Answer:
32 notebooks will fit.
Step-by-step explanation:
Find the slope of the line tangent to the graph of (x^2)-((xy)^(1/2))=(2y^2)+3x at the point (4,1).
Compute [tex]\frac{\mathrm dy}{\mathrm dx}[/tex] using implicit differentiation:
[tex]x^2-(xy)^{1/2}=2y^2+3x[/tex]
[tex]\dfrac{\mathrm d(x^2)}{\mathrm dx}-\dfrac{\mathrm d(xy)^{1/2}}{\mathrm dx}=\dfrac{\mathrm d(2y^2)}{\mathrm dx}+\dfrac{\mathrm d(3x)}{\mathrm dx}[/tex]
[tex]2x-\dfrac1{2(xy)^{1/2}}\left(\dfrac{\mathrm dx}{\mathrm dx}y+x\dfrac{\mathrm dy}{\mathrm dx}\right)=4y\dfrac{\mathrm dy}{\mathrm dx}+3[/tex]
[tex]2x-\dfrac1{2(xy)^{1/2}}\left(y+x\dfrac{\mathrm dy}{\mathrm dx}\right)=4y\dfrac{\mathrm dy}{\mathrm dx}+3[/tex]
[tex]2x-\dfrac12\left(\dfrac yx\right)^{1/2}-\dfrac12\left(\dfrac xy\right)^{1/2}\dfrac{\mathrm dy}{\mathrm dx}=4y\dfrac{\mathrm dy}{\mathrm dx}+3[/tex]
[tex]2x-3-\dfrac12\left(\dfrac yx\right)^{1/2}=\left(4y+\dfrac12\left(\dfrac xy\right)^{1/2}\right)\right)\dfrac{\mathrm dy}{\mathrm dx}[/tex]
[tex]4x-6-\left(\dfrac yx\right)^{1/2}=\left(8y+\left(\dfrac xy\right)^{1/2}\right)\right)\dfrac{\mathrm dy}{\mathrm dx}[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4x-6-\left(\frac yx\right)^{1/2}}{8y+\left(\frac xy\right)^{1/2}}[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4x(xy)^{1/2}-6(xy)^{1/2}-y}{8y(xy)^{1/2}+x}[/tex]
Plug in x = 4 and y = 1 to find that the tangent line's slope is 19/20.
Which pound bag is the lowest price per pound of dog food?
They are all the same cost per pound.
30
8
22
Today only, a table is being sold at a 62% discount. The sale price is $144.40.
What was the price yesterday?
$ 232.90
Step-by-step explanation:62% ........... $144.40
100% ..........$ x
x = 144.40×100/62
= 14440/62
= $ 232.90
A jug contains 20 3/8 cups of lemonade. If you are serving guests at a summer picnic, how many glasses can you fill if each guest gets 1 1/2 cups of lemonade?
Answer:
13 glasses
Step-by-step explanation:
Given:
Amount of of lemonade available = 20⅜ cups
Amount of lemonade per guest = 1½ cups
Required:
Number of glasses to be filled
SOLUTION:
Number of glass to be filled = amount of lemonade available ÷ amount of lemonade per guest
= 20⅜ ÷ 1½
Change both mixed fractions to improper fractions
= [tex] \frac{163}{8} [/tex] ÷ [tex] \frac{3}{2} [/tex]
Flip the fraction on your right upside down and change the division to multiplication
[tex] = \frac{163}{8} * \frac{2}{3} [/tex]
[tex] = \frac{163*2}{8*3} [/tex]
[tex] = \frac{163*1}{4*3} [/tex]
[tex] = \frac{163}{12} = 13.58 [/tex]
Number of glasses that would be filled is roughly 13 glasses.
4x - 7 (2 - x) = 3x + 2
Answer:
x=2
Step-by-step explanation:
4x−7(2−x)=3x+2
4x+(−7)(2)+(−7)(−x)=3x+2(Distribute)
4x+−14+7x=3x+2
(4x+7x)+(−14)=3x+2(Combine Like Terms)
11x+−14=3x+2
11x−14=3x+2
Step 2: Subtract 3x from both sides.
11x−14−3x=3x+2−3x
8x−14=2
Step 3: Add 14 to both sides.
8x−14+14=2+14
8x=16
Step 4: Divide both sides by 8.
x=2
Write an expression that is equivalent to 5(x + 2) - 7(x + 2)?
Answer:
-2x-4
Step-by-step explanation:
Just simplify
5
Select the correct answer.
if(t + 4) is a factor of polynomial p, which statement must be true?
OA. p(4)
0
B. p(4) < 0
OC. P(-4) = 0
OD. p(-4) > 0
What’s the answer
Answer:
[tex]p(-4) = 0[/tex]
Step-by-step explanation:
Given
[tex]Polynomial: p[/tex]
[tex]Factor: (t + 4)[/tex]
Required
Which statement is true
First we need to equate t + 4 to 0; then solve for t
[tex]t + 4 = 0\\[/tex]
[tex]t = 0 - 4[/tex]
[tex]t = -4[/tex]
Represent the polynomial as a function of t:
[tex]p(t) = 0[/tex]
Substitute -4 for t
[tex]p(-4) = 0[/tex]
Find the probability for one roll of a number cube.
P(number greater than or equal to 7)
A. 1/7
B. 0
C. 1/6
D. 1
The only possible outcomes on a standard number cube (aka a die or dice) are {1,2,3,4,5,6}
It is not possible to roll a 7 or larger, so we say the probability is 0. A probability of 0 means "impossible".
Which ratio is greater than 5/8 ? A. 12/24 B. 3/4 C. 15/24 D. 4/12
B is the 3/4 = .75 and 5/8 = .625
Find the unknown length y in the pair of similar triangles.
Step-by-step explanation:
If 2 triangles are similar then the ratio of any 2 sides of one triangles will be equal to the ratio of any 2 sides of the another triangle.
So,
[tex] \frac{30}{8} = \frac{20}{y} [/tex]
Cross-multiplying the denominators gives,
[tex]30y = 160[/tex]
[tex] = > y = \frac{160}{30} = \frac{16}{3} [/tex]
Factorize 6p2 - 7p + 2
Answer:
(2p - 1)(3p - 2)
explain briefly what you understand by each of the following techniques of investment appraisal.
1. profitability index
Answer:
Is Calculated by dividing the present value of future cash flows that will be generated by the project by the project
Step-by-step explanation:
BRAINILIEST PLEASEEEEEE
A negative number divided by a negative number will result in a _ Quotient
Answer:
Positive
Step-by-step explanation:
Two negatives make a positive.
box contains five while balls, four red balls and three blue balls. Suppose that three balls are randomly selected. a. What is the probability that exactly two of the balls are white ? b. What is the probability that one ball of each color is selected ? c. What is the probability that all three of the selected balls have the same color ?
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Number of white balls = 5
Number of red balls = 4
Number if blue balls = 3
Probability = required outcome / Total possible outcomes
Total possible outcomes (Total number of balls) = 5 + 4 + 3 = 12
a. What is the probability that exactly two of the balls are white?
(White, white, not white) or (not white, white, white) or (white, not white, white)
Assume balls were picked without replacement ;
P(white, white, not white) = (5/12 × 4/11 × 7/10) = 0.1060606
P(not white, white, white) = (7/12 × 5/11 × 4/10) = 0.1060606
P(white, not white, white) = (5/12 × 7/11 × 4/10) = 0.1060606
P(exactly 2 white balls) = 3×(0.1060606) = 0.3181818
b. What is the probability that one ball of each color is selected ?
(White, red, blue) or (red, white, blue) or (red, blue, white) or (blue, red, white), (white, blue, red), (blue, white, red)
P(white, red, blue) = (5/12 * 4/11 * 3/10) = 0.0454545
(0.0454545 × 3) = 0.272727
c. What is the probability that all three of the selected balls have the same color ?
P(white, white, white) or P(blue, blue, blue) or P(red, red, red)
P(white, white, white) = (5/12 * 4/11 * 3/10) = 0.0454545
P(blue, blue, blue) = (3/12 * 2/11 * 1/10) = 0.0045454
P(red, red, red) = (4/12 * 3/11 * 2/10) = 0.0181818
(0.0454545 + 0.0045454 + 0.0181818) = 0.0681817
Estimate the difference.
858.9 - 172
Use rounding to estimate the difference.
Answer:
can u answer my question plz
Step-by-step explanation: A kitchen wall tile is shaped like a parallelogram. The base of the tile is two times the height of the tile. The height of the tile is 2 in. The length of the other side of the tile is 3 in. What is the area of the tile?
work out the difference in minutes between 1 hour 25 minutes and 1 1/4 hours step by step please :)
[tex]\huge\boxed{\boxed{\bold{10\ \bftext{minutes}}}}[/tex]
[tex]\hrulefill[/tex]
First, let's change both of these times into just minutes. (We know that one hour is sixty minutes.)
[tex]\text{First time: } 1*60+25=60+25=85[/tex]
[tex]\text{Second time: } 1*60+\frac{1}{4}*60=60+15=75[/tex]
Now, just subtract:
[tex]85-75=\large\boxed{10}[/tex]
1.) (-18, -20) (18, 16)
2.) (-7, 14) (-11, 4)
3.) (-5, -4) (3, 9)
4.) (13, -8) (-9, -1)
1.) (-18, -20) (18, 16)
m= 1
2.) (-7, 14) (-11, 4)
m= 5/2
3.) (-5, -4) (3, 9)
m= 13/8
4.) (13, -8) (-9, -1)
m= -7/22
Pls help pls ASAP 1,2,3,4
Answer:
3
Step-by-step explanation:
Answer: the third on i think
Step-by-step explanation:
What is the value of x
Answer:
x =68
Step-by-step explanation:
The sum of the angles of a triangle are 180
37+75+x = 180
Combine like terms
112+x = 180
Subtract 112 from each side
112+x-112=180-112
x =68
Question 7
2 pts
If you bought something in Wyoming for $54, you would be charged $3.56 in state sales tax. What is the
state sales tax rate in Wyoming?
Insert your answer as a percentage to the tenth WITHOUT the % symbol.
Question 8
2 pts
Answer:
6.6
Step-by-step explanation:
The way to do this is to find the tax as a decimal. Worry about the 100 later.
54 * x = 3.56
Divide by 54
x = 3.56/54
x = .06593
Now use the 100
0.06592 * 100 = 6.593
But you want it rounded to the 1/10
So you should get 6.6 %
I really need help with this question
Answer:
The answer is 235.6
Step-by-step explanation:
You plug in the numbers to the equation.
1. Four times a number increased by 3 is -89. what is the correct equation?!? PLEASE HELP ME!!!
A. 3+= 89
C. 4n+3 = -89
B. 4n-3= -89
D.4+3n = -89
. Which table does NOT show y as a function of x?
I 름
4
1
A.
7
Х
10
14
9
9
11
y
18
17
15
16
110
90
B.
14
х
100
80
100
y
-0.2
1.0
-0.9
8.1
-1.3
4.4
C.
0.6
-3.7
Х
-0.2
5.8
y
29
24
21
-27
2.5
2.5
D.
- 24
Х
2.7
2.8
2.7
Y У
o
Differentiate the function. f(x) = sin(9 ln(x))
Answer: [tex]f'(x)=\dfrac{9\cos(9\ln (x))}{x}[/tex].
Step-by-step explanation:
The given function is
[tex]f(x)=\sin(9\ln (x))[/tex]
Using chain rule differentiate w.r.t. x.
[tex]f'(x)=\cos(9\ln (x))\dfrac{d}{dx}(9\ln (x))[/tex] [tex]\left[\because \dfrac{d}{dx}\sin x=\cos x\right][/tex]
[tex]f'(x)=\cos(9\ln (x))\left[9\dfrac{d}{dx}(\ln (x))\right][/tex]
[tex]f'(x)=\cos(9\ln (x))\left[9\times \dfrac{1}{x}\right][/tex] [tex]\left[\because \dfrac{d}{dx}\ln x=\dfrac{1}{x}\right][/tex]
[tex]f'(x)=\dfrac{9\cos(9\ln (x))}{x}[/tex]
Therefore, [tex]f'(x)=\dfrac{9\cos(9\ln (x))}{x}[/tex].
As a cube what is -1/64 ________ to the power of ^3
Answer:
(-1/64)= (-1/4)^3
Explanation:
[tex]\sqrt[3]{-\frac{1}{64} }=-\frac{1}{4}[/tex]
[tex](-\frac{1}{4})^3=-\frac{1}{64}[/tex]
Can anyone help with this question
Answer: A) x=6
Step-by-step explanation: my trick that i do with these questions are to just fill in the x's with the different choices that they give you.
so... first try out 6. fill in every x with a 6. so now, x isn't x anymore, it's 6.
(8-6)=2
9 times 2= 18
3 times 6= 18
this means that x would equal 6
if that first one doesn't work, try out the other ones. but this one works, so we know we have the right answer. i hope this helps with this problem, and i hope it helps with other problems like this too.
:)
X- 3 = 9 workings pls
What is the horizontal distance between the two points (-7,-4) and (12,-4)? Remember that distance is always positive! Hint: The horizontal distance is represented by the 1st number in each coordinate. What is the difference between -7 and 12?
==================================================
Explanation:
Draw out a number line. Plot -7 and 12 on the number line. Draw in the tickmarks between them. You should find the distance from -7 to 12 is 19 units since you need to go 19 spaces from either -7 to 12, or vice versa.
You can use subtraction to get
-7-12 = -19
or
12-(-7) = 12+7 = 19
The final result is made positive since negative distance does not make sense.
So you'd have |-7-12| = |-19| = 19 or |12-(-7)| = |19| = 19.
All of this only works because the two y coordinates are the same, which makes a horizontal line through the two given points.
Subtract. −3 2/7 − (−5/7)
Enter your answer in the box as mixed number in simplest form.
___
Answer:
-2 4/7
Step-by-step explanation:
−3 2/7 − (−5/7)
Subtracting a negative is like adding
−3 2/7 + (5/7)
Since the signs are difference we subtract and take the sign of the larger number
3 2/7 - 5/7
Borrow from the whole number
2+ 7/7 + 2/7 - 5/7
2 9/7 - 5/7
2 4/7
The sign of the larger number is negative so add the negative sign
- 2 4/7
Answer:
- 2 4/7
Step-by-step explanation:
k12
Which of the following inequalities is graphed on the coordinate plane?
Answer: A
Step-by-step explanation:
This picture is very blurry, but the line appears to be a solid line. Since it is a solid line, it tells us that the inequality is ≤ or ≥. We can eliminate C and D. Now, the difference between A and B is the shading. Since the shading is showing that the numbers are increasing, we know that the inequality is ≥. Therefore, A is the correct answer.