Answer:
[tex]\bold\purple{Quadratic \: \: eq {}^{n} = x {}^{2} - ( \alpha + \beta )x + \alpha \beta} \\ [/tex]
Sum of roots ,
[tex]( \alpha + \beta ) = (3 + 9) = 12[/tex]
Product of roots ,
[tex]( \alpha \beta ) = (3)(9) = 27[/tex]
Substituting the values in the above equation ,
[tex]\bold{x {}^{2} - ( \alpha + \beta )x + \alpha \beta} \\\\ \bold{⇢ x {}^{2} - (12)x + 27} \\\\ \bold\blue{ ⇢x {}^{2} - 12x + 27}[/tex]
hope helpful~
Francisca has 40 paperbacks in her bookcase. This is 32% of the books in the bookcase. How many books are in Francisca's bookcase? Use an equation with a variable. Show your work
The total number of books that are in Francisca's bookcase is 125 books.
Let the total number of books be B.
Given the following data:
Number of paperbacks = 40.
Percentage = 32%.
How to calculate the total number of books.In this exercise, you're required to determine the total number of books that are in Francisca's bookcase if there she has 40 paperbacks in her bookcase. Thus, we would write a mathematical expression for the word problem.
Translating the word problem into an algebraic expression, we have;
[tex]\frac{32}{100} \times T=40\\\\0.32T=40\\\\T=\frac{40}{0.32}[/tex]
T = 125 books.
Read more on word problems here: brainly.com/question/13170908
Dany bought a total of 20 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy?
Answer:
He bought 12 $0.25 costing cards and 8 $0.15 costing cards.
Step-by-step explanation:
Let the number of $0.25 costing cards he bought be s,
Let the number of $0.15 costing cards he bought be t,
According to the question,
He bought a total of 20 game cards,
Thus,
s + t = 20
or, s = 20 - t ------(i)
Now,
Since, he bought s and t no of cards each and it amounted to $4.2, we know,
$0.25s + $0.15t = $4.2
or, $0.25(20 - t) + $0.15t = $4.2 [From (i)]
or, $5 - $0.25t + $0.15t = $4.2
or, $5 - $4.2 = $0.1t
or, $0.8/$0.1 = t
t = 8
From (i),
s = 20 - t = 20 - 8 = 12
Therefore, he bought 12 $0.25 costing cards and 8 $0.15 costing cards.
The answer has to be in scientific notation.
1.7 x 10^4/2 x 10^-2
Answer:
Write these in Scientific Notation:
0.0002
2 x 10-4
20 x 10-4
2 x 104
20 x 104
2.) 0.000049
49 x 106
4.9 x 105
49 x 10-6
4.9 x 10-5
3.) 0.000000000845
84.5 x 1011
8.45 x 1010
8.45 x 10-10
84.5 x 10-11
4.) 0.000000000008
80 x 10-13
8 x 10-12
80 x 1013
8 x 1012
5.) 0.00000127
1.27 x 106
12.7 x 107
12.7 x 10-7
1.27 x 10-6
6.) 0.0000000000752
7.52 x 10-11
75.2 x 10-12
7.52 x 1011
75.2 x 1012
7.) 0.000000301
30.1 x 10-8
3.01 x 10-7
3.01 x 107
30.1 x 108
8.) 0.00000000633
63.3 x 1010
6.33 x 109
6.33 x 10-9
63.3 x 10-10
9.) 0.00000009
9 x 10-8
90 x 10-9
9 x 108
90 x 109
10.) 0.0000536
5.36 x 105
53.6 x 106
53.6 x 10-6
5.36 x 10-5
11.) Rewrite these in standard notation.
6 x 10-6
0.0006
0.00006
0.000006
0.0000006
12.) 4 x 10-5
0.00004
0.000004
0.0000004
400,000
13.) 1.8 x 10-11
0.000000000018
0.00000000018
180,000,000,000
1,800,000,000,000
14.) 1.7 x 10-4
17,000
170,000
0.00017
0.000017
15.) 7.6 x 10-10
0.00000076
0.000000076
0.0000000076
0.00000000076
16.) 7.79 x 10-12
0.0000000000779
0.00000000000779
779,000,000,000,000
7,790,000,000,000,000
17.) 1.98 x 10-8
19,800,000,000
198,000,000
Need help struggling with this question
E O
What is the common ratio between successive terms in the sequence?
2, 4, 8, -16, 32, 64, ...
O-2
06
O 6
O2
Answer:
-2
Step-by-step explanation:
-16/2= 8
8/-16=-2
not sure though
The common ratio of the geometric progression is r = 2
What is Geometric Progression?A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The nth term of a GP is aₙ = arⁿ⁻¹
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
Let the geometric progression be represented as A
Now , the value of A is
A = 2, 4, 8, 16, 32, 64, ...
Now , the common ratio r = second term / first term
On simplifying , we get
r = 4 / 2
r = 2
Hence , the common term of GP is r = 2
To learn more about geometric progression click :
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f(x)=(x-1)^2-32 in standard form
4. Parallelogram TIME with diagonals MT
diagonals MT and EI intersect point S. If
MS = 4x +3 and ST = 5x – 4, find the measure of MT.
Answer: 62
Step-by-step explanation:
Three hundred high school seniors were surveyed about their intended college majors. The results are displayed in the Venn Diagram below: A Venn Diagram titled College Majors with two circles labeled Math and Science. In the math portion is 120. In the intersection is ??. In the Science portion is 50. The area outside the two circles is labeled 100. If a student is randomly selected from the group, what is the probability that they are majoring in both math and science? Round your answer to the nearest whole percent. 10% 17% 33% 40%.
The probability of selecting one student who is both from math and science is 1/10
There are the total number of student = 300
Out of which,the number of students who are only in Maths = 120
The number of students who are only in Science = 50 and the students who are not from any subject = 100
What is the formula for the total students?
Total no of students=science student+math students +none
Therefore,the number of student who are from both math and science = Total student - Math student (only) - science student (only) - None
= 300 - 120 - 50 - 100
= 30
That is, there are 30 students who are both from science and math,
Thus, the probability of selecting one student who is both from math and science = 30/300 = 1/10
To learn more about the probability visit:
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A rectangle has a height of 4 and a width of x^2 + 3x + 2.
Express the area of the entire rectangle.
Expression should be expanded.
x^2
3x
2
1
4
Area=?
Step-by-step explanation:
area = length × width = 4(x² + 3x + 2) =
= 4x² + 12x + 8
What time is it in new orleans louisiana right now.
New Orleans, Louisiana is in the Central Time Zone. Currently, March, 3rd, 2022, it is 10:25 am.
What is the value of tea in the following equation 1/4t =2 7/12
1/4t =2(7/12)
t=8(7/12)
t=7(2/3)
t=4.6666...
Can someone explain this to me?
Answer:
200
Step-by-step explanation:
So its basically you multiply the length by the width which is 15 times 5 which is 75 then you multiply 75 times 4 which is 200 so the answer is 200.
I need help with these equations as well
Answer:
0=10
0= -5
Step-by-step explanation:
[tex]1. - 10 = - 14x + 14x[/tex]
cancel (-14) with (+14)
[tex] - 10 = 0[/tex]
so , The above equation has no solution .
-----------------------------------[tex](ii) \: 3(3 - x) + 5x = 2(x + 2) \\ \\ 9 - 3x + 5x = 2x + 4 \\ \\ 9 + 2x = 2x + 4 \\ \\ 2x - 2x = 4 - 9 \\ \\ 0 = - 5.[/tex]
The above equation has no solution .
Solve for x to the nearest tenth.
Answer: 11.4
Step-by-step explanation:
calculate 1+ 1/2+1/4÷3/2
Answer : 5/3
◊ YusuCr ◊
Answer:
1 2/3
Step-by-step explanation:
[tex]\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}[/tex]
[tex]\mathrm{Multiply\:and\:divide\:(Left\:to \:right)}[/tex] [tex]\frac{1}{4}[/tex] ÷ [tex]\frac{3}{2}:\frac{1}{6}[/tex]
[tex]=1+\frac{1}{2}+\frac{1}{6}[/tex]
[tex]\mathrm{Add\:and\:Subtract\:(Left\:to \:right)}[/tex] [tex]1+\frac{1}{2}+\frac{1}{6}:\frac{5}{3}[/tex]
[tex]=\frac{5}{3}[/tex]
[tex]\mathrm{Convert\:improper\:fractions\:to\:mixed \:numbers}: \frac{5}{3}=1\frac{2}{3}[/tex]
[tex]=1\frac{2}{3}[/tex]
[tex]Answer = =1\frac{2}{3}[/tex]
[RevyBreeze]
4. Find the perimeter.
Am I correct??
Answer:
30.84 cm
Step-by-step explanation:
Correct.
You need half the perimeter of half a circle plus the 12-cm diameter.
Remember to include the units, cm.
Answer: 30.84 cm
How many tiles to cover a floor measuring 24m x 20m if the measure of the tile is 12 cm x 10 cm
Answer:
4 tiles
Step-by-step explanation:
12 * 10 = 120 for each tile
24 * 20 = 480 for entire floor
480/120 = 4
4 tiles
Answer: Below
Step-by-step explanation:
This is a pretty simple problem, so hopefully you catch on to it quickly.
Since we have two measurements for two sides of a rectangle, we know they are referring to square centimeters for both the floor and the tiles. Since the units match up, we can divide.
24 * 20 = 480 cm squared
12 * 10 = 120 cm square.
480/120 = 4 tiles.
Our answer is 4 tiles.
Noah mows 1/2 of his property and leaves the rest wild. He decides to use 1/5 of the weld area for a vegetable garden. What fraction of the property is used for the garden ?
Solving the Question
We're given:
[tex]\dfrac{1}{2}[/tex] of the property was mowed[tex]\dfrac{1}{5}[/tex] of the unmowed property was used for a vegetable gardenWe must first find how much of the property was unmowed.
If [tex]\dfrac{1}{2}[/tex] of the property was mowed, then that leaves [tex]\dfrac{1}{2}[/tex] of the property unmowed.
⇒ [tex]1-\dfrac{1}2}=\dfrac{1}2[/tex]Now, we can find the fraction of the property used for the garden.
[tex]\dfrac{1}5}[/tex] of the [tex]\dfrac{1}2[/tex] of the property was used for the garden. To find this as a fraction, multiply [tex]\dfrac{1}5}[/tex] by [tex]\dfrac{1}2[/tex]:
[tex]\dfrac{1}5*\dfrac{1}2=\dfrac{1}{10}[/tex]
AnswerTherefore, [tex]\dfrac{1}{10}[/tex] of the property was used for the garden.
A pediatric client with a ventricular septal defect repair is placed on a maintenance dose of digoxin. The safe dose is 0. 03 mg/kg/day, and the client's weight is 7. 2 kg. The primary health care provider (PHCP) prescribes the digoxin to be given twice daily. How much digoxin should the nurse administer to the client at each dose?
Using proportions, it is found that the nurse should administer 0.108 mg of digoxin to the client in each dose.
What is a proportion?A proportion is a fraction of a total amount.
In this problem, the daily amount is of 0. 03 mg/kg, hence for a person of 7.2 kg, the amount is:
T = 0.03 x 7.2 = 0.216 mg.
This daily amount is given in two equal doses, hence the amount of each dose is given by:
E = 0.216/2 = 0.108 mg.
More can be learned about proportions at https://brainly.com/question/24372153
A bus driver gets paid $38,871 a year, if he works 42 weeks a year.
How much does he earn every week ?
How many weeks will it take him to earn $5500 ?
What is the bus driver’s hourly wage if he works 40 hours a week?
Answer:
he mask 925.5 dollars every week
Answer:
$1295.70 a week
4 weeks
???
Step-by-step explanation:
hope this helps
In triangle ABC, c= 8, b= 6, and C= 60°.
sin2B=
Answer:
ggabdfsa
Step-by-step explanation:
A slug travels 3 centimeters in 3 seconds. A snail travels 6 centimeters in 6 seconds. Both travel at constant speeds. Mai says, “The snail was traveling faster because it went a greater distance.” Do you agree with Mai? Explain or show your reasoning.
Help! Due soon. No links.
Answer:
24º each angle
Step-by-step explanation:
A circle = 360º
there are 15 sections
360 / 15 = 24 each angle
please help meeeeeeeeeeeeeeeeeeeeeeeeeee pls 6th grade math
Answer:
1. 3
2. 3
3. 44
Step-by-step explanation:
Remember, for all percetanges, we need to turn them into a decimal!!! :)
Now lets solve them!!
1.
60 x 5%
60 x 0.05
3
She burned 3 cupkakes out of 60 :)
2.
8 x 40%
8 x 0.4
3.2
Since we cant have 0.2 of a student, we will round to the nearest whole number and that is 0.
3 students turned in their biographies :)
3.
47 x 94%
47 x 0.94
44.18
Remeber, since we cant havea part of something we need to round to the nearest whole number!
44.2
Since 2 is still not bigger than 5, the correct answer will be 44 :)
44 basketball players are going to the banquet
You did it! Now you know how to solve this type of problems!!
Have a great day!!
Please rate and mark brainliest!!
can anyone help me?????
Answer:
answer for a. a^2
answer for b. c
Jeremiah realiza una encuesta y descubre que a medida que disminuye la primera variable de la encuesta, aumenta la segunda variable. ¿Qué tipo de asociación existe entre las dos variables?
Answer:
Que uno sube y el otro baja.
19a + 44 - 19a
Need help with this was not paying attention in class
19a + 44 - 19a
Group like terms.
[tex]19a - 19a + 44[/tex]
Add similar elements.
[tex]19a - 19a = 0[/tex]
[tex]=44[/tex]
Answer:
44
Step-by-step explanation:
Hahaha, fair enough.
This one may look more difficult than it is. In algebra, there are variables and there are constants.
A constant is a number that is constantly the same, in the example you posted, 44 is the constant.
A variable is like a place holder, it indicates that there is a number that will be substituted in, we just don't know what that number is yet. In your example, the variable is represented by the letter "a."
If youre still a little unsure what a variable is, think of it like this:
Every morning, you like to have one, single cup of coffee, but some days you feel like putting 1 spoon of sugar in, some mornings you want no sugar, and some mornings you really want something sweet and so you have 3 spoons of sugar.
In algebra, your morning cup of coffee is represented 1 + s. 1 is the number of cups of coffee you have and "s" represents how much sugar you put in it. "s" can equal 1, 3, or even 0 spoons of sugar. "s" will represent the number of spoons of sugar consistantly, BUT, keep in mind that while the value of a variable is the same within that one term or equation it can represent a different value in another term or equation.
1 + s on Monday could equal 4 because you really want some sugar at the beginning of your week so you put 3 sugars in. 1 + 3 = 4. But on Thursday, you don't want any sugar, so 1 + 0 = 1. Monday and Thursday are different terms/equations.
SO, because a variable always has the same value within a term/equation, in your example 19a + 44 - 19a, "a" will always have the same value. if a = 1 then your example is 19(1) + 44 - 19(1). If the value of "a" is 1,000,000, then your example looks like 19(1,000,000) + 44 - 19(1,000,000).
We can rewrite your question a little to make it clearer. 19a - 19a + 44, we just swapped the positions of 44 and -19a. So you can see, that no matter what value "a" represents, they will cancel each other out. leaving you with 44 as your answer.
Find the factors of each expression. x^2+36
Answer:
x²+36+2(x)(6).. is the correct answer..Which ratio is equivalent to 9:12?
129
18:24
12:19
10:12
Write as an algebraic expression : Two less than the product of y and 4 "
Answer:
4y-2
Step-by-step explanation: