Answers
1. [tex]\frac{x^3}{x^8}=x^{-5}[/tex]
2. [tex]\frac{6x}{2x^8} = 3x^{-7}[/tex]
3. [tex]\frac{28x^6}{21x^2} = \frac{4}{3}x^4[/tex]
Step-by-step explanation:
1. x^3/x^8
Given fraction is:
[tex]\frac{x^3}{x^8}[/tex]
When the bases are same in both numerator and denominator then the exponents can be added
i.e.
[tex]\frac{x^a}{x^b} = x^{a-b}[/tex]
So,
[tex]\frac{x^3}{x^8} = x^{3-8} = x^{-5}[/tex]
Part b:
[tex]\frac{6x}{2x^8}\\= \frac{3.2.x}{2.x^8}\\=\frac{3x}{x^8}\\=3x{1-8}\\=3x^{-7}[/tex]
Part c:
Given
[tex]\frac{28x^6}{21x^2}\\= \frac{7.4.x^6}{7.3.x^2}\\=\frac{4}{3} x^{6-2}\\=\frac{4}{3}x^4[/tex]
Keywords: Fractions, exponents
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Related Questions
11) Matthew goes hiking every 12 days and
swimming every 25 days. He did both kinds of
exercise today. How many days from now will he
go both hiking and swimming again?
Answers
Answer:
300
Step-by-step explanation:
12 and 25 have no common factors, so their least common multiple is their product:
12·25 = 300
Matthew will do both again in 300 days.
Ryan is trying to determine whether 2.7x – 5.9 is equivalent to 2.8x – 5.9. To test this, he substitutes 0 for x into both expressions. Explain why this will not give him the correct answer.
Answers
Answer:
read explanation
Step-by-step explanation:
This won't give him the correct answer because if he substitutes zero into anything he will get -5.9. 0 multiplied by anything is 0 and if you put that into bot equations you get the same answer so it won't help him. he should instead try 1 or something like that.
You randomly draw a marble from a bag of marbles that contains 3 blue marbles, 4 green marbles, and 5 red marbles.
What is P(draw a blue marble)?
If necessary, round your answer to 2 decimal places.
Answers
Answer:
0.25
Step-by-step explanation:
number of trial = 12
probability of getting blue marbles = 3/12
0.25
y and z are whole numbers. y<80 and z less than or equal to 70 work out the largest possible value of y+z
Answers
Final answer:
The largest possible value for y + z, with y < 80 and z ≤ 70, is 149, achieved by taking the maximum whole numbers within those limits: y = 79 and z = 70.
Explanation:
To find the largest possible value of y + z given that y is a whole number less than 80 and z is a whole number less than or equal to 70, we must choose the largest whole numbers that fit these conditions. For y, the largest whole number less than 80 is 79, and for z, the largest whole number less than or equal to 70 is 70 itself. Therefore, the largest possible value for y + z is 79 + 70.
The calculation is straightforward:
79 (maximum y) + 70 (maximum z) = 149
This is the largest sum of y + z based on the given conditions.
Factor the expression using the GCF: 15x - 25
Answers
To factor the expression 15x - 25 using the greatest common factor (GCF), divide each term by the GCF. The factored form is 5(3x - 5).
Explanation:To factor the expression 15x - 25 using the greatest common factor (GCF), we need to find the largest number that divides both terms evenly. In this case, the GCF is 5. We can then divide each term by 5 to factor out the GCF:
15x ÷ 5 = 3x
-25 ÷ 5 = -5
Therefore, the factored form of the expression 15x - 25 is 5(3x - 5).
The expression 15x - 25 is factored by finding the Greatest Common Factor, which is 5, and then dividing each term by 5 to get the factored expression 5(3x - 5).
To factor the expression using the Greatest Common Factor (GCF), we need to identify the highest number that divides both coefficients in the expression 15x - 25. In this case, both 15 and 25 are divisible by 5, so 5 is the GCF of the expression. Applying the distributive property, we factor out the GCF:
Determine the GCF: 5.Divide each term by the GCF: 15x/5 = 3x and 25/5 = 5.Write the factored expression: 5(3x - 5).Now, the expression 15x - 25 is fully factored as 5(3x - 5).
The dimensions of a rectangular prism are shown in the diagram below. Write an expression that represents the volume of the rectangular prism?
Hint: Aprism= Length x width x height
Answers
Answer:
[tex]V=(a^{4})(b^{6})\ units^3[/tex]
Step-by-step explanation:
we know that
The volume of a rectangular prism is equal to
[tex]V=LWH[/tex]
In this problem we have
[tex]L=ab^2\\W=ab^3\\H=a^2b[/tex]
substitute
[tex]V=(ab^2)(ab^3)(a^2b)[/tex]
Applying property of exponents
[tex]x^{m} x^{n}x^{r} =x^{m+n+r}[/tex]
[tex]V=(a^{4})(b^{6})\ units^3[/tex]
write a multiplication equation with one variable, and one fraction that has a solution of 8
Answers
1/2x =8
Final answer:
To create an equation yielding a solution of 8, use a variable x and the fraction 1/4. By multiplying x by 32, the equation will result in 8.
Explanation:
To write a multiplication equation with one variable and one fraction yielding a solution of 8:
Start with the fraction 1/4.
Multiply that fraction by x = 32 to get a product of 8.
When a number is decreased by 78%, the result is 16. What is the original
number to the nearest tenth?
Answers
Answer:
70
Step-by-step explanation:
16÷(100%-78%) = 16÷22% = 72.73 =70(correct to the nearest tenth)
How can you write the expression with a rationalized denominator? square root of three minus six over square root of three plus six
Answers
Answer:
[tex]- (\frac{15 - 4\sqrt{3} }{11} )[/tex]
Step-by-step explanation:
[tex]\frac{\sqrt{3}-6}{\sqrt{3} +6} = \frac{(\sqrt{3}-6)(\sqrt{3}-6)}{(\sqrt{3} +6)(\sqrt{3} -6)}[/tex]
[tex]= \frac{(\sqrt{3})^2 - (2\times6\times\sqrt{3}) +6^{2} }{(\sqrt{3})^2 - 6^{2}} = \frac{9 - 12\sqrt{3} + 36}{3 - 36}[/tex]
[tex]\frac{45 -12\sqrt{3} }{-33} =- (\frac{15 - 4\sqrt{3} }{11} )[/tex]
PLEASE HELP PLEASE HELP
List four values that would be a solution to -2x > 10. Then, in 2 to 3 complete sentences, explain how you know your four values are solutions.
Answers
Answer:
-6, -7, -8, -9
Step-by-step explanation:
-2x > 10
x < -5
So x can be -6, -7, -8, -9
Any number less than -5 is a solution.
The listed ones are the solutions because they satisfy the the inequality,
-2x > 10
x = -6, -2(-6) > 10 12 > 10
x = -7, -2(-7) > 10 14 > 10
x = -8, -2(-8) > 10 16 > 10
x = -9, -2(-9) > 10 18 > 10
Are the following like terms: 7x and 9x
Answers
Answer: Yes
Step-by-step explanation: 7x and 9x are called terms and the numbers in front of the variables, +7 and +9 are called coefficients.
Because the variables, x and x are identical, the two terms in this problem are called like terms so yes, 7x and 9x are like terms.
What steps can be used To solve 6\7x+1/2=7/8
Answers
I'm guessing you mean (6/7)x+(1/2)=7/8
Subtract 1/2 (also 4/8) from both sides: (6/7)x=3/8
Divide both sides by 6/7: x=21/48=7/16
So x is 7/16
Hope this helped!
Find the quantity represented by each percent.
1. 46% of 340 gallons
2. 65% of 180 pounds
3. 75% of 72 hours
4. 120% of $590
5. 245% of 860 kilograms
Answers
2) 180•0.65 = 117 pounds
3) 72•0.75= 54 hours
4) 590•1.20= $228
5) 860•2.45=2107 kg
A single die is rolled twice. The 36 equally-likely outcomes are shown to the right.
Find the probability of getting two numbers whose sum is 4.
Answers
Answer:
1/12
Step-by-step explanation:
There are 3 ways to get two numbers whose sum is 4:
1 and 3, 2 and 2, and 3 and 1
So the probability is 3/36 = 1/12.
The simple interest due on a six month loan of $2500 is $125. What is the monthly payment of the loan?
Answers
The monthly payment of the loan is =$ 437.5
Step-by-step explanation:
Given , the simple interest due on a six month loan of $2500 is $125.
Total amount he paid =$ (2500+125)
=$2625
The monthly payment of the loan is =$(2625÷6)
=$ 437.5
The profits for video game companies depend on what game platform the game runs on, which can either be a portable system (p) with a built in screen, or a standard system (s) that you have to hook up to a television. The profit off of a portable game system is $72, while the profit from a standard game system is $90. The store manager has to make at least $360 per day in order to keep the store open. Which graph represents this inequality? Write the inequality that represents the number of games that must be sold everyday to meet or beat the sales goal.
Answers
To meet or beat the sales goal, the inequality 72x + 90y ≥ 360 can be used to represent the number of games that must be sold every day. The graph of this inequality would show the region above or on the line 72x + 90y = 360.
To meet or beat the sales goal of at least $360 per day, we can set up an inequality based on the profits from selling games. Let x be the number of portable game systems sold and y be the number of standard game systems sold. The inequality representing the number of games that must be sold every day is 72x + 90y ≥ 360.
To graph this inequality, we can plot the points on a graph where each point represents a combination of x and y. Then we shade the region that satisfies the inequality, which is the region above or on the line 72x + 90y = 360.
See the graph in the attached image for visual representation.
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William has 24 24 cans of fruit and 60 60 cans of vegetables that he will be putting into bags for a food drive. He wants each bag to have the same number of cans of each type of food. He uses all the cans.how much of each of this bigs will have and how much cans of fruitwill they have and how much cans of vegetables will they have
Answers
Answer:
William will make 12 bags of food and each of the bag will contains 2 cans of fruit and 5 cans of vegetables.
Step-by-step explanation:
Given:
Number of fruits cans = 24
Number of veggies cans = 60
William will have to distribute them in equal bags with equal cans of fruits and vegetables respectively.
For this:
We have to find the GCF (greatest common factor) of 24 and 60.
GCF by listing out the factors method.
Factors of 24 : [tex]1,2,3,4,6,8,12,24[/tex]
Factors of 60 : [tex]1,2,3,4,5,6,10,12,15,20,30,60[/tex]
So,
The greatest common factor of [tex]24[/tex] and [tex]60[/tex] is [tex]12[/tex].
The number of bags William will used for equal distribution = [tex]12[/tex]
Now,
We have to distribute the veggies and fruits in equal number of cans to these [tex]12[/tex]bags.
Number of fruits cans used in each bag = [tex]\frac{24}{12} = 2[/tex]
Number of vegetables can used in each bag = [tex]\frac{60}{12} =5[/tex]
We can say that:
William will make 12 bags of food and each of the bag will contains 2 cans of fruit and 5 cans of vegetables.
Final answer:
By computing the greatest common divisor (GCD) of 24 and 60, it is determined that William can create 12 equal bags with each bag having 2 cans of fruit and 5 cans of vegetables.
Explanation:
The student is asking how to divide 24 cans of fruit and 60 cans of vegetables into bags such that each bag contains the same number of cans without any leftovers. This requires finding the greatest common divisor (GCD) of 24 and 60, which is 12. Therefore, William can make 12 bags, with each bag containing 2 cans of fruit and 5 cans of vegetables.
the sum of twice a number and 4 times another number is 4. the first number decreased by the second number is 5. Find the numbers
Answers
The two numbers being asked in the question are 4 and -1.
Explanation:This question can be solved using a system of linear equations. Let's call the first number x and the second number y.
From the first statement, we can create one equation: 2x + 4y = 4
From the second statement, we can create another equation: x - y = 5
To solve this system, we can use substitution or elimination method. If we multiply the second equation by 2, we get 2x - 2y = 10. Now, we can subtract the second equation from the first: (2x + 4y) - (2x - 2y) = 4 - 10, which simplifies to 6y = -6. Dividing both sides by 6, we get y = -1.
Substitute y = -1 into the equation x - y = 5, we get x - (-1) = 5. Therefore, x = 5 - 1 = 4.
So, the first number x is 4 and the second number y is -1.
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Can someone plz help me with this I am in “confusion”.
Answers
Answers are 1. a = 32, b = 2, 3. c = 4, 4. x = -3, 5. y = -7, 6. z = -2, 7. m = -7, 8. n = -4, 9. s = -3, 10. r = 5, 11. t = 3, 12. p = 2, 13. x = 9, 14. w = 6, 15. g = 1.5, 16. v = -16, 17. b = -6, 18. h = -5, 19. k = -2.5, 20. d = -3.5, 21. r = -8, 22. z = -9, 23. x = -7, 24. y = 3.5, 25. y = 9, 26. w = 8.
Step-by-step explanation:
Step 1; To solve the given equations we keep the unknown variable on one side while the known numbers are taken to the other side. If both sides are negative the answer has a positive value while if one side is positive and one side is negative, the answer is negative.
Step 2; Solve
1. a = 9/3= 3,
2. b = 14/7 = 2,
3. c = 36/9 = 4,
4. x = -15/5 = -3,
5. y = 28/-4 = -7,
6. z = -16/8 = -2,
7. m = 28/-4 = -7,
8. n = 8/-2 = -4,
9. s = -21/7 = -3,
10. r = -25/-5 = 5,
11. t = -18/-6 = 3,
12. p = -18/-9 = 2,
13. x = 18/2 = 9,
14. w = 24/4 = 6,
15. g = 9/6 = 1.5,
16. v = -32/2 = -16,
17. b = -18/3 = -6,
18. h = -35/7 = -5,
19. k = 20/-8 = -2.5,
20. d = 14/-4 = -3.5,
21. r = -72/9 = -8,
22. z = 27/-3 = -9,
23. x = -35/5 = -7,
24. y = 28/8 = 3.5,
25. y = 81/9 = 9,
26. w = 16/2 = 8.
Enter the number
15.666666666667 rounded to the nearest hundredth (two decimal places):
Answers
Answer: 15.67
Step-by-step explanation:
Pot Santa
Answer:
15.67
Step-by-step explanation:
focus only on the underlined area
15.666666666667
round the last 6 underlined is what we are going to use to round the one before it
5 or more goes up so the six is now rounded to a seven on that part leaving you with 15.67
What is the definition of unit?
Answers
Answer:
an individual thing or person regarded as single and complete but which can also form an individual component of a larger or more complex whole
Which of the following are quadratic equations
(i) (P + 1) (P + 2) (P+4) (ii) (x + 2)(square)= 7
(iii) k +2/5 - 5 = 0 (iv) M(square)– 1 = 0
(v) (x – 3)(cube) + 4 = 0
Answers
Answer:
(ii) (x+2)²=7(iv) M²-1 = 0HOPE U UNDERSTOOD★THANKS★
ANY DOUBTS? COMMENT PLEASE
Mother ordered 4 boxes of cupcakes for John's birthday party. As they had more guests than expected, mother ordered 2 more similar boxes of cupcakes. How many cupcakes did each box contain, if there were in total 108 cupcakes for John's birthday party?
Answers
Answer:
each box contained 18
Step-by-step explanation:
because 108 divided by the total number of boxes = 18
Final answer:
To determine how many cupcakes were in each of the 6 boxes for John's party with a total of 108 cupcakes, simply divide 108 by 6, resulting in 18 cupcakes per box.
Explanation:
The question asks us to determine how many cupcakes each box contained if there were a total of 108 cupcakes for John's birthday party, and 6 similar boxes were ordered in total. To find the answer, we divide the total number of cupcakes by the total number of boxes.
First, we know that the mother ordered 4 boxes initially and then ordered 2 more boxes, which gives us a total of 4 + 2 = 6 boxes. Then, we are given the total number of cupcakes, which is 108. To find out how many cupcakes each box contained, we divide the total number of cupcakes by the number of boxes:
108 cupcakes ÷ 6 boxes = 18 cupcakes per box
Therefore, each box contained 18 cupcakes.
The graph of a linear function is shown.
A coordinate plane with a straight line. The line starts at (negative 5, negative 1) and continues up and to the right passing through (0, 0) and (5, 1).
Which word describes the slope of the line?
positive
negative
zero
undefined
Answers
See picture for answer and explanation.
We can completely define a line equation by only knowing two points on the line, so we will use that to find our line's slope.
The slope is positive. (We will see that the slope is equal to 1/5).
The first general rule is that, if the line, readen from lest to right increases, then the slope is positive. (Here by the description we know that it increases).
But let's find the slope to see this.
If we know that the line passes through two points (x₁, y₁) and (x₂, y₂) then we can write the slope as:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we can use two of the given points to find the slope, I will use the first two: (-5, -1) and (0, 0)
We will get:
[tex]a = \frac{0 - (-1)}{0 - (-5)} = \frac{1}{5}[/tex]
So the slope is 1/5, which is positive.
Then the correct option is the first one.
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What is 3x 2/7 as a fraction
Answers
Answer: 3 2/7
Step-by-step explanation: Your answer would normally be 23/7. Just round and you should get 3 2/7. Also there is a fraction calculator online you could use, it shows you how to work out any problem dealing with fractions. Hope I have helped!
The value of 3 × 2/7 as a fraction is 6/7.
What is a fraction?A fraction describes some part of the total amount. Fractions are of two types one is a proper fraction and another is an improper fraction.
We know a fraction can be written as a form of p/q, where q ≠ 0.
p is the numerator and d is the denominator.
Given 3 × 2/7, we know 3 = 3/1 as every integer can be written as a rational number.
∴ 3/1 × 2/7
= 6/7.
We have to simply multiply the numerator with the numerator and the denominator with the denominator.
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A triangular prism has a base area or 20 square feet and a height of 4 feet. What’s the volume
Answers
Answer:
Just multiply four times twenty and youll get your answer
See picture for solution to your problem.
A Physician instructs a patient with an ulcer to start Tagamet HB (OTC) 200mg tablets BID PO For 14days.
How many tablets are needed to fill this RX?
Answers
Answer:
28
Step-by-step explanation:
2 pills for 14days=28 pills in total
Solve by substitution:
2x+6y=16
3x-5y=-18
Answers
Answer:
Step-by-step explanation:
y= 16
x=15
Using the substitution method,
The value of x is -1 and y is 3.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 8 is an equation.
We have,
2x + 6y = 16 _____(1)
3x - 5y = -18 ______(2)
From (1) we get,
2x = 16 - 6y
x = (16 - 6y)/2
Substituting in (2).
3x - 5y = -18
3 x (16 - 6y)/2 ) - 5y = -18
3 x (8 - 3y) - 5y = -18
24 - 9y - 5y = -18
24 + 18 = 9y + 5y
42 = 14y
y = 42/14
y = 3
And,
x = (16 - 6y)/2
x = (16 - 6 x 3) / 2
x = (16 - 18) / 2
x = -2/2
x = -1
Thus,
x = -1 and y = 3.
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the nutritional label on a carton of soy milk says that one glass contains 7 grams of protein. How many miligrams of proten does one glass contain?
Answers
Answer:
700 milligrams of protein is contained in one glass.
Step-by-step explanation:
Given:
Protein present in on glass of soy milk = 7 grams
To Find:
How many milligrams of protein does one glass contain =?
Solution:
We have to convert grams to milligrams
We know that 1 gram = 100 milligram
then 7 grams will be = [tex]7 \times 100[/tex] milligrams
7 grams = 700 milligrams
Therefore in one glass of soy milk there will be 700 milligrams of proteins
Expand.
If necessary, combine like terms.
(4x + 1)(4x + 1) =
Answers
Answer: 16x² + 8x + 1
Step-by-step explanation:
(4x + 1)(4x + 1)
This expansion can be done in two ways either by direct expansion or by indirect expansion
(1) Direct expansion
(4x + 1)(4x + 1 )
4x X 4x + 4x X 1 + 1 X 4x + 1 X 1
= 16x² + 4x + 4x + 1
= 16x² + 8x + 1
(2) Method
This can be written thus:
(4x + 1 )(4x + 1 ) = (4x + 1 )²
= (4x)² + 2( 4x X 1 ) + 1²
= 16x² + 2(4x) + 1
= 16x² + 8x + 1.
(4x + 1)(4x + 1)
4x · 4x = 16x²
4x · 1 = 4x
1 · 4x = 4x
1 · 1 = 1
16x² + 4x + 4x + 1
16x² + 8x + 1