Answer:
Step-by-step explanation:
Consider the equation:
6x+55=x^2
1) Rewrite the equation by completing the square.
Your equation should look like (x+c)^2=d(x+c)
2
=dleft parenthesis, x, plus, c, right parenthesis, squared, equals, d or (x-c)^2=d(x−c)
2
=dleft parenthesis, x, minus, c, right parenthesis, squared, equals, d.
2) What are the solutions to the equation?
Step-by-step explanation:
1.
Subtract the coefficient from both sides, keep 55 on the same side.
[tex] {x}^{2} - 6x = 55[/tex]
Complete the square by dividing the coefficient by two and squaring it.
[tex] {x}^{2} - 6x + 9 = 55 + 9[/tex]
Use binomial to factor the left side.
[tex](x - 3) {}^{2} = 64[/tex]
2. Solve for x.
[tex](x - 3) = 8[/tex]
[tex]x = 11[/tex]
Remeber the square root of 64 is also -8 so
[tex]x - 3 = - 8[/tex]
[tex]x = - 5[/tex]
So the solutions are -5 and 11
Answer:
Answers
1) We can rewrite the equation as 64=(x−3)^2
2) The solutions to the equation are x=3±8
what is the greatest number that divides 45 and 60 without leaving a remainder
The answer is in the picture. Click on it
A quality control inspector has drawn a sample of 10 light bulbs from a recent production lot. Suppose 20% of the bulbs in the lot are defective. What is the probability that exactly 6 bulbs from the sample are defective? Round your answer to four decimal places.
Answer:
33.33 repeating percent.
Step-by-step explanation:
So using the 20 percent, we can guess there will be 2 bulbs that are defective in the sample. So 2/10. But we are guessing there will be 6;6/10. We alreadly know the proablity of that is low. To be exact 2/6 (as they are both over ten we can get rid of that) or 1/3, or 33.333 repeating percent.
Hope this helps!
When a particular type of thumbtack is dropped, it will land point up (A flat-top thumbtack resting on its flat top) or point down (A flat-top thumbtack resting on the edge of its flat top and the tip of its needle). This experiment was repeated times with the following results: point up: 48 times; point down: 52 times.
a. What is the experimental probability that a particular type of thumbtack will land point up?
b. What is the experimental probability that a particular type of thumbtack will land point down?
c. If the experiment was tried another 100 times would the same results occur? Why?
d. Is it expected that nearly the same results occur on a second trial? Why?
Answer:
0.48
0.52
No
Yes
Step-by-step explanation:
Result of experiment :
Point up = 48
Point down = 52
Total number of trials = 100
Recall :
Experimental probability = number of outcomes / number of trials
1.)
P(Landing point up) = 48 / 100 = 0.48
2.)
P(Landing point down) = 52 / 100 = 0.52
3.)
The same result will not occur has the outcomes of trials aren't fixed.
4.) Yes, nearly the same result could occur on the second trial, as the number of possible outcubes are just 2 and the number if trials is high.
a) 2(x+3)=x-4
Could anyone help?
Is this graph a function?
Find the equation of the line through point (5,1) and perpendicular to 5x−y=−3.
Answer:
you will need to specify a scale and draw the line from which I will solve with simultaneous linear equations
Janelle sketched the picture below showing distances that were measured
from trails around her cabin. She knows that AFPC - ANPW. Calculate
the length across the pond located next to the cabin.
NEED HELP ASAP thanks in advance, Check the picture
Answer:
The answer is C.
Step-by-step explanation:
In order to solve the problem, we have to prove that triangle FCP and triangle WNP are similar triangles.
The fraction of NP to PF is 19/60.8 or 5/16 when simplified.
The fraction of WP to PC is 28/89.6 or also 5/16 when simplified.
Finally, angle FPC and angle WPN are equal to each other since they are opposite angles.
Hence, it proves that triangles FCP and WNP are similar to each other using Side-Angle-Side.
Since these two triangles are similar, the fraction of WN to FC is also 5/16.
Hence, the length FC is 26 * 16/5 = 83.2
In the equation what is the value of x 1/4(x+4x) + 12= 1/2(2-x)+10
Answer:
[tex]x=-2\frac{2}{3}[/tex]
Step-by-step explanation:
1/4(x + 4x) + 12 = 1/2(2 - x) + 10
0.25(x + 4x) + 12 = 0.5(2 - x) + 10
0.25x + x + 12 = x - 0.5x + 10
1.25x + 12 = 0.5x + 10
1.25x + 12 - 12 = 0.5x + 10 - 12
1.25x = 0.5x - 2
1.25x - 0.5x = 0.5x - 0.5x - 2
0.75x = - 2
0.75x ÷ 0.75 = - 2 ÷ 0.75
[tex]x=-2\frac{2}{3}[/tex]
in 1995,there were 400 cell phone subscribers in the small town of Centerville. the number of subscribers increased by 50% per year after 1995 .
how many cell phone subscribers were in Centerville in 1999 ?
( the equation has to be in y = ab^x where y is the number of phone users and x is the years after 1995)
(show work)
Answer:
800
Step-by-step explanation:
50% of 400 = 200
1995-1999= 4 years
200x4= 800
After selling your house and purchasing a new house you have $25,000 left you wish to invest. The first
option you have is a one year T-Bill with a par value of $25,000 which costs $23,250. Your second option
is to invest in a 12 month CD with a 6.5% interest rate. Of these two available options which would allow you to receive a higher rate of return.
Answer:
Of course CD is higher then investing in T-bill
Solve the following inequality: 3-5x-x^2>=0
Answer:
-5/2+-1/2√37≤x≤-5/2+1/2√37
Step-by-step explanation:
Step 1: Find the critical points
-x^2-5x+3=0
For this equation: a=-1, b=-5, c=3
−1x^2+−5x+3=0
x=−b±√b2−4ac/2a
x=−(−5)±√(−5)2−4(−1)(3)/2(-1)
x=5±√37 /−2
x=-5/2+1/2√37
Step 2: Check intervals in between critical points
x≤-5/2+1/2 √37 (Doesn't work in original inequality)
-5/2+-1/2√37≤x≤-5/2+1/2√37 (Works in original inequality)
x≥-5/2+1/2 √37 (Doesn't work in original inequality)
I need help asap i will give brainlist
How many solutions exist for the system of equations graphed below?
none
one
two
infinitely many
Answer:
no solutions
Step-by-step explanation:
The lines are parallel and never intersect. The solutions occur when the lines intersect, so there are no solutions
The system of equations which is graphed have no solution.
What is system of linear equations?A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables.
A system of linear equation has only one solution when the graphs intersect at a point.A system of linear equation has no solution when the graph are parallel.A system of linear equation has infinite solutions when the graph are the exact same.According to the given question.
We have a graph.
In the given graph the two lines are drawn, which are parallel to each other. So, they don't have a common point.
Therefore, the system of equations which is graphed have no solution.
Find out more information about system of equations here:
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PLEASE HELP QUICKLYYYY
9514 1404 393
Answer:
x = 48
Step-by-step explanation:
The sum of the angles in a pentagon is 540°, so you have ...
90° +100° +110° +2x° +3x° = 540°
5x = 240 . . . . . . . divide by °, subtract 300
x = 48 . . . . . . . . . divide by 5
_____
Additional comment
The sum of angles in a convex n-gon is (n -2)×180°. For a pentagon, that's 3×180° = 540°.
Use the drop-down menus to label the graph according to its type.
one-to-one function
function (but not one-to-one)
relation (but not a function)
Answer:
relation ( but not a function)
Step-by-step explanation:
Answer:
The 1st is C, relation ( but not a function)
The 2nd one is A, one-to-one function.
Step-by-step explanation:
Please help will mark BRAINLIEST!
=====================================================
Explanation:
We have n = 5 sides. This means the interior angles sum up to...
S = 180(n-2)
S = 180(5-2)
S = 180(3)
S = 540
All five interior angles of this pentagon add up to 540 degrees.
what is the solution set of the equation (x-a) (x+b)=0
Answer:
Would it be x (squared) -ax +bx -a(b)
Or is it ax(squared) +bx +c?
If it isn't those then I think we need more information.
Step-by-step explanation:
Which of the following functions is graphed below?
A.y=[x+5]+4
B.y=[x+5]-4
C.y=[x-5]+4
D.y=[x-5]-4
Evaluate + for x = 6, y=-4, and z=-2.
09
0 27
0-9
0-27
Answer:
-27
Hope this helped in anyway
Answer:
the answer to this is -27.
Which statement best describes a strategy for estimating the perimeter of the figure below if the grid squares have side
lengths 1 cm?
Answer:
First one
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
9. Divide 15x^7-45x^5/3x^4
10. Divide (3x-2)(x-4)-(x-4)(6-5x)/(4-x)(8x-1)
The rational equations after division is
a) A = ( 5x³ - 15x )
b) B = - ( 3x - 2 ) ( x - 4 ) ( 6 - 5x ) / ( 8x - 1 )
What is rational function equation?
A rational equation can be defined as an equation that involves at least one rational expression
A rational function is a function of the form f( x )=P( x ) / Q( x ) ,
f( x ) = P( x ) / Q( x ) , where P( x ) and Q( x ) are both polynomials.
A rational function f ( x )=P( x ) / Q( x )
f( x ) = P( x ) / Q( x ) may have a vertical asymptote
The domain is the set of all real numbers for which Q( x ) ≠ 0
Given data ,
a)
Let the first function be P ( x ) = ( 15x⁷ - 45x⁵ )
Let the second function be Q ( x ) = 3x⁴
On simplifying , we get
A = P ( x ) / Q ( x )
A = ( 15x⁷ - 45x⁵ ) / 3x⁴
A = 3x⁴ ( 5x³ - 15x ) / 3x⁴
On further simplification , we get
A = ( 5x³ - 15x )
b)
Let the first function be P ( x ) = ( 15x⁷ - 45x⁵ )
Let the second function be Q ( x ) = 3x⁴
On simplifying , we get
B = P ( x ) / Q ( x )
B = ( 3x - 2 ) ( x - 4 ) ( x - 4 ) ( 6 - 5x ) / ( 4 - x ) ( 8x - 1 )
B = - ( 3x - 2 ) ( x - 4 ) ( x - 4 ) ( 6 - 5x ) / ( x - 4 ) ( 8x - 1 )
On further simplification , we get
B = - ( 3x - 2 ) ( x - 4 ) ( 6 - 5x ) / ( 8x - 1 )
Hence , the rational equations are solved
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Pls help math NO LINKS
A Fifty dog owners and 50 people who do not own dogs are each given a test to evaluate their stress levels. Dog owners are found to have significantly lower stress levels than people who do not own dogs. Which of the following statements are true?
1. This study provides good evidence that owning a dog is effective in reducing stress.
2. It is likely that a confounding variable could be a contributing explanation for the difference between these two groups.
3. This is an observational study, not an experiment.
a. I only
b. II only
c. III only
d. II and III only
e. I and III only
Answer: 2. It is likely that a confounding variable could be a contributing explanation for the difference between these two groups.
3. This is an observational study, not an experiment.
Step-by-step explanation:
Based on the information given, the statement that's true include:
• It is likely that a confounding variable could be a contributing explanation for the difference between these two groups.
• This is an observational study, not an experiment.
It is an observational study as the researcher observed just observed the scenarios without him trying to change the people that are being exposed to it or controlling it.
Therefore, the correct options are II and III only.
What are the domain and range of the function f(x)= -log(5- x)+9?
Domain; x<5
range: 29
domain: x <5
range: (-0.co) domain: x29
range: (-0.CO)
domain: x29
range: 29
Answer:
Domain: X<5
Range: f(x)∈ R
Step-by-step explanation:
Each gram of fat is 9 calories. Each serving of cake is 700 calories. What percent of these calories are from fat?
Answer:
1.3%
Step-by-step explanation:
[tex]\frac{9}{700}[/tex]
9 ÷ 700
0.0129
0.0129 × 100
1.3%
If Anna's test grades are 66, 90, and 99, what is her test average?
Answer:
90 because it is the mean
Answer: it’s 83%
Step-by-step explanation: you add them up and divide by 3
4 statistics professors and 6 chemistry professors are available to be advisors to a student organization. The student organization needs two of the professors to be advisors. If each professor has an equal chance of being selected, what is the probability that both professors are chemistry professors?
You want to buy a pair of shoes that usually cost $100. Today the store is
having a sale: 20% off everything.
You also have a coupon that
promises 10% off the price at the
register. How much do you save? *
Pls help and pls show how you got it! I am very confused.
Thank you
Answer:
You saved $30
Step-by-step explanation:
20% + 10% = 30%
30% = 0.30
$100 * 0.30 = $30
$100 - $30 = $70
Hope this is helpful
2. If x is directly proportional to y^3 and x=32 when y=2, i) Find an equation
connecting x and y, ii) Find the value of x when y=6, iii) Calculate the value
of y when x=108. *
Answer:
(i)
[tex] x \alpha y {3} \\ \frac{x}{y {3} } = k[/tex]
(ii)
[tex] \frac{x}{y {3}^{} } = \frac{x}{y {3}^{} } \\ \frac{32}{ {2}^{3} } = \frac{x}{6 {}^{3} } \\ \frac{32}{8} = \frac{x}{216} \\ x = 864[/tex]
(iii)
[tex] \frac{32}{8} = \frac{108}{y {}^{3} } \\ {y}^{3 } = 27 \\ y = \sqrt[3]{27 } \\ y = 3[/tex]
