If you have saved some money to purchase five different songs to download to your portable music device. The inequality that represents the prices you can pay for each song if you have saved no more than 20 dollars is : 5 x ≤ 20.
InequalityGiven:
Numbers of different songs to download = 5
Cost = $20
Hence,
The inequality is ; 5 x ≤ 20
Now let solve the inequality
5 x ≤ 20
x = 20 /5
x = 4
So,
= x ≤ 4
Therefore the inequality is 5 x ≤ 20.
Learn more about inequality here: https://brainly.com/question/25275758
#SPJ1
Please help for 50 points
Which of the following points are solutions to the given system?
3x-4y<10
2x+6y≥-8
Select all that apply
(0, 4)
(2, –1)
(2, –2)
(8, 2)
(–1, –1)
Answer: (0,4) and (-1,-1)
Step-by-step explanation:
1) Plug in all of each equation
1a) (0,4)
3(0)-(4)<10
0-4< 10
-4< 10
2(0)+6(4)>=-8
0+24 >= -8
24>= -8
Works!
1b) (2,-1)
3(2)-4(-1)<10
6+4<10
10<10
Nope.
1c) (2,-2)
3(2)-4(-2)<10
6+8<10
14<10
Nope.
1d) (8,2)
3(8) -4(2) < 10
24 - 8 < 10
16<10
Nope.
1f) (-1,-1)
3(-1)-4(-1) < 10
-3 +4 < 10
1 < 10
2(-1)+6(-1)>=-8
-2+-6 >= -8
-8 >= -8
Works.
PLEASE HURRY
Simplify:
6m/m-3 + m/m+1
Simplify
Identify the common factor
{6m/m-3 + m/m+1
(m+1) . (6-3) /(m+1) + (m-3)/ (m+1)
Add fractions with the same denominator together.
terms to put constants on the left and reorder them
Solution
7m^{2}+3m / m^2-2m-3
The answered are 7 3 2 3
What does the algebraic expression M mean?
The slope of a line is represented by the letter "m" in algebra. A line's slope defines both its direction and steepness.
The order in which you perform operations in arithmetic and algebra is governed by a number of laws. The Commutative, Associative, and Distributive Laws are the three that receive the most attention. People have discovered over time that adding or multiplying doesn't depend on the order of the numbers
to learn more about algebraic expression
https://brainly.com/question/4541471
#SPJ13
I WILL GIVE BRAINLEST 1+1
it is 2 becuase 1 plus 1 is two when you have an apple and a freind gives you an apple you have 2 appelapples
Answer:
1+1=2
Step-by-step explanation:
if you have one of me then you duplicate me or make a dopleganger than you now have 2
have a great day^^
The bill amount for Diana's brunch was $35.80. She wanted to leave 18% of the total bill as a tip. How much should the tip
be?
Let f(x)=2x²+x-11 and g(x)=x-1. Perform the function operation and then find the domain.
(f+g)(x)
(f+g)(x) = (Simplify your answer.)
Answers:
[tex](f+g)(\text{x}) = \boldsymbol{2\text{x}^2+2\text{x}-12}[/tex]
Domain = set of all real numbers
========================================================
Work Shown:
[tex](f+g)(\text{x}) = f(\text{x})+g(\text{x})\\\\(f+g)(\text{x}) = (2\text{x}^2+\text{x}-11)+(\text{x}-1)\\\\(f+g)(\text{x}) = 2\text{x}^2+\text{x}-11+\text{x}-1\\\\(f+g)(\text{x}) = 2\text{x}^2+(\text{x}+\text{x})+(-11-1)\\\\(f+g)(\text{x}) = 2\text{x}^2+2\text{x}-12\\\\[/tex]
The domain of each f(x) and g(x) is "set of all real numbers" since we can replace x with any real number to get some output.
By extension, this means the domain of (f+g)(x) is also "set of all real numbers".
It turns out any polynomial will have this domain. We don't have to worry about things like applying square roots to negatives, or dividing by zero. This is why there isn't a restriction on x.
To write "set of all real numbers" in interval notation, we would say [tex](-\infty, \infty)[/tex] to indicate x is anything between negative infinity and positive infinity.
please look at the image and answer, Thank you!
f(n)=3.3n-1 for n ≥ 1
The first five terms of the given function is:
f(1) = 2.3
f(2) = 5.6
f(3) = 8.9
f(4) = 12.2
f(5) = 15.5
Functions: The core concept of mathematics calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h.
The given function is f(n) = 3.3n-1 for n>= 1
The first 5 terms of this function are as follows:
f(1) = 3.3(1)-1
= 3.3-1 = 2.3
f(2) = 3.3(2)-1
= 6.6-1 = 5.6
f(3) = 3.3(3)-1
= 9.9-1
=8.9
f(4) = 3.3(4)-1
= 13.2-1
=12.2
f(5) = 3.3(5)-1
= 16.5-1
= 15.5
Learn more about functions:
https://brainly.com/question/12431044
#SPJ1
Did I get these right
Answer:
Almost!
Step-by-step explanation:
Problems 1-9 and 11 are correct, but not problem 10 or 12
For problem 10, 12/6 does equal 6/1, so it would just be the whole number of 6 as your final answer as it doesn't need to be simplified further.
For problem 12, -4/6 can be simplified further to -2/3 by dividing by 2.
Answer: Very close!
Step-by-step explanation:
Problems 7, 8, 9, and 11 are correct but not 10 or 11, because they are not in simplest form.
2/1 can be simplified to 2, and -4/6 can be simplified to -2/3.
If 3/5 of Ellen’s class has brown eyes and there are 25 people in Ellen’s class, how many of them have brown eyes?
Answer: The answer is 15
Step-by-step explanation: 25* 3/5 is 15 so 15 out of 25 is what percent of the class has brown eyes
ABC has vertices at A(4,1), B(-3,-2), and C(-1,3). what is the perimeter of ABC?
If ABC is a triangle, which when plotted on the cartesian coordinate system, has it's vertices at A(4, 1), B(-3, -2), and C(-1, 3), then the perimeter of triangle ABC will be [√58/(√2 - 1)]
As per the question statement, ABC is a triangle, which when plotted on the cartesian coordinate system, has it's vertices at A(4, 1), B(-3, -2), and C(-1, 3).
We are required to calculate the perimeter of triangle ABC.
To solve this question, first we need to calculate the distances between AB, BC ad AC, which are the three sides of our concerned triangle ABC, and then add them up to obtain our desired answer. And to calculate the lengths of AB, BC ad AC, we will need to use the distance formula which goes as,
"The distance between any two points (x₁, y₁) and (x₂, y₂) can be given by
√[(x₂ - x₁)² + (y₂ - y₁)²]
Considering points A(4, 1) and B(-3, -2), we can say that [(x₁, y₁) = (4, 1)] and [(x₂, y₂) = (-3, -2)]. Therefore, distance AB = √[{(-3) - 4}² + {(-2) - 1}²]
Or, AB = √[{-(3 + 4)}² + {-(2 + 1)}²]
Or, AB = √[(-7)² + (-3)²]
Or, AB = √[(49 + 9)]
Or, AB = √58
Similarly considering points A(4, 1) and C(-1, 3), we can say that
[(x₁, y₁) = (4, 1)] and [(x₂, y₂) = (-1, 3)].
Therefore, distance AB = √[{(-1) - 4}² + (3 - 1)²]
Or, AC = √[{-(1 + 4)}² + (3 - 1)}²]
Or, AC = √[(-5)² + (2)²]
Or, AC = √[(25 + 4)]
Or, AC = √29
Finally considering points B(-3, -2) and C(-1, 3), we can say that
[(x₁, y₁) = (-3, -2)] and [(x₂, y₂) = (-1, 3)].
Therefore, distance BC = √[{(-1) - (-3)}² + {3 - (-2)}²]
Or, BC = √[{-(1) + 3}² + (3 + 2)²]
Or, BC = √[(3 - 1)² + (5)²]
Or, BC = √[(4 + 25)]
Or, BC = √29
Therefore, the perimeter of Triangle ABC = (AB + BC + AC)
Or, perimeter of Triangle ABC = (√58 + √29 + √29)
Or, perimeter of Triangle ABC = [√(29 * 2) + √29 + √29]
Or, perimeter of Triangle ABC = [(√29*√2) + √29 + √29]
Or, perimeter of Triangle ABC = √29(√2 + 1 + 1)
Or, perimeter of Triangle ABC = √29(√2 + 2)
Or, perimeter of Triangle ABC = (√29*√2)(1 + √2)
Or, perimeter of Triangle ABC = (√58)(1 + √2)
Or, perimeter of Triangle ABC = [tex]\frac{\sqrt{58} (1+\sqrt{2})(1-\sqrt{2}) }{(1-\sqrt{2})} =\frac{\sqrt{58} [(1)^{2}-(\sqrt{2})^2 }{(1-\sqrt{2})}}[/tex]
Or, perimeter of Triangle ABC = [tex]\frac{\sqrt{58} [(1-2) }{(1-\sqrt{2})}}=\frac{-\sqrt{58}}{(1-\sqrt{2})}}=\frac{\sqrt{58}}{(\sqrt{2}-1)}}[/tex]
Perimeter: In Geometry, a perimeter is a closed path that bounds, surrounds, or outlines, either a two dimensional shape or a one-dimensional length.To learn more about Perimeters, click on the link below.
https://brainly.com/question/28660527
#SPJ1
In a pond, the ratio of toads to frogs was 3: 10.
9 more frogs then entered the pond, and the ratio of toads to frogs became
3:11.
Work out how many toads are in the pond.
Toads are in the pond is 27.
What is a ratio?The quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
"the ratio of men's jobs to women's is 8 to 1".
Given that,
The ratio of toads to frogs was 3: 10.
Let the number of toads = 3x
number of frogs = 10x
9 more frogs then entered the pond and the ratio of toads to frogs became 3:11.
[tex]\frac{3x}{10x+9} =[/tex] [tex]\frac{3}{11}[/tex]
[tex]\frac{x}{10x+9} = \frac{1}{11}[/tex]
11x = 10x+9
x = 9
number of toads = 3x = 3×9 = 27
Hence, Toads are in the pond is 27.
To learn more about ratio from the given link:
https://brainly.com/question/2914376
#SPJ9
Taylor and her children went into a movie theater and she bought $81 worth of bags of popcorn and candies. Each bag of popcorn costs $9 and each candy costs $4.50. She bought 6 more candies than bags of popcorn. Graphically solve a system of equations in order to determine the number of bags of popcorn, x,x, and the number of candies, y,y, that Taylor bought.
Answer:
x = bags of popcorn = 4y = candies = 10Step-by-step explanation:
You want to find the number of bags of popcorn (x) and candies (y) Taylor bought for $81, given that popcorn costs $9 and candies cost $4.50, and she bought 6 more candies than popcorns.
EquationsThe equations relating x and y are ...
6x +4.5y = 81 . . . . . . . . the total cost of the snacksx + 6 = y . . . . . . . . . . . there were 6 more candies than popcornsSolutionThe attached graph shows the solution of thees equations is ...
(x, y) = (4, 10)
Taylor bought 4 bags of popcorn and 10 candies.
<95141404393>
Which of the following proves these triangles are congruent?
A. neither
B. SAA
C. ASA
Answer:
Step-by-step explanation:
Neither, they are not congruent.
write 34,000 , 43,000,000 , 0.0000087 , 91,000,000 , 16.6 x 10^3 , and 0.00372 x 10^-3 in scientific notation
To write a number in scientific notation you must know:
1. A number in scientific notation is written as the product of a number (integer or decimal) and a power of 10
2. A number can be converted to scientific notation by increasing the power of 10 by one for each place the decimal point is shifted to the left.
Then so:
[tex]34000=3,4x10^3[/tex][tex]43000000=4.3x10^7[/tex][tex]0.0000087=8.7x10^{-6}[/tex][tex]91000000=9.1x10^7[/tex][tex]16.6x10^3=1.66x10^4[/tex][tex]0.00372x10^{-3}=3.72x10^{-6}[/tex]The midpoint of segment AB is M. If the coordinates of M are (1/2,-2) and the coordinates of B are (6,1), what are the coordinates of A?
The coordinates of A are (-5, -5).
How to determine the midpoint of a given segment?
The center point of a straight line can be located using the midpoint formula. We can use this midpoint formula to determine the coordinates of the supplied line's midpoint in order to discover its location on a graph. Assuming that the line's endpoints are (x₁, y₁) and (x₂, y₂), the midpoint (a, b) is determined using the following formula:
(a , b) ≡ (((x₁ + x₂)/2), ((y₁ + y₂)/2))
Given, the line segment under consideration is AB as endpoints.
And, the co-ordinate of B is = (6, 1)
Also, the midpoint of segment AB i.e. M is = (0.5, -2)
Let the co-ordinate of A be = (x, y)
Using the available literature and formula, we get
(0.5, -2) ≡ (((x + 6)/2), ((y + 1)/2))
Equating both parts in the given equation,
0.5*2 = x + 6 ⇒ 1 = x + 6 ⇒ x = -5
and, (-2)*2 = y + 1 ⇒ -4 = y + 1 ⇒ y = -5
Therefore, the co-ordinates of A are (-5, -5).
To learn more about this, tap on the link below:
https://brainly.com/question/5566419
#SPJ9
3. Given the perimeter of the figure is 76 ft, Find
the dimensions of the shape.
R
(4x-5) ft
(25-x) ft
(13 + x) ft
S
T
(3x+1) ft
All the dimensions of the shape is found as 19 ft.
What is termed as the perimeter?The perimeter of any closed shape is the total length of its boundary. The total length around a shape is described as its perimeter. It is the length of any two-dimensional spatial shape's outline or boundary. Depending on the dimensions, the perimeters of irregular shapes can indeed be equal in size.For the given question, the dimensions of the shape is given as;
(4x-5) ft(25-x) ft(13 + x) ft(3x+1) ftThe perimeter of the shape = 76 ft.
The formula of the perimeter = sum of length of all sides.
Let 'P' be the perimeter.
P = (4x-5) + (25-x) + (13 + x) + (3x+1) ing
Simplifying
P = 4x - x + x + 3x - 5 + 25 + 13 + 1
76 = 7x + 34
7x = 76 - 34
7x = 42
x = 6
Thus, the dimensions of the shape is; Put x = 6
(4×6-5) ft = 19 ft(25-6) ft = 19 ft(13 + 6) ft = 19 ft(3×6+1) ft = 19 ftThus, all the dimensions of the shape is found as 19 ft.
To know more about the perimeter, here
https://brainly.com/question/1229669
#SPJ13
IMAGE ATTACHED Help with this please.
Part of a full number and a means of dividing a number into equal pieces are represented by fractions.The denominator is the total number of parts in the whole, while the numerator is the number of equal portions being counted.
Solve the problem ?
An element of a whole is a fraction.The number is represented mathematically as a quotient, where the numerator and denominator are split.Both are integers in a simple fraction.A fraction appears in the numerator or denominator of a complex fraction.The numerator of a proper fraction is less than the denominator.Richard can finish reading a book in (missing) hours.Need something in those places to determine the precise response, but generally speaking if you simply want to get his unit rate, first convert the data into a fraction:Books per hour equal books per hourThen, to determine his unit rate, divide the top by the bottom (books per 1 hour).For instance:Richard would read one book in an hour if he could finish reading half of a book in that time.It becomes a little more complicated: if he can read 2 1/4 th of a book in an hour, he can read: 2 1/4/ 1/12= 0.5/0.083 = 6.024I'm not sure if you'll be dealing with fractions, decimals, or entire numbers, but if they're fractions, bear in mind that you divide fractions by keeping the first fraction the same, multiplying it, and then flipping the second fraction. 2 1/4/ 1/12= 0.5/0.083 = 6.024To learn more about fraction refer
https://brainly.com/question/17220365
#SPJ13
bu sorunun çözümünü yazarmısınız çok acil lütfennnnn
Answer:
Step-by-step explanation:
i poopeyd in ma pants
Aaron has two summer jobs. During the week he works in the grocery store, and on the weekend he works at a nursery. He gets paid $20 per hour to work at the grocery store and $21 per hour to work at the nursery. How much does he earn if he works 13 hours at the grocery store and 9 hours at the nursery? How much does he earn if he works gg hours at the grocery store and n hours at the nursery?
Total pay, 13 hours at the grocery store and 9 hours at the nursery:
Total pay, g hours at the grocery store and n hours at the nursery:
If he gets paid $20 per hour to work at the grocery store and $2 per hour to work at nursery,
Part a
He will earn $449 if he works 13 hours at the grocery store and 9 hours at the nursery
Part b
He will earn 20g + 21n, if he works g hours at the grocery store and n hours at the nursery
The payment at the grocery store per hour = $20
The payment at the nursery per hour = $21
Part a
Number of hours he works at the grocery store = 13 hours
Number of hours he works at nursery = 9 hours
Total pay = 13×20 + 9×21
= 260 + 189
= $449
Part b
Number of hours he works at the grocery store = g hours
Number of hours he works at nursery = n hours
Total pay = 20g + 21n
Hence, If he gets paid $20 per hour to work at the grocery store and $2 per hour to work at nursery,
Part a
He will earn $449 if he works 13 hours at the grocery store and 9 hours at the nursery
Part b
He will earn 20g + 21n, if he works g hours at the grocery store and n hours at the nursery
Learn more about total pay here
brainly.com/question/17043970
#SPJ1
Given 4 1/10 -3 5/12 determine the product
The product of 4 1/10 and -3 5/12 is -14 1/120
What are fractions?Fractions are simply described as a subset of a whole or the part of a whole.
They are several types of fractions, some of which includes;
Mixed fractionsProper fractionsImproper fractionsSimple fractionsComplex fractionsSome examples of mixed fractions; 3 1/4, 5 1/2, 6 1/4
Some examples of simple fractions; 1/2, 1/4, 1/6
Some examples of proper fractions; 3/4, 4/5, 6/7
Some examples of improper fractions; 3/2, 4/3, 6/5
Given the mixed fractions;
4 1/10 × -3 5/12
convert to improper fractions
41/10 × - 41/12
Multiply through
- 1681/120
Find the ratio
- 14 1/ 120
Hence, the value is - 14 1/ 120
Learn more about fractions here:
https://brainly.com/question/11562149
#SPJ1
If the area of a triangle is 2x^2-2x-4 and it has a height of x-2, write the base of the triangle.base of the triangle:_________________
The base of the triangle = 4(x + 1)
Explanations:The Area of a triangle is given by the formula:
[tex]\text{Area = }\frac{1}{2}\times\text{ base }\times\text{ height}[/tex][tex]\begin{gathered} \text{Area = 2x}^2-2x-4 \\ \text{Height = x -2} \end{gathered}[/tex]Substituting these expressions into the formula for the area of a triangle:
[tex]\begin{gathered} 2x^2-2x-4\text{ = }\frac{1}{2}\times\text{ b }\times(x-2) \\ 2(2x^2-2x-4)\text{ = b (x - 2)} \\ 4x^2-4x-8\text{ = b (x-2)} \\ 4x^2-8x\text{ + 4x - 8 = b (x - 2)} \\ 4x(x\text{ - 2) + }4(x\text{ - 2) = b(x-2)} \\ (4x+4)(x-2)\text{ = b(x-2)} \\ b\text{ = }\frac{(4x+4)(x-2)}{(x-2)} \\ b\text{ = 4x + 4} \end{gathered}[/tex]b = 4 (x + 1)
The base of the triangle = 4(x + 1)
if the total value of the coins is $5.50 and kayleigh has 17 quarters, how many nickels does she have?
Kayleigh have 25 nickels with her.
Given,
The total value of coins Kayleigh have = $5.50
Number of quarters with Kayleigh = 17 quarters
We have to find the number of nickels Kayleigh with her.
Lets see:
1 dollar = 4 quarters
1 dollar = 20 nickels
Here, we have a total of 5.50 dollar
In this, 17 quarters are there.
So,
17 / 4 = 4.25
That is, the value of coins as quarters is $4.25
Now,
5.50 - 4.25 = 1.25
That is,
$1.25 is in the form of nickels.
Number of nickels = 1.25 × 20
Number of nickels = 25
Therefore,
Kayleigh have 25 nickels with her.
Learn more about coins here:
https://brainly.com/question/26944236
#SPJ1
The area of a triangle is 1/2bh
1) rewrite the formula for b
2)rewrite the formula for h
Answer:
1. b = 2A/h
2. h = 2A/b
Step-by-step explanation:
All you have to do is isolate the variable.
1.
Isolate b:
A = 1/2 x b x h
Multiply each side by 2
2A = b x h
Isolate b by dividing both sides by h
b = 2A/h
2.
Isolate h:
A = 1/2 x b x h
Multiply each side by 2
2A = b x h
Isolate h by dividing both sides by b
h = 2A/b
please na solve it please please.
Solution given to both questions below, they reveal the given answers.
The steps are self-explanatory, let me know if anything is unclear.
Question 24[tex]\cfrac{2}{(x-2)(x-3)} +\cfrac{2}{(x-1)(3-x)}+\cfrac{1}{(1-x)(2-x)} =[/tex][tex]\cfrac{2}{(x-2)(x-3)} -\cfrac{2}{(x-1)(x-3)}+\cfrac{1}{(x-1)(x-2)} =[/tex][tex]\cfrac{2(x-1)}{(x-1)(x-2)(x-3)} -\cfrac{2(x-2)}{(x-1)(x-2)(x-3)}+\cfrac{x-3}{(x-1)(x-2)(x-3)} =[/tex][tex]\cfrac{2x-2-2x+4+x-3}{(x-1)(x-2)(x-3)} =[/tex][tex]\cfrac{x-1}{(x-1)(x-2)(x-3)} =[/tex][tex]\cfrac{1}{(x-2)(x-3)}[/tex]Question 25[tex](4x - 1)(x + 2) = 2 + 7x[/tex][tex]4x^2+8x-x-2=2+7x[/tex][tex]4x^2+7x-2=2+7x[/tex][tex]4x^2=4[/tex][tex]x^2=1[/tex][tex]x=\sqrt{1}[/tex][tex]x=\pm1[/tex]Answer:
[tex]\textsf{24.} \quad \dfrac{1}{(x-2)(x-3)}[/tex]
[tex]\textsf{25.} \quad x=1, \quad x=-1[/tex]
Step-by-step explanation:
Question 24Given expression:
[tex]\dfrac{2}{(x-2)(x-3)}+\dfrac{2}{(x-1)(3-x)}+\dfrac{1}{(1-x)(2-x)}[/tex]
When adding rationals with different denominators, make the denominators the same by finding the least common denominator.
Create a common denominator by:
[tex]\textsf{Multiplying the first fraction by $\dfrac{x-1}{x-1}$}.[/tex]
[tex]\textsf{Multiplying the second fraction by $\dfrac{-(x-2)}{-(x-2)}$}.[/tex]
[tex]\textsf{Multiplying the third fraction by $\dfrac{x-3}{x-3}$}.[/tex]
[tex]\implies \dfrac{2}{(x-2)(x-3)} \cdot \dfrac{x-1}{x-1}+\dfrac{2}{(x-1)(3-x)}\cdot \dfrac{-(x-2)}{-(x-2)}+\dfrac{1}{(1-x)(2-x)}\cdot \dfrac{x-3}{x-3}[/tex]
[tex]\implies \dfrac{2(x-1)}{(x-1)(x-2)(x-3)}+\dfrac{-2(x-2)}{-(x-1)(x-2)(3-x)}+\dfrac{x-3}{(1-x)(2-x)(x-3)}[/tex]
[tex]\implies \dfrac{2(x-1)}{(x-1)(x-2)(x-3)}+\dfrac{-2(x-2)}{(x-1)(x-2)(-3-(-x))}+\dfrac{x-3}{(-(-1+x))(-(-2+x))(x-3)}[/tex]
[tex]\implies \dfrac{2(x-1)}{(x-1)(x-2)(x-3)}+\dfrac{-2(x-2)}{(x-1)(x-2)(x-3)}+\dfrac{x-3}{(x-1)(x-2)(x-3)}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{d}+\dfrac{b}{d}+\dfrac{c}{d}=\dfrac{a+b+c}{d}:[/tex]
[tex]\implies \dfrac{2(x-1)-2(x-2)+(x-3)}{(x-1)(x-2)(x-3)}[/tex]
Expand the numerator:
[tex]\implies \dfrac{2x-2-2x+4+x-3}{(x-1)(x-2)(x-3)}[/tex]
[tex]\implies \dfrac{x-1}{(x-1)(x-2)(x-3)}[/tex]
Cancel the common factor (x - 1):
[tex]\implies \dfrac{1}{(x-2)(x-3)}[/tex]
Question 25Given equation:
[tex](4x-1)(x+2)=2+7x[/tex]
Expand the left side:
[tex]\implies 4x^2+7x-2=2+7x[/tex]
Subtract 7x from both sides:
[tex]\implies 4x^2+7x-2-7x=2+7x-7x[/tex]
[tex]\implies 4x^2-2=2[/tex]
Add 2 to both sides:
[tex]\implies 4x^2-2+2=2+2[/tex]
[tex]\implies 4x^2=4[/tex]
Divide both sides by 4:
[tex]\implies \dfrac{4x^2}{4}=\dfrac{4}{4}[/tex]
[tex]\implies x^2=1[/tex]
Square root both sides:
[tex]\implies \sqrt{x^2}=\sqrt{1}[/tex]
[tex]\implies x= \pm 1[/tex]
Therefore, the solutions are:
[tex]x=1, \quad x=-1[/tex]
Mrs Flores 'sixth grade class has 15 students 9 of which are boys .What is the ratio of boys and girl in Mrs flores classroom in the simplest form ?
It know it 3:2 but can you tell me why because I am confused
Answer:
see explanation
Step-by-step explanation:
there are 15 students , 9 of which are boys, then
number of girls = 15 - 9 = 6
ratio of boys : girls = 9 : 6 = 3 : 2 ← in simplest form
A bicycle has cash price $16 319.50. It can be bought on hire purchase with a deposit of $6 900 and ten monthly installments of $1 224.50 each.
a. What is the total hire purchase price for the bicycle? [3 marks]
b. Find the difference between the hire purchase price and the cost price for the bicycle. [1 mark]
c. Express your answer in (b) above as a percentage of the cash price.
a) Total purchase price for the bicycle is $19,145
b) The difference between the hire purchase price and the cost price for the bicycle is $2,825.50
c) The percentage of difference between the hire purchase price and the cost price for the bicycle is 17%
Percentage:
Percentage means a fraction or a ratio in which the value of whole is always 100.
Given,
A bicycle has cash price $16,319.50. It can be bought on hire purchase with a deposit of $6,900 and ten monthly installments of $1,224.50 each.
Here we need to following:
a) Purchase price for the bicycle
b) Difference between the hire purchase price and the cost price for the bicycle
c) Percentage of the cash price.
The total purchase price is calculated by adding the deposit and the ten month installment.
So, the total purchase price is,
=> 6900 + (10 x 1224.50)
=> 6900 + 12245
=> 19145.
Therefore, the total purchase price is $19145.
Now, the difference between the hire purchase price and the cost price for the bicycle is calculated as,
=> 19145 - 16319.50
=> 2825.50
So, the difference between the hire purchase price and the cost price for the bicycle is $2,825.50
Now, we have to calculate the percentage by using the following expression,
x% of 16,319.50 = 2825.50
x% = 2825.50/16319.50
x% = 0.1731
x = 17.31.
Therefore, there is 17% difference in the hire purchase price and the cost price for the bicycle.
To know more about Percentage here.
https://brainly.com/question/16797504
#SPJ1
Gloria is making flower arrangements for a wedding. She has a total of 112 flowers and 14 vases to fill. What is the unit rate of
flowers per vase? (1 point)
O 8 flowers
O 14 flowers
10 flowers
6 flowers
use the english and metric equivalents to the right, along with dimensional analysis, to convert the given measurement to the unit indicated. in. to cm
It should be noted that the conversion of the measurement of 290 inches will be 0.7366 decameter.
How to illustrate the information?
It should be noted that from the information,.it about equivalents dimensional analysis, to convert the given measurement to the unit indicated.
In this case, we want to convert 290 in. to dam.
It should be noted that we have to divide rye length value by 393.7
Therefore, it should be noted that 290 inches will be:
= 290 / 393.7
= 0.7366 decameter.
Therefore, it should be noted that the conversion of the measurement of 290 inches will be 0.7366 decameter.
Learn more about of measurement here
https://brainly.com/question/28764773
#SPJ4
Which of the following numbers is NOT equivalent to 40%? A 0.04 B 0.40 c.? D *I • 10
The option that is not equivalent to the given percentage of 40% is; A:0.04.
What is the correct percentage?
We are given the percentage as 40%.
Now, this percentage can be rewritten as a proper fraction as;
40% = 40/100
In decimal form, this is expressed as 0.40
Now, the proper fraction 40/100 can be broken down into;
40/100 = 4/10
Further more when we divide both numerator and denominator by 2, we will get the fraction 2/5.
Thus, the only option that is not equivalent to the given percentage is option A which is 0.04.
Read more about Percentage at; https://brainly.com/question/24877689
#SPJ1
The correct options are;
A) 0.04
B) 0.40
C) 2/5
D) 4/10
Since wY, XZ, and AB intersect at 0, WOA ~ BOY and
XOB by the vertical angles theorem. It is given that
AOZ. By the transitive property, BOY XOB.
AOZ
WOA
What is the conclusion reached by this proof?
the conclusion is that angle AOZ and XOB is approximately equal
We are given that WOA and AOZ are equal, and since the AB intersects the line WY and XZ, were from the vertical angles theorem, This hypothesis says that when two straight lines meet, they frame two sets of linear sets with congruent angles, then angle WOZ and XOY equal and XOW and YOZ are too, now since the Ab intersects those angle on pint A and by the transitive property If any angles or segments are congruent to the same angle, at that point they are consistent to each other, according to which it was clear that both the angle BOY and XOB are approximately equal, there vertical angle which are angles WOA and AOZ are equal to them, So it can be concluded that the angle AOZ and XOB are equal too.
To know more about angles refer to the link https://brainly.com/question/28451077?referrer=searchResults.
#SPJ9
Answer:
b
Step-by-step explanation:
for edmuntum