Answer:
16,242. 7 cm^3.
Step-by-step explanation:
We need to cut off a square piece at the 4 corners of the cardboard.
Let the length of their edges be x cm.
The volume of the box will be:
V = height * width * length
V = x(100-2x)(40-2x)
V = x(4000 - 200x - 80x + 4x^2)
V = x(4x^2 - 280x + 4000)
V = 4x^3 + - 280x^2 + 4000x
Finding the derivative:
dV / dx = 12x^2 - 560x + 4000 = 0 ( when V is a maxm or minm.)
4(3x^2 - 140x + 1000) = 0
x = 37.86, 8.80.
Looks like x = 8.80 is the right value but we can check this out be looking at the sign of the second derivative:
V" = 24x - 560, when x = 8.8 V" is negative so this is a Maximum for V.
So the maximum volume of the box is when x = 8.8 so we have
V = 8.8(100-2(8.8)(40 - 2(8.8)
= 16,242. 7 cm^3.
When the polynomial P(x)=ax^3+bx^2+3x-10 is divided by x+1, the remainder is -8. P(x) has a factor of x+5. Find the values of a and b.
Answer:
a = 1, b = 6
Step-by-step explanation:
The equation given is as follows;
P(x) = a·x³ + b·x² + 3·x - 10
The above equation has a factor of x + 5, therefore, we have;
P(-5) = 0 = a·(-5)³ + b·(-5)² + 3·(-5) - 10
-125·a + 25·b + (-15) - 10 = 0
-125·a + 25·b - 25 = 0
-125·a + 25·b = 25...........(1)
Also, we are given that;
a·x³ + b·x² + 3·x - 10 divided by x + 1 as a remainder, R = -8, therefore;
P(-1) = -8 = a·(-1)³ + b·(-1)² + 3·(-1) - 10
-a + b - 13 = -8
-a + b = -8 + 13 = 5
-a + b = 5............................(2)
Multiply equation (2) by 25 and subtract from (1) gives
-125·a + 25·b - 25(-a + b) = 25 - 25×5
-100·a = 25 - 125 = -100
a = 1
Therefore, from equation (2) we have;
-1 + b = 5
b = 5 + 1 = 6.
What is an equation of the line that passes through the point
(−1,5) and is parallel to the line
x−y=6?
Answer:
The equation in slope-intercept form is y = x + 6
Step-by-step explanation:
For this question, we will use point slope form, where you can put in a point and a slope and get an equation of the line that passes through the point with that slope.
The point slope formula is y - y1 = m(x-x1) where y1 is the y coordinate of the point, m is the slope, and x1 is the x coordinate.
We are trying to find a line parallel to x - y = 6, so our line will have the same slope as it. To find the slope of x - y = 6, subtract x and divide by -1. This gives us y = x - 6, where the slope is 1.
Now we have all necessary information.
Plug in the values: y - 5 = 1(x + 1)
Simplify: y - 5 = x + 1
Add 5 to both sides: y = x + 6
The answer is y = x + 6
Identify the graph of y^2+8x=0 for theta=π/6 and write an equation of the translated or rotated graph in general form.
Answer:
parabola; (x)^2-2(square root 3) xy+3(y)^2 +16 (square root 3) x+16=0
Step-by-step explanation:
edge’s possible answer 2020
express x^2-8x+20 in the form (x-a)^2+a where a is an integer
Answer:
(x-4)²+4
Step-by-step explanation:
Answer:
[tex](x-4)^2+4[/tex]
Step-by-step explanation:
[tex]x^2 - 8x + 20\\**********************************\\\frac{8}{2} =( 4 )^2 = 16 \\\\20 - 16 = 4\\**********************************\\x^2 - 8x + 16 + 4\\(x-4)^2+4[/tex]
Help please!!
Solve the equation -5m = -20.
m = 1/4
m = -1/4
m = -4
m = 4
Answer:
m=4
Step-by-step explanation:
-5m=-20
m= - 20/-5
m=4
Answer:
M=4
Step-by-step explanation:
This question was on my online school assignment. I can go back on my assignments and review and I had got it right.
What is the slope of the line represented by the equation y=4/5x-3? A.-3 B.-4/5 C.4/5 D.3
Answer:
4/5
Step-by-step explanation:
y = 4/5 x -3
This is written in slope intercept form
y =mx + b where m is the slope and b is the y intercept
the slope is 4/5 and the y intercept is -3
TRUE OR FALSE
(b^4)^3 = b^12
Answer:
TRUE
Step-by-step explanation:
if it was b^4 x b^3 then false. but here, would would multiply b^4 by b^3 to make it 12 so true
sorry for bad explanation
Answer:
True
Step-by-step explanation:
If b=2, 2^4 is 16, and 16^3 is 4096.
Also 2^12 is 4096.
So they are equivalent.
If 8a^2+ 2b^2= 10 and ab = 2, then what is the value of (2a+b)^2
Answer:
13
Step-by-step explanation:
We have:
8a^2 + 2b^2 = 10
Dividing both sides by 2,
=> 4a^2 + b^2 = 5
or (2a)^2 + b^2 = 5
We also have ab = 2
=> (2a + b)^2
= (2a)^2 + 2(2a)(b) + b^2
= (2a)^2 + b^2 + 4ab
= 5 + 4(2)
= 5 + 8
= 13
Which statement describes the end behavior of the function f(x) = 3|x − 7| − 7? A. As x approaches negative infinity, f(x) approaches negative infinity. B. As x approaches negative infinity, f(x) approaches positive infinity. C. As x approaches positive infinity, f(x) approaches negative infinity. D. As x approaches positive infinity, f(x) is no longer continuous.
Answer:
Our expressions is f(x) = 3|x-7|-7
in positive values |x-7| is x-7 ⇒f(x) = 3x-28in negative ones |x-7| is 7-x wich is the opposite⇒f(x) = 14-3xLet's calculate the limits in +∞ and -∞
[tex]\lim_{x \to +\infty} (3x-28)=[/tex][tex]\lim_{x \to+ \infty} 3x[/tex] = +∞ [tex]\lim_{x \to- \infty} (14-3x) = \lim_{x \to- \infty} -3x[/tex] =+∞So the right staement is B
As x approaches positive infinity, f(x) approaches negative infinity.
What is a function?A relation is a function if it has only One y-value for each x-value.
The function f(x) = 3|x − 7| − 7 is a piecewise function, where the absolute value function has two cases depending on the sign of (x - 7).
When (x - 7) is positive, the function becomes 3(x - 7) - 7 = 3x - 28, and when (x - 7) is negative, the function becomes -3(x - 7) - 7 = -3x + 14.
As x approaches positive infinity, both cases approach negative infinity because the dominant term in each case is the linear term (3x or -3x) as x becomes large.
Therefore, the end behavior of the function is that as x approaches positive infinity, f(x) approaches negative infinity.
To learn more on Functions click:
https://brainly.com/question/30721594
#SPJ3
A "necklace" is a circular string with several beads on it. It is allowed to rotate a necklace but not to turn it over. How many different necklaces can be made using 13 different beads? help plz i will give brainlyist to right awnser :3
Answer:
We have 13 different beads to use in our necklace, and the thing that will make a necklace different to others, is the position of the beads.
And because we can not turn the necklaces over, the mirrored necklaces are different (the positions of the beads are mirrored)
For the first bead, we have 13 options, for the second, 12 options, and so on
the total number of combinations is equal to the product of the options for each selection, then we have:
C = 13*12*11*10*9*8*7*6*5*4*3*2*1 combinations:
C = 6,227,020,800.
Now, we are allowed to rotate the necklace, this means that a combination.
a b c d e f g h i j k l m (each letter is equivalent to one of the different beads)
is the same as other ordered as
m a b c d e f g h i j k l
And for each combination, we have 13 rotations, then the actual number of combinations is:
C/13 = 6,227,020,800/13 = 479,001,600
Using arrangements, it is found that 6,227,020,800 different necklaces can be made using 13 different beads.
The beads can be exchanged among the positions to form the necklace, hence, the arrangements formula is used.
This formula gives the number of possible arrangements of n elements, and is defined by:
[tex]A_n = n![/tex]
In this problem, the necklaces are formed by 13 beads, hence [tex]n = 13[/tex] and:
[tex]A_{13} = 13! = 6227020800[/tex]
6,227,020,800 different necklaces can be made using 13 different beads.
A similar problem is given at https://brainly.com/question/24648661
.Nisha bought a backpack that was on sale at 35% off for $63. How much was the original price of the backpack?
Answer:
$180
Step-by-step explanation:
100%=x
35%=$63
63 x 100=6300/35=$180
Answer:
96.92
Step-by-step explanation:
If the backpack was 35% off you will still pay 100 -35 or 65%
Let x be the original price
x * 65% = 63
Change to decimal form
x * .65 = 63
Divide each side by .64
x*.65/.65 = 63/.65
x =96.92
what is the product of the polynomials below? (8x^2-4x-8) (2x^2+3x+2)
Answer:
B
Step-by-step explanation:
you can FOIL or set up a box that is 3 x 3 (which is what I recommend) to solve it.
The product of the given polynomials is [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]. The correct option is- B. [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]
Product of polynomialsFrom the question, we are to determine the product of the given polynomials
The given polynomials are
(8x^2-4x-8) (2x^2+3x+2)
Their product can be determined as follows
[tex](8x^2-4x-8) (2x^2+3x+2)[/tex]
[tex](8x^2) (2x^2+3x+2)-4x(2x^2+3x+2)-8 (2x^2+3x+2)[/tex]
Clear the brackets
[tex]16x^4 +24x^3+16x^2 -8x^3-12x^2-8x-16x^2-24x-16[/tex]
Now, collect like terms
[tex]16x^4 +24x^3 -8x^3-12x^2+16x^2-16x^2-8x-24x-16[/tex]
Simplifying
[tex]16x^4 +16x^3 -12x^2-32x-16[/tex]
Hence, the product of the given polynomials is [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]. The correct option is- B. [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]
Learn more on Product of polynomials here: https://brainly.com/question/12885308
#SPJ2
Which point is an x-intercept of the quadratic function f(x)=(x-8)(x+9)? 1. (0,8) 2.(0,-8) 3.(9,0) 4.(-9,0) If yk how to do these, pls help with my other questions :( <3
Answer:
x intercept is when y = 0, so when y is 0, x should be -9 or 8, so 4. is the only that satisfies it, therefore (-9,0)
Step-by-step explanation:
Follow me at "btracta" on insta and we can talk
What's your instagram then?
Yes 80 followers following 10 is me
Which expression is equivalent to (–3y – x) – (5y – 8x)?
Answer:
-8y +7x
Step-by-step explanation:
(–3y – x) – (5y – 8x)Distribute
-3y -x -5y +8x
Combine like terms
-3y-5y -x+8x
-8y +7x
Jenny wants to show the gym on a scale drawing. She uses a scale of 1:75. The gym has a length of 12.3 metres. Jenny works out the length of the gym on the scale drawing is 18cm. Is she correct?
Answer:
She is wrong
Step-by-step explanation:
Let us use the scale 1 : 75 to find the length of the gym on the scale drawing.
The scale means that 1 m on the drawing represents 75 m in real life.
Therefore, if the length of the gym is 12.3 cm, then the length of the gym in the scale drawing is:
12.3 / 75 = 0.164 m
Converting to cm:
1 m = 100 cm
0.164 m = 0.164 * 100 = 16.4 cm
She is wrong.
92.6 % of 103.93 km Give your answer rounded to 2 DP.
Answer:
[tex]Result = 96.24\ km[/tex]
Step-by-step explanation:
Given
92.6 % of 103.93 km
Required
Solve (to 2 decimal places)
To solve this, we simply multiply both 92.6% and 103.93 km together;
[tex]Result = 92.6\% * 103.93\ km[/tex]
Convert percentage to fraction
[tex]Result = \frac{92.6}{100} * 103.93\ km[/tex]
Combine to form a single fraction
[tex]Result = \frac{92.6 * 103.93\ km}{100}[/tex]
[tex]Result = \frac{9623.918\ km}{100}[/tex]
[tex]Result = 96.23918\ km[/tex]
[tex]Result = 96.24\ km[/tex] (Approximated to 2 decimal places)
Which function represents the following graph?
Answer:
y = ∛(x+3) + 3
Step-by-step explanation:
I plugged each equation into a graphing calculator.
precalculus help! i'm having some trouble with my summer assignment. help would be very appreciated :)))
6.
[tex]y^2\sqrt[8]{8}[/tex]
Step-by-step explanation:
[tex]\sqrt[8]{8*y*y*y*y*y*y*y*y*y*y*y*y*y*y*y*y}[/tex]
Since there are eight y's in two groups we can take them out which turns into
[tex]y^2\sqrt[8]{8}[/tex]
:)
3.
Problem 3:
We are given the following complex number and I'm assuming we want to simplify it:
[tex]\dfrac{5+i}{6+i}[/tex]
Using the complex arithmetic rule (research about this if you're not familiar with it, it's very helpful):
[tex]=\dfrac{(5\times6+1)+(6-5)i}{6^2+1^2}[/tex]
[tex]=\dfrac{31+i}{37}[/tex]
Simplifying gives us:
[tex]=\dfrac{31}{37}+\dfrac{1}{37}i[/tex]
Problem 6:
You seem to have done this problem correctly
[tex]\sqrt[8]{8y^{16}}[/tex]
Expanding gives us:
[tex]=\sqrt[8]{y^{16}}\times\sqrt[8]{8}[/tex]
[tex]=y^2\sqrt[8]{8}[/tex]
This can't be simplified further as the 8th root of 8 gives us an irrational number
Let me know if you need any clarifications or extra help, thanks!
Martin is an after-school math tutor. He noticed that 6 people still needed help and only 2/5 of the tutoring session time was left. Since each person is to be given an equal amount of time, Martin wrote the expression below to find the fraction of the tutoring session each person who still needed help would be allotted. 2/5÷6 Which expression is equivalent to Martin’s expression? A.6/15÷6 B.6/5÷2 C.5/2÷6 4.2/5÷6 Help!! A:18 ÷2/9 B:18×2/9 C:2/9
Answer:
A
Step-by-step explanation:
Trust me on this and I also have a reason.
Divide 2/5 by 6 to get 1/15, then divide 6/15 by 6 to get 1/15, and both of these are simpflied.
Can I also get brainlest, I hope you do well!
The expression equivalent to Martin's expression is A. 6/15 ÷ 6.
What is Division?Division is simply the opposite operation of multiplication. It is one of the basic mathematical operations where a number is divided into equal parts as that of another number.
The number being divided is called dividend and the number which divides dividend is called divisor. The resulting number after the operation is called quotient.
We have to divide the expression 2/5 ÷ 6.
When a fraction is divided by another number the divisor is change into it's reciprocal and the multiplied to the dividend.
Here dividend = 2/5 and divisor = 6
Reciprocal of 6 = 1/6
So 2/5 ÷ 6 = (2/5) × (1/6) = 2/30 = 1/15
Simplify the numbers in the options.
A. 6/15 ÷ 6 = (6/15) × (1/6) = 1/15
Hence the equivalent expression of 2/5 ÷ 6 is 6/15 ÷ 6.
Learn more about Division here :
https://brainly.com/question/21416852
#SPJ3
Please answer for brainliest!!!Find the equation of a line that passes through the point (-2,1) and has a gradient of 3. Leave your answer in the form ax+by=c Where a, b and c are integers
Answer:
3x - y = - 7
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = 3 and (a, b) = (- 2, 1) , thus
y - 1 = 3(x + 2) ← distribute
y - 1 = 3x + 6 ( subtract 6 from both sides )
y - 7 = 3x ( subtract y from both sides )
- 7 = 3x - y, that is
3x - y = - 7 ← in standard form
help me please ill give brainly :D please dont answer for my points :(
Answer:
15 days
Step-by-step explanation:
5 people * 16 days * 6 hrs= 480 hours
8 people * x days * 4 hours= 32x hours
32x=480x= 480/32x= 15 daysthe picture is the qestion
Answer:
12/18 bcz simplyfing 12/18 will give us 2/3
6/9 (divided by 2)
2/3 (divided by 3)
Step-by-step explanation:
cos^4a=1/8(3+4cos2a+cos4a)
Answer:
Below.
Step-by-step explanation:
cos2a = 2 cos^2 a - 1
cos^4a = 8cos^4 a - 8cos^2 a + 1
Right side of the identity =
1 /8(3 + 4cos2a + cos4a)
= 1/8( 3 + 4(2 cos^2 a - 1) + 8cos^4 a - 8cos^2 a+1)
= 1/8 (3 + 8 cos^2 a - 4 + 8 cos^4 a - 8cos^2 a + 1)
= 1/8 (8cos^4 a)
= cos^4 a = the left side.
I realised that I should have derived the identity for cos 4a as well , which i have done in the picture.
The given identity, cos⁴a = 1/8(3 + 4cos2a + cos4a) is proved.
How is proving identities done?To prove a given identity, say f(a) = f(b), we proceed to simplify any of the expressions among the L.H.S. f(a) and the R.H.S. f(b), to get the other term. If we get the simplified form as the other term, our identity holds and is proved.
How do we solve the given question?We know cos2A = 2cos²A - 1.
Going by the same formula, we derive the value of cos4A.
cos4A = 2cos²2A - 1
or, cos4A = 2(2cos²A - 1)² - 1, putting value of cos2A
or, cos4A = 2(4cos⁴A - 4cos²A + 1) - 1, (expanding (2cos²A - 1)² using the formula of (a-b)² = a² -2ab + b²)
or, cos4A = 8cos⁴A - 8cos²A + 2 - 1, (expanding)
or, cos4A = 8cos⁴A - 8cos²A + 1, (simplifying)
∴ cos4A = 8cos⁴A - 8cos²A + 1.
Given identity to us is, cos⁴a = 1/8(3 + 4cos2a + cos4a).
To prove the identity, we proceed with the R.H.S.:
= 1/8(3 + 4cos2a + cos4a)
We put values of cos2A and cos4A in this expression, to get
= 1/8(3 + 4(2cos²a - 1) + (8cos⁴a - 8cos²a + 1))
Expanding the equation, we get
= 1/8(3 + 8cos²a - 4 + 8cos⁴a - 8cos²a + 1)
Simplifying, we get
= 1/8(8cos⁴a) = cos⁴a = L.H.S.
Hence, the given identity is proved.
Learn more about proving identities at
https://brainly.com/question/7331447
#SPJ2
Write the equation of the line that passes through (2, 3) and is parallel to the line 12x – 5y = 2.
Answer:
The answer is
5y - 12x = - 9Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
12x - 5y = 2
5y = 12x - 2
Divide both sides by 5
y = 12/5x - 1/5
Comparing with the above formula
Slope / m = 12/5
Since the lines are parallel their slope are also the same.
Slope the parallel line = 12/5
Equation of the line using point (2,3) is
[tex]y - 3 = \frac{12}{5} (x - 2) [/tex]
Multiply through by 5
That's
5y - 15 = 12(x - 2)
5y - 15 = 12x - 24
We have the final answer as
5y - 12x = - 9Hope this helps you
Plz Help!!! I really do not get this lesson and I really need to pass it to move onto the next I am kind of getting it, I want to make sure my answer is correct. IS it sas?
Answer:
SSS
Step-by-step explanation:
I think it would be SSS (side, side, side)... let me know if I'm wrong and I'll try again:)
Check out the diagram below. I've marked the angles and sides that are congruent. Notice how the marked sides are not between the marked angles for either triangle. So we're dealing with AAS instead of ASA. The order is important. If we wanted to use ASA, then we would have to know DE = TU, both of those sides are between the marked angles.
Please help me with this question!!
Answer: Choice B) The conjecture is valid given the focus is on proportional equivalence of two sectors.
This is another way of saying "the two pie slices are the same percentage in area". By this, I mean the percentage of the entire cake. For instance, the shaded slice could be 20% of the entire circle area, for each circle.
It's probably easier to see this is the angle was 90 degrees (split the cake into 4 equal slices, only shade one slice). Or probably even easier if you cut the cake into two slices and only shade one slice (to form a central angle of 180 degrees). For the first example, the slice would be 25% of the whole area, while the second slice is 50%.
Choice C is close, but the two sectors are not the same area. This is because the bottom circle has a larger radius, and therefore its sector area is larger.
Alonso is packing a box for shipping. The box contains 3 square ceramic plates with side lengths of 8 inches. He estimates that he will need 102 • 4 – 3(8 • 8 • 1) cubic inches of packing foam. Simplify to find the number of cubic inches of packing foam he will need.
Answer:
216 cubic inches
Step-by-step explanation:
We want to simplify:
102 * 4 - 3(8 * 8 * 1)
We will apply BODMAS:
Solving the Bracket first:
102 * 4 - 3(64)
102 * 4 - 192
=> 408 - 192
= 216 cubic inches
He will need 216 cubic inches of packing foam.
The following function represents an arithmetic sequence.
f(1)=2
f(n+1)=f(n)+4
What is f(10)?
Enter your answer as a number, like this: 42
Answer:
f(10)=34
Step-by-step explanation:
This is an arithmetic sequence of common difference "d = 4" (the number added to a term in order to get the next term), and first term 2,
Then we use the formula to find the nth term of an arithmetic sequence with is:
[tex]f(n)=f(1) +\,(n-1)\,d[/tex]
In our case this formula for the term number 10 becomes:
[tex]f(n)=f(1) +\,(n-1)\,d\\f(10)=f(1)+(10-1)\,4\\f(10=2+9*4\\f(10)=2+32\\f(10)=34[/tex]
Answer: Just took it!!!
f(10)=38
Step-by-step explanation:
f(1)=2
f(n+1)=f(n)+4
f(2)=6
f(3)=10
f(4)=14
f(5)=18
f(6)=22
f(7)=26
f(8)=30
f(9)=34
f(10)=38
Example A
Find the area of the blue sector. Leave your answer in terms of TT.
Answer: [tex]10\frac{2}{3}\pi[/tex]
Step-by-step explanation:
Do you really need it? If so, reply, if not, mark brainliest.
which number produces an irrational number when added to 1/2?
A. 0.373737...
B. 3.14159265...
C. √16
D. -4/7
The number 3.14159265 produces an irrational number when added to 1/2.
What is the sum of an irrational number and a rational number?
The sum of any rational number and any irrational number will be always an irrational number.
What is irrational number?An irrational number is a type of real number which cannot be represented as a simple fraction.
What is rational number?A number that can be represented as the quotient p/q of two integers such that q ≠ 0 is called a rational number.
According to the given question
We have a rational number 1/2.
Since, 0.373737373.... is a rational number because it is recurring and its behavior it known that 37 is repeating.
And we know that when any rational number is added with a rational number it with number we will get always a rational number.
⇒ 0.3737373737... + [tex]\frac{1}{2}[/tex] = rational number.
3.14159265... is an irrational number because its behavior is not known and it is not terminating.
So, when we add 1/2 to 3.14159265.. we get a irrational number.
√16 = 4 is a rational number. And it can be written as [tex]\frac{4}{1}[/tex].
So, [tex]\frac{4}{1} + \frac{1}{2} = \frac{9}{2}[/tex] which is a rational number.
-4/7 is a rational number. And when we add 1/2 to -4/7 we get a rational number.
i.e. [tex]\frac{-4}{7} + \frac{1}{2} = \frac{-1}{14}[/tex] which is rational number.
Hence, the number 3.14159265 produces an irrational number when added to 1/2.
Learn more about rational and irrational number here:
https://brainly.com/question/17005818
#SPJ2