Answer:
4x^2 +9xy +6y^2
Step-by-step explanation:
Combine like terms. I find it useful to factor out the variable part of the expression so I can see what coefficients are being combined.
7x^2+5xy-3y^2 - (2x^2+3xy-5y^2 + x^2-7xy-4y^2)
= (7 -2 -1)x^2 +(5 -3+7)xy +(-3 +5 +4)y^2
= 4x^2 +9xy +6y^2
31. One serving of party drink is comprised of 3oz of syrup, 4oz of water, and 3oz of apple juice. If a large bowl of the drink contains 237oz of apple juice, how much of the total drink is in the bowl
Answer:
790 oz
Step-by-step explanation:
Ratio:
3oz syrup : 4oz water : 3oz apple juice: 1 serving: 10oz total mixture
We know there is 10oz total mixture because 3oz of syrup + 4oz of water + 3oz of apple juice = 10oz total mixture
We want to find
237oz apple juice: ?oz total mixture
To do this, we can multiply the ratio
3oz apple juice: 10oz total mixture by 237/3, because 237/3 * 3 = 237, getting us to 237oz apple juice on one side and maintaining the ratio so that we can find the total mixture amount, so we have
237oz apple juice: 10*237/3 oz total mixture = 10*79 = 790 oz
What is the slope of the line that passes through the points (-3, 3)(−3,3) and (-21, 18) ?(−21,18)? Write your answer in simplest form.
Answer:
-5/6
Step-by-step explanation:
to find the slope between to lines we can subtract the second y by the first y and subtract the second x by the first x and dividing them by each other
(18 - 3) / (-21 + 3)
minusing a negative is basically adding
after subtracting them you get this
15 / -18
then reduce
-5/6
the slope is -5/6
this is for 8th grade pls answer .
Step-by-step explanation:
We have that
[tex](x + \frac{1}{x} ) {}^{2} = 3[/tex]
We are trying to find the number value so that we can apply in the later equation.
Qe first simplify.
Remeber that
[tex](a + b) {}^{2} = a {}^{2} + 2ab + {b}^{2} [/tex]
Also remeber that
[tex] \frac{1}{x} = {x}^{ - 1} [/tex]
so
[tex](x + x {}^{ - 1} ) {}^{2} = {x}^{2} + 2x {}^{0} + {x}^{ - 2} = 3[/tex]
We then simply remeber that x^0=1 so
[tex] {x}^{2} + 2 + \frac{1}{ {x}^{2} } = 3[/tex]
Multiply both sides by x^2.
[tex] {x}^{4} + 2 {x}^{2} + 1 = 3 {x}^{2} [/tex]
Subtract both sides by 3x^2
[tex] {x}^{4} - {x}^{2} + 1 = 0[/tex]
Notice that x^4= (x^2)^2.
So our reformed equation is
[tex]( {x}^{2} ) {}^{2} - {x}^{2} + 1 = 0[/tex]
Let a variable , w equal x^2. This means that we subsitute variable, w in for x^2.
[tex]w {}^{2} - w + 1 = 0[/tex]
Now we use the quadratic formula
[tex] w = \frac{ - b + \sqrt{b {}^{2} - 4ac } }{2a} [/tex]
and
[tex]w = - b - \frac { \sqrt{b {}^{2} - 4ac } }{2a} [/tex]
Let a=1 b=-1 and c=1.
[tex]w = \frac{1 + \sqrt{1 - 4(1)} }{2} [/tex]
[tex]w = \frac{1 - \sqrt{1 - 4} }{2} [/tex]
Now, we get
[tex]w = \frac{1}{2} + \frac{i \sqrt{3} }{2} [/tex]
and
[tex]w = \frac{1}{2} - \frac{ i\sqrt{3} }{2} [/tex]
Now since we set both of these to the x^2 we solve for x.
and
[tex] {x}^{2} = \frac{1}{2} + \frac{i \sqrt{3} }{2} [/tex]
and
[tex] {x}^{2} = \frac{1}{2} - \frac{i \sqrt{3} }{2} [/tex]
We can represent both of these as complex number in the form of a+bi. Next we can convert this into trig form which is
[tex] {x}^{2} = 1( \cos(60) + i \: \sin(60) [/tex]
and
[tex] {x}^{2} = 1( \cos(300) + i \: sin(300))[/tex]
Next we take the sqr root of 1 which is 1, and divide the degree by two.
[tex] {x} = 1( \cos(30) + i \: sin \: 30)[/tex]
and
[tex]x = 1( \cos(150) + i \: sin(150)[/tex]
We are asked for the 2nd root so just add 180 degrees to this and we have
[tex]x = 1 \cos(210) + i \: sin \: 210)[/tex]
and
[tex]x = 1( \cos(330) + i \: sin(330)[/tex]
which both simplified to
[tex]x = - \frac{ \sqrt{3} }{2} - \frac{1}{2} i[/tex]
and
[tex]x = \frac{ \sqrt{3} }{2} - \frac{1}{2} i[/tex]
Now we must find
x^18+x^12+x^6+1.
We just use demovire Theorem. Which is a complex number raised to the nth root is
[tex] {r}^{n} (cos(nx) + i \: sin(nx)[/tex]
So let plug in our first root.
[tex]1( \cos(330 \times 18)) + i \: sin \: (330 \times 18))) + 1( \cos(12 \times 330)) + i \: sin(12 \times 330) + 1( \cos(6 \times 330) + i \: sin(6 \times 330))) + 1[/tex]
To save time we multiply the angle and use rules of terminals angle and we get
[tex]1( \cos(180) + i \sin(180) ) + 1( \cos(0) + i \: sin \:( 0) + 1( \cos(180) + i \: sin(180) + 1[/tex]
And we get
[tex] - 1 + 1 + - 1 + 1 = 0[/tex]
So one of the answer is x=0
And the other, let see
[tex]1 \cos(210 \times 18) + i \: \sin(210 \times 18) + 1 \: cos(210 \times 12) + i \: sin(210 \times 12) + 1 \cos(210 \times 6) + \:i sin(210 \times 6) + 1[/tex]
[tex] \cos(180) + i \: sin(180) + 1 \cos(0) + i\sin(0) +1( \cos(0) + i \sin(0) + 1[/tex]
We get
[tex] - 1 + 1 + 1 + 1 = 2[/tex]
So our answer are 2.
So the answer to the second part is
0 and 2.
a farm has chickens and cows all the cows have 4 legs and all chickens have 2 legs. altogether there are 82 cow and chicken legs on the farm.complete the table to show some possible combinations of chickens and cows to get 82 total legs.
mark me brinilylist pls
An analyst surveyed the movie preferences of moviegoers of different ages. Here are the results about movie preference, collected from a random sample of 400 moviegoers.
A 4-column table with 4 rows. The columns are labeled age bracket and the rows are labeled type of movie. Column 1 has entries cartoon, action, horror, comedy. Column 2 is labeled children with entries 50, 22, 2, 24. Column 3 is labeled teens with entries 10, 45, 40, 64. Column 4 is labeled adults with entries 2, 48, 19, 74.
Suppose we randomly select one of these survey participants. Let C be the event that the participant is an adult. Let D be the event that the participant prefers comedies.
Complete the statements.
P(C ∩ D) =
P(C ∪ D) =
The probability that a randomly selected participant is an adult prefers comedies is symbolized by P(C ∩ D).
Using it's concept, it is found that the probabilities are given as follows:
P(C ∩ D) = 0.185.P(C ∪ D) = 0.5775.What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there is a total of 400 moviegoers.
From the table, 74 are adults who prefer comedies, hence:
P(C ∩ D) = 74/400 = 0.185.
2 + 48 + 19 + 74 = 143 are adults, while 24 + 64 = 88 are not adults but prefer comedies, hence the "or probability" is given by:
P(C ∪ D) = (143 + 88)/400 = 0.5775.
More can be learned about probabilities at https://brainly.com/question/14398287
Answer:
0.3575
0.405
Step-by-step explanation:
HELLPPPP MEEEEE ASAPPPPPPP PLEASEEEEEEEEEEEEWEEEEEEEE
Answer:SORRY CANT HELP U THERE
Step-by-step explanation:
PLS HELP TY!!
Two functions, function A and function B, are shown below:
Function A
x y
7 14
8 16
9 18
Function B The first quadrant of a coordinate grid is shown from 0 to positive 8 on both axes at intervals of 1. The title is Function B. Only the even numbers are shown on the scale. A line is drawn by connecting the points on ordered pairs 1, 3 and 2, 6 and 3, 9.
Which statement best compares the rate of change of the two functions? (1 point) The rate of change of both functions is 2.
The rate of change of both functions is 3.
The rate of change of function A is greater than the rate of change of function B. The rate of change of function B is greater than the rate of change of function A.
Answer:
The rate of change of function B is greater than the rate of change of function A
Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child tickets for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. What is the price each of one senior citizen ticket ?
Senior citizen ticket: $
A company rents out 15 food booths and 22 game booths at the county fair. The fee for a food booth is $175 plus $8 per day. The fee for a game booth is $80 plus $7 per day. The fair lasts for d days, and all the booths are rented for the entire time. Enter a simplified expression for the amount, in dollars, that the company is paid.
Answer: ($2100+96d) + ($2755+116d)
= $4855+212d
Help me with this
-22*3 +12*2 -6*2 +4+2
[tex]\red{\bf{ {Answer = \: \: - 48}}} [/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf \underbrace {-22 \times 3} + \underbrace {12 \times 2} - \underbrace {6\times 2} + 4 + 2[/tex]
We carry out the three multiplications.
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf \underbrace {-66 \: + \: 24} \: - \: 12 \: + \: \underbrace {4 \: + \: 2}[/tex]
Now we make the ones that are marked.
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf \underbrace {-42} \: \: - 12 \: \: + \underbrace {6} \: \: [/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf \underbrace {-36 \: \: \: - \: \: \: 12}[/tex]
[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf -48[/tex]
if the compound interest on a sum for 2 years at 4% p.a. is ₹408, then the simple interest on the same sum at the same rate and for the same period is (I) ₹400 (ii) ₹398 (iii) ₹200 (iv) ₹204
Given that:
CI = ₹408
years = 2 years
Rate of interest = 4%
A = P{1+(R/100)}^
A-P = p{1+(R/100)}^n - P
I = P[1+(R/100)}^n - 1]
408 = P[{1+(4/100)²} - 1]
= P[{1+(1/25)²} - 1]
= P[(26/25)² - 1]
= P[(676/625) - 1]
= P[(676-625)/625]
408 = P(51/625)
P = 408*(625/51)
= 8*625 = 5000
Sum = 5000
Simple Interest (I) = (P*R)/100
= 5000*2*(4/100)
= 50*2*4 = 400
From the given above options, option (a) ₹400 is your correct answer.
Pointing to a photograph, a man said, "I have no brother, and that man's father is my father's son." Whose photograph was it?
The man’s son. Since the man has no brothers and the father of the man in the photograph is the man’s father’s son, the father of the man in the photograph must be the man. That means that the man in the photograph is the man’s son.
What is √101.6064 in to 1 decimal place and in standard form?
NEED ASAP
Note that
10² = 100
0.08² = 0.0064
and
101.6064 = 100 + 1.6 + 0.0064
It also happens that
1.6 = 2 • 10 • 0.08
which means
101.6064 = 100 + 1.6 + 0.0064
101.6064 = 10² + 2 • 10 • 0.08 + 0.08²
101.6064 = (10 + 0.08)²
101.6064 = 10.08²
which means
√101.6064 = 10.08
which, to one decimal place, is approximately 10.1.
Anthony is gathering workout clothes. There are 4 pairs of running shoes and 10 workout shirts to choose from. How many different workout outfits can Anthony make?
Answer:
40
Step-by-step explanation:
For what integer value of x is f(x) = -10 if f(x) = - 4x + 2?
Answer:
x = 3
Step-by-step explanation:
Given the linear function, f(x) = -4x + 2, for which we must determine the integer value of x that will provide an output of f(x) = -10:
Solution:The first step is to substitute the output value, f(x) = -10, into the given function, and solve for its corresponding input value, x:
f(x) = -4x + 2
-10 = -4x + 2
Subtract 2 from both sides:
-10 - 2 = -4x + 2 - 2
-12 = -4x
Divide both sides by -4 to solve for x:
[tex]\displaystyle\mathsf{\frac{-12}{-4}\:=\:\frac{-4x}{-4} }[/tex]
x = 3
Hence, when x = 3, f(x) = -10.
Double-check:Substitute the value of x = 3 into the original function:
f(x) = -4x + 2
f(3) = -4(3) + 2
f(3) = -12 + 2
f(3) = -10 ⇒ f(x) = -10.
Therefore, the input value of x = 3 gives an output value of f(x) = -10.
Three consecutive integers add up to 30. Which integers are they?
Answer:
30 31 33 are the three integer consective
Lily has 7 fewer ribbons than Dora. Lily has 13 ribbons. How many ribbons does Dora have?
Answer: 6
Step-by-step explanation:
13-7=6
Find two numbers that round to 387.4 when rounded to the nearest tenth.
what is -4(2x - 3) equal
Answer:
-8x + 12
Step-by-step explanation:
-4(2x - 3)
then -4*2x and -4*-3(an even number of negative signs multiplied equals to a positive sign)
therefore= -8x + 12
what is the slop of the line 2x - 5y=9
The slope is 2The slope is 2The slope is 2The slope is 2The slope is 2The slope is 2
Answer:
(5,2)
Step-by-step explanation:
Can someone help please !
Answer:
2
Step-by-step explanation:
[tex]16^{\frac{1}{4} }[/tex] can be rewritten as [tex]\sqrt[4]{16}[/tex].
Solve for the 4th root of 16.
16=4*4=(2*2)(2*2)=2
Marcus has twice as many pens as Bryan. Together they have 36 pens. How many pens does each boy have?
Answer:
Marcus has 24 pens while Bryan has 12 pens.
Step-by-step explanation:
Let u rep 1 unit.
Marcus = 2u
Bryan = u
2u+u=36
3u=36
u=36÷3
=12
No. of pens Marcus has
= 2u
= 2×12
= 24
No. of pens Bryan has
= u
= 12
What are the steps to convert a number from standard notation to scientific notation?
Answer:
Step-by-step explanation:
The goal in scientific notation is to express a value in terms of a number that contains a single unit before the decimal point.
Examples:
10000: 1.0 x 10^4
23456: 2.3456x10^4
In both cases, the x10^4 is telling us to multiply the first number by 10,000. 10^4 is the same as 10x10x10x10 = 10,000
The justification for scientific notation is that is makes expression large and small numbers much easier, as well as reduces errors due to an incorrectly placed decimal.
An example: Divide 2500000000 by 5000. That would normally require setting up a long-hand division problem that not only wastes paper and pencil, but is also prone to decimal point errors.
Do the same problem with scientific notation:
Count the places you want to move the decimal point backwards to just beyond the 5 in 2500000000. It takes nine steps to move the decimal point to between the 2 and 5: 2.5 followed by 8 zeros. That's a total of next steps to go in front of the 5. This is written 2.5 x 10^9
5000 is represented by 5.0x10^4
Now when we divide the same numbers, but in scientific format, it is easier to see the answer:
(2.5x10^9)/(5.0x10^4)
2.5/5 = 0.5
10^9/10^4 = 10^5 [The exponents are subtracted when dividing with exponents: 9-4 = 5]
Put them together to find the final answer: 0.5x10^5
Then move the decimal point one spot to the right and reduce the exponent by 1:
5.0x10^4
------
Add exponents when multiplying: 10^3 x 10^5 = 10^8 (3+5=8)
Subtract when dividing: 10^7/10^2 = 10^5 (7-2=5)
Multiply when there is an exponent raised to another exponent: (10^4)^3 = 10^12 (4x3 = 12)
What is the reciprocal of 64?
What is the sum of the first 32 terms in the arithmetic
series 3 + 10 + 17 + …?
Answer:
30
Step-by-step explanation:
Which of the following correctly simplifies the expression
(3^2 X 5^0 /4) ^2
On Saturday Kendra ran 2.721 kilometers. On Sunday she ran 1.79 kilometers. How much farther did she
run on Saturday than on Sunday?
Answer:
0.9km(rounded to 1dp)
Step-by-step explanation:
2.7km on sat
1.8km on sun
2.7km-1.8km=0.9km
Solve the system of linear equations by substitution
6x-9=y
y=-3x
Answer:USE SUBSTITUTION METHOD. Algebra work right here
Step-by-step explanation:
If triangles ADE and ABC shown in the
figure to the right are similar, what is the
value of x?
Step-by-step explanation:
similar means that (with all angles being the same) the side lengths of one triangle all correlate to the corresponding side lengths of the second triangle by the same factor.
and so, because AD = 2 is 1/3 of AB = 4+2 = 6, we need to apply the same factor 1/3 to x compared to 12.
12 × 1/3 = 4.
so, A is correct.
To qualify for a scholarship, a student must score at least 90% on a written test. The test is 64 questions. Using this metric, what is the greatest number a student can miss and still qualify for the scholarship?
Answer:
6 questions
Step-by-step explanation:
First, you divide the total score of 100 by the 64 questions to get 1.5625 points per question. Next, you divide the lowest score to qualify of 90 by the 1.5625 to get 57.6 questions correct to qualify. Then, you round 57.6 questions correct up to 58 questions correct because a fraction of a question correct doesn't make sense. Finally, you subtract the total number of questions (64) by the required correct answers (58) to get 6 questions you can miss to still qualify for the scholarship.