The complete square of the given polynomial is
[tex](x+\frac{3}{2})^2=\frac{43}{12}[/tex]
What is the completing the square method?For solving the quadratic equation by completing the square, we first need to ensure that the constant of the square variable is unit.
Following are the steps involved
[tex]5x^2+15x-4=0[/tex]
divide both side by 5
[tex]x^2+3x-\frac{4}{3}=0[/tex]
add 9 on both sides of the equations
[tex]x^2+3x-\frac{4}{3}-9/4+ 9/4=0[/tex]
[tex]x^2+3x+ 9/4=\frac{4}{3}+9/4\\(x+3/2)^2=43/12[/tex]
Therefore we the complete square of the given polynomial is
[tex](x+\frac{3}{2})^2=\frac{43}{12}[/tex]
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Answer:
A
Step-by-step explanation:
if A and B are two distinct points on the plane then distance between them is
A)zero
B)1
C)negative
D)positive
By definition, the distance between two points is always positive, so the correct option is D.
How to get the distance between two points?
Let's say that our plane has rectangular coordinates, so it would be something like a xy-plane.
Each point has 2 coordinates, so we can write:
A = (x₁, y₁)
B = (x₂, y₂)
The distance between the points is given by:
[tex]D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
As you can see, the distance is defined as positive (indifferent of the coordinates of the points).
So the correct option is D, the distance is always positive.
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Select the correct answer.
Mary and Nikki are collecting signatures for a petition. Function m models the total number of signatures on Mary’s petition x days after they started collecting signatures. Function n models the total number of signatures on Nikki’s petition at the same time.
m(x) = 252 + 21x
n(x) = 211 + 16x
Which function correctly represents the number of signatures Mary and Nikki have gathered altogether, x days after they started collecting signatures?
A. (m + n)(x) = 41 + 37x
B. (m + n)(x) = 463 + 5x
C. (m + n)(x) = 463 + 37x
D. (m + n)(x) = 41 + 5x
Answer:
C. (m + n)(x) = 463 + 37x
Step-by-step explanation:
How do we find the difference between principal and interest?
Answer:
Principal is the money that you originally agreed to pay back. Interest is the cost of borrowing the principal.
Step-by-step explanation:
First, calculate the interest portion of the payment by multiplying the mortgage balance by the annual interest rate. Then divide the result by 12, for the number of months in the year:
What is the completely factored form of 3x5 – 7x4 6x2 – 14x? (x superscript 4 baseline 2 x) (3 x minus 7) x superscript 4 baseline (3 x minus 7) (2 x minus 1) x (x cubed 2) (3 x minus 7) x (3 x superscript 4 baseline minus 7 x cubed 6 x minus 14)
A polynomial is an expression. The completely factored form of the polynomial 3x⁵-7x⁴+6x²-14x is (x⁴+2x)(3x-7).
What are polynomial?Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.
The completely factored form of the polynomial can be done in the following manner,
[tex]3x^5-7x^4+6x^2-14x\\\\= x^4(3x-7)+2x(3x-7)\\\\=(x^4+2x)(3x-7)[/tex]
Hence, the completely factored form of the polynomial 3x⁵-7x⁴+6x²-14x is (x⁴+2x)(3x-7).
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Answer:
A on edge
Step-by-step explanation:
I passed the test!
Which of the following statements regarding the transmission of pathogens from environmental surfaces are true?
a. Pathogens can be spread by contact with contaminated surfaces.
b. Placing a resident in a room previously occupied by a C. diff positive resident increases the risk for acquiring C. diff. c. You must touch a surface for at least 3 minutes for pathogenic transfer to occur. d. Most pathogens can only survive on surfaces for a few minutes
TRUE statements regarding the transmission of pathogens via environmental surfaces are the statements in option A and B.
What are Pathogens?Pathogens can be referred to as microscopic organisms which can cause diseases and illness. They are bacteria, fungi, virus or other disease causing organisms.
These pathogens can be transmitted via environmental surfaces especially by coming in contact with contaminated surfaces. Some pathogens survive longer on surfaces, while some only survive for few minutes.
If someone is placed in a room previously occupied by an infected person, the chances of contacting that same disease is high.
Thus, the statements that are TRUE regarding the transmission of pathogens via environmental surfaces are the statements in option A and B.
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A school collects money for the local shelter. If the students collect $275 in the first month, $210 in the second month, and $136 in the third month, how much do they collect altogether?
Answer:
$621
Step-by-step explanation:
To find the total amount they collected, sum the amounts collected in each month.
[tex]\begin{tabular}{c l} & 275\\+ & 210\\+ & 136\\\cline{1-2} & 621\\\cline{1-2} & ^1^1\\\end{tabular}[/tex]
i need help 9th grade math
Answer:
$ 6875.05
Step-by-step explanation:
Check out the attached photo
Two groups of students took the same test. Their results are indicated in the dot plot below.
Which statement is true?
answers:
A. Based on visual inspection, Group B appears to have less variability in scores than Group A.
B. Because Group A has a lower minimum score than Group B, it has a lower median as well.
C. Because both distributions have a mean score of 80, they are very similar in terms of variability.
D. Based on visual inspection, Group A appears to have a higher average score than Group B.
Which equation is true?
A) 3 x (5 + 1) = 3+ (5 x 1)
B) 5 x (2+8)= 10 +8
C) 8 x (2+9)= (8 x 2) + (8 x 9)
D) 4+ (2 +9)= (4 + 2) + (4 +9)
Answer:
C. 8 x (2 + 9) = (8 x 2) + (8 x 9)
Step-by-step explanation:
Let's solve to see!
Solve using PEMDAS:
Parenthesis
Exponents
Mulitplication/Division (depending on which one comes first - starting from left to right)
Addition/Subtraction (depending on which one comes first - starting from left to right)
A)
3 x (5 + 1) = 3 + (5 x 1) <== parenthesis first
3(6) = 3 + 5 <== multiply and add
18 = 8
False
B)
5 x (2 + 8) = 10 + 8 <== parenthesis first
5(10) = 10 + 8 <== multiply and add
50 = 18
False
C)
8 x (2 + 9) = (8 x 2) + (8 x 9) <== parenthesis first
8(11) = 16 + 72 <== multiply and add
88 = 88
True
D)
4 + (2 + 9) = (4 + 2) + (4 + 9) <== parenthesis first
4 + 11 = 6 + 13 <== add
15 = 19
False
Therefore, the correct answer is C.
Hope this helps!
Which of the following best describes a problem that occurs when the majority criterion is observed?
A) The majority criterion cannot be upheld with the Condorcet method.
B) The majority criterion only considers the first-place votes.
C) The majority criterion must be used for first place, second place, third place, and so on to be valid.
D) The majority criterion never applies when the plurality method is used.
Answer:
i belive its A if you get it wrong im sorrry
Step-by-step explanation:
Option C is the statement that best describes a problem that occurs when the majority criterion is observed. This is because the majority criterion is a single-winner system.
Majority criterion:This criterion states that "if one candidate is ranked first by a majority, then that candidate must win".This method complies with the other criteria like the Condorcet method and Plurality method etc.This is applied in such a situation where one person has to be selected.Given information:It is given that all the options except option C are true about the majority criterion.
Option C - "The majority criterion must be used for first place, second place, third place, and so on to be valid" is not correct because this criterion is used only for choosing the first place.
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The Great Pyramid of Giza in Egypt is a square pyramid. The height is approximately 450 feet, and the side length of the base is approximately 750 feet. What is the lateral surface area of the pyramid rounded to the nearest thousandth?
A. 563,000 square feet
B. 1,312,000 square feet
C. 1,441,000 square feet
D. 879,000 square feet
879,000 square feet is the lateral surface area of the pyramid
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The lateral surface area of a square pyramid can be calculated using the formula L = (1/2)Pl
where P is the perimeter of the base and l is the slant height of the pyramid.
Since the base of the pyramid is a square, the perimeter is 4 times the length of one side, or 4 × 750 = 3000 feet.
To find the slant height, we can use the Pythagorean theorem with one leg equal to half the length of the base (375 feet) and the other leg equal to the height (450 feet):
l =√375² + (450)²
= 583.095 feet
Therefore, the lateral surface area is:
L = (1/2) × 3000 × 583.095
= 879,000 square feet
Hence,879,000 square feet is the lateral surface area of the pyramid
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Int the number 78.9 what digit is the ones place
How do I do this fraction with Distributive Property???
Answer:
[tex]3a - 1[/tex]
Explanation:
[tex] \frac{9a - 3}{3} [/tex]
Factor out 3
[tex] \frac{3(3a - 1)}{3} [/tex]
Cancel out the common factor 3
[tex]3a - 1[/tex]
if rx - st = r , which expression represents x
The product of two numbers is 26 and one of the numbers is one larger than six times the other number. find the numbers.
The numbers that the product is 26 and one of the numbers is one larger than six times the other number are 2 and 13.
How to form equation and solve for the variable?The product of two numbers is 26.
let the two numbers be x and y.
Therefore,
xy = 26
One of the numbers is one larger than six times the other number. Therefore,
x = 1 + 6y
Hence,
xy = 26
(1 + 6y)y = 26
y + 6y² = 26
6y² + y - 26 = 0
using quadratic formula,
[tex]\frac{-b + \sqrt{b^{2} -4ac } }{2a}[/tex]
where
a = 6
b = 1
c = - 26
Therefore,
y = 2 or - 13 / 6
We can only use the positive value.
Hence,
2x = 26
x = 26 / 2
x = 13
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2a x a x 3a + b x 4b
Simplify
At a factory, Joe assembles 12 parts each minute. He
has assembled 156 parts when Sheila starts on the line,
assembling at a pace of 15 parts per minute. If their
assembly rates continue, will Sheila ever catch up to Joe?
Explain and show all work.
Answer:
yes, after 52 minutes
Step-by-step explanation:
If t represents the time in minutes each person is working after Sheila arrives, then the number of parts produced is ...
Eric: 156 +12t
Sheila: 15t
These values are equal when ...
156t +12t = 15t . . . . . Eric's part count is equal to Sheila's part count
156 = 3t . . . . subtract 12t
52 = t . . . . divide by 3
Sheila will catch up to Joe after 52 minutes.
Please help!!!!!!!!!!!!!
Answer:
G
Step-by-step explanation:
when x = -1 the two equations equal the same thing -2
so they both go thru the point (-1,-2)
Which will have a negative number?
A)
(-3)(-9)
B)
(-6)(4)
C
-4 --5
D)
-7+9
Answer:
B
positive times negative equal to negative
(-6)(4) = -24
At a summer camp, a student has to choose an activity from group A and an activity from group B. How many different combinations of activities can he choose from?
Group A
swimming
canoeing
kayaking
snorkeling
Group B
archery
rappelling
crafts
cooking
A:8
B:2
C:4
D:16
Answer:
16
Step-by-step explanation:
each activity is worth 4.
Someone help me please!
*not a test or quiz*
whenever you see this kind of question you don't need to start doing all the expressions, but look at the first and last numbers of the answer, the ones that cannot be changed (have no x or y or have those that cannot be changed in this expression):
the answer can't be a or c because in the given expression we can find 3x²y² and that's the only number where we can find x²y², so it cannot be changed. (you'll have 3x²y² in the answer)
now let's look at the last digit, that doesn't have a x or a y:
in b and d we can find 2 different results so this can determine which answer is correct:
let's look back at the given expression: -7+4= -3
so the answer is b
the smallest number that has 1, 2, 3, 4, and 5 asfactors.
Answer:
The answer is 60
(30 points and Brainliest)
If the value of a in the quadratic function f(x) = ax^2 + bx + c is 4, the function will_____.
A)open down and have a minimum
B)open up and have a minimum
C)open down and have a maximum
D)open up and have a maximum
Answer:
I honestly believe it's B I'm sorry if it's wrong
What is the quotient of (x3 – 3x2 3x – 2) ÷ (x2 – x 1)?
Answer:
-18x^2+3x-2/x
Step-by-step explanation:
How many ways can a president, vice-president, and secretary be chosen from a club with 9 members?
This type of problem is a permutation problem. Permutation is the arrangement of a set with certain order. In the problem, if there are 9 members, and 3 positions are available without repeating, we can write the expression as 9P3 - 3 non repeating positions in a set of 9 elements. By evaluating, we will have 9! / (9-3)! = 504. The answer is 504.
Can anybody help me with any of these questions?
Answer:
I can't help sorry which grade ??
If you borrow $1425 for 9 years at an interest rate of 4%, how much interest will you pay?
Answer:
You would pay $242 in total interest over the life of this loan.
Step-by-step explanation:
Triangle ABC has a perimeter of 40 inches. What is AC?
Answer:
AC is a Side of Traingle .....................
The measure of the side length of AC will be 13 inches
What is the perimeter of a triangle?Let the triangle be ABC. Then the perimeter of the triangle will be
Perimeter = AB + BC + CA
Triangle ABC has a perimeter of 40 inches.
The side's lengths are given as AB = 12 inches and BC = 15 inches.
Then the measure of the side length of AC will be
40 = 12 + 15 + AC
40 = 27 + AC
AC = 13 inches
The missing diagram is given below.
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PLEASE HELP I NEED IT REALLY BAD
Btw, my mistake, correction for the volume of prism, it's supposed to be:
Area of cross section × height
Hope this helps =)
Each Handle is 1/4 the width of the handlebars. How many inches long is each Handle. Width of Handlebar is 2 ft
Answer:
1/2 feet
Step-by-step explanation:
1/4 of 2 feet is 1/2
There are 1/2 inches long is each Handle.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Each Handle is 1/4 the width of the handlebars.
And, Width of Handlebar is 2 ft
Hence, Lenght of each Handle is,
⇒ 1/4 of 2
⇒ 1/4 x 2
⇒ 1/2 feet
Thus, There are 1/2 inches long is each Handle.
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