The sum of the squares of two consecutive positive odd integers is 202. Find the numbers. Please use a let statement and algebraic solution. thanks! :)
Answers
Answer:
9 and 11
Step-by-step explanation:
The sum of the squares of two consecutive positive odd integers is 202.
Let first number be x and other number is (x+2).
According to question,
\(x^2+(x+2)^2=202\\\\x^2+x^2+4+4x=202\\\\2x^2+4x+4=202\\\\2x^2+4x-198=0\)
It is a quadratic equation. The solution of a quadratic equation is given by :
\(x=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}\)
We have, a = 2, b = 4 and c = -198
So,
\(x=\dfrac{-b+ \sqrt{b^2-4ac} }{2a}, \dfrac{-b- \sqrt{b^2-4ac} }{2a}\\\\x=\dfrac{-4+ \sqrt{4^2-4\times 2\times (-198)} }{2(2)}, \dfrac{-b- \sqrt{b^2-4ac} }{2a}\\\\x=9, -11\)
So, first positive odd integer is 9 and second one is (9+2)=11
Related Questions
What is 75/8. I am bad a division. I am offering 10 points for it. PLEASE ANSWER!!!!
Answers
Answer:
9.375
Step-by-step explanation:
9
8 | 7 5
7 2
3
9 with a remainder of 3
~~~~~~~~
9 . 3 7 5
8 | 7 5 .
7 2 .
3 . 0
2 . 4
6 0
5 6
4 0
4 0
9.375
The height of a stack of DVD cases is in a proportional relationship to the number of cases in the stack. A stack of 6 cases and its height are shown. The height of 6 DVD cases is 66 mm. Find the constant of proportionality. Then use the constant of proportionality to find the height of a stack of 14 cases.
Answers
Answer:
The answer is 11 becasue 66 divided by 6 equals 11
Step-by-step explanation:
Hope this helped
Use the Midpoint Rule with \(n=5\) to estimate the volume obtained by rotating about the y-axis the region under the curve \(y=\sqrt{1+x^3}\), \(0\leq x\leq 1\).
Answers
To estimate the volume using the Midpoint Rule with \(\displaystyle n=5\), we need to divide the interval \(\displaystyle 0\leq x\leq 1\) into \(\displaystyle n\) subintervals of equal width. Since \(\displaystyle n=5\), each subinterval will have a width of \(\displaystyle \Delta x=\frac{1-0}{5}=\frac{1}{5}\).
Now, let's calculate the volume using the Midpoint Rule. The formula for the volume obtained by rotating about the y-axis is:
\(\displaystyle V\approx 2\pi \sum _{i=1}^{n}y_{i}\Delta x\)
where \(\displaystyle y_{i}\) represents the value of the function \(\displaystyle y=\sqrt{1+x^{3}}\) evaluated at the midpoint of each subinterval.
First, let's find the midpoints of the subintervals. Since the width of each subinterval is \(\displaystyle \Delta x=\frac{1}{5}\), the midpoint of the \(\displaystyle i\)-th subinterval is given by:
\(\displaystyle x_{i}=\frac{\Delta x}{2}+\left( i-\frac{1}{2}\right) \Delta x=\frac{1}{10}+\left( i-\frac{1}{2}\right) \frac{1}{5}\)
Substituting \(\displaystyle x_{i}\) into the function \(\displaystyle y=\sqrt{1+x^{3}}\), we obtain:
\(\displaystyle y_{i}=\sqrt{1+\left( \frac{1}{10}+\left( i-\frac{1}{2}\right) \frac{1}{5}\right) ^{3}}\)
Now, we can calculate the approximate volume using the Midpoint Rule:
\(\displaystyle V\approx 2\pi \sum _{i=1}^{5}y_{i}\Delta x\)
Substituting the values of \(\displaystyle y_{i}\) and \(\displaystyle \Delta x\) into the formula, we can evaluate the sum and compute the estimated volume.
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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
Micah uses the coordinate grid to draw a rectangle. Three verticles of the rectancle are (-4, 5),(-4,3) and (6,5). What are the coordinates of the fourh vertex? show micahs rectangles on the coordinate grid
Answers
Answer:
(6, 3)
Step-by-step explanation:
We already have two coordinates that make one side of the rectangle up.
(-4, 5) and (-4, 3)
Notice how only the y-coordinates change.
So, based on this logic, we should get:
(6, 5) and (6, 3)
So, the missing coordinate is (6,3)
Answer:
(6,3) is the missing 4th vertex.
Step-by-step explanation:
We know that, a rectangle is made up of 4 sides , 4 vertices and 4 edges.
According to the question, there are 3 vertices marked.
The three vertices are:
(-4,5)(-4,3)(6,5)IMPORTANT NOTEIf we are measuring the sides of a quadrilateral on a coordinate grid, we have to remember that each and every point comes twice in adjacent sides.
For example:
In the given figure, (-4) and 5 appeared twice in the three given vertices.
Now, we should remove (-4) and 5 from the three vertices.
We will be left with 6 and 3.
So, the 4th point will be the combination of 6 and 3.
Hence, we will get the 4th point as (6,3).
Hope my answer helps you ✌️
Which statement below is false?
A. Thermal energy transfers can be tracked as it flows through a system.
B. A constant input of energy, often in the form of heat, is needed to keep an endothermic reaction going.
C. In order to build a chemical bond energy is needed.
D. An exothermic reaction is a chemical reaction in which more energy is needed to break bonds in the reactants than is released when new bonds form in the products.
Answers
Answer: I believe D
D. An exothermic reaction is a chemical reaction in which more energy is needed to break bonds in the reactants than is released when new bonds form in the products
Step-by-step explanation:
D. An exothermic reaction is a chemical reaction in which more energy is needed to break bonds in the reactants than is released when new bonds form in the products.
The dot plot shows the number of movies 15 people watched in a month: Dot plot labeled Number of Movies Seen shows 2 dots over 0, 2 dots over 7, 3 dot over 8, 3 dots over 9, and 5 dots over 10. Is the median or the mean a better center for this data and why? (1 point) Mean; because the data is normally distributed and has an outlier Mean; because the data clusters on the right and is not symmetric Median; because the data is normally distributed and has an outlier Median; because the data clusters on the right and is not symmetric
Answers
Answer:Median; because the data is not symmetric and there are outliers.
Step-by-step explanation:We know that a median is a central tendency of a data and it best represents the given data set.
From the given information we see that the data is skewed to the right since most of the data points takes the higher value and the data is not symmetric as it is skewed.
Hence, last option is the correct answer.
Please answer fast! I’ll give brainliest to the best answer if it’s right!look at the picture
Answers
Multiply the pairs of numbers and match them with their products. Tiles (-5)(4.2) (-7)(-3) (4) (5) (2.5)(-9) Pairs 22.5 21 -22.5 -21 111
Answers
Here are the pairs matched with their products:
- (-5)(4.2) matches with -21
- (-7)(-3) matches with 21
- (2.5)(-9) matches with -22.5
Pairs (4) and (5) do not have corresponding products in the given options.
(-5)(4.2) = -21
(-7)(-3) = 21
(4)(5) = 20
(2.5)(-9) = -22.5
So, the pairs of numbers and their products are as follows:
(-5)(4.2) = -21 matches with -21.
(-7)(-3) = 21 matches with 21.
(4)(5) = 20 matches with 20.
(2.5)(-9) = -22.5 matches with -22.5.
I hope this helps!
A bag of marbles contains only yellow, blue and green marbles. There are 4 yellow marbles and 2 blue marbles, and 1/3 of the marbles are green. If a marble is picked out at random, what is the probability it will be blue? Please give an answer ASAP!
Answers
Answer:
2/9
Step-by-step explanation:
There are 4 yellow marbles and 2 blue marbles = 6 marbles
This is 2/3 of the marbles since 1/3 are green
2/3 of the total marbles are 6 marbles
2/3 * m = 6
m = 6 * 3/2 = 9
1/3 m = green marbles = 1/3 *9 = 3
4 yellow marbles and 2 blue marbles 3 green marbles = 9 marbles
P ( blue) = blue/total = 2/9
only answer question twelve …
Answers
Answer:
I c a n t read the question
Step-by-step explanation:
HELP IS NEEDED ASAP PLEASE!!!!!!! (I only need the m<3 part please!)
Answers
At the zoo, for every 666 adult camels, there are 555 baby camels. There are a total of 444444 adult and baby camels at the zoo.
Complete the table.
Original ratio Number in the zoo
Baby camels 555
Adult camels 666
Total camels
444444
Answers
Answer:
1 adult camel for every 11 baby camels, or 1:11
The histogram shows the number of points scored by a basketball team for one season. A histogram titled points scored in one season shows the number of games in which a certain number of points were scored. The data is as follows. 69 to 76 points: 3 games. 77 to 84 points: 6 games. 85 to 92 points: 8 games. 93 to 100 points: 1 game. According to the histogram, in what percentage of games did the team score between 77 and 92 points? Enter your answer in the box. Round your answer to the nearest percent.
Answers
Find the total number of games with points scored between 77 & 92 pts - 14
To find the percentage divide 14/18 - .777
Multiply .777*100 - 77.7
Round to 78%
Percentage of games the team scored between 77 and 92 is 77.7% .
Given data from the histogram shows the number of games that are played in the range of 77 - 92.
Total number of games played = 18
Number of games played in the range 77 - 92 = 14
Percentage of games played in the range 77-92 = (Number of games played in the range 77 - 92) / (Total number of games played) × 100
Percentage = (14)/(18) × 100
= 77.7% .
Hence the number of games played in the given range is 77.7%.
Learn more about percentage,
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PLS I NEED HELP!! I'LL GIVE U THANKS AND RATES AND MARK U AS BRILLIANT BUT PLS HELP !! IT'S FOR TOMORROW!! :(
Answers
Step-by-step explanation:
10)We have to calculate the average speed if we know the distance and time that Johnatan can jog. The distance
distance=3 2/5 miles = 3.4 miles.
Time=7/8 hour = 0.875 h
Then we will use the formula for the average speed ( velocity )
velocity=distance/time. v = 3.4 m / 0.875 h = 3.866 mph
so therefore The average speed is 3.866 mph.
11) divide 120 / 7/4 (remember 120 = 120/1)
Which means you have to cross multiply (an important part on fraction division, that is, your division would be 120x4 / 1x7).
Then 120x4= 480
And 1x7 = 7
Then you get 480/7, which is the same as 68 4/7 mph
12)8 1/3=25/3
25/3 pages of a book in 10 minutes
Multiply both numbers by the reciprocal of 10, which is 1/10
25/3 x 1/10=25/30=5/6
10 x 1/10=1
So, Charlotte reads 5/6 pages of a book in 1 minute.
13)45 1/2% = 45.5% = 45.5/100 = 91/200
30 1/4% = 30.25% = 30.25/100 = 121/400
75 1/3% = 75.3333...% = 75.333.../100 = 11/15
Answer:
what he said
Step-by-step explanation:
Please I need help Asp please help me solve the equation in the picture below also please show steps on how to solve
Answers
Answer:
\(x=-6\dfrac{7}{8}\)
Step-by-step explanation:
\(Solve\:9\:\dfrac{1}{4}\:+\:x\:=\:2\:\dfrac{3}{8}\)
Step 1:
Convert all mixed fractions to improper fractions.
This will make it easier to add and subtract
Mixed fraction \(a\dfrac{b}{c}\) can be converted to an improper fraction using
\(a\dfrac{b}{c}=\dfrac{a\cdot \:c+b}{c}\)
\(9\dfrac{1}{4}=\dfrac{9\cdot 4+1}{4} = \dfrac{37}{4}\)
\(2\dfrac{3}{8}=\dfrac{2\cdot 8+3}{8} =\dfrac{19}{8}\)
Step 2:
Replace every mixed fraction in the original equation with its equivalent improper fraction:
\(\dfrac{37}{4}+x=\dfrac{19}{8}\)
Step 3
Solve for x
\(\dfrac{37}{4}+x-\dfrac{37}{4}=\dfrac{19}{8}-\dfrac{37}{4}\)
Simplify:
\(x =\dfrac{19}{8}-\dfrac{37}{4}\)
To calculate the right side value, multiply \(\dfrac{37}{4}\) by 2 on both numerator and denominator. This will get the denominator as 8 for both fractions and we can simply subtract the numerator:
\(\begin{aligned}x & = \dfrac{19}{8} - \dfrac{37 \times 2 }{4 \times 2} \\ & = \dfrac{19}{8} - \dfrac{74}{8}\\& = \dfrac{19 - 74}{8}\\& = - \dfrac{55}{8}\\\end{aligned}\\\\\)
\(\mathrm{Convert\:to\:mixed\:number:\:Quotient\dfrac{Remainder}{Divisor}}\)
55 goes into 8 six times so the whole part(quotient) is 6
Remainder = 55 - 8 x 6 = 55 - 48 = 7
So the fractional part = remainder/divisor = 7/8
Result:
\(x=-6\dfrac{7}{8}\)
Some students recorded how many minutes they spent on the phone in one day. They put the results in a Stem-and-Leaf Plot.
What is the mean number of minutes spent on the phone?
Answers
Explanation:
The data from the stem-and-leaf plot is:
10,
24,25,26,
30,30,32,33,
40,45,46
Add up those values
10+24+25+26+30+30+32+33+40+45+46 = 341
Then divide over n = 11 which is the sample size.
341/11 = 31 is the arithmetic mean.
Answer:
341/11 = 31 is the arithmetic mean.
Step-by-step explanation:
PLEASE ANSWER QUICK One year, the population of a city was 164,000. Several years later it was 182,040. Find the percent increase.
Answers
Answer:
There was an 11% increase.
Step-by-step explanation:
The formula to find a percent increase is this: (original amount - new amount / original amount) * 100
If you fill in the formula, you get this:
(164,000 - 182,040 / 164,000) * 100
Solve:
(-18,040 / 164,000) * 100 ---> If the number being divided is negative, find the absolute value.
(18,040 / 164,000) * 100 =
0.11 * 100
11%
What do I do where it says "Rewrite The False Statement To Make It True"?
Answers
Answer:
the rate of change is $50
Step-by-step explanation:
each ticket costs $50 not 100
Each ticket cost 50$ and 2 cost 100
PLEASE NO LINKS OR FILES ALL IM ASKING IS FOR AN HONEST ANSWER PLASE AND THANK YOU WILL GET BRAILEAST IF CORRCT :))
Answers
Answer:
7?
Step-by-step explanation:
72/10 squares = about 7
VIEWS The number of daily views during the first 10 days for a video posted on the Internet decreases according to the function 20(0.8¹). In the equation, x represents the number of days since the video was released and y represents the number of daily views, in thousands. Identify the relevant domain and range. Round to the nearest tenth if necessary.
Answers
Answer:
Answer is b i took the test
How can Diego package all the 48 brownies and 64 cookies so that each bag has the same combination of items? How many bags can he make, and how many of each will be in each bag? Find all the possible ways to package both items.
I don't know how to do this, can someone please walk me through the process and help with the answer(s)?
Answers
Divide 48(brownies) by 2, you get 24, and if you divide 64(cookies) by 2, you get 32. So you will need 2 boxes ( since we divided both the numbers by 2 ) and each box will have 24 brownies and 32 cookies in each.
2nd way:
Divide 48( brownies) and 64(cookies) by 4, and you will get 12(brownies) and 16(cookies), so you will need 4 boxes with 12 brownies and 16 cookies in each since we divided the numbers by 4.
So basically, you can keep doing this until no more numbers equal to 48 or 64 when you divide them. And the number you divide them with is how many boxes you will need. Hope this helps.
Daniel has a collection of stamps worth $6. He has 5 more 8 cent stamps then 30 cent stamps. The number of 6 cent stamps is 2 times the amount of 30 cent stamps. The number of 5 cent stamps is 12. How many of each kind of stamps does Daniel have?
Please list the number of 30, 5, 6, 8 cent stamps he has.
First gets Brainliest!!!
Answers
Answer:
12 of the 5 cents stamps,
20 of the 6 cents stamps
15 of the 8 cents stamps
10 of the 30 cents stamps.
Step-by-step explanation:
Let's name:
x = number of 5 cent stamps,
w = number of 6 cent stamps,
y = number of 8 cent stamps,
z = number of 30 cent stamps,
Create the following system of equations based on the info provided:
z + 5 = y
w = 2 * z
x = 12
600 = 5 (12) + 6 w + 8 y + 30 z
replace everything in terms of "z":
600 = 60 + 6 (2 * z) + 8 (z + 5) + 30 z
540 = 12 z + 8 z + 40 + 30 z
500 = 50 z
z = 10
and now we can find the rest:
y = 5 + 10 = 15
w = 2 * 10 = 20
Therefore there are:
12 of the 5 cents stamps,
20 of the 6 cents stamps
15 of the 8 cents stamps
10 of the 30 cents stamps.
Alex had 12 gumball machines. Each had about 47 gumballs.
Using compatible numbers, what is the best estimate for the number of gumballs Alex had?
Alex had about ______ Gumballs
DO I do Multiplication or whattt
Answers
Answer:
The answer would be 600 gumballs.
Step-by-step explanation:
The first step that you would do to solve this problem is multiply 12 by 47, which would give you 564.
The second step that you would do is round it. 564 rounded to the hundredths place is 600.
Therefore, your answer is 600.
Answer: 500
Step-by-step explanation:
its 500 round 47 u get 50 then round 12 u get 10 50 . 10=500
i really need help please
Answers
Answer: -10, -7, -5, -3, -2.1, -2.01, -2.001.
Step-by-step explanation: The numbers you need to pick, have to be less than -2. -10, -7, -5, -3, -2.1, -2.01, and -2.001, are less than 2. -2, -1.999, -1.99, -1.9, -1, 1, 3, and 6, are all greater than 2, so they won't fit the equation.
Using compatible numbers, which number is the best estimate of 72.67÷7.8?
A.8
B. 9
C. 10
D. 11
Answers
Because if you divide 72.67/7.8 it gives you 9.37
Determine the domain for the function in the following image:
Answers
x-2≠0
Solve, which means that x is not equal to 2
x≠2
This means that there is a vertical asymptote present at 2. The domain is all real numbers except for 2.
The answer can be written as:
Domain: x≠2
Answer:
When solving this problem you first need to set x-2 not equal to zero
x-2≠0
Solve, which means that x is not equal to 2
x≠2
This means that there is a vertical asymptote present at 2. The domain is all real numbers except for 2.
The answer can be written as:
Domain: x≠2
Step-by-step explanation:
I want to make sure im doing this right, if you could help it would be great
Answers
Answer:
84
Step-by-step explanation:
7(9+3) you multiply 7 to both numbers like this
63+21 and then you can simplify
84
If you need the other 3 done just comment on this question to tell me
Also please mark brainliest
Answer:
Step-by-step explanation:
1.84
2.32
3.30
4.88
1.
84 because PEMDAS(parenthesis/Exponents/Multiply/Divide/Add/Subtact) says you do parenthesis first. So you add 9 and 3 to get 12. The you do 12*7 to get 84.
Aquarium I contains 4.6 gallons of water. Louise will begin filling Aquarium I at a rate of 1.2 gallons per minute.
Aquarium II contains 54.6 gallons of water. Isaac will begin draining Aquarium II at a rate of 0.8 gallon per minute.
After how many minutes will both aquariums contain the same amount of water?
148 minutes
125 minutes
25 minutes
50 minutes
Answers
Answer:
The answer is 25 :)
Step-by-step explanation:
Ok, this explanation will probably be super confusing so sorry about that but you get two statements about each aquarium. Aquarium 1 starts with 4.6 gallons and will INCREASE by 1.2 gallons every minute. So now you have statement one, so let's plug it into the y=mx+b formula. y is the result/ the answer you get, m is the slope/how much your points INCREASE or DECREASE. x is the variable you use to plug and b is your starting point. So you are trying to find the y which means we cannot plug it in yet so right now we have y=mx+b. your next letter to switch out is m. Like I said, M is how much each point increases or decreases and if you go back, the statement says "will increase by 1.2 gallons every minute." so your m is 1.2 and will be positive because of the keyword INCREASE. now we have y=1.2x+b. B is your starting point so let's go back to the statement to find the starting point/ number, it states "Aquarium 1 contains 4.6 gallons" meaning aquarium 1 starts with 4.6 gallons, so let's plug it into the equation. you should have y=1.2x+4.6, which is your first equation. Your next equation will be a bit more tricky. we start with y=mx+b and we start with finding m, how much each point will increase or decrease. "Isaac will begin DRAINING aquarium 2 at a rate of 0.8 gallon per every minute." so M will be .8 but notice the keywords DRAINING, meaning decreasing. So because Isaac isn't filling and increasing, but he is decreasing, you will make .8 negative. so you should currently have y=-.8x+b. Now let's find the starting point, or B. "Aquarium 2 contains 54.6 gallons of water." making your m 54.6 gallons of water. Let's plug it in. y=-.8x+54.6. Now that you have to equations, this is how you will find when both equations have a point intercepting, or in other words, the answer you are looking for. you will remove the "y=" on both equations, and place an "=" between them. You should have something looking like this on your paper. "1.2x+4.6 = -.8x+54.6". Now you are going to combine like terms, so look on both sides of the equation and look for the 2 numbers with no "x" next to them. You should find "4.6" on your left and "54.6" on your right side of the equal sign. you are going to equal out "4.6" with itself by writing "-4.6" underneath it but because you did this on one side of the equal sign, you have to do it on the other side but before you do so you should have "1.2x = -.8x+54.6". now let's subtract "4.6" to "54.6" you will write "-4.6" underneath "54.6" to get your new number, "50". your problem should look like "1.2x = -.8x + 50". now we are going to do the same for your number's with an "x" by it. on the right side of the equation, you will cancel out "-.8x". notice it's NEGATIVE so, in order to cancel out a negative number, you just make the number positive. so you will ADD ".8x" to "-.8" to get 0 but because you added ".8x" to one side, you have to do it to the other side. Let's check what we have first, you should have "1.2x = 50". so now let's ADD ".8x" to "1.2x". you will get "2x" so now you should have both equations simplified like this, "2x = 50" and now we are going to make x one so we will divide "2x" by "2" to get "x", but because you did this to one side, you have to do it to the other. so now you divide "50" by "2" to get 25. now you should have written down "x = 25". Thank you so much for reading this and please let me know if this was helpful or confusing. :)))
The time at which both aquariums contain the same amount of water is 25 minutes and this can be determined by forming the linear equation.
Given :
Aquarium I contains 4.6 gallons of water. Louise will begin filling Aquarium I at a rate of 1.2 gallons per minute.Aquarium II contains 54.6 gallons of water. Isaac will begin draining Aquarium II at a rate of 0.8 gallons per minute.The following steps can be used in order to determine the time at which both aquariums contain the same amount of water:
Step 1 - Let the time be 't' at which both aquariums contain the same amount of water.
Step 2 - The amount of water in the Aquarium I at time 't' is given by:
V = 4.6 + 1.2t
where V is the total amount of water at time 't'.
Step 3 - The amount of water in the Aquarium II at time 't' is given by:
V' = 54.6 - 0.8t
where V' is the total amount of water at time 't'.
Step 4 - So, time at which both aquariums contain the same amount of water is given by:
V = V'
4.6 + 1.2t = 54.6 - 0.8t
Step 5 - Simplify the above equation.
50 = 2t
t = 25 minutes
Therefore, the correct option is C).
For more information, refer to the link given below:
https://brainly.com/question/11897796
There are 4 figures shown. The first figure has a 1 dot, the second has 3 dots, and the third figure has 6 dots, and finally, the fourth one has 10 dots.
If the following pattern continues, how many more dots are there in Figure 100 than in Figure 98?
(Offering 30points for this question for Math Olympiad! Thank you! <3)
Answers
Answer:
Figure100=5050dots Figure98=4851
150% of 48 is ___.
Explain your method.
Answers
Answer:
72
Step-by-step explanation:
48*1.5=72
turn 150% into decimal and multiply by 48 to get the answer.