PLEASE HELP ME!!!
What is the simplified form of the quantity 15 x y squared over x squared minus 5x plus 6 all over the quantity 5 x squared y over 2x squared minus 7x plus 3 ?
Answers
[tex]\frac{3y(2x-1)(x-3}{x(x-6)(x+1)} [/tex]
Answer: [tex]\frac{3y(2x-1)}{x(x-2)}[/tex]
Step-by-step explanation:
Given problem to simplify is [tex]\frac{\frac{15xy^2}{x^2-5x+6} }{\frac{5x^2y}{2x^2-7x+3} } \\\\=\frac{15xy^2}{x^2-5x+6}\cdot\ \frac{2x^2-7x+3} {5x^2y}............\text{(by fractional division property,the denominator invert and its reciprocal multiply to numerator)}\\\\=\frac{15xy^2}{(x-3)(x-2)}\cdot\frac{(x-3)(2x-1)} {5x^2y}.........\ \text{(factorizing quadratic equation)}[/tex]
[tex]=\frac{3y(2x-1)}{x(x-2)}........\text{(cancelling like terms with same degree and coefficients from numerator and denominator)}[/tex]
so the simplified form of the given problem is [tex]\frac{3y(2x-1)}{x(x-2)}[/tex]
Related Questions
The volume of
100
drops of a liquid is
0.1
fluid ounce.
What is the volume of
10,000
drops?
Answers
Final answer:
The volume of 10,000 drops of liquid, given that 100 drops equal 0.1 fluid ounce, is calculated to be 10 fluid ounces.
Explanation:
The question is asking to calculate the volume of 10,000 drops of a liquid, given that the volume of 100 drops is 0.1 fluid ounce. First, we determine the volume of a single drop. Then, we multiply that volume by 10,000 to find the total volume.
To start, we have the following relationship:
100 drops = 0.1 fluid ounce.
Next, we calculate the volume of one drop:
1 drop = 0.1 fluid ounce / 100 drops.
Then, we multiply the volume of one drop by 10,000 to find the volume of 10,000 drops:
10,000 drops * (0.1 fluid ounce / 100 drops) = 10 fluid ounces.
Therefore, the volume of 10,000 drops of the liquid is 10 fluid ounces.
The sum of 6 consecutive even numbers is 270. What is the second number in this sequence?
Answers
6x + 30= 270
6x = 240
x = 40
all numbers are 40,42,44,46,48,50
second number = 40 + 42 = 42
Let's take a look at this problem... okay so it tells us we have six consecutive even numbers... *** this means that there are six even numbers that come after each other in order *** ( for example: 2, 4, 6, 8...)
since we don't know these numbers let's start off by giving them variable values....
x = 1st number
x + 2 = 2nd number ----> I added 2 to x cuz the next even number comes x + 4 = 3rd number two spots after
x + 6 = 4th number
x + 8 = 5th number
x + 10 = 6th number
now let's form an equation with all this....
(x) + (x+2) + (x+4) + (x+6) + (x+8) + (x+10) = 270
6x + 30 = 270
6x = 240
x = 40
Now we plug x into the 2nd number's "equation"....
x + 2
40 + 2
42 <----- That's your answer!
Hope this helps! :D
Please vote me for Brainliest if there is a second answer!
A pair of huskies can comfortably pull a sled with a person weighing 126 pounds If Marjorie wishes to carry an additional 252 pounds of gear, how many dogs will she need altogether?
Answers
He was right the correct answer is six dogs
I need some help please
Answers
answer (0,10) see pic:
This is the 3rd one I have helped with, you should start seeing a pattern with the answers.
The given series has six terms. What is the sum of the terms of the series? 1 + 3 + 5 + . . . + 11
Answers
5 + _ + _ + 11
To find them, add 2 to 5, which gives us 7, so the 4th term is 7, and then add 7 +2, which gives 9, so 9 is the 5th.
Now add all: 1 + 3 + 5 + 7 + 9 + 11 = 36
Your answer is 36.
Answer: The required sum of the terms is 36.
Step-by-step explanation: We are given that the following series has six terms :
1 + 3 + 5 + . . . + 11.
We are to find the sum of the terms of the series.
We see the following pattern in the consecutive terms of the series :
[tex]3-1=5-3= ~~.~~.~~.~~=2.[/tex]
So, the given series is an ARITHMETIC series with fist term 1 and common difference 2.
We know that
the sum of first n terms of an arithmetic series with first term a and common difference d is given by
[tex]S_n=\dfrac{n}{2}(2a+(n-1)d).[/tex]
For the given series,
first term, a = 1 and common difference, d = 2.
Therefore, the sum of first six terms will be
[tex]S_6=\dfrac{6}{2}(2\times 1+(6-1)\times2)=3(2+5\times2)=3(2+10)=3\times12=36.[/tex]
Thus, the required sum of the terms is 36.
Parallelogram FGHI on the coordinate plane below represents the drawing of a horse trail through a local park: (Via Image)
In order to build a scale model of the trail, the drawing is enlarged on the coordinate plane. If two corners of the trail are at point A(0, 4) and point D(−6, −5), what is another point that could represent a corner of the trail?
1) (4, 4)
2) (11, 4)
3) (6, −5)
4) (−17, −5)
Answers
This is because the scale between the drawing and the new model is 3.
The only point that matches the new scale is (6,-5)
I'm sorry if this explanation is confusing but I hope it helps.
Answer:
Correct choice is 3)
Step-by-step explanation:
Enlargment is a dilation. A dilation is a transformation that preserves parallel lines and each side length of the pre-image parallelogram is multiplied by the same coefficient.
Note that
[tex]\overrightarrow{IF}=(-7-(-9),5-2)=(2,3);\\ \\\overrightarrow{DA}=(0-(-6),4-(-5))=(6,9)=3\cdot (2,3)=3\overrightarrow{IF}.[/tex]
From this statement you can conclude that the factor of dilation is 3.
Since
[tex]\overrightarrow{FG}=(-3-(-7),5-5)=(4,0),[/tex]
then
[tex]\overrightarrow{AB}=3\overrightarrow{FG}=3(4,0)=(12,0)\ \text{or}\ \overrightarrow{BA}=(12,0)[/tex]
and
[tex]\overrightarrow{DC}=(12,0)\ \text{or}\ \overrightarrow{CD}=(12,0)[/tex]
Yhis gives you that B(12,4) (or B(-12,4)) and C(6,-5) (or C(-18,-5)).
Brad wants to buy flowers for his friend with $15. The daisies are $1 each and the roses are $3 each. He buys 3 more daisies than roses how much did the roses cost?
Answers
d = r + 3
r + 3 + 3r = 15
4r + 3 = 15
4r = 15 - 3
4r = 12
r = 12/4
r = 3 ....he bought 3 roses, at $ 3 per rose = $ 9 <==
d = r + 3
d = 3 + 3
d = 6....he bought 6 daisies, at $ 1 per daisy = $ 6
-daisies=x- -roses=y-
x+y=15
the sentence how he buys 3 more daisies than roses so...
(y=x-3)
you then plug in the value of y in the equation to have only one variable...
x+ 3(x-3)=15
you then multiply 3 to the parenthesis...
x+3x-9=15
then add 9 on both sides...
4x=24
and then divide 4 on both sides...
x=6
if you plug the value of x(daisies) in the equation...
6+y=15
you subtract 6 on both sides and get...
y=9
you can also get the answer by solving for y with x...
y=3(x-3)
(x=6)
plug in x...
y=3(6-3)
y=3(3)
y=9
Answer: the roses cost $9
Which of the following shows 18/8 as a mixed number and 1 7/12 as an improper fraction?
A) 18/8 = 2 2/8 and 1 7/12=8/12
B) 18/8 = 1 5/4 and 1 7/12 = 1 12/7
C)18/8 = 9/4 and 1 7/12 = 17/12
D)18/8 = 2 1/4 and 1 7/12 = 19/12
Answers
Add 3 7/12 + 2 7/9. Simplify the answer and write as a mixed number
A)13/36
B)5 1/3
C) 6 13/36
D)5 2/3
The exact answer to this question is option d that is 18/8 = 2 1/4 and 1 7/12 = 19/12
What is improper fraction and mixed number ?
An improper fraction is a fraction where the numerator is greater than or equal to the denominator. Example 9/4 , 7/2
A mixed number is a number consisting of a whole number and a proper fraction. Example 1 3/8 , 3 1/3
FOR SOLVING THE QUESTION:
Rewriting 18/8 as a mixed number:
8/8=1 whole
So, let's see how many wholes we can get out of 18/8
18/8= (8+8+2)/8
= 8/8 +8/8 + 2/8
=1+ 1+1/4
18/8=2 1/4
Rewriting 1 7/12 as an improper fraction
1 7/12= 1+ 7/12
=12/12 + 7/12
=(12+7)/12
=19/12
Therefore, 1 7/12= 19/12
The exact answer to this question is option d that is 18/8 = 2 1/4 and 1 7/12 = 19/12
Learn more about improper fraction and mixed number here :
https://brainly.com/question/14517500
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What is the solution to the linear equation?
Answers
mrs. Williams uses the following recipe for crispy rice treats. She decided to make 2/3 of the recipe. 2 cups of melted butter, 24 oz marshmallow, 13 cups rice crispy treats.
Answers
Butter: 2•2/3=4/3=1&1/3 cups
Marshmallows: 24•2/3=16 oz
Cereal: 13•2/3= 26/3=8&2/3 cups
Fraction number is used to represent the part of a whole. For cook the 2/3 of the recipe Mr. Williams need 4/3 cups of melted butter, 16 oz marshmallow, and 26/3 cups of rice crispy treats.
Given -To cook full recipe Mr. Williams needs the 2 cups of melted butter, 24 oz marshmallow, and 13 cups rice crispy treats.
In the given question Mr. Williams wants to cook 2/3 of the recipe. For this he need to add all the ingredients in the 2/3 value as compare to the original recipe units.
Fraction numberFraction number is used to represent the part of a whole.
Required cups of melted butter is,[tex]\rm Butter = \dfrac{2}{3} \times 2[/tex]
[tex]\rm Butter = \dfrac{4}{3}[/tex]
Hence, the for the above question we need 4/3 cups of melted butter.
Required oz marshmallow-[tex]\rm oz \ marshmallow= \dfrac{2}{3} \times 24[/tex]
[tex]\rm oz \ marshmallow= 16[/tex]
Hence, the for the above question we need 16 units of oz marshmallow.
Required cups of rice crispy treats-[tex]\rm Rice \ crispy \ treats=\dfrac{2}{3} \times 13[/tex]
[tex]\rm {Rice \; crispy \; treats}=\dfrac{26}{3}[/tex]
Hence, for cook the 2/3 of the recipe Mr. Williams need 4/3 cups of melted butter, 16 oz marshmallow, and 26/3 cups of rice crispy treats.
Form more about the measurement follow the link-https://brainly.com/question/5014667
write an equation with an even product
Answers
product is multiplication:
2 * 2 = 4
Eva has borrowed 200 songs from her friend. She plans to download an equal number of songs on her music player each week for 5 weeks. The graph shows the number of songs left to download, y, for a certain number of weeks, x: A graph titled Song Downloading shows Number of Weeks on x-axis and Number of Songs Left to Download on y-axis. The x-axis scale is shown from 0 to 5 at increments of 1, and the y-axis scale is shown from 0 to 280 at increments of 40. A straight line joins the ordered pairs 0, 200 and 1, 160 and 2, 120 and 3, 80 and 4, 40 and 5, 0. Part A: What is the rate of change and initial value of the function represented by the graph, and what do they represent in this scenario? Show your work to find the rate of change and initial value. (6 points) Part B: Write an equation in slope-intercept form to model the relationship between x and y. (4 points)
Answers
PART A)
The rate of change is -40 songs each week, because the amount of songs left to be downloaded decrease by 40 every week.
the initial value is 200 at 0 weeks, which means that there are 200 songs to be downloaded at the beginning
PART B)
calculate the slope:m = (y2- y1)/(x2 - x1) = (160 - 200)/(1 - 0)
m = -40
now use the line equation in form of point-slope
y - y1 = m(x - x1)
y - 200 = -40(x - 0)
y = -40x + 200
Answer:
Each week the amount of songs that need to download decreases by 40. So The rate of change is -40 songs each week. The initial value is 200 because that is the number of songs left to download.
Part B:
y = -40x + 200
Write the phrase as an algerbraic expression. 4 times the sum of a number and 20
Answers
Solve 2x - 1 < 7 and 5x + 3 < 3. {x | x < 0} {x | x < 4} {x | 0 < x < 4}
Answers
5x + 3 < 3; then, 5x < 0; then x < 0;
Finally, {x / x < 0};
Answer:
Solution for givrn system of inequalities: [tex]\{x ~| ~x < 0\}[/tex]
Step-by-step explanation:
We are given a system of two inequalities:
[tex]2x-1 < 7\\5x+3 < 3[/tex]
Solving the inequalities individually:
[tex]2x-1 < 7\\2x<7+1\\2x < 8\\x < 4\\\text{In interval notation: } x \in (-\infty, 4) \\\\5x + 3 < 3\\5x < 3-3\\5x < 0\\x< 0\\\text{In interval notation: } x \in (-\infty, 0)[/tex]
The intersection of the two solution will give us the solution to the system of inequalities:
[tex]x \in (-\infty, 4) \cap (-\infty, 0)\\ x \in (-\infty, 0) \\\{x ~| ~x < 0\}[/tex]
Find the excluded value of the rational expression 2x + 6/4x - 8
Answers
(2x + 6)/(4x - 8) = [2(x+3)]/[4(x-2)] = (x+3)/[2(x-2)] => excluded value is 2
Answer:
for connections
1.a
2.c
3.d
4.c
Step-by-step explanation:
Rita's mother is 4 times as old as she is. Her grandmother is twice as old as her mother. If the sum of their age is 194, how old are Rita, her mother, and her grandmother?
Answers
Through setting up and solving an algebraic equation, we find that Rita is 15 years old, her mother is 60 years old, and her grandmother is 120 years old. These ages satisfy the conditions that the sum of their ages is 194, Rita's mother is 4 times her age, and her grandmother is twice the age of her mother.
Explanation:Let's use algebra to solve the problem of finding the ages of Rita, her mother, and her grandmother. We will start by defining the variable x to represent Rita's age. According to the information provided, Rita's mother's age is 4 times as old as Rita, so we can express that as 4x. The grandmother is twice as old as the mother, which can be written as 2(4x) or 8x.
Next, we need to use the fact that the sum of their ages is 194. We can set up the following equation based on all the information we have:
x (Rita's age) + 4x (Mother's age) + 8x (Grandmother's age) = 194
Combining like terms, we get:
13x = 194
Now, we solve for x by dividing both sides of the equation by 13:
x = 194 / 13
x = 14.923 (As ages are typically expressed as whole numbers, we would round this to the nearest whole number if necessary, but in this case, 194 is evenly divisible by 13, so x = 15).
Now that we know Rita's age, we can find out her mother's and grandmother's ages:
These are the ages of Rita, her mother, and her grandmother.
jace estimated the product of (34.57)(–0.74) by rounding each number to the nearest tenth. What was Jace’s estimate?
Answers
Answer:
–24.22
Step-by-step explanation:
Answer:
-24.22
Step-by-step explanation:
(aka B on edge)
7,125,000,000 what is this to the nearest billion
Answers
A room contains 5 cats and 2 dogs. If the ratio is 5 to 2 the rate can be expressed as 5 cats __ 2 dogs
Answers
Answer:
Per is the answer (Apex)
Step-by-step explanation:
Esmerelda rents a car from a company that rents cars by the hour. She has to pay an initial fee of $50, and then they charge her $9 per hour. She has $200 available to spend on car rental. What is the greatest number of hours for which she can rent the car? (The car cannot be rented for part of an hour.)
Answers
50 + 9x ≤ 200
9x ≤ 150
x ≤ 16.6
They said that the car cannot be rented for part of an hour so that means we must found it down. the max she can rent it for is 16 hours.
Check: 9*16 + 50 = 194 which is just under her budget
The correct answer is 16 hours
A student runs 100 meters in 11 second s . What is the speed of the student
Answers
to find the speed, divide these numbers, and you get .11, which is how many meters he ran per second
the speed of the student is .11 meters per second
What is the domain of the function f(x) = 3|x + 4| + 1? all real numbers all real numbers less than or equal to −4 all real numbers greater than or equal to 1 all real numbers greater than or equal to −4
Answers
Answer:
The correct option is A.
Step-by-step explanation:
The vertex form of an absolute function is
[tex]g(x)=a|x-h|+k[/tex]
Where, (h,k) is vertex.
Domain is the set of input values.
The given function is
[tex]f(x)=3|x+4|+1[/tex]
It is the vertex from of an absolute function. Here h=-4 and k=1, so the vertex of the function is (-4,1).
These functions are defined for all real values of x. So, the domain of the given absolute function is all real numbers
Therefore the correct option is A.
Which expression is equivalent to 56 + 21?
PLZ NEED HELP
Answers
8 • 7 = 56. And 7 • 3 is 21.
Hope this helps :)
Our question is:
"Which expression is equivalent to 56 + 21?
A.) 7(49 + 14)
B.) 8(7 + 21)
C.) 8(48 + 13)
D.) 7(8 + 3)"
It appears our question wants us to answer our question with two-step expressions by applying the Distributive Property.
The Distributive Property allows any number/variable outside a parenthesis (with no order of operation symbol between the number/variable and the parenthesis) to multiply by all numbers/variables inside the parenthesis.
For example, this is how to properly apply the Distributive Property;
2(1 + 3)
2(1) + 2(3)
2 + 6
This is NOT how to properly apply the Distributive Property;
2(1 + 3)
2 + 4
Now that we've covered the basics of what we're dealing with, let's try to solve our question using the Distributive Property on our answer choices.
A.) 7(49 + 14);
7(49) + 7(14)
343 + 98.
343 + 98 [tex] \neq [/tex] 56 + 21
B.) 8(7 + 21);
8(7) + 8(21)
56 + 126.
56 + 126 [tex] \neq [/tex] 56 + 21
C.) 8(48 + 13)
8(48) + 8(13)
384 + 104
384 + 104 [tex] \neq [/tex] 56 + 21
Now, all we are left with is D, likely making it our only correct answer, but let's test it out anyways.
D.) 7(8 + 3);
7(8) + 7(3)
56 + 21
56 + 21 = 56 + 21
Your correct answer is D.) 7(8 + 3).
I hope this helps!
If you have any questions or concerns as to how I came to my answer or how to handle this, feel free to send me a message and I will respond asap. :)
William buys a basket of pomegranates on sale for $10 before tax. The sales tax is 17%, percent. What is the total price William pays for the basket of pomegranates?
Answers
Solve the inequality for b 10 < -2/3(9+12b)
Answers
-30/2>9+12b. (If you Multiply or divide by a negative Number the inequality Signal(<>≤≥) turns around()
-9
-15-9>12b. :12
-24:12>b
-2>b
Final answer:
To solve the inequality 10 < -2/3(9+12b), distribute -2/3 inside the parentheses, simplify, and divide by -8, which reverses the inequality. The solution is b < -2.
Explanation:
To solve the inequality 10 < -2/3(9+12b), we must first distribute the -2/3 across the parentheses:
Multiply -2/3 by 9 to get -6.
Multiply -2/3 by 12b to get -8b.
The inequality now looks like this: 10 < -6 - 8b. Next, we simplify by moving the constant term -6 to the left side:
Add 6 to both sides: 10 + 6 < -8b.
Combine like terms: 16 < -8b.
Finally, we divide both sides by -8, remembering that this reverses the inequality symbol:
Divide by -8: -2 > b or b < -2.
Therefore, the solution to the inequality is b < -2.
Anybody know? Also, what pattern?
Answers
If you have 24 square pieces of wood, describe all the different ways you could make a rectangle by placing them side by side
Answers
You have 24 square pieces of wood. You could lay them out in the following fashion. First number is the number of rows. Second number is the number of columns. For example:
1,24 is 1 row by 24 columns. Here goes:
1,24
2,12
3,8
4,6
6,4
8,3
12,2
24,1
i believe that's all.
It winds up being the number of ways you can multiply two integers to get 24.
Find the quotient of quantity of negative 5 times x to the 3rd power plus 15 times x to the 2nd power minus 10 times x all over negative 5 times x. (5 points)
x2 + 3x − 2
x2 − 3x + 2
−x2 + 15x − 10
x2 − 15x + 10
Answers
Answer:
x^2 - 3x +2
Step-by-step explanation:
[tex]\frac{-5x^3+15x^2-10x}{-5x}[/tex]
We divide the whole expression by -5x
When we divide by negative the sign of each term changes
We divide each term separately by -5x
-5x^3 / -5x = x^2
15x^2 / -5x = -3x
-10x/ -5x = +2
So the expression becomes x^2 - 3x +2
Margot is sewing a ribbon on a seam along the perimeter of a square pillow. The side length of the pillow is 2x^2+1 inches, and its perimeter is 4(2x^2+1) inches. If x=3.5, how much Robbin does she need?
Answers
2x3.5*2 power=24.5
4(24.5+1)=102
The total mass of Abdul and his baby brother is 15.25kg . The mass of Abdul and his father is 72.25kg . The mass of Abdul's father is 13 times as heavy as Abdul's baby brother. What is Abdul's mass?
Answers
a+f=72.25, since f=13b
a+13b=72.25 so now we have two equation in two variables...
a+13b=72.25 and a+b=15.25 so we can say:
(a+13b=72.25)-13(a+b=15.25)
a+13b-13a-13b=72.25-198.25
-12a=-126
a=10.5 kg
So Abdul's mass is 10.5 kilograms.