The values of x that would result in the given expression being equal to 0 is -2, 6
Finding the solution to quadratic functionsGiven the following expression
f(x) = (x-6)(x+2)
If the function f(x) = 0, then;
(x-6)(x+2) = 0
x - 6 = 0 and x + 2 = 0
Determine the value of x
x = 6 and x = -2
Hence the values of x that would result in the given expression being equal to 0 is -2, 6
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Using Newton-Raphson method to find the approximate root of the equation x log_{10}x=1.2
( Carry out three iterations ). [tex] \\ \\ [/tex]
Thank uh!
Answer:
[tex]x \approx 2.740646096[/tex]
Step-by-step explanation:
Given:
[tex]x\log_{10}x=1.2[/tex]
Rewrite so that it's equal to zero:
[tex]\implies x\log_{10}x-1.2=0[/tex]
Therefore:
[tex]\implies f(x)=x\log_{10}(x)-1.2[/tex]
Differentiate the function:
Use the product rule to differentiate [tex]x\log_{10}(x)[/tex]:
[tex]\textsf{Let }u=x \implies \dfrac{du}{dx}=1[/tex]
[tex]\textsf{Let }v=\log_{10}(x) \implies \dfrac{dv}{dx}=\dfrac{1}{x \ln 10}[/tex]
[tex]\begin{aligned}\implies \dfrac{dy}{dx} & = u\dfrac{dv}{dx}+v \dfrac{du}{dx}\\& = \dfrac{x}{x \ln 10}+\log_{10}(x)\\& = \dfrac{1}{\ln 10}+\log_{10}(x)\end{aligned}[/tex]
[tex]\implies f'(x)=\dfrac{1}{\ln 10}+\log_{10}(x)[/tex]
[tex]\implies f'(x)=\dfrac{1+\ln 10 \log_{10}(x)}{\ln 10}[/tex]
Newton-Rhapson iteration formula
[tex]x_{n+1}=x_n-\dfrac{f(x_n)}{f'(x_n)}[/tex]
Substitute the function and its derivative into the formula, replacing x with [tex]x_n[/tex]:
[tex]\implies x_{n+1}=x_n-\dfrac{x_n\log_{10}(x_n)-1.2}{\dfrac{1+\ln 10 \log_{10}(x)}{\ln 10}}[/tex]
[tex]\implies x_{n+1}=x_n-\dfrac{x_n\ln 10\log_{10}(x_n)-1.2\ln 10}{1+\ln 10 \log_{10}(x_n)}[/tex]
Therefore, the iteration formula is:
[tex]x_{n+1}=x_n-\dfrac{x_n\ln 10\log_{10}(x_n)-1.2\ln 10}{1+\ln 10 \log_{10}(x_n)}[/tex]
Let [tex]x_0=3[/tex]
Substitute this into the formula and carry out 3 iterations:
[tex]\implies x_{1}=3-\dfrac{3\ln 10\log_{10}(3)-1.2\ln 10}{1+\ln 10 \log_{10}(3)}=2.746149035[/tex]
[tex]\implies x_2=2.740648841[/tex]
[tex]\implies x_3= 2.740646096[/tex]
The scatter plot shows the number of households, in millions, that have cable television over eight consecutive years. Which of the following is an appropriate line of best fit?
The equation of the appropriate line of best fit is y = 1.25x + 2
How to determine the line of best fit?Start by drawing a line through the points (see attachment)
From the attached graph, we have:
(x, y) = (0,2) and (4,6.5)
Calculate the slope (m) using:
m = (y2 - y1)/(x2 - x1)
This gives
m = (6.5 - 4)/(2 - 0)
Evaluate
m = 1.25
The equation is then calculated as:
y = m(x - x1) + y1
This gives
y = 1.25(x - 0) + 2
Expand
y = 1.25x + 2
Hence, the equation of the appropriate line of best fit is y = 1.25x + 2
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Please help fast!!
Multiply and reduce to lowest terms. Convert into a mixed number if necessary.
[tex]3 \times \frac{2}{5} [/tex]
Answer:
[tex]1\frac{1}{5}[/tex]
Step-by-step explanation:
3 = 3/1
(multiply top and bottom separately for fractions)
[tex]\frac{3}{1}[/tex] × [tex]\frac{2}{5}[/tex] = [tex]\frac{6}{5}[/tex]
[tex]\frac{6}{5} = \frac{5}{5}+\frac{1}{5}= 1\frac{1}{5}[/tex]
Answer:
1 1/5Step-by-step explanation:
3×2/5multiplying three (3) and two(2) and express the product of three and two over five.
6/5five can enter in six three times , remainder 1
The fraction in lowest terms is one whole number , one over five.
1 1/5John bought 8 watches for $56 and his friend victor bought 7 watches for $63. whose watch is expensive ?
A bike store rents bikes for $9 an hour in addition to a helmet rental fee of $15. If
Emmanuel paid $51, for how many hours did he rent the bike?
Answer:
4 hours
Step-by-step explanation:
First we need to subtract the one pay fee (the helmet rental fee, $15)
So 51 - 15 = 36
Then we need to divide 36 by the amount of money it costs for each hours to find how many hours he rented the bike
So 39/9 = 4
If 5 hours at a computer terminal costs $25, what is the cost of 6 hours?
A. $30
B. $45
C. $150
D. $12
Answer:
30 dollars
Step-by-step explanation:
25/5 = 5 dollars per hour
so 6 hours would be 5 * 6 = 30 dollars
Answer:
It would be B
Step-by-step explanation:
First, we need to find out the unit rate
5/25=1/5
Therefore, that means in one hour the cost would be $5
Since you are going from one hour to 6 hours you need to multiply both numbers by 6
Since 5x6=30, it would be 30$ :)
4
12 + 17 < -18 *
True
False
Which graph shows h(x) = f(x)g(x)
The attached graph represents the function h(x), where h(x) = f(x)g(x)
Complete questionConsider the functions f(x) = x - 6 and g(x) = x + 6. Which graph shows h(x) = f(x)g(x)?
How to determine the graph of h(x)?We have
f(x) = x - 6
g(x) = x + 6
The equation h(x) = f(x)g(x) means
h(x) = f(x) * g(x)
So, we have:
h(x) = (x - 6) * (x + 6)
Expand
h(x) = x² - 36
See attachment for the graph of function h(x)
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Answer:
A on edg. 2020
Step-by-step explanation:
Which graph shows h(x) = f(x)/g(x)
Which of the following terms is defined as 1/sin?
Answer: cosecant
Formula's are:
Secant:
1/cos(x) = sec(x)
Cosecant:
1/sin(x) = cosec(x)
Cotangent:
1/tan(x) = cos(x)/sin(x) = cot(x)
MARKING BRAINLIEST TO THE FIRST CORRECT ANSWER If triangle BCD was reflected over the x-axis, what would be the coordinates of the new triangle's vertices?
If BCD was reflected over the x axis then the coordinates will be B(-1,0) C(-1,2) and D(-4,1).
Given BCD is a triangle having coordinates (-1,0),(-1,-2),(-4,-1).
When the triangle is reflected over the x axis then all the values of y will change from negative to positive and the values of x remains same because in the second and third quadrant the values of x remains same and in the second quadrant the values of y used to be positive and in the third quadrant the values of y used to be negative.
So coordinates of B will change from (-1,0) to (-1,0)
coordinates of C will change from (-1,-2) to (-1,2)
coordinates of D will change from (-4,-1) to (-4,1)
New coordinates will be (-1,0) (-1,2) (-4,1).
Hence if BCD was reflected over x axis the new coordinates will be (-1,0) (-1,2) (-4,1).
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MARKING BRAINLIEST TO FIRST CORRECT ANSWER If quadrilateral JKLM had a translation where all the vertices were in the third quadrant, what would be the coordinates of the vertices?
If quadrilateral JKLM were in third quadrant then the coordinates will be (-1,0),(-4,-1),(-4,-2)(-1,-2)
Given Quadrilateral JKLM is in fourth quadrant and coordinates (1,0),(4,-1),(4,-2)(1,-2)
We know that the coordinates of x used to negative in third quadrant and positive in fourth quadrant. Coordinates of y used to negative in third and fourth quadrant.
So in order to change the coordinates from fourth to third we need to change the coordinates of x axis to negative and the coordinates will be :
Coordinates of J will change from (1,0) to (-1,0)
Coordinates of K will change from(4,-1) to (-4,-1)
Coordinates of L will change from (4,-2) to (-4,-2)
Coordinates of M will change from (1,-2) to (-1,-2).
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Determine the values for the pronumerals that make the following piece-wise functions continuous. (I really need help please).
Step-by-step explanation:
A function is continuous at x is
Limit as x approaches c= f(c).
Step 1: Find f(4).
4 is defined for 2x-1 so plug in. 4 for x.
[tex]2(4) - 1 = 7[/tex]
Note that what we just calculated was not only f(4) but also the left sided limit of f(x).
Step 2: Make sure the left sided and right sided limit are equal to 7.
[tex]a + 5x = 7[/tex]
Plug in 4 for x
[tex]a + 5(4) = 7[/tex]
[tex]a = - 13[/tex]
find x ratio y... help please, i have a test tomorrow.
thanks
Answer:
27/4
Step-by-step explanation:
added in the picture
Find the distance between -6.77777 and 3.55555.
O 10.3
O 10.33332
O 10.3333332
13.33332
Answer:
10.33332
Step-by-step explanation:
-6.77777 is 6.77777 units away from 0. So there's 6.77777+3.55555 which is 3.55555 units away from 0.
Add those two numbers together and it's 10.33332
Answer:
10.33332
Step-by-step explanation:
distance between -6.77777 and 3.55555 is 10.33332
p=f/a, where f=70 and a=20 f is increased by 10 a is increased to by 10
Answer:
P=3.5
P=2.667
Step-by-step explanation:
p=f/a
P=70/20
P=3.5
then f is increased by 10
f=70+10=80
and a is increased by 10
a=20+10
a=30
therefore; P=f/a
P=80/30
P=2.667
Teresa is factoring this polynomial by grouping. Which common factors should be used in the next step of factoring?
10x3+3x2−20x−6
(10x3+3x2)+(−20x−6)
x2 and −2x
2x2 and −2x
x2 and −2
2x2 and −2
Answer: [tex]x^2[/tex] and [tex]-2[/tex]
Step-by-step explanation:
original :
[tex](10x^3+3x^2)+(-20x-6)[/tex]
factored :
[tex]x^2(10x+3)+-2(10x+3)[/tex]
Answer :
[tex]x^2[/tex] and [tex]-2[/tex]
w and x are whole numbers
w>60
x<50
Work out the smallest possible value of x-z
Using the given information, the smallest possible value of x - z is 12
Evaluating an expressionFrom the question, we are to determine the smallest possible value of x - z
From the given information,
w and x are whole numbers
and
w > 60
x < 50
∴ w = 61, 62, 63, 63, 65, ...
x = 49, 48, 47, 46, 45, ...
Then,
The smallest possible value of x - z is
x - z = 61 - 49
x - z = 12
Hence, the smallest possible value of x - z is 12
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A ship is stationary at sea.
A tugboat is 36 km away at a bearing of 130°, and a yacht is 27 km from the tugboat at a bearing of 260°.
Draw a scale diagram showing the positions of the three vessels.
Use a scale of 1 : 450,000.
Measure the distance from the ship to the yacht to the nearest km.
Bearing is a topic that deals with the distance and location of a given object with respect to a reference point. Thus in the given question, the ship is 57.23 km to the yacht.
Bearing is a topic that considers the distance and position of a given object with respect to a reference point. Thus the angles are usually measured with reference to the north pole.
Thus to solve the given question, let the required distance be represented by x.
Applying the cosine rule, we have;
[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2ab Cos C
The angle C between the line from ship to tugboat and from tugboat to yacht can be determined as;
C = [tex]10^{o}[/tex] + [tex]40^{o}[/tex]
C = [tex]50^{o}[/tex]
Thus,
[tex]c^{2}[/tex] = [tex]36^{2}[/tex] + [tex]27^{2}[/tex] + 2(36 x 27) Cos [tex]50^{o}[/tex]
= 1296 + 729 + 1944(0.6429)
= 2025 + 1249.8
[tex]c^{2}[/tex] = 3274.8
c = [tex]\sqrt{3274.8}[/tex]
= 57.2259
c = 57.23
Therefore, the distance from the ship to the yacht is 57.23 km.
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Kindly contact a 1-on-1 tutor if more explanations are needed.
The product (
[tex](a+b)(a-b) = a^2 - ab + ba - b^2 = a^2 - b^2[/tex]
Since the middle terms cancel each other out, what is left is the difference of two squares.
In your example (x+6)(x-6) = x² -36
Describe the correlation in terms of strength (weak or strong) and direction positive or negative).
The description of the correlation in terms of strength (weak or strong) and direction positive or negative) is as explained below.
How to Interpret Correlation Problems?
A correlation coefficient, is expressed as r and it indicates a measure of the direction and strength of a relationship between two variables.
Now, in terms of strength, Correlation strength ranges from -1 to +1. Thus, The closer the correlation is to 0, the weaker it is while the closer it is to ±1, the stronger it is.
Now, in terms of direction;
A correlation of +1 indicates a perfect positive correlation which tells us that both variables move in the same direction together. A correlation of –1 indicates a perfect negative correlation, which tells us that as one variable goes up, the other goes down.A zero correlation suggests that the correlation statistic does not indicate a relationship between the two variables.Read more about Correlation at; https://brainly.com/question/4219149
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Which function is graphed below?
Answer: The second option, y = 3(1/3)^x
Step-by-step explanation: Input each equation into a graphing calculator (preferably GeoGebra online) and check the answer. I linked the equation, but make sure to check anyway just in case :)
Which is mostly likely to be the first step in solving a system of nonlinear equations by substitution
Answer: To solve a system of equations by substitution, we can rewrite a two-variable equation as a single variable equation by substituting the value of a variable from one equation into the other. Let’s start by solving the system of equations that we looked at above: x=4 x = 4 y+x=12 y +x = 12
Step-by-step explanation:
Answer:
Isolating a variable in one of the equations.
Step-by-step explanation:
Which equation completes the system that is satisfied by the solution (1, 1)?
02x+y = 2
O4x - 2y = 2
02x - 2y = 2
Ox+y = 4
Answer: B. 4x-2y=2
Step-by-step explanation:
We will work this out one by one. Plug in the x and y values of the solution to the equations and you will see which one is true or false.
A. [tex]2(1)+y(1)=2\\2+1\neq 2[/tex] B. [tex]4(1)-2(1)=2\\4-2=2[/tex]
C. [tex]2(1)-2(1)=2\\2-2\neq 2[/tex] D. [tex]x(1)+y(1)=4\\1+1\neq 4[/tex]
With this information, we see that B is the correct answer.
I hope this helped!! Pls mark brainliest!! :))
Need help with this math question (pic included)
Answer:
8
Step-by-step explanation:
If the only zero for this function is at x = - 4 it looks like this:
f(x) = (x+4)(x+4) = x^2 +8x + 16 so j = 8
Answer:
Step-by-step explanation:
x² +jx +k = 0
If there is only one root ( - 4 ), then (x + 4)² = 0
or
x² + 8x + 16 = 0
j = 8 and k = 16
if x=p+2 and y=p-3, show that x+y+1=2p and x-y-5=0
If [tex]x=p+2[/tex] and [tex]y=p-3[/tex], then
[tex]x+y = (p+2) + (p-3) = 2p - 1 \implies x+y+1=2p[/tex]
and
[tex]x-y = (p+2)-(p-3) = 5 \implies x-y-5=0[/tex]
as required.
A similarity transformation maps AABC to AJKL The measure of ZA of prelmage AABC Is 105°. The scale factor of the dilation in the similarity
transformation is 1.5. If ZA In the prelmage corresponds to ZJ in the image, what is m
a 70°
b 140°
c 105°
d 35°
its reserved.
Answer:
The answer is 105.
Step-by-step explanation:
What are the exact solutions of x2 − 3x − 5 = 0? (1 point) a x = the quantity of negative 3 plus or minus the square root of 29 all over 2 b x = the quantity of 3 plus or minus the square root of 29 all over 2 c x = the quantity of 3 plus or minus the square root of 11 all over 2 d x = the quantity of negative 3 plus or minus the square root of 11 all over 2
x = the quantity of 3 plus or minus the square root of 29 all over 2. Then the correct option is B.
What is the solution of the quadratic equation by formula method?The quadratic equation is given as ax² + bx + c = 0.
Then the solution is given as
[tex]\rm x = \dfrac{-b\pm \sqrt{b^2 - 4ac}}{2a}[/tex]
The quadratic equation is given below.
x² – 3x – 5 = 0
Then the solution of the equation will be
[tex]\rm x = \dfrac{-(-3)\pm \sqrt{(-3)^2 - 4 *1*(-5)}}{2*1}\\x = \dfrac{3 \pm \sqrt{29}}{2}[/tex]
Then the correct option is B.
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PLEASE HELP ME WITH THIS
Answer:
Decreases
Step-by-step explanation:
A negative correlation means the y is big when the x is small. As x gets bigger, y gets smaller.
Trey graphs the equations y = –x2 + 2x + 3 and y = x2 – 2x + 3 to solve the equation –x2 + 2x + 3 = x2 – 2x + 3. His graph is shown below.
What are the solution(s) of –x2 + 2x + 3 = x2 – 2x + 3?
The solution of the equation -x^2 + 2x + 3 = x^2 - 2x + 3 are the x-coordinates of common points on the graphs are x=0 and x=2.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
As we can see from the attached graph these graphs intersect at points (0,3) and (2,3).
The system of equation are;
[tex]y = x^2 + 2x + 3 \\y = x^2 - 2x + 3[/tex]
So,
[tex]-x^2 + 2x + 3 = x^2 - 2x + 3 \\\\2x^2 - 4x = 0\\\\2x ( x - 2) = 0[/tex]
Then the solutions of the equation are x=0 and x=2.
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Answer:
0 and 2
Step-by-step explanation:
b on edge
Determine the measure of each indicated angle.
Answer:
∠ABC = 52°
∠BCA = 48°
∠CAB = 80°
Step-by-step explanation:
Angle sum property of triangle: Sum of all the angles of a triangle is 180.
13x² + 12x² + 20x² = 180
Combine like terms,
45x² = 180
x² = 180 ÷ 45
x² = 4
x = √4
x = ± 2
x = 2 ; -2
∠ABC = 13x² = 13*4 = 52°
∠BCA = 12x² = 12 *4 = 48°
∠CAB = 20x² = 20 *4 = 80°
The value of x is +2 and -2 and the angles will be given as ∠ABC = 52 ∠ACB = 48 and ∠CAB = 80.
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
Given that:-
∠ABC = 13x² ∠ACB = 12x² and ∠CAB = 20x²
The angles will be calculated as follows:-
13x² + 12x² + 20x² = 180
45x² = 180
x² = 4
x = ±2
The angles will be:-
∠ABC = 13x² = 13 x ( 2² ) = 52
∠ACB = 12x² = 12 ( 2² ) = 48
∠CAB = 20x² = 20 ( 2² ) = 80
Therefore value of x is +2 and -2 the angles will be given as ∠ABC = 52 ∠ACB = 48 and ∠CAB = 80.
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