Answer:
3√5 or ≈6.7082
Step-by-step explanation:
1) √45
2) Factor out the perfect square: √3²×5
3) The root of a product is equal to the product of the roots of each factor: √3²√5
4) Reduce the index of the radical and exponent with 2: 3√5
5) Solution: 3√5 or ≈ 6.7082
after removing the perfect square factor from inside the square root of 45, we are left with 3√5.
To remove all perfect squares from inside the square root of √45, we need to factorize 45 and separate the perfect square factors.
The prime factorization of 45 is 3 × 3 × 5. Since 3 is repeated twice, it represents a perfect square factor.
We can rewrite the square root of 45 as the square root of (3 × 3 × 5). Using the property of square roots (√ab = √a × √b), we can simplify it as √(3 × 3) × √5.
The square root of 3 × 3 equals 3, so the expression simplifies to 3√5.
Therefore, after removing the perfect square factor from inside the square root of 45, we are left with 3√5.
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Point A has coordinates (2, 4), and point C has coordinates (5, 0). what is AB?
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{5}~,~\stackrel{y_2}{0})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AC=\sqrt{(5-2)^2+(0-4)^2}\implies AC=\sqrt{3^2+(-4)^2} \\\\\\ AC=\sqrt{9+16}\implies AC=\sqrt{25}\implies AC=5[/tex]
c. What is the relationship between a + b and b + a?
d. What is the relationship between a - b and b - a?
Answer:
c. They are equal to each other.
d. They are the negative of each other.
Step-by-step explanation:
c. Adding c to d and d to c are the same and thus both expressions are equal. In addition, the numbers can be added in any order and will result in the same final answer. This is also known as commutative property.
d. a-b= -(b -a)
In this case, subtracting b from a is not equal to subtracting a from b. The order of terms in subtraction affects the final answer.
Estimate square root of 43 to the nearest tenth
Answer:
6.6
Step-by-step explanation:
√(43)= 6.5574385243
So your tenth is the coefficient (number) on the right side of the decimal which in this case would be 5 so when rounding you look at the hundredths place which is 2 spaces away from the decimal going right so in this case would be 5 as well, if the number you're rounding to is 5 or above (5-9) then you change then number in front of it by adding 1.
For example: 0.4815 if were rounding the tenths place we look at the 8 (hundredths place) and since 8 is over 5 we make the 4 (tenths place) into a 5 giving us the answer .5
so for your problem the answer would be 6.6
What is 10 × 7 thousands in unit form
Answer:
70000
Step-by-step explanation:
According to the Zero-Product Rule, multiply 7 by 1000 to get 7000, then attach that extra 0 to the answer, giving you 70000.
I am joyous to assist you anytime.
Solve m² + 8m = -3 by completing the square.
(Use a comma to separate multiple values.)
What the answer for this?
Answer:
Step-by-step explanation:
m² + 8m = -3
(m² + 8m+16) -16 = -3
(m+4)² = 13.....continue
express 20% as a fraction please show me the working
Answer:
1/5
Step-by-step explanation:
Lets start with the number 100. We know that 1/10 of 100 is 10! 1/10 can also be written as 10%.
Now lets think about it, We're looking for 20%. If 1/10 of 100 is 10%, then 2/10 of 100 is 20%!
So you've got the fraction 2/10! Now you need to simplify it :)
Both the numerator (2) and the denominator (10) can be divided by 2!
(2/2)=1
(10/2)=5
Therefore, after simplifying 2/10 your final answer should be 1/5!
How do I solve this problem? PLEASE HELP/ due tomorrow.
Answer:
10200000
Step-by-step explanation:
102 times 100,000 because you have to multiply 10, 5 times like this for example, 10 x 10 x 10 x 10 x 10
Noah is running a portion of a marathon at a constant speed of 6 mph. Complete the table to predict how long it would take him to run different distances at that speed and how far he would run in different time intervals.
Time in hours Miles traveled at 6mph
1.
1/2
1 1/3
1 1/2
9
4 1/2
Answer:
[tex]\begin{array}{cc}\text{Time}&\text{Distance}\\ \\1&6\\ \\\dfrac{1}{2}&3\\ \\1\dfrac{1}{3}&8\\ \\1\dfrac{1}{2}&9\\ \\9&54\\ \\4\dfrac{1}{2}&27\end{array}[/tex]
Step-by-step explanation:
Noah's running speed = 6 mph.
Use formula [tex]D=v\cdot t,[/tex] where
D is the distance,
v is the speed,
t is the time.
If [tex]t=1[/tex] hour, then [tex]D=6\cdot 1=6[/tex] miles.
If [tex]t=\dfrac{1}{2}[/tex] hour, then [tex]D=6\cdot \dfrac{1}{2}=3[/tex] miles.
If [tex]t=1\dfrac{1}{3}[/tex] hours, then [tex]D=6\cdot 1\dfrac{1}{3}=6\cdot \dfrac{4}{3}=8[/tex] miles.
If [tex]t=1\dfrac{1}{2}[/tex] hours, then [tex]D=6\cdot 1\dfrac{1}{2}=6\cdot \dfrac{3}{2}=9[/tex] miles.
If [tex]t=9[/tex] hours, then [tex]D=6\cdot 9=54[/tex] miles.
If [tex]t=4\dfrac{1}{2}[/tex] hours, then [tex]D=6\cdot 4\dfrac{1}{2}=6\cdot \dfrac{9}{2}=27[/tex] miles.
So, the table is
[tex]\begin{array}{cc}\text{Time}&\text{Distance}\\ \\1&6\\ \\\dfrac{1}{2}&3\\ \\1\dfrac{1}{3}&8\\ \\1\dfrac{1}{2}&9\\ \\9&54\\ \\4\dfrac{1}{2}&27\end{array}[/tex]
Please find attached the answers in the attached diagram
Average speed is the total distance travelled per time.
Average speed = total distance / total time
Noah's average speed is 6mph
From the above formula, the formula to determine miles run is average speed x time
Total miles he ran in 1 hour = 6 x 1 = 6 miles
Total miles he ran in 1/2 hours = 6 x 1/2 = 3 miles
Total miles he ran in 1 1/3 hours = 6 x 4/3 = 8 miles
The formula to determine total time: total distance / average speed
Time it took Noah to run 1 1/2 miles = 3/2 ÷ 6 = 1/4 miles
Time it took Noah to run 9 miles = 9 ÷ 6 = 1 1/2 miles
Time it took Noah to run 4 1/2 miles = 9/2 ÷ 6 = 3/4 miles
Please find attached an image of the table used in answering this question
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A student finds an object with a mass of 64.54g and a volume of 14cm3. Find the density of the object.
Answer:
4.61 g/cm3
Step-by-step explanation:
density is mass divided volumen
[tex]density \: = \frac{64.54g}{14 {cm}^{3} } = 4.61 \frac{g}{ {cm}^{3} } [/tex]
The density of the object is 4.61 g/cm³
Using the parameters given for our Calculation;
mass of object = 64.54 Volume = 14cm³The density of an object can be calculated as the ratio of the mass to the volume of the object.
Density = mass / VolumeInputting the values thus;
Density = 64.54 / 14 = 4.61 g/cm³Hence, the density is 4.61 g/cm³
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What is a rational number? Please explain it as though you're explaining to a child (I'm just that dumb)
Answer:
Step-by-step explanation:
A rational number is a number that can be expressed as a fraction p/q where p and q are integers and q!=0. A rational number p/q is said to have numerator p and denominator q. Numbers that are not rational are called irrational numbers. The real line consists of the union of the rational and irrational numbers. The set of rational numbers is of measure zero on the real line, so it is "small" compared to the irrationals and the continuum.
A retailer buys a calculator for $5.30. What selling price would represent a 210% markup?
Answer:
The selling price is $16.43
Step-by-step explanation:
we know that
A markup percentage is the amount of the cost of an item that you add on to create the selling price
we have that
[tex]100\%+210\%=310\%=310/100=3.10[/tex]
To find out the selling price, multiply the cost of a calculator by the factor 3.10
so
[tex]\$5.30(3.10)=\$16.43[/tex]
therefore
The selling price is $16.43
I have very little cash and yet he says that I had a good year with $15,000 net income. He said it was because we use accrual accounting (whatever that means). I know I paid 6 month’s rent ($1,400 a month) in advance at the end of the year. I also paid my insurance for the next year. Insurance cost $6,000. I have several customers who had a lot of services done on credit and haven’t paid yet. I think that totals $11,948 owed to me. Can you explain?
Step-by-step explanation:
Accrual - the accumulation or increase of something over time, especially payments or benefits.
(Accumulation Accounting)
Net Income: $15,000
Spent: 6($1,400)+$6,000
$8,400+$6,000 = $14,400
Current Total (In-hand): $600
Not Been Paid Yet (Not In-hand): $11,948
Accrual accounting is a method of accounting that records transactions when they occur, not when cash is exchanged. It takes into account revenues earned and expenses incurred during a specific period. In this case, the student's net income of $15,000 is calculated based on revenues earned and expenses incurred, even though there may be little cash on hand.
Explanation:Accrual accounting is a method of accounting where transactions are recorded when they occur, not when the money is exchanged. It takes into account both revenues earned and expenses incurred during a specific period, regardless of when the cash is received or paid.
In your case, even though you have little cash on hand, your net income of $15,000 is calculated based on revenues earned and expenses incurred. Let's break it down:
You paid 6 months' rent in advance at the end of the year, which amounts to 6 x $1,400 = $8,400. This is considered an expense incurred during the year, even though the cash was paid in advance.You also paid your insurance for the next year, which is $6,000. Again, this is considered an expense incurred during the current year.You have several customers who haven't paid yet, and they owe you $11,948. This is considered revenue earned during the current year, even if you haven't received the cash yet.So, your net income of $15,000 takes into account these revenues and expenses, in accordance with accrual accounting principles.
8. In order to qualify for the year-end tennis tournament,
Sam must win at least 60 percent of his matches this
year. To date, Sam has won 14 of his 18 matches. Of
Sam's 13 matches remaining in the year, what is the
least number that he must win in order to qualify for
the year-end tournament?
H 4
B. 5
C. 6
D. 7
E. 8
Answer:
(14 + x)/31 ≥ .6
14 + x ≥ 18.6
x ≥ 5
The correct answer is B.
Sam needs to win at least 5 more of his 13 remaining matches in order to achieve at least a 60% win rate and qualify for the year-end tournament.
Explanation:The question: how many of Sam's 13 remaining matches must he win to qualify for the year-end tournament by winning at least 60% of his matches this year, is a mathematics question related to percentage and probability. To solve it, you need to figure out the total number of matches Sam will play in the year and calculate what number constitutes 60% of that total. Sam is set to play a total of 31 matches (18 + 13). Sixty percent of 31 is 18.6, we will round this up to 19 as you cannot win portion of a match. Given that Sam has already won 14 matches, he needs to win at least 5 more of his 13 remaining matches (19-14 = 5) in order to win at least 60 percent of his matches for the year. So, the correct answer is 5.
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Find the 85th term of the arithmetic sequence - 25, 37, 49, ...
[tex]\bf -25~~,~~\stackrel{-25-12}{-37}~~,~~\stackrel{-37-12}{-49}~~,~~...\qquad \qquad \qquad \stackrel{\textit{common difference}}{d = -12} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=-25\\ d= -12\\ n = 85 \end{cases}[/tex]
[tex]\bf a_{85}=-25+(85-1)(-12)\implies a_{85}=-25+(84)(-12) \\\\\\ a_{85}=-25+(-1008)\implies a_{85}=-25-1008\implies a_{85}=-1033[/tex]
The 85th term of the arithmetic sequence – 25, -37, -49, ... is -1033
Explanation:
Explicit Arithmetic Sequence:
aₙ = a₁+ (n-1)d
Here Common difference ,d = -37-(-25) = -12 , n = 85 and a₁ = -25 .
[tex]a_{85}[/tex] = -25 + (85 - 1 ) -12
[tex]a_{85}[/tex] = -25 + (84) -12
[tex]a_{85}[/tex] = -25 + (-1008)
[tex]a_{85}[/tex] = - 1033
Complete Question : The question should be Find the 85th term of the arithmetic sequence -25, -37, -49, ...
simplify!!!
I need help please
Answer:
[tex]\frac{4^{21}}{5^{6}}[/tex]
Step-by-step explanation:
[tex]\frac{4^{7*3}}{5^{2*3}}=\frac{4^{21}}{5^{6}}[/tex]
PLEASE ANSWER!
Alejandro has gone to school 5/7 of the last 35 days. Which expression can be used to determine the number of days Alejandro has gone to school?
A. 35 / 5/7
B. 35 * 5/7
C. 5/7 / 35
D. 7/5 / 35
Answer:
i am pretty sure it is b
Step-by-step explanation: