Exit Ticket Which method do you believe is the most efficient when solving for the following equations? n2 – 2n – 3=0 Factor/Zero Product Property Completing the Square Quadratic Formula
Answers
The factoYou ar/zero product property is the most efficient method for solving the equation
Explanation:The given quadratic equation can be factored as:
[tex]\begin{gathered} n^2-2n-3=0 \\ (n+1)(n-3)=0 \end{gathered}[/tex]The factor/zero product property is the most efficient method for solving the equation
Related Questions
Write two numbers that multiply to the value on top and add to the value on bottom.-14Х5
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Let the first number be m while the second num
Select the correct answer from each drop-down menu. The general form of the equation of a circle is 7x2 + 7y2 − 28x + 42y − 35 = 0. The equation of this circle in standard form is . The center of the circle is at the point , and its radius is units.
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In the last three years, Franks basketball team won 20 more games than they lost. if they won 130 games, what was the ratio of wins to looses? Write in fraction form.
Red
2.) Green Beans are canned by 2 companies. The Del Monte Company sells
14.5 oz for $1.75 and the Green Giant company sells 15.5 oz for $1.95.
Who has the best deal?
3.)In the last three years, Frank's basket ball team won 20 more games than
they lost. If they won 130 games, what was the ratio of wins to losses?
Write in fraction form.
((. 3 questions into one pls answer !))
Jeff has 45 pounds of organic apples. He earns $4.50 for every 3/4of a pound of organicapples he sells. How much money will Jeff receive if he sells all his organic apples?
Answers
Given data:
The total weight of the apples Jeff have W=45 pounds.
The amount Jeff earned for every 3/4 pound of apple is A=$4.50.
The expression for the given statement is,
[tex]\begin{gathered} \frac{3}{4}\text{ pound =\$4.50} \\ 1\text{ pound =\$6} \end{gathered}[/tex]Multiple the above expression by 45 on both sides.
[tex]\begin{gathered} 45(\text{ 1 pound)=45(\$6)} \\ 45\text{ pounds =\$270} \end{gathered}[/tex]Thus, the amount Jeff earned is $270.
what is 100 divided by 74 rounded to the nearest 10
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
100 ÷ 74
Step 02:
What is syntax? PLS HURRY
Referring to a dictionary when you are unsure of a word's meaning
The careful and purposeful choice of words to reach a desired effect
The way writers arrange words and punctuation to create sentences
Using a clue in a sentence to determine the meaning of a word
Answers
The study of syntax in linguistics focuses on how words and morphemes come together to produce longer language constructs like phrases and sentences.
What is syntax?The study of syntax in linguistics focuses on how words and morphemes come together to produce longer language constructs like phrases and sentences. Word order, grammatical relationships, hierarchical sentence structure (constituency), agreement, the nature of cross-linguistic diversity, and the connection between form and meaning are among the primary issues of syntax (semantics). There are many different approaches to syntax, each with a unique set of underlying premises and objectives.A division of grammar is syntax. The entire set of rules that make up a language, including syntax, is referred to as grammar. "Syntax skills help us comprehend how sentences work—the meanings underlying word order, structure, and punctuation. Syntax deals with the way that words are placed together to make phrases, clauses, and sentences.Therefore, the study of syntax in linguistics focuses on how words and morphemes come together to produce longer language constructs like phrases and sentences.
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Answer:
the study of syntax in linguistics focuses on how words and morphemes come together to produce longer language constructs like phrases and sentences.
Step-by-step explanation:
Logan made 5 1/4 pounds of trail mix. If he puts 3/4 pounds into each bag how many bags can Logan fill?
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Find the tangent of the larger acute angle in a right triangle with side lengths 3, 4, and 5.
Write your answer as a fraction.
The tangent of the larger acute angle is ______?______
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The tangent should be in fraction is 4/3
Calculation of the tangent:
Since in a right triangle with side lengths 3, 4, and 5
Here there is the larger acute angle in the 3, 4 and 5 so it should be lies between 3 and 5
So, it should be like
= opposite side ÷ adjacent side
= 4/3
Hence, The tangent should be in fraction is 4/3
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Approximate one of the solutions to the system of equations graphed below? 4 d 194 (0,5) O (4,-5) (3, 0) (-3, -3)
Answers
SOLUTION
Method:
The solution is gotten at the coordinates of the point of intersection.
The points of intersections are (-2, 0) and (4, -5)
Final answer:
(4, -5)
Here are the numbers of times 14 people ate out last month.7,5, 3, 6, 3, 3, 6, 5, 6, 3, 6, 5, 5,4Send data to calculatorFind the modes of this data set.If there is more than one mode, write them separated by commas.If there is no mode, click on "No mode."
Answers
Given,
The numbers of times 14 people ate out last month is,
7,5, 3, 6, 3, 3, 6, 5, 6, 3, 6, 5, 5,4
Arranging the data is ascending order,
3, 3, 3, 3, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7
The frequency of 3, 5 and 6 is same.
The number with maximum frequency is called the mode of the data.
The mode of the data set is 3, 5, 6.
[in the following write an expression in terms of the given variables that represents the indicated quantity.]the sum of three consecutive integers if the greatest integer is x.the expression for the sum of the three consecutive integers is _________
Answers
Answer
Sum of the three consecutive integers = 3x - 3
Explanation:
Find the sum of three consecutive integers
Condition given: Greatest integer should be x
Since, x is the greatest integer, therefore, the other integers should be less than x
The three consecutive integers are: x, x - 1, and x - 2
Sum of the three integers = x + x - 1 + x - 2
Sum = x + x - 1 + x - 2
Collect the like terms
= x + x + x - 1 - 2
Sum = 3x - 3
Therefore, the sum of the three consecutive integers is 3x - 3
9. Josie has $30 to spend at a festival. It costs $5 to enter the festival, and the game she wants to play costs $1.40. Write the inequality and use it to determine the number of games (g) that Josie can play.
Answers
She has only $30 with her.
It will cost her $5 to enter the festival and the game she wants to play cost $1.40 .
let
g = number of games
Therefore, the inequality for the number of games she can play can be represented below
[tex]\begin{gathered} 5+1.40g\leq30 \\ \text{where} \\ g=\text{ number of games she can play} \end{gathered}[/tex]The number of games she can play can be calculated below
[tex]\begin{gathered} 5+1.40g\leq30 \\ 1.40g\leq30-5 \\ 1.40g\leq25 \\ \text{divide both sides by }1.40 \\ g\leq\frac{25}{1.40} \\ g\leq17.8571428571 \\ g\leq17.86 \\ \text{she can only play approximately 17 games} \end{gathered}[/tex]5.) figure 12.16 shows the floorplan for a modern one story house. Bob calculates the area of the floor of the housing this way: 36•72-18•18 = 2268 feet squared. what might Bob have in mind? Explain why Bob’s method is a legitimate way to calculate the floor area of the house, and explain clearly have one or both of the moving and additivity principles on area apply in this case
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From the given image, the Area of the floor can be calculated by removing/subtracting the area of the two triangles from the area of the rectangle.
Area of a rectangle is;
[tex]\begin{gathered} A_r=lb \\ A_r=36.72 \end{gathered}[/tex]Area of the two triangles;
[tex]\begin{gathered} A_t=\frac{1}{2}bh+\frac{1}{2}bh=\frac{1}{2}(18.18)+\frac{1}{2}(18.18) \\ A_t=18.18 \end{gathered}[/tex]The Area of the floor is;
[tex]\begin{gathered} A=A_r-A_t \\ A=36.72-18.18 \\ A=2592-324 \\ A=2268ft^2 \end{gathered}[/tex]Kyle throws a baseball straight up from a height of 5 feet with an initial speed of 41feet per second.What is the maximum height of the baseball?
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We will determine the maximum height of the baseball as follows:
We will need the following formulas:
[tex]v=u+at[/tex][tex]s=ut+\frac{1}{2}at^2[/tex]Here "u" represents the original speed, "t" represents the time, "a" the acceleration of the body and "s" is the total discance moved. [We will find s to solve the problem].
So:
First we have that the acceleation that the body will experience is -9.8m/s^2 [Since the object is going upwards and gravity is pulling on it towards the ground]. [acceleration of gravity using feet over second squared is 32.17 ft/s^2].
[tex]v=(12.4968)+(-9.8)t[/tex]But the maximum height will be reached when the velocity after certain time has passed is 0 ft/s, so:
[tex]0=(12.4968)+(-9.8)t\Rightarrow9.8t=12.4968[/tex][tex]\Rightarrow t=1.275183673\ldots\Rightarrow t\approx1.3[/tex]So, at approximately 1.3 seconds the maximum heigth willl be reached.
Now, we solve for s:
[tex]s=(12.4968)(1.275183673)+\frac{1}{2}(-9.8)(1.275183673)^2\Rightarrow s=7.967857665[/tex][tex]\Rightarrow s\approx8[/tex]So, the maxumum altitude for the baseball will be 8 meters, but we have to add the initial 5 feet at which it was launched:
[tex]h\approx8+1.524\Rightarrow h\approx9.491857665[/tex]And taking that to feet we will have:
[tex]h\approx31.141265305118\ldots[/tex]So, the solution must be the last option. [The discrepanc
The area of a new wctabfle is 28m^2 and the length of the rectangle is 1m more than double the width. Find the dimensions
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Represent the sides of the rectangle
Let the length be represented by l
Let the width be represented by w
STEP 2: Interpret the statements in the question.
[tex]\begin{gathered} length\text{ is 1m more than the double of the width:} \\ double\text{ of the width}\Rightarrow2w \\ 1m\text{ more than the double}\Rightarrow2w+1 \\ \therefore l=2w+1 \end{gathered}[/tex]STEP 3: Equate the area of the rectangle to given measure
[tex]\begin{gathered} Area=length\times width \\ length=2w+1,width=w \\ Area=(2w+1)\cdot w=28 \\ By\text{ simplification,} \\ w(2w+1)=28 \end{gathered}[/tex]STEP 4: Solve for the width
[tex]\begin{gathered} w(2w+1)=28 \\ By\text{ expansion,} \\ 2w^2+w=28 \\ Subtract\text{ 28 from both sides} \\ 2w^2+w-28=28-28 \\ 2w^2+w-8=0 \end{gathered}[/tex]STEP 5: Solve the equation using quadratic formula
[tex]quadratic\text{ formula}\Rightarrow\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]From the equation,
[tex]a=2,b=1,c=-28[/tex]By substitution,
[tex]\begin{gathered} w_{1,\:2}=\frac{-1\pm\sqrt{1^2-4\cdot\:2\left(-28\right)}}{2\cdot\:2} \\ \sqrt{1^2-4\times2(-28)}=15 \\ By\text{ substitution,} \\ w_{1,\:2}=\frac{-1\pm \:15}{2\cdot \:2} \\ \mathrm{Separate\:the\:solutions} \\ w_1=\frac{-1+15}{2\cdot \:2},\:w_2=\frac{-1-15}{2\cdot \:2} \\ w=\frac{-1+15}{2\times2}=\frac{14}{4}=\frac{7}{2}=3.5 \\ w=\frac{-1-15}{2\cdot\:2}=\frac{-16}{4}=-4 \end{gathered}[/tex]Since the width cannot be negative, this means that the value of the width is 3.5m
STEP 6: Solve for the length
By substitution into the formula in step 2, we have:
[tex]\begin{gathered} l=2w+1 \\ l=2(3.5)+1=8 \\ l=8 \end{gathered}[/tex]Hence,
length = 8m
width = 3.5m
Which of the following represents the equation of a quadratic curve?y = 3x + 7y = 8 - 3x + 7x2y = 7(3)xy = 8 x 6
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An equation will be a quadratic curve when the expression has the following definition
[tex]y=ax^2+bx+c[/tex]We can have b and c equal to 0, but never a, therefore we have few variations like
[tex]\begin{gathered} y=ax^2+bx \\ y=ax^2+c \\ y=ax^2 \end{gathered}[/tex]All they are quadratics. Looking at the options we can see that the only function that has that definition is
[tex]y=8-3x+7x^2[/tex]Therefore the correct answer is
[tex]y=8-3x+7x^{2}[/tex]Evaluate the expression and leaving your answer in polar form.
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Complex numbers z₁ = 6 · [tex]e^{i\,\frac{17\pi}{20} }[/tex] and z₂ = 6 · [tex]e^{i\,\frac{27\pi}{20} }[/tex] are the square roots of the complex number in polar form.
How to find the square root of a complex number in polar form
In this problem we find a complex number in polar form, that is, a complex number of the form:
z = r · [tex]e^{i\,\theta}[/tex]
Where:
r - Norm of the complex number.θ - Direction of the complex number, in radians.The square root of this number can be found by means of the De Moivre's theorem:
[tex]\sqrt{z} = \sqrt{z} \cdot e^{i\,\left(\frac{\theta + 2\pi\cdot k}{n} \right)}[/tex], for k = {0, 1}
If we know that z = 36 and θ = 17π / 10, then the roots of the complex number are:
z₁ = 6 · [tex]e^{i\,\frac{\frac{17\pi}{10}}{2} }[/tex]
z₁ = 6 · [tex]e^{i\,\frac{17\pi}{20} }[/tex]
z₂ = 6 · [tex]e^{\frac{\frac{17\pi}{10} + 2\pi }{2} }[/tex]
z₂ = 6 · [tex]e^{i\,\frac{27\pi}{20} }[/tex]
The solutions are z₁ = 6 · [tex]e^{i\,\frac{17\pi}{20} }[/tex] and z₂ = 6 · [tex]e^{i\,\frac{27\pi}{20} }[/tex].
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A certain type of cell doubles every 5 hours. If you started with 38 cells, how manywould you have after 15 hours? (gridded response)
Answers
First divide 15 hours by 5 :
15/5 = 3
So, we obtain that the cell will double 3 times
since the initial number o f cells is 38
5hours = 38x2 = 76
10 hours = 76x2= 152
15 hours =152 x2 = 304
304 cells
4. An object is at rest if all forcesacting on the object have a netforce of zero. If an object has aforce of -5.5 Newtons applied toit, what force needs to be appliedin order for the object to be atrest?
Answers
The object will be at rest if the resultant forces = 0
For the given object, a force of -5.5 Newtons applied to it
So, to be at rest we will add another force equal in magnitude and opposite in direction
So, the answer will be the required force = +5.5 newtons
Which would you use to compare 10 / 12 and 2 / 5 a common numerator or common denominator?
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We can compare 2 fractions by means of the cross multiplication method. In our case, we have
since 50 is greater than 24 then 10/12 is greater than 2/5:
[tex]\frac{10}{12}>\frac{2}{5}[/tex]Question 7. Y=(5/2)^xSketch the graph of each of the exponential functions and label three points on each graph.
Answers
Given:
[tex]y=\mleft(\frac{5}{2}\mright)^x[/tex]To sketch the graph:
First find the three points.
Put x=-1 we get,
[tex]\begin{gathered} y=(\frac{5}{2})^{-1} \\ =\frac{2}{5} \\ =0.4 \end{gathered}[/tex]Put x=0 we get,
[tex]\begin{gathered} y=(\frac{5}{2})^0 \\ =1 \end{gathered}[/tex]Put x=1 we get,
[tex]\begin{gathered} y=(\frac{5}{2})^1 \\ =2.5 \end{gathered}[/tex]Therefore, the three points are, (-1, 0.4), (0, 1), and (1, 2.5).
The graph is,
When 7 times a number is decreased by 1, the result is 9 more than 5 times the number?So I got this below: 7x-1 = 9+5yHow do I find the number?
Answers
5
1) Translating that into a mathematical expression, we can write out the following. Let's call this number by "n":
[tex]\begin{gathered} I)7n-1 \\ II)9+5n \\ 7n-1=9+5n \\ 7n-5n=9+1 \\ 2n=10 \\ \frac{2n}{2}=\frac{10}{2} \\ n=5 \end{gathered}[/tex]Just one mistake: when we refer to the same number we use the same variable.
Four times a number plus two is equal to 3 times the number.
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We have to find the number that satisfies: "Four times a number plus two is equal to 3 times the number".
Four times a number is 4x.
Then, we can write and solve the expression as:
[tex]\begin{gathered} 4x+2=3x \\ 4x-3x=-2 \\ x=-2 \end{gathered}[/tex]The number is -2.
I need the answer for this question on math
Answers
Answer:
12.8 grams per 1 package
102.4 grams per 8 packages
128 grams per 10 packages
Step-by-step explanation:
we can take
25.6 ÷ 2
to get the unit rate (number of grams per 1 package)
25.6 ÷ 2 = 12.8
12.8 grams per 1 package
multiply 12.8 by 8 to get the amount of grams per 8 packages
12.8 * 8 = 102.4
102.4 grams per 8 packages
we can set up a proportion to find the number of packages for 128 grams
let p = number of packages
12.8/1 = 128/p
12.8 = 128/p
multiply by "p" on both sides to get rid of the "p" in the denominator
12.8*p = (128/p )* p
12.8p = 128
divide by 12.8 on both sides to isolate "p"
12.8p = 128
÷12.8 ÷12.8
p = 10
128 grams per 10 packages
total of students 50 students that dont wear glasses and 12 that do what the ratio
Answers
the ratio is 6:25, because for every 25 students that dont wear glesses there are 6 that do.
Answer:
The ratio of students that wear glasses to the total number of students is: (12:62) or, when simplified (6:31)
The ratio of students that do not wear glasses to the total number of students is:
(50:62) or when simplified (25:31)
The ratio of students that do not wear glasses to the students that do wear glasses is:
(50:12) or when simplified (25:6)
The ratio of students that do wear glasses to the students that wear glasses is:
(12:50) or when simplified (6:25)
Step-by-step explanation:
The ratio of students that wear glasses to the total number of students is: (12:62) or, when simplified (6:31)
The total number of students is 62, and 12 of them wear glasses.
The ratio of students that do not wear glasses to the total number of students is:
(50:62) or when simplified (25:31)
The total number of students is 62, and 50 of them do not wear glasses.
The ratio of students that do not wear glasses to the students that do wear glasses is:
(50:12) or when simplified (25:6)
The 50 students do not wear glasses, while 12 students wear glasses.
The ratio of students that do wear glasses to the students that wear glasses is:
(12:50) or when simplified (6:25)
There are 12 students who wear glasses and 50 who do not.
Hi! Can someone please check my work real quick? I’m not sure what I’m doing wrong. I’m trying fo find the remainder using synthetic division.
Answers
Given:
The polynomial is given as,
[tex]\begin{gathered} p(x)=2x^3+4x^2-5 \\ g(x)=x+3 \end{gathered}[/tex]The objective is to divide the polynomial by synthetic division.
Explanation:
The general equation of a polynomial with degree 3 is,
[tex]f(x)=ax^3+bx^2+cx+d[/tex]So, consider the given polynomial as,
[tex]p(x)=2x^3+4x^2+0x-5[/tex]The divisor can be converted as,
[tex]\begin{gathered} x+3=0 \\ x=-3 \end{gathered}[/tex]To find synthetic division:
Now, the synthetic division can be evaluated as,
Hence, the remainder of the division is -23.
An ice cream shop offers 27 different flavors of ice cream and 11 different toppings.How many different sundaes can you create using one of the ice cream flavors and one of the toppings
Answers
297 different sundaes can you create using one of the ice cream flavors and one of the toppings.
Define multiplication.We can rapidly determine the total number of things by multiplying. In order to do this, we will consider the number of groups with equal sizes and the number of items in each group.
The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers. When we need to merge groups of similar sizes, we employ it.
Given,
An ice cream shop offers 27 different flavors of ice cream and 11 different toppings.
Multiplying,
27 × 11
297
297 different sundaes can you create using one of the ice cream flavors and one of the toppings.
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The figure below shows an upside-down pyramid with a square base.inverted pyramid with a square baseNote: figure not to scale.Which shape does the intersection of the horizontal plane with the pyramid look like?
Answers
ANSWER:
EXPLANATION:
Given:
Since the pyramid has a square base, therefore intersection of the horizontal plane will produce a shape that looks like a square.
2. Which expression is equivalent to x⁴+6x²+9? * A. g(x)=2(x–3)²–72B. g(x)=2(x²–6x–27)C. g(x)=2(x–9)(x+3)D. g(x)=2x²–18x+6x–54
Answers
Explanation:
The best way to find the zeros of the function is to write the polynomial as a product of linear terms with the form (x - c). Therefore, the right answer is:
C. g(x) = 2(x - 9)( x + 3)
Because is written as a product and all factors are linear.
In this case, we can identify the zeros making each
Ian is a salesperson who sells computers at an electronics store. He makes a base payof $80 each day and then is paid a $5 commission for every computer sale he makes.Make a table of values and then write an equation for P, in terms of x, representingIan's total pay on a day on which he sells x computers.
Answers
ANSWER
[tex]P=5x+80[/tex]EXPLANATION
Let the number of computers sold be x.
Let the total pay be P.
We have to find the equation that represents the total pay in terms of the number of computers sold.
The equation that represents the total pay is a linear equation and a linear equation has a general form of:
[tex]y=mx+b[/tex]where m = slope
b = y intercept
To find the slope, we have to apply the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1, y1) and (x2, y2) are two sets of points from the table.
Let us pick (0, 80) and (3, 95)
Therefore, the slope, m, is:
[tex]\begin{gathered} m=\frac{95-80}{3-0} \\ m=\frac{15}{3} \\ m=5 \end{gathered}[/tex]Now, we apply the point-slope formula to find the equation:
[tex]P-P_1=m(x-x_1)[/tex]Note: P is used in place of y (the dependent variable)
Therefore, we have:
[tex]\begin{gathered} P-80=5(x-0) \\ P-80=5x \\ \Rightarrow P=5x+80 \end{gathered}[/tex]That is the equation that represents the total pay, P.
Challenge The vertices of ABC are , , and . ABC is reflected across the y-axis and then reflected across the x-axis to produce the image A''B''C''. Graph and .
Answers
The graph shows triangle ABC with vertices as follows;
[tex]\begin{gathered} A=(-5,5) \\ B=(-2,4) \\ C=(-2,3) \end{gathered}[/tex]When translated 6 units to the right, and 7 units down, its becomes,
[tex]\begin{gathered} A^{\prime}=(1,-2) \\ B^{\prime}=(4,-3) \\ C^{\prime}=(4,-4) \end{gathered}[/tex]That means its reflected across the y-axis and the x-axis as follows;
[tex](x,y)\rightarrow(x+6,y-7)[/tex]After this the translation is complete.