The value to be added to both sides of the equation to make the left side a perfect square trinomial is; -36.
To make the equation x2 – 12x = 1 look similar to the completing the square kind of expression where the left hand side of the equation becomes a perfect square, we must do the following;
First, the completing the square method usually takes the form; x² + bx = (x + b/2)² + cIn this scenario, the term (x² - 12x) can be rewritten as; (x - 6)² - 36.
This so because the expansion of (x - 6)² becomes;
x² - 12x + 36.Therefore, there's a need to subtract 36 from both sides of the equation so that the equation x2 – 12x = 1 is retained.
Therefore, the value to be added to both sides of the equation to make the left side a perfect square trinomial is; -36.
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On her 21st birthday, Sydney deposited $400 in a new bank account that earns 3.7% interest compounded continuously. If there are no other deposits or withdrawals, how much interest will she have earned by her 60th birthday
Answer:
$1,649.80
Step-by-step explanation:
Sydney will have earned $1293.35 in interest by her 60th birthday.
How to find interest?To solve this problem, we need to use the formula for continuously compounded interest:
A = P [tex]e^{rt}[/tex]
Where:
A is the final amount of money in the account (including principal and interest)
P is the initial principal (in this case, $400)
r is the interest rate (in this case, 3.7% per year)
t is the number of years the money is invested (in this case, 39 years)
e is the mathematical constant approximately equal to 2.718
Plugging in the values from the problem, we get:
A = $400[tex]e^{0.037 \times 39}[/tex]
Calculating this, we find that A = $400[tex]e^{1.443}[/tex] = $1693.35
Therefore, he will have earned $1693.35 - $400 = $1293.35 in interest by her 60th birthday.
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hi someone help with these two questions. Thanks
Answer:
1). Option (d)
2). Options (a), (b) and (d)
Step-by-step explanation:
Question 1
a). [tex]3x^5-6x^3+9x-12x^{-1}[/tex]
Any expression with negative exponent is not a polynomial.
b). [tex]4\sqrt{x}+5[/tex]
Any expression having variable with square root is not a polynomial.
c). [tex]\frac{4x+5}{3x-1}[/tex]
Any expression having variables in the form of a fraction is not a polynomial.
d). [tex]-\frac{3}{2}x^{12}-7x^5+\frac{2}{3}x-10[/tex]
It's a polynomial.
e). [tex]-5x^{\frac{3}{2}}-7x^2+6[/tex]
Expressions having variables with square root are not the polynomial.
Therefore, Option (d) is a polynomial.
Question 2.
P(x) = (2x + 1)(5x³ - 8x + 4)
= 2x(5x³ - 8x + 4) + 1(5x³ - 8x + 4)
= 10x⁴ - 16x² + 8x + 5x³ - 8x + 4
= 10x⁴ - 5x³ - 16x²+ 4
a). Degree of polynomial = 4
True
b). P(0) = 10(0) - 5(0) - 16(0) + 4
= 4
True
c). P(-1) = 10(-1)⁴ - 5(-1)³ - 16(-1)² + 4
= 10 + 5 - 16 + 4
= 3
False
d). Coefficient of x₂ is -16.
True
e). Coefficient of x is -16
False
Therefore, Options (a), (b) and (d) are correct.
3/4•3/4???? I can’t do it in my head and I don’t know how to make a decimal into a fraction
Answer:
0.5625
Step-by-step explanation:
3/4 as a decimal is 0.75
0.75×0.75=0.5625
Answer:
0.75 x 0.75 = 0.5625
Step-by-step explanation:
3/4=.75
2 1/4 + 3 1/2 = ???
Answer:
[tex]5\frac{3}{4}[/tex]
Step-by-step explanation:
You need to set bot denominators equal so multiply the second fraction by two for both the top and bottom.
[tex]2\frac{1}{4} +3\frac{1}{2} \\ =2\frac{1}{4} +3\frac{2}{4}\\\\ =5\frac{3}{4}[/tex]
(9x² + 6x – 7) + (-9x – 5)
Answer:
-12
Step-by-step explanation:
A photo of an ant in a science book is increased to 655% as large as the actual size. If the ant is 14 millimeters, what is the size of the ant in the photo?
Answer: [tex]91.7\ mm[/tex]
Step-by-step explanation:
Given
The size of the ant is enlarged by [tex]655\%[/tex]
The actual size of the ant is [tex]14\ mm[/tex]
Enlarged size is
[tex]\Rightarrow 14\times \dfrac{655}{100}\\\\\Rightarrow 91.7\ mm[/tex]
Which quadrilateral makes this statement true?
Quadrilateral ABCD
В
46
26
26
A (98
98)
118
11.7 11.7
D
Quadrilateral ABCD
Answer:i have no idea
Step-by-step explanation:
Does n e one get t?
2xyz - 3xy2z - 5x3z
help me please
Answer:
2xyz - 3x[tex]y^{2}[/tex]z-5[tex]x^{3}[/tex]z
Step-by-step explanation:
Each year, roughly 100 computer programmers each make about $
105. How much money is this all together? Express your answer both
as a power of 10 and as a dollar amount.
6. Select the expression that is equivalent to 24 + 64x
. A 8(3 + 8x)
B (8.3) + (8.x)
C 4(6 + 8x)
D 4(6 + x)
Answer:
A
Step-by-step explanation:
A. 8(3+8x)
8 times 3 is 24. 8 times 8 is 64 making it 24+64x
Negative ten is no less than two times a number plus fourteen.
Answer:
i this like true or false,if so its true
:)
Step-by-step explanation:
A recipe that serves 20 people uses ⅝ cup of water. How many cups of water are needed to serve 70 people?
Answer:
43.75 or simplified as 43 3/4 which is a mixed number
Step-by-step explanation:
How I did it is divide 5 and 8 and got 0.625 and I divided 70 by 0.625 and got 43.75 and I simplified it as a maxed number and got 43 3/4
please please please please please please help help!!!
Answer:
25
Step-by-step explanation:
the number of plants can be determined by adding the frequencies together
2 + 5 + 6 + 8 + 3 + 1 = 25 plants
hiroshi earns $6.50 an hour. He wants to buy a cd player that costs $117. Write an equation and find how many hours hiroshi will have to work to buy the cd player.
1. Whats the exact value of Y?
2. Whats the exact value of X?
Answer:
Hello! The answer is in this link.
Step-by-step explanation:
8518-06-04-10-15-instructional.mp4. I hope this helps! Have a great rest of your day!
Help plz i will give brainliest!!
PLEASE HELP ASAP!!!!!!!! 2+2
Answer:
4
Step-by-step explanation:
it's four imma just goo
how many solutions does 3(4x - 2) = -12x - 6 have
first part to last question
Answer:
For question 4 you would have 1560000. For question 5 you would have 660000
Step-by-step explanation:
What is the percent of change from 56 t0 22
idea 34 I did 56-22 0.0
Answer:
I think it is -60.71428571 percent.
What number makes the equation true? 27 +_ = 46
27 + x = 46
x = 46 - 27
x = 19 Ans .
Answer:
19
Step-by-step explanation:
Subtract- 46-26=19
Therefore, 27+19=46
Gabriel is building a roof for a shed. He uses plywood to make the roof with the dimensions shown (rounded to the nearest tenth of a foot), but with an open bottom.
A rectangular pyramid has a rectangular base with length of 7 feet and height of 5 feet. 2 triangles have a base of 5 feet and height of 6 feet. 2 triangles have a base of 7 feet and height of 5.5 feet.
Answer:
171
Step-by-step explanation:
Answer:
171
Step-by-step explanation:
Part A: The average rate of change between the 2nd and 3rd point is Select a Value Part A: The average rate of change between the 3rd and 4th point is Select a Value Part B: The average rate of change between the 2nd and 3rd point is Select a Value Part B: The average rate of change between the 4th and 5th point is Select a Value
Answer:
[tex]Rate = 6[/tex]
[tex]Rate = 10[/tex]
[tex]Rate = 18[/tex]
[tex]Rate = 162[/tex]
Step-by-step explanation:
Given
See attachment for table
Solving (a): Rate of change between 2nd and 3rd point on A
The rate of change is calculated as:
[tex]Rate = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
In table A, the 2nd and 3rd point is:
[tex](x_1,y_1) =(1,7)[/tex]
[tex](x_2,y_2) =(2,13)[/tex]
So, the average rate of change is:
[tex]Rate = \frac{13 - 7}{2 - 1}[/tex]
[tex]Rate = \frac{6}{1}[/tex]
[tex]Rate = 6[/tex]
Solving (b): Rate of change between 3rd and 4th point on A
In table A, the 3rd and 4th point is:
[tex](x_1,y_1) =(2,13)[/tex]
[tex](x_2,y_2) =(3,23)[/tex]
So, the average rate of change is:
[tex]Rate = \frac{23 - 13}{3 - 2}[/tex]
[tex]Rate = \frac{10}{1}[/tex]
[tex]Rate = 10[/tex]
Solving (c): Rate of change between 2nd and 3rd point on B
In table B, the 2nd and 3rd point is:
[tex](x_1,y_1) =(2,11)[/tex]
[tex](x_2,y_2) =(3,29)[/tex]
So, the average rate of change is:
[tex]Rate = \frac{29 - 11}{3 - 2}[/tex]
[tex]Rate = \frac{18}{1}[/tex]
[tex]Rate = 18[/tex]
Solving (d): Rate of change between 4th and 5th point on B
In table B, the 4th and 5th point is:
[tex](x_1,y_1) =(4,83)[/tex]
[tex](x_2,y_2) =(5,245)[/tex]
So, the average rate of change is:
[tex]Rate = \frac{245 - 83}{5 - 4}[/tex]
[tex]Rate = \frac{162}{1}[/tex]
[tex]Rate = 162[/tex]
Dr. Campbell is ordering new student desks for 4th and 5th graders. There are 6 desks in each box that is delivered to the school. There are 43 4th graders and 40 5th graders. Write an expression to determine how many boxes Dr. Campbell should order to have a desk for each student?
Answer:
they should buy three more for the 5th grade to match the 4th grade
What is the area of sector GPH?
Answer:
28.26
Step-by-step explanation:
A = area of a sector
π = 3.14
r = 9
θ = 40
A=πr²*θ/360=3.14*81*40/360=28.26
What is the equation of the graphed line written in
standard form?
2x + 3y = -6
2x + 3y = 6
y= -2/3x - 2
v= 2/3x - 2
Answer:
A. 2x + 3y = -6
Step-by-step explanation:
[tex](-3,0) (0,-2)[/tex]
[tex]slope:\frac{-2-0}{0+3} =\frac{-2}{3}[/tex]
[tex]y-0=\frac{-2}{3} (x+3)[/tex]
[tex]3y=-2x-6[/tex]
[tex]3y+2x+6=0[/tex]
[tex]2x+3y=-6[/tex]
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hope it helps...
have a great day!!
A triangle with side lengths of 21, 17, and 18 is classified as acute, obtuse, right, or equiangular?
Answer:
Acute
Step-by-step explanation:
and angle lower than 90 is acute exactly 90 is an right angle from 90 to 180 obtuse 180 to 360 reflex angle and equalateral is 60 degrees on each angle
pls solve this fast pls help me fast
Fern has 2 1/4 gallons of paint. Each gallon of paint will cover 375.5 ft2. How many square feet will fern be able to cover if she uses all the paint?
Need help ASAP please anyone
Answer:
Step-by-step explanation: