Option A
[tex]\left(y^{\frac{4}{3}} \cdot y^{\frac{2}{3}}\right)^{\frac{-1}{2}} = \left(y^{2}\right)^{\frac{-1}{2}}[/tex]
Solution:
Given expression is:
[tex]\left(y^{\frac{4}{3}} \cdot y^{\frac{2}{3}}\right)^{\frac{-1}{2}}[/tex]
Product of powers property:
The product of powers property tells us that when you multiply powers with the same base you just have to add the exponents
Which is represented as,
[tex]a^m.a^n = a^{m+n}[/tex]
Therefore, the given expression becomes,
[tex]\left(y^{\frac{4}{3}+\frac{2}{3}}\right)^{\frac{-1}{2}}[/tex]
Now add the exponents, we get
[tex]\left(y^{\frac{4+2}{3}}\right)^{\frac{-1}{2}}[/tex]
Simplify the above expression
[tex]\left(y^{\frac{6}{3}}\right)^{\frac{-1}{2}}[/tex]
Simplify the exponent of y, we get
[tex]\left(y^{2}\right)^{\frac{-1}{2}}[/tex]
Thus Option A is correct
Answer:
The answer is A
Step-by-step explanation:
A gift basket that contains jars of jam and packages of bread mix costs $45. There are 8 items in the basket. Jars of jam cost $6 each, and packages of bread mix cost $5 each. Write and solve a system of linear equations to find the number of jars of jam and the number of packages of bread mix in the gift basket.
5 jars of jam and 3 packages of bread mix are in gift basket
Solution:
Let "x" be the number of jars of jam
Let "y" the number of packages of bread mix
Cost of 1 jars of jam = $ 6
Cost of 1 package of bead mix = $ 5
There are 8 items in the basket
Therefore,
number of jars of jam + number of packages of bread mix = 8
x + y = 8 ---------- eqn 1
A gift basket that contains jars of jam and packages of bread mix costs $45
Therefore, we frame a equation as:
number of jars of jam x Cost of 1 jars of jam + number of packages of bread mix x Cost of 1 package of bead mix = 45
[tex]x \times 6 + y \times 5 = 45[/tex]
6x + 5y = 45 --------- eqn 2
Let us solve eqn 1 and eqn 2
From eqn 1,
x = 8 - y --------- eqn 3
Substitute eqn 3 in eqn 2
6(8 - y) + 5y = 45
48 - 6y + 5y = 45
y = 48 - 45
y = 3Substitute y = 3 in eqn 3
x = 8 - 3
x = 5Thus 5 jars of jam and 3 packages of bread mix are in gift basket
This table gives a (x,y) pairs of a line in the coordinate plance
Simplify 3(4x + 2) - 6x
6-6x
6x+6
2-6x
6x+2
3(4x + 2) - 6x
12x + 6 - 6x
6x + 6
Hope this helps! ;)
Answer:
The correct answer is B. 6x + 6
Step-by-step explanation:
Let's simplify the expression, this way:
3(4x + 2) - 6x
12x + 6 - 6x
6x + 6
After solving the parenthesis, multiplying, adding and subtracting, the correct answer is B. 6x + 6
What is the solution to the system of equations? 6x-3y=3 and y=2x-4
Answer:
empty set or have no soln
Step-by-step explanation:
Answer:
Step-by-step explanation:
y = 2x + 4....this is just a matter of substitution...so sub in 2x + 4 for y back into the other equation
6x - 3y = 3
6x - 3(2x + 4) = 3......distribute the -3 thru the parenthesis
6x - 6x - 12 = 3 ...combine like terms
-12 = 3 (incorrect)
these equations have NO SOLUTION because they are parallel lines
A circle of center (a, o) passes through the point (o, -a) find it equation
Answer:
(x -a)^2 + y^2 = 2a^2
Step-by-step explanation:
The equation of a circle with center (h, k) and radius r is ...
(x -h)^2 +(y -k)^2 = r^2
Here r^2 is the square of the distance between the center and the point on the circle. That can be found using the distance formula:
d^2 = r^2 = (x2-x1)^2 +(y2 -y1)^2 = (0-a)^2 +(-a-0)^2 = 2a^2
Filling in the above formula with (h, k) = (a, 0) and r^2 = 2a^2, we find the equation to be ...
(x -a)^2 +y^2 = 2a^2
Simplify each expression then factor the expression 14-28t-5(7+10t)
Answer:
Simplified: -21-98t
Factored: -7(14t+3)
Step-by-step explanation:
The given expresion is:
14-28t-5(7+10t)
We expand the parenthesis to get:
[tex]14 - 28t -35 - 70t[/tex]
We group like terms to get:
[tex]14 -35 - 28t- 70t[/tex]
We combine similar terms to get:
[tex] - 21- 98t[/tex]
We now factor to obtain:
[tex] - 21- 98t = - 7(14t + 3)[/tex]
Can some help me with this problem
Answer:
The range is [tex]\{-9,-8,-7,-6,-5\}[/tex]
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y=x-7[/tex]
The domain is the interval [tex]\{-2,-1,0,1,2\}[/tex] ----> given problem
Remember that
The domain of a function is the set of all possible values of x
The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.
To find out the range of the function , find the value of y for each value of x
so
For x=-2 ----> y=-2-7=-9
For x=-1 ----> y=-1-7=-8
For x=0 ----> y=0-7=-7
For x=1 ----> y=1-7=-6
For x=2 ----> y=2-7=-5
therefore
The range is [tex]\{-9,-8,-7,-6,-5\}[/tex]
The graph in the attached figure
What is 3a-2a+6= Simplified?
Answer:
1a + 6 or a + 6
Step-by-step explanation:
3a - 2a + 6
3a - 2a = 1a or a
1a + 6 or a + 6
plz mark brainliest i just need 3 more plz plz plz
Answer:
3a-2a+6= (3-2)×a + 6 = (1)×a + 6 = a + 6
Dimitri determined that the ordered pair (2, –2) is a solution to the system of linear equations 7x + 9y = –4 and 5x – 2y = 6 as shown. Equation 1: 7 x + 9 y = negative 4. 7 (2) + 9 (negative 2) = negative 4. 14 + (negative 18) = negative 4. Negative 4 = negative 4. Equation 2: 5 x minus 2 y = 6. 5 (2) minus 2 (negative 2) = 6. 10 minus 4 = 6. 6 = 6. What was Dimitri’s mistake? He mixed up the coordinates of the ordered pair when substituting it into the equations 7x + 9y = –4 and 5x – 2y = 6. He checked the equation 7x + 9y = –4 first when he should have checked 5 x minus 2 y = 6 first. He made a mistake in his calculations when substituting the ordered pair into the equation 7x + 9y = –4 and simplifying. He made a mistake in his calculations when substituting the ordered pair into the equation 5x – 2y = 6 and simplifying.
Answer:
The correct answer is He made a mistake in his calculations when substituting the ordered pair into the equation 5x – 2y = 6 and simplifying.
Step-by-step explanation:
I just took the test ;) good luck on yours
Answer:
He made a mistake in his calculations when substituting the ordered pair into the equation 5x – 2y = 6 and simplifying.
Step-by-step explanation:
If Jose's present age is 3n, how old will he be in 5 years?
Answer:
3n + 5
Step-by-step explanation:
You can't add 5 to 3n. So in 5 years he will 3n + 5.
José's age in 5 years will be 3n + 5, where 3n represents his current age.
Explanation:If José's present age is 3n, and we want to find out how old he will be in 5 years, we need to add 5 to his current age expressed as 3n. This can be done with a simple algebraic expression:
Age in 5 years = Current Age + 5 = 3n + 5
Without the value of n, we can't calculate his exact future age, but we know that in 5 years, his age will be 5 years older than it is now.
The dairy king hold 64 cups of ice cream jerry uses a scoop that hold 1/4.how many scoops of ice cream can jerry get out each bucket of ice cream
Answer:
16 cups
Step-by-step explanation:
64 × .25=16
When the total amount of ice cream, 64 cups, is divided by the scoop size, which is 1/4 cup, it gives us 256. Therefore, Jerry can get 256 scoops of ice cream from each bucket.
Explanation:The amount of ice cream in each bucket is given as 64 cups. Jerry's scoop holds 1/4 cup of ice cream. In order to figure out how many scoops Jerry can get from one bucket, we need to divide the total amount of ice cream (64 cups) by the amount Jerry's scoop holds (1/4 cup).
To carry out this operation, we divide 64 by 1/4 which is equivalent to multiplying 64 by the reciprocal of 1/4 (i.e., 4/1 or simply 4). This results in 64 * 4 = 256. So, Jerry can get 256 scoops of ice cream out of each bucket.
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_____________________________________
Answer:
OPTION B: 229.28 $
Step by-step explanation:
Whenever a deposit is made the balance increases and when a withdrawal is made the balance is decreased.
So, to compute the balance on Friday, assuming that he hasn't deposited on Friday, we add all the deposits and subtract all the withdrawals.
On Monday he has 225 $. He withdraws 27.25 $. So, the balance would be: 225 - 27.25 = 197.75
On Tuesday he deposits money. So, the balance would be 197.75 + 75.5
= 273.25
On Wednesday he deposits and withdraws. So, it would be
273.25 + 32.19 - 61 . 95 = 243.49
On Thursday, he withdraws. So, the balance would be: 243.49 - 14.21
= 229.28 $ which will be the balance on Friday.
Hence, OPTION B is the answer.
Please answer them
This is homework
Answer:
Step-by-step explanation:
31) Y = -3x² + 18 x -25 = -3*x² + -3*-6x -25
= -3(x² -6x) - 25
( (a-b)² =a² - 2ab + b²; here a = x; 2ab = -6x = -2*x*3; and so b = 3)
= -3(x² -6x + 9 - 9) - 25
{ when we add and subtract 9, the equation will not change}
= -3[(x -3)² - 9] -25
= -3(x - 3)² - (-3)*9 - 25
= -3(x - 3)² + 27 -25
= -3(x - 3)² + 2
32) y= -3x² - 18x - 25
= -3 (x² + 6x )-25
= -3 (x² + 6x + 9 - 9) -25
= -3 [ (x+ 3)² - 9] -25
=-3 (x + 3)² - (-3)*9 - 25
= -3(x + 3)² + 27 - 25
= -3(x+3)² +2
Jason begins at the start of a path and rides his bike 11 1/2 miles on the path
The path is 12 1/4 miles long
Enter the distance in miles Jason must ride to reach the end of the path.
Answer:
Jason has to ride 0.75 i.e. [tex]\frac{3}{4}[/tex] miles to reach the end of the path.
Step-by-step explanation:
Jason begins at the start of a path and rides his bike [tex]11\frac{1}{2}[/tex] miles on the path . The path is [tex]12\frac{1}{4}[/tex] miles long.
Therefore, the path is 12.25 miles long and Jason rides the distance of 11.5 miles.
We are asked to determine the distance that Jason must ride to reach the end.
Hence, Jason has to ride (12.25 - 11.5) = 0.75 i.e. [tex]\frac{3}{4}[/tex] miles to reach the end of the path. (Answer)
It costs ABC electronics company $2.50 per unit to produce a part used in a popular brand of desktop computers. The company has monthly operating expenses of $350 for utilities and $3300 for salaries. Write the linear equation to model the company's monthly expenses in the form y=mx+b
Answer:
y=2.5x+3650
Step-by-step explanation:
since you don't know the amount of units sold you make that x
you do know that the company has to pay a set amount each month for utilities and salaries. 350+3300
put this together, and you get the equation:
y=2.5x+3650
y=total expenses
2.5= price per unit
x= total units sold
3650=amount payed each month for utilities, and salaries
Write as an equation: The sides of a triangle are 7, x and (x + 1). The perimeter is 30.
A. 30 =7+ (x+1)
B. 30 - 7 = 2x
C. 30 = 7 + 2(x + 1)
D.30 = 8+2x
Answer:
d
This is because 7+x+1=30 (this is the equation btw).
You combine the like terms so you get 30=8+2x (7+1 and x+x)
do the equation so you get:
30=8+2x
-8 -8
22=2x
divide both sides by 2
11=x
Answer:
D
Step-by-step explanation:
Perimeter = addition of all sides
30 = 7 + x + x + 1
30 = 8 + 2x
Collecting like terms
30 - 8 = 2x
22 = 2x
Dividing by 2
22/2 = 2x/2
11 = x
The results of a survey showed that 40% of 300 Students chose, serving natural resources as the top propriety for their generation
Answer:
72
Step-by-step explanation:
Here is the complete question: The results of a survey showed that 40% of 300 Students chose conserving natural resources as the top priority for their generation. Suppose only 24% of 300 students chose conserving natural resources. How many students chose conserving natural resources?
Given: 24% of 300 students chose conserving natural resources.
Now, finding the number of student chose conserving natural resource.
Using percentage to find the answer.
[tex]Number\ of\ student\ chose\ conserving\ natural\ resources= \frac{24}{100} \times 300[/tex]
⇒ [tex]Number\ of\ student\ chose\ conserving\ natural\ resources= 24\times 3[/tex]
∴ [tex]Number\ of\ student\ chose\ conserving\ natural\ resources= 72\ students[/tex]
Hence, there are 72 students chose conserving natural resources.
A boat traveled 336 miles downstream and back. The trip downstream took 12 hours. The trip back took 14 hours. What is the speed of the boat in still water? What is the speed of the current?
speed of a boat when it goes downstream is 336/12 = 28 mi/h
speed of a boat when it goes upstream is 336/14 = 24 mi/h
Let v is speed of the boat in still water and x is speed of the current. Then,
v + x = 28
v - x = 24
Solve the system for v and x and get v = 26 mi/h, x = 2 mi/h
Mark as BrainliestThe value of y varies directly with x, and y = 63 when x = 14. Find y when x = 28. I have been stuck on this for a while...
y = 112
y = 126
y = 4.5
y = 6.2
(the answer choices)
I think it is the second one
Complete the equation of the line whose slope is -2−2minus, 2 and y-intercept is (0,3)
Answer:
[tex]y=-2x+3[/tex]
Step-by-step explanation:
Given the slope of line [tex]m[/tex] is [tex]-2[/tex].
And y-intercept is [tex](0,3)[/tex]
We can write the equation of line by using the slope-intercept form.
The slope-intercept from is
[tex]y=mx+b[/tex]
Where [tex]m[/tex] is the slope of line. And [tex]b[/tex] is the y-intercept.
In our problem y-intercept is given as [tex]b=3[/tex].
Plugging these we get,
[tex]y=-2x+3[/tex]
You have 6 red marbles, 7 green and 2 blue marbles. What is the probability of pulling a red marble and then without replacing the first marble grabbing a green marble?
Answer:
P(red marble) = 6÷15
Step-by-step explanation:
First, we add all of it we get 15.
Now the probability of getting a red marble will be = number of favorable outcomes ÷ total out comes.
Here the favorable outcomes to red is 6,and the total outcome is 15.
So it is 6÷15.
Now we took one marble. And kept it away.
Now the total number of outcomes are 15-1=14
Now the favorable outcomes for green is 7,snd total outcomes are 14.
So the probability is 7÷14.
Remember don't subtract the one marble u took in every similar question. Do it only if it is told to keep away the first marble you took.
Feel free to ask any further questions and also pls follow me and make this the brainliest answer.
Use the drop-down menus to complete each equation so the statement about its solution is true.
Answer:
Part A: For no solution ⇒ 3x + 9 + 4x + x = 8x + 0
Part B: For one solution ⇒ 3x + 9 + 4x + x = 0 * x + 1
Part C: For infinitely many solutions ⇒ 3x + 9 + 4x + x = 8x + 9
====================================
Step-by-step explanation:
Part A:
3x + 9 + 4x + x = 8x
8x + 9 = 8x ⇒ Subtract 6x from both sides,
9 = 0 which is absurd and hence the equation has no solution.
=====================================
Part B:
3x + 9 + 4x + x = 0 * x + 1
∴ 3x + 9 + 4x + x = 1
8x + 9 = 1 ⇒ Subtract 9 from both sides.
8x = 1 - 9 = -8 ⇒ Divide both sides by 8.
x = -1 ⇒ this is the only solution.
======================================
Part C:
3x + 9 + 4x + x = 8x + 9
8x + 9 = 8x + 9
Subtract 8x from both sides,
9 = 9, both sides are balanced which means, the equation has infinitely many solutions.
Answer:
See diagram below:
Step-by-step explanation:
Scarlett has set up a lemonade stand outside her house and sells small cups and large
cups of lemonade. Each small cup holds 10 ounces of lemonade and each large cup
hold 20 ounces of lemonade. Scarlett sold 70 cups of lemonade totaling 1000 ounces.
Determine the number of small cups sold and the number of large cups sold.
Answer: 40 small cups sold and 30 large cups sold.
Step-by-step explanation:
Let be "s" the number of small cups sold and "l" the number of large cups sold.
Based on the information given in the exercise, you can set up the following system of equations:
[tex]\left \{ {{s+l=70} \atop {10s+20l=1000 }} \right.[/tex]
You can use the Elimination Method to solve the system of equations:
1. Multiply the first equation by -10.
2. Add both equations.
3. Solve for "l".
Then, you get:
[tex]\left \{ {{-10s-10l=-700} \atop {10s+20l=1000 }} \right.\\.........................\\10l=300\\\\l=\frac{300}{10}\\\\l=30[/tex]
4. Finally, substitute the value of "l" into any original equation and solve for the variable "s" in order to find its value.
This is:
[tex]s+30=70\\\\s=70-30\\\\s=40[/tex]
What is the y-intercept of the line defined by the equation y + 3x - 4 = 0?
-4
-4/3
4/3
4
Answer:
y intercept is 4
Step-by-step explanation:
rearranging the equation,
y = -3x + 4
so 4 is the intercept on y axis
The area of a circle is 28.26 square meters. What is the circle's diameter?
Answer: area for circle is πr² so πr² =28.26 and we can sub 3.14 as pi
3.14*r²=28.26 we can divide by 3.14 to get r² on it's own
r²=28.26/3.14
then we root both sides to get r on it's own
28.26/3.14=9 √9=3
and the diameter is double the radius 3*2=6 so the diameter is 6
Step-by-step explanation:
A fruit bowl contains apples, oranges, and bananas. The radius of one of the oranges is 1.35 inches. What is the approximate volume of the orange? Use 3.14 for pi.
Answer:
[tex]10.3\ in^3[/tex]
Step-by-step explanation:
Orange has the shape of a ball.
The volume of a ball with radius r inches is
[tex]V=\dfrac{4}{3}\pi r^3\ in^3[/tex]
The radius of one of the oranges is 1.35 inches.
Hence, its volume is
[tex]V=\dfrac{4}{3}\cdot \pi \cdot (1.35)^3\approx \dfrac{4}{3}\cdot 3.14\cdot 2.460375=10.30077\ in^3 \approx 10.3\ in^3[/tex]
Answer:
10.3 in^3
Step-by-step explanation:
Here is a list of incoming and outgoing expenditure for the arena, for one day. Work out the final profit of the arena rounded to the nearest thousand. Incoming / Outgoing Profit / Cost Events £22,765 Staff -£6,711 Security -£3,452 Maintenance -£500 Merchandise £967 The final profit of the arena rounded to the nearest thousand is
Answer:
Final Profit = £11,000
Step-by-step explanation:
Incoming / Outgoing Profit / Cost Events £22,765
Staff £6,711
Security £3,452
Maintenance £500
Merchandise £967
Final Profit = £22,765 - £6,711 - £3,452 - £500 - £967 = £11,135
A trail map shows the distances of the four trails at a state park: 5.9 kilometers, 3.35 kilometers, 4.1 kilometers, and 3.4 kilometers. What is the distance of the shortest trail?
Answer:
3.35
Step-by-step explanation:
Answer:
3.35
Step-by-step explanation:
Maddie earned an 88 on her first test and an 80 on second test. What is her average test score
Answer:
Step-by-step explanation:
the average can be found by adding up all ur numbers and dividing by how many numbers u have
so her average test score is : (88 + 80) / 2 = 168/2 = 84 <==
To find Maddie's average test score, add up her scores (88+80=168) and divide by the number of tests (2). This gives us an average of 84.
Explanation:The subject of this question is Mathematics, specifically the concept of calculating averages. To calculate Maddie's average test score, you'll need to add up the scores she received and then divide the sum by the number of tests she took.
In this case, Maddie earned an 88 on her first test and an 80 on her second test. You would add these two scores together (168), then divide by 2 (since she took 2 tests), which gives us an average of 84.
So, Maddie's average test score is 84.
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Simplify the expression.
(6.75) =
The expression (6.75) is already in its simplest form. This is because 6.75 is a decimal number that cannot be reduced further or broken down into a simpler expression.
Explanation:The mathematical expression you've shared, (6.75), is already considered to be in its simplest form. Therefore, simplifying the expression doesn't change it because 6.75 is a decimal number. It can't be reduced further or broken down into a simpler expression. The expression remains as is, which is 6.75. In mathematics, simplifying an expression typically involves combining like terms or reducing fractions, however, this is not applicable in this situation as you've provided a single decimal number.
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