Answers
Answer:
3/4
Step-by-step explanation:
Related Questions
- Which product is greater, (-4) • (-6) or
(-7).(-8)? Explain
Answers
Answer:
(-7)*(-8)
Step-by-step explanation:
Two negatives make a postive so 7*8=56 and 4*6=24.
It takes Ms. Brown 5/12 hours to hike 11 miles. At this rate, how long will it take her to hike the remaining 7 miles to her camp site?
Answers
Answer:
It will take 4 hours and 20 minutes to hike the rest of the 7 miles
Step-by-step explanation:
a^6 + b^6 ≤ 12 a^2 b^2 - 64
Answers
[tex]\large\underline{\sf{Solution-}}[/tex]
Given that
[tex]\rm \longmapsto\:a > 0 \: \: and \: \: b > 0[/tex]
and
[tex]\rm \longmapsto\: {a}^{6} + {b}^{6} \leqslant 12 {a}^{2} {b}^{2} - 64[/tex]
can be rewritten as
[tex]\rm \longmapsto\: {a}^{6} + {b}^{6} + 64 - 12 {a}^{2} {b}^{2} \leqslant 0[/tex]
[tex]\rm \longmapsto\: {( {a}^{2}) }^{3} + {( {b}^{2} )}^{3} + {(4)}^{3} - 3( {a}^{2})( {b}^{2})(4) \leqslant 0[/tex]
We know
[tex]\mathfrak{ {x}^{3}+{y}^{3}+{z}^{3}-3xyz =(x + y + z)( {x}^{2}+{y}^{2}+{z}^{2}-xy-yz - zx}[/tex]
So, using this identity, we get
[tex] \rm( {a}^{2}+{b}^{2} + 4)( {a}^{4} + {b}^{4} + 16 - {a}^{2} {b}^{2} - 4 {b}^{2} - 4 {a}^{2}) \leqslant 0[/tex]
Let we consider,
[tex]\bf{ \longmapsto\:{a}^{4} + {b}^{4} + 16 - {a}^{2} {b}^{2} - 4 {b}^{2} - 4 {a}^{2}}[/tex]
can be rewritten as
[tex]\bf{ \: = \dfrac{1}{2}\bigg[2{a}^{4} + 2{b}^{4} + 32 - 2{a}^{2} {b}^{2} - 8 {b}^{2} - 8{a}^{2}\bigg]}[/tex]
[tex]\bf{ = \dfrac{1}{2}\bigg[{a}^{4} + {a}^{4} + {b}^{4} + {b}^{4} + 16 + 16 - 2{a}^{2} {b}^{2} - 8 {b}^{2} - 8{a}^{2}\bigg]}[/tex]
can be re-arranged as
[tex]\bf{ \: = \dfrac{1}{2}\bigg[({a}^{4} + {b}^{4} - 2{a}^{2} {b}^{2})+({b}^{4} + 16- 8 {b}^{2}) + (16 + {a}^{4} - 8{a}^{2})\bigg]}[/tex]
[tex]\bf{ \: = \dfrac{1}{2}\bigg[( {a}^{2} - {b}^{2})^{2} + {( {b}^{2} - 4) }^{2} + {( {a}^{2} - 4)}^{2} \bigg]}[/tex]
As sum of squares can never be negative.
[tex]\bf {⇛\:{a}^{4} + {b}^{4} + 16 - {a}^{2} {b}^{2} - 4 {b}^{2} - 4 {a}^{2} \geqslant 0}[/tex]
[ Equality of zero holds when a = b = 2 ]
And if a and b are distinct, then
[tex]\bf{⇛\:{a}^{4} + {b}^{4} + 16 - {a}^{2} {b}^{2} - 4 {b}^{2} - 4 {a}^{2} > 0}[/tex]
and
[tex]\bf{( {a}^{2}+{b}^{2} + 4)( {a}^{4} + {b}^{4} + 16 - {a}^{2} {b}^{2} - 4 {b}^{2} - 4 {a}^{2}) > 0}[/tex]
So,
[tex] \bf{( {a}^{2}+{b}^{2} + 4)( {a}^{4} + {b}^{4} + 16 - {a}^{2} {b}^{2} - 4 {b}^{2} - 4 {a}^{2}) \geqslant 0}[/tex]
So, for the given statement,
[tex]\rm \longmapsto\: {a}^{6} + {b}^{6} \geqslant 12 {a}^{2} {b}^{2} - 64[/tex]
So, we concluded that
If a = b = 2, then
[tex]\rm \longmapsto\: {a}^{6} + {b}^{6} = 12 {a}^{2} {b}^{2} - 64[/tex]
And
If a and b are distinct, then
[tex]\rm \longmapsto\: {a}^{6} + {b}^{6} > 12 {a}^{2} {b}^{2} - 64[/tex]
So, given statement is partially true for a = b = 2 otherwise false.
Write the ratio in simplest form as a fraction.
32 inches to 1 foot
Answers
Answer:
8/3
Step-by-step explanation:
1 foot = 12 inches, so it would be 32/12. After simplifying and dividing 4 on both sides, you would get 8/3.
In which pair can figure “a” take figure “b”
Answers
Answer:
2
Step-by-step explanation:
Help help help help help help
Answers
Answer:
where is the questions I don't know
Please, if you can answer this, answer my other similar ones as well. I appreciate any help so much!
Answers
Answer:
C. Definition of Supplementary Angles
Step-by-step explanation:
You know this because they are opposites
I hope I could help!!!
For the given triangle let a = 14.3, b = 16.4, c = 11.7, d = 19.0. Find the perimeter of the triangle.
Answers
Answer:
49.7
Step-by-step explanation:
you just add them. thats perimeter
7+2^2⋅6+2^3−6
wat dis using pedmas plz :(
Answers
Answer:
9^-4 + 2^-3
Step-by-step explanation:
It can't be broken down anymore under the law of indices.
ANSWER
this answer is 33 pls picke me brainliest
10.
Write an equation for the translation of y = |x|.
15.5 units down
A. y = |x| + 15.5
B. y = |–15.5x|
C. y – 15.5 = |x|
D. y = |x| – 15.5
Answers
Answer:
D
Step-by-step explanation:
what is the simplest form of
-1/4 + 3/8
---------------
5/8
for 20 pts
Answers
Answer:
the fraction in simplest form is [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
Hope this helps!
Answer:
you may not find this helpful,
Step-by-step explanation:
0.125 is the answer
Write the following times in words. 8:10am
Answers
Answer:
Step-by-step explanation:
eight ten a.m.
Wendy is conducting a marketing survey. She mailed 35,400 surveys and got 12,744 responses. What is the percentage
Answers
Answer:
0.036%
Step-by-step explanation:
A TV has an original price of $549. Enter the new price after the given percent of change.
20% decrease
The new price is $
.
Answers
Answer:
439.20
Step-by-step explanation:
to find 549 deceased by 20% percent you need to find what's 20% percent of 549 is.
Which of the following points lie on a line that passes through the origin with a slope of −25? Select all that apply. Multiple select question. cross out A) (0, 0) cross out B) (1, −25) cross out C) (−2, 5) cross out D) (−1, 25) cross out E) (4, 10) cross out F) (−5, 2)
Answers
9514 1404 393
Answer:
A) (0, 0)
B) (1, −25)
D) (−1, 25)
Step-by-step explanation:
For the point to lie on the line, the y-value must be -25 times the x-value. That is the case for points A, B, D.
Jamie drives her car 42 miles using 2 gallons of gas how many miles per gallon does her car get
Answers
21 miles per gallon
Step-by-step explanation:
42 ÷ 2 = 21
Alguien me dice si ya está correcto el trabajo?
Answers
Answer:
el que está debajo del que está marcado con un círculo es correcto
Step-by-step explanation:
12 out of 15 soccer players attended practice. What percentage of soccer players attended practice?
Answers
Answer:
1.25
Step-by-step explanation:
Answer:
12/15 > 4/5 equals 80%
Step-by-step explanation:
What is the place value in the 9 in the decimal 409.5
Answers
Answer:
The 9 is in the ones place.
:)
I need help rn I am going to fail
Answers
Answer:
slope is 0
Step-by-step explanation:
Slope formula: m= y2-y1/x2-x1
in (0,-1) (-3-1)
0 is x1
-1 is y1
-3 is x2
-1 is y2
-1-(-1) is 0
-3-0=-3
0/-3 is 0
Thus the slope is 0
Hope this helps!
[tex]70 \times 20[/tex]
I need help please
Answers
[tex] \sf \: 70 \times 20[/tex]
[tex]\sf \longmapsto1400[/tex]
OR the question can also be written as
[tex] \sf \: 70 (20)[/tex]
[tex]\sf \longmapsto1400[/tex]
-8x + 14y = -30
4x - 7y = 18
Answers
Answer:
I think you may have written it down wrong because no solution for that is possible.
Jackson's mom limits the amount of time he is allowed to play video games. After
Jackson plays for 9 minutes, his mom tells him that he has used up 15% of his time. How
many more minutes can Jackson play before he uses all of his time?
Answers
Answer:his mom sounds like a push over
Step-by-step explanation: she’s limiting his video games dude
A piece of wire 22 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area
Answers
9.56 m of the wire should be used for the square, to maximize the total area of the wire
Let x be the side length of the square.
So, the perimeter of the square is:
[tex]\mathbf{P_s=4x}[/tex]
Let y represent the side length of the equilateral triangle.
So, the perimeter of the triangle is:
[tex]\mathbf{P_t=3y}[/tex]
The length of the wire is given as:
[tex]\mathbf{P=22}[/tex]
This implies that:
[tex]\mathbf{P_s + P_t=22}[/tex]
Substitute values for Ps and Pt
[tex]\mathbf{4x + 3y=22}[/tex]
Make y the subject
[tex]\mathbf{y=\frac{22 -4x}3}[/tex]
For an equilateral triangle of side length y, the height (h) of the triangle is:
[tex]\mathbf{h =\frac y2\sqrt 3}[/tex]
The area of the triangle is then calculated as:
[tex]\mathbf{A_t = \frac 12 yh}[/tex]
This gives
[tex]\mathbf{A_t = \frac 12 y\times \frac y2\sqrt 3}[/tex]
[tex]\mathbf{A_t = \frac{y^2}{4}\sqrt 3}[/tex]
The area of the square is:
[tex]\mathbf{A_s = x^2}[/tex]
So, the total area is:
[tex]\mathbf{A = A_s + A_t}[/tex]
[tex]\mathbf{A = x^2 + \frac{y^2}{4}\sqrt 3}[/tex]
Substitute [tex]\mathbf{y=\frac{22 -4x}3}[/tex]
[tex]\mathbf{A = x^2 + (\frac{22 - 4x}{3})^2 \times \frac{\sqrt 3}{4}}[/tex]
Differentiate
[tex]\mathbf{A' = 2x + \frac{\sqrt 3}{4} \times \frac 19 \times 2(22 - 4x) \times (-4)}[/tex]
[tex]\mathbf{A' = 2x - \sqrt 3 \times \frac 19 \times 2(22 - 4x) }[/tex]
[tex]\mathbf{A' = 2x - \frac{2\sqrt 3}9 (22 - 4x) }[/tex]
Set to 0
[tex]\mathbf{2x - \frac{2\sqrt 3}9 (22 - 4x) = 0}[/tex]
Rewrite as:
[tex]\mathbf{2x = \frac{2\sqrt 3}9 (22 - 4x) }[/tex]
Divide through by 2
[tex]\mathbf{x = \frac{\sqrt 3}9 (22 - 4x) }[/tex]
Multiply through by 9
[tex]\mathbf{9x = \sqrt 3 (22 - 4x) }[/tex]
Open bracket
[tex]\mathbf{9x = 22\sqrt 3 - 4x\sqrt 3 }[/tex]
Collect like terms
[tex]\mathbf{9x +4x\sqrt 3= 22\sqrt 3 }[/tex]
Factor out x
[tex]\mathbf{x(9 +4\sqrt 3)= 22\sqrt 3 }[/tex]
Solve for x
[tex]\mathbf{x= \frac{22\sqrt 3}{9 +4\sqrt 3} }[/tex]
Simplify
[tex]\mathbf{x= \frac{38.11}{9 +6.93} }[/tex]
[tex]\mathbf{x= \frac{38.11}{15.93} }[/tex]
[tex]\mathbf{x= 2.39 }[/tex]
Recall that, the perimeter of the square is:
[tex]\mathbf{P_s=4x}[/tex]
So, we have:
[tex]\mathbf{P_s=4 \times 2.39}[/tex]
[tex]\mathbf{P_s=9.56}[/tex]
Hence, 9.56 m of the wire should be used for the square
Read more about maximizing lengths at:
https://brainly.com/question/3433355
Given the equation px^2 + 8x + 8 = 0 has equal roots find the value
of p.
Answers
[tex]\\ \sf\longmapsto px^2+8x+8=0[/tex]
Equal roots means Discriminate=0
[tex]\\ \sf\longmapsto D=0[/tex]
[tex]\\ \sf\longmapsto b^2-4ac=0[/tex]
[tex]\\ \sf\longmapsto 8^2-4(8)(p)=0[/tex]
[tex]\\ \sf\longmapsto 64-32p=0[/tex]
[tex]\\ \sf\longmapsto 32p=64[/tex]
[tex]\\ \sf\longmapsto p=2[/tex]
Answer:
p = 2Step-by-step explanation:
Since the roots are equal, the given equation should be a perfect square:
px² + 8x + 8 = 0Let p = 2q, since with odd value of p we can't get a perfect square:
2qx² + 8x + 8 = 0, divide all terms by 2qx² + 4x + 4 = 0The value of q should be 1 to make it a perfect square:
x² + 4x + 4 = 0(x + 2)² = 0Since q = 1, the value of p is:
p = 2q = 2*1 = 2The initial population of a town 2700, and it grows with a doubling time 10 years . What will the population be in 8 years
Answers
Answer:
There were 2160 people in 8 years.
Step-by-step explanation:
find unit rate
10/2700 = 270 people per year
270 x 8 = 2160
What is the value of the digit in the number based on the location of the digit
Answers
Answer:
Do u have a photo??
Step-by-step explanation:
cuzz I do not know
write an equation for the red line.
Answers
Answer:
Its is the second one
Step-by-step explanation:
Remember: rise over run
The b of the equation is -2 because that is how far it goes down on the y axis.
The slope is 3x.
Put the slope like this 3/1= rise/run
Sorry for the delayed response!
Pre Points Follow por more
Answers
nani .-. why tho?
why need followers?
must reason why
Answer:
JUPITER SATURN MARS
Step-by-step explanation:
A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the translation?
(x, y) → (x + 5, y – 3)
(x, y) → (x + 5, y + 3)
(x, y) → (x – 3, y + 5)
(x, y) → (x + 3, y + 5)
Answers
Answer: Choice C
(x, y) → (x – 3, y + 5)
=================================================
Explanation:
The "5 units up" portion means that each y value increases by 5. Therefore, we go from y to y+5. Going from x to x-3 means that we shift each point 3 units to the right.
For example, if the starting point is (1,7), then we have the following steps:
[tex](x,y) \to (x-3,y+5)\\\\(1,7) \to (1-3,7+5)\\\\(1,7) \to (-2,12)\\\\[/tex]
The point (1,7) moves 5 units up and 3 units to the left to arrive at (-2,12).
Note that the order doesn't matter. We could start moving 5 units up, then go 3 units left. Or we could start going 3 units left, then 5 units up. We'll arrive at the same destination.
