The answer to the given quadratic equation is y = ( x + 4 )²
How do we solve a question by completing the square method?A(x + m)2 + n is the formula for completing the square, where m is any real number and n is a constant factor.
The following straightforward formula can be used to finish the square instead of the intricate step-by-step procedure. Find the following in order to complete the square in the phrase ax2 + bx + c:
N = c - (b2/4a) and m = b/2a
Enter these numbers where they belong: ax2 + bx + c = a(x + m)2 + n. These equations are geometrically derived.
Given : A quadratic equation y = 7x² + 56x + 117
this can also written as y = x² + 8 x + 17
y = x² + 4² - 4² + 17
y = ( x + 4 )²
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Hamad lends $5,500 at a rate of 5 ½%. Find how long it will take for his investment to earn $205 in interest? Round to the nearest day
The time taken to earn the interest of $205 on the investment by Hamad is 2563 days.
Define the term simple interest?Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest does not really compound, therefore a borrower will only charge interest mostly on principal sum, and a borrower will never be required to pay further interest on the interest that has already incurred.The formula for calculating the simple interest is-
SI = PRT/100
In which,
SI = simple interest (= $205)P = principal amount ($5,500)R = rate of interest (5 ½%) = 11/2 %T= time in years.Put in formula.
205 = 5,500×11×T/200
T = 205×200 / 5,500×11
T = 0.67 years
T = 8.13 months = 253 days.
Thus, the time taken to earn the interest of $205 on the investment by Hamad is 2563 days.
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Identify all of the roots of f(x) = x² + 2x + 2.
Answer: -1-1i and -1+1i
Step-by-step explanation:
Your Spanish club is selling T-shirts for $20 each. The club has $400 in its account left over
from last year and needs to have a total of $2000 for a trip. How many T-shirts does your club
need to sell to reach its goal of $2000.
Had:
T-shirts:
otal:
Answer:
80
Step-by-step explanation:
first you need to substract 400 from 2000, then you divide the remaining by 20
An object is traveling at a steady speed of 10 and 1 tenth mi/h. How long will it take the object to travel 1 and 9 tenth mi? First round to the nearest integer to find the estimated answer. Then find the exact answer. (First Person To Answer Gets A Surpise!!)
Estimated Answer=1/2 hour
Exact Answer= 49/101 hour
Step-by-step explanation:
Steady speed of the object =10 and one tenth km/h = 10 1/10 km
Distance to be Covered=4 and nine tenths km = 4 9/10 km
To the nearest integer,
Steady speed of the object = 10 km/hr
Distance=5km
= 5/10 =1/2 hr
The estimated answer is 1/2 hr.
The exact time taken is 49/101 hours
Find side x to one decimal place
Answer:
10.8 cm
Step-by-step explanation:
To solve this answer, we should use sine law.
[tex]\frac{SinA}{a}[/tex]=[tex]\frac{SinB}{b}[/tex]
[tex]\frac{Sin40}{7}[/tex]=[tex]\frac{Sin81}{x}[/tex] (cross multiply)
xSin40 = 7Sin81
xSin = [tex]\frac{7Sin81}{40}[/tex]
x= [tex]\frac{7Sin81}{Sin40}[/tex]
x= 10.8 cm
Help me find one possible solution to the inequality and show how it makes sense in the situation.
A yearbook company promises to give the junior class a picnic if they spend at least $28,000 on yearbooks and class rings. Each yearbook costs $35, and each class ring costs $140. How many yearbooks and class rings must the junior class buy to get their picnic?
here is the inequality: 35x + 140y ≥ 2800
Answer:A - 200
B - 1 Class Ring and 796 yearbooks
C - No, they would come up short 2800 dollars
Step-by-step explanation:
Ameekah is working with consecutive integers. If she uses x to represent her first number, what should she use to represent her second number?
x
x + 1
x + 2
2x
She should use (b) x + 1 to represent her second number
How to determine the representation of the second number?From the question, we have the following statements that can be used in our computation:
She uses x to represent her first numberThe numbers are consecutive numbersAs a general rule
Consecutive numbers are number that have a difference of 1 i.e both numbers are next to each other
Take for instance:
2 and 3, 5 and 6, 10 and 11 are all instances of consecutive numbers
Recall that she uses x to represent her first number
This means that the next number is
Next number = First number + 1
Substitute the known values in the above equation, so, we have the following representation
Next number = x + 1
Hence, the second number is (b) x + 1
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relative maxima and relative minima of the function f(x) = x^5 - 4x^3 + 3x^2 - 8x - 6
The relative maxima and relative minima of the function
f(x) = x^5 - 4x^3 + 3x^2 - 8x - 6
the relative maxima is -1.871the relative minima is 1.518How to fine the relative maxima and minimaThe relative minima and maxima is calculated
by differentiating the given function find the critical values or roots of the equationdifferentiate the second tiesubstitute the critical value that are real numbersthe critical value that gave a negative value is the maximathe critical value that gave a positive value is minimaThe procedure is done as follows
x^5 - 4x^3 + 3x^2 - 8x - 6
differentiating gives
5x^4 - 12x^2 + 6x - 8
solving the equation for the critical values are
x₁ = 0.176 + 0.73i
x₂ = 0.176 - 0.73i
x₃ = 1.518
x₄ = -1.871
The second derivative
5x^4 - 12x^2 + 6x - 8
differentiating gives
20x^3 - 24x + 6
substituting x = 1.58
20 * 1.58^3 - 24 * 1.58 + 6
= 46.966 (positive hence minima)
substituting x = -1.871
20 * -1.871^3 - 24 * -1.871 + 6
= -169.9 (negative hence maxima)
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6. The supplement of an angle is 8 less than three times the measure of the angle. Find
the measure of both angles.
X =180
m/1=
m/2 =
By using the concept of supplementary angle, it can be calculated that
The two angles are 47° and 133°
What are supplementary angles?
At first it is important to know about angle.
When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.
Two angles are said to be supplementary if the sum of the angles is 180°
Let one angle be x
Other angle = 180 - x
The supplement of an angle is 8 less than three times the measure of the angle
By the problem
180 - x = 3x - 8
3x + x = 180 + 8
4x = 188
x = [tex]\frac{188}{4}[/tex]
x = 47°
Other angle = 180 - 47 = 133°
The two angles are 47° and 133°
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professor elderman has given the same multiple choice final exam in his principles of microeconomics class for many years. after examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12. what is the probability professor elderman's class of 36 has a class average below 78
The probability Professor elderman's class of 36 has a class average below 78 is 0.9987.
Given that;
In his principles of microeconomics subject, Professor Elderman has utilized the same multiple-choice final exam for many years. He looks over the last ten years' worth of statistics and discovers that the scores have a mean of 76 and a standard deviation of 12.
µ = 76 , σ = 12 , n = 36
Using Normal Distribution;
For x = 70
z = (x - µ) / (σ/√n) = (70-76)/(12/√36) = -3.00
P( average greater than 70 ) = P(X>70)
= 1 - P(X<70)
= 1 - P(Z<-3.00)
= 1 - 0.0013
= 0.9987
The probability Professor elderman's class of 36 has a class average below 78 is 0.9987.
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there are 5 yellow flowers there are red flowers.how many are in there all togerther
The total number of flowers is 8 flowers.
How to calculate the addition?From the information given, there are 5 yellow flowers there are 3 red flowers.
It should be noted that in order to get the total value of the flowers, we have to add them. This will be:
Yellow flowers = 5
Red flowers = 3
Total flowers = Yellow + Red
= 5 + 3
= 8
The total flowers is 8.
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Complete question
There are 5 yellow flowers there are 3 red flowers.how many are in there all togerther
At the local petting zoo, 65% of the goats are female. A researcher selects a sample of five and the goats and notes that three are female. What are p nd p^(p-hat) for female goats?
The values of p and ρˆ (p-hat) in the sample are
p = 0.65 and ρˆ (p-hat) = 0.4
How to determine the values of p and ρˆ (p-hat)?From the question, we have the following parameters that can be used in our computation:
Proportion of female goats = 65%
Sample = 5
Female = 3
The proportion of female represents the variable p
So, we have
p = Proportion of female = 65%
This gives
p = 65%
Express as decimal
p = 0.65
The variable ρˆ (p-hat) is then calculated as
ρˆ = x/n
In this case,
x = Female = 2
n = Male + Female = 2 + 3 = 5
So, we have
ρˆ = 2/5
Evaluate
ρˆ = 0.4
Hence, the values are 0.48 and 0.44, respectively
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A textbook store sold a combined total of 423 psychology and math textbooks in a week. The number of psychology textbooks sold was two times the number of math textbooks sold. How many textbooks of each type were sold?
Taking into account the definition of a system of linear equations, the textbook store sold 141 math textbooks and 282 psychology textbooks.
System of linear equationsA system of linear equations is a set of linear equations (that is, a system of equations in which each equation is of the first degree) in which more than one unknown appears.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.
This caseIn this case, a system of linear equations must be proposed taking into account that:
"p" is the number of psychology textbooks sold."m" is the number of math textbooks sold.You know:
A textbook store sold a combined total of 423 psychology and math textbooks in a week. The number of psychology textbooks sold was two times the number of math textbooks sold.The system of equations to be solved is
p + m= 423
p=2m
It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, substituting the second equation in the first one you get:
2m + m= 423
3m=423
m= 141
Substituting this value in the second equation you get:
p= 2m
p= 2×141
p= 282
Finally, 141 math textbooks and 282 psychology textbooks were sold by the textbook store.
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what Is the inequality shown?
The inequality shown is -4 ≤ x ≤ 3.
We are given a diagram of the number line. The diagram shows the range of the inequality. An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line. Let the variable "x" represent all the values contained in the inequality. The minimum value contained in the inequality is -4. The maximum value contained in the inequality is 3. All the values between the minimum and maximum limits are included in the inequality. Hence, we can write the following inequalities :
-4 ≤ x
x ≤ 3
We can combine these into a single inequality.
-4 ≤ x ≤ 3
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In 2001 there were 6680 electric-powered vehicles in use in the United States. In 1998 only 4760 electric vehicles were being used. (Source: U. S. Energy Information Administration)
a. Assume that the relationship between time, x, and number of electric-powered vehicles, y, is linear. Write an equation in slope-intercept form describing this relationship. Use ordered pairs of the form (years past 1998 comma number of vehicles).
An equation of slope-intercept form describing this relationship. Use ordered pairs of the form the equation, y = 640x + 4760
Since there were 4760 electric vehicles in 1998, when x=0 (indicating 0 years have passed since 1998), y=4760. There were 1,920 more electric vehicles on the road after three years. 1920 / 3 = 640 is the average rate of change every year. Between 1998 and 2001, there were 640 more automobiles every year.Our slope measures m=640. By dividing the change in y by 4760, or 1920, we can determine the slope.The y-intercept is just the starting point, or x=0. At this point, x=0. The y-intercept is shown here: (0, 4760). Equation of slope intercept: y = 640x + 4760 where b=4760.
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Select the correct answer. Solve the following equation for x. x2 - 36 = 0
Answer:
Step-by-step explanation:
x2-36=0
+36 +36
x2=36
/2 /2
x=18
write down the ratio 240kg:6kg give your answer in its lowest form
Answer:
40kg:1kg
Step-by-step explanation:
240kg:6kg
Both sides can be divided by 6 so we that to simplify
40kg:1kg
Hopes this helps please mark brainliest
240 : 6
answer = 1 : 4 the simplest form of 240 : 6
f(x)=x^2. which of these is g(x)?
please help!
Answer: C
Step-by-step explanation:
g(5)=1
mandy begins bicycling west at 30 miles per hour at 11:00 a.m. if liz leaves from the same point 20 minutes later bicycling west at 36 miles per hour, when will she catch mandy?
The time at which Liz will catch up with Mandy is 1 pm.
Here we have to find the time when Mandy and Liz meet.
Let t be the time taken by Liz to meet Mandy
Given:
Speed of Mandy = 30mile/hr
Speed of Liz = 36 miles/hr
Formula:
Speed = Distance/ time
Distance by Mandy = 30t
Distance by Liz = 36( t - 20/60)
As the distance covered by both is the same. So we have
30t = 36( t - 1/3)
6t = 12
t = 2
2 hours past 11 am is 1 pm.
Therefore Liz catch Mandy at 1 pm.
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CAN SOMEONE HELP ME
Michael has v sweets.
Lily has 5 more sweets than Michael.
James has 8 more sweets than Lily.
They have 75 sweets altogether.
what is the number of sweets Michael has.
Answer:
Michael has 19 sweets
Step-by-step explanation:
19+24+32 = 75
Lilly has: 24
James has: 32
you are constructing a cardboard box from a piece of cardboard with the dimensions 4 m by 8 m. you then cut equal-size squares from each corner so you may fold the edges. what are the dimensions (in m) of the box with the largest volume?
The dimensions (in m) of the cardboard box with the largest volume is obtained as 2 m length.
Define the term largest volume?Volume is a mathematical term that describes how much three-dimensional space an object or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc. Volume is sometimes referred to as capacity.Dimensions of piece of cardboard;
Length = 8 mWidth = 4 m.Let the corner cut length be 'x',
New dimensions;
Length = 8 - 2x Width = 4 - 2xHeight = xVolume = length x width x height
Put the values;
V = ( 8 - 2x ) (4 - 2x) x
Find the solution of the obtained quadratic equation by quadratic formula.
x = 0, 2 and 4.
As, x ≠ 0 and 4.
Thus, x = 2.
Thus, the dimensions (in m) of the box with the largest volume is obtained as 2 m length.
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bob can do a job in 5 hours while bill can do the same job in 8 hours. how many hours would it take them, working together, to do this job?
Hours taken by Bob and Bill if they work together is 3 1/13.
Here it is given that Bob can do a job in 5 hours and Bill can do the job in 8 hours.
We have to find the time taken by both to do the work if done together.
Time ratio of Bob and Bill = 5: 8
Efficiency of Bob and Bill = 8: 5
Total amount of work done = 5× 8 = 8× 5 = 40
The total efficiency of Bob and Bill = 13
Hours took by both bob and bill to do the work if done together = 40/13
= 3 [tex]\frac{1}{13}[/tex]
Therefore the work done together is 3 [tex]\frac{1}{13}[/tex] hours.
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A professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. The professor has informed us that 8. 75 percent of her students received grades of a. What is the minimum score needed to receive a grade of a?.
The minimum score needed to receive a grade of A is 88.51
Let, X, be the scores of the student's
X follows Normal Distribution with mean = μ = 73 and standard deviation = σ = 11
The professor has informed us that 7.93 percent of her students received grades of A.
That is P( X > a ) = 7.93% = 0.0793 .
We have to find a.
P( X > a ) = 7.93% = 0.0793
So, P( X <= a ) = 1 - 0.0793 = 0.9207
Using function = NORMINV( probability , μ ,σ )
a = NORMINV( 0.9207, 73 , 11 ) = 88.51
The minimum score needed to receive a grade of A is 88.51
We have to find P( X <= 57.93 )
Using function = NORMDIST( x, μ , σ , 1 )
P( X <= 57.93 ) =NORMDIST( 57.93 , 73 , 11 , 1 ) = 0.0853 = 8.53%
8.53 percent of students failed the course
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Graph the line that passes through the points (-9,8) and (-7,8) and determine the equation of the line
ans=y=8
look for the gradient[tex] \frac{change \: in \: y}{change \: in \: x?} [/tex]
change in y8-8=0
change in x-7--9=2
hence the gradient is 0÷2=0
looking for the equationgradient(0)=
[tex] \frac{y - 8}{x - - 9?} [/tex]
so..,0=y-8
hence the equation is y=8
divide and find quotient
(a⁴-b⁴) ÷ (a+b)
(step by step explanation)
Answer:
Step-by-step explanation:
(a⁴-b⁴)/(a-b)
using..(a+b²)=(a+b)(a-b)
=(a²+b²)(a²-b²)/(a-b)
=(a²+b²)(a+b)(a-b)/(a-b)
=(a²+b²)(a+b)
Jerald is having drain issues at his home and decides to call a plumber. The plumber charges $35 to come to his house and $60 for every hour they work. If the plumber charges Jerald a total of $305, how many hours did the plumber work?
Write and solve an equation to determine the number of hours worked by the plumber.
35x + 60 = 305; x = 7 hours
35x − 60 = 305; x = 10.4 hours
60x + 35 = 305; x = 4.5 hours
60x − 35 = 305; x = 5.7 hours
Answer:
60x + 35; x = 4.5 hours
(x is not actually equal to 4.5, it is equal to 4.67)
Step-by-step explanation:
The description says that the plumber charges a one time fee of 35 dollars to come to someones house, and then 60 dollars an hour. The total pay is 305 dollars. x will be the number of hours that the plumber works.
60x + 35 = 305
Subtract 35 from both sides: 60x = 280
Divide by 60: x = 280/60
Simplify: x=14/3
Fraction to decimal: x=4.67
Answer: C (60x + 35 = 305; x = 4.5 hours)
It's right trust me! Wish you luck!
Brainliest?
A function is shown. F(x) = -7/8x + 11
What's the x-intercept?
What's the y-intercept?
Answer:
x-intercept (88/7,0), y-intercept (0,11)
Answers:
x intercept = 88/7
y intercept = 11
===============================================
Explanation:
To find the y intercept, we replace f(x) with 0 and solve for x.
f(x) = (-7/8)x + 11
0 = (-7/8)x + 11
(7/8)x = 11
7x = 8*11
7x = 88
x = 88/7 is the x intercept
It is located at (x,y) = (88/7, 0)
The x intercept always occurs when y = 0.
88/7 = 12.5714 approximately, but I would stick to the fraction form since it's most exact.
-------------------------------
The y intercept always occurs when x = 0.
f(x) = (-7/8)x + 11
f(0) = (-7/8)*0 + 11
f(0) = 0 + 11
f(0) = 11 is the y intercept
It is located at (0,11)
The y intercept is much easier to find since we just need to read off the last value of the function (aka the constant value).
The length and width of a rectangle are consecutive integers. The perimeter of the
rectangle is 54 centimeters. Find the length and width of the rectangle.
Answer:
length = 13 cm , width = 14 cm
Step-by-step explanation:
let the length be n , then the width is n + 1
the perimeter (P) of a rectangle is calculated as
P = 2(l + w) ← l is the length and w the width
given P = 54 , then
2(n + n + 1) = 54 ( divide both sides by 2 )
2n + 1 = 27 ( subtract 1 from both sides )
2n = 26 ( divide both sides by 2 )
n = 13
n + 1 = 13 + 1 = 14
so, length = 13 cm and width = 14 cm
18. a rectangular page is to contain 42 square inches of printable area. the margins at the top and bottom of the page are each 1 inch, one side margin is 1 inch, and the other side margin is . what should the dimensions of the page be so that the least amount of paper is used?
The page is in landscape mode with a width : height is 3: 2
Given that,
The printable area is should be 42 square inches on a rectangular page. The margins at the top and bottom of the page are each one inch, while the margins on one side are one inch and two inches, respectively.
x = length of the horizontal side of the printable area
y = length of the vertical side of the printable area
XY = 42 inch²
y = 42/x
page height = y + 1 + 1
page width = x + 1 + 2
A = area of an entire sheet of paper
= (x+3)(y+2)
= (x+3)(42/x+2)
= x(42/x+2)+3(42/x+2)
= 42+2x+126/x+6
A = 2x+126/x+48
Extremes occur when A' = 0:
A' = 0 = 2 – 126/x²
1 = 63/x²
x² = 9*7
x = 3√(7), x has to be positive
y = 42/x = 42/(3√(7)) = 14√(7)/7 = 2√(7)
What should the dimensions of the page be so that the least amount of paper is used?
page width = x + 3 = 3√(7) + 3 = 3(√(7) + 1)
page height = y + 2 = 2√(7) + 2 = 2(√(7) + 1)
So, the page is in landscape mode with width: height is 3: 2.
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Bobbi wants to buy a bandana that costs 3.75$ But she has only 7.75$ in her budget what is her budget deficit
The budget deficit is how much less the budget is to buy a thing, thus Bobbi has the budget deficit as $3.75 - $0.75 = $3.00 thus option (B) is correct.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects.
In other meaning, subtraction is a mathematical operation such that two values are going to subtract and give a resultant value.
As per the given,
Cost of bandana = $3.75
Budget = $0.75
Budget deficit = $3.75 -$0.75
⇒ $3.00
Hence, "The budget deficit is how much less the budget is to buy a thing, thus Bobbi has the budget deficit as $3.75 - $0.75 = $3.00".
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The given question is incorrect, the correct question follows;
Bobbi wants to buy a bandanna that costs $3.75, but she has only $0.75 in her budget. What is her budget deficit?
A. $0.20
B.$ 3.00
C. $5.00
D.$4.50
