Answer:
16
Step-by-step explanation:
5x + 2y - 7z
(x = 2, y = 10, z = 2)
First things first you would want to take the letters that the numbers are equal to and replace them with the numbers.
5(2) + 2(10) - 7(2)
Then you multiply the number that's beside the parentheses, 5(2) is the same as 5 x 2.
5(2) = 10
2(10) = 20
7(2) = 14
so now you have
10 + 20 - 14
10 + 20 = 30
30 - 14 = 16
and 16 is your final answer!
Prove that if r is any rational number, then 3r2 − 2r + 4 is rational. The following properties may be used in your proof. Property 1: Every integer is a rational number. Property 2: The sum of any two rational numbers is rational. Property 3: The product of any two rational numbers is rational. Note: Property 1 is Theorem 4.3.1, Property 2 is Theorem 4.3.2, and Property 3 is Exercise 15 in Section 4.3. Using these properties, choose explanations for each step in the given proof.
Given:
Expression is
[tex]3r^2-2r+4[/tex]
To prove:
If r is any rational number, then [tex]3r^2-2r+4[/tex] is rational.
Step-by-step explanation:
Property 1: Every integer is a rational number. It is Theorem 4.3.1.
Property 2: The sum of any two rational numbers is rational. It is Theorem 4.3.2.
Property 3: The product of any two rational numbers is rational. It is Exercise 15 in Section 4.3.
Let r be any rational number.
We have,
[tex]3r^2-2r+4[/tex]
It can be written as
[tex]3(r\times r)-2r+4[/tex]
Now,
3, -2 and 4 are rational numbers by property 1.
[tex]r^2=r\times r[/tex] is rational by Property 3.
[tex]3r^2\text{ and }-2r[/tex] are rational by Property 3.
[tex]3r^2+(-2r)+4[/tex] is rational by property 2.
So, [tex]3r^2-2r+4[/tex] is rational.
Hence proved.
We want to prove that if r is rational, then:
[tex]3*r^2 - 2r + 4[/tex] Is also rational.
The proof is below:
Remember that a rational number is any number that can be written as a quotient of two integer numbers.
Then we have:
[tex]r = \frac{a}{b}[/tex]
Where a and b are integers.
If we replace that in our equation, we get:
[tex]3*(\frac{a}{b}) ^2 - 2*(\frac{a}{b}) + 4\\\\\frac{3a^2}{b^2} - \frac{2a}{b} + \frac{4}{1}[/tex]
Note that if a is an integer, then 3*a^2 is also an integer.
If b is an integer, then b^2 is also an integer.
Now we can perform the sum of these fractions to get:
[tex]\frac{3a^2}{b^2} - \frac{2a}{b} + \frac{4}{1}\\\\\frac{3a^2 - 2ab + 4b^2}{b^2}[/tex]
And because integers are closed under the addition, then the numerator of that fraction is also an integer, then we have that the given expression can be written as a quotient of two integers, thus, it is a rational number.
If you want to learn more, you can read:
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The number of trout in America since 2000 is given by the following formula:
[tex]y=x^2+3x+2[/tex]
"x" is the number of years and "y" is the number of trout in the millions.
Based on this formula, estimate the number of trout in the years 2005, 2010, and 2015.
Describe the trend in the number of trout as the years increase.
Answer:
See below
Step-by-step explanation:
Given formula
y = x² + 3x + 2x- is the number of years after 2000,y - is the number of troutYear 2005, finding number of trout
x = (2005 - 2000) = 5y = 5² + 3*5 + 2 = 42 millionsYear 2010, finding number of trout
x = (2010 - 2000) = 10y = 10² + 3*10 + 2 = 132 millionsYear 2015, finding number of trout
x = (2015 - 2000) = 15y = 15² + 3*15 + 2 = 272 millionsNumber of trout is trending up with significant increase over yeas
Answer:
42 million132 million272 millionThe number of trout inceases a lot each 5 years that pass.Step-by-step explanation:
Number of trout in 2005.
Find the number of years apart from 2000 to 2005.
2005 - 2000 = 5
Substitute for x and solve for y.
y = x² + 3x + 2
y = (5)² + 3(5) + 2
y = 25 + 15 + 2
y = 40 + 2
y = 42 million
Number of trout in 2010.
Find the number of years apart from 2000 to 2010.
2010 - 2000 = 10
Substitute for x and solve for y.
y = x² + 3x + 2
y = (10)² + 3(10) + 2
y = 100 + 30 + 2
y = 130 + 2
y = 132 million
Number if trout in 2015.
Find the number of years apart from 2000 to 2015.
2015 - 2000 = 15
Substitute for x and solve for y.
y = x² + 3x + 2
y = (15)² + 3(15) + 2
y = 225 + 45 + 2
y = 270 + 2
y = 272 million
Best of Luck!
what is the greatest common facter of 48 and 84
Answer:12
Step-by-step explanation:
The prime factorization of 84 is 2×2×3×7 . The prime factorization of 48 is 2×2×2×2×3 . . Therefore, the GCF is 2×2×3=12
Which of the following steps would you use to
evaluate (a + b)??
Answer:
(a+b)(a+b)
Step-by-step explanation:
For adults who sailed on the Titanic on its fateful voyage, the odds ratio20 between gender (female, male) and survival (yes, no) was 11.4. a. What is wrong with the interpretation, "The probability of survival for females was 11.4 times that for males?" Give the correct interpretation. b. The odds of survival for females equaled 2.9. For each gender, find the proportion who survived. Find the value of RR in the interpretation, "The probability of survival for females was RR times that for males."
What is 74 divided by 12?plz help I need this assignment done before 3:30 and it’s 2 hours until time
Answer:
6.16.
Step-by-step explanation:
hope this helps.
Answer:
37/6
Step-by-step explanation:
You are certain to get 2 Kings when selecting 50 cards from a shuffled deck. express the indicated degree of likelihood as a probability value between zero and one inclusive
Answer:
1
Step-by-step explanation:
The probability of this happening would be a 1 when placing a value between zero and one inclusive. One in this case would indicate a 100% probability. This is the case because in the question it is stated that it is "certain" that you will get 2 kings when selecting 50 cards, this means that no matter what it will happen every time 50 cards are drawn, thus making the probability 100%. If the question were phrased differently such as "what is the probability of getting 2 kings from 50 cards drawn?" then the probability would be 0.04 or 4% which is 2/50.
Using probability concepts, it is found that the likelihood is of 1.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
A few observations regarding probabilities are important.
It assumes values between 0% and 100% as percentages and between 0 and 1 as decimals.If an event is certain not to happen, the probability is of 0% = 0.If an event is certain to happen, the probability is of 100% = 1.In this problem, you are certain to get 2 Kings when selecting 50 cards from a shuffled deck, hence the likelihood is of 1.
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3)
Blair expects an increase of 3% in her current annual
salary of $42,000. What would her new annual salary
be?
Answer:
$43,260
Step-by-step explanation:
You have the 3% annual income, which you can convert to a decimal. This gives:
42000 * 1.03
42000 represents Blair's initial income, and 0.03 represents the 3% increase.
I chose 1.03 because I don't have to subtract 97% and add it to 42000.
what is the square root of 27000
Answer:
164.316767252
Step-by-step explanation:
Answer:
164
Step-by-step explanation:
2х - Зу= 2
х= бу - 5
X=
Y=
Answer:
2x-3y=2
x=6y-5
2(6y-5)-3y=2
use the distributive property.
2*6y=12y
2*-5=-10
12y-10-3y=2
combine like terms
12y-3y=9y
9y-10=2
add 10 to both sides.
9y-10+10=9y
2+10=12
9y=12
divide both sides by 9
9y/9=y
y=about 1.33
plug in the value of y in the expression equal to the value of x.
x=6(1.33)-5
solve
6*1.33=7.98
x=7.98-5
7.98-5=2.98
Step-by-step explanation:
x=2.98
y=1.33
PLSSSSS HELPOLP URGENT!!!!
What are the coordinates of the endpoints of P'Q' after a reflection of PQ
over x = -3?
Find the midpoint of the segment with the endpoints: (-2, 6) and (-3, 7)
Answer:
The midpoint is ( -2.5, 6.5)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates of the endpoints and divide by 2
(-2+-3)/2 = -5/2 = -2.5
To find the y coordinate of the midpoint, add the y coordinates of the endpoints and divide by 2
(6+7)/2 = 13/2 = 6.5
The midpoint is ( -2.5, 6.5)
What is an equation of a line with slope −2/3 and a y-intercept of −4?
21 students went on an exchange program to hong kong. There were 11 more women than men. How many woman are there?
Answer:
11
Step-by-step explanation:
11 + 10 = 21
how do i solve for m in i=pm
Answer:
Divide by P
Step-by-step explanation:
i = P x M
divide by P to get M alone, which means you have to do it to both sides
i/P = M
Which expression can be modeled using the number line?
I NEED THIS ASAP
A number line going from 0 to 1 in increments of StartFraction 1 Over 10 EndFraction. Arrows go between each increment until StartFraction 7 Over 10 EndFraction.
StartFraction 1 Over 10 EndFraction divided by 7
StartFraction 7 Over 10 EndFraction divided by StartFraction 1 Over 10 EndFraction
StartFraction 1 Over 10 EndFraction divided by StartFraction 7 Over 10 EndFraction
7 divided by StartFraction 7 Over 10 EndFraction
Answer:
c is incorrect they just made me fail my quiz... :(
Step-by-step explanation:
Answer:
7/10 divided by 1/10
Step-by-step explanation:
Drag the divisor fraction to the dividend bar to see how many
parts of the divisor are in the dividend
Use fraction bars and the rules of dividing signed
numbers to divide
15
Dividend
15 3
5 5
o
18
cila
o
Divisor
o
12
O -5
Answer:
Is B
Step-by-step explanation:
The dividend is 2 and the divisor is 2/5
What is Division?A division is a process of splitting a specific amount into equal parts.
The given fraction is 2 ÷ 2/5
The number which is getting divided here is called the dividend.
The number which divides a given number is the divisor.
In the given division the dividend is 2
The divisor is 2/5
Hence, the dividend is 2 and the divisor is 2/5
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The third term of an A.P is 4m - 2n. If the ninth term of the progression is 2m - 8n. Find the common difference in terms of m and n
Let [tex]a_n[/tex] denote the n-th term in the progression. So
[tex]a_n=a_{n-1}+d[/tex]
for some constant difference between terms d.
Solve for [tex]a_n[/tex] explicitly:
[tex]a_4=a_3+d[/tex]
[tex]a_5=a_4+d=a_3+2d[/tex]
[tex]a_6=a_5+d=a_3+3d[/tex]
and so on, up to
[tex]a_n=a_3+(n-3)d[/tex]
We're told that the third term is [tex]a_3=4m-2n[/tex], and the ninth term is [tex]a_9=2m-8n[/tex], and according to the recursive rule above, we have
[tex]a_9=a_3+6d[/tex]
Solve for d :
[tex]2m-8n=(4m-2n)+6d[/tex]
[tex]-2m-6n=6d[/tex]
[tex]d=-\dfrac{2m+6n}6=\boxed{-\dfrac{m+3n}3}[/tex]
PLZ, HELP WILL GET BRAINLIEST AND A LOT OF POINTS.
What is the exponential function rule for the following points
x f(x)
1 8
2 32
3 128
4 512
Answer:
y=2(4^x)
Step-by-step explanation:
if you notice, all the y-values are multiplied by 4 for each x-value. this means 4 is raised to the power of x. however, when you plug this in, you realize that the value produced is only half the actual y-values, so you multiply this whole thing by 2.
y=2(4^x)
Answer:
f(x) = 2^(2x+1)
Step-by-step explanation:
You can tell that each of the outputs of f(x) are powers of 2, so all you have to do is figure out the pattern of the exponents.
2^3 = 8
2^5 = 32
2^7 = 128
2^9 = 512
the relationship between the sequence
3,5,7,9
when you start on 1 is
2x+1
2(1)+1 = 3
2(2)+1 = 5
etc.
3. Write an exponential function that represents the table and graph. y=0-b*
please help!!
What is | -8|
—16
-8
8
16
Answer:
8
Step-by-step explanation:
scince it has the lines that mean that it will always be positive.
Answer:
8
Step-by-step explanation:
Have a nice day!
Given m||n, find the value of x.
t
>m
(3x+14)
(7x-4)
Answer:
(3x+14°) + (7x-4)° = 180°
=> 10x + 10 = 180
=> 10x = 180 – 10
=> x = 170/10
=> x = 17
The value of x is 17
Which expression is equivalent to (cd)5
Answer:
A
Step-by-step explanation:
help find the value of x
Answer:
40
Step-by-step explanation:
I'm confused. Hopefully, you can help me.
Answer:
C
Step-by-step explanation:
a straight line is 180, 180-40=140
plz help I will mark brainlest!
Answer:
-1.71 the answer is d
Step-by-step explanation:
.........
Laina reads 25 : 30
If laine reads 200 pages at the same rate how long will it take her
Answer:
i sorry but idk the annswer
Answer:
240
Step-by-step explanation:
200/25=8
30x8=240
hope this helps i didn't really understand the question much
Which equation represents a line that has a slope of One-third and passes through point (–2, 1)?
Answer:
y=1/3x+5/3
Step-by-step explanation:
y=1/3x+b
1=1/3(-2)+b (plug in ya points)
1=-2/3+b
5/3=b
y=1/3x+5/3
Answer:
the answer is y=1/3x+5/3
Step-by-step explanation:
hope this helps
did it on edge
A lady decides she wants to start saving more money so she can buy a house. So, she decides to trick herself into saving by creating a challenge for herself. She bought a box of 100 envelopes and wrote the numbers 1-100 on separate envelopes. Twice a week, she drew two envelopes at random and put the corresponding amount of cash inside. (So, if she drew envelope 23, she put $23 inside). How much will she save? How long will it take her to fill all the envelopes?
Answer:
she should at least have $1,150 in at least 575 weeks
Step-by-step explanation:
Geometry The sides of a yield sign all have the same
length (see figure). The perimeter of a roadway yield
sign is 225 centimeters. Find the length of each side.
YIELD
Figure for 51
Figure for 52
Answer:
75 cm
Step-by-step explanation:
Given:
Perimeter of the triangular yield sign = 225 cm
Side lengths = x, x and x
Required:
Length of each side
SOLUTION:
Perimeter of the triangular yield sign = sum of all sides of the triangular yield sign
225 cm = x + x + x
Solve for x
225 = 3x
Divide both sides by 3
225/3 = 3x/3
75 = x
x = 75
The length big each side is 75 cm