Answer:
-56 + 3 sqrt(2) /2
Step-by-step explanation:
f(x) = x^2 +2/sqrt{x}.
2f(2) - f(8).
First find f(2)
f(2) = 2^2 +2/sqrt{2} = 4 + 2/ sqrt(2)
Then f(8)
f(8) = 8^2 +2/sqrt{8} = 64 + 2 / sqrt(4)sqrt(2) = 64+ 2/2sqrt(2) = 64 + 1/ sqrt(2)
2f(2) - f(8).
2 * (4 + 2/ sqrt(2)) - (64 + 1/ sqrt(2))
8 + 4/ sqrt(2) - 64 - 1/ sqrt(2)
Combine like terms
-56 + 3 / sqrt(2)
Rationalizing the second term
-56 + 3/ sqrt(2) * sqrt(2)/sqrt(2)
-56 + 3 sqrt(2) /2
3/7 of the people who live in the apartment building are men. 5/8 of the remaining people are women. The rest are children. a total of 275 men and women live in the building. How man people live in the apartment building altogether?
Answer:
Step-by-step explanation:
people in building ---- x
children --- y
men + women + children = x
(3/7)x + (5/8)(4/7)x + y = x
3x/7 + 5x/14 + y = x
times 14
6x + 5x + 14y = 14x
14y = 3x
y + 220 =x
sub into the other one
14y = 3(y+220)
11y = 660
y = 60
then 14(60) = 3x ---> x = 280
So we have 280 people in the building.
check: 3/7 of 280 are men = 120
leaving 160 women and children
5/8 of these ot 100 are women
so we have 120 men, 100 women and 60 children!
The perimeter of the rectangle below is 94 units. Find the value of x.
Answer:
The value of x = 9 units
Step-by-step explanation:
The complete question is attached to this solution.
The perimeter of a rectangle is given as
P = 2 (L + B)
L = Length of the rectangle = 3x - 1
B = Breadth of the rectangle = 2x + 3
P = Perimeter of the rectangle = 94 units
94 = 2 [(3x - 1) + (2x + 3)]
3x - 1 + 2x + 3 = (94/2) = 47
5x + 2 = 47
5x = 47 - 2 = 45
5x = 45
x = (45/5) = 9 units
Hope this Helps!!!
A cube has a side length of 10 inches. Jada says the surface area of the cube is
600 in?, and Noah says the surface area of the cube is 3,600 in?. Remember we
calculate surface area by finding the area of all the surfaces and adding them up.
Here is how each of them reasoned:
Jada's Method:
Noah's Method:
6. 102
6.102
6.100
602
600
3,600
Do you agree with either of them? Explain your reasoning.
Answer:
I agree with Jada
Step-by-step explanation:
So first you would find the area of one of the faces and it is 100 and then you would multiply the area of one face by 6 because there are 6 faces so you would get 600 inches so Jada would be right
Answer:
Jada is correct in this situation.
Step-by-step explanation: Noah's math is not correct. He goes from 6 times 10^2 to 60^2, which you cannot do. You first must do the exponents (10^2=100) and then multiply it by 6. Jada's method should be similar to that.
Mr. Weaver invested part of his $6000 inheritance in an account that earns 4%
simple interest and the other part in an account that earns 7% simple interest.
How much did he invest in each account if the two accounts earned $360 after
the first year?
Answer:
Mr. Weaver invested $ 2,000 in the 4% simple interest account and $ 4,000 in the 7% simple interest account.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Amount of the inheritance = $ 6,000
Interest rate of the first part = 4% simple
Interest rate of the second part = 7% simple
Interest of the accounts after the first year = $ 360
2. How much did he invest in each account?
For answering the question, we will use the following equation:
x = Amount invested in the first account
6,000 - x = Amount invested in the second account
0.04x + 0.07 * (6,000 - x) = 360
0.04x + 420 - 0.07x = 360
-0.03x = 360 - 420 (Subtracting 420 at both sides)
-0.03x = -60
x = -60/-0.03
x = 2,000 ⇒ 6,000 - x = 4,000
Mr. Weaver invested $ 2,000 in the 4% simple interest account and $ 4,000 in the 7% simple interest account.
pls i need help 15 points!!!!! The treehouse will be 8 feet off the ground. Peter will hang a rope, with knots tied for footholds. Each knot uses an additional 2 inches of rope. Write an expression for the length of the rope needed if Peter ties n knots and wants the rope to touch the ground. How many inches of rope are needed if there are 8 knots? Explain.
Answer:
Step-by-step explanation:
First, we can figure out how many additional inches of rope are needed. If there are 8 knots, 16 additional inches will be needed. Peter would need 9 feet 4 inches of rope, or 112 inches.
The formula for finding the length of the rope needed would be 8+2n.
Hope this helps!
Answer:
112 inches
Step-by-step explanation:
Each knot needs 2 inches of rope
There are 2 knots
2*8 = 16 inches
He wants 8 ft from the ground, but he wants it in inches
8 ft* 12 inches per foot = 96 inches for the rope
96+ 16 =112 inches of rope
The operation symbol and the exponent are missing in the equation shown below.
7,320
10
0.07320
Which operation symbol and exponent should go in the boxes to make the
equation true?
Answer:
The operating symbol is divide (/) and the exponent is 5
[tex]7,320 / \ 10^5 = 0.07320[/tex]
Step-by-step explanation:
Given
[tex]7,320 \ \_\ 10^{\_} = 0.07320[/tex]
Required
Fill in the gap
[tex]7,320 \ \_\ 10^{\_} = 0.07320[/tex]
Multiply the right hand side by 1
[tex]7,320 \ \_\ 10^{\_} = 0.07320 * 1[/tex]
Express 1 as 100000/100000 because 100000/100000 = 1
[tex]7,320 \ \_\ 10^{\_} = 0.07320 * \frac{100000}{100000}[/tex]
Split the fraction
[tex]7,320 \ \_\ 10^{\_} = 0.07320 * 100000 * \frac{1}{100000}[/tex]
Multiply 0.7320 and 10000
[tex]7,320 \ \_\ 10^{\_} = 7,320 * \frac{1}{100000}[/tex]
Express [tex]\frac{1}{100000}[/tex] as an exponent
[tex]7,320 \ \_\ 10^{\_} = 7,320 * \frac{1}{10^5}[/tex]
Change the * sign to /
[tex]7,320 \ \_\ 10^{\_} = 7,320 / \frac{10^5}{1}[/tex]
[tex]7,320 \ \_\ 10^{\_} = 7,320 / \ 10^5[/tex]
Compare the expression on the right hand side with the left hand side base on the order of appearance;
[tex]7,320 = 7,320[/tex]
[tex]The first\ \ _ = \ /[/tex]
[tex]10 = 10[/tex]
[tex]The second\ \_ = 5[/tex]
Hence, the operating symbol is / and the exponent is 5
Here is another easy question to answer: What is the mean of the data sets {41,19,29,12,49,30}, {28,22,10,30,15}, {49,24,18,53,38}?
Answer:
Data set A {41,19,29,12,49,30} = 30
Data set B {28,22,10,30,15} = 21
Data set C{49,24,18,53,38} = 36.4
Step-by-step explanation:
Data set A {41,19,29,12,49,30} =
Mean = Sum of terms/ number of terms
Number of term = 6
Mean = 41 + 19 + 29 + 12 + 49 + 30/ 6
= 180/6 = 30
Data set B {28,22,10,30,15} =
Mean = Sum of terms/ number of terms
Number of term = 5
Mean = 28 + 22 + 10 + 30 + 15/ 5
= 105/5 = 21
Data set C{49,24,18,53,38} =
Mean = Sum of terms/ number of terms
Number of term = 5
Mean =49 + 24 + 18 + 53 + 38/ 5
= 182/5 = 36.4
Brett is making chocolate bars. He wants to make 35 bars from Monday to Friday. One cocoa pod makes ⅚ of bar. If he harvests the same number of cocoa pods each day, how many cocoa pods should he harvest each day to reach his goal of making 35 bars total from Monday to Friday?
Answer:
9
Step-by-step explanation:
one cocoa pod makes 5/6 bar
to make 35 bars, he needs
35 / (5/6) = 35 * 6/5 = 42 pods
Monday - Friday is 5 days
42/5 = 8.4
He needs more than 8 pods per day, so he must harvest 9 pods per day.
Answer:
8.4
Step-by-step explanation:
Which formula can be used to describe the sequence? –81, 108, –144, 192, ...
Answer:
a(n) = -81(-4/3)^(n - 1)
Step-by-step explanation:
The first term is -81. From -81 we obtain the next term, 108, by multiplying -81 by -4/3. Note how (-4/3)(108) = -144 as anticipated.
Thus, the common ratio is -4/3.
The explicit function for this geometric series is
a(n) = -81(-4/3)^(n - 1)
Answer:
C
Step-by-step explanation:
Part 1: What is the range of the data set? Part 2: What is the interquartile range of the data set? Part 3: What is the mean absolute deviation of the data set? [Round both the mean and the mean absolute deviation to the nearest tenth.]
Answer:
Part 1: The range is 7-1 = 6
Part 2: 1 - 0.5 = 0.5
Part 3: 4 ( already rounded off )
Step-by-step explanation:
hope this helped <33
which expressions are equivalent to 252 check all that apply
Answer:
answer is5th one
Step-by-step explanation:
5th one is the answers...its equal to the expression given
if a = -5 find the value of 3a ²
Answer:
75
Step-by-step explanation:
We just need to plug in -5 for a so the answer is:
3a² = 3 * (-5)² = 3 * 25 = 75
Answer:
75
Step-by-step explanation:
A= (-5)²= 25
3(25)=75
How can you tell the difference between systems with no solution and infinite solutions?
Answer:
The given system of equations has "No solution” means that the constants are the numbers without variables. If the coefficients are the equal on both sides then their constants will not equal,they did not satisfy the given equations and therefore it said to have no solution
The given system of equations has "infinitely many solutions" if the given linear system of equations has both the equations represents to the same line.
Step-by-step explanation:
No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true.
Lewis needed to find the difference in lengths between the hypotenuse and the longest leg of this triangle. His work is shown below.
What errors did Lewis make? Check all that apply.
He simplified incorrectly. It should be 20 instead of 200.
He found the difference between the hypotenuse and the short leg instead of the long leg.
He evaluated incorrectly. It should be .
He evaluated incorrectly. It should be .
He should not have taken the square root of each side to get rid of the exponent.
*see the attachment below showing Lewis' work
Answer:
*He simplified √400 incorrectly. It should be 20 instead of 200.
*He found the difference between the hypotenuse and the short leg instead of the long leg
Step-by-step explanation:
=>Going through the work of Lewis, you'd observe that in the 5th line where Lewis was supposed to simplify √400, he made a mistake by writing 200 instead of 20. The square root of 400 is 20 not 200.
=>Also, the length of the longest leg of the right angled triangle that Lewis is supposed to subtract from the length of the hypothenuse is 16 NOT 12.
The difference between the length of the hypothenuse and the length of the longest Leg = 20 - 16 = 4
Answer: A & B homies...
person up top is correct also...
Step-by-step explanation: on edg 2020
You buy boxes of strawberries at the market. Each box cost $6. Write an equation for the number of dollars, d, you spend on b boxes. Yesterday, you purchased 2 boxes. Today you purchase 5 boxes. Place points on the graph to show your purchases yesterday and today.
Answer:
Heyyyy... Your ans!
Plz follow. Me..
Step-by-step explanation:
Answer:
Your answer is d=6b
Step-by-step explanation:
pls help me if you can
Answer:
v=lwh
Step-by-step explanation:
which is length×width×height.
Let ABCDEFGH be a cube.
a) How many different segments can you form by connecting the vertices of the cube?
b) How many different triangles can you form by connecting 3 of the vertices of the cube?
Answer:
a) 28
b) 56
Step-by-step explanation:
A cube is a three dimensional shape gotten from a square. It has 6 faces, and an equal line segment that form its sides.
A vertex is the edge of a figure.
In the given cube ABCDEFGH, since the vertices to be considered are not only the adjacent vertices, then;
a) By connecting the vertices of the cube, 28 different segments can be obtained.
b) The number of triangles that can be formed by connecting 3 of the vertices of the cube is 56.
im badd i kinda understand but not really understanding it
Answer:
40
Step-by-step explanation:
if you add all the numbers up it becomes 96 and 96 goes Into. 480 5 times so you multiply 5 times the number of giant swallow tails
Answer:
If they are proportional we can expect 40
lol iready
plz help me i have a fever and i don't want to do math
Answer:
Four books because there are the most dots over that spot on the bottom number line thingy
Hi I really need help on this problem. Thank you!
Answer:
9
Step-by-step explanation:
because the angle is 45 deg, it is 1/8 of the full circle
the arc it intercepts will also be 1/8 the circumference of the full circle
72*1/8=9
A spinner has 3 options and a bag
has 4 numbered marbles. You spin
the spinner once and randomly
pull i marble. What is the PROB-
ABILITY of spinning the letter 'C'
or pulling an odd number?
Answer:
1/6
Step-by-step explanation:
Spinner = 1 out of 3
Marbles = 2 out of 4
1/3x2/4=2/12=1/6
Point P has coordinates P(-2, 4). What are the coordinates of the image P'' after I translate point P: 4 units to the right 2 units down and then 1 unit to the left and 5 up? 1. The x-coordinate of P'' is: 2.The y-coordinate of P'' is:
Answer:
P''(1, 7)
Step-by-step explanation:
4 units right and 1 left will add a net of +3 to the x-coordinate.
2 down and 5 up will add a net of +3 to the y-coordinate.
The coordinates of P with 3 added to each are ...
P'' = P(-2, 4) +(3, 3) = P''(1, 7)
help meee plz plz me now
Answer:
if they are proportional he will give away 20
Answer:
20 should expect to get lizard treats
Step-by-step explanation:
There are 4+10+6 treats = 20 treats
10 out of the 20 are lizard treats
10/20 = 1/2
There are 40 people
1/2 * 40 = 20
20 should expect to get lizard treats
What solid is represented by this net? A. cylinder B. triangular pyramid C. rectangular prism D. triangular prism E. cone F. rectangular pyramid
i guess it is hexagonal pyramid
as it has 7 verticies
PLEASE HELP!! 20 POINTS
Answer:
5/12
Step-by-step explanation:
take the number of students who read under6 books (5) and divide by total amount of students (12)
5/12
Answer:
5/12
Step-by-step explanation:
there are a total of 12 books read and a frequency of 5 books read that is fewer than 6 books
The elevation of New Orleans, Louisiana, is -6 feet. Which of the following best describes -6 feet? A. 6 feet below sea level B. 3 feet below sea level C. 3 feet above sea level D. 6 feet above sea level
Answer:
Hey there!
-6 ft is 6 ft below sea level.
Hope this helps :)
What is the length of the transverse axis of the conic section shown below?
(y+2)^2/25 - (x-3)^2/4=1
Answer:
Length of transverse axis = 2 b = 10
Length of conjugate axis = 2 a = 4
Step-by-step explanation:
Explanation:-
Given Hyperbola
[tex]\frac{(y+2)^{2} }{25} -\frac{(x-3)^{2} }{4} =1[/tex]
Standard form of Hyperbola
[tex]\frac{(y-(K))^{2} }{b^{2} } -\frac{(x-h)^{2} }{a^{2} } =1[/tex]
Center (h , k ) = (3 , -2 ) , a = 2 and b = 5
Length of transverse axis = 2 b = 2(5) = 10
Length of conjugate axis = 2 a = 2 (2) = 4
Determine if the two triangles shown are similar. If so, write the similarity statement. options: A) ΔUVW ∼ ΔFGH B) The triangles are not similar. C) ΔWUV ∼ ΔFGH D) Impossible to determine.
Answer:
B (from down below) They are similar but your q does not match up with the picture
Step-by-step explanation:
to determine if two triangles are similar you have to make sure the ratios are the same. So 10 / 8 = 1.25, so all sides should have this ratio. 15 / 12 is also 1.25 so you know to sides are similar and also the triangles ARE SIMILAR. So The statement would be KMN is similar to KLP.
PLEASE HELP. FIRST CORRECT ANSWER WILL GET BRANLIEST. IF YOU ANSWER WITHIN A FEW MINUTES AFTER ASKED, WILL GIVE 10 THANKS
Answer:
[tex]x=19[/tex]
Step-by-step explanation:
First, note that Angle X and angle Y are angles formed when two parallel lines are being cut by a transversal. This makes Angle X and Y consecutive interior angles. Consecutive interior angles are supplementary.
Therefore:
[tex](3x-5)+(90+2x)=180[/tex]
[tex]5x-5=90[/tex]
[tex]5x=95[/tex]
[tex]x=19[/tex]
Find m to the second power + 1/m to the second power if m+1/m = square root of 71 . WILL MARK BRAINLIEST
=============================================
Explanation:
Note that m + 1/m and m^2 + 1/(m^2) are very similar. If we square (m + 1/m), then we end up with something in the form (a+b)^2 = a^2 + 2ab + b^2, where a = m and b = 1/m. The 2ab portion is equal to 2*m*(1/m) = 2 which allows us to isolate m^2 + 1/(m^2) fully.
The steps below show this
[tex]m + \frac{1}{m} = \sqrt{71}\\\\\left(m + \frac{1}{m}\right)^2 = \left(\sqrt{71}\right)^2\\\\m^2 + 2*m*\frac{1}{m} + \frac{1}{m^2} = 71\\\\m^2 + 2 + \frac{1}{m^2} = 71\\\\m^2 + 2 + \frac{1}{m^2} - 2 = 71-2\\\\m^2 + \frac{1}{m^2} = 69\\\\[/tex]
-------------
Alternatively, you can isolate m in the equation [tex]m + \frac{1}{m} = \sqrt{71}[/tex] to get two irrational solutions. Plug either solution into m^2 + 1/(m^2) and you should get the same result as above.