Answer:
21 and 22
Step-by-step explanation:
Let the two whole numbers be a and b.
Their product is 462. Hence, we can write that:
[tex]ab=462[/tex]
Likewise, because their sum is 42:
[tex]a+b=43[/tex]
This yields a system of equations:
[tex]\displaystyle \begin{cases} ab = 462 \\ a + b = 43 \end{cases}[/tex]
We can solve the system using substitution.
Isolating one variable in the second equation yields:
[tex]a=43-b[/tex]
From substitution:
[tex](43-b)(b)=462[/tex]
Distributing yields:
[tex]-b^2+43b=462[/tex]
Solve for b by factoring:
[tex]\displaystyle \begin{aligned} b^2 - 43d & = -462 \\ \\ b^2 - 43d + 462 & = 0 \\ \\ (b-21)(b-22) &= 0 \\ \\ b = 21 \text{ or } b & = 22 \end{aligned}[/tex]
Solve for a:
[tex]\displaystyle \begin{aligned} a& =43-(21) & \text{ or } a& =43-(22) \\ a&=22&\text{ or } a&=21\end{aligned}[/tex]
In conclusion, the two whole numbers are 21 and 22.
Death Valley is the location of the lowest land elevation in the USA which is 282 feet below sea level.The location with the highest level is 20,320 feet above sea level.What is the difference in the elevations of these two locations
Answer:
20,038
Step-by-step explanation:
20,320 - 282
(HELP MEH) Why is √5 irrational?
A.) because it is less than one
B.) because it has no opposite
C.) because all square roots are irrational
D.) because it cannot be expressed as a ratio of integers
Answer:
D.) because it cannot be expressed as a ratio of integers
Step-by-step explanation:
The root of any integer that is not a perfect square is irrational. 5 is not a perfect square, so is irrational—it cannot be expressed as the ratio of integers.
__
Proof
Suppose √5 = p/q, where p and q are mutually prime. Then p² = 5q².
If p is even, then q² must be even. We know that √2 is irrational, so the only way for q² to be even is for q to be even—contradicting our requirement on p and q.
If p is odd, then both p² and q² will be odd. We can say p = 2n+1, and q = 2m+1, so we have ...
p² = 5q²
(2n+1)² = 5(2m+1)²
4n² +4n +1 = 20m² +20m +5
4n² +4n = 4(4m² +4m +1)
n(n+1) = (2m+1)²
The expression on the left will be even for any integer n; the expression on the right will be odd for any integer m. This equation cannot be satisfied for any integers m and n, so contradicting our assumption √5 = p/q.
We have shown using "proof by contradiction" that √5 cannot be the ratio of integers.
If 630 sweets were distributed among Ben,
Lucy and Jane in ratio 2: 3: 4. How many
sweets does Jane get?
A 140
B. 210
C. 260
D. 270
E 280
Answer:
E
Step-by-step explanation:
630/2+3+4=630/9=70
Multiply each value in the ratio by 70.
Jane: 70*4=280
If f(x) = 4x - 7 and g(x) = 3x + 9 find (f+g) (5)
Answer: (f+g)(5)=37
Step-by-step explanation:
(f+g) (5) is the same as saying f(5)+g(5). Since we are given f(x) and g(x), we can use them to solve. There are two ways to solve. One is to find f(5) and g(5), and then add them together. Another way is to do (f+g)(x), then plug in x=5. I will show both methods.
Method 1
f(5)=4(5)-7 [multiply]
f(5)=20-7 [subtract]
f(5)=13
g(5)=3(5)+9 [multiply]
g(5)=15+9 [add]
g(5)=24
(f+g)(5)=13+24 [add f(5) and g(5)]
(f+g)(5)=37
--------------------------------------------------------------------------------------------------------
Method 2
(f+g)(x)=4x-7+3x+9 [combine like terms]
(f+g)(x)=7x+2
(f+g)(5)=7(5)+2 [plug in x=5]
(f+g)(5)=35+2 [add]
(f+g)(5)=37
--------------------------------------------------------------------------------------------------------
Now, we know that (f+g)(5)=37. We confirmed this with both methods.
10 students of a class had a mean score of 70. The remaining 15
students of the class had mean score of 80. What is the mean score of
the entire class?
Oops someone else answered it before me
How much interest does a $10,000 investment earn at 5.6% over 18 years?
3x(x + 2) ......................
Answer:
3x^2+6x
Step-by-step explanation:
3x(x+2)
First distribute the 3x
You end up with
(3x^2+6x)
and that is the answer.
35 POINTSThe line contains the point (-8,7) and is perpendicular to 3x+2y=-7 The equation of the line is:
Answer:
The answer is
[tex]y = \frac{2}{3} x + \frac{37}{3} [/tex]Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the perpendicular line we must first find the slope of the original line
We must first write the equation in the general form above in order to find the slope
3x + 2y = - 7
2y = - 3x - 7
Divide both sides by 2
y = - 3/2x - 7/2
Comparing with the general equation above
Slope = - 3/2
Since the lines are perpendicular to each other the slope of the perpendicular line is the negative inverse of the original line
Slope of perpendicular line = 2/3
So the equation of the line using point (-8,7) and slope 2/3 is
[tex]y - 7 = \frac{2}{3} (x + 8) \\ y - 7 = \frac{2}{3} x + \frac{16}{3} \\ y = \frac{2}{3} x + \frac{16}{3} + 7[/tex]
We have the final answer as
[tex]y = \frac{2}{3} x + \frac{37}{3} [/tex]
Hope this helps you
morgan bought a pair of shoes at a sale of 25% . if the amount she paid was $1000 , find the market price ?
Answer:
$4,000
Step-by-step explanation:
to find the market price you:
1000x100=100000
100000/25=4000
Answer:
4,000
Step-by-step explanation:
a medical transcriptionist has a four drawer cabinet. one drawer is 4/5 full and one is 1/2 full and one drawer is 3/4 full. can the contents be combined into 3 drawers why or why not
Answer:
well the sum of all the fraction combined are 2.05, so you could fill 2 1/2 drawers. So technically you could use 3 drawers, but the 3rd one won't be full.
hope that helps
A cylindrical can has a volume of 16 cm 3. What dimensions yield the minimum surface area? 1. The radius of the can with the minimum surface area is ______ cm. (Simplify your answer.) 2. The height of the can with the minimum surface area is ______ cm. (Simplify your answer.)
Answer:
radius = 1.37 cm
height = 2.71 cm
Step-by-step explanation:
We are given volume = 16 m³.
Formula for volume of a cylinder is;
V = πr²h
Thus,
πr²h = 16
h = 16/πr²
Now formula for the surface area is;
S = 2πr² + 2πrh
Putting 16/πr² for h gives;
S = 2πr² + 2πr(16/πr²)
S = 2πr² + 2π(16/πr)
S = 2π(r² + 16/πr)
To minimize, we will find the derivative of S and equate to zero
S' = 2π(2r - 16/πr²) = 0
4πr - 32/r² = 0
4πr = 32/r²
r³ = 32/4π
r = ∛(32/4π)
r = 1.37 cm
From h = 16/πr²;
h = 16/(π × 1.37²)
h = 2.71 cm
which angles are supplementary to each other?
Answer:
Angles 2 and 3 are supplementary to each other
Step-by-step explanation:
A supplementary angle is 2 angles that when you add the sum is 180.
what are the even numbers -7,-4,2,14,21,34,42
Answer:
-4, 2, 14, 34, and 42
Step-by-step explanation:
These are all even because they are multiples of 2. Also, for it to be even, the ones place MUST be one of the following: 0, 2, 4, 6, 8
Answer:
-4,2,14,34,42
Step-by-step explanation:
Even numbers are divisible by 2
-4/2 =-2
2/2 =1
14/2 = 7
34/2 = 17
42/2 = 21
which number sets does 3/4 belong to?
The answer is it BELONGS TO THE RATIONAL SET
The number 3/4 is belong in Rational number.
Here,
The number is 3/4.
We have to find the number sets of 3/4 belong to.
What is Rational number?
A number that can be represented as the quotient p/q of two integers such that q ≠ 0.
Now,
The number is 3/4.
Clearly, the number is in the form of fraction p/q such that q ≠ 0.
Hence, The number 3/4 is belong in Rational number.
Learn more about the rational number visit:
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Robert has 4 shirts (blue, white, gray, and red) and 3 ties (striped, solid, polka dotted). Robert reaches into his closet and grabs 1 shirt and 1 tie, without looking. Find the probability that Robert chooses the white shirt and striped tie
Answer:
1/12
Step-by-step explanation:
Total shirts: 4
White shirts: 1
p(white shirt) = 1/4
Total ties: 3
Striped ties: 1
p(striped tie) = 1/3
The overall probability is the product of the individual probabilities.
p(white shirt & striped tie) = p(white shirt) * p(striped tie) = 1/4 * 1/3 = 1/12
Answer:
The answer is 1/2
Step-by-step explanation:
4 shirts that mean 1/4
and 3 ties that mean 1/3
If we choose one it will be 1/2
sry if you don't get it
Find the quotient: –10/19÷(−5/7)
Answer:
14/19
Step-by-step explanation:
Note that there are two " - " signs here. Thus, the end result will be " + "
We move from left to right, obtaining first 10/19 divided by (5/7):
10
----- ÷ (5/7)
19
To divide by (5/7), invert (5/7) and then multiply. We get:
10 7 2(7)
----- * ----- = ------- = 14/19
19 5 19
28) Solve the formula for g
Answer:
S=1/2gt2
you cross multiple
2s/t2 =gt2/t2
divide both sides by t2
to get
g=2s/t2
which is C
A car can travel 38 miles on each gallon of gasoline. At that rate, how many gallons of gasoline will it take to travel
190 miles?
2
5
20
50
Answer:
5 gallons of gasoline
Step-by-step explanation:
since we have the number of miles the car drives per gallon (38) we can set up an equation
the equation would be the number of miles per gallon (38) times the number of gallons it would take to drive 190 miles (x) equals 190 miles
38x = 190
you then divide 190 by 38
x = 5 gallons
Five gallons of gasoline must be taken to travel 190 miles.
What is the unitary method?The unitary method is a problem-solving methodology that involves first finding the value of a single unit and then finding the necessary value by multiplying the single unit value.
How many gallons of gasoline will it take to travel 190 miles?On one-gallon gasoline, the car can travel 38 miles.
Let x gallons of gasoline be taken to travel 190 miles.
So, 38x=190
⇒x=190/38=5
Hence, 5 gallons of gasoline is taken to travel 190 miles.
Learn more about the unitary method from- https://brainly.com/question/22056199?referrer=searchResults
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8 A television show uses 15 minutes of every hour for commercials, leaving
the remaining 45 minutes for the actual show. Which ratio below represents
the commercial minutes to the show minutes?
A1: 4
B 4:1
C1:3
D3:1
ILL GIVE YOU BRAINLIST !!! HAVE TO GET IT RIGHT !!
Evaluate the expressions
Answer:
-32/3
Step-by-step explanation:
-10 2/3 , -10.6
Answer:
-32 I just looked it up on photomath
What can you conclude about the slope of the values in
the table? Check all that apply.
lope
The slope is 0.
The slope is undefined.
The graph will be a horizontal line.
The graph will be a vertical line.
The graph will have a line with a positive slope.
Answer:
The slope is undefined.
The graph will be a vertical line.
Step-by-step explanation:
just did it
The graph will be a vertical line. Option C is correct.
Given that,
The slope of the line is zero we have to determine what are the conditions.
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
What is simplification?
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The slope of the line is zero,
m = 0
tanФ = 0
y / x = 0
for the above condition, Δy must be zero or Δx must be infinite and the line will be a verticle.
Thus, the graph will be a vertical line. Option C is correct.
Learn more about slopes here:
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HAVE TO EVALUATE SHOW WORK !!!!!
2ny + x
Answer:
9
Step-by-step explanation:
2ny + x
Start with n and y
n= 3/4
y = 6
2*n*y = 2* 3/4 * 6 2 * 6 = 12
12 * 3/4 = 36 / 4 = 9
There are many ways to do this. I have chosen one that does not require cancellation.
twelve thousand four hundred three in standard form
Answer:
12,403
Step-by-step explanation:
twelve thousand = 12,000
four hundred = 400
three = 3
Add them all up.
Your answer is 12,403.
Hope this helps!
Answer: 12,403
twelve thousand = 12,000
four hundred = 400
three = 3
The answer is 12,403. Hope this helps!
The double box plot shows the test scores for Miss Robinson's second and fourth period
classes. Based on the double box plot, which sentence is true?
Answer: The second period class has the greater first quartile.
The second-period class has the greater first quartile. Then the correct option is A.
What is a double box?Like the other twin graph styles discussed in earlier sections, double package plots provide for a fast detailed evaluation of two sets of data.
The double box plot shows the test scores for Miss Robinson's second and fourth-period classes.
Based on the double box plot. Then the true sentence will be
The second-period class has the greater first quartile. Test Scores
Then the correct option is A.
More about the double box link is given below.
https://brainly.com/question/15272710
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Find the sum in lowest terms 1/55+6/11
Answer:
31/55
Step-by-step explanation:
The LCD is 55.
1/55 + 6/11 =
= 1/55 + 30/55
= 31/55
31 is prime, so the fraction cannot be reduced.
Answer: 31/55
-5/10 + 7/10 . what is the answer
Answer:
2/10
Step-by-step explanation:
-5+7=2, since the denominator stays the same.
2/10, simplified is 1/5
Answer:
2/10 or 1/5
Step-by-step explanation:
Because -5/10 and 7/10 both have 10 as the denominator we don't have to do anything about that, so you just add and simplify.
If you need me to go through it in depth let me know, but I hope that helps!
Have a great day!
Paul has 16 fish pictures and 12 deer pictures. He wants to arrange the pictures in rows with the same numbers of fish and of deer pictures in each row. What are the possible numbers of rows
Answer:
4 rows
Step-by-step explanation:
GCF of 12 and 16 is4
work out (7x10^5)\div (2x10^2) give your answer in standard form
answer: 200dvi
I hope this helped, not entirley sure if I did it correctly.
Hey there!
(7 * 10^5) ÷ (2 * 10^2)
10^5
= 10 * 10 * 10 * 10 * 10
= 100 * 100 * 10
= 10,000 * 10
= 100,000
10^2
= 10 * 10
= 100
= (7 * 100,000) ÷ (2 * 100)
7 * 100,000
= 700,000
2 * 100
= 200
700,000 ÷ 200
= 3,500
Therefore, your answer is: 3,500
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Fill in the blank to make the equation true: []+3×7=15
Answer:
-6
Step-by-step explanation:
(-6) + 3 x 7 = 15
IQs as measured by the Wechsler Adult Intelligence Scale are approximately Normal with mean 100 and standard deviation 15. About 84% of people will have IQs below 115 because 115 is _____ standard deviation(s) above the mean.
Answer:
1 standard deviation
Step-by-step explanation:
Given that :
IQs as measured by the Wechsler Adult Intelligence Scale are approximately Normal with:
Mean = 100
Standard deviation = 15
About 84% of people will have IQs below 115 because:
84% = 0.84
From z - table, 0.84 corresponds to a z- score of about 0.995
0.995 = 1. 00
The z-score gives the number of standard deviations by which a raw score is above or below the average or mean value.
Raw score = 115
Mean = 100
Standard deviation (sd) = 15
Mean + number of sd's
100 + 1(sd)
100 + 1(15) = 100 + 15 = 115