G + ∠H = 180
Substitute the values into the equation.
∠G + ∠H = 180=> 65 + ∠H = 180Subtract 65 both sides.
=> 65 - 65 + ∠H = 180 - 65=> ∠H = 180 - 65 = 115°I need this class to graduate
Answer:
math
Step-by-step explanation:
because it is one of your main classes
Write down the numbers in condensed form 200+40+5+0,3+0,07
Answer:
Step-by-step explanation:
240.37
Trigonometric ratios in right triangles. Find tan (b) in the triangle. A,b,c 3,4,5
Check the picture below.
What factor could you pull out of 10x AND 5?
2
x
10
5
WILL GIVE BRAINLY
Hi! I hope you're enjoying your day!
The common factor of 10x and 5 is
5.
What is a factor?
It's a number that a number is evenly divisible by.
Example: 2 is a factor of 10, because 10 is evenly divisible by 2.
Also, it may be tempting to say, "Well, 2 is the common factor!"
And that's not true in this case, because 5 isn't divisible by 2.
x is also not a common factor; 5 is a constant, it doesn't have any variables next to it.
Hence, the factor is
[tex]\boxed{\boxed{\bold{5}}}[/tex]
Hope everything is clear.
If you have any questions, please comment.
#LearningIsFun