Given expression: [tex]2\sqrt{3} *(\sqrt{2}+ \sqrt{3})[/tex].
We need to distribute and simplify.
We have 2√3 in front of paranthesis.
We need to distribute 2√3 over paranthesis.
2√3*(√2+√3) would give : 2√3 * √2 + 2√3 * √3.
We need to multiply radical numbers inside radicals and outside number by outside number.
On simplifying, we get
2√6 + 2 * 3 = 2√6 + 6.
Therefore, final answer is 6+2√6.
Answer:
6+2√6
Step-by-step explanation:
D on edg
the sum of 367 and 863 is equal to the sum of 863 and another number. what is that number?
Answer:
Sum of 367 and 863 is equal to the sum of 863 and 367. Thus, 367 is the required number.
Step-by-step explanation:
Commutative property of Addition
Let a and b be two real numbers. Then commutative property of addition states that the sum of a and b is equal to the sum of b and a that is
[tex]a + b = b + a[/tex]
Similarly, we a re given here,
[tex]367 + 863 = 1230\\1230 = 863 + 367[/tex]
Thus, sum of 367 and 863 is equal to the sum of 863 and 367.
Thus, 367 is the required number.
Explain why a number that is divided by a multiple of 3 is also divisible by 3
It is a reciprocal. Multiplying is the opposite of Dividing, so if I multiply 3 times 4 I get 12. If i divide 12 by 3 I get 4.
Dion is at a basketball game and he wants to buy some hamburgers and drinks. His friend joe brought 2 Hamburgers and 5 drinks for $8.00 and Felicia brought 2 hamburgers and 3 drinks for $6.00. Help Dion determine the cost of one hamburger and one drink
For this one, the best way to do it is write out you formulas, then solve for the first one and see if it works for the second one.
I am going to use h for hamburgers and d for drinks to make it easier.
2h+5d=8
2h+3d=6
So what I did was make the drinks 1, this way you can see if you need to raise it or if the hamburgers could come out even. When you do that here is what it looks like:
2h+5(1)=8
2h+5=8
2h=3
h=1.50
So here is what you have as of now
h= 1.50 and d= 1
now plug that into the next problem
2h+3d=6
2(1.50)+3(1)=6
3+3=6
So that is your answer
Hamburgers are $1.50
and Drinks are $1
Hope this helps!
Hamburgers cost 1.50 each and its 1.00 for each drink
Look at the equation below.
M = 4G − z
Which of the following is the same equation solved for G?
A. G = M+z/4
B. G = 1/4 M + z
C. G = 4M + z
D. G = 4(M − z)
By isolating 'G' in the given equation, 'M = 4G - z', we find that 'G' is equal to '(M + z) / 4', which matches with choice A in the question.
Explanation:The given equation is M = 4G - z. To solve this equation for G, we should first move 'z' over to the other side of the equation, which will give us M + z = 4G. In the next step, we divide each side of the equation by 4 to isolate 'G'. Our answer is then G = (M + z) / 4. This is equivalent to the choice A. G = M+z/4 given in the original question.
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The sum of two numbers is 76. Their difference is 36. Find the numbers
The sum of two numbers is 76. Their difference is 36. Find the numbers
X+y= 76
X-y=36
Add x+x , y cancels out, add76+36
2x= 112
Divide 2 both sides
X= 61
Now substitute your x answer into first original equation
X+y =76
61+y =76
Subtract 61 both sides to get y .
Y= 76-61
Y= 15
Your two numbers are 61 and 15
You've been told fans will be given a free rally towel every 8 games.Also the knicks are going to wear their throwback jerseys every 12 games.If the fans were given a rally towel and the knicks wore their throwback jerseys tonight how many games will it be untill the next time when both happened?
We need to find the lowest common multiple of 8 and 12.
Reminder that the LCM is the lowest number that divides evenly with both of the given numbers.
We can make a chart and see that:
Multiples of 8: 8, 16, 24, 32
Multiples of 12: 12, 24...wait! We have a match with 24!
Therefore, there will be 24 more games until both events will occur.
At a school concert,the orchestra plays 8 songs that are 4.25 min long and 3 songs that are twice as long as each of the others.how long is the concert?
Answer: 59.5 minutes.
Step-by-step explanation:
1. You have the following information given in the problem above:
- 8 songs are 4.25 minutes long.
- 3 songs are twice as long as each of the others.
2. Therefore, the total time of 8 songs is:
[tex](8)(4.25min)=34min[/tex]
3. And the total time of the 3 songs is:
[tex](2)(3)(4.25min)=25.5min[/tex]
4. Therefore, you have that the result is:
[tex]34min+25.5min=59.5min[/tex]
The concert is 59.5 minutes long.
Let's break down the problem step-by-step:
The orchestra plays 8 songs that are each 4.25 minutes long.The orchestra also plays 3 songs that are twice as long as each of the 4.25 minute songs.First, we calculate the total time for the 8 songs:8 songs x 4.25 minutes = 34 minutes
Next, we calculate the length of the songs that are twice as long as the 4.25 minute songs:2 x 4.25 minutes = 8.5 minutes per song
We then find the total time for these 3 songs:3 songs x 8.5 minutes = 25.5 minutes
Finally, we add the time for all the songs to get the total duration of the concert:34 minutes + 25.5 minutes = 59.5 minutes
So, the total duration of the concert is 59.5 minutes.
The value of the digit in the hundredths place is——— times as much as the digit in the tenths place.
Answer:
the answer is 10
Step-by-step explanation:
how do you solve this question
2(x-2)+3(x+1)=9
2(x - 2) + 3(x + 1) = 9
2x - 4 + 3x + 3 = 9 distributed the 2 and 3 on the left side
5x - 1 = 9 added like terms (2x + 3x) and (-4 + 3)
5x = 10 added 1 to both sides
x = 2 divided 5 from both sides
Answer: x = 2
please help me with this!
Answer:
-13F is less than -12F, and -9F is greater than -12F
Step-by-step explanation:
You can prove this because in the problem is states that -13F < -12F < -9F
If you utilize this, you find that the first statement is quite obvious:
-13F is less than -12F
The second statement is a little trickier. Since in the original inequality is states that -12F < -9F, but you want to know the relationship between the switch, you would just flip the sign in the middle, getting you:
-9F is greater than -12F
You could also prove this simply with the rules of negative values (which work inversely from positives).
Y=x+ 5
Y=5 x + 10
Y= 5 x + 5
Y = x + 10
y = x + 5
check
for x = 5 → y = 5 + 5 = 10 CORRECT
for x = 10 → y = 10 + 5 =15 CORRECT
for x = 15 → y = 15 + 5 = 20 CORRECT
for x = 20 → y = 20 + 5 = 25 CORRECT
Find The FACTORS of 48
1, 2, 3, 4, 6, 8, 12, 16, 24, 48
a barrel of oil is extracted at a cost of $51 then transparent to and from the refinery at a cost of $6 each way. the oil is refined 3 times at $9 per time. whats the profit, in dollars per barrel, if one barrel is sold for $93
Two questions plz help asap. 1.what is the value of a? [tex]-2(a - 8) + 6a = 36[/tex] 2. whats the value of n[tex]\frac{3n + 6}{3} = 15[/tex]
1. What is the value of a?
-2(a - 8) + 6a = 36
Remember to follow PEMDAS. First, distribute -2 to all terms within the parenthesis
-2(a - 8) = -2a + 16
-2a + 16 + 6a = 36
Simplify. Combine like terms
6a - 2a = 4a
4a + 16 = 36
Isolate the a. Do the opposite of PEMDAS. First, note the equal sign. What you do to one side, you do to the other.
Subtract 16 from both sides
4a + 16 (-16) = 36 (-16)
4a = 36 - 16
4a = 20
Divide 4 from both sides
4a/4 = 20/4
a = 20/4
a = 5
5 is your answer for a
-------------------------------------------------------------------------------------------------------------------
2. What is the value of n in (3n + 6)/3 = 15
Remember to do the opposite of PEMDAS. Note the equal sign. First, multiply 3 to both sides
(3n + 6)/3(3) = 15(3)
3n + 6 = 45
Next, subtract 6 from both sides
3n + 6 (-6) = 45 (-6)
3n = 45 - 6
3n = 39
Finally, isolate the n. Divide 3 from both sides
3n/3 = 39/3
n = 39/3
n = 13
13 is your answer for n
-------------------------------------------------------------------------------------------------------------------
hope this helps
I have written the solution in images attached.
compare and contrast subtracting integers and subtracting whole numbers
Subtracting whole numbers does not include subtracting negative numbers, whereas when subtracting integers you can include negative numbers.
Answer:When subtracting whole numbers it is like normal addition whereas in subtraction of integers you can include any integers including negative ones
Step-by-step explanation:
A dance school allows a maximum of 15 students per class. If 112 students sing up for dance class, how many classes does the school need to offer to accommodate all the students?
The answer is 8.
In order to accommodate (or provide space for) all students, with the maximum students per class being 15, there needs to be at least enough for 112. A way to figure this out is 112 / 15 (the total amount of people signed up divided by the amount per class). The quotient is 7.466..., which does not work since you cannot have a 0.466... of a human in a class. This means you must round to the nearest whole number. If there were more students it could accommodate 8 more being that 15 * 8 is 120, but in this case there are only 112.
Hope I helped! Please give Brianliest if I did!
Please explain so i could understand
The domain is the input values ( x values).
These would be the numbers that the arrows are pointing away from.
The domain is (-2, 0 , 1, 3 , 5)
Hello!) this is math :( can you help me please?
As in the first four terms, I assume that means using the equation with 1,2,3,4.
11) if n = 1, the answer would be 3.
If n = 2, the answer would be 10.
If n = 3, the answer would be 17.
If n = 4, the answer would be 24.
12) If n = 1, the answer would be 55.
If n = 2, the answer would be 45.
If n = 3, the answer would be 35.
If n = 4, the answer would be 25.
An explicit formula is used to find any term in a sequence by putting in the number of that term in place of the unknown variable.
In order to find the first four terms, we need to plug values, from 1-4, separately in each of the formulas.
For f(n) = 7(n+1) - 11, put values from 1-4 in place of n:
f(1) = 7(1+1) - 11 = 3 ----> First term
f(2) = 7(2+1) - 11 = 10 ----> Second term
f(3) = 7(3+1) - 11 = 17 ----> Third term
f(4) = 7(4+1) - 11 = 24 ----> Fourth term
For f(n) = 65 - 10n, put values from 1-4 in place of n:
f(1) = 65 - 10(1) = 55 ----> First term
f(2) = 65 - 10(2) = 45 ----> Second term
f(3) = 65 - 10(3) = 35 ----> Third term
f(4) = 65 - 10(4) = 25 ----> Fourth term
What is the slope of the line passing through the points (0,4) and (-8,-1)
What is 2n+n equal to
Combine like terms. Note that both terms given have the same amount of variables, (n)
Combine: 2n + n = 3n
3n is your answer
hope this helps
Three consecutive odd integers have a sum of 99. Write an equation, then find the three integers.
Solve for x.
78(−32−48x)+36=23(−33x−18)−10x
Answer:
2
Step-by-step explanation:
Find the product.
6 x 500 = 6 x (blank) hundreds
= (blank) hundreds
= (blank)
**needing the “blanks” answered/solved.
The first blank should contain the number 50. The second blank should contain the number 300 which represents hundreds. Lastly, the third blank should contain the number 30,000 when converted back from hundreds.
Explanation:The original equation given is: 6 x 500. We can re-write this first in terms of hundreds as: 6 x (5,000/100) which means 6 times 50 hundreds. Hence, the first blank is 50.
Subsequently, you would find the product of 6 x 50 hundreds = 300 hundreds. Therefore, the value for the second blank is 300.
Finally, you would turn 300 hundreds back into a standard number by multiplying 300 by 100, which equals 30,000. So, the third blank would be 30,000.
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at East Middle School there 58 left hand students in 609 right-handed students the numbers of left and right handed students at West Junior High are proportional to the number at East Middle School if they're 48 left-handed students at West Junior High how many right-handed students are there
the answer is 504 because 609/58 is 10.5 and then multiply 48 times 10.5 and you get 504
Answer:
There are 504 right handed students in west junior high school.
Step-by-step explanation:
Number of left handed students in east middle school = 58
Number of right handed students in east middle school = 609
Number of left handed students at west junior high = 48
Let the number of right handed students are west junior high be = x
As given, there a a proportional relation between the two, we can denote this as:
[tex]\frac{58}{609}= \frac{48}{x}[/tex]
Now solving for x;
[tex]58x=609*48[/tex]
[tex]58x=29232[/tex]
x = 504
Therefore, there are 504 right handed students in west junior high school.
Forty-five states in a country have four-star hotels. Assume the country has 50 states. (a) What fraction of the states can claim at least one four-star hotel? (b) How many states do not have a four-star hotel? (c) Write the fraction of states without a four-star hotel.
Stanley ran a 5 kilometer race in 30 minutes. what was his speed in kilometers per hour? round to the nearest tenth
If the triangle TSR is similar to triangle TNM, what is the length of x?
Answer:
120:240, 1:2
1:2, 70:140
Answer: x=140
Step-by-step explanation:
3m-7=8 solve please NEED HELP
Solve for m.
Add 7 to both sides to get 3m=15
Then divide by sides by 3 to get m=5.
The final answer is m=5.
A fish tank that holds 80 gallons of water is 55 % full. how many gallons are in the tank now?
Answer:
[tex]44\ gallons[/tex]
Step-by-step explanation:
we know that
A fish tank holds [tex]80[/tex] gallons of water
so
By proportion
Find how many gallons represent [tex]55\%[/tex] of the total tank capacity.
[tex]\frac{80}{100}\frac{gallons}{\%} = \frac{x}{55}\frac{gallons}{\%}\\ \\x=55*80/100\\x= 44\ gallons[/tex]
There are 44 gallons of water in the tank. This is calculated by converting the percentage full into a decimal (0.55) and multiplying it by the total capacity of the tank (80 gallons).
Explanation:The question is asking how many gallons are currently in the fish tank that is 55% full and has a total capacity of 80 gallons.
First, you need to convert the percentage of the tank that is full (55%) to a decimal. To do this, you divide the percentage by 100.
So, 55 divided by 100 equals 0.55.
Next, you multiply this decimal by the total capacity of the tank to find out how many gallons are currently in the tank. 0.55 times 80 equals 44. Therefore, there are 44 gallons of water in the fish tank now.
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Approximately how many feet is in a 100-meter dash? Show your math.
1meter=3.28 feet. So multiply 100 times 3.28 and that’s your answer