First a few reminders:
• For a ≠ 0 and b ≥ 0, [tex]\sqrt[a]{b}=b^{\frac1a}[/tex]
• 4 = 2² and 8 = 2³
• For real numbers a, b, c, we have [tex](a^b)^c=a^{bc}[/tex]
• For any real numbers a and n (so long as both are not zero), we have [tex]\frac1{a^n}=a^{-n}[/tex]
• For any numbers a, b, c, [tex]a^b\times a^c=a^{b+c}[/tex]
So we have
[tex]\sqrt2=2^{\frac12}[/tex]
[tex]\dfrac1{\sqrt2}=2^{-\frac12}[/tex]
[tex]\dfrac1{\sqrt8}=\dfrac1{(2^3)^{\frac12}}=2^{-\frac32}[/tex]
Then the given expression can be rewritten as
[tex]2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=2\times2^{\frac12}-3\times2^{-\frac12}+2^2\times2^{-\frac32}[/tex]
[tex]2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=2^{1+\frac12}-3\times2^{-\frac12}+2^{2-\frac32}[/tex]
[tex]2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=2^{\frac32}-3\times2^{-\frac12}+2^{\frac12}[/tex]
Pull out a factor of [tex]2^{-\frac12}[/tex]:
[tex]2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=2^{-\frac12}\left(2^{\frac32+\frac12}-3+2^{\frac12+\frac12}\right)[/tex]
Simplify this:
[tex]2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=2^{-\frac12}\left(2^2-3+2^1\right)=2^{-\frac12}(4-3+2)=3\times2^{-\frac12}=\dfrac3{\sqrt2}[/tex]
Rationalize this last result to get the square root out of the denominator:
[tex]2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=\dfrac3{\sqrt2}\times\dfrac{\sqrt2}{\sqrt2}=\dfrac{3\sqrt2}{(\sqrt2)^2}=\boxed{\dfrac{3\sqrt2}2}[/tex]
I cant seem to get it can you help me, please.
What is the solution to the equation 1.2m - 0.8 = -2.Om?
m = 0.25
m = 0.4
m = 1
m = 4
8th Grade Math! Help Please.
Answer:
bolded
Step-by-step explanation:
2. 11= 3z +5
6 = 3z z= 2
3. 2s - 4 = 6
2s=10 s= 5
4. 5r + 8 = -12
5r = -20 r= -4
5. -6p - 3 = 9
-6p = 12 p= -2
6. 3x + x -2 = -14
4x = -12 x= -3
7. 5c + 2 -3c = 10
2c = 8 c=4
8. 3 + 7n +2n = 21
9n = 18 n=2
9. 6r + 5 - 7r =21
-1r =16 r= -16
10. 8 - 5b= -7
-5b = -15 b= 3
11. 6 - 4m= -10
-4m = -4 m= 1
12. -3t + 4 =19
-3t = 15 t= -5
13. a= 18
Determine whether the pair of coordinate pairs will make the linear inequality true or false.(10, 6).Y ≤ -5/5x+3
Answer:
False.
Step-by-step explanation:
We have the ordered pair (10, 6) and we want to see if this ordered pair is a solution of the inequality:
y ≤ -5/5x+3
Remember that a generic ordered pair is written as (x, y)
Then for the ordered pair (10, 6) we have:
x = 10
y = 6
So we just need to replace these two values in the inequality and see if the inequality is true or false.
Replacing these values we get:
6 ≤ (-5/5*10) + 3
6 ≤ (-1/10) + 3
This is false, 6 is not less than the thing at the right, so we can conclude that (10, 6) is not a solution of the inequality.
So the coordinate pair makes the inequality false.
Explain how to draw a line segment that measures 72 millimeters.
Answer:
get a ruler and meshure out 72 millimeters.
Step-by-step explanation:
did exam
I NEED HELP WITH THIS IVE RETAKEN IT LIKE 4 TIMES PLS HELP
Answer:
(a)=40 (b)=60
Step-by-step explanation:
(a)=
So first 70 +70 = 140 then 180-140 = 40
(b)
So first 180/3 = 60 all angles =60
a.When the numerator and the denominator have no common factor other than 1; he fraction is either a proper fraction or mixed number
Answer:
The fraction is a proper fraction (and irreducible)
Step-by-step explanation:
Given
[tex]x = Numerator[/tex]
[tex]y = Denominator[/tex]
[tex]Common\ factor = 1[/tex]
Required
The type of fraction
A fraction with the given features is a proper fraction and cannot be further reduced.
Take for instance:
[tex]x = 2[/tex]
[tex]y = 7[/tex]
The only common factor between [tex]2\ and\ 7[/tex] is 1
[tex]\frac{x}{y} = \frac{2}{7}[/tex]
See that 2/7 is a proper fraction and also 2/7 cannot be reduced (simplified)
The above logic is applicable to all fraction that have the attribute stated in the question (e.g. 3/7, 3/8, 4/9, 7/10, etc.)
- ( Intercepts form two points form )
If A ( a , b ) and B ( b , a ) lie in 6x-y =1 and 2x - 5y = 5 respectively , find the equation of AB. Show your workings too!
~Thanks in advance! :D
Answer:
Solution given:
A(a,b) lie in 6x-y =1
substituting value of A in equation ,we get
6a-b=1...................(1)
B(b,a) lie in 2x - 5y = 5
substituting value of B in equation ,we get
2b-5a=5
b=5(a+1)/2............(2)
substituting value of b in equation 1 ,we get
6a-5(a+1)/2=1
12a-5a-5=2
7a=2+5
a=[tex] \frac{7}{7} [/tex]=1
substituting value of a in equation 1 ,we get
6×1-b=1
6-1=b
b=5
so points are A(1,5) and B(5,1)
we have
equation of line having two points
[tex](y - y1) = \frac{y2 - y1}{x2 - x1} (x - x1) [/tex]
[tex](y - 5) = \frac{1-5}{5-1} (x - 1) [/tex]
[tex](y - 5) = -1 (x - 1) [/tex]
y-5=1-x
x+y=6 is a required equation of line AB.
Each Serving of pasta is 1/2 pound. Drag to correct equation to each amount to show how many 1/2 pound serving Can be made
Step-by-step explanation:
4 pounds is 4÷1=8
2
5 pounds is 5÷1=10
2
David buys 3 movie tickets for $6 each and 2 bags of popcorn
for $2 each. Simplify the expression 3.6 +2.2 to find out how
much money David spent in all
Answer:
5.8 thats the answer you get when it is simplified and 1 movie ticket=$2 and 1 bag of popcorn= $1
Step-by-step explanation:
What is c the number of baseball cards in coles cole collection ? * I will give brainliest pleaseee help
Answer:
24
Step-by-step explanation:
120/5
Answer:
d i hope am sorry if i calcuc wrong
Step-by-step explanation:
The measurement of one angle of a right triangle is 42°.
What is the measurement of the third angle?
56°
42
138
48
Answer:
48
Step-by-step explanation:
42 + 90 + x = 180
x = 48
Sam and Dave, who are both Park Rangers, each manage a nature preserve. Devin's nature reserve is 14 hectares and Sam's nature reserve is 14\cdot 10^{6}14⋅10 6 square meters. Who manages the smaller nature preserve? Note: 1 hectare = 10,000 square meters
Answer: Devin's
Step-by-step explanation:
Given
Devin's nature reserve is 14 hectares
Sam's nature reserve is [tex]14\times 10^6\ m^2[/tex]
Also, [tex]1\ \text{hectare}=10,000\ m^2[/tex]
Devin reserve in square meter [tex]14\ \text{hectares}=14\times 10^4\ m^2[/tex]
Clearly, [tex]14\times 10^6> 14\times 10^4[/tex]
So, Devin's manages smaller area
50 POINTS!! Please please help find height and volume of pyramid!!!
Answer:
44.68.8m³
hope it helps please mark Brainliest
Select all the expressions that are equivalent to 20% of 150.
Answer:
2 and 3
Step-by-step explanation:
30 is 20% of 150
I hope this helps
Have a great day
Which right circular cylinder has the greater volume
Answer:
the blue cylinder
Step-by-step explanation:
Which pair of points graphed below have values that are opposites
Q.1 What value of p will make this equation true?
Q.2 what value of x makes this equation true?
Answer:
[tex]1. \: p = 10 \\ 2. \: x = 4[/tex]
A - 3/4 = 1/8 step by step explanation
Answer:
A-3/4=1/8 is the equation, if you expand 3/4 it is 6/8, in order to get 1/8 you need to subtract 6/8 from 7/8
7/8-6/8=1/8 therefor A=7/8
I need this done for a test, and if someone can answer one of my past questions, thank you
Answer: #1 D 60 2# H
Step-by-step explanation:
What is vertices A(1, 4), B(2, 7), C(7, 7), and D(6, 4) reflected over the x-axis . PLS HELP ME
Step-by-step explanation:
A(1,4)=A'(1,-4)
B(2,7)=B'(2,-7)
C(7,7)=C'(7,-7)
D(6,4)=D'(6,-4)
Topic: Matrix Row Reduction
Write the system as an augmented matrix:
[tex]\left[\begin{array}{cc|c}1&5&22\\4&-7&7\end{array}\right][/tex]
Add -4 (row 1) to row 2 :
[tex]\left[\begin{array}{cc|c}1&5&22\\0&-27&-81\end{array}\right][/tex]
Multiply row 2 by -1/27 :
[tex]\left[\begin{array}{cc|c}1&5&22\\0&1&3\end{array}\right][/tex]
Add -5 (row 2) to row 1 :
[tex]\left[\begin{array}{cc|c}1&0&7\\0&1&3\end{array}\right][/tex]
Then x = 7 and y = 3.
Please help me I’ll give brainly
Answer:
9 and 10
Step-by-step explanation:
square root of 96 is 9.79795897113
Answer:
9 and 10
Step-by-step explanation:
because square of 9 is 81
and square of 10 is 100
81<96<100
so it lies between 9 and 10
It takes Jack 11 hours to pick 40 bushels of apples alone. Jill can pick 40 bushels of apples in 9 hours. How long will it take Jack and Jill to pick 40 bushels of apples together. Round to the nearest hour.
Answer:
5 hours
Step-by-step explanation:
Jack 40/11 = 3.64 bushels per hour
Jill 40/9 = 4.44 bushels per hour
together they pick 3.64 + 4.44 = 8.08 bushels per hour
40/8.08 = 4.95 hours
The perimeter ratio of two similar triangular prisms are 13:7. If the surface area of the smaller prism is 52km2 , then calculate the larger surface area.
Answer:
96.5714285714 km^2
Step-by-step explanation:
You have to multiply 52 by 13/7
Answer:
96.5714285714 km^2
hope it helps
1.) Mr. Sno-Cone tracked how many snow cones he sold during a week. What is the range of
his data?
25
30
28
22
32
40
31
Number
Sold
Write an equation in standard form for a line that is perpendicular to the line with an equation of y = 3x —5 that passes through the point (8, 5).
Answer:
x + 3y = 23
Step-by-step explanation:
m = -1/3, find 'b'
5 = -1/3(8) + b
15/3 = -8/3 + b
23/3 = b
y = -1/3x + 23/3
multiply each side by 3 to get:
3y = -x + 23
x + 3y = 23
Shawn wrote down the activities for his day on Saturday. In which situation will his activity result in a final value of zero? *
A. Shawn places four quarters in a jar of quarters which contains four quarters.
B. In the morning, Shawn added six hard candies to a jar which contained four hard candies. By the end of the day he ate ten candies from this jar.
C. Shawn starts out on the ground and then climbs ten feet on a ladder.
D. Shawn travels east ten feet and then travels south ten feet.
NO SCAM LINKS
Answer:
B
Step-by-step explanation:
B. In the morning, Shawn added six hard candies to a jar which contained four hard candies.
So he had 10 candies.
By the end of the day he ate ten candies from this jar.
Now he had 10-10 = 0, zero candies.
Answer:
B
Step-by-step explanation:
A 4+4=8
B 10-10=0
C 10'
D 10'E 10'S
can someones please help me i dont get this
Answer:
176.25in^2
Step-by-step explanation:
You can tell that the two triangles on the left, and the two triangles on the right make a rectangle if you flip one of them. Because of this, you can multiply the base and height to get the area of both.
7.5*16=120 (left side)
7.5*7.5=56.25 (right side)
Now we add them to get the full area:
120+56.25=176.25in^2
What is the lateral surface area of the triangular prism?
Select one:
96 ft
36ft
60ft
84ft²
Answer:
96 feetStep-by-step explanation:
thats the answer po