Evaluate the expression x+2y when x=2 and y=−2.5.

First, rewrite

[tex]x^y=e^{\ln x^y}=e^{y\ln x}[/tex]

[tex]5^{x-y}=e^{\ln5^{x-y}} = e^{\ln(5)(x-y)}[/tex]

Now, differentiate both sides using the chain rule:

[tex]\dfrac{\mathrm d\left(e^{y\ln x}\right)}{\mathrm dx}=\dfrac{\mathrm d\left(e^{\ln(5)(x-y)}\right)}{\mathrm dx}[/tex]

[tex]e^{y\ln x}\dfrac{\mathrm d(y\ln x)}{\mathrm dx}=e^{\ln(5)(x-y)}\dfrac{\mathrm d(\ln(5)(x-y))}{\mathrm dx}[/tex]

[tex]x^y\left(\dfrac{\mathrm dy}{\mathrm dx}\ln x+y\dfrac{\mathrm d(\ln x)}{\mathrm dx}\right)=\ln(5)5^{x-y}\left(\dfrac{\mathrm d(x)}{\mathrm dx}-\dfrac{\mathrm dy}{\mathrm dx}\right)[/tex]

[tex]x^y\left(\ln x\dfrac{\mathrm dy}{\mathrm dx}+\dfrac yx\right)=\ln(5)5^{x-y}\left(1-\dfrac{\mathrm dy}{\mathrm dx}\right)[/tex]

[tex]\left(x^y\ln x+\ln(5)5^{x-y}\right)\dfrac{\mathrm dy}{\mathrm dx}=\ln(5)5^{x-y}-yx^{y-1}[/tex]

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\ln(5)5^{x-y}-yx^{y-1}}{x^y\ln x+\ln(5)5^{x-y}}[/tex]

Answer:

c on edge

Step-by-step explanation:

fr

Answer:

(B) Stretch z by a factor of 3 and rotate π/6 radians counterclockwise.

Step-by-step explanation:

edge:2022 Happy new year!

Answer:

120 seconds

Step-by-step explanation:

60         20

120        40

180       60

            80

            100

            120

Answer:

yes it is parallel because the alternate interior angles are equal

Answer:

x=-1

Step-by-step explanation:

The first thing we can do is subtract 3x from both sides (it makes solving the equation easier if you get rid of the variable first).

3x+6=4x+7

-3x    -3x

6=x+7

All we need to do now is subtract 7 on both sides.

6=x+7

-7    -7

-1=x  or  x=-1  (they both mean the same thing!)

Hope this helps!! Have a wonderful day c:

Answer:

(x-18)^2+(y+6)^=36

Step-by-step explanation:

circle basic equation is (x-h)^2+(y-k)^2=r^2

center is (18,-6) it is also externally tangent

so

(x-18)^2+(y+6)^2=36 answer

The equation of a circle that is externally tangent to the given circle and has a center at (18, −6) is [tex](x-18)^2+(y+6)^=36[/tex]

A circle can be characterized by its center's location and its radius's length. Let the center of the considered circle be at (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

Given that the circle basic equation is [tex](x-2)^2+(y+6)^2=100[/tex]

The center is (18,-6) it is also externally tangent;

Therefore,

[tex](x-18)^2+(y+6)^2=36[/tex]

Therefore, the equation of a circle that is externally tangent to the circle is; [tex](x-18)^2+(y+6)^2=36[/tex]

Learn more about equation of a circle here:

https://brainly.com/question/10165274

#SPJ2

Answer: 2,9

(3,3) & (-2,6) midpoints

Answer:

(0.5,4.5)

Step-by-step explanation:

Use the midpoint formula to find the answer: ((x1+x2/2),(y1+y2/2))

((3-2/2),(3+6/2))

((1/2),(9/2))

(0.5,4.5)

Answer:

44 degrees

Step-by-step explanation:

Because a right angle triangle if added all angles will=to 180 degrees

so 46+90=136

180-136=44

Answer:

44

Step-by-step explanation:

You add 46 to the 90 degree angle (right angle) and get 136. Then, because the angles of a triangle add up to 180 degrees all the time, you would do 180-136 and get 44.

Answer:

im gonna say 4 if im wrong its my fault

Answer:

6(8+x)

Step-by-step explanation:

Notice that the constant and the coefficient have a greatest common factor of 6. Therefore, we can just factor the 6 out to get 6(8+x).

Answer:

Step-by-step explanation:

[tex]48 + 6x\\\\\mathrm{Rewrite\:}48\mathrm{\:as\:}6\times\:8\\\\=6x+6\times\:8\\\\\mathrm{Factor\:out\:common\:term\:}6\\\\=6\left(x+8\right)[/tex]

Answer:

y = -[tex]3^{2}[/tex] + 7x - 2

Step-by-step explanation:

-9-2= -11

y = -11 +7x

+11

y+11 = 7x

/7

1.57142857143= x

Answer:

MO is 13 units

Step-by-step explanation:

If point lies on a segment, then this point divides the segment into two parts, the sum of their lengths equals the length of the segment

∵ Point N ∈ segment MO

→ That means point N divide segments MO to two parts MN and NO

∴ Point N divides segment MO into two parts MN and NO

→ That mans the length of segment MO equals to the sum of

   lengths of MN and NO

∴ MO = MN + NO

∵ MN = 8 units

∵ NO = 5 units

∴ MO = 8 + 5

∴ MO = 13 units

Answer:

If 10 men dig a ditch in 12 days .

Total man-days required to dig the ditch

= 10 men × 12 days

= 120 man-days

how long would 15 men take to dig it?

No of days required to finish the job by 15 men

= 120 men-days / 15 men

= 8 days

Answer: 8 days will be required to finish the job by 15 men

Step-by-step explanation:

Hope this helps u

Crown me as brainliest:)

Answer:

153.158 ; 177.642

Step-by-step explanation:

Given the following:

Sample mean (m) = 165.40

Sample standard deviation (s) = 21.70

Sample size (n) = 17

α = 98%

Confidence interval = m ± z(SE)

z at 98% = 2.326

SE = s/√n

SE = 21.70/√17 = 5.2630230

Hence,

Confidence interval = 165.40 ± 2.326(5.2630230)

165.40 - 12.241791498 OR 165.40 + 12.241791498

153.158 ; 177.642

Answer:

81/100

Step-by-step explanation:

Answer:

81/100

Step-by-step explanation:

Answer:

m<WYZ = 23°

m<ACB = 87°

Step-by-step explanation:

Problem 1: Find WYZ

Given,

m<WVX = (3x - 7)°

m<VYZ = (16x - 3)°

∆WYZ ~ ∆WVX, therefore:

m<WYZ = m<WVX (corresponding angles of similar triangles are congruent)

m<WYZ = (3x - 7)° (substitution)

Create an equation to find the value of x.

m<WYZ + m<VYZ = 180° (linear pair)

(3x -7)° + (16x - 3)° = 180° (substitution)

Solve for x

3x - 7 + 16x - 3 = 180

Add like terms

19x - 10 = 180

Add 10 to both sides

19x - 10 + 10 = 180 + 10

19x = 190

Divide both sides by 19

19x/19 = 190/19

x = 10

m<WYZ = (3x - 7)

Substitute x = 10

m<WYZ = 3(10) - 7 = 30 - 7

m<WYZ = 23°

Problem 2: Find m<ACB

Given,

m<A = 62°

m<AED = (11x - 2)°

m<B = (6x + 13)°

∆ADE ~ ∆ACB, therefore:

m<AED = m<B (corresponding angles of similar ∆s are congruent)

(11x - 2)° = (6x + 13)°

Solve for x

11x - 2 = 6x + 13

Collect like terms

11x - 6x = 2 + 13

5x = 15

Divide both sides by 5

5x/5 = 15/5

x = 3

m<ACB + m<B + m<A = 180° (sum of ∆)

m<ACB + (6x + 13) + 62° = 180° (substitution)

Plug in the value of x and solve

m<ACB + (6(3) + 13) + 62° = 180°

m<ACB + (6(3) + 13) + 62° = 180°

m<ACB + (18 + 13) + 62° = 180°

m<ACB + 31° + 62° = 180°

m<ACB + 93° = 180°

Subtract 93 from both sides

m<ACB = 180° - 93°

m<ACB = 87°

Answer:

8.2/10

Step-by-step explanation:

Answer:

42/50

Step-by-step explanation:

Answer:

114 liters

Step-by-step explanation:

120 x 0.95 = 114

Answer:

i^15=-i

i^32=1

1^99=-i

i^22=-1

hope this helps :)

im sorry for the late answer, i put all the answers incase some one needs them, have a nice day!

Step-by-step explanation:

Answer: The answer is "1".

Step-by-step explanation:

Correct on edgen.

Step-by-step explanation:

toke a while to finish it, but there you go

cheers and have a good night :D

Answer:

36 feet.

Step-by-step explanation:

2 goes into 24 12 times, 12 times 3 is 36 therefore the actual house is 36 feet tall.

Answer:

b

Step-by-step explanation:

Answer:

the answer is B

Step-by-step explanation:

Answer:

A. [tex] (4n + 22) + (8n - 10) = 180 [/tex]

B. [tex] n = 14 [/tex]

C. 78° and 102°

Step-by-step explanation:

A. The relationship between the two angles that are a linear pair is: their sum gives us 180°. That is:

[tex] (4n + 22) + (8n - 10) = 180 [/tex]

B. [tex] (4n + 22) + (8n - 10) = 180 [/tex]

Solve for n.

[tex] 4n + 22 + 8n - 10 = 180 [/tex]

Collect like terms

[tex] 12n + 12 = 180 [/tex]

Subtract 12 from both sides

[tex] 12n + 12 - 12 = 180 - 12 [/tex]

[tex] 12n = 168 [/tex]

Divide both sides by 12

[tex] \frac{12n}{12} = \frac{168}{12} [/tex]

[tex] n = 14 [/tex]

C. Plug in the value of 14 to get the measurement of both angles

[tex] (4n + 22) = 4(14) + 22 = 56 + 22 = 78 [/tex]

[tex] (8n - 10) = 8(14) - 10 = 112 - 10 = 102 [/tex]

Answer:

31

Step-by-step explanation:

To solve this problem, we must find the lowest common multiple of 21, 35 and 63

   Find the prime factors of the number;

 Prime factors of 21  = 3 x 7

                            35 = 3 x 5

                            63 = 3 x 3 x 7

  The lcm = 3 x 3 x 5 x 7 = 315

The numbers between  1 and 10, 000 divided by these three numbers;

   First number  = 315

    Last number  = 9765

Now the total number:

      = [tex]\frac{first number - last number }{315} + 1[/tex]

      = [tex]\frac{9765 - 315}{315}[/tex] + 1

     = 30 + 1

     = 31