b) The graph of y = x2 – 2x + 5 is
drawn on the axes on the left.
Use the graph to estimate the
values of x when y = 6.
Give your answers to 1 decimal
place.
Please Help!!!!
Answers
Answer:
[tex]x = 1+\sqrt{2} = 2.4\\or\\x= 1-\sqrt{2} = -0.4[/tex]
Step-by-step explanation:
[tex]y = x^2-2x+5\\\\6=x^2-2x+5\\\\x^2-2x-1=0\\\\\\\frac{-b+-\sqrt{b^2-4ac} }{2a} = x\\a = 1, b = -2, c = -1\\\\\frac{2+-2\sqrt{2} }{2\\}\\\\x = 1+\sqrt{2} = 2.4\\or\\x= 1-\sqrt{2} = -0.4[/tex]
The value of the x is -0.4 when y = 6 and the graph is drawn on the left.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given:
The quadratic equation,
y = x² – 2x + 5
To find the value of x:
When y = 6.
So,
x² – 2x + 5 = 6
x² – 2x - 1 = 0
Comparing the quadratic equation with standard quadratic equation,
ax²+ bx +c = 0
We get,
a = 1, b = -2 and c = -1
So,
x = {-b ±√(b²-4ac)}/2a
Substituting the values,
x = (2±√8)/2
x = 1 ± √2
x = 2.41421 and x = −0.414214
And the graph is drawn on the left so x = −0.414214 = -0.4 to one decimal place.
Therefore, the value of the x is -0.4.
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Related Questions
Help help help help help
Answers
Answer:
area = 254.5 m²
Step-by-step explanation:
area = πr² = (3.14159)(9²) = 254.46 m²
cheng drew the model below to represent an equation.What value of x makes the equation true?
Answers
Answer:
So what’s the answer?
Step-by-step explanation:
What is the 3 example of quadratic equation?
Answers
The three examples of quadratic equations are x(x - 2) = 4, x(2x + 3) = 12 and 3x(x + 8) = -2
The term quadratic equation also known as quadratic expression referred as an equation containing one term in which the unknown is squared and no term in which it is raised to a power higher than 2.
Here the examples of quadratic equations in other forms is written as follows:
=> x(x - 2) = 4
Here we have to multiply and then moving the 4, then we get the quadratic expression as,
=> x² - 2x - 4 = 0
Another example like the following,
=> x(2x + 3) = 12
Here we have to multiplying and moving the 12, then we get the resulting expression as,
=> 2x² - 3x - 12 = 0
Final example for quadratic expression is written as
=> 3x(x + 8) = -2
When we multiplying and moving the -2, then we get the simplified form as
=> 3x² + 24x + 2 = 0
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The scatter plot shows a hikers elevation above sea level overtime. The equation of the trend line is shown y equals 8.77x plus 686. To the nearest whole number predicted hikers elevation will be at 145 minutes
Answers
The predicted elevation of hikers at 145 minutes, based on the trend line equation, y = 8.77x + 686 is 1,958.
What is a trend line equation?A trend line equation is the equation of a linear relationship, represented as y = mx + b.
In this linear equation, y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept.
Equation:y = 8.77x + 686, where x = 145 minutes
Therefore,
y = 8.77(145) + 686
y = 1,271.65 + 686
y = 1,957.65
y = 1,958
Thus, after 145 minutes of hiking, hikers' elevation will be 1,958 units.
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The four-digit numeral $3AA1$ is divisible by $9$. What digit does $A$ represent?
Answers
The digit A stands for 7 when the four-digit number is divisible by 9 and is given by 3AA1.
Characteristics of numbers that divide by 9A number is divisible by 9 if the sum of its digits is also 9-divisible.
Numbers that are 9 - divisible are also called multiples of 9. Multiples in mathematics are the outcomes of multiplying an integer by a certain number.
Using the aforementioned attribute, we can say
3 + A + A +1 = 9, 18, or 27
4 + 2A = 9, OR 18, OR 27
taking 18
2A = 18 - 4
2A = 14
A = 7
Because of this, the whole digits are 3771
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45 PTS (find:m<3) don’t explain.
Answers
Answer:
142
Step-by-step explanation:
38+x = 180
x = 142
Step-by-step explanation:
Hey, there!
Let's simply solve it.
As there is given that L and M are parallel. Use all
the condition or properties of parallel lines.
Here use:
vertically opposite angle.
coointerior angles sum is 180°.
Now,
angle 6= 38° { Vertically opposite angle}. angle 6+ angle 5 = 180° { as sum of coointerior angles are equal to 180°}
38°+angle 5 = 180° or, angke 5 = 180°-38°
Therefore, angle 5 = 142°
Now, angle 3 = angle 5 { Vertically opposite angle} Therefore, the measure of angle 3 is 142°. hope it helps...
What are the roots of the equation 2x^2 3x 5 0?
Answers
The roots of the equation 2x² - 3x - 5 = 0 are 5/2 and -1.
The quadratic formula is a formula that can be used to find the solutions (or roots) of a quadratic equation. For a quadratic equation written in the form ax² + bx + c = 0, where a, b, and c are constants, the quadratic formula is given by:
x = (-b ± √(b²- 4ac))/(2a)
Where x is the solution, a, b, and c are the coefficients of the equation.
Plug in the coefficients of the equation 2x² - 3x - 5 = 0 to the quadratic formula to find the roots.
x = (-b ± √(b²- 4ac))/(2a)
x = (3 ± √((-3)²- 4(2)(-5)))/(2)(2)
x = (3 ± 7)/4
x = 5/2 ; x = -1
Hence, the roots of the equation are 5/2 and -1.
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Write mathematical sentence of X→ a.
Answers
Answer:
X tends to a or x approaches to a .
7. $5,000 was invested at a simple interest
rate. In 15 years, the account was worth
65 hundred dollars. What was the interest
rate?
A 0.2%
B 1.5%
C 2%
D 2.15%
Answers
Answer:
C. 2%
Step-by-step explanation:
(6500-5000) / 15 / 5000 x 100% = 1500 / 15 / 5000 x 100% = 100 / 5000 x 100% = 0.02 x 100% = 2%
Given: (↔AB) ║ (↔CD)
If the coordinates of point A are (8 , 0) and the coordinates of point B are (3 , 7), the y-intercept of (↔AB) is (?) . If the coordinates of point D are (5 , 5), the equation of line (↔CD) is y =(?) x +(?).
can someone please help me figure out what the (?) is.
Answers
y = mx + b
m = 7 - 0/3 - 8
y = -7/5x + 11.2
2) y= -7/5x + 12
(the slope or m stays the same because the two equations are parallel)
Answer:
1. 56/5
2. -7/5
3. 12
Step-by-step explanation:
3x + 8 = 3x
x=________________
Answers
Answer:
No Solutions
Step-by-step explanation:
3x + 8 = 3x
*subtract 3x from each side*
3x - 3x = 0
3x - 3x cancels out
we're left with 8 = 0
Hence there are no solutions to the problem
Answer:
0=-8
Step-by-step explanation:
3x+8=3x
-8. -8
3x=3x-8
-3x -3x
0= -8
At the gift shop entrance, fans go
through security at a rate of 15 people in
25 seconds. At that rate, approximately
how many people will go through security
in 135 seconds?
Answers
n 2010, the population of a small town in Alabama was 8,250 people. By 2015, the population had decreased by 10%. From 2015, to 2020, the population then increased by 15%. What was the population of the town in 2020
Answers
The population of a city is increasing at a rate of 4% each year. In 2020, there were. 236,000 people in the city.
What is population?A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic. In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped by a common feature can be said to be a population.A sample may also refer to a statistically significant portion of a population, not an entire population. For this reason, a statistical analysis of a sample must report the approximate standard deviation, or standard error, of its results from the entire population. Only an analysis of an entire population would have no standard error.Given, In 2015, the population of the town decreased by 10%, so [tex]8250 x 10/100 = 825[/tex] people left the town, bringing the population down to [tex]8250 - 825 = 7425.[/tex]
From 2015 to 2020, the population increased by 15% so [tex]7425 x 15/100 = 1113.75[/tex] people came back to the town, bringing the population to [tex]7425+1113.75 = 8538.75[/tex]
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Use the Zero Product Property to find the x-intercepts (roots) of the following quadratic equations. You MUST show all work for full credit!
a. `y=(2x+7)(x-13)
Answers
Answer:
x=-7/2, x=13
Step-by-step explanation:
2x+7=0
2x=-7
x=-7/2
x-13=0
x=13
What are the terms of expression 4x² 3xy?
Answers
The given expression , 4x2 – 3xy is having two terms which are 4x2 and –3xy.
The term 4x2 is a product of 4 and x, whereas the other term (–3xy) is a product of (–3), x and y.
When we will join these two terms using the addition operation we will get the result as 4x2 – 3xy .
The given equation is an example of an algebraic expression and they are made up of combination of constants and variables. They are joined to each other by various operations such as addition , multiplication , division and subtraction.
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Solve = 3/5k + 7/10 = 11/15k – 2/5
Answers
i get 11/2 is this wright answer??
The rate of growth dP / dt of a population of bacteria is proportional to the square root of t, where P is the population size and t is the time in days (0 ? t ? 10) as shown below.
dP/dt=k \sqrt{t}
The initial size of the population is 300. After 1 day the population has grown to 600. Estimate the population after 8 days. (Round your answer to the nearest whole number.)
Answers
The population of bacteria after 8 days is 7088
Here, we have been given an equation for the rate of growth of a population of bacteria
dP/dt = k√t
where P is the population size
and t is the time in days (0 ≤ t ≤ 10)
We rewrite above equation as,
dP = k√t dt
Integrating both sides, we get,
P = (2/3) × kt^(3/2) + C
We find the value of C.
For t = 0, P = 300 as the initial size of the population is 300.
Substitute t = 0 in above equation.
300 = 0 + C
C = 300
So, the above equation becomes,
P = 300 + (2/3) × kt^(3/2) .......(1)
Now we find the value of k.
After 1 day the population has grown to 600.
substitute t = 1, P = 600 in equation (1)
600 = 300 + (2/3) × k
(2/3)k = 300
k = 900/2
k = 450
So, the equation of population of bacteria after time t is:
P = 300 + [(2/3) × 450 × t^(3/2)]
P = 300 + 300 × t^(3/2)
P = 300 (1 + t^(3/2))
To find the population after 8 days, substitute t = 8
P = 300 (1 + 8^(3/2))
P = 7088.22
P ≈ 7088
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Alex conducted an experiment with a spinner. He recorded the frequency of each spin landing on letters A through D. Based on the data in the table, what is the experiment probability that the next spin will land on the letter B ?
Answers
For example you reach into a bag of 10 marbles 4 are blue and 6 are red what is the probability of getting a blue marble? Easy 4/10 cause there’s only 4
HELPPPPPP PLEASEeeeeeeeeeeeeee
Answers
it is this answer x≥
3
8
I don't know the step by step solution
is the following table Proportional or Non proportional?
HELP PLS:(
Answers
Answer: proportional
Step-by-step explanation: I took the test and looked it up on 3 different websites like duh
Write 63 521. 769 correct to the nearest hundred
Answers
HURRY WILL GIVE BRAINLIEST Maria lives at the corner of 3rd Avenue and 5th Street. Pierre lives at the corner of 9th Avenue and 14th Street. They decide to leave their houses and meet at the library located 13of the distance from Maria's apartment. In their city, avenues run eastto west and streets run north to south. If each street and avenue is spaced 1 unit apart, at what intersection will Pierre and Maria meet?
Answers
Answer:
5th Avenue and 8th street
Step-by-step explanation:
The points are (3,5) and (9,14) for their locations where x= avenue and y= street.
The distance is 1/3 so it can be calculated in the following way
1/3 of ( 9-3) +3 = 1/3*6 + 3= 2+3= 5
1/3 of (14-5) + 5= 1/3*9 + 5= 3+5=8
5th Avenue and 8th street
Pierre and Maria will meet at 5th Avenue and 8th street
Help please s s s what is ittyt
Answers
9514 1404 393
Answer:
point (-12, -5)slope 1/2Step-by-step explanation:
Compare the given equation to ...
y -k = m(x -h) . . . . . line with slope m through point (h, k)
You find that k = -5, m = 1/2, h = -12.
The point is (h, k) = (-12, 5). The slope is m = 1/2.
What is a 2 step equation example?
Answers
The general two steps to solve the two-step equations are:
Step 1: Addition and subtraction to isolate the variable.
Step 2: Multiplication or division to determine the value of the variable.
Now, According to the question:
Solving Two Step Equations:
Two step equations are very easy to solve. It includes just one extra step as compared to one-step equations to solve. We can solve a two-step equation by isolating the variable (usually represented by an alphabet or letter) on one side of the equation and all other values on the other side. The general two steps to solve the two-step equations are:
Step 1: Addition and subtraction to isolate the variable.
Step 2: Multiplication or division to determine the value of the variable.
Generally, two step equations are of the form ax + b = c, where a, b, c are real numbers. A few examples of two step equations are:
2x + 3 = 70.3y + 5 = 1(2/3)z - 12 = 10Learn more about Two-Step equation at:
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PLEAS EHLP ME I DONT UNDERSTAND EXTRA POINTS AND BRAINLIEST PLEASE HLEPS!!!!!!!!!!!!!!!!!!!!
Karsik borrowed $8,500 from a bank. During a period of five years, he paid a total of $2,125 in interest. What was the simple annual interest rate that the bank charged Karsik for his loan?
0.05%
0.5%
5%
7.7%
Answers
Answer:
5%
Step-by-step explanation:
7.3 significant figure
Answers
Answer:
7.0
Step-by-step explanation:
from the first figure which is not a 0
7.3-7.0(1 significant figure)
a group of classmates surveyed how other students travel to school the results of the survey are shown in the table at right make a circle graph showing the results of the survey using percents, bus- 90, ride bike- 30, ride in car- 75, walk- 45.
Answers
So, on solving the provided question, we can say that equation of diagonal WY is 13.03 units
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
by d=√((x2 – x1)² + (y2 – y1)²).
Coordinates of W = (-4,5) and Y = (3,-6)
= √((3 – (-4))² + (-6 – 5)²)
= √170
= 13.03 units
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What the function?
y = 2.5x + 8
Answers
Answer:
Step-by-step explanation:
This is a linear function with y-intercept (0, 8) and slope 2.5.
symplify the following equation 28 - 3(2+4) divided by 9
Answers
Answer:
10 / 9
Step-by-step explanation:
[ 28 - 3 ( 2 + 4 ) ] / 9
= [ 28 - 3 ( 6 ) ] / 9
= [ 28 - 18 ] / 9
= 10 / 9
write as the opposite of a square root: -2 times square root of 3
Answers
the answer would be -144
you would have to multiply 3 by square 2, then multiply them which would be 3*4=12 and then you would square that which is 144 and because it is negative it would be -144