[tex]\large {\text {$ \sf \cfrac{1}{2x^2} -2 = 0 $}}[/tex]
Now, we will multiply per 2x² both sides of equation...[tex]\large {\text {$ \sf \cfrac{1}{2x^2}\cdot \:2x^2-2\cdot \:2x^2=0\cdot \:2x^2 $}[/tex]
[tex]\searrow[/tex]
[tex]\large {\text {$ \sf 1-4x^2=0$}}[/tex]
We have to write in standard form...[tex]\large {\text {$ \sf -4x^2+1 = 0 $}}[/tex]
[tex]\large {\text{$\sf x=\cfrac{-b\pm\sqrt{b^2-4ac}}{2a} \quad\rightarrow\quad x=\cfrac{-0\pm\sqrt{0^2-4\cdot (-4) \cdot1} }{2\cdot (-4) } \:\rightarrow\:\: x=\cfrac{-0^2 \pm4}{2 \cdot(-4)} $}}[/tex]
[tex]\huge {\text {$ \sf \downarrow$}}[/tex]
[tex]\large {\text {$\sf {\bf x_1} = \cfrac{-0+4}{2\left(-4\right)}= \cfrac{-1}{2} $}}[/tex] [tex]\large {\text {$\sf {\bf x_2 }=\cfrac{-0-4}{2\left(-4\right)} = \cfrac{1}{2} $}}[/tex]
At this point, we're going to add the values of x₁ and x₂:[tex]\large {\boxed {\boxed { \bf x_1 + x_2= -\cfrac{1}{2}+ \cfrac{1}{2} = 0} }}[/tex]
[tex]\huge {\text {$ \it Alternative \: A $}}[/tex]
What is the coefficient of x^8 in the expansion of (x+4)^12 ?
Can someone help me with this question and show me how to solve them pleases?
Answer:
126720x⁸
Step-by-step explanation:
explanations are in the images above .. you can reach me personally for expanded help
solve (algebra 1)− 0.32 + 0.18 = 0.25 − 1.95
Answer:
0.50=1.7. They do not equal each other
Step-by-step explanation:
Thats what I got from this question
Which expression is equivalent to 3/2?
Answer: the answer is D. I took the test & got it right
Step-by-step explanation:
The expression is equivalent to 3/2 will be;
⇒ 3y/(2y - 6) + 9/(6 - 2y)
Option D is true.
What is an expression?
Expression in math is defined as the collection of the numbers, variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
Equivalent expression is 3/2.
Now,
Let the expression is;
⇒ 3y/(2y - 6) + 9/(6 - 2y)
Solve the expression as;
⇒ 3y/(2y - 6) - 9/(2y - 6)
⇒ (3y - 9) / (2y - 6)
⇒ 3 (y - 3) / 2 (y - 3)
⇒ 3/2
So, The expression is equivalent to 3/2 will be;
⇒ 3y/(2y - 6) + 9/(6 - 2y)
Option D is true.
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[tex]solve : - \\ \\ (2 ^{2} + 4 {}^{2}) = {?}[/tex]
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {20}}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]
[tex] = ( {2}^{2} + {4}^{2} )[/tex]
[tex] = [(2 \times 2) + (4 \times 4)][/tex]
[tex] = (4 + 16)[/tex]
[tex] = 20[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Thank\:you! }}{\orange{❦}}}}}[/tex]
The graph of F(X) shown below resembles the graph of G(x)-, but it has
been changed somewhat. Which of the following could be the equation of
F(x)?
F(x) = 2
G(X) = 1x1
5
-5
The function F(x) would be F(x) = 0.2x² - 3.
What is Function?A mathematical phrase, rule, or legislation that establishes the link between an independent variable and a dependant variable (the dependent variable).
We are given a graph of the function G(x) as:
G(x) = x²
We are required to determine a potential representation of the function F (x).
We are aware that the function F(x) graph is a horizontal extension of the function G(x).
This indicates that "k" is the factor that is multiplied by G(x).
where 0< k <1.
The graph is also 3 units vertically down, which causes the graph.
So, the graph is shifted 3 units vertically down hence the graph of the resulting function F(x) is:
F(x) = 0.2x² - 3
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You deposit $100 into a savings account that gives you 5.5% annual interest rate, compounded quarterly. What will be your balance after 4 years?
Answer:
$124.42.
Step-by-step explanation:
Given data
Principqp= $100
Rate= 5.5%
time=4 years
First, convert R as a percent to r as a decimal
r = R/100
r = 5.5/100
r = 0.055 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt // Since we are compounding quarterly
A = 100.00(1 + 0.055/4)(^4)(4)
A = 100.00(1 + 0.01375)^(16)
A = $124.42
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $100.00 at a rate of 5.5% per year compounded 4 times per year over 4 years is $124.42.
What conversion ratio was skipped in this multiple-step conversion?
Answer:
B
Step-by-step explanation:
B was missed. You have to convert this from hours into minutes before you can deal with seconds.
The perimeter of a rectangular swimming pool is 154 meters. Its length is 2m more than twice its breadth. What are the length and the breadth of the pool?
Step-by-step explanation:
Hey there!
According to the question;
Perimeter of rectangle (p) = 154 m
Let the breadth of rectangle be "X" then length will be 2x+2.
Then;
Perimeter (p) = 2(l+b)
154 = 2((2x+2) + x)
154 = 2(3x+2)
154 = 6x + 4
or, 6x = 154-4
or, X = 150/6
Therefore, X= 25.
Hence;
Length = 2*25+2 = 52 m
Breadth = 25 m
Hope it helps!
We can assume,
Perimeter of rectangle = 154 m
Breadth = x
Length = 2x + 2
Now, perimeter = 2(l+b)
[tex] \sf \to 154= 2((2x+2) + x)[/tex]
[tex] \sf \to 154 = 2(3x+2)[/tex]
[tex] \sf \to 6x = 154-4[/tex]
[tex] \sf \to x = \frac{150}{6} = 25[/tex]
Then,
Breadth = 25 m
Length [tex] \sf = 2x + 2[/tex]
[tex] \sf \to (2 \times 25) + 2[/tex]
[tex] \sf \to 52 \: m[/tex]
Can someone help me with this math homework please!
Answer:
During that time, math symbols (like the division and multiplication sign) and numbers weren't invented yet, so they used words because that was the only choice either than verbally speaking.
Step-by-step explanation:
This is open-ended question, so you can write something similar to the answer I wrote or add on to it :-)
I searched online for the answer and found it on Brainly just to let you know because I was unsure about it loll
Credit: Edufirst
Hope it helps (●'◡'●)
Solve for X.
-3/2(x-2)=45/14
Please show work.
Answer:
-1/7
Step-by-step explanation:
-3/2(x-2)=45/14
x-2=(45/14)/(-3/2)
x-2=(45/14)(-2/3)
x-2=-90/42
simplify -90/42 into -15/7
x-2=-15/7
x=-15/7+2
x=-15/7+14/7
x=-1/7
what's the middle number between 20 and 30?
Answer:
25
Step-by-step explanation:
you can find the middle number by solving for the mean/average
20+30=50
50/2=25
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{What's the middle number between 20 \& 30?}[/tex]
[tex]\mathsf{\dfrac{20+30}{2}}[/tex]
[tex]\large\textsf{20 + 30 = \bf 50}[/tex]
[tex]\mathsf{=\dfrac{ 50}{2}}[/tex]
[tex]\large\textsf{= \bf 25}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: middle number between 20 \& 30 is: \bf 25}}}\\\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A man invests $ 16800 in savings plan that pays simple interest at a rate of 5% per annum. Find the Tim’s taken for his investment to grow to $18900
Answer:
2.5 years
Step-by-step explanation:
The given amount invested, which is the principal, P = $16,800
The simple interest rate, R = 5% per annum
The intended total value of the investment, A = $18,900
The simple interest on the principal, I = A - P
∴ I = $18,900 - $16,800 = $2,100
The formula for the simple interest, I, is given as follows;
[tex]I = \dfrac{P \times R \times T}{100}[/tex]
Therefore, we have;
[tex]T = \dfrac{I \times 100}{P \times R}[/tex]
Plugging in the values, gives;
[tex]T = \dfrac{2,100 \times 100}{16,800 \times 5} =2.5[/tex]
The time it will take the investment to grow to $18,900 is T = 2.5 years
Solve the inequality 6 is greater or equal than m- 1
Answer:
7 ≥ m OR m ≤ 7
Step-by-step explanation:
You can actually solve this in two ways , either :
6 ≥ m - 1
6 + 1 ≥ m
7 ≥ m
OR
m -1 ≤ 6
m ≤ 6 + 1
m ≤ 7
Both are correct.
Which of the following statements considered as always true?
A. All intersecting lines are perpendicular.
B. All parallel lines cut by a transversal line.
C. All perpendicular lines are intersecting line.
D. All transversal line is for parallel lines only
Someone please help me on this and please tell me the answer directly please !!
Answer:
HAVE A NİCE DAY
Step-by-step explanation:
GREETİNGS FROM TURKEY ¯ツ
For what value of b will f(x) = x^2 + bx + 400 have -20 as its only zero? Record your answer and fill in the bubbles on your answer document.
The polynomials f(x) = x^2 + bx + 400 have -20 as its only zero then the value of b is 40.
The polynomials f(x) = x^2 + bx + 400 have -20 as its only zero
Then x=-20
What is the zero of a polynomial?The zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero.
x=-20 is the zero of the given polynomial
Therefore it satisfies the given polynomial
[tex]f(-20)=(-20)^2+b(-20)+400[/tex]
[tex]0=400-20b+400\\800-20b=0\\-20b=-800\\b=\frac{-800}{-20} \\b=40[/tex]
Therefore the value of b is 40.
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CAN SOMEONE HELP ME ASAP!!!
Answer:
5÷35 = 1/7× 100
Step-by-step explanation:
P(E)= n(E)÷ n(s)
Answer:
17%
Step-by-step explanation:
Add all of the students up and then form a ratio:
30 students in total; 5 seniors/30 students
5/30 = 1/6 = 16.67%
(I think that's the answer, hope it helps)
Can someone help and explain this to me,if you do it means a lot :)
Answer:
0 zero
Step-by-step explanation:
you must find gf(x) first
g[ f(x) ] = g [ 2 + 1 ]
= 3-2+x which is you sub fx tu g
g [ f (-1) ] = 3-2-1
=0
LIn runs for 25 sec at 8.2 meters per second . What is her finish point?
Answer:
205 meters
Step-by-step explanation:
25 * 8.2 = 205
Help me out please, thanks
Hello!
f(x) = x² + 12x <=>
<=> a = 1, b = 12 <=>
<=> x = -12/2×1 <=>
<=> x = -6 <=>
<=> f(-6) = -36 <=>
<=> (-6; -36)
Good luck! :)
(x2/5)n
For what value of n, written as a decimal, will the expression equal x?
Given:
The expression is:
[tex]\left(x^{\frac{2}{5}\right)^n[/tex]
To find:
The decimal value of n so that the value of the given expression is equal to x.
Solution:
We have,
[tex]\left(x^{\frac{2}{5}\right)^n[/tex]
This expression is equal to x.
[tex]\left(x^{\frac{2}{5}\right)^n=x[/tex]
[tex]x^{\frac{2}{5}n}=x^1[/tex] [tex][\because (a^m)^n=a^{mn}][/tex]
On comparing the exponents, we get
[tex]\dfrac{2}{5}n=1[/tex]
[tex]2n=5[/tex]
[tex]n=\dfrac{5}{2}[/tex]
[tex]n=2.5[/tex]
Therefore, the required value of n is 2.5.
One group of new freshmen is given a study-skills training course during the first week of college and a second group does not receive the course. At the end of the semester, the grade point average is recorded for each student. For this study, what is the dependent variable
Answer:
The dependent variable is the grade point average recorded for each student.
Step-by-step explanation:
The dependent variable is defined as the variable that is to be tested or even measured in an experiment.
In this question, At the end of the semester, the variable that is being tested is the grade point average for each student.
Thus it is the dependent variable.
help me solve this problem please
Step-by-step explanation:
nope guy but little you now
What is the solution to log Subscript 5 Baseline (10 x minus 1) = log Subscript 5 Baseline (9 x + 7)
Answer:
x = 8Step-by-step explanation:
Given:
log₅ (10x - 1) = log₅ (9x + 7)10x - 1 = 9x + 710x - 9x = 7 + 1x = 8▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
[tex]\sf{log_{5}}(\tt{10x-1})=\sf{log_{5}}(\tt{9x+7})\\\\10x-1=9x+7\\\\10x-9x=7+1\\\\\pmb{\green{\underline{\sf{x=\frak{8}}}}}[/tex]
▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
A basketball court measures 998 inches on the sides while the baseline stretches 700 inches. There is a circle in the middle of the court that has a diameter of 72 inches. The team can fit 14 people in the circle at one time. How many people can fit on a court?
698,600 people
50,000 people
1296 people
2402 people
Answer:
2402 people.
Step-by-step explanation:
Since a basketball court measures 998 inches on the sides while the baseline stretches 700 inches, and there is a circle in the middle of the court that has a diameter of 72 inches, and the team can fit 14 people in the circle at one time To determine how many people can fit on a court, the following calculation must be performed:
Area of a circle:
3.14 x (72/2) ^ 2 = X
3.14 x 36 ^ 2 = X
3.14 x 1.296 = X
4,069.44 = X
Area of a rectangle:
998 x 700 = X
698,600 = X
4,069.44 / 14 = 290.67
698,600 / 290.67 = 2,402
Which expressions are in the simplest form? Check all that apply.
(Please help, I've been stuck on this all afternoon)
Answer:
All options are correct.
Step-by-step explanation:
We have to find the expression which are in the simplest form.
A.[tex]x^{-3}+y^3[/tex]
The expression cannot solve further.
Therefore, the given expression is in the simplest form .
B.[tex]\frac{1}{x^4}[/tex]
The expression cannot solve further.
The given expression is in the simplest form.
C.[tex]\frac{w^7}{x^2}[/tex]
[tex]x^2[/tex] cannot divide [tex]w^7[/tex].
The expression cannot solve further.
Hence, the given expression is in the simplest form.
D.[tex]a^{-9}[/tex]
The expression cannot solve further.
The given expression is in the simplest form.
E.[tex]\frac{1}{a^2}+b^2[/tex]
The expression cannot solve further.
Hence, the given expression is in the simplest form.
F.[tex]\frac{1}{b^5}[/tex]
The expression cannot solve further.
Hence, the given expression is in the simplest form.
Hence, all options are true.
The concession stand at the local high school sells pretzels and lemonade. The total cost of two pretzels and a lemonade is $5.75. The total cost of two lemonades is $0.25 more than the cost of a pretzel. What is the cost of a pretzel?
Answer:
$2.25
Step-by-step explanation:
>givens:
2 pretzels + 1 lemonade = $5.75
2 lemonades = 1 pretzel + $0.25
>find from the first equation how much is 1 lemonade
2 pretzels + 1 lemonade = $5.75, subtract 2 pretzels from both sides
1 lemonade = 5.75 -2 pretzels
>substitute in the second equation 2 lemonades with 2(5.75-2 pretzels)
2 lemonades = 1 pretzel + $0.25
2(5.75-2 pretzels) = 1 pretzel + $0.25, distribute 2 in parentheses
11.5 -4 pretzels = 1 pretzel +0.25, isolate like terms
11.5-0.25 = 1+4 pretzels, combine like terms
11.25 = 5 pretzels, divide both sides by 5
1 pretzel = $2.25
*you can use the letter "p" for pretzel and "l" for lemonade to make the equations more concise
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the systems of equations to their solutions.
[tex]x = 2 \\ y = 7[/tex]
is the answer to:
[tex]y = 11 - 2x \\ 4x - 3y = - 13[/tex]
_________________________________________
[tex]x = 5 \\ y = 2[/tex]
is the answer to:
[tex]2x + y = 12 \\ x = 9 - 2y[/tex]
_________________________________________
[tex]x = 3 \\ y = 5[/tex]
is the answer to:
[tex]2x + y = 11 \\ x - 2y = - 7[/tex]
_________________________________________
[tex]x = 7 \\ y = 3[/tex]
is the answer to:
[tex]x + 3y = 16 \\ 2x - y = 11[/tex]
[tex]frac{12(x+y)^{3} }{9(x+y)}[/tex]
he area of a rectangle is 44m , and the length of the rectangle is less than twice the width. Find the dimensions of the rectangle.
Answer:
4m x 11m
Step-by-step explanation:
4 is your width. 11 is your length.
4 x 4=16 > 11