(05.03 LC)

The equation shows the relationship between x and y:

y = −4x + 9

What is the slope of the equation? (5 points)

Group of answer choices

−9

−4

4

9

Applying implicit differentiation, it is found that dy/dt when y=π/4 is of:

a-) -√2 / 2.

Implicit differentiation is when we find the derivative of a function relative to a variable that is not in the definition of the function.

In this problem, the function is:

xcos(y) = 2.

The derivative is relative to t, applying the product rule, as follows:

[tex]\cos{y}\frac{dx}{dt} - x\sin{y}\frac{dy}{dt} = 0[/tex]

[tex]\frac{dy}{dt} = \frac{\cos{y}\frac{dx}{dt}}{x\sin{y}}[/tex]

Since dx/dt=−2, we have that:

[tex]\frac{dy}{dt} = -2\frac{\cos{y}}{x\sin{y}}[/tex]

When y = π/4, x is given by:

xcos(y) = 2.

[tex]x = \frac{2}{\cos{\frac{\pi}{4}}} = \frac{2}{\frac{\sqrt{2}}{2}} = \frac{4}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = 2\sqrt{2}[/tex]

Hence:

[tex]\frac{dy}{dt} = -2\frac{\cos{y}}{x\sin{y}}[/tex]

[tex]\frac{dy}{dt} = -\frac{1}{\sqrt{2}}\cot{y}[/tex]

Since cot(pi/4) = 1, we have that:

[tex]\frac{dy}{dt} = -\frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = -\frac{\sqrt{2}}{2}[/tex]

Which means that option a is correct.

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Answer:

Step-by-step explanation:

a-b=21

5a-2b=18

Using elimination, we have

5a-5b=105

5a-2b=18

So:

3b=-87 so b=-29

Substituting, a=-8

(a,b)=(-8,-29)

The coefficient of 2(3)(6)Q is 2(3)(6)

The expression is given as:

2(3)(6)Q

For an expression

AQ

Where A is a number or product of numbers and Q is a variable

The number A represents the coefficient

By comparing:

AQ and 2(3)(6)Q

We have

A = 2(3)(6)

Hence, the coefficient of 2(3)(6)Q is 2(3)(6)

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Answer:$2346

Step-by-step explanation: Assuming that the students' numbers start at 1, we have 1+2+3+4.....+65+66+67+68 as the total amount of money raised. We can see that 1+68 = 69 and 2+67 also equals 69. So, we can use this method to figure out how many 69s are in the sum. Since 68 divided by 2 is 34, there are 34 69s in the sum. 34x69 = 2346.

The standard form of the quadratic function f(x) = -3x^2 + 6x - 2 is f(x) = -3x^2 + 6x - 2

The quadratic function is given as

f(x) = -3x^2 + 6x - 2

The standard form of a quadratic function is represented as:

f(x) = ax^2 + bx + c

When both equations are compared, we can see that the function f(x) = -3x^2 + 6x - 2 is already in standard form

Where

a = -3

b = 6

c = -2

Hence, the standard form of the quadratic function f(x) = -3x^2 + 6x - 2 is f(x) = -3x^2 + 6x - 2

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The probability that the value of p(x) is greater than 315 is 0.063754

From the question, the given parameters about the distribution are

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (315 - 283)/21

Evaluate the difference of 315 and 283

z = 32/21

Evaluate the quotient of 32 and 21

z = 1.524

The probability that the value of p(x) is greater than 315 is then calculated as:

P(x > 315) = P(z > 1.524)

From the z table of probabilities, we have;

P(x > 315) = 0.063754

Hence, the probability that the value of p(x) is greater than 315 is 0.063754

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Answer:

y= -3x+4

Step-by-step explanation:

y=mx+c

m= y2-y1 ÷ x2-x1

m= -3

y=-3x+c

7=-3(-1)+c

c=4

y=-3+4

Answer:

show the image because we cant answer it if there's no picture or image

Step-by-step explanation:

1 week = 7 days

10 weeks = 10×7 days

= 70 days

if Ellen reads 1 book in a day

Therefore,

1 day = 1 book

70 days = 70×1

= 70 books.

Thus Ellen reads 70 books in 10 weeks.

Hope helps

Answer:

70 books

Step-by-step explanation:

Ellen reads one book per day for 10 weeks.

All we need to do to know the number of books Ellen read overall is to multiply 1 (number of books he read each day) and 10 weeks (total number of days).

Each week is 7 days, so 10 weeks is equal to 70 days.

The equation will be: 1 x 70

We can conclude that Ellen read 70 books overall within 10 weeks.

Answer:

12

Step-by-step explanation:

f(x) = -x^3 + x^2

Let x = -2

Evaluate the expression

f(-2) = -(-2)^3 + (-2)^2

       = - (-2)*(-2) * (-2)  + ( -2) * (-2)

       = -(-8) + ( 4)

    = 8 + 4

   = 12

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Take HJ = a, GH = b and GJ = c

put the value of a from equation 1 in equation 2

[tex]\qquad❖ \: \sf \:c = (b + 2) + b - 17[/tex]

[tex]\qquad❖ \: \sf \:c = 2b - 15[/tex]

now, put the value of a and c in equation 3

[tex]\qquad❖ \: \sf \:b + 2 + b + 2b - 15 = 73[/tex]

[tex]\qquad❖ \: \sf \:4b - 13 = 73[/tex]

[tex]\qquad❖ \: \sf \:4b = 86[/tex]

[tex]\qquad❖ \: \sf \:b = 21.5 \: \: in[/tex]

Now, we need to find HJ (a)

[tex]\qquad❖ \: \sf \:a = b + 2[/tex]

[tex]\qquad❖ \: \sf \:a = 21.5 + 2[/tex]

[tex]\qquad❖ \: \sf \:23.5 \: \: in[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer:

23.5 in

Step-by-step explanation:

To find the length of HJ in triangle GHJ, create three equations using the given information, then solve simultaneously.

Equation 1

HJ is two inches longer than GH:

⇒ HJ = GH + 2

Equation 2

GJ is 17 inches shorter than the sum of HJ and GH:

⇒ GJ + 17 = HJ + GH

Equation 3

The perimeter of ΔGHJ is 73 inches:

⇒ HJ + GH + GJ = 73

Substitute Equation 1 into Equation 2 and isolate GJ:

⇒ GJ + 17 = GH + 2 + GH

⇒ GJ + 17 = 2GH + 2

⇒ GJ = 2GH - 15

Substitute Equation 1 into Equation 3 and isolate GJ:

⇒ GH + 2 + GH + GJ = 73

⇒ 2GH + GJ = 71

⇒ GJ = 71 - 2GH

Equate the two equations where GJ is the subject and solve for GH:

⇒ 2GH - 15 = 71 - 2GH

⇒ 4GH = 86

⇒ GH = 21.5

Substitute the found value of GH into Equation 1 and solve for HJ:

⇒ HJ = 21.5 + 2

⇒ HJ = 23.5

Answer:

d = [tex]\sqrt{29}[/tex]

Step-by-step explanation:

The distance between two points is given by

d = [tex]\sqrt{ ( x2 - x1) ^2 - ( y2-y1)^2}[/tex]  where ( x1,y1) and ( x2,y2) are the two points

d = [tex]\sqrt{( 0 - -5) ^2 + (4 - 2) ^2}[/tex]

d = [tex]\sqrt{5^2 + 2^2}[/tex]

d = [tex]\sqrt{25 +4}[/tex]

d = [tex]\sqrt{29}[/tex]

Answer: [tex]\Large\boxed{Distance=\sqrt{29} }[/tex]

Step-by-step explanation:

Given information

[tex](x_1,~y_1)=(-5,~2)[/tex]

[tex](x_2,~y_2)=(0,~4)[/tex]

Given the distance formula

[tex]Distance =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute values into the formula

[tex]Distance =\sqrt{((0)-(-5))^2+((4)-(2))^2}[/tex]

Simplify values in the parenthesis

[tex]Distance =\sqrt{(0+5)^2+(4-2)^2}[/tex]

[tex]Distance =\sqrt{(5)^2+(2)^2}[/tex]

Simplify the exponents

[tex]Distance =\sqrt{25+4}[/tex]

Simplify values in the radical sign

[tex]\Large\boxed{Distance =\sqrt{29}\approx5.4}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

9x3 - 6x2 + 3x

Step-by-step explanation:

(27x 4 - 18x 3 + 9x 2) ÷ 3x

Dividing each term between 3x we have:

9x3 - 6x2 + 3x

We can check the result:

(9x3 - 6x2 + 3x) * (3x)

= (27x4 - 18x3 + 9x2)

Using the z-distribution, the p-value for the test is of 0.0040.

The test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

For this problem, the parameters are given as follows:

[tex]\overline{x} = 33.8, \mu = 32, \sigma = 4.3, n = 40[/tex]

Hence the value of the test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

z = (33.8 - 32)/(4.3/sqrt(40))

z = 2.65.

Using a z-distribution calculator, with z = 2.65 and a right-tailed test, as we are testing if the mean is greater than a value, the p-value is of 0.0040.

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The perimeter of the minor segment is 77. 4m

The formula for determining the perimeter of the minor segment is given as;

Perimeter = θ/360 × 2πr + 2r sin θ/2

where;

Substitute into the formula;

Perimeter = (72/360 × 2 × 3. 142 × 24. 5) +( 2 × 24. 5 × sin 72)

Perimeter = 30. 79 + 46. 60

Perimeter = 77. 4 m

Thus, the perimeter of the minor segment is 77. 4m

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Answer:

1.6 and 9.6

Step-by-step explanation:

Answer: [tex]4x^3 -29x^2 +10x-21[/tex]

Step-by-step explanation:

[tex](4x^2 -x+3)(x-7)\\\\=4x^3 -28x^2 -x^2 +7x+3x-21\\\\=4x^3 -29x^2 +10x-21[/tex]

Answer:

45

Step-by-step explanation:

Assuming this is a trapezoid,

[tex]\frac{29+WZ}{2}=37 \\ \\ 29+WZ=74 \\ \\ WZ=45[/tex]

Answer:

xy-49

Step-by-step explanation:

x x y is xy and -7x7 is 49 so the answer is xy- 49

Answer:

Initial population: 222 fish

After 7 years: 871 fish

Step-by-step explanation:

Initial population size:

Let t=0

∴P(0)=[tex]\frac{2000}{1+8e^0}[/tex]

       =[tex]\frac{2000}{1+8}[/tex]

       =[tex]\frac{2000}{9}[/tex]

       =222 fish

After 7 years:

Let t=7

∴P(7)=871 fish

Answer:

no solutions

Step-by-step explanation:

The nickels in the envelope is $0. 12

From the information given, we have that;

Dimes + nickels = $1. 20

1/4 dimes + dimes = $ 1. 35

Let dimes = d

Nickels = n

d + n = 1. 20    equation a

d/4 + d = 1. 35   equation b

Make 'd' subject from equation a

d = 1. 20 - n

Substitute into equation b

1. 20 - n/ 4 + 1. 20 - n = 1. 35

0. 3 - 0. 25n + 1. 20 - n = 1. 35

collect like terms

- 1. 25n = 1. 35 - 1. 5

- 1. 25 = - 0. 15

n = -0. 15/ -1. 25

n = 0. 12

Thus, the number of nickels in the envelope is $0. 12

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The given focal points and the lengths of the minor and major axis of 16 and 20 gives the equation of the ellipse as the option;

[tex] B. \: \frac{(x + 3)^{2}}{ 100} + \frac{(y - 2)^{2}}{ 64} = 1 [/tex]

The equation of an ellipse is presented as follows;

[tex] \mathbf{ \frac{(x - h)^{2}}{ {a}^{2} } + \frac{(y - k)^{2}}{ {b}^{2} } } = 1 [/tex]

Where;

(x, y) = Coordinates of the center of the ellipse

a = Semi major axis

b = Semi minor axis

Length of minor axis = 16 units

Length of major axis = 20 units

By observation of the coordinates of the focal point, we have;

y-value of the center of the ellipse, k = 2

x-value of the center, h = (-9 + (3 - (-9))/2 = -3

The equation of the ellipse is therefore;

[tex] \frac{(x - ( - 3))^{2}}{ {10}^{2} } + \frac{(y - 2)^{2}}{ {8}^{2} } = 1 [/tex]

[tex] \frac{(x + 3)^{2}}{ 100} + \frac{(y - 2)^{2}}{ 64} = 1 [/tex]

The equation that represents the ellipse is the option;

[tex] B. \: \frac{(x + 3)^{2}}{ 100} + \frac{(y - 2)^{2}}{ 64} = 1 [/tex]

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Answer:

16 liters of 70% alcohol

4 liters of 20% alcohol

Step-by-step explanation:

Let x = volume of 70% alcohol and y = volume of 20% alcohol. Since we need total of 20 liters, the first equation is x + y = 20. Next, calculate the amount of alcohol in the 20 liters of 60% alcohol. 60% is equivalent to 0.6, so there is 20*0.6 = 12 liters of alcohol in the 20 liter solution. Therefore the second equation is 0.7x + 0.2y = 12.

x + y = 20

0.7x + 0.2y = 12

2x + 2y = 40

7x + 2y = 120

-5x = -80

x = 16

16 + y = 20

y = 4

Answer:

3

Step-by-step explanation:

First we look at our problem 1/2 + 5/2. We can see our denominator is the same so we can add our numerators. 1/2 + 5/2 equals 6/2 = 3.

Answer:

If you add this fraction in fraction strip instead of equivalent fraction method

Step-by-step explanation:

firstly draw 5 1/2 fraction strip

then draw 12 1/4 fraction strip

we taking 1/4 bcoz 1/4 is multiple of 1/2, under 1/2 there is 2 1/4.

The end product will be 12/4

cancel out it 12/4 by 2 ans = 6/2 still we can cancel so cancel out 6/2 by 2 at the end ans will be 3/1 = 3

if you think it wrong then use the equivalent fraction method to see the answer..

1/2 + 5/2

denominators are same so we will take only one denominator and will directly add the numerators

1 + 5 = 6 so

6/2 cancel it the ans will be 3/1 and it's equal to 3.

Answer:

68?

Step-by-step explanation:

multiples of 5 end in 5 or 0

_ _ _

last digit has 2 choices ( 5 and 0 )

1,3,5,7,9 are odd

so tens digit has 5 choices but we see that 5 is repeated so we split into more cases

when last digit is 0, tens digit has 5 choices then hundreds digit has 8 choices so 1*5*8=40

when last digit is 5, tens digit has 4 choices and hundreds digit has 7 choices (0 can't be first digit) 1*4*7=28

40+28=68

Answer: She started with 28 pieces of candy.

Step-by-step explanation: In the beginning of the question it says that heather took 8 pieces. Then she divided the rest evenly amongst her 5 kids. Each received 4, so that make the equation 8+(5x4) which gives us 8+(20). Or 8+20 which is 28.

Answer:

She started with 28 candies.

Explanation:

Let the total amount of candies be c

Build equation:

→ remaining: c - 8

→ each gets: (c - 8)/5

Here given each gets 4 candies

So,

(c - 8)/5 = 4

c - 8 = 5(4)

c - 8 = 20

c = 20 + 8

c = 28

Answer:

Your answer is - 28

Step-by-step explanation:

Given,

          a = 2

          b = - 3

          c = - 1

          d = 4

Now,

       - 2 ( b²  -  5 c )

= - 2 ( -3²  -  5 ( - 1 ) )

= - 2 ( 9 + 5 )

= - 2 × 14

= - 28   ans….

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