Answers
Answer:
G
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Simplifying the radicals in the expression
[tex]\sqrt{52}[/tex]
= [tex]\sqrt{4(13)}[/tex]
= [tex]\sqrt{4}[/tex] × [tex]\sqrt{13}[/tex]
= 2[tex]\sqrt{13}[/tex]
------------------
[tex]\sqrt{117}[/tex]
= [tex]\sqrt{9(13)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{13}[/tex]
= 3[tex]\sqrt{13}[/tex]
Then
[tex]\sqrt{52}[/tex] + [tex]\sqrt{117}[/tex]
= 2[tex]\sqrt{13}[/tex] + 3[tex]\sqrt{13}[/tex]
= 5[tex]\sqrt{13}[/tex] → G
[tex]{\small\sf{The\:expression \sqrt{52} + \sqrt{117} \:is \: equivalent \: to}}[/tex]
[tex]\small\bf{F.} \: \sf{13} [/tex]
[tex]\small\bf{G.}\sf \:5 \sqrt{13} [/tex]
[tex]\small\bf{H.}\sf\:6 \sqrt{13} [/tex]
[tex]\small\bf{J.}\sf\:13 \sqrt{13} [/tex]
Solution:-[tex]\small\sqrt{52}+\sqrt{117}\sqrt{4•13} +\sqrt{9•13}\tiny\sf\purple{(Product\:Property)}[/tex]
[tex]\small{ \: \:\: \: \: \: \: \:=\sqrt{2²•13}+\sqrt{3²•13}\tiny\sf\purple{(Prime\:Factorization)}}[/tex]
[tex]\small{\: \:\: \: \: \: \: \:=\sqrt{2²}\sqrt{13}+\sqrt{3²}\sqrt{13}\tiny\sf\purple{(Product\:Property)}}[/tex]
[tex]\small{\: \:\: \: \: \: \: \:=2\sqrt{13}+3\sqrt{13}\tiny\sf\purple{(Simplify)}}[/tex]
[tex]\small{\: \:\: \: \: \: \: \:=5\sqrt{13}\tiny\sf\purple{(Simplify)}}[/tex]
Answer:-So, the correct option is D.
=======================#Hope it helps!
(ノ^_^)ノ
Related Questions
Leila is arranging 11 cans of food in a row on a shelf. She has 4 cans of corn, 1 can of peas, and 6 cans of beets. In how many distinct orders can the cans be arranged if two cans of the same food are considered identical.
Answers
Answer:
2310 ways
Step-by-step explanation:
We are given;
Number of cans = 11
Number of cans of corn = 4
Number of cans of peas = 1
Number of cans of beets = 6
Following the rule of combination and permutations and applying it to this question, we have;
Number of ways = 11!/(6! × 1! × 4!)
Number of ways = 2310 ways
7
10
6
What is the area of the triangle shown above?
Answers
Answer:
Area of triangle = 0.5* base * height
A = 0.5*6*10
A = 30
After a certain number of football matches , a footballer averages 1 goal per game.He only scored 2 goals in the next 10 games and his average dropped to 0.8 goals per game .How many football matches did he play altogether?
Answers
Answer:
He played 40 matches in total, scoring 32 goals.
Step-by-step explanation:
Since after a certain number of football matches, a footballer averages 1 goal per game, and he only scored 2 goals in the next 10 games and his average dropped to 0.8 goals per game, to determine how many football matches did he play altogether you must perform the following calculation:
10/10 + 2/10 = 12/20 = 0.6
8/8 + 2/10 = 10/18 = 0.55
12/12 + 2/10 = 14/22 = 0.64
20/20 + 2/10 = 22/30 = 0.73
24/24 + 2/10 = 26/34 = 0.76
30/30 + 2/10 = 32/40 = 0.8
Thus, he played 40 matches in total, scoring 32 goals.
Write the quadratic equation whose roots are - 6 and -4, and whose leading coefficient is 4.
(Use the letter x to represent the variable.)
Answers
Answer:
Step-by-step explanation:
y=4(x+6)(x+4)
y=4(x^2+10x+24)
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
Match each expression on the left with its equivalent on the right. Some answer choices on the right will not be used.
Answers
Answer:
8200 * 100 = 820,00
820,000 ÷ 10 = 82,000
820 * 10 = 8200
82,000 ÷ 1,000 = 82
Step-by-step explanation:
Love your username btw
Arithmetic operations contain operations such as Addition, Subtraction, Multiplication, and Division.
What is meant by arithmetic operations?Arithmetic operations exist as a branch of mathematics, that concerns the analysis of numbers and operation of numbers that exist valid in all the other constituents of mathematics. It essentially contains arithmetic operations such as Addition, Subtraction, Multiplication, and Division.
8200 [tex]*[/tex]100 = 8,20,000
820000 ÷ 10 = 82,000
820 [tex]*[/tex] 10 = 8,200
82000 ÷ 1000 = 82
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Is 256.78 power by 10 100 or 1000
Answers
Answer:
I would say 100 since 256.78 is closer to 100 then 1000 or 10
Step-by-step explanation:
Which equation represents a line that passes through (-2, 4) and has a slope of ?
Answers
Answer:
y - 4 = (2/5)(x + 2)
Step-by-step explanation:
point slope form is
y - y₁ = m(x - x₁)
(x₁, y₁) is a point on the line and m is the slope
------------------------
Given (x₁, y₁) = (-2, 4) and m = 2/5
y - 4 = (2/5)(x + 2)
Which
expression iS equivalent to (a^8)^4
Answers
Answer:
Step-by-step explanation:
What are the nasser choices
Answer:
a^32.
Step-by-step explanation:
Using one of the laws indices:
(a^8)^4
= a^(8*4)
= a^32.
Help me thanks If you can
Answers
8. 5, 6, 3, -5
9. Winter, Colder
10. 5, 6, 10, 12, 7
11. Units squared and Units cubed, the difference is that with cubed you're getting the area of three planes instead of two.
A factory produces 2985 bulbs in a day. how many bulbs did it produce in that year.
Answers
Answer:
1089525
Step-by-step explanation:
2985 is per day of bulbs and a year has 365 days
so we multiply bulbs by day and days in a year
which will give us 1089525
Factory produces 2985 bulbs - 1 day
-> 365 x 2985 = 1089525 bulbs a year
If 1 year = 366 days
-> 366 x 2985 = 1092510 bulbs a year
What is the standard form equation of the ellipse that has vertices (-6, 2) and (14, 2) and foci (-3,2) and (11, 2)?
Answers
Answer:
Step-by-step explanation:
Who knows a lot about proofs in geometry? Please message me!
Answers
Answer:
I do and im always ready to help
Records show that 12% of all college students are foreign students who also smoke. It is also known that 40% of all foreign college students smoke. What percent of the students at this university are foreign
Answers
Answer: the percent of the students at this university are foreign = 30%
Step-by-step explanation:
Given: Probability that college students are foreign students who also smoke: P(S|F)=0.12
Probability that foreign college students smoke P(S∩F)=0.4
The probability that the students at this university are foreign :
[tex]P(F)=\dfrac{P(S\cap F)}{P(S|F)}[/tex] [By conditional probability formula]
[tex]=\dfrac{0.12}{0.4}\\\\=0.3[/tex]
Hence, the percent of the students at this university are foreign = 30%
CAN SOMEONE PLEASE ANSWER THISS ASAP PLEASE
f(n) = 10(1.02)n
Part A: When the scientist concluded his study, the height of the plant was approximately 11.04 cm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(n) represent? (2 points)
Part C: What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent? (4 points)
Answers
Answer:
Step-by-step explanation:
11.04 = 10(1.02)^n
1.104 = 1.02^n
ln 1.104 = ln 1.02^n
ln 1.104 = n ln 1.02
n = ln 1.104/ ln 1.02
n = 4.99630409516
4.99 can be rounded to 5.
So a reasonable domain would be 0 ≤ x < 5
PART B)
f(0) = 10(1.02)^0
f(0) = 10(1)
f(0) = 10
The y-intercept represents the height of the plant when they began the experiment.
f(1) = 10(1.02)^1
f(1) = 10(1.02)
f(1) = 10.2
(1, 10.2)
f(5) = 10(1.02)^5
f(5) = 10(1.1040808)
f(5) = 11.040808
f(1)=10(1.02)^1
f(1)=10.2
Average rate= (fn2-fn1)/(n2-n1)
=11.04-10.2/(5-1)
=0.22
the average rate of change of the function f(n) from n = 1 to n = 5 is 0.22.
Do you think someone would steal a led light controller???
Cause it was lost yesterday at night in my room when my friends where over but the day before it was they’re?
Does it sound like we lost it our they stole it?
Answer ASAP
Answers
Answer:
yeah dude they might of. First look around everywhere in ur room before accusing them.
Step-by-step explanation:
good luck
HELP WITH MY MATH PLEASEEE
Answers
Answer:
x = 18
Step-by-step explanation:
JM = LM
8x - 3 = 141
8x = 141 + 3
8x = 144
x = 144/8
x = 18
Answer:
since its a square each side is equal so
8x-3=141
8x=144
x=18
so
A: x=18
Hope This Helps!!!
4.000.000 x 4.000.000 = ?????
Helpp
Answers
I think the answer is 16 but I'm not 100% sure
If the profits in your consulting business increase by 6% one year and decrease by 3% the following year, your profits are up by 3% over two years
Answers
Answer:
its 1.388 p
Step-by-step explanation:
i hope this helps
Find the area of this semi-circle with radius,
r
= 15cm.
Give your answer rounded to 1 DP.
Answers
Answer:
Semicircle = 353.25 cm²
Step-by-step explanation:
Area of semicircle = πr²/2
substitute the values
semi circle = 3.14 × 15 × 15 / 2
Area of semicircle = 353.25 cm²
4 7/8 - 2 3/8 simplest form
Answers
Answer:
2 1/2
Step-by-step explanation:
4 7/8= 39/8
2 2/8= 19/8
39/8 - 19/8 = 20/8 = 2 4/8 = 2 1/2
If ⅔ of a number is 20 what is ½ of the number?
Answers
Answer:
15
Step-by-step explanation:
2/3 of 30 is 20, so 1/2 of 30 is 15
the answer is in the image above
An industrial process produces batches of a chemical whose impurity levels follwo a normal distribution with standard deviation 1.6 grams of chemical. A random sample of 100 batches is selected in order to estimate the population mean impurity level. The probability is 0,0367 that the sample mean impurity level exceeds the population mean by how much?
Answers
Answer:
The probability is 0,0367 that the sample mean impurity level exceeds the population mean by 0.2864 grams of chemical.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Standard deviation 1.6 grams of chemical. Random sample of 100.
This means that [tex]n = 100, s = \frac{1.6}{\sqrt{100}} = 0.16[/tex]
The probability is 0,0367 that the sample mean impurity level exceeds the population mean by how much?
Z multiplied by s, in which Z has a p-value of 1 - 0.0367 = 0.9633, so Z = 1.79.
1.79*0.16 = 0.2864.
The probability is 0,0367 that the sample mean impurity level exceeds the population mean by 0.2864 grams of chemical.
Which of the following is a benefit of doing business with an online bank?
A. Greater variety of services
B. Personalized service
Ο Ο
C. Variety of deposit locations
O
D. Typically higher savings rates
Answers
Jsnsjsjns
What is the first step to solve the equation 12z - 21 = 92?
Answers
12z - 21 = 92
12z - 21 + 21 = 92 + 21
12z = 113
z = 113/12
a container has 16 1/2 cups of lemonade. Asher gives each of his classmates 3/4 of a cup if lemonade. if asher gives away all of the lemonade how many classmates does asher give lemonade to
Answers
Answer this question to receive 10 points
Answers
Answer:
153.86.
Step-by-step explanation:
Use the formula pi times radius squared.
Translate this sentence into an equation.
60 is the sum of 15 and Mabel's age.
Use the variable m to represent Mabel's age.
Answers
Answer:
60 = 15+m
Step-by-step explanation:
sum is the outcome or total of an addition problem
Find the exact value of sec A in simplest radical form
Answers
Answer:
sec A = sqrt(61) / 6
Step-by-step explanation:
sec theta = hypotenuse / adjacent side
sec A = sqrt(61) / 6
How many numbers are there from x to 7x-8
Answers
Answer:
6x + 7
Step-by-step explanation:
7x - 8 - x
=>6x - 8
=> 6x - 8 + 1 (including x as number)
=>6x + 7
There are numbers in between (x) to (7x - 8), as per linear equation.
What is a linear equation?"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, 'x' is a variable, 'A' is a coefficient and 'B' is constant."
Given two numbers are (x) and (7x - 8).
Therefore, total numbers in between (x) and (7x - 8) are:
= (7x - 8) - x + 1
= 6x - 7
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Find (x,y) such that (8,2)(x,y) = (28,22)
Answers
Answer:
(x,y) = (3.5, 11)
Step-by-step explanation:
(8,2)(x,y) = (28,22)
Dot product, so:
[tex](8,2)(x,y) = (8x,2y) = (28,22)[/tex]
Then
[tex]8x = 28[/tex]
[tex]x = \frac{28}{8} = 3.5[/tex]
And
[tex]2y = 22[/tex]
[tex]y = \frac{22}{2} = 11[/tex]
So
(x,y) = (3.5, 11)