The area of the rectangle is increasing at the rate of 156 [tex]cm^{2}[/tex]/s .
Let the length (cm) be l , width (cm) be w , area be A ([tex]cm^{2}[/tex]) and time (s) be t .
Given : dl / dt = 6 cm/s and dw / dt = 8 cm/s
Area of rectangle = l * w
Differentiating wrt. t ,
dA / dt = ( l ) ( dw / dt ) + ( dl / dt ) ( w )
Therefore , dA / dt = 8l + 6w
Hence , when l = 12 cm and w = 10 cm
dA / dt = ( 8 * 12 ) + ( 6 * 10 )
dA / dt = 156 [tex]cm^{2}[/tex]/s .
The area of the rectangle is increasing at the rate of 156 [tex]cm^{2}[/tex]/s .
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Find the product. (a2)(2a3)(a2 â€"" 8a 9) 2a7 â€"" 16a6 18a5 2a7 â€"" 16a6 â€"" 18a5 2a8 â€"" 16a7 18a6 2a12 â€"" 16a7 18a6
Kaela wants to purchase a pair of shoes at Macy’s that cost $80. If Macy’s charges a
6% sales tax, how much will Kaela pay for the shoes, including tax?
Answer: $84.80
Step-by-step explanation:
The actual sales tax was 4.80 because 6% of 80 is 4.80
Then add the 4.80 to the 80 to get your total
Hope this helped :)
a survey of 500 high school students was taken to determine their favorite chocolate candy. of the 500 students surveyed, 118 like snickers, 185 like twix, 179 like reese's peanut butter cups, 60 like snickers and twix, 87 like twix and reese's peanut butter cups, 57 like snickers and reese's peanut butter cups, and 17 like all three kinds of chocolate candy. how many students like snickers, but not twix or reese's peanut butter cups? a) 118 b) 101 c) 100 d) 18 e) 83 f) none of the above.
There are 18 students who like snickers but not twix or reese's peanut butter cups.
Given, that 500 high school students was taken to determine their favorite chocolate candy.
118 like snickers, 185 like twix, 179 like reese's peanut butter cups,
60 like snickers and twix, 87 like twix and reese's peanut butter cups, 57 like snickers and reese's peanut butter cups,
and 17 like all three kinds of chocolate candy.
Let A = Set of students like snickers
B = Set of students like twix
C = Set of students like reese's peanut butter cups
Now, we have to find the number of students like snickers but not twix or reese's peanut butter cups i.e. A - A∩B - A∩C + A∩B∩C
A - A∩B - A∩C + A∩B∩C = 118 - 60 - 57 + 17
A - A∩B - A∩C + A∩B∩C = 135 - 117
A - A∩B - A∩C + A∩B∩C = 18
Hence, there are 18 students who like snickers but not twix or reese's peanut butter cups.
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what is the distance between point P (-5,7) and point Q (6,7) ?
Answer:
11
Step-by-step explanation:
Distance formula is square root of (x2-x1)^2+(y2-y1)^2
square root of (6-(-5))^2+(7-7)^2
square root of (11)^2+(0)^2
square root of 121+0
square root of 121
11
distance is 11
lin rode he skateboard 3 miles in 9 minutes. she rode at a constant speed. how far did she go if she only went for 1 minute?
First, break down the problem.
Someone can skate 3 miles in 9 minutes.
What is their speed? How far would they go if they did that speed for 1 minute?
To find speed given time and distance, divide distance by time.
3/9 = 1/3
Speed is 1/3 mile per minute
if they travel one minute, they will travel 1/3 of a mile
hope this helps :)
The demand function for a certain make of replacement cartridges for a water purifier is given by the equation p=−0. 01x2−0. 1x+21 where p is the unit price in dollars and xis the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the market price is set at $9/cartridge. (Round your answer to two decimal places. )
The demand function for a certain is given by the equation p=−0. 01x2−0. 1x+21 then the determined values will be −50.905557, −0.427737,41.333295.
From the given values,
R=px
9 = (−0. 01x2−0. 1x+21) x
0.01x3+0.1x2−21x−9=0
By reducing the equation,
X = −50.905557, −0.427737,41.333295.
Therefore, the determined values will be −50.905557, −0.427737,41.333295.
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The perimeter of a rectangle can be found using the equation P = 2L + 2W, where P is the perimeter, L is the length, and W is the width of the rectangle.
Solve the equation for the variable w
When you have done that
state the value of 'w' if the perimeter of the rectangle is equal to 37 feet and the length is equal to 4 feet.
hurrryyyy pls
Answer:
14.5 feet
Step-by-step explanation:
To make subject as 'w' and solving:To make the subject as 'w', isolate w.
To isolate 'w', subtract 2L from both sides .2L + 2W =P
2W = P - 2L
Now, divide both sides by 2.[tex]\sf W = \dfrac{P-2L}{2}\\\\W =\dfrac{P}{2}-\dfrac{2L}{2}\\\\ \boxed{W = \dfrac{P}{2}-L}[/tex]
P = 37 feet
L = 4 feet
[tex]\sf W =\dfrac{37}{2}-4\\\\[/tex]
= 18.5 - 4
W = 14.5 feet
Mrs. Shelly paid $3 for 6 muffins and Mrs. Kloske paid $9 for 18 muffins. How much did
Mrs. Smith pay for 30 muffins?
Explain your answer
a) $3
b) $10
c) $15
d) $30
(Help!)
#8 The tables represent some points on the graphs of lines m and n. Which system of equations is represented by lines m and n?
(A) −6x − y = 8 −3x + 2y = 9
(B)6x + y = −8 3x − 2y = 9
(C) 6x − y = −8 −3x − 2y = 9
(D) 6x − y = 8 3x + 2y = 9
#9 A produce company sells crates filled with a mixture of apples and oranges during the holiday season to grocery stores. Each crate contains a total of 72 pieces of fruit. Suppose that a crate has 8 more apples than oranges.
Which system of linear equations can be used to determine the number of pieces of each kind of fruit in the crate?
(A) a + o = 72 o = a + 8
(B) 8a + o = 72 a + o = 8
(C) a + o = 72 a = o + 8
(D) a + 8o = 72 a + o = 8
#10 The tables represent some points on the graphs of lines r and s. Which system of equations is represented by lines r and s?
(A) −4x + 3y = 12 2x − 5y = −10
(B) −4x − 3y = −12 −2x + 5y = 10
(C) 4x + 3y = −12 2x − 5y = 10
(D) 4x − 3y = −12 −2x − 5y = 10
The linear functions representing the systems of equations in each case are given as follows:
8. (D) 6x − y = 8 3x + 2y = 9
9. (C) a + o = 72 a = o + 8.
10. (C) 4x + 3y = −12 2x − 5y = 10.
What is a linear function?The slope-intercept representation of a linear function is presented by the rule as follows:
y = mx + b
The coefficients of the function and their meaning are listed as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x increases by one.b is the y-intercept of the function, being the numeric value of the function when the input variable x assumes a value of 0.For the line m, we have that when x increases by 6, y increases by 36, hence the slope is:
m = 36/6 = 6.
Considering the positive slope of 6, at x = 0, the numeric value is 12 less than the numeric value at x = 2, hence the intercept is:
b = 4 - 2 x 6 = -8.
Hence the equation is:
y = 6x - 8.
6x - y - 8.
Thus option d is correct.
For item 9, we use the variables a and o. The total is of 72, hence:
a + o = 72.
Suppose that a crate has 8 more apples than oranges, hence:
a = o + 8.
Thus option c is correct.
For line r in item 10, when x increases by 3, y decays by 4, hence the slope is:
m = -4/3.
When x = 0, y = -4, hence the intercept is:
b = -4.
Thus the equation is:
y = -4x/3 - 4
3y = -4x - 4.
4x + 3y = -12.
Meaning that option c is correct.
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[tex]x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} \\[/tex]
Answer: [tex]x^{26}[/tex]
Step-by-step explanation:
The [tex]x^2[/tex] appears 13 times. Using the exponent rule [tex]x^a x^b=x^{a+b}[/tex], we get that:
[tex]x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2=x^{2(13)}=x^{26}[/tex]
Solve the double-ended inequality:
2x-5<4x+2<2x-3
Answer: _ _ x _ _
Answer with a number in the first box, inequality in the second box, than after the x an inequality in the 3rd box and a number in the last box.
EG 5 > x > 18
The solution of the double-ended inequality is -7/2 < x < -5/2
Solving Linear InequalitiesFrom the question, we are to solve the doubled ended inequality.
The given inequality is
2x - 5 < 4x + 2 < 2x -3
From the inequality, we can write that
2x - 5 < 4x + 2 and 4x + 2 < 2x - 3
Now, we will solve each of the inequalities separately
Solving 2x - 5 < 4x + 2
Add 5 to both sides
2x - 5 + 5 < 4x + 2 + 5
2x < 4x + 7
Subtract 4x from both sides
2x - 4x < 4x - 4x + 7
-2x < 7
Divide both sides by -2 and reverse the sign
x > -7/2
-7/2 < x
Solving 4x + 2 < 2x - 3
Subtract 2x from both sides of the equation
4x - 2x + 2 < 2x - 2x -3
2x + 2 < -3
Subtract 2 from both sides
2x + 2 -2 < -3 - 2
2x < -5
Divide both sides by 2
x < -5/2
Putting the two solutions together, we get
-7/2 < x and x < -5/2
-7/2 < x < -5/2
Hence, the solution is -7/2 < x < -5/2
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prove that cos A - sin A +1 / cos A + sin A-1 = cosec A+ cot A
(Pls help, urgently needed)
We have to prove (cosA−sinA+1)/(cosA-sinA-) = cotA+cosecA using Trigonometric Functions
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
L.H.S=(cosA−sinA+1)/(cosA-sinA-)
dividing by sinA
=cotA+1−cosecA/cotA−1+cosecA
=(cotA−1+cosecA)(cotA+1+cosecA)/(cotA+1)²-cosec²A
=(cotA+cosec)²-1/2cotA
=cotA+cosecA(R.H.S)
Hence the above trigonometric function is proved.
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Could someone help quick
The constant of proportionality is known to be the ratio of two proportional values that is said to be in a constant value.
What is the constant of proportionality?The constant of proportionality is a term that is defined as the rate or the ratio of two proportional values which are known to be at the same value.
constant of proportionality = 2.5
Given : y = 2.5x.
To find : What is constant of Proportionality in the equation.
Solution : We have given
y = 2.5x.
On comparing with equation of proportionality : y = kx,
Where, k is the constant of proportionality.
On comparing y = 2.5 x by y = kx .
We get k = 2.5
So, constant of proportionality = 2.5
Therefore, constant of proportionality = 2.5
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The value of constant proportionality is 2.5. The constant of proportionality is known to be the ratio of two proportional values that is said to be in a constant value.
What is the constant of proportionality?The constant of proportionality is a term that is defined as the rate or the ratio of two proportional values which are known to be at the same value.
constant of proportionality = 2.5
Given : y = 2.5x.
To find : What is constant of Proportionality in the equation.
Solution : We have given
y = 2.5x.
On comparing with equation of proportionality : y = kx,
Where, k is the constant of proportionality.
On comparing y = 2.5 x by y = kx .
We get k = 2.5
So, constant of proportionality = 2.5
Therefore, constant of proportionality = 2.5
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everyone can someone help me here please (complete solution and graph)
Answer:
1: x^2+y^2-6x-4y-3=0
2: x^2+y^2-10x+4y=0
3: x^2+y^2-10x+2y+1=0
Select all correct answers. which values are part of the solution set based on the result of the inequality? -4x + 24 < -2x + 2 9.5 -10 11.5 15 10 -3
11.5 and 15 are the values that are part of the solution set of the inequality.
Inequality is defined as relationship between non-equal numbers or expressions. The solution of an inequality is the set of values that satisfies the given inequality.
To determine the solution set of the given inequality, isolate the variable to one side and simplify.
-4x + 24 < -2x + 2
-4x + 2x < -24 + 2
-2x < -22
22 < 2x
11 < x
Hence, the solution set of the given inequality is the set of numbers greater than 11. Among the given choices, 11.5 and 15 are both greater than 11.
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Select the correct answer.
What is the domain of function f?
Answer:
D
Step-by-step explanation:
The domain of this function is all real numbers because you can see that there are no endpoints on the graph. The function is going off of the graph, which means it is continuing aka never-ending.
(-∞,∞) aka all real numbers
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The function has a maximum value of 30 at x = 3.
Given Function:
f(x) = -3[tex]x^{2}[/tex]+18x+3
here a = -3 , b = 18 , c = 3
a is negative so it has maximum value
x = -b/2a
= -18/2*(-3)
= -18/-6
= 18/6
= 3
f(x) = -3*[tex]3^2[/tex] + 18*3 + 3
= -3*9+54+3
= -27+54+3
= 27+3
= 30
Therefore the function has a maximum value of 30 at x = 3.
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In the image below, the measure of angle 3 is equal to the sum of the measures of angle 6 and what other angle?
For the given figure, angle 3 will be equal to angle 2.
According to the question,
We have the following information:
We have a figure where some angles are marked in form of numbers and the measure of angle 3 is equal to the sum of the measures of angle 6.
Now, we know that vertically opposite angles are equal and angle 1 and angle 4 are vertically opposite angles like angle 2 and angle 3.
(More to know: the sum of three angles of a triangle is equal to 180°.)
Hence, for the given figure, angle 3 will be equal to angle 2.
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Help pls I'll give you brainliest and 15 points asap.
How does the graph of g(x)=4⌊x⌋ differ from the graph of f(x)=⌊x⌋?
1. Multiplying by 4 shifts the graph of g(x)=4⌊x⌋ up 4 units.
2.Multiplying by 4 shifts the graph of g(x)=4⌊x⌋ down 4 units.
3.Multiplying by 4 stretches the graph of g(x)=4⌊x⌋ vertically by a factor of 4.
4.Multiplying by 4 shifts the graph of g(x)=4⌊x⌋ right 4 units.
Question 2
How does the graph of g(x)=⌊x⌋−3 differ from the graph of f(x)=⌊x⌋?
1.The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted right 3 units.
2.The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted left 3 units.
3.The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted up 3 units.
4.The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted down 3 units.
Answer:
Question 1: #3 is correct.
Question 2: #4 is correct.
examples of linear equation
how do i solve 8x-8=4x
The solution to the algebraic equation 8x - 8 = 4x is x = 2
How to solve algebraic equation?Algebra: This is the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
8x - 8 = 4x
Collect like terms8x - 4x = 8
4x = 8
divide both sides by 4x = 8/4
x = 2
Check:
8x - 8 = 4x
substitute x = 2 into the equation
8(2) - 8 = 4(2)
16 - 8 = 8
8 = 8
Other examples of algebraic equation
3x + 5 = 11
substract 5 from both sides
3x = 11 - 5
3x = 6
divide both sides by 3
x = 6/3
x = 2
Therefore, the value of x from the equation is given by 2
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Find the missing exponent. 2 =32
Answer:
5
Step-by-step explanation:
The only way I know how to go about this is to multiply 2 until it becomes 32
2x2=4
4x2=8
8x2=16
16x2=32
Now just count how many 2 I used and I used 5 so the missing exponent is 5
Hopes this helps please mark brainliest
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A sample survey of 54 discount brokers showed that the mean price charged for a trade of 100shares at 50 per share was $33. 77 (AAII Journal, February 2006). The survey is conducted annually. With the historical data available, assume a known population standard deviation of $15.
a. Using the sample data, what is the margin of error associated with a 95% confidence interval?
b. Develop a 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share
a) The margin of error associated with a 95% confidence interval is 4.
b) The 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77,$37.77)
a) We are given with the information that the mean for 54 discount brokers is $50 for 100 shares is $33.77 Also the population standard deviation is $15.
The formula for margin of error is Z = zα/2 σ √ n
Now we know from our z-table that value of zα/2 for 95% confidence interval is 1.96
So, the value of error margin is zα/2 σ √ n =1.96 (15/√54) = 1.96 x 2.04
= 4
b) We know from part a that margin of error is 4.
Also, the mean price charged for a trade of 100shares at 50 per share was $33. 77
The value of confidence interval for population mean is,
x ± zα/2 σ √ n = 33.77 ± 4 = (29.77,37.77)
Thus, the 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77,$37.77)
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What is the quotient (x2 − 9x + 20) ÷ (x − 4)? (1 point) x − 5 x − 4 x + 4 x + 5
Answer:
The guy under me is correct
Step-by-step explanation:
Answer:
x - 5
Step-by-step explanation:
Factor the expressions that are not already factored
(x^2 - 9x + 20) / (x - 4)
Cancel out x - 4 in both numerator and denominator
[tex]\frac{(x-5)(x-4)}{x-4}[/tex]
x - 5
Which algebraic expression represents “the apples were divided equally into seven boxes”?
Answer:
Step-by-step explanation:
a=apples
a/7
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The number of bicycles that must be manufactured to minimize the cost of 250 and the minimum cost is $11,500.
In the given question,
The cost C in dollars of manufacturing x bicyles at a production plant is given by the function shown below;
C(x) = 3x^2-1500x+199,000
(a) In the given question we have to find the number of bicyles that must be manufactured to minimize the cost.
The given function is
C(x) = 3x^2-1500x+199,000
To find the maximum or minimum value we firstly find the value of f'(x).
C'(x) = 6x-1500
Now put f'(x)=0
6x-1500=0
Add 1500 on both side, we get
6x=1500
Divide by 6 on both side we get
x=250
Hence, the number of bicycles that must be manufactured to minimize the cost of 250.
(b) Now finding the value of function at x=250
C(250) = 3(250)^2-1500*250+199,000
C(250) = 3*62,500-375,000+199,000
C(250) = 187,500-375,000+199,000
C(250) = 11,500
The minimum cost is $11,500.
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A line segment has endpoints at (–4, –6) and (–6, 4). Which reflection will produce an image with endpoints at (4, –6) and (6, 4)?
The required expression of the reflection of the point is (-x, y).
Given that,
A line segment has endpoints at (–4, –6) and (–6, 4). Which reflection will produce an image with endpoints at (4, –6) and (6, 4) is to be determined.
The expression is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
A line segment has endpoints at (–4, –6) and (–6, 4) and an image with endpoints at (4, –6) and (6, 4) is produced the equation of the reflection is given as,
(x, y) ----> (-x, y)
Thus, the required expression of the reflection of the point is (-x, y).
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a fair coin is tossed 28 times. what is the probability that at most 25 tails occur? a) 0.99998628 b) 0.00000152 c) 0.99999848 d) 0.00001220 e) 0.01001372 f) none of the above.
The probability that at most 25 tails occur is 0.99999848.
We know that,
P(x = x) = ⁿCₓ × pˣ × [tex]q^{n-x}[/tex]
p = probability of success = 0.5
n = number of trials = 28
q = 1 - p = 0.5
The probability of the tail occurring at most 25 times can be written as
P(X ≤ 25) = P (X = 0) + P(X = 1) + ..... + P(X = 25)
Using a binomial probability calculator,
P(X ≤ 25) = 0.99999848
Therefore the probability that at most 25 tails occur is 0.99999848
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ZABC is bisected by ray BD. m2 ABC = 80°. What is mZ ABD?
OA. 50⁰
OB. 40°
O C. 100⁰
OD. 75⁰
The require angle, angle ABD = 40 degrees
What do you mean by angle bisector ?A bisector has two primary characteristics:
Any point along an angle's bisector is equally - spaced from the angle's sides.
The angle bisector divides the other side of a triangle in proportion to the other two sides.
Given : ∠ ABC is bisected by a ray BD
∠ ABC = 80°
Since the angle ABC is being bisected this means that the angles are equal
Let the bisected angle be x
thus we can write it mathematically as
x + x = 80
2x = 80
dividing both the sides as 2 we would get
x = 40 degrees
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