Answer:
[tex]n = 162[/tex]
Step-by-step explanation:
Given
[tex]6\sqrt{2187[/tex]
Required
Determine the order of the surd
If a surd is represented as [tex]n\sqrt{r[/tex], then the order of the surd is [tex]n[/tex]
[tex]6\sqrt{2187[/tex]
Express 2187 as [tex]3^6 * 3[/tex]
[tex]6\sqrt{2187} = 6\sqrt{3^6 * 3}[/tex]
Split the surd
[tex]6\sqrt{2187} = 6\sqrt{3^6} * \sqrt{3}[/tex]
Apply the following law of indices:
[tex]\sqrt{a} = a^{\frac{1}{2}}[/tex]
The expression becomes:
[tex]6\sqrt{2187} = 6 * 3^{\frac{6}{2}} * \sqrt{3}[/tex]
[tex]6\sqrt{2187} = 6 * 3^{3} * \sqrt{3}[/tex]
[tex]6\sqrt{2187} = 6 * 27 * \sqrt{3}[/tex]
[tex]6\sqrt{2187} = 162 * \sqrt{3}[/tex]
[tex]6\sqrt{2187} = 162 \sqrt{3}[/tex]
By comparing [tex]162 \sqrt{3}[/tex] to [tex]n\sqrt{r[/tex], we can say that:
[tex]n = 162[/tex]
[tex]r = 3[/tex]
Conclusively, the order of the surd is 162
x + y = 42, xy = 108 then what is x and y. Is there any (non-quadratic)formula for finding this instead of the process of elimination
Answer:
when x = 39.25, y = 2.75
when x = 2.75, x = 39.25
Step-by-step explanation:
use substitution method
x+y = 42 ------ (1)
xy = 108 ------ (2)
from (1) ,
x+y = 42
y = 42-x ------ (3)
substitute (3) into (2)
xy = 108
x( 42-x ) = 108
42x - x² = 108
-x² + 42x - 108 = 0
x² - 42x + 108 = 0
use the following formula to solve the value of x:
[tex]i) \: x = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \: \\ ii) \: x = \frac{ - b - \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
a = 1
b = -42
c = 108
[tex]i) \: x = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
[tex]x = \frac{ - ( - 42) + \sqrt{( - 42) {}^{2} - 4(1)(108)} }{2(1)} [/tex]
[tex]x = \frac{42 + \sqrt{1764 - 432} }{2} [/tex]
[tex]x = \frac{42 + \sqrt{1332} }{2} [/tex]
[tex]x = \frac{42 + 6 \sqrt{37} }{2} [/tex]
[tex]x = 21 + 3 \sqrt{37} [/tex]
[tex]x = 39.25[/tex]
[tex]ii) \: x \: \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
[tex]x = \frac{ - ( - 42) - \sqrt{( - 42) {}^{2} - 4(1)(108} }{2(1)} [/tex]
[tex]x = \frac{42 - \sqrt{1764 - 432} }{2} [/tex]
[tex]x = \frac{42 - \sqrt{1332} }{2} [/tex]
[tex]x = \frac{42 - 6 \sqrt{37} }{2} [/tex]
[tex]x = 21 - 3 \sqrt{37} [/tex]
[tex]x = 2.75[/tex]
the 2 values of x are x = 39.25 and x = 2.75
substitute x = 39.25 into (3)
y = 42-x
y = 42-39.25
y = 2.75
substitute x = 2.75 into (3)
y = 42-x
y = 42-2.75
y = 39.25
when x = 39.25, y = 2.75
when x = 2.75, x = 39.25
Louisa has a goal of collecting 100 pounds of dog food for a local shelter. She records how many pounds of food she collects each week. Week Pounds Collected 1 20.5 2 18 and three-fourths 3 32.75 How many more pounds of dog food does Louisa need to reach her goal? 18 27 28 72
Given:
Louisa has a goal of collecting 100 pounds of dog food for a local shelter.
The table of values which represents the number of pounds of food she collects each week.
To find:
The number of more pounds of dog food Louisa need to reach her goal.
Solution:
For first week = 20.5 pounds
For second week = [tex]18\dfrac{3}{4}=18.75[/tex]
For third week = 32.75
Now,
[tex]\text{Remaining pounds of dog food Louisa needs}=100-(20.5+18.75+32.75)[/tex]
[tex]\text{Remaining pounds of dog food Louisa needs}=100-72[/tex]
[tex]\text{Remaining pounds of dog food Louisa needs}=28\text{ Pounds}[/tex]
Therefore, the correct option is C.
SUPER EASY SOLVE THIS ILL MARK AS BRAINLIEST PLEASE
THE ATTACHMENT
Answer:
7
40
the answer is 7 fortyths
working out
3 quarters - 3 eighths = 3 eighths*7 nineths= 7 twentyforths
5 sixths +1 third + 1 half = 10 sixths
7 twentyforths divided by 10 sixths= 7 fortyths
A membership to the gym costs $25 per person in 1995. The membership cost has increased by an average of $6 per person for each year since 1995. Write a linear equation for the cost of a gym membership for one person since 1995.What is the cost of a gym membership in 2009?
Answer:
The cost of a gym membership would be 109
Step-by-step explanation:
2009-1995=14
thats how many years apart from each other
so its been 14 years $6 for each year so 14x6=84
so the regular price was $25 and went up 84 dollars last 14 years.
25+84=109 so the price of gym membership would be $109
Find the slope of the lines that go through the following points.
Answer:
use the formula y2 - y1 / x2 - x1
Answer:
y2-y1 /x2-x1
Step-by-step explanation:
slope is the same as gradient
follow this principle (x,y)
Gradient (m) =y2-y1 /x2-x1
I have no idea how to find the values of x and y in that diagram. Can someone help?
Answer:
Multiple choice?
Step-by-step explanation:
Last year's cost, c, of a water park season pass increased 35%. The expression C+0.35c can be used to represent the increased price of a season pass. What is another expression that can be used to find the the new cost of a season pass?
Answer:
c+35/100c
Step-by-step explanation:
Find the area of the irregular shape !!!
Step-by-step explanation:
Area of triangle = base × height ×½
triangle = 9×8×½=36cm²
rectangle = length×width
rectangle = 15×26=390cm²
area of irregular fig= 390+36 =426cm²
click on the volume of this rectangular prism.
Answer: 192 cubic inches
Step-by-step explanation:
Which statements are true about the ordered pair (10, 5) and the system of equations?
{ 2x−5y=−5
{ x+2y=11
Select each correct answer.
The ordered pair (10, 5) is a solution to the first equation because it makes the first equation true.
The ordered pair (10, 5) is a solution to the second equation because it makes the second equation true.
The ordered pair (10, 5) is not a solution to the system because it makes at least one of the equations false.
The ordered pair (10, 5) is a solution to the system because it makes both equations true.
Answer:
the solution to the system is (5,3)
Step-by-step explanation:
the first statement is True: 2(10) - 5(5) = -5
20 - 25 = -5
-5 = -5
the second statement if False: 10 + 2(5) ≠ 11
the third statement is True
the last statement is False
Rewrite y - 3 = 4(x + 2) in slope intercept form. Type in your answer without using any spaces. Example: y=-3/4x+12
Answer:
y=4x+11
Step-by-step explanation:
Answer:
y=4x+11
Step-by-step explanation:
y - 3 = 4(x + 2)
=
y - 3 =4x + 8
=
y - 3 (+3) = 4x + 8 (+3)
=
y=4x+11
At the end of the harvest season, Omar wonders if it is time to cover the garden with a tarp. He understands that as the temperature decreases, moisture in the air condenses into dew which freezes at 0 degrees Celsius and may damage the plants in the garden. * At 4:00 pm, the temperature is 5 degrees Celsius * The temperature is predicted to decrease 0.5 degrees Celsius every two hours until 4:00 am. #4 Part A: Does Omar need to cover the garden
Answer:
Non il n'a pas besoin de couvrir le jardin
Step-by-step explanation:
Comme à 16h il fait 5°C, on enlève 0.5°C toutes les deux heures donc à 18h il fera 4.5°C, à 20h il fera 4°C, à 22h il fera 3.5°C, à 0h il fera 3°C, à 2h il fera 2.5°C et à 4h la dernière heure où la température baisse il fera 2°C
Please help!!!! I don’t get it
Answer:
x = 9
m<b = 54
m<e = 54
Step-by-step explanation:
Error Analysis
On a math test a student, Jake, has to identify all the coefficients and constants of
the expression 7b+ m + 8. Jake says that 7 is a coefficient and 8 is a constant. Identify all the
coefficients and constants of the expression. What error might Jake have made?
The coefficient(s) of the expression is are __
Use a comma to separate answers as needed.)
The constant(s) of the expression is/are __
(Use a comma to separate answers as needed.)
What error might Jake have made?
A. Jake said 7 is a coefficient. It is actually a constant.
OB. Jake said 8 is a constant. It is actually a coefficient.
OC. Jake did not include the constant 1.
OD. Jake did not include the coefficient 1.
Click to select your answer's).
The coefficient(s) of the expression is/are 7, 1
Use a comma to separate answers as needed.)
The constant(s) of the expression is/are 8
(Use a comma to separate answers as needed.)
What error might Jake have made?
OD. Jake did not include the coefficient 1.
Click to select your answer's
a girl paid 6.28 for 3/4 pound of shrimp. what was the unit price in dollars per pound?
Divide the amount spent by the weight:
6.28 / 3/4 = 8.37
Unit price is $8.37 per pound
Each of three colored cups covers one of three objects. 1) The red cup is somewhere to the left of the white cup. 2) The coin is somewhere to the left of the bean. 3) The gray cup is somewhere to the right of the shell. 4) The bean is somewhere to the right of the gray cup. Under which color cup is the shell?
Answer:
Shell is under Red color cup
Step-by-step explanation:
We have 3 cups and 3 objects which they cover under them.
Taking into consideration (4) and (2) as they both describe the position related to bean
(4) Gray cup →Bean (right) (2) coin ← bean (left)
that means coin can either under Gray cup or left to gray cup.
Now
(1) Red ← White (left) (3) Shell → Gray (right)
This means if we consider coin to be left of gray cup then we can't place shell to the left of gray cup as required in (3)
so coin will be under gray cup
on forming the Color of cups and the coin below them
C1 C2 C3
Red Gray White
__ __ __
Shell coin Bean
So Shell is under Red color cup
Consider the enlarged triangle.
A smaller triangle has side lengths 4, 5, 3. A larger triangle has side lengths 8, 10, 6.
Which steps should be used to find the perimeter? Check all that apply.
Find the scale factor: enlarged over original = 6 over 3 = 2
Find the scale factor: enlarged over original = 3 over 6 = one-half
Calculate the perimeter of the original figure.
Divide the perimeter of the original figure by the scale factor.
Multiply the perimeter of the original figure by the scale factor.
Find the scale factor: StartFraction enlarged over original EndFraction = StartFraction 6 over 3 EndFraction = 2
Calculate the perimeter of the original figure.
Multiply the perimeter of the original figure by the scale factor.
Step-by-step explanation:
A, C, D
The steps which could be used to find the perimeter are Find the scale factor: enlarged over original = 6 over 3 = 2, Calculate the perimeter of the original figure and Multiply the perimeter of the original figure by the scale factor.
What is Scale Factor?Scale factor is the ratio of the dimension of the given original object and the dimension of the new object from the original.
Given that,
A smaller triangle has side lengths 4, 5, 3. A larger triangle has side lengths 8, 10, 6.
First find the scale factor.
Scale factor of enlarged over original = 8/4 = 10/5 = 6/3 = 2
Now, find the perimeter of the original figure.
Perimeter of the original figure = 4 + 5 + 3 = 12
Now.
Perimeter of enlarged figure = Scale factor × Perimeter of original figure
= 2 × 12
= 24
Hence the correct steps are first, third and last step.
Learn more about Scale Factor here :
https://brainly.com/question/29929067
#SPJ3
What does the word Expressions mean in mathematics in your own words?
Answer:
Expression in mathematics means word problem.
Please help I got to get this done to move on in math (my teacher wont unlock anything till i get this done i have till tomorrow)
Step-by-step explanation:
please see it my steps to work this problem
==============================================
Explanation:
The multiplicative inverse of x is 1/x, and vice versa. This is true as long as x is not 0.
The multiplicative inverse of 1/5 is 5. These two values multiply to 1. This is true of any multiplicative inverse pairing.
----------
What we need to do is multiply 5 with (2x-1/5)
Use the distributive property to get the following
5*(2x-1/5)
5*(2x) - 5*(1/5)
10x - 5/5
10x - 1
I multiplied the outer 5 by each term inside (the 2x and 1/5) and simplified.
Solve :x^7/x^5+2x^4+x^3 × (x+1)^3/x^4
Pls help I’m timed on my test
what is the y- intercept of the linear function?
Y = -1/3 x + 1
Answer:
+1
Step-by-step explanation:
the last number is the y intercept
Answer:
The y-intercept is (0,1).
Step-by-step explanation:
y=mx+b
b is the y-intercept
Will give crown! Help
Answer: The slope is -5/7
Step-by-step explanation:
Slope is rise/run
The rise is -5, and the run is 7
This is why the slope is -5/7
Answer:
The rise is 6 and the run is 7 6/7
To be a member of the choir, you must go to an audition. Henry's cousin is a member of the choir. What conjecture can you make about Henry's cousin?
A.) Henry’s cousin practices with the choir
B.) Henry is in the choir
C.) Henry’s cousin went to an audition
Answer:
b
Step-by-step explanation:
Answer:
Henry's cousin went to an audition.
Step-by-step explanation:
express the scientific notation:4830000000 with all formula
Answer:
4.83 * 10^9
Step-by-step explanation:
Here, we want to express the given number in scientific notation
What we have to do here is to place the decimal number at the back of the first non zero number
The first non zero number is 4
So
let us count the number of digits after the first non zero number
That will be 9
So we make this the power of 10
And our answer will be;
4.83 *10^9
If you buy every item in the song, The Twelve Days of Christmas, how many items will you buy?
Answer:
Total item = 364
Step-by-step explanation:
1 partridge for 12 days = 12 x 1 = 12
2 turtle doves for 11 days = 11 x 2 = 22
3 french hens for 10 days 10 x 3 = 30
4 calling birds for 9 days = 9 x 4 = 36
5 gold rings for 8 days = 8 x 5 = 40
6 geese a-laying for 7 days = 7 x 6 = 42
7 swans a-swimming for 6 days = 6 x 7 = 42
8 maids a-milking for 5 days = 5 x 8 = 40
9 ladies dancing for 4 days = 4 x 9 = 36
10 lords a-leaping for 3 days = 3 x 10 = 30
11 pipers piping for 2 days = 2 x 11 = 22
12 drummers drumming for 1 day = 1 x 12 = 12
Total item = 364
please help!!! if anyone knows
Answer:
The answer is 24in a am very sure
Step-by-step explanation:
Answer: The missing side is 24 inches
Step-by-step explanation:
Since it is a right angle that means that we can use the Pythagorean Theorem formula to solve for the B.
The formula says that a^2 + b^2 = c^2 Since we know a is 18 and c is 30 we will input the value into the formula to solve for b.
18^2 + b^2 = 30^2
324 + b^2 = 900
-324 -324
b^2 = 576
b = [tex]\sqrt{576}[/tex]
b = 24
Solve for x.
(x + 13) ft
24 ft
Answer:
x = 9.
Step-by-step explanation:
If you meant (x + 13) = 24, then we first must subtract 24 by 13.
24 - 13 = 9
Now, check your work by replacing the "x" with 9.
(9+ 13) = 24
24 = 24 <----- This is a true statement.
Therefore, x = 9.
Hope this helps! :D
Rochelle wants to use all of her raisins to bake batches of granola. She has 3/4 cup of raisins.
Each batch requires 1/8 cup of raisins. How many batches can she make?
Answer:
She has 3/4 and each batch requires 1/8. 3/4 can be turned into 6/8 she can make 6 batches.
please help meeeeeeeeeee
Answer:
x=-5
Step-by-step explanation:
If f(x)=0, then x=-5
Drawing the line y=0 shows this visually
=
105 min
game
?hr.
game
Help please
Answer:
105 minutes= 1 hour and 45 minutes
Answer:
1 hour and 45 minutes
or
1.75 hours