To make the quadratic polynomial x² + 18x into a perfect square, we add 81 to it.
What is a quadratic polynomial?A quadratic polynomial is a polynomial in which the highest power of the unknown is 2.
What is a perfect square?A perfect square is a number suvh that it is equal to another number multiplied by itself
How to make the quadratic polynomial a perfect square?Since we have the quadratic polynomial x² + 18x, and we wnat to convert it to a perfect square.
To be a perfect square, we want it in the form (x + a)² = x² + 2ax + a² (1)
Compring the quadratic polynomial with equation (1), we have that
2a = 18
a = 18/2
a = 9
⇒ a² = 9² = 81
So, substituting a = 9 into equation (1), we have
(x + a)² = x² + 2ax + a²
(x + 9)² = x² + 2(9)x + 9²
= x² + 18x + 81
Thus we see that to make x² + 18x into a perfect square, we add 81 to it.
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Can anyone explain how to solve this?
[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\\\ \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_3(y)=11.03\hspace{5em}\log_3(z)=7.74\hspace{5em}\log_3(t)=5.44 \\\\[-0.35em] ~\dotfill[/tex]
[tex]12\log_3\left( \cfrac{z^7}{y^5 t^2} \right)\qquad \textit{let's nevermind the 12 for now} \\\\\\ \log_3\left( \cfrac{z^7}{y^5 t^2} \right)\implies \log_3(z^7)-\log_3(y^5 t^2)\implies \log_3(z^7)-[\log_3(y^5)+\log_3(t^2)] \\\\\\ \log_3(z^7)-\log_3(y^5)-\log_3(t^2)\implies 7\log_3(z)-5\log_3(y)-2\log_3(t) \\\\\\ 7(7.74)-5(11.03)-2(5.44)\implies \stackrel{\textit{let's put back the 12}}{12 ~~ [7(7.74)-5(11.03)-2(5.44)]} \\\\\\ ~\hfill \text{\LARGE -142.2}~\hfill[/tex]
(Histograms and Line Plots LC)
The following is a list of movie tickets sold each day for 10 days.
14, 35, 20, 23, 42, 87, 131, 125, 64, 92
Which of the following intervals are appropriate to use when creating a histogram of the data?
0 – 29, 30 – 59, 60 – 89, 90 – 119, 120 – 149
0 – 30, 30 – 55, 55 – 80, 80 – 105, 105 – 130
0 – 24, 25 – 49, 50 – 74, 75 – 99, 100 – 125
0 – 35, 35 – 70, 70 – 105, 105 – 140
The class intervals appropriate to use in creating a histogram of the data are 0 – 30, 30 – 55, 55 – 80, 80 – 105, and 105 – 130. The correct option is B.
What are the class intervals?A histogram is used to represent data graphically. the histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval.
The width of the intervals must be equal. This means that the difference between the lower bound and the upper bound must be equal. Also, the upper bound of the preceding interval must be the same as the lower bound of the next interval.
This means that the intervals must be overlapping. Of all the options, it is 0 – 30, 30 – 55, 55 – 80, 80 – 105, and 105 – 130 that satisfy both conditions.
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Answer:first option
Step-by-step explanation:
PLEASE HELP! 47: Complete the two-column proof.
Applying the definition of supplementary angles, the reasons that complete the two-column proof that proves x = 15 are:
a. Substitution property
b. Combine like terms
c. Division property of equality.
What is the Definition of Supplementary Angles?Two angles are supplementary angles if their sum is equal to 180 degrees when they are added together.
Given that m∠RST = 5x° and m∠UVW = 7x°, and both angles are supplementary angles, the two-column proof that proves x = 15 is shown below.
Statement Reason
m∠RST = 5x°; m∠UVW = 7x° Given
∠RST and ∠UVW are
supplementary angles.
m∠RST + m∠UVW = 180 Definition of supplementary angles
5x + 7x = 180 Substitution property
12x = 180 Combine like terms
x = 15 Division property of equality
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a rumor spreads among a group of 400 people. the number of people who have heard the rumor after t hours is given by:
Time required to spread the rumor so that half of the given heard the rumor is equal to 15 hours (approximately).
As given in the question,
Number of people among whom rumor is spread = 400
Number of people is represented by N(t)
Time is represented by 't' hours
Function representing relation between number of people who heard about the rumor and time
N(t) = 400/ ( 1+ 399 × e^(-0.4t) )
Condition : Half of the given number of people heard the rumor
N(t) = 400/2
= 200
Substitute the value in the function we get,
200 = 400/ ( 1+ 399 × e^(-0.4t) )
⇒ ( 1+ 399 × e^(-0.4t) ) = 400 ÷ 200
⇒ 1 + 399 × e^(-0.4t) = 2
⇒ 399 × e^(-0.4t) = 2 - 1
⇒ e^(-0.4t) = 1 ÷ 399
⇒ e^(-0.4t) = 0.002506
⇒ -0.4t = [tex]log _{e}[/tex] (0.002506)
⇒ t= 14.97 hours
⇒ t= 15 hours (round off)
Therefore, time required to spread the rumor among half of the given number of people is equal to 15hours(approximately).
The complete question is:
A rumor spreads among a group of 400 people. The number of people, N(t), who have heard the rumor by the time t in hours since the rumor started to spread can be approximated by a function of the form
N(t) = 400 / (1+399e^(-0.4t))
Approximately how long will it take until half the people have heard the rumor?
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Find the indicated real nth root(s) of a. n = 4, a = 625
Answer:
5
Step-by-step explanation:
Good points please answer
The values of sin2x, cos2x and tan2x is [tex]-\frac{3\sqrt{13}}{11}[/tex], 2/11 and [tex]-\frac{3\sqrt{13}}{2}[/tex] respectively.
What is tan function?
The tan function, one of the primary six trigonometric functions, is typically expressed as tan x. It is the ratio of the angle's opposite and adjacent sides when a right-angled triangle is being considered.
Tangent is a verb that means "to touch" in Latin, from the root tangere. A circle is precisely the point at which a line tan to it intersects. In trigonometry, the tan function, a periodic function, is crucial. Utilizing the unit circle will make understanding the tangent function the simplest possible.
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What is the solution for the equation 4(3x-1) =-3(2x-6) + 1 To earn full credit, show your work using a method explained in the Orientation.
Answer: x= 23/18
Step-by-step explanation:
4(3x-1) =-3(2x-6) + 1
12x - 4 = -6x + 18 + 1
12x -4 = -6x + 19
18x -4 = 19
18x = 23
x = 23/18
To which family does the function y = (x + 2) superscript one-half baseline + 3 belong?.
The function y = (x + 2)^(1/2) + 3 belongs to the family of square root functions. A square root function is a type of function in which the independent variable (in this case, x) is under the radical sign.
What are functions?In mathematics, a function is a relationship between a set of potential inputs and an equally likely set of outputs, with the condition that each input is associated to just one possible outcome. In other terms, a function is a category of mathematical action that accepts one or more parameters for input and generates a return result. Equations or graphs are frequently used to depict functions, which are useful for both modeling and solving mathematical issues.
In computer programming, a function is a block of code that completes a particular task and can be used repeatedly throughout a program. Programmers have the option of creating their own functions or using ones that are already included in the language.
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Khadija has $0.90 worth of nickels and dimes. She has a total of 10 nickels and dimes altogether. By following the steps below, determine the number of nickels, x, and the number of dimes, y, that Khadija has.
Determine three ways to have a total of 10 coins:
Khadija has 8 nickels and 2 quarters
How to determine the number of each coin?From the question, we have the following parameters that can be used in our computation:
Worth of coins = $0.90
Type of coins = Dimes and quarters
Represent the nickels with n and the quarters with q
So, we have the following representation
n + q = 10
0.05n + 0.25q = 0.9
Make n the subject
n = 10 - q
So, we have
0.05(10 - q) + 0.25q = 0.9
Evaluate the products
0.5 - 0.05q + 0.25q = 0.9
This gives
0.2q = 0.4
Divide both sides by 0.2
q = 2
Recall that
n = 10 - q
So, we have
n = 10 - 2
Evaluate
n = 8
Hence, the number of nickels is 8
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Courtney is collecting coins she already has two coins in her collection and plans to add four coins each week after six week she has 26 coins write an equation that can be used to determine the number of coins y Courtney will have after x weeks
Answer:
y = 4x + 2
Step-by-step explanation:
24 coins gained after 6 weeks
24 / 6 = 4 coins a week
y = 4x + 2
Kareem makes muffins using a ratio of 3. 5 3. 5 cups of flour for every 1. 75 1. 75 cups of sugar. If he has 3. 5 3. 5 cups of sugar, how much flour does he need to make the muffins?.
If Kareem has 3.5 cups of sugar then the amount of flour that Kareem need to make the muffins is 7 cups .
In the question ,
it is given that ,
the ratio that Kareem uses to make the muffin is 3.5 cups of flour for every 1.75 cups of sugar .
let the number of cups of flour be "y" and
the number of cups of sugar be "x" .
So , y ∝ x ,
y = k*x , where k is the constant of proportionality .
From the given data ,
3.5 = k*1.75
k = 3.5/1.75
k = 2 .
we have to find the cups of flour that Kareem needs , if he has 3.5 cups of sugar .
the equation becomes ,
y = 2*3.5
y = 7
Therefore , Kareem needs 7 cups of flour .
The given question is incomplete , the complete question is
Kareem makes muffins using a ratio of 3. 5 cups of flour for every 1. 75 cups of sugar. If he has 3. 5 cups of sugar, how much flour does he need to make the muffins ?
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If you buy 11 half gallons of milk, how many liters of milk do you have?
Answer: About 20.82 liters.
Step-by-step explanation:
To go from gallons to liters, we will multiply by 3.785. Since we are in half gallons, we will multiply 11 by 0.5 for 5.5 full gallons. Now, we will multiply;
5.5 gallons * 3.785 = 20.8198 ≈ 20.82 liters
A store is instructed by corporate headquarters to put a markup of 11% on all items. An item costing $18 is displayed by the store manager at a selling price of $2. As an employee, you notice that this selling price is incorrect. Find the correct selling price. What was the manager's likely error?
The manager's likely error is $20 if a store is instructed by corporate headquarters to put a markup of 11% on all items. An item costing $18 is displayed by the store.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
A markup of 11% on all items. An item costing $18 is displayed by the store manager at a selling price of $2.
The manager’s likely error was forgetting to add the $2 back to the $18.
$2= 11% of $18 = 1.98(=2)
For a markup,
= $2 + $18
= $20
Thus, the manager's likely error is $20 if a store is instructed by corporate headquarters to put a markup of 11% on all items. An item costing $18 is displayed by the store.
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Solve the following quadratic equation for all values of xx in simplest form.
(x-1)^2-20=
(x−1)
2
−20=
44
x = 9 or -7 is the solution of the quadratic equation
How to solve a quadratic equation for all values of xx in simplest form?
Given: the quadratic equation (x−1)²−20 = 44
(x−1)²−20 = 44
Add 20 to both sides:
(x−1)² = 44+20
(x−1)² = 64
Take the square root of both sides:
(x−1)² = 64
x-1 = ±√64
x = 1±√64
x = 1±8
x = 1+8 or 1-8
x = 9 or -7
Therefore, the solution of the equation is x = 9 or -7
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please help me! my h.w is due tomorrow.
3x+18+2x-14 what operation are performed to simplify? and what property are you using?
3x+2x+18-14 what operation are performed to simplify? and what property are you using?
5x+4 what operation are performed to simplify? and what property are you using?
The Burj Khalifa building in Dubai, United Arab Emirates, is one of the tallest buildings in the world at 2,722 feet tall. An American football field is 360 feet in length.
A photo of the Burj Kalifa building in Dubai, United Arab Emirates is shown. The caption reads the Burj Kalifa is one of the tallest buildings in the world. The bracket from the ground to the top of the building is labeled two thousand seven hundred twenty-two feet.
Approximately how many football fields tall is the Burj Khalifa building? Round to the nearest tenth.
Answer:
7.6
Step-by-step explanation:
You want to know the number of 360 ft football fields tall the 2722 ft Burj Khalifa building is.
Football fieldsThe ratio of height to football field length is ...
(2722 ft)/(360 ft/field) ≈ 7.6 fields
The height of the building is about 7.6 football field lengths.
Rearrange the total expense equation to calculate the amount of variable expenses. E=F+V Enter the correct answer in the box.
The rearranged equation for V is V = E - F
How to rearrange the equation?From the question, we have the following parameters that can be used in our computation:
E=F+V
Rewrite the above equation properly
So, we have the following representation
E = F + V
The variable expense is V
So, we have
E = F + V
Subtract F from both sides
V = E - F
hence, the equation is V = E - F
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Select the correct answer from each drop-down menu. consider this quotient. the simplest form of this quotient has a numerator of and a denominator of _______. the expression does not exist when ______.
The simplified form of the given expression has a numerator of (x + 9)(2x + 1) and the denominator of (x + 7) and the expression does exist when (x = 9) and this can be determined by factorizing the given expression.
What is factorizing?By identifying the biggest factors that the terms in the equation have in common, factoring is a technique used in mathematics to simplify algebraic expressions.
Given :
Expression - [tex]\frac{3x^2 - 27x}{2x^2+13x-7}[/tex] ÷ [tex]\frac{3x}{4x^2-1}[/tex]
First, factorize the expression, [tex]4x^2-1[/tex]
So, [tex]4x^2-1[/tex] = [tex](2x-1) (2x+1)[/tex]
Now, factorize the equation: [tex]2x^2+13x-7[/tex]
[tex]2x^2+13x-7[/tex] = [tex]2x^2+14x -x -7[/tex]
= [tex]2x(x+7) -1(x+7)[/tex]
= [tex](2x-1) (x+7)[/tex]
Now, factorize the equation: [tex]3x^2-27x[/tex]
So, [tex]3x^2-27x[/tex] = [tex]3x(x-9)[/tex]
Now, substitute the factorized terms in the given expression:
= [tex]\frac{3x(x-9)}{(2x-1) (x+7)}[/tex] ÷ [tex]\frac{3x}{(2x-1) (2x+1)}[/tex]
= [tex]\frac{(x+9) (2x+1)}{(x+7)}[/tex]
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The complete question is as follows:
Select the correct answer from each drop down menu. The simplest form of this quotient has a numerator of... and a denominator of.... The expression does exist when x=......
Diego's high school soccer team started a fundraiser selling treats at their games. They spent $1000 to start and an additional $0.30 on each candy bar and can of soda. They decide to sell both the candy and the soda for $2.00 each to make things simple
How much do they need to sell to break even (where revenue is equal to cost)?
How much do they need to sell to make at least $5,000 in profit?
Do you think it is likely for them to make at least $5,000 in profit? In what situations
would it be possible for them to make at least $5,000 in profit?
The answer to this Question based on Profits is No they cant make 5000$ profit
What is profit?
Profit is simply the extra money we earn on selling good etc things and there are tonnes of different ways of making money and profit
Solution:
Here Diego high school soccer team started a fundraiser selling treats at their games
Initial money spent = 1000$
They decided to make 0.3$ revenue on both candy and soda hence total 0.6$ revenue in one pack
one pack costs for 2$ where 0.6$ is revenue and actual cost is 1.4$
Total packs to sell = 1000/1.4
= 714 packs
hence total profit = 714 * 0.6 = 428$
hence maximum revenue they can make is 428$ and it is maximum
hence they cant make 5000$ profit
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William buys a T.V that is on sale for 40% off the original price. The original price is $140 more than the sale price.
What is the original price of the T.V?
The original price of the T.V is 350 dollars
What is a percentage?a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
le the original price of T.V be x.
so if the t.v was sold 40% off, I means that the sale price of T.V = 60x/100
0.6x.
if the original price is 140 more than sale price, it means sale price is 140 less = x - 140
Equating both expressions we have
x - 140 = 0.6x
x - 0.6x = 140
0.4x = 140
x = 140/0.4
x = 350 dollars
In conclusion, the original price of tv is 350 dollars
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please help
some one
PLEASE HELP!!(DUE TMRW)!!!!!
Answer:
Step-by-step explanation:
12
x=12y
2:3
3:14
nope-60/2=30
495/9=55
Which equation can be used to prove 1 + tan2(x) = sec2(x)? startfraction cosine squared (x) over secant squared (x) endfraction + startfraction sine squared (x) over secant squared (x) endfraction = startfraction 1 over secant squared (x) endfraction startfraction cosine squared (x) over sine squared (x) endfraction + startfraction sine squared (x) over sine squared (x) endfraction = startfraction 1 over tangent squared (x) endfraction startfraction cosine squared (x) over tangent squared (x) endfraction + startfraction sine squared (x) over tangent squared (x) endfraction = startfraction 1 over tangent squared (x) endfraction startfraction cosine squared (x) over cosine squared (x) endfraction + startfraction sine squared (x) over cosine squared (x) endfraction = startfraction 1 over cosine squared (x) endfraction.
The equation that is used to prove 1 + tan²(x) = sec²(x) is Cos²(x)/Cos²(x) + Sin²(x)/Cos²(x) = 1/Cos²(x) , the correct option is (d) .
In the question ,
a trigonometric equation is given as 1 + tan²(x) = sec²(x) ,
we have to find the equation that will be used in proving .
the equation is 1 + tan²(x) = sec²(x)
rewriting the equation ,
we get ,
1+Sin²(x)/Cos²(x) = 1/Cos²(x)...because tan(x) = Sinx/Cosx and Secx = 1/cosx
taking the LCM as Cos²(x) , and solving further ,
we get ,
Cos²(x)/Cos²(x) + Sin²(x)/Cos²(x) = 1/Cos²(x)
that is option (d) .
Therefore , the equation is Cos²(x)/Cos²(x) + Sin²(x)/Cos²(x) = 1/Cos²(x) .
The given question is incomplete , the complete question is
Which equation can be used to prove 1 + tan²(x) = sec²(x) from the options given in the image below ?
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What is the answer i need answers now I'm am going to fail
pls explain to
Answer:
Yes, the runners number of strides will fit evenly into the length of the race.
Step-by-step explanation:
The bridge is 138,435 feet. You would divide this to get 46,145 as a whole number.
Answer:
Step-by-step explanation:
You are dividing 138435 by 3.
The quotient would be 46145 with no remainder. So the answer would be yes.
A 2nd way to do this is to see if 183435 is a multiple of 3.
Hope this helps!
Have a great day!
can the median of a set of numbers ever be the greatest number in the set of data? explain.
Answer: It should not be able to
Step-by-step explanation:
It should always be in the middle, aka its name, "Median"
a certain polynomial has these factors and no others: (3x-2), (x^2-1), and (x+4) what are the zeros of this polynomial
The zeroes of the polynomial in discuss whose factors are; ( 3x - 2), ( x² - 1 ), and ( x + 4 ) are; 2 / 3, +1, -1 and -4.
What are the zeroes of polynomials whose factors are; (3x-2), (x^2-1), and (x+4)?To determine the zeroes of a polynomial, the factors of the polynomial must be equated to zero.
On this note, since the given factors of the polynomial are; (3x-2), (x^2-1), and (x+4).
The zeroes are determined as follows;
3x - 2 = 0; 3x = 2; Therefore; x = 2 /3.
x² - 1 = 0; x² = 1; Therefore, x = ±1.
x + 4 = 0; Therefore; x = -4.
Consequently, it can be concluded that the zeroes of the polynomial as determined from its factors are; 2 / 3, -1, +1, -4.
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- 5/8x+10for x=-8
show work
Answer: To solve the equation "-5/8x + 10" for x when x equals -8, we can first substitute -8 for x in the equation:
-5/8(-8) + 10
Next, we can simplify the expression by performing the calculations within the parentheses:
-5/8(-8) + 10 = 5/8(8) + 10 = 5(8)/8 + 10 = 40/8 + 10 = 5 + 10 = 15
Therefore, the value of "-5/8x + 10" when x equals -8 is 15.
Figure out what the slope and points from the equation are
y + 9 = 2(x + 5)
y - 4 = -3(x - 3)
Answer:
y + 9 = 2(x + 5): slope is 2
y - 4 = -3(x - 3): slope is -3
(12/5, 29/5)
Step-by-step explanation:
y + 9 = 2(x + 5)
y + 9 - 9 = 2(x + 5) - 9 ==> subtract both sides by 9 to isolate y
y = 2(x + 5) - 9 ==> simplify
y = 2x + 2*5 - 9 ==> distribute x and 5 by multiplying them by 2
y = 2x + 10 - 9
y = 2x + 1 ==> slope is 2
y - 4 = -3(x - 3)
y - 4 + 4 = -3(x - 3) + 4 ==> add both sides by 4 to isolate y
y = -3(x - 3) + 4
y = -3x - 3(-3) + 4 ==> multiply x and -3 by -3 by distributive property
y = -3x - (-9) + 4
y = -3x + 9 + 4 ==> simplify
y = -3x + 13 ==> slope is -3
Since y = -3x + 13 and y = 2x + 1:
2x + 1 = -3x + 13 ==> solve for x
2x + 3x + 1 = -3x + 3x + 13
5x + 1 = 13
5x + 1 - 1 = 13 - 1
5x = 12
x = 12/5
y = 2x + 1
y = 2(12/5) + 1 ==> plug in 12/5 for x
y = 24/5 + 1 ==> solve for y
y = 24/5 + 5/5
y = (24+5)/5 ==> y = 29/5 ==> (x, y) = (12/5, 29/5)
Evaluate the expression:
(5/6)÷(−3/5)=
Answer:
ANS:- = -25/18
Step-by-step explanation:
= (5/6)/(-3/5)
=5*5/6*(-3)
=25/-18
= -25/18
Solve.
2/13−1/2x=−2/3
Enter your answer in the box.
x =
Answer:
x=64/39
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
Step 2: Subtract 2/13 from both sides.
Step 3: Multiply both sides by 2/(-1).
Answer:
1 25/39
Step-by-step explanation:
on my test