AB is tangent to ⊙C at point B and AD is tangent to ⊙C at point D.

Circle C is shown. Line segments C B and C D are radii. Line segments B A and D A are tangents to circle C. Angle B C D is 124 degrees.

What is m∠A?
34°
62°
56°
124°

The tangent line has the largest slope at x = 3√2 and x = -3√2 on the curve y = 1 + 60x³ − 2x⁵.

First, let's find the derivative of the given function y = 1 + 60x³ − 2x⁵ using the power rule for differentiation:

dy/dx = 0 + 3(60)x² - 5(2)x⁴

= 180x² - 10x⁴

To find the critical points, we set the derivative equal to zero and solve for x:

180x² - 10x⁴ = 0

Factoring out common terms, we get:

10x²(18 - x²) = 0

Setting each factor equal to zero, we have:

10x² = 0 or 18 - x² = 0

From the first equation, we find x = 0.

From the second equation, we have:

18 - x² = 0

x² = 18

Taking the square root, we get:

x = ±√18

= ±3√2

So the critical points are x = 0, x = 3√2, and x = -3√2.

Now we need to evaluate the slope at these critical points. We can do this by plugging each x-value into the derivative:

When x = 0:

dy/dx = 180(0)² - 10(0)⁴ = 0

When x = 3√2:

dy/dx = 180(3√2)² - 10(3√2)⁴ = 180(18) - 10(216) = 3240 - 2160 = 1080

When x = -3√2:

dy/dx = 180(-3√2)² - 10(-3√2)⁴ = 180(18) - 10(216) = 3240 - 2160 = 1080

The slope is 0 when x = 0 and 1080 when x = 3√2 or x = -3√2.

Therefore, the tangent line has the largest slope at x = 3√2 and x = -3√2 on the curve y = 1 + 60x³ − 2x⁵.

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The complete question is as follows:

At which points on the curve y = 1 + 60x³ − 2x5⁵ does the tangent line have the largest slope?

Answer:  te correct answer is A

Step-by-step explanation:

He has $50,000 more in assets than in liabilities.

Answer:

1. He has $50,000 more in assets than in liabilities.

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

A segment parallel to a side of a triangle cuts off proportional segments on the sides.

48/6 = (3x + 7)/5

8 = (3x + 7)/5

3x + 7 = 40

3x = 33

x = 11

Subtracting the volume of the cylinder from the volume of the prism, the volume of metal in the hex nut to the nearest tenth exists [tex]$$23.6 cm^3[/tex]

Diameter of the cylinder be d = 1.6 cm

Apothem of the hexagon be a = 2 cm

Thickness of the steel hex nut be t = 2 cm

Volume of the prism be [tex]V_p[/tex]

Volume of the cylinder be [tex]V_c[/tex]

Volume of metal in the hex nut,

[tex]$$V = V_p - V_c[/tex]

To estimate the volume of a prism,

[tex]$$V_p = A_b h[/tex]

Ab = n L a / 2

Number of the sides, n = 6

The side of the hexagon be L

Height of the prism, h = t = 2 cm

Central angle in the hexagon, A = 360°/n

A = 360°/6 = 60°

[tex]$tan (\frac{A}{2} )=(\frac{L/2}{a})[/tex]

simplifying the value of L, we get

[tex]$tan (\frac{60}{2} )=(\frac{L/2}{2})[/tex]

[tex]$tan 30}=(\frac{L/2}{2})[/tex]

[tex]$tan (\frac{\sqrt{3}}{3} )=(\frac{L/2}{2})[/tex]

Solving for L/2:

[tex]$\frac{2 \sqrt{3}}{3} =\frac{L}{2}[/tex]

Solving the value of L, we get

[tex]$2\frac{2 \sqrt{3}}{3} =L[/tex]

[tex]$\frac{4 \sqrt{3}}{3} =L[/tex]

[tex]$L=4 \sqrt{3}/3 cm[/tex]

Ab = n L a / 2

Substitute the values in the above equation, we get

[tex]$A_b=\frac{6 (4 \sqrt{3}/3)(2)}{2}[/tex]

[tex]$$A_b=24 \sqrt{3}/3 $$cm^2[/tex]

[tex]$A_b=8 \sqrt{3} cm^2[/tex]

[tex]V_p = A_b h[/tex]

substitute the values in the above equation, we get

[tex]$V_p=(8 \sqrt{3})(2)[/tex]

[tex]$V_p=16 \sqrt{3} cm^3[/tex]

[tex]$$V_p=16 (1.732) cm^3[/tex]

[tex]$$V_p=27.712 cm^3[/tex]

To estimate the volume of cylinder,

[tex]$V_c[/tex] = (π[tex]d^2[/tex]/4) h

Here, π = 3.14 and d = 1.6 cm

Height of the cylinder, h = t = 2 cm

substitute the values in the above equation, we get

[tex]$V_c=[3.14 (1.6) / 4] (2)[/tex]

[tex]$V_c=[3.14 (2.56) / 4] (2)[/tex]

[tex]$V_c=(2.0096) (2)[/tex]

[tex]$$V_c=4.019 cm^3[/tex]

Substitute the values in the equation, we get

[tex]$$V=V_p-V_c[/tex]

[tex]$$V=27.712 - 4.019[/tex]

[tex]$$V=23.693 cm^3[/tex]

[tex]$$V=23.6 cm^3[/tex]

Therefore, the volume of metal in the hex nut, to the nearest tenth exists [tex]$$23.6 cm^3[/tex].

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Answer:

±5

Step-by-step explanation:

-5k²+20k-30

if u look at the equation ±5 are the greatest common factors so we ±5(±k²±4k±6)

The percentage form of given fraction is 60% and the hundredths form is 0.60

According to the statement

we have given that the a fraction and we have to find the percentage of that fraction and write in the form hundredths.

So, For this purpose,

The given fraction is 12/20.

Then the definition of the percentage is that

The Percentage, a relative value indicating hundredth parts of any quantity.

so, the percentage of given fraction is :

Percentage fraction = 12/20 * 100

After solving it, The percentage fraction will become:

Percentage fraction = 60%

and Now convert into the hundredths form then

In the hundredths form it will become

from 60% to 0.60.

So, The percentage form of given fraction is 60% and the hundredths form is 0.60

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The area of the parallelogram is 55 square feet

From the figure, we have the following dimensions:

Height = 5 ft

Base = 11 ft

The area of the parallelogram is calculated as:

Area = Base * Height

This gives

Area = 5ft * 11ft

Evaluate the product

Area = 55 square feet

Hence, the area of the parallelogram is 55 square feet

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Answer: x =   -1

Step-by-step explanation:

To remove the radical on the left side of the equation, square both sides of the equation.

√1−3x2=(x+3)2

Simplify each side of the equation.

1−3x=x2+6x+9

Solve for x

x=−1−8

Exclude the solutions that do not make true

√1−3x=x+3

x=−1

Answer:7 21/100

Step-by-step explanation: We will covert 7.21 into a fraction. .21 = 21/100. Since 21 can only be divided by 3 and 7, the simplest form of 21/100 is 21/100. So, the mixed number is 7 and 21/100

Answer:

7 and 21/100

Step-by-step explanation:

Since .01 is 1/100, 7.21 will be 7 and 21/100. There is no way to further simplify this, therefore, it is our final answer. Hope this helps! :)

Answer:

169.74+26.80

= 196.54

the correct decimal answer is 196.54

The vertex of the function f(x) exists (1, 5), the vertex of the function g(x) exists (-2, -3), and the vertex of the function f(x) exists maximum and the vertex of the function g(x) exists minimum.

Given:

[tex]$\mathrm{f}(\mathrm{x})=-(\mathrm{x}-1)^{2}+5$[/tex] and

[tex]$\mathrm{g}(\mathrm{x})=(\mathrm{x}-2)^{2}-3$[/tex]

The generalized equation of a parabola in the vertex form exists

[tex]$y=a(x-h)^{2}+k[/tex]

Vertex of the function f(x) exists (1, 5).

Vertex of the function g(x) exists (-2, -3).

Now, if (a > 0) then the vertex of the function exists minimum, and if (a < 0) then the vertex of the function exists maximum.

The vertex of the function f(x) exists at a maximum and the vertex of the function g(x) exists at a minimum.

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Answer:

- For the function f(x) = -(x - 1)^2/5, the vertex is a maximum point.

- For the function g(x) = x^4 - 3, the vertex is a minimum point.

Step-by-step explanation:

To determine if the vertex for each function is a minimum or a maximum, we need to analyze the leading coefficient of each function.

Let's start with the function f(x) = -(x - 1)^2/5. This function is already in vertex form, where the vertex is (1, 0).

Since the leading coefficient is negative (-1/5), the graph of f(x) opens downward. In this case, the vertex is a maximum point. You can visualize it as a peak on a graph.

Now, let's move on to the function g(x) = (x^2)^2 - 3. This function can be rewritten in vertex form as g(x) = x^4 - 3.

The leading coefficient is positive (1), so the graph of g(x) opens upward. In this case, the vertex is a minimum point. You can visualize it as a valley on a graph.

In summary:

- For the function f(x) = -(x - 1)^2/5, the vertex is a maximum point.

- For the function g(x) = x^4 - 3, the vertex is a minimum point.

Remember, the sign of the leading coefficient determines whether the vertex is a minimum or maximum point.

Answer:

(2 dimes + 6 pennies)

(4 nickels + 6 pennies)

(1 dime + 2 nickels + 6 pennies)

( 2 dimes + 1 nickels + 1 penny)

(1 dime + 3 nickels + 1 penny)

5 different ways that Jamie can make 26 cents.

Answer:

y = 3

Step-by-step explanation:

(5y - 3)/4 + 6 = 3y

5y - 3 + 24 = 12y

7y = 21

y = 3

Check.

(5*3 - 3)/4 + 6 = 3*3

(15 - 3)/4 + 6 = 9

12/4 + 6 = 9

3 + 6 = 9

9 = 9

Answer: y = 3

Step-by-step explanation:

Given equation

[tex]\frac{5y~-~3}{4} ~+~6~=~3y[/tex]

Multiply 4 on both sides (to eliminate fraction)

[tex]\frac{5y~-~3}{4} *4~+~6*4~=~3y*4[/tex]

[tex](5y~-~3)~+~24~=~12y[/tex]

Expand parenthesis and combine like terms

[tex]5y~-~3~+~24~=~12y[/tex]

[tex]5y~+~21~=~12y[/tex]

Subtract 5y on both sides

[tex]5y~+~21~-~5y~=~12y~-~5y[/tex]

[tex]21~=~7y[/tex]

Divide 7 on both sides

[tex]21~/~7~=~7y~/~7[/tex]

[tex]\Large\boxed{y=3}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Area of the base = 60 inches²

Height of the prism = 4 inches

perimeter of the base = 34 inches

Surface area of the rectangular prism =  256 inches²

The surface area of a rectangular prism can be calculated as follows;

area of the base = B = 12 × 5 = 60 inches²

Height of the prism = 4 inches

Perimeter of the base is the sum of the whole side of the base of the rectangular prism.

Therefore,

perimeter of the base = 12 + 12 + 5 + 5 = 34 inches

Surface area of the rectangular prism = 2B + ph

where

Therefore,

Surface area of the rectangular prism = 2(60) + 34(4)

Surface area of the rectangular prism = 120 + 136

Surface area of the rectangular prism =  256 inches²

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Answer:

6x + 4y = 16

Step-by-step explanation:

2(3x + 2y = 8)

2(3x + 2y) = 2(8)

6x + 4y = 16

Answer:

6x+4y=16

Step-by-step explanation:

2 (3x+2y=8)

2×3x+2×2y=2×8

=6x+4y=16 ans.

Answer:

3, 1, - 1, - 3, - 5

Step-by-step explanation:

using the recursive formula and f(1) = 3 , then

f(2) = f(1) - 2 = 3 - 2 = 1

f(3) = f(2) - 2 = 1 - 2 = - 1

f(4) = f(3) - 2 = - 1 - 2 = - 3

f(5) = f(4) - 2 = - 3 - 2 = - 5

first 5 terms are 3, 1, - 1, - 3, - 5

Answer:

EVALUATE

false

Step-by-step explanation:

Complex number

(39+5=5a=9)

Answer:

  d.  x = 5

Step-by-step explanation:

Chords that subtend congruent arcs are congruent.

Chord lengths are the same:

  AB = CD

  16x -2 = 14x +8

  2x = 10 . . . . . . add 2-14x

  x = 5 . . . . . . . . divide by 2

Here is the answer :

people who like both the songs is 35 and

people who like only folk songs is 100.

Answer:

Step-by-step explanation:

A square is made up of 4 sides that are equal in length. They can all be called "x" or "s" or whatever variable you want. The formula for the area of a square (and also the area of a rectangle) is Area = side × side.

If you called your sides "x", then the formula is A = x × x or A = x². Another way to note the area of either a square or a rectangle is to call the "bottom" the base and one of the sides the height and then the area formula looks like this:

A = b × h

or

A = length × width

They are all the same thing.

In the given diagram, the value of the dashed side of rhombus OABC is 5

From the question, we are to determine the length of the dashed line (OA), in rhombus OABC

In the diagram, we can observe that the length of OA is the distance between point A and the origin (O).

Using the formula for calculating distance between two points,

d =√[(x₂-x₁)² + (y₂-y₁)²]

In the diagram,

The coordinate of the origin is (0, 0)

The coordinate of point A is (3, 4)

Thus,

x₁ = 0

x₂ = 3

y₁ = 0

y₂ = 4

Putting the parameters into the formula, we get

OA =√[(3-0)² + (4-0)²]

OA =√(3² + 4²)

OA =√(9+16)

∴ OA =√25

OA = 5

Hence, in the given diagram, the value of the dashed side of rhombus OABC is 5

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Answer:

The exact amount of time would be 8 2/9 weeks, but if we are only counting full weeks, it would be finished in 9 weeks.

Step-by-step explanation:

y = xm

18 1/2 = 2 1/4x  Change both numbers into improper fractions

18 1/2 would be 37/2  The denominator (bottom number) stays 2.  To get the top number you would (2 x 18) + 1 or 37.  That makes 37/2 equivalent to 18 1/2.

Now do the same thing to 2 1/4.  The bottom number stays the same.  We get the top number (4 x 2) + 1 or 9.  That makes 9/4 equivalent to 2 1/4.

We know have

37/2 = 9/4 x  We can solve for x by multiplying both sides of the equation by 4/9

37/2(4/9) = (9/4)(4/9)x

148/18 = x  If we divide both the top and the bottom by 2 we would get 74/9 = x  If we divide 74 by 9 we get 8 2/9

correct answer is 28.

If the mean of four numbers is 25 and three numbers are 36, 12 and 24 then fourth number is 28.

given terms are:

first number =36

second number=12

third number=24

fourth number=?

let us assume the fourth number be x.

we know the formula to find mean is:

Mean=addition of given terms / total number of terms

According to given statement, we put the values in above equation and we get,

25=(36+12+24+x) / 4

By rearranging, we get

36+12+24+x=100

72+x=100

x=100-72

x=28

so, the fourth number is 28.

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Using the proportionality theorem, the measurements are: c. E = 22 and F = 55.

If two transversals intersect three or more parallel lines, they divide the lines in such a way that the smaller segments are proportional to each other or have ratios that are equal to each other.

Given the following:

A = 36,

B = 24,

C = 60

D = 33.

Since all lines are parallel, then:

A/D = B/E = C/F

Find the measure of E using the ratio, A/D = B/E:

36/33 = 24/E

Cross multiply

E = (24 × 33)/36

E = 22

Find the measure of F using the ratio, A/D = C/F:

36/33 = 60/F

Cross multiply

F = (60 × 33)/36

F = 55

The answer is: c. E = 22 and F = 55.

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The volume of the triangular prism as described is; 15 cubic foot.

A triangular pyramid simply refers to any geometric solid with a triangular base, and all three lateral faces are also triangles with a common vertex

It follows from the formula for calculating the volume of a triangular prism that;

Volume = (1/3) × base area × height.

Consequently,

volume of the prism is; = (1/3) ×9 × 5

Volume = 15 cubic foot

Therefore, volume of the triangular prism as described is; 15 cubic foot.

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Answer:

  t = 7

Step-by-step explanation:

You can use your knowledge of powers of 2, or you can use logarithms to find the value of t.

  2^1 = 2

  2^2 = 4

  2^4 = 16

  128 = 16×4×2 = (2^4)(2^2)(2^1) = 2^(4+2+1) = 2^7

Now, the equation is ...

  f(t) = 2^t = 2^7

Equating exponents, we have ...

  t = 7

Taking the log of both sides of the equation ...

  2^t = 128

we have ...

  t×log(2) = log(128)

  t = log(128)/log(2) = 7 . . . . . divide by the coefficient of t

The value of t is 7.

__

Additional comment

The relevant rule of exponents is ...

  (a^b)(a^c) = a^(b+c)

The relevant rule of logarithms is ...

  log(a^b) = b×log(a)

Step-by-step explanation:

You got your fraction messed up

It should be -3/2 or -1.5

Step-by-step explanation:

Set A is a subset of set B if all the elements of A are also the elements of Set B.. (common element)

The above set have 0 common elements so.. if there is no common element and are subsets then it means that there arent any elements in both the sets

so, the answer for the question would be "both the Sets A and B are the empty sets"