Hello!
x² + 6x + 1 = 0 <=>
<=> x = -6±√6²-4×1×1/2×1 <=>
<=> x = -6±√36-4/2 <=>
<=> x = -6±√32/2 <=>
<=> x = -6±2²√2/2 <=>
<=> x = -6±4√2/2 <=>
<=> x = -6+4√2/2 <=>
and
<=> x = -6-4√2/2 <=>
<=> x = -3+2√2 <=>
and
<=> x = -3-2√2 <=>
x1 = -3-2√2 and x2 = -3+2√2
Good luck! :)
Write each as a decimal round to the thousands place 44%
Answer:
44 as a decimal is 0.44 and you can multiply 0.44 by a number to get 44 percent of that number.
Solve the equation below:
5x – 11 = 19
x = 4
x = 6
x = 4.4
x = 1.6
pls answer i need help today
Answer:
x=6
Step-by-step explanation:
5x - 11 = 19
5x = 30
x = 6
20characters
5x = 19+11 5x = 30 x = 30/5 x = 6
11. What is 6:12 in simplest form?
A. 2:1
B. 1:2
C. 12:6
D.2
Find a formula for the given polynomial.
In this question, we have to identify the zeros of the polynomial, along with a point, and then we get that the formula for the polynomial is:
[tex]p(x) = -0.5(x^3 - x^2 + 6x)[/tex]
------------------------
Equation of a polynomial, according to it's zeros:
Given a polynomial f(x), this polynomial has roots such that it can be written as: , in which a is the leading coefficient.
------------------------
Identifying the zeros:
Given the graph, the zeros are the points where the graph crosses the x-axis. In this question, they are:
[tex]x_1 = -2, x_2 = 0, x_3 = 3[/tex]
Thus
[tex]p(x) = a(x - x_{1})(x - x_{2})(x-x_3)[/tex]
[tex]p(x) = a(x - (-2))(x - 0)(x-3)[/tex]
[tex]p(x) = ax(x+2)(x-3)[/tex]
[tex]p(x) = ax(x^2 - x + 6)[/tex]
[tex]p(x) = a(x^3 - x^2 + 6x)[/tex]
------------------------
Leading coefficient:
Passes through point (2,-8), that is, when [tex]x = 2, y = -8[/tex], which is used to find a. So
[tex]p(x) = a(x^3 - x^2 + 6x)[/tex]
[tex]-8 = a(2^3 - 2^2 + 6*2)[/tex]
[tex]16a = -8[/tex]
[tex]a = -\frac{8}{16} = -0.5[/tex]
------------------------
Considering the zeros and the leading coefficient, the formula is:
[tex]p(x) = -0.5(x^3 - x^2 + 6x)[/tex]
A similar problem is found at https://brainly.com/question/16078990
The formula that represents the polynomial in the figure is [tex]p(x) = x^{3}-x^{2}-6\cdot x[/tex].
Based on the Fundamental Theorem of Algebra, we understand that Polynomials with real Coefficient have at least one real Root and at most a number of Roots equal to its Grade. The Grade is the maximum exponent that Polynomial has and root is a point such that [tex]p(x) = 0[/tex]. By Algebra we understand that polynomial can be represented in this manner known as Factorized form:
[tex]p(x) = \Pi\limits_{i=0}^{n} (x-r_i)[/tex] (1)
Where:
[tex]n[/tex] - Grade of the polynomial.
[tex]i[/tex] - Index of the root binomial.
[tex]x[/tex] - Independent variable.
We notice that polynomials has three roots in [tex]x = -2[/tex], [tex]x = 0[/tex] and [tex]x = 3[/tex], having the following construction:
[tex]p(x) =(x+2)\cdot x \cdot (x-3)[/tex]
[tex]p(x) = (x^{2}+2\cdot x)\cdot (x-3)[/tex]
[tex]p(x) = x^{3}+2\cdot x^{2}-3\cdot x^{2}-6\cdot x[/tex]
[tex]p(x) = x^{3}-x^{2}-6\cdot x[/tex]
The formula that represents the polynomial in the figure is [tex]p(x) = x^{3}-x^{2}-6\cdot x[/tex].
Here is a question related to the determination polynomials: https://brainly.com/question/10241002
prove that tan² theta + cot² theta = sec² theta cosec² theta- 2
Step-by-step explanation:
Tan² theta = sec² theta - 1
Cot² theta = cosec² theta - 1
Tan²+Cot² = sec²-1+cosec²-1
= sec²+cosec²-2
Please find attached herewith the solution of your question.
If you have any doubt, please comment.
if f(n) = 6-2n, find f(-1)
Answer:
8
Step-by-step explanation:
f(n)= 6-2n
f(-1) = 6- 2(-1)
= 6+2
=8
Find the equation of the tangent line at the point (0,1) of the graph of the function f(x) = x^3 - 2x + 1 ?
9514 1404 393
Answer:
y = -2x +1
Step-by-step explanation:
The derivative of the function is ...
f'(x) = 3x^2 -2
so the slope at x=0 is f'(0) = -2. In slope-intercept form, the equation of the tangent line is ...
y = -2x +1
The expression 2(l + w) is used to calculate the perimeter of a rectangle, where l is length and w is width. If the length is Fraction 2 over 5 unit and the width is Fraction 1 over 5 unit, what is the perimeter of the rectangle in units?
Fraction 3 over 5 unit
1 unit
1Fraction 1 over 5 units
2Fraction 3 over 5 units
Answer:
Step-by-step explanation:
L = ⅖ unit
W = ⅕ unit
L+W = ⅗ unit
Perimeter = 2×⅗ = 6/5 units = 1⅕ units
Answer:
L = ⅖ unit
W = ⅕ unit
L+W = ⅗ unit
Perimeter = 2×⅗ = 6/5 units = 1⅕ units
Step-by-step explanation:
Solve the given differential equation by using an appropriate substitution. The DE is of the form dy/dx = f(Ax + By + C), which is given in (5) of Section 2.5. dy/dx = 4 + (y − 4x + 6)^1/2
dy/dx = 4 + √(y - 4x + 6)
Make a substitution of v(x) = y(x) - 4x + 6, so that dv/dx = dy/dx - 4. Then the DE becomes
dv/dx + 4 = 4 + √v
dv/dx = √v
which is separable as
dv/√v = dx
Integrating both sides gives
2√v = x + C
Get the solution back in terms of y :
2√(y - 4x + 6) = x + C
You can go on to solve for y explicitly if you want.
√(y - 4x + 6) = x/2 + C
y - 4x + 6 = (x/2 + C )²
y = 4x - 6 + (x/2 + C )²
A clothing manufacturer purchased 50 yd of cotton and 80 yd of wool for a total cost of $1,330. Another purchase, at the same prices, included 75 yd of cotton and 20 yd of wool for a total cost of $895. Find the cost per yard of the cotton and of the wool.
Answer:
The cotton is $9 per yard and the wool is $11 per yard
Step-by-step explanation:
Create a system of equations where c is the cost per yard for the cotton and w is the cost per yard for the wool.
50c + 80w = 1330
75c + 20w = 895
Solve by elimination by multiplying the bottom equation by -4:
50c + 80w = 1330
-300c - 80w = -3580
Add these together and solve for c:
-250c = -2250
c = 9
Plug in 9 as c into one of the equations, and solve for w:
50c + 80w = 1330
50(9) + 80w = 1330
450 + 80w = 1330
80w = 880
w = 11
The cotton is $9 per yard and the wool is $11 per yard.
The quadrilaterals JKLM and PQRS are similar. Find the length x of SP
Answer:
4.8
Step-by-step explanation:
The scale factor is (3.6)/3=1.2. Hence x/4=1.2, x=4.8
consider a study conducted to determine the average protein intake among an adult population. Suppose that a confidence level of 85% is required with an interval about 10 units wide. if a preliminary data indicates a standard deviation of 20g, what sample of adults should be selected for the study?
Answer:
made up of about 20 common amino acids. The proportion of these amino acids varies as a characteristic of a given protein, but all food proteins—with the exception of gelatin—contain some of each. Amino nitrogen accounts for approximately 16% of the weight of proteins. Amino acids are required for the synthesis of body protein and other important nitrogen-containing compounds, such as creatine, peptide hormones, and some neurotransmitters. Although allowances are expressed as protein, a the biological requirement is for amino acids.
Proteins and other nitrogenous compounds are being degraded and resynthesized continuously. Several times more protein is turned over daily within the body than is ordinarily consumed, indicating that reutilization of amino acids is a major feature of the economy of protein metabolism. This process of recapture is not completely efficient, and some amino acids are lost by oxidative catabolism. Metabolic products of amino acids (urea, creatinine, uric acid, and other nitrogenous products) are excreted in the urine; nitrogen is also lost in feces, sweat, and other body secretions and in sloughed skin, hair, and nails. A continuous supply of dietary amino acids is required to replace these losses, even after growth has ceased.
Amino acids consumed in excess of the amounts needed for the synthesis of nitrogenous tissue constituents are not stored but are degraded; the nitrogen is excreted as urea, and the keto acids left after removal of the amino groups are either utilized directly as sources of energy or are converted to carbohydrate or fat.
write two properties of Zero
Answer:
the addition properties of zero and multiplication properties of zero
zero is even, not odd not neutral.
zero is neither positive or negative.
A cupboard costing Rs.16800 is depreciated at the rate of 15% per year. What will be the cost of the cupboard after 2 years.
Answer:
Rs. 11132
Step-by-step explanation:
formula for depriciation= P(1-R/100)^T
p= principal, r=rate, t=time
Answer:
15162
Step-by-step explanation:
after 1 year= 16800*95%= 15960
after 2 year= 15960*95%= 15162
Solve this equation for x. Round your answer to the nearest hundredth.
8 = In(x + 3)
Answer:
2977.96 =x
Step-by-step explanation:
8 = In(x + 3)
Raise each side to the base of e
e^8 = e^ ln(x+3)
e^8 = x+3
Subtract 3 from each side
e^8 -3 = x+3-3
e^8 -3= x
2977.95798 = x
Rounding to the nearest hundredth
2977.96 =x
Answer:
[tex]\displaystyle x = 2977.96[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra II
Natural logarithms ln and Euler's number eStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle 8 = ln(x + 3)[/tex]
Step 2: Solve for x
[Equality Properties] e both sides: [tex]\displaystyle e^8 = e^{ln(x + 3)}[/tex]Simplify: [tex]\displaystyle x + 3 = e^8[/tex][Equality Property] Subtract 3 on both sides: [tex]\displaystyle x = e^8 - 3[/tex]Evaluate: [tex]\displaystyle x = 2977.96[/tex]so sánh 198*202 và 200^2
Step-by-step explanation:
198×202=39,996
200×200=40,000
hence,
39,9996 < 40,000
hope it helps
Subtract.
7x2 - 5x+3
(2x² + 7x-4)
Answer:
7×=14
5×3=15
5+3=8
7×4=28
7-4=3
2×2=4
if add this all will get the answer as 72
if we will subtraction answer will be as -44
Step-by-step explanation:
so we will get the answer asaddition = 72
subtraction= -44
so this is the answerplease give me points
Find the measure of the missing angles.
Answer:
e- 77
d- 52
f- 51
Step-by-step explanation:
Step-by-step explanation:
d=52° (,vertically opposite angle)
77+52+f=180 (linear pair)
f=180- 129
f=51°
52+51+e=180
e=180- 103
e=77°
Please help! There is 2 questions in this pic! Thank you so much to whoever helps me
Answer:
[tex]{ \sf{thats \: it}}[/tex]
A restaurant is doing a special on burgers. If the home team get a sack, the next day, burgers will cost$1.00
Normally, they cost $3,99. If every fan who attended the game (86,047 people) buys a $1.00 burger, how much
money did the restaurant lose with this discount?
3.99-1 = 2.99 they lose 2.99 per burger
Multiply the number of people by the amount lost per burger:
2.99 x 86,047 = 257,280.53
They would lose: $257,280.53
Answer:
86043.01
Step-by-step explanation:
According to the U.S. National Center for Health Statistics, there is a 98% probability that a
20-year-old male will survive to age 30.
(a) Using statistical software, simulate taking 100 random samples of size 30 from this
population.
(b) Using the results of the simulation, compute the probability that exactly 29 of the 30 males
survive to age 30.
(c) Compute the probability that exactly 29 of the 30 males survive to age 30, using the
binomial probability distribution.
(d) Using the results of the simulation, compute the probability that at most 27 of the 30 males
survive to age 30.
(e) Compute the probability that at most 27 of the 30 males survive to age 30 using the
binomial probability distribution.
(f) Compute the mean number of male survivors in the 100 simulations of the probability
experiment. Is it close to the expected value?
(g) Compute the standard deviation of the number of
male survivors in the 100 simulations of the probability experiment. Compare the result to the
theoretical standard deviation of the probability distribution
Answer:
0.03398 or 3.398%
Step-by-step explanation:
-This is a binomial probability problem.
-Given p=0.24, n=100, the probability that exactly 30 people is calculated as:
Hence, the probability that exactly 30 people have hypertension is 0.03398
Find the sum of the arithmetic series given ai = 45, an = 85, and n = 5.
Answer:
C. 325.
Step-by-step explanation:
The last term a5 = 85
a1 = 45
Sum of n terms = n/2 (a1 + l)
So here we have n = 5, a1 = 45 and the last term l = 85
= (5/2)(45 + 85)
= 5/2 * 130
= 325.
The required sum of the arithmetic series is 325.
Arithmetic series is defined as a sequence of numbers arranged in a particular pattern.
The sum of the nth term of an arithmetic sequence is expressed as:
[tex]S_n = \frac{n}{2}[a+l]\\[/tex] where:
n is the number of terms
a is the first term
l is the last term
Given the following
a = 45
n = 5
an = l = 85
Substitute the given values in the formula above:
[tex]S_5= \frac{5}{2}(45+85)\\ S_5=\frac{5}{2}(130)\\ S_5=5 \times 65\\S_5=325[/tex]
Hence the sum of the arithmetic series is 325
Learn more here: https://brainly.com/question/21473794
Find the slope and the y-intercept of the line with the given equation.
f(x) = 7 -4/5x
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The slope is
(Type an integer or a simplified fraction.)
B. The slope is undefined.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The y-intercept is
(Simplify your answer. Type an ordered pair, using integers or fractions.)
B. There is no y-intercept.
Answer:
The slope is -4/5
The y intercept is (0,7)
Step-by-step explanation:
f(x) = 7 -4/5x
Rewriting
y = -4/5x +7
This is in slope intercept form
y = mx+b where m is the slope and x is the y intercept
The slope is -4/5
The y intercept is (0,7)
Solve for X
(Ignore the math I did on top)
The lin 2x - 3y = 4 does not passes through the point :
A) (1/2,-1)
B) (2,0)
C) (1, -2/3)
D) (2,-1)
I would really appreciate it if some helps me with this question!
Answer:
The choose D (2, –1)
2x-3y=4 —> 3y=2X-4 —> y= 2/3x – 4/3
y=mx+b —> So ; m= 2/3 , b= - 4/3
y-intercept :(0, -4/3)
0=2/3x –4/3 —> 2/3x = 4/3 —> X=2
x-intercept ; (2,0)
By drawing a straight line from point 2 on the x-axis and point -4/3 on the y-axis, the points that are on the axis have been extracted, but the point (2,-1) is not on the axis . :)
I hope it helped you ^_^
HELP !
Find the measure it the given angle.
Answer:
it's 90
Step-by-step explanation:
inscribed angle intercepts a semicircle is always 90
What is the vertex of the graph of this function
y= -(x+2) (x+4)
Answer:
y=-(x+2)(x+4)
y=-(x^2+4x+2x+8)
y=-(x^2+6x+8)
y=-(x^2+4x+2x+8)
Y=-x(x+4)+2(x+4)
y=-(x+2)(X+4)
So vertex is (2,4)
Curtis purchased a bicycle on credit. When he received his credit card statement, he noticed several charges he did not make. What should he do?
Answer: He should call the card card company and discuss the charges and make it known that he did not make those charges. He should address each charge by the amount shown. Once he has finished, the credit card company will call the company that sent in the request for payment and inform the company there are questions about the charges and request that the charges be removed.
.
Step-by-step explanation:
11. What is the reciprocal of 6/5?
OA. 12/20
OB.11/5
OC.1
OD.576
Answer: The answer is D, 5/6.
Step-by-step explanation: The reciprocal of a fraction is that fraction but the numerator and denominater swapped places.
Answer:
5/6
Step-by-step explanation:
The reciprocal is where you flip the fraction
6/5 -> reciprocal -> 5/6
I'm not sure about your answer choices tho, sorry
Plz help me find side x and y thanks
Answer:
2sqrt3
Step-by-step explanation:
Since this seems to be a 45, 45, 90 triangle, x and y are the same.
The hypoteneuse is always the side lengths *sqrt2
We divide the hypoteneuse by sqrt 2 and get sqrt12
sqrt12 simplified is 2sqrt3
