Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
Answers
The three steps which Patel could use to solve the quadratic equation include the following:
A. 8(x² + 2x + (2/2)²) = -3 + 8.
B. x = -1 ±√5/8
E. 8(x² + 2x) = -3.
How to solve the quadratic equation?In order to solve the given quadratic equation, we would use the completing the square method as follows;
Separating the variables in the quadratic equation from constant, we have the following;
8x² + 16x + 3 = 0
8x² + 16x = -3
By factorizing the common variables in the quadratic equation from constant, we have the following;
8(x² + 2x) = -3 (step 1).
By completing the squares in the brackets and then balancing the expression on the right-hand side, we have the following;
8(x² + 2x + (2/2)²) = -3 + 8 (step 2).
8(x² + 2x + 1) = -3 + 8
8(x + 1)² = 5
Dividing both sides of the quadratic equation by 8, we have the following;
(x + 1)² = 5
Taking the square root of both sides of the quadratic equation, we have the following;
(x + 1) = ±√5/8
x = -1 ±√5/8 (step 3).
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Related Questions
35% of ____ = $3.50 find the unknown number
Answers
Answer:
10
Step-by-step explanation:
35% of x = 3.5 To change a percent to a decimal, divide by 100%
.35x = 3.5 Divide both sides by 3.5
[tex]\frac{.35x}{.35}[/tex] = [tex]\frac{3.5}{.35}[/tex]
x = 10
Check:
.35 x 10 = 3.3.5 = 3.5
Answer:
10
Step-by-step explanation:
Let the unknown number be x.
35% of x = 3.50
35/100 * x = 3.50
35x = 3.50 * 100
35x = 350
x = 350/35
x = 10
Hence, the unknown number is 10.
Find the value of x.
x+16
9
Answers
Answer:
x = - 7
Step-by-step explanation:
given that the 3 angles in the triangle are congruent, then the triangle is equilateral with the 3 sides congruent , then
x + 16 = 9 ( subtract 16 from both sides )
x = - 7
Answer:
x=-7
Step-by-step explanation:
The triangles sides are all the same in length, therefore, you need all the sides to be equal to 9.
-12+16=4 This addition problem does not equal to 9 so it is not correct.
-7+16=9 This is correct because -7+16 or 16-7 = 9.
-9+16=7 This addition problem does not equal to 9 so it is not correct.
-11+16=5 This addition problem does not equal to 9 so it is not correct.
So, x = -7.
Four thousand two hundred carnations were reserved for use on thge float. If this was 7/10 of the flowers needed, how many glowers would be on the float
Answers
The flowers on the float would be 6.000 flowers. The result is obtained by using fraction multiplication.
How to count a set of objects using fractions?Fraction represents the part of a set of objects. It has two parts separated by a dividing line, namely numerator at the top and denominator at the bottom.
For example:
1/4 (one-fourth)2/5 (two-fifth)It means one of four parts and two of five parts.
We have four thousand two hundred carnations on the float. It was 7/10 of flowers needed. Find the whole flowers on the float!
The carnations of a set of flowers is 7/10. It is 4200 carnations.
The carnations part is 7 and the whole part of flowers is 10.
Using fraction, the whole flowers would be
= 10/7 × 4200
= 6.000 flowers
Hence, the number of flowers needed to be on the float is 6.000 flowers.
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What is complete angle Class 7?
Answers
The angle with the measure 360° is known as a complete angle. A complete angle is one full rotation measuring 360°.
When the final point coincides with the initial point, after one whole rotation, then the angle so created is known as the complete angle. A complete angle is also known as a full angle or a round angle.
The measure of a complete angle is equal to 2π radians = 360 degrees which is the central angle of a circle. Also, if we combine four right angles or two straight angles it makes a complete angle. A complete angle is identical to a zero angle but the difference is only the amount of rotation.
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Sabreena is playing a card game, and the odds of her winning after drawing the next card are 5:7. What is the probability of her not winning? Enter your answer as a decimal rounded to the nearest thousandth, like this: 0.423
Answers
The probability that Sabreena is going to lose is given as 0.5833
How to solve for the probabilityProbability is a measure of the likelihood of a specific event or outcome occurring. It is typically expressed as a decimal number between 0 and 1, or as a percentage between 0% and 100%.
A probability of 0 indicates that an event is impossible and will never occur, while a probability of 1 indicates that an event is certain and will always occur.
If the odds that Sabreena has of winning in this game is 5: 7, this is written as 5 / 7
In this case, the odds of Sabreena winning are 5:7,
so the probability of winning is 5/(5+7)
the probability of not winning is 1 - 5/12
The probability of not winning is approximately 0.5833
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What type of graph is an inverse relationship?
Answers
On a graph, an inverse relationship always has a negative slope.
What is an inverse relationship?In statistics, if higher values of one variable tend to be related to lower values of the other, there is a negative association or inverse relationship between the two variables.
A negative link between two variables typically denotes a negative correlation, or what is similar in some cases, a negative slope on the associated graph.
Anticorrelation or inverse correlation are other terms for a negative correlation between two variables.
When two variables change in an inverse relationship, they do so in opposite directions: one increases while the other drops, and vice versa.
Y declines as X rises in an inverse relationship.
An inverse relationship always has a negative slope on a graph.
Therefore, on a graph, an inverse relationship always has a negative slope.
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A book is 6 inches wide and 9 inches tall.
A rectangle is shown. The length of the rectangle is labeled 6 inches. The width of the rectangle is labeled 9 inches.
A publisher wants to use a scale factor of 1.5 to enlarge a book. What will the area of the front of the book be after the book is enlarged? (5 points)
a
54 in2
b
81 in2
c
121.5 in2
d
78.75 in2
Answers
The area of the front of the book after it has been enlarged would be = 121.5 in². That is option C.
What is a rectangle?A rectangle is defined as the type of quadrilateral which has two opposite sides that are equal and parallel and with four angles that are equal to 90°.
The length of the rectangular book= 6 inches
The width of the rectangular book = 9 inches
Using the scale factor of 1.5 the new length and width is thus:
length = 6 × 1.5 = 9 inches
9× 1.5 = 13.5
Therefore area of the book = l×W = 9 × 13.5 = 121.5 in².
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How many divisors of 4! x 3! x 2! x 1! are perfect squares?
Answers
There are 2 divisors of 4! x 3! x 2! x 1! which are perfect squares.
What is Number system?A number system is defined as a system of writing to express numbers.
The factorial 4! is 24
Factorial value of 3!=6
Factorial value 2!=2
Factorial value 1!=1
4! x 3! x 2! x 1! =24×6×2×1=288
288 can be written as a product 2 and 144 which are perfect squares.
So 2 and 144 are the divisors of 4! x 3! x 2! x 1!
Hence, there are 2 divisors of 4! x 3! x 2! x 1! which are perfect squares.
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Type the correct answer in each box.
Table A: Inventory Stock
Product Store A Store B Store C
X 543 356 643
Y 364 476 419
Z 376 903 409
Table B: July Unit Sales
Product Store A Store B Store C
X 102 78 97
Y 98 87 59
Z 54 89 79
Table A shows the total inventory of three products for three Sports Equipment Corporation stores on July 1. Table B shows unit sales data for the month of July.
If you create a matrix, C, to show the inventory at the end of July, the value of the entry represented by c22 is
.
In a matrix with components aij, which represent unit sales for July, the maximum possible value that a31 can have is
Answers
The matrix C shows the inventory of the three products for the three Sports Equipment Corporation stores at the end of July. The value of the entry represented by c22 is 389, which is the value for Store B for Y in Table B.
Table C: Ending Inventory
Product Store A Store B Store C
X 441 278 546
Y 266 389 360
Z 322 814 330
The value of the entry represented by c22 is 389, which is the value for Store B for Y in Table B.
The maximum possible value that a31 can have is 903, which is the value for Store C for Z in Table A.
The value of the entry represented by c22 in the matrix C that shows the inventory at the end of July is 389, and the maximum possible value that a31 can have is 903.
The matrix C shows the inventory of the three products for the three Sports Equipment Corporation stores at the end of July. The value of the entry represented by c22 is 389, which is the value for Store B for Y in Table B. The maximum possible value that a31 can have is 903, which is the value for Store C for Z in Table A. This value indicates that the maximum number of units of Product Z that can be stored in Store C is 903. In summary, the value of c22 in the matrix C is 389, and the maximum value of a31 is 903.
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Answer the questions about the following polynomial.
8x³+6x-1
The expression represents a
term is
the leading term is
polynomial with
terms. The constant
, and the leading coefficient is
Answers
The expression represents a polynomial with three terms.
What is polynomial?A polynomial is an expression consisting of variables (often denoted by x, y, z, etc.) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. Polynomials can be used to express a wide range of algebraic equations, from simple linear equations to more complex equations. Polynomials can also be used to construct functions with properties that are useful for solving real-world problems.
The expression represents a polynomial with three terms.
The constant term is -1, and the leading coefficient is 8. The leading term is 8x³.
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The intensity level of sound, L measured in decibels (dB), is a function of the sound
intensity, S watts per square metre (W m-2). The intensity level is given by the following
formula.
(a) An orchestra has a sound intensity of 6. 4 × 10-3 Wm-2. Calculate the intensity level, L of
the orchestra.
(b) A rock concert has an intensity level of 112 dB. Find the sound intensity, S
Answers
(a) If an orchestra has a sound intensity of [tex]6.4 \times 10^-^3\ Wm^{-2[/tex], then
the intensity level of sound, L, is 98.062 dB.
(b) If a rock concert has an intensity level of 112 dB, then the sound intensity, S, is [tex]10^{-0.8}\ Wm^{-2[/tex].
Sound intensity, also known as acoustic intensity, is defined as the dominion ferried by sound waves per unit area in a direction perpendicular to that area.
Given that the intensity level of sound, L, measured in decibels (dB), is a function of the sound intensity, S, watts per square meter ([tex]Wm^{-2[/tex]) as
[tex]L = 10log_{10}(S\times10^1^2), S\geq 0[/tex]
(a) If an orchestra has a sound intensity of [tex]6.4 \times 10^-^3\ Wm^{-2[/tex], then
the intensity level of sound,
[tex]L = 10log_{10}(6.4\times10^{-3}\times10^1^2)[/tex]
[tex]= 10log_{10}(6.4\times10^9)\\= 10(log_{10}6.4\ +\ log_{10}10^9 )\\= 10(0.8062\ +\ 9)\\=10 \times 9.8062\\= 98.062\ dB[/tex]
(b) If a rock concert has an intensity level of 112 dB, then
[tex]112 = 10log_{10}(S\times10^1^2)\\log_{10}(S\times10^1^2) = \frac{112}{10}\\log_{10}(S\times10^1^2)= 11.2\\S\times10^1^2 = 10^{11.2}\\S = \dfrac{10^{11.2}}{10^1^2} \\S = 10^{-0.8}\ Wm^{-2[/tex]
The sound intensity is [tex]10^{-0.8} Wm^{-2[/tex].
Hence, (a) L = 98.062 dB and (b) S [tex]= 10^{-0.8}\ Wm^{-2[/tex].
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A computer is programmed to generate a sequence of three digits, where each digit is either 0 or 1, and each of these is equally likely to occur. Construct a sample space that shows all possible three-digit sequences of 0s and 1s and then find the probability that a sequence will contain exactly one 0. a. 000, 001, 010, 011, 100, 101, 110, 111; the probability is . b. 001, 011, 101, 111; the probability is . c. 000, 010, 011, 101, 111; the probability is . d. 000, 001, 010, 011, 100, 101, 110, 111; the probability is .
Answers
The probability that a sequence will contain exactly one 0 as calculated from the data given is found to be 3/8.
Taking into consideration the sequences where the digit 0 occurs , we will get the possibilities of getting 0 and 1 as 2 .
The number of sample points in the sample space will be ,
2 x 2 x 2 = 8 sample points.
These sample space are, S = {111, 110, 101, 011, 100, 010, 001, 000},
Now , the sequence having all three 0 as seen from the sample space is found to be 3.
So the probability becomes , P(0) = no of favorable outcomes / total number of outcomes =3/8.
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What is the equation for the linear model in the scatter plot obtained by choosing the two points closest to the line?
A)Y = -3 x+ 56
B)Y = -2 x +46
C)Y = -2 x +56
D)Y = 2 x + 56
Answers
The equation for the linear model in the scatter plot is Y = -2x + 56.
To calculate this equation, we need to find the slope (m) and the y-intercept (b). The slope is calculated with the formula m = (y2 - y1) / (x2 - x1), where x and y represent the coordinates of two points on the graph.
The two points closest to the line in the scatter plot are (2, 48) and (4, 52). Substituting these values into the formula gives us m = (52 - 48) / (4 - 2) = 4/2 = 2.
The y-intercept is the point where the line crosses the y-axis. To find it, we need to substitute the slope and one point's coordinates into the equation y = mx + b. For our equation, we will use the coordinates (2, 48). Substituting these values into the equation gives us 48 = 2x + b, and solving for b gives us b = 48 - 2(2) = 44.
Therefore, the equation for the linear model in the scatter plot is Y = -2x + 56.
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Geometry: Applications of All Right Triangles
Look at the attachments below to answer this question.
Answers
Given:
A length of a side of an equilateral triangle = 32 cm
Formula Used:
If in an equilateral triangle with side length 'a' then,
Area of an equilateral triangle = [(√3)/4] × a2
Calculations:
Area of an equilateral triangle = [(√3)/4] × 322
⇒ (1024 × √3)/4
⇒ 256√3 cm2
Decompose one number to subtract 726-340
Answers
The subtraction of the given number would be = 386
What is subtraction?Subtraction is defined as one of the major arithmetic operations that is used to remove a value from another given values.
The subtraction of the value 340 from 726 would be = 386.
That is; 726 - 340 = 386
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Subtract -2a+7b=-5 from the other equation so the b-terms become opposites
Answers
When subtracted -2a+7b=-5 from the other equation so the b-terms become opposites, we get 2a -7b = 5 as the result.
What is equation?In mathematics, an equation is an expression or a statement made up of two algebraic expressions with the same value that are separated by the equal sign. It is a mathematically quantified version of an otherwise expressed statement. Equations can take many different forms. Equations are used to compare two expressions.
To Subtract -2a+7b=-5 from the other equation so the b-terms become opposites, we need to make +7b to -7b
This is only possible when the other term has 14,
Lets solve
2a + 7b = - 5
- 4a + 14b = -10
-2a -7b = 5
Thus, when subtracted -2a+7b=-5 from the other equation so the b-terms become opposites, we get 2a -7b = 5 as the result.
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What is 2x10-2+6 please help
Answers
Answer:
24
Step-by-step explanation:
What is 2x10-2+6?
2 × 10 - 2 + 6 = (remember PEMDAS)
20 - 2 + 6 =
18 + 6 =
24
Answer:
24 should be your answer
Find an equation for the line that passes through the points (-5, 2) and (3, 4)
Answers
Step-by-step explanation:
1. Find the slope first using y2 - y1/ x2 - x1. This should look like 4 -2/ 3 - (-5), which can also be written as 4 - 2/ 3 + 5.
2. Simplify the fraction. This should look like 2/8, which can also be written as 1/4 once you divide it by 2.
3. Use the point-slope formula to find the y-intercept of the equation now. The formula is y2 - y1 = m (x2 - x1). Input either (-5, 2) or (3,4) into the equation. I'll use (3,4) as an example. After inputting that point, the equation would be y - 4 = 1/4 (x - 3).
4. Simplify this equation by distributing the 1/4 into the parentheses first. Once done, the equation will be y - 4 = 1/4x - 0.75.
5. Add 4 on both sides of the equation to get y by itself. After that the equation will be y = 1/4x + 3.25.
Dawson says that the expression (2 4/10+ 8 4/5)-3 1/5 is equal to a whole num do you agree explain hurry
Answers
If Dawson says that the expression [tex](2\frac{4}{10}+8\frac{4}{5})-3\frac{1}{5}[/tex] is equal to a whole number , then we can say that Dawson is correct .
The Mixed fraction expression is given as : [tex](2\frac{4}{10}+8\frac{4}{5})-3\frac{1}{5}[/tex] ;
first , we need to convert the mixed fraction in to simpler fractions ,
On converting ,
we get ;
the expression as : [tex](\frac{24}{10}+\frac{44}{5})-\frac{16}{5}[/tex] ;
taking the LCM of 10 and 5 as 50 ,
we get ;
⇒ [tex](\frac{24}{10}+\frac{88}{10})-\frac{16}{5}[/tex]
⇒ [tex](\frac{112}{10})-\frac{16}{5}[/tex]
Simplifying further ,
we have ;
⇒ [tex](\frac{112}{10})-\frac{32}{10}[/tex] ,
⇒ [tex]\frac{80}{10}[/tex]
= 8 , which is a whole number .
Therefore , we can agree with Dawson's statement that the expression [tex](2\frac{4}{10}+8\frac{4}{5})-3\frac{1}{5}[/tex] equals to a whole number "8" .
The given question is incomplete , the complete question is
Dawson says that the expression ([tex]2\frac{4}{10}[/tex] + [tex]8\frac{4}{5}[/tex]) - [tex]3\frac{1}{5}[/tex] is equal to a whole number . Do you agree ? Explain .
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Jeris Shoppe marks up every item 75% over the wholesome price. If a sweater costs $16.00 from the wholesaler, how much will the sweater retail for at Jeris?
Answers
Answer:
$28
Step-by-step explanation:
175%*16.00 = 175/100 * 16.00
Put it int he calculator to get 28 dollars
While Tanya wa hopping, he overheard the aleman at Electronic Mania ay that if they old 30% more computer than they old lat month, they would get a bonu. Lat month they old 27 computer. How many computer mut the ale team ell to receive the bonu? Explain your reaoning
Answers
The sales team must sell 8 more computers than they sold last month to receive the bonus.
Last month the sales team of Electronic Mania sold 27 computers.
If they sold 30% more computer than they sold last month, they would get a bonus.
First we find the 30 percent if 27
27 × 30/100
= 8.1
Let m be the total number of computers sold.
So, the total number of computers sold would be,
m = 27 + 8.1
m = 35.1
m ≈ 35
Therefore, they need to sell 35 computers in total.
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select the correct answer. Solve the quadratic equation. (x + 4)(x + 1) = 0
x = 4 or x = 1
x = -4 or x = 1
x = -4 or x = -1
x = 4 or x = -1
Answers
Answer:
x = -4 or x = -1
Step-by-step explanation:
Let's check
x = -4
(-4 + 4)(-4 + 1) = 0
(0)(-3) = 0
0 = 0
Let's check x = -1
(-1 + 4)(-1 + 1) = 0
(-3)(0) = 0
0 = 0
So, x = -4 or x = -1 is correct answer!
In the figure shown, what is the value of x?
PLEASE HURRY JUST GIVE ME THE ANSWER THANK YOU
Answers
Answer: x= 23
Step-by-step explanation:
An item on ale cot 20% of the original price if the original price wa $95 what i the ale price
Answers
By using formula and solving we get the item is on sale for $76.
What is selling price?
The selling price is the amount of money that a seller asks for in exchange for a product or service. It is also known as the "list price" or "retail price" and it is the price at which an item is intended to be sold. Selling price is usually set by the manufacturer or the retailer, taking into account the cost of production, distribution, and marketing, as well as competition and market demand. The selling price is usually higher than the cost of production, which includes the cost of the materials, labor, and overhead expenses.
What is the formula to calculate selling price?The formula to calculate the selling price of a product or service depends on the information available and the desired level of accuracy. However, there are a few common formulas used to calculate the selling price based on different factors.
Cost-plus pricing formula: This formula calculates the selling price by adding a markup percentage to the cost of the product or service.
The formula is: Selling price = Cost + (Cost x Markup percentage)
If the original price of an item was $95 and it is now on sale for 20% off, we can calculate the sale price using the following formula:
Sale price = Original price x (1 - Discount percentage)
In this case, the discount percentage is 20%, so we can express it as 0.2. Therefore, the formula becomes:
Sale price = $95 x (1 - 0.2)
To calculate the sale price, we need to multiply the original price by (1 - 0.2) which is (1-0.2) = 0.8
Sale price = $95 x 0.8
Sale price = $76
So, the item is on sale for $76.
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A lottery game contains 24 balls numbered 1 through 24. What is the probability of choosing a ball numbered 25
Answers
Selecting ball number 25 has no chance of happening.
Explain about the probability?Probability is only the likelihood that something will occur. When we don't know how something will turn out, we might discuss the likelihood of various outcomes or the potential of one. Statistics is the scientific study of events that conform to a probability distribution.
It is predicated on the likelihood that something will take place. The rationale for probability serves as the theoretical probability's essential tenet. A coin has a 12% chance of landing on its head, for instance, when it is flipped.
Probability is a statistic that is used to indicate the likelihood or potential for an event to occur. Both fractions from 0 to 1 and percentages from 0% to 100% can be used to indicate probabilities.
In 25th Ball it is 0
Because there is no 25th ball
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Meri is making birdhouses. Each birdhouse uses 58 yard of wood. What is the total length of wood Meri will need to make 12 birdhouses? Drag each of the numbers from the box to complete and solve the equation. Each number will be used once
Answers
Meri will need 696 yards of wood to make 12 birdhouses, as each birdhouse requires 58 yards of wood.
Meri is making birdhouses and each birdhouse needs 58 yards of wood. To find out the total length of wood needed for making 12 birdhouses, we can use the formula:
length of wood per birdhouse x number of birdhouses = total length of wood
So, in this case, we can substitute the given values in the formula:
58 yards x 12 birdhouses = 696 yards
This means Meri needs 696 yards of wood to make 12 birdhouses.
This equation works because it uses the concept of the unitary method, where we find the total length of wood by multiplying the number of birdhouses by the length of wood used in each birdhouse, this way we are able to find the total amount of wood needed.
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geometry stuff pls help
Answers
Answer:
Step-by-step explanation:
SQR-PRQ-SRP
SP/RP=RP/PQ
QP/QR=RQ/SQ
It takes 3 hours to drive 180 miles. How long will it take to drive 330 miles?
Answers
Answer:
5.5
Step-by-step explanation:
180/3 =60 (60/1 hr)
330/60 =5.5
explanation with steps
Answers
Answer:
x = 40° , y = 140° z = 10°
Step-by-step explanation:
the sum of the 3 angles in a triangle is 180° , then
x + 60° + 80° = 180°
x + 140° = 180° ( subtract 140° from both sides )
x = 40°
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
y is an exterior angle of the triangle , then
y = 60° + 80° = 140°
x is also an exterior angle , then
30° + z = x
30° + z = 40° ( subtract 30° from both sides )
z = 10°
I don't get this question can some one please help me solve it
Answers
Answer:
3, 2
Step-by-step explanation:
In order for the equation to be equal to zero, the following must be true:
x-3 = 0 or,
x-2 = 0
Therefore the 2 solutions are x=3, x=2