Answer:
Rational; irrational; irrational.
Step-by-step explanation:
a/3b is a rational number, as it is represented by a fraction and b ≠ 0. This means the first blank is "rational."
√5 is an irrational number. This means the second blank is "irrational."
Since we have an irrational number set equal to a rational number, this is a contradiction. This means our original assumption is wrong, and the number is irrational. This is the third blank.
There are Rational, irrational, and irrational are the correct options respectively.
What is a rational number?A rational number is defined as a numerical representation of a part of a whole that represents a fraction number.
It can be a/b of two integers, a numerator a, and a non-zero denominator b.
Given Number = 3√5
We have to prove that 3√5 is an irrational number.
Let us assume 3√5 is a rational number.
Because it is represented as a fraction and b ≠ 0, a/3b is a rational number. This implies that the first blank is "reasonable."
The number √5 is irrational. This indicates that the second blank is "irrational."
This is a contradiction since we have an irrational number set equal to a rational number. This signifies that our initial assumption was incorrect, and the number is irrational.
Therefore, the assumption is wrong, and the product is irrational.
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Please WILL GIVE BRAINLIEST!
What is this expression in radical form?
(4x^3y^2)^3/10
Let n be the smallest composite number such that it can be written as the product of two positive integers that differ by 10. How many distinct prime factors does n have?
Answer: n has two distinct prime factors 2 and 3.
Step-by-step explanation:
As given the smallest composite number such that it can be written as the product of two positive integers that differ by 10.
i.e. if first number be x then the other number be x+10 and n=x(x+10), where n must be composite number.
So after putting the values of x by positive integer
1) x=0 then n=0(10+0)=0...which is not a composite number.
2) x=1 then n=1(1+10)=11..... which is not a composite number.
3)x=2 then n=2(2+10)=24......which is a composite number.
so our n=24 and we know that 24=2×2×2×3
Therefore its distinct prime factors are 2 and 3.
Answer:
2
Step-by-step explanation:
Solution:
The smallest pair of numbers that differ by 10 is 1 and 11; however, they multiply to 11 which is not composite. We try the next pair up: 2 and 12, which multiply to 24 which is composite, so [tex]$n=24$[/tex]. [tex]$24$[/tex] factors as [tex]$2^3 \cdot 3$[/tex], so it has [tex]$\boxed{2}$[/tex] prime factors: 2 and 3.
Hope this helped! :)
what's the value of y
(3y +10) /4 = 2y
Multiply both sides by 4:
4(3y +10) = 4(2y)
12y +40 = 8y
Subtract 40 from each side:
12y = 8y -40
Subtract 8y from each side:
4y = -40
Divide both sides by 4:
y = -40 / 4
y = -10
The answer is A. -10
evaluate 15k when k=3
if k=3 than 15k (5 mutiple k) 5*3=45
The value of the expression 15k when the value of k is 3, will be 45.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
It is also known as the product. If the object n is given to m times then we just simply multiply them.
The expression is given below.
⇒ 15k
If the value of the k is 3, then the value of the expression will be
⇒ 15 × 3
⇒ 45
The value of the expression 15k when the value of k is 3, will be 45.
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Which of the following expressions is equivalent to 1/4(8x+12)
The equivalent expression for the given expression is 2x+3.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given expression is 1/4 (8x+12).
Here, multiply 1/4 into a bracket, we get
= 8x/4 +12/4
= 2x+3
Therefore, the equivalent expression for the given expression is 2x+3.
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Which number sentences show how to solve the problem?
The truck driver loaded 72 crates of eggs. There are 36 eggs in each crate. The driver will make 6 deliveries and unload the same number of eggs at each delivery stop.
How many eggs will the driver unload at each stop?
Choose all answers that are correct.
72 ÷ 6 = 12 and 12 × 36 = 432
72 ÷ 6 = 12 and 12 × 12 = 144
72 ÷ 36 = 2 and 2 × 72 = 144
72 × 36 = 2,592 and 2,592 ÷ 6 = 432
72 ÷ 6 = 12 and 12 × 36 = 432 and 72 × 36 = 2,592 and 2,592 ÷ 6 = 432
Record the product 51 times 77
the answer is 128 because 51 + 77= 128
The product is 3927.
Select Equal or Not Equal to correctly classify each statement.
Only the second row is equal. The first row can't be equal because it says -2=-1/2
Best estimate for 61/7
I would say the best estimate would be 9 because the real answer is 8.71 and if you round that to the 1 place the answer would be 9.
Will give alot of points!
Need help Finding the side length X.
Because the 2 triangles are similar, find the ratio of 2 known sides.
Side XY = 10
Side AB = 25
25 / 10 = 2.5
This means the larger triangle is 2.5 times larger than the smaller one.
Now find the side of the smaller triangle, that would be the same side as X on the larger triangle and multiply that by 2.5.
XZ is the same side as AC
So X = 6 x 2.5
X = 15
A washer and a dryer cost $800 combined. The washer costs $50 less than the dryer. What is the cost of the dryer?
This is what I think:
#1: 800 - 50 = 750
#2: 800 divided by 2 = 400 - 50 = $350
i think the dryer costs 450$ and the washer 350$
a house is valued £210 000, correct to 2 significant figures, what is the lowest possible value of the house and the highest possible value of the house?
The lowest possible value of the house is £205000 and highest possible value is £214999.99...
Given that:
The house is valued £210000, correct to 2 significant figures.
Since its correct to 2 significant figures, thus there is error of approx 10000 range in £210000
The lowest possible number that would round up to 2 significant numbers to £210000 is £205000 since any value lower than that would look like £204..... which won't round up to £21..... but £20....
Similarly, the highest possible number that would round up to 2 significant figures to £210000 is £214999.999... since any real number bigger than that would make starting digit of the number as £215.... and thus 2 significant figure rounding will lead to £22....
Thus, the lowest possible value of the house is £205000 and highest possible value is £214999.99...
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Complete the synthetic division problem below 2|1 7 -18 WHATS is the quotient polynomial form? a x+7 b x+9 c x-9 d x-7
Answer:
x+9
Step-by-step explanation:
Synthetic division calc on Mathaway
The quotient is x+9 and the remainder is 0 if the synthetic division problem is 2|1 7 -18.
What is synthetic division?In the case of dividing by a linear factor, synthetic division is a shorthand, or quicker, technique of polynomial division.
W have:
2 | 1 7 -18
2 | 1 7 -18
__________
1
2 | 1 7 -18
____2×1 = 2______
1 7+2 = 9
2 | 1 7 -18
______2___2×9=18___
1 9 -18+18 = 0
The quotient is x+9, and the remainder is 0.
Thus, the quotient is x+9 and the remainder is 0 if the synthetic division problem is 2|1 7 -18.
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if the mean of a symmetrical distribution is 56, which of the values could be the median of the distribution 56,14,28,42
First you want to organize the numbers in order to find the median so it should look like this: 14, 28, 42, 56. Then you want to find the one in the middle. But oh wait there are TWO in the middle so add 42 and 28 up 70 then divide it by 2 which equals your median of 35.
Answer: 56
Step-by-step explanation: Apex
Samuel and Leticia are playing a game. After the first round of the game, Samuel's score was -19 and Leticias score was 21. The score with the greater absolute value wins each round. Who won the first round? Explain
Answer: Leticia won the first round
==============================================================
Your teacher is basically asking "which value is further from zero on the number line?". The value -19 is 19 units away from zero; while 21 is 21 units away from zero.
See the attached image below. Each "space" is a distance of 1
Absolute value measures distance along the number line. Distance is never negative. In terms of notation, you would say
|-19| = 19 and |21| = 21
The outputs 19 and 21 are then compared. We see that 21 is larger, so therefore, Leticia has the higher score and she won the first round.
(6,-2),(r,-6),m=4 find the value of r so that the line passes through each pair of points has a given slope
r = 5
calculate the slope m using the gradient formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with ( x₁, y₁ ) = (6, - 2 ) and (x₂, y₂ ) = (r, - 6)
m = [tex]\frac{-6+2}{r-6}[/tex] = [tex]\frac{-4}{r-6}[/tex] = 4
cross multiply
4(r - 6 ) = - 4
4r - 24 = 4 ( add 24 to both sides and divide by 4 )
4r = 20
r = [tex]\frac{20}{4}[/tex] = 5
The value of r so that the Slope of a line passes through the points (6,-2) and (r,-6) with a slope of 4 is 7.
In mathematics, the slope of a line through two points can be determined using the formula m = (y2 - y1) / (x2 - x1), where m is the slope, (x1, y1) and (x2, y2) are the coordinates of two points on the line.
In your case, the given points are (6, -2) and (r, -6) and the slope (m) is given to be 4. So, insering these values in the formula, you get: 4 = (-6 - (-2)) / (r - 6).
By simplifying the above equation, we find that r = 7.
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during his first year as a pilot, rob flies 6,692 miles. he flies 16,429 miles the second year and 24,211 miles the third year. he wants to estimate how many more miles he flew in the third year than the first and second year combined. which shows one way rob could estimate?
First years flies = 6,692 miles ≈7000 miles.
Second year flies = 16,429 miles ≈ 16000.
Third year flies = 24,211 miles ≈ 24000
Total number of miles flies in first and second year = 7,000miles +16,000 miles
Number of more miles he flew in the third year than the first and second year combined = Number of miles flies in third year - Total number of miles flies in first and second year
Number of more miles he flew in the third year than the first and second year combined 24,000 - (7,000+16,000)
Therefore, 24,000 - (7,000+16,000) estimation of how many more miles he flew in the third year than the first and second year combined.
Which of the following is an arithmetic sequence? a.2,4,16,32 b.2,3,7,1, c.3,0,-3,-6 d.5,-5,5,-5
Answer:
c apex im positive
Step-by-step explanation:
Option C of the following is an arithmetic sequence. 3,0,-3,-6 is the correct arithmetic sequence.
What is a sequence?A sequence is a collection of items that have been arranged in a logical order, with members appearing either before or after each other. A series is a collection of sequences.
3,0,-3,-6 is the correct arithmetic sequence.
d is the common difference of the series;
3,0,-3,-6
d=0 - 3= - 3 - 0 = -6 - (-3)
d= - 3
An arithmetic sequence has an equal common difference in each progressive term.
Hence, option C of the following is an arithmetic sequence.
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Help me please , and thank you .
Remark
There is a 4 year difference between Sal and Carrie. Carrie is the older. She is going to occupy 1 side of the equation. The other side is Sal and the 4 years.
Let Sal = S
Let Carrie = C
Carrie = Sal + 4
Equation
C = S + 4
A commuter has $245 in his savings account this account changes by -$15 each week he buys a ticket.in one time period, the account changed by -$240.for hot many weeks did the commuter buy tickets?
Convert 6 x 10 to the power of 5 into standard form
First let's write it out with just numbers
6×[tex]10^{5}[/tex]
Now solve!
Solve exponent first
10^5 = 100,000
Now multiply
6 x 100,000 = 600,000
600,000 is your answer
The number 6 x 10^5 in standard form equates to 600000. The conversion involves moving the decimal place the same number of steps as the power of ten indicates
Explanation:The conversion of 6 x 10 to the power of 5 into standard form involves interpreting the exponent as the number of places to shift the decimal point. In this case, the decimal point will be moved five places to the right.
Thus, 6 x 10 is equivalent to 600000 in standard form.
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what is the greatest common factor of 16y^3 z^3 and 56y^4z
Answer:
8y^3z
Step-by-step explanation:
8, y^3 and z are common to both expressions. Thus, the GCF is 8y^3z.
A speed reader can read 850 efficient words per minute. An average reader can read at approximately 1/7 that speed. How many efficient words per minute does an average reader read?
Answer:
An average reader can read 121.43 words per minute efficiently.
Explanation:
A speed reader can read 850 efficient words per minute.
An average reader can read at approximately 1/7 that speed.
Total word read by an average reader per minute is given = 850* 1/7
= 121.43 words per minute
So an average reader can read 121.43 words per minute efficiently.
Find the area of a square piece of cardboard for which the length of the side is 8”sq root sign”
Answer:
Area of square = 64 square units .
Step-by-step explanation:
Given : length of the side is √8.
To find : Find the area of a square piece of cardboard .
Solution : We have given side length of square cardboard = √8.
Area of square = side * side .
Area of square = √8 *√8.
Area of square = 64 square units .
Therefore, Area of square = 64 square units .
The temperature was -3 C last night. It is now -4 C. What was the change in temperature
-1 C, that's the only logical answer I can think of. Or does it have to be in F?
The change in temperature is a decrease of 1°C, which is calculated by subtracting the initial temperature from the final temperature.
The question involves calculating the change in temperature from -3°C to -4°C. To find the change in temperature, you subtract the initial temperature from the final temperature. In this case, the change would be:
-4°C - (-3°C) = -4°C + 3°C = -1°C.
So the change in temperature is a decrease of 1°C.
Juan bought a desktop computer and a laptop computer. Before finance charges, the laptop costs $300 more than the desktop. He paid for the computers using two different financing plans. For the desktop the interest rate was 6% per year, and for the laptop it was 7% per year. The total finance charges for one year were $398. How much did each computer cost before finance charges?
Answer:
The cost of each computer before finance is:
Desktop: $2900.00, Laptop: $3200.00
Step-by-step explanation:
Lets say the cost of Desktop is 'D' dollars.
The cost of laptop is [tex]=D+300[/tex] dollars.
Total finance charge for 1 year is given by:
[tex]0.06\times D+0.07 \times (D+300)=398[/tex]
Solving for D we get:
[tex]0.06D+0.07D+21=398[/tex].......(equation 1)
[tex]0.13D=398-21=377[/tex]
[tex]D=\frac{377}{0.13} =2900[/tex]
Now the cost of laptop is D+300:
[tex]D+300=2900+300=3200[/tex]
So before finance, the cost of desktop was $2900.00 and the cost of laptop was $3200.00.
P.S: You can check if your calculation is correct by plugging the values of the cost of laptop and desktop in the equation 1.
onsider the sequence of steps to solve the equation: 3(x − 4) + 5x = 9x − 36 Given ⇒ 3(x − 4) + 5x = 9x − 36 Step 1 ⇒ 3x − 12 + 5x = 9x − 36 Step 2 ⇒ 3x + 5x − 12 = 9x − 36 Step 3 ⇒ 8x − 12 = 9x − 36 Step 4 ⇒ 8x − 8x − 12 = 9x − 8x − 36 Step 5 ⇒ 0 − 12 = x − 36 Step 6 ⇒ −12 = x − 36 Step 7 ⇒ −12 + 36 = x − 36 + 36 Step 8 ⇒ 24 = x + 0 Step 9 ⇒ 24 = x Which property yields Step 6? A) Additive Inverse Property B) Additive Identity Property C) Addition Property of Equality D) Commutative Property of Addition
3(x - 4) + 5x = 9x - 36 Given
(3)(x) + (3)(-4) + 5x = 9x - 36 Distributive Property
3x - 12 + 5x = 9x - 36
(3x + 5x) - 12 = 9x - 36 Combine like terms
8x - 12 = 9x - 36
8x - 8x - 12 = 9x - 8x - 36 Subtraction Property of Equality
0 - 12 = x - 36 Additive Identity Property
-12 = x - 36
-12 + 36 = x - 36 + 36 Addition Property of Equality
24 = x
Answer: Additive Identity Property
Answer:Additive Identity Property
Step-by-step explanation:
the perimeter of a rectangle photograph is 22in the length of the photograph is 1 inch more than the width what are the dimensions of the photograph
Assume that the width=w
22=2w+2(w+1)
22=2w+2w+2
22=4w+2
20=4w
w=5
The dimensions are 4 by 5.
The dimensions of the rectangle photograph are 5.5 inches (width) by 6.5 inches (length), calculated by setting the given perimeter equal to twice the sum of the length and the width, and then solving for the width and length.
Explanation:The perimeter of a rectangle is the sum of all its sides. Given that the perimeter of the photograph is 22 inches, you can work out the length and width using algebra. Let's denote the width of the photograph as 'x' (in inches). Thus, the length is 'x + 1' since it is one inch more than the width. Since the rectangle has two equal lengths and two equal widths, its perimeter can be represented as 2*(length + width) or 2*(x + x + 1). Setting this equal to 22 (the perimeter), we get 2*(2x + 1) = 22. Solving for 'x' gives us the width, which is 5.5 inches. The length is therefore 6.5 inches, being 1 inch more than the width. Therefore, the dimensions of the rectangle are 5.5 inches by 6.5 inches.
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Find the mean of the set data. -17 32 -9 0 52 12 -14??
To find the mean you must:
-17 + -14 + -9 + 0 + 12 + 32 + 52 = 56
Then divide 56 by how many numbers are in this set so there are 7 numbers so we divide 56 by 7 and I don't even have to do the work for this because it's basic multiplication.
The answer is: 8.
Answer:
Mean is 8
Step-by-step explanation:
Given observations,
-17, 32, -9, 0, 52, 12, -14
Sum of the observations = -17 + 32 + (-9) + 0 + 52 + 12 + (-14)
= 96 - 40
= 56
Number of observations = 7,
Hence,
[tex]\text{Mean} = \frac{\text{Sum of the observations}}{\text{Number of the observations}}[/tex]
[tex]=\frac{56}{7}[/tex]
= 8