Answers
Answer:
\(\begin{array}{|l|l|c|c|c|}\cline{1-5} \textbf{Equation} & \textbf{Standard Form} & \textbf{a} & \textbf{b} & \textbf{c}\\\cline{1-5} \text{1.}\:\:x^2+x=20 & x^2+x-20=0 & 1 & 1 & -20\\\cline{1-5} \text{2.}\:\:4x^2-2x=28 \phantom{)))}& 4x^2-2x-28=0 \phantom{)))}& 4 & -2 & -28\\\cline{1-5} \text{3.}\:\:5x^2=225 & 5x^2-225=0 & 5 & 0 & -225\\\cline{1-5} \text{4.}\:\:x^2-x=36 & x^2-x-36=0 & 1 & -1 & -36\\\cline{1-5} \text{5.}\:\:3x^2-4=7x & 3x^2-7x-4=0 & 3 & -7 & -4 \\\cline{1-5}\end{array}\)
Step-by-step explanation:
Standard form of a quadratic equation:
\(\boxed{ax^2+bx+c=0}\)
Question 1
Given:
\(x^2+x=20\)
Rearrange to standard form by subtracting 20 from both sides:
\(\implies x^2+x -20=20-20\)
\(\implies x^2+x -20=0\)
Therefore:
a = 1b = 1c = -20Question 2
Given:
\(4x^2-2x=28\)
Rearrange to standard form by subtracting 28 from both sides:
\(\implies 4x^2-2x-28=28-28\)
\(\implies 4x^2-2x-28=0\)
Therefore:
a = 4b = -2c = -28Question 3
Given:
\(5x^2=225\)
Rearrange to standard form by subtracting 225 from both sides:
\(\implies 5x^2-225=225-225\)
\(\implies 5x^2-225=0\)
Therefore:
a = 5b = 0c = -225Question 4
Given:
\(x^2-x=36\)
Rearrange to standard form by subtracting 36 from both sides:
\(\implies x^2-x-36=36-36\)
\(\implies x^2-x-36=0\)
Therefore:
a = 1b = -1c = -36Question 5
Given:
\(3x^2-4=7x\)
Rearrange to standard form by subtracting 7x from both sides:
\(\implies 3x^2-4-7x=7x-7x\)
\(\implies 3x^2-4-7x=0\)
\(\implies 3x^2-7x-4=0\)
Therefore:
a = 3b = -7c = -4Related Questions
14. Carrie has 11 board games. Carrie has 8 more board games than Marisol has. How many board games does Marisol have?
Answers
Answer:
3
Step-by-step explanation:
11-8=3 because 8 more than 3 is 11
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P(X≤2), n=4, p=0.2
Answers
The number of trials and the probability of obtaining success will be given as P(X ≤ 2) = 0.9728.
How to find that a given condition can be modeled by binomial distribution?Binomial distributions consist of n independent Bernoulli trials.
Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as
X \sim B(n,p)
The probability that out of n trials, there'd be x successes is given by
\(\rm P(X =x) = \: ^nC_xp^x(1-p)^{n-x}\)
Assume the random variable X has a binomial distribution with the given probability of obtaining success.
Then the number of trials and the probability of obtaining success will be
P(X ≤ 2), n = 4, p = 0.2
Then we get
\(\rm P(X =2) = \: ^4C_2(0.2)^2(1-0.2)^{4-2}\\\\P (X=2) = 6 \times 0.0256 \\\\P (X=2) = 0.1536\)
Then the cumulative probability will be
\(\rm P(X\leq 2) = 0.9728\)
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Robert can complete 10 inspections in 8 hours. Which represents the unit rate for the number of inspections he completes per hour?
Answers
Answer: 5 inspections in 4 hours, because if its 8 hours it would be 10 inspections
Step-by-step explanation:
Answer:
1.25
Step-by-step explanation:
10 ÷ 8 = 1.25
Solve the inequality for x:
8 + 4(x - 3) + 3x < 24
Answers
Answer:
7x - 4 < 24
Step-by-step explanation:
8 + 4x - 12 + 3x < 24
3x + 4x - 12 + 8 < 24
7x - 4 < 24
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Answer:
8 + 4x - 12 + 3x < 24
3x + 4x - 12 + 8 < 24
7x - 4 < 24
Step-by-step explanation:
Simplify all ratios and keep them as improper fractions
If arc cos = -8/17 and arc sin is negative, then arcsin is _____ and arctan is ______
Answers
To find arcsin, we need to use the identity:
sin(arcsin(x)) = x
Since arcsin is negative, sin(arcsin) is also negative. Therefore, we can say:
sin(arcsin) = -sqrt(1 - (cos)^2)
where (cos)^2 = 8/17
Substituting, we get:
sin(arcsin) = -sqrt(1 - (8/17))
Simplifying, we get:
sin(arcsin) = -sqrt(17/17 - 8/17)
Simplifying further, we get:
sin(arcsin) = -sqrt(9/17)
Therefore, arcsin = -sqrt(9/17)
To find arctan, we need to use the identity:
tan(arctan(x)) = x
Substituting, we get:
tan(arctan) = -8/17
Therefore, arctan = -8/17
So, arcsin is -sqrt(9/17) and arctan is -8/17.
PLEASE TELL ME WHAT TO WRITE HERE :’))
Answers
Answer: (Answer in explanation)
Step-by-step explanation:
(12)B > 180
Her goal is to make more than 180 so if she wants to sell each book for $12 then so if she sells 14 books or above she would get more than $180.
So B could equal anything 16 and above but in my case I chose 24
(12)24 = 288 > 180
So write a equation like mine that equals a number that's greater than 180. Keep in mind each book sells for $12 each. Then solve for B which is how many books she has to sell to get the number greater than 180.
Higher Order Thinking Morgan read
a thermometer at 7:00 P.M. The
temperature was 16°C. This temperature
was 9°C less than the temperature at
2:00 P.M. The temperature at 2:00 P.M.
was 10°C higher than the temperature at
8:00 A.M. What was the temperature at
8:00 A.M.?
Answers
The temperature at 8:00 A.M. was 15°C.
Using the given information:
1. At 7:00 P.M., the temperature was 16°C.
2. This temperature was 9°C less than the temperature at 2:00 P.M.
We can use this information to find the temperature at 2:00 P.M.:
Temperature at 2:00 P.M. = 16°C (temperature at 7:00 P.M.) + 9°C
Temperature at 2:00 P.M. = 25°C
3. The temperature at 2:00 P.M. was 10°C higher than the temperature at 8:00 A.M.
Now, we can find the temperature at 8:00 A.M.:
Temperature at 8:00 A.M. = 25°C (temperature at 2:00 P.M.) - 10°C
Temperature at 8:00 A.M. = 15°C
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Help pls i dont understand this
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The percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.
What is the percentage?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.
The total number of water bottles the company manufactured in February, March, and April.
In February, the company manufactured 4,100 water bottles. In March, the company manufactured 7% more water bottles than in February, which is 7/100 * 4,100 = 287 water bottles.
Therefore, the total number of water bottles the company manufactured in March is 4,100 + 287 = 4,387 water bottles. In April, the company manufactured 500 more water bottles than in March, which is 4,387 + 500 = 4,887 water bottles.
This is calculated as (4,887 - 4,100) / 4,100 = 0.195 or 19.5%.
Therefore, the percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.
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Using lexicographic ordering of 4-sets, select the two inequalities that are both correct. O {2,1,4,5}<{1,16,67,4} {1,5,7,8}<{1,6,67,8} O {2,1,4,5}>{1,16,67,4} {1,5,7,8}<{1,6,67,8} O{2,1,4,5}<{1,16,67,4} {1,5,7,8}>{1,6,67,8} O {2,1,4,5}>{1,16,67,4} {1,5,7,8}>{1,6,67,8}
Answers
Using lexicographic ordering of 4-sets, the two correct inequalities are {2,1,4,5}<{1,16,67,4} {1,5,7,8}<{1,6,67,8}
Lexicographic ordering, also known as a dictionary or alphabetical order, is a method of comparing sequences of elements. In this case, we are comparing 4-sets. When comparing two sets, we start by comparing the first elements of each set. If they are equal, we proceed to compare the second element, and so on until we find a pair of elements that are different. The set with the smaller element at that position is considered smaller in lexicographic order.
1. In the first inequality, {2,1,4,5}<{1,16,67,4}, we can see that the first element of the first set (2) is greater than the first element of the second set (1). Therefore, the second set is smaller in lexicographic order, making the inequality correct.
2. In the second inequality, {1,5,7,8}<{1,6,67,8}, the first elements are equal (1). So, we proceed to compare the second elements. The second element of the first set (5) is smaller than the second element of the second set (6), so the first set is smaller in lexicographic order, making the inequality correct.
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Dead leaves accumulate on the ground in a forest at a rate of 5 grams per square centimeter per year. At the same time, these leaves decompose at a continuous rate of 65 percent per year.A. Write a differential equation for the total quantity Q of dead leaves (per square centimeter) at time t:dt/dQ= ?B. Sketch a solution to your differential equation showing that the quantity of dead leaves tends toward an equilibrium level. Assume that initially (t=0) there are no leaves on the ground.What is the initial quantity of leaves? Q(0)= ?What is the equilibrium level? Qeq= ?
Answers
Answer:
ik this not an answer but i reccomend a science calculaor with these questions
Step-by-step explanation:
Which single transformation can be applied to the graph of y = 72 StartRoot x EndRoot to produce the graph of y = 9 StartRoot x EndRoot?
- vertical translation
- vertical compression
- horizontal translation
- horizontal compression
Answers
Answer:
vertical....
Step-by-step explanation:
NawfSide 38 Baby
Answer:
B vertical compression
Step-by-step explanation:
edge :)
The diameter of a semicircle is 4 yards. What is the semicircle's perimeter?
Use 3.14 for x.
d=4 yd
Answers
The diameter of a semicircle is 4 yards. The perimeter for a semicircle having a diameter of 4 yards is 10.28 yards.
The perimeter of a shape is the distance of the path or boundary that surrounds the shape.
The formula for the perimeter of a semicircle is πr + 2r
π(pie)=3.14
r(radius)=2 yards (∴ radius=1/2diameter)
∴ the perimeter of a semicircle = πr + 2r
= 3.14×2+2×2
=10.28 yards.
∴ The perimeter of a semicircle with a diameter of 4 yards is 10.28 yards.
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Simplify the expression √48
Answers
4√3
Decimal Form:
6.92820323
Ms. Francis is planning a birthday party for her daughter. There will be 22 children at the party, and in order to seat them all she
needs to rent square card tables. Only 1 child can sit at each side of a card table.
Ms. Francis wants to arrange the tables in a rectangular shape so they look like one large table. The room is large enough that
the rectangle can be made with more than one row of tables.
1122 children2
Answers
Answer:
she can rent 28 tables and arrange them in 4 rows and 7 columns
■■■■■■■
■■■■■■■
■■■■■■■
■■■■■■■
to seat 22 children
Please help! NO LINKS (Answer and explanation please :( )
Answers
Answer:
sum of angles in a quadrilateral is 360
Step-by-step explanation:
3x-15 +3x+15+y+30+D=360
hope that explanation helps
Use Elimination for the answer on both :)
Answers
The value of x and y after solving the equation -5x - 10y = 30 and - 3x + 3y = 27 by elimination method is -6 and 3 respectively.
What is the equation?A formula known as an equation uses the equals sign to denote the equality of two expressions.
Given:
-5x - 10y = 30 and - 3x + 3y = 27
Solve by using the elimination method,
Divide the equation - 3x + 3y = 27 by 3 and equation -5x - 10y = 30 by 5 on both sides,
(- 3x + 3y) / 3 = 27 / 3 and (-5x - 10y) / 5 = 30 / 5
-x + y = 9 and -x - 2y = 6
Subtract equation
-x + y = 9 - (-x - 2y = 6)
-x + y - 9 = x - 2y - 6
y = 3
and - x + 3 = 9, x = -6
Therefore, the value of x and y after solving the equation -5x - 10y = 30 and - 3x + 3y = 27 by elimination method is -6 and 3 respectively.
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A person invests 4000 dollars in a bank. The bank pays 5.75% interest compounded quarterly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 5900 dollars?
Answers
Answer:
t = 6.8 years
Step-by-step explanation:
The formula for compound interest is
\(A(t)=P(1+r/n)^n^t\), where P is the principal/amount invested, r is the interest rate, n is the number of compound periods per year (4 for quarterly), and t in the time in years.
We know that A = $5900, P = $4000, and r = 0.0575 (we must convert the percentage to a decimal). We must solve for t and round to the nearest tenth:
\(5900=4000(1+0.0575/4)^(^4^t^)\\\\59/40=(1623/1600)^4^t\\\\log(59/40)=log(1623/1600^4^t)\\\\log(59/40)=4t*log(1623/1600)\\\\log(59/40)/log(1623/1600)=4t\\\\1/4(log(59/40)/log(1623/1600))=t\\\\6.80773607=t\\\\6.8=t\)
Suppose that addition and subtraction had higher precedence than multiplication
and division. Then the expression
2 + 3 * 12 / 7 - 4 + 8
would evaluate to which of the following?
(A) 11
(B) 12
(C) 5
(D) 9
(E) -4
Answers
A) The addition and subtraction had higher precedence than multiplication and division is 11
The precedence's correct order is Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction. Note that Multiplication and Division are left to right whichever is first, same for addition and subtraction.Operator precedence decides how an expression is evaluated. For example, Multiplication has higher precedence than addition, therefore a+b*c will be evaluated as a + (b*c). (expression in bold is evaluated first, then added to a)
The expression 2 + 3 × 12 / 7 - 4 + 8 would evaluate to 11 if addition and subtraction had higher precedence than multiplication and division because the expression would be calculated as follows:
\(2 + (3 * 12 / 7) - 4 + 8 = 2 + (36 / 7) - 4 + 8 = 2 + 5 - 4 + 8 = 11.\)
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Convert the following decimal numbers to BCD and add them. Convert the result back to decimal to check your answer
(a) 8
(b) 43
(c) 12 + 16
(d) 47 +38
(e) 36 +22
(f) 80 + 23 + 72
(g) 12 +89
(h) 99
Answers
Answer and Step-by-step explanation:
Solution:
(a) 8 + 3
Convert into BCD:
8 = 1000
3 = 0011
Add them:
8 + 3 = 11
1000 + 0011 = 1011
Answer is correct.
(b) 43 + 72
Convert into BCD:
43 = 0100 0011
72 = 0111 0010
Add them:
43 + 72 = 115
0100 0011 + 0111 0010 = 0001 0001 0101
(c) 12 + 16
Convert into BCD:
12 = 0001 0010
16 =0001 0110
Add them:
12 + 16 = 28
0001 0010 + 0001 0110 = 0010 1000
00101000 = 00101000
Hence Answer is correct.
(d) 47 + 38
Convert into BCD:
47 = 0100 0111
38 =0011 1000
Add them:
47 + 38 = 85
0100 0111 + 0011 1000= 1000 0101
(e) 36 + 22
Convert into BCD:
36=0011 0110
22=0010 0010
Add them:
36 + 22 = 85
0011 0110 + 0010 0010 = 1000 0101
(f) 80 + 23 + 72
Convert into BCD:
80 =1000 0000
23 = 0010 0011
72 = 0111 0010
Add them:
80 + 23 + 72 =175
1000 0000 +0010 0011+ 0111 0010 = 0001 0111 0101
(g) 12 + 89
Convert them into BCD:
12 = 0001 0010
89 = 1000 1001
Add them:
12 + 89 = 101
0001 0010 + 1000 1001 = 0001 0000 0001
(h) 99
Convert into BCD:
99 = 1001 1001
It takes 20 days using 12 machines to produce a batch of pens.
due to a fault only 3 machines were used for the first 8 days, all 12 machines were used from day 9 onwards.
how many days in total to produce the batch of pens
Answers
It would take a total of 20 days to produce the batch of pens.
Let's calculate the work done by the 3 machines for the first 8 days:
Work done by 3 machines in 8 days = (3/12) * 8 = 2 days' worth of work
The remaining work that needs to be done by all 12 machines is:
Remaining work = 1 - (2/20) = 0.9
Now, we can use the work formula to find the total number of days needed to complete the remaining work with 12 machines:
Total work = 0.9
Work done by 12 machines in one day = 12/20 = 0.6
Total number of days needed = 0.9/0.6 = 1.5
Therefore, the total number of days needed to produce the batch of pens is:
8 (days with 3 machines) + 1.5 (days with 12 machines) = 9.5 days
However, we also need to add the 10.5 days it would take for all 12 machines to complete the batch from the beginning:
10.5 + 9.5 = 20 days
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please help me!! thank you!!
Answers
9514 1404 393
Answer:
2.5 cm
Step-by-step explanation:
The diameter of the circle is shown as 5 cm. The reminder tells you that the radius is half the diameter:
radius = diameter/2
radius = (5 cm)/2
radius = 2.5 cm
Need help ASAP
Will Mark, you brainlist
Answers
Answer:
(4,-1)
Step-by-step explanation:
Yell at me if im wrong.
Answer:
¼
Step-by-step explanation:
Compare the coordinates of two points to find the rate of change.
Using (0,-5) and (4,-6):
Δy/Δx = ((-6)-(-5))/(4-0) = (-1)/4 = -¼
I’ll give you 15 points if you know the answers to this question
Answers
It would be B)no.
Hope This Helps!
#9 find the area of parallelogram B.
Answers
Donde esta la foto??
:3
54 out of the 60 magazines at the bookstore are women's magazines. What percentage of the magazines at the bookstore are women's magazines?
Answers
Answer:
90
Step-by-step explanation:
for percentage
\(\frac{54}{60}\)×100
= 0.9×100
=90
4m^(3)+10m^(2)-84m
Solve by factoring.
Answers
x=0
x=7/2
x=-6
2. Use the image to answer the questions.
(a) What is the center and the radius of the circle?
(b) What are the equations of the circle in graphing form and in general form? Show your work.
Answers
Answer:
Center = (-1, 1)
Radius = 3
Graphing form
(x + 1)² + (y - 1)² = 3²
General form
x² + y² + 2x - 2y - 7 = 0
Step-by-step explanation:
Center = (-1, 1)
Radius = 3
Graphing form
(x + 1)² + (y - 1)² = 3²
General form \Expand graphing form\
(x² + 2x + 1) + (y² - 2y + 1) - 9 = 0
Rearrange
x² + y² + 2x - 2y - 7 = 0
A textile fiber manufacturer is investigating a new drapery yarn which the company claims have a mean thread elongation of 12kg with standard deviation of 0.5kg. The company wishes to test H0 : μ = 12 against H1 : μ < 12 using a random sample of 4 specimens.
What is the type I error probability if the critical region is defined as x < 11.5?
Answers
A textile fiber manufacturer is investigating a new drapery yarn which the company claims have a mean thread elongation of 12kg with a standard deviation of 0.5kg. the probability of observing a sample mean elongation of less than 11.5kg is approximately 0.0228
What is type I error probability?Generally, In order to answer this question, you need to know the shape of the distribution of the thread elongation of the new drapery yarn. If the thread elongation follows a normal distribution, then you can use a normal distribution to approximate the sampling distribution of the sample mean elongation.
If the null hypothesis is true, then the population mean elongation is 12kg and the standard deviation of the sampling distribution is
0.5/√(4) = 0.25kg.
Under these conditions, the probability of observing a sample mean elongation of less than 11.5kg is equal to the type I error probability.
You can use a normal distribution calculator or table to find this probability.
If the null hypothesis is true and the sample mean elongation is normally distributed with a mean 12kg and a standard deviation 0.25kg, then the probability of observing a sample mean elongation of less than 11.5kg is approximately 0.0228. This is the type I error probability.
Z score = x - μ/σ
= 11.5 - 12/0.25
= -2
P-value from Z-Table:
P(x<11.5) = 0.02275
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can someone tell me step by step how to solve this?
\((\frac{1}{3}-\frac{1}{10})^{2} -\frac{1}{5}:(\frac{2}{5} )^{2}\)
Answers
Answer:
Step-by-step explanation:
I take it that this is some sort of ratio. Start by solving the brackets on the left.
Brackets: 1/3 - 1/10
Brackets: 10/30 - 3/30
Brackets: 7/30
Brackets^2: 49/900
Brackets^2 - 1/5: 49/900 - 180/900
Brackets^2 - 1/5: -131/900
(2/5)^2 = 4/25
The way this read, it should be
\(\frac{\frac{-131}{900} }{\frac{4}{25} }\)
Which when you invert and multiply becomes
\(\frac{-131}{900} * \frac{25}{4}\)
which finally becomes
\(\frac{-131}{144}\)
Suppose that a group of 10 people join a weight loss program for 3 months. Each person's weight is recorded at the beginning and at the end of the 3-month program. To test whether the weight loss program is effective, the data should be treated as:
Answers
To test the effectiveness of the weight loss program, a PAIRED SAMPLE test distribution is used.
The weight loss data collated for the program for both the beginning and end of the program period was obtained with one subject or person having two separate readings, these shows that the samples are NOT INDEPENDENT.
When performing a test which involves DEPENDENT or MATCHED samples, whereby means of two measurements taken from the SAME subject are involved, a PAIRED SAMPLE TEST DISTRIBUTION IS ADOPTED.
Therefore, the effectiveness of the weight loss programme will be accurately evaluated using a PAIRED SAMPLE TEST.
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