Answer:
The given Expression is
[tex]4\sqrt{16x^4y^12[/tex]
= 4 × terms under square root are non negative.so we can break it into different terms.
= 4 × √16 ×[tex]\sqrt{x^4}\times\sqrt {y^{12}}[/tex]
Breaking into factors
= 4 × [tex]\sqrt{2\times2\times\times2\times2 } \times\sqrt{x \times x \times x \times x } \times \sqrt{ y \times y \timesy \times y \timesy \times y \times y \times y \times y \times y \times y \times y \times y \times y[/tex]
= 4× [tex]2 \times2 \times x \times x \times y\times y\times y\times y\times y\times y[/tex]
= 16× [tex]x^{1+1}\times y^{1+1+1+1+1+1}[/tex]
= 16 [tex]x^2 y^6[/tex]
The solution of the expression 4√(16x⁴y¹²) will be 16x²y⁶.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
The given expression is 4√(16x⁴y¹²). The expression will be solved as:-
E = 4√(16x⁴y¹²)
E = 4 √ [( 4 x 4 ) ( x² x x² ) ( x⁶ x x⁶ )]
E = 4 ( 4 x x² x y⁶ )
E = 16x²y⁶.
Therefore, the solution of the expression 4√(16x⁴y¹²) will be 16x²y⁶.
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What value of x would make the expression -12 + 84 equal to zero?
Solution is given in attachment below.
Ou are driving to visit a friend in another state who lives 440 miles away. You are driving 55 miles per hour and have already driven 275 miles. Write and solve an equation to find how much longer in hours you must drive to reach your destination.
Jerry is a judge. He hears 5 cases in 2 3/8 hours. How many cases does he hear per hour
Answer:
Jerry does [tex]2.11[/tex] cases per hour (Rounded to 2 decimal places). As we cannot do 0.11 cases. We can say Jerry does 2 cases per hour.
Step-by-step explanation:
to find the number of cases per hour, we have to divide the number of cases by number of hours taken for those cases,
Number of cases per hour = [tex]\frac{5cases}{2\frac{3}{8} hours}[/tex]
=[tex]\frac{5}{\frac{19}{8} } \\[/tex] cases per hour
=[tex]\frac{5*8}{19}[/tex] cases per hour
=[tex]\frac{40}{19}[/tex] cases per hour
=[tex]2.11[/tex] cases per hour (Rounded to 2 decimal places)
As we cannot do 0.11 cases. We can say Jerry does 2 cases per hour.
Suppose 255,113 people live in a city. Is it reasanoble to say that about 300,000 people live in the city? Use the number line to help you solve the problem. Explain.
Jayden bought a slice of pizza for $1.25, a box of popcorn for $0.75, and a drink for $0.60. If he paid with a 5-dollar bill, how much change should he get?
Victor baked 30 chocolate chip cookies, 18 peanut butter cookies, and 24 sugar cookies. He wants to split them into equal identical bags to sell at the bake sale. What is the greatest number bags of cookies Victor can make?
Answer:
6
Step-by-step explanation:
The greatest common factor (GCF) of 18, 24, and 30 is 6.
Victor can make at most 6 bags with equal numbers of each type of cookie.
_____
18 = 6×3
24 = 6×4
30 = 6×5
One way to look for the GCF is to consider the differences between the numbers. The smallest difference between any pair is 6, which also divides all of the numbers evenly. Hence 6 is the GCF.
By finding the greatest common divisor (GCD) of the counts of each type of cookie (30, 18, 24), it is determined that Victor can make 6 identical bags for the bake sale.
Explanation:To determine the greatest number of bags Victor can make, we need to find the greatest common divisor (GCD) of the counts of each type of cookie: 30 chocolate chip cookies, 18 peanut butter cookies and 24 sugar cookies. The GCD is the largest number that exactly divides all these counts.
First, list the divisors of each number:
Divisors of 30: 1, 2, 3, 5, 6, 10, 15, 30 Divisors of 18: 1, 2, 3, 6, 9, 18 Divisors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Find the highest number that appears in each list. The highest common factor of 30, 18, and 24 is 6, so Victor can make a total of 6 equal bags with each type of cookie.
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Use the Law of Sines to find the missing angle of the triangle.
Find m∠C to the nearest tenth.
Answers
C = 58.84
B = 97.16°
Explanation
The sine rule states:
SinA/a = sinB/b
∴ sin24 / 77 = sinC / 162
sinC = (162 × sin24)/77
= 65.89/77
= 0.85573
C = 58.84°
Angles in a triangle add up to 180°
∴ B + 24 + 58.84 = 180
B = 180 - 24 - 58.84
= 180 - 82.84
= 97.16°
=
Using the Law of Sines, which states that the ratio of a side length to the sine of its opposite angle is the same for all sides, you can solve for the missing angle. Rearrange the formula to sinC = c * sinA / a, then take the inverse sine of both sides to find the measure of the missing angle.
Explanation:To find the missing angle m∠C using the Law of Sines, you first need to know the lengths of the sides of the triangle and one of the angles. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all three sides of the triangle. In other words, if a, b, and c represent the lengths of the sides and A, B, and C represent the measures of the opposite angles, we have: sinA/a = sinB/b = sinC/c.
To solve for m∠C, you rearrange the Law of Sines to: sinC = c * sinA / a. After that you take the inverse sine (or arcsin) of both sides to find m∠C = arcsin(c * sinA / a). Notice that you are assuming that the sine of the missing angle is positive, which is valid for angles less than 180 degrees.
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the temperature dropped from 80°F to 70°F. what is the percent drop in temperature?
Final answer:
The percent drop in temperature from 80°F to 70°F is calculated as (10°F / 80°F) × 100%, which equals 12.5%.
Explanation:
To find the percent drop in temperature from 80°F to 70°F, we need to calculate the decrease in temperature and then express that decrease as a percentage of the original temperature. The decrease in temperature is 80°F - 70°F = 10°F. To find the percent drop, we use the formula for percentage change, which is (Change/Original) × 100%.
Therefore, the percent drop = (10°F / 80°F) × 100% = 12.5%. So, the temperature dropped by 12.5% from 80°F to 70°F.
Final answer:
To find the percent drop in temperature from 80°F to 70°F, calculate the difference between the temperatures and divide by the original temperature, then multiply by 100%. The result is a 12.5% decrease in temperature.
Explanation:
The question asks to find the percent drop in temperature when it drops from 80°F to 70°F. To calculate this, we use the formula for percent decrease, which is (original value - new value) / original value × 100%. Applying this formula, the original temperature is 80°F, and the new temperature is 70°F.
(80°F - 70°F) / 80°F × 100% = 10°F / 80°F × 100% = 0.125 × 100% = 12.5%.
Therefore, the temperature dropped by 12.5% when it fell from 80°F to 70°F.
Which of the given expressions results in 0 when evaluated at x = 5?
A. 5x(x-7)
B. (x-8)(x-5)
C. (x+7)(x-2)
D. (x+5)(x-8)
Answer:
B. (x-8)(x-5).
Step-by-step explanation:
Given : Equations .
To find : Which of the given expressions results in 0 when evaluated at x = 5.
Solution : We have given equations
We need the result zero.
We can see from the given equation (x-8) (x-5)
If we plug x = 5.
(5 -8 )( 5 -5).
-3 (0).
0. ( multiply with zero to any number it will always be zero )
Therefore, B. (x-8)(x-5).
When solving inequalities with multiple operations, addition and subtraction are undone before multiplication and division.
True
False
Please help asap 25 pts
Today is Tony's 10th birthday. His parents have decided to start giving him a monthly allowance, but they suggest a different plan.
Tony's mother wants to give him $0.01 each month this year, $0.10 each month next year, $1.00 each month the third year, and so on multiplying the monthly amount by 10 each year until Tony's 16th birthday.
Tony's father wants to give him $10.00 each month this year, $20.00 each month next year, $30.00 each month the third year and so on, adding $10.00 to his monthly allowance each year until his 16th birthday.
Which deal is better his mom or his dad and why is it the best one?
There are 20 cards labeled from 1 to 20 in a bag. A card is randomly selected from the bag.
What is the probability of getting an even number or a 1?
9/20
11/20
1/2
3/5
Answer:
option 2=11/20 is the answer.
Step-by-step explanation:
given that there are 20 cards numbers 1,2... 20.
A card is randomly drawn.
We have to find the probability of drawing either 1 or even card.
P(drawing even card) = no of even cards/total cards = 10/20= 0.5
P(drawing one) = no of 1's/total cards = 1/20 = 0.05
P(drawing both one and even card) = 0 (since impossible)
Hence P(drawing even or one) =0.5+0.05-0
=0.55
= 11/20
Hence option 2 is the answer.
Answer : 11/20
There are 20 cards labeled from 1 to 20 in a bag. A card is randomly selected from the bag.
Total number of outcomes = 20
outcomes of an even number ={2,4,6,8,10,12,14,16,18,20}
So number of outcomes of even number = 10
outcomes of a 1 ={1}
So number of outcomes of a 1 = 1
Number of outcomes of even number and a 1 = 10+1 = 11
Probability ( any event) =number of favorable outcomes divide by total number of outcomes
Probability (getting an even number or a 1) = [tex]\frac{11}{20}[/tex]
What is the value of the underlined digit 783,549,201 the number 4 in 549
Samantha has 23 strawberries and wants to put 4 strawberries into each bowl. How many bowls can samantha put exactly 4 strawberries into?
Which expression represents x2−12x+36 in factored form? (x−4)(x−9) (x+6)2 (x+6)(x−6) (x−6)2
Two factors of x²-12x+36 are
(x-6) and (x-6)
Solution;
x²-12x +36
x²-6x -6x +36 ( split -12x in two parts such that if add them we will get-12x and if multiply will get 36x²)
Taking x common from first two terms and 6 from next two terms
x(x-6) -6(x -6)
taking (x-6) common
(x-6)(x-6)
Answer:
[tex]x^2 - 12x + 36 = (x-6)(x-6) = (x-6)^2[/tex]
Step-by-step explanation:
We are given the following expression:
[tex]x^2 - 12x + 36[/tex]
We need to factor the given expression.
We will do this with the help of technique of splitting the middle term.
Factorization can be done as:
[tex]x^2-12x + 36\\=x^2 - 6x-6x+36\\=x(x-6)-6(x-6)\\=(x-6)(x-6)\\=(x-6)^2[/tex]
Thus, the factored form of given expression is:
[tex]x^2 - 12x + 36 = (x-6)(x-6) = (x-6)^2[/tex]
MATTTTTTTTTTTTTTTTHHHHHHHH , i neeed help
A rectangular garden has an area of 80m^2. Its length is 2 meters longer than its width. How much fencing is needed to enclose the garden?
a.36meters
b.54meters
c.24meters
d.18meters
e.40meters
The fencing that is needed to enclose the garden is 36 meters.
Let the width be represented by x.
Let the length be represented by x+2.
The area is given as 80m².
Therefore, the length and width will be calculated thus;
x(x + 2) = 80
x² + 2x - 80 = 0
x² + 10x - 8x - 80 = 0
x(x + 10) - 8(x + 10) = 0
x - 8 = 0
x = 8
The width is 8 meters and the length is 10m.
The perimeter will be:
= 2(8m + 10m)
= 2 × 18m
= 36m
In conclusion, the correct option is 36 meters.
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If you know 12×24=288,how can you find 1.2×2.4?
If 12*24=288 then your answer for 1.2*2.4=2.88
If it's wrong let me know and I'll help again.
Answer: It would be 2.88
Step-by-step explanation:
There are 30 blue balls, 40 red balls, and 30 white balls in a bag of balls. What is the conditional probability of choosing a blue ball, given that a white ball was not chosen?
Answer: So, the probability will be
[tex]P( \text{getting a blue ball })=\frac{30}{70}=\frac{3}{7}[/tex]
Step-by-step explanation:
Since we have given that
Number of blue balls =30
Number of red balls = 40
Number of white balls = 30
Since there are 100 balls in total ,
As we have given that there is no white ball chosen.
So, only 70 balls are left with us , from which we choose a blue ball
So, the probability will be
[tex]P( \text{getting a blue ball })=\frac{30}{70}=\frac{3}{7}[/tex]
The conditional probability of picking a blue ball given that a white ball was not picked is 0.43. This is calculated by dividing the number of blue balls by the total remaining balls after excluding the white balls.
Explanation:To solve this question, we need to understand the concept of conditional probability. Given that we have 30 blue balls, 40 red balls, and 30 white balls, we have a total of 100 balls in the bag. The problem states that a white ball was not chosen. From that, we have eliminated the 30 white balls from the total, leaving us with 70 balls (30 blue and 40 red).
In the case of the conditional probability of choosing a blue ball, given that a white ball was not chosen, we are just focused on the remaining 70 balls. So, the probability is calculated by dividing the number of blue balls by the total remaining balls. Hence, the conditional probability is 30/70 = 0.43 (approximately).
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Question 1)
The function g is defined by g(y)=2y+7
What is the value of g(8)
A)35
B)23
C)17
Question 2)
You are at a concert and the seating area is shown below. Using a standard rule of thumb, estimate the attendnce (to the nearest whole person)
(See Image)
A)367,500 People
B)245,000 People
C)183,750 People
D)147,000 People
Question 3)
You are at a concert and the seating area is shown below. Suppose you think each person takes up 2 square feet, estimate the attendance (to the nearest whole person)
(See Image)
A)367,500 People
B)245,000 People
C)183,750 People
D)147,000 People
Answer:
1. Option B.
2. Option D.
3. Option C.
Step-by-step explanation:
(1)
The given function is
[tex]g(y)=2y+7[/tex]
Substitute y=8 to find the value of g(8).
[tex]g(8)=2(8)+7=16+7=23[/tex]
The value of g(8) is 23. Therefore, the correct option is B.
(2)
Area of a rectangle is
[tex]Area=length\times width[/tex]
From the given figure it is clear that the length of the seating area is 700 ft and width of the seating area is 525 ft.
The total seating area is
[tex]Area=700\times 525[/tex]
[tex]Area=367500[/tex]
The seating are is 367500 ft².
According to the “rule of thumb,” circulation Area comprises roughly 25 to 40% of the total Usable Area.
40 % of total area is
[tex]367500\times \frac{40}{100}=147000[/tex]
Using a standard rule of thumb the attendance is 147,000 People.
Therefore, the correct option is D.
(3)
Each person takes up 2 square feet. Then the total number of persons is
[tex]People=\frac{367500}{2}[/tex]
[tex]People=183750[/tex]
Therefore, correct option is C.
Which of the following is the correct notation for the complex number 93+√-75?
A) 93+5√3
B) 93+5i√3
C) 93+3i√5
D) 93-3i√5
Which of the following statements are equivalent to the statement "price decreased by 1/3"?
Choose ALL correct answers-
(A) The price doubled
(B) The price is 150% of the price before
(C) The price was reduced by a quarter
(D) The price became a half of what it was before
(E) The price is now 1.5 of what it was before
(F) The price now is 66 2/3 % of what it was before
(G) The price now is 200% of what it was before
(H) The price is 75% of what it was before
Using proportion concepts, it is found that the equivalent statement is:
(F) The price now is 66 2/3 % of what it was before
The statement is:
"price decreased by 1/3"
It decreases by 1/3, thus it is [tex]\frac{2}{3} = 0.6667 = 66\frac{2}{3}\%[/tex] of what was before, which means that the equivalent statement is given by option F.
As for the other statements, they do not have the correct percentage or ratio, which we found above.
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Simplify x + 3x – 36.
A) 3x – 36
B) 3x2 – 36
C) 4x – 36
D)4x2 – 36
ANSWER: C) 4x-36
Hey there!!
Equation Given : x + 3x - 36
In order to solve this, we will need to combine the like terms.
What are like terms?
Like terms are terms which have the same variable, in the equation given, the variable mentioned is x and hence, the like terms are x and 3x.
Now, we will need to combine x and 3x.
Let's take x as 1x and 3x as 3x.
Now, we will need to add both these like terms.
1x + 3x
x will be common, we will need to add 1 and 3
1 + 3 is 4 and hence, 1x + 3x = 4x
Hence, the final equation would be :
4x - 36
Hence, the answer is option ( c )
Hope my answer helps!
Answer:
4x-36 C
Step-by-step explanation:
Commutative property of addition for 5x+20+3x+9x+7
Answer:
The commutative property lets you group like terms together:
... 5x +3x +9x +20 +7
Step-by-step explanation:
If we divide the expression into 4 groups:
...[5x] +(20) +(3x +9x) +[7]
according to the commutative property of addition, we can swap the groups in curved parentheses.
... [5x] +(3x +9x) +(20) +[7]
_____
The distributive property lets you combine x terms:
... (5 +3 +9)x +27
... 17x +27 . . . . . . the simplified form of the expression
The number of seconds in a 40-hour work week can be calculated as follows:
40hrs*60mins/1hr=2400mins
2400mins*60secs/min=144,000secs
First we can calculate how many seconds there are in an hour:
Since 1 hour has 60 minutes and each minute has 60 seconds.
Then 1 hour = 60 minutes * 60 seconds/1minute = 3,600 seconds.
Now we have to multiply x 40 to calculate how many seconds there are in 40 hours.
In a 40-hour work week = 40 hours * 3,600 seconds/1hour = 144,000 seconds
Answer : 144,000 seconds there are in a 40-hour work week
Hope this helps!
[tex]\textit{\textbf{Spymore}}[/tex]
What is the value of the expression given below?
(5+3i) - (5+3i)(5-5i
Solution:
The given complex expression is,
→(5+3 i) - (5+3 i)(5-5 i)
Keep in mind, i=√-1, i²= -1
=(5 + 3 i)[1- (5-5 i)]
=(5 + 3 i)[1-5+ 5 i]
= (5 + 3 i)[-4 + 5 i]
=5 × (-4 + 5 i) + 3 i×(-4 + 5 i)→→Used the identity, (a+b)×(c+d)=a×(c+d)+b×(c+d), Also Used distributive property of multiplication over addition and subtraction.
= -20 + 25 i-12 i +15 i²
= - 20 + 13 i-15
= -35 + 13 i
On friday 2 1/3 was used on saturday 1 1/5 was used how many more gallons was used on friday
Answer:12/4
Step-by-step explanation:
PLEASE HELP QUICK
1) If you conduct an experiment and randomly pull a card from a deck of cards 10,000 times, getting a Queen of Hearts 187 times, what is the experimental probability of drawing a Queen of Hearts the next time?
2) If a kicker has kicked a ball 479 times for the extra point and scored the point 449 times, what is the experimental probability of the kicker making the next field?
1) The probability of getting a queen is 187/10000 which is 0.0187 = 1.87%
2) The probability is 449 / 479 which is 0.937 = 93.7%
You may need to round the answers. It doesn't say if they need to be rounded or not.
Hi ShadowHawk,
1) If you conduct an experiment and randomly pull a card from a deck of cards 10,000 times, getting a Queen of Hearts 187 times, what is the experimental probability of drawing a Queen of Hearts the next time?
187/10,000 = 1.87% = 1.9%
2) If a kicker has kicked a ball 479 times for the extra point and scored the point 449 times, what is the experimental probability of the kicker making the next field?
449/479 = 93.7% = 94%
Avery water bottle holds 28 mm Sean's container holes 3/4 as much water how many millimeters of water do both contain hold
-QUICK PLEASE-
Question: The table below shows the number of times the dishwasher was used in three different houses over three days.
-On Friday, 17.5 total gallons of water were used. On Saturday, 31.5 total gallons were used. On Sunday, 24.75 total gallons were used. What is the difference between the water use per load of the dishwasher that uses the most water and the dishwasher that uses the least water?
A. 0.5 gallon
B. 0.75 gallon
C. 3 gallons
D. 4 gallons
WILL MARK BRAINLIEST! Picture below.
Answer:
Option B. 0.75 gallons is the right answer.
Step-by-step explanation:
Let the load of dishwasher used in house A = x gallons
Let the load of dishwasher used in house B is = y gallons
and similarly we assume for house C = z gallons
Now from the given question
On Friday amount of water used in all three houses = 17.5 gallons
From the table we will make the equation
x + 2y + 2z = 17.5-----(1)
For Saturday
2x + 3y + 4z = 31.5 ----(2)
For Sunday
2x + 2y + 3z = 24.75 -----(3)
By subtracting equation 3 from 2
y + z = 31.5 - 24.75 = 6.75 ------(4)
Equation (1) multiplied by 2 - equation (2)
2×(x + 2y + 2z) - (2x + 3y + 4z) = 17.5×2 - 31.5
y = 35 - 31.5 = 3.5
By putting y = 3.5 in the equation (4)
z = 6.75 - 3.5 = 3.25
By putting y = 3.5 and z = 3.25 in the equation (1)
x + 7 + 6.5 = 17.5
x = 17.5 - 13.5 = 4
Now the difference between load of dishwasher that uses least water and the most.
x - z = 4 - 3.25 = 0.75 gallons
Option B is the right answer.
Answer:
Option B. 0.75 gallons is the right answer.
Step-by-step explanation:
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