1. If A*B= A·B+1 and A□ B = A+B/2, then find 3 *[(7 □ 3) □ (3*4)].

2. If * represents and operation defined by a*b= a^b +b, find (1*2)*3.

Explain PLEASE!!!

Answer:

seventeen degrees(17⁰)

The central angle is approximately 2.357 radians.

To find the central angle, we can use the formula:

Central angle (θ) = arc length ÷ radius

Given:

Arc length (mXY) = 18 in

Radius (ZY) = 7.64 in

Plugging in the values:

Central angle (θ) = 18 in ÷ 7.64 in

Calculating the division:

θ ≈ 2.357 radians

Therefore, the central angle is approximately 2.357 radians.

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Answer:

The answer is B.

Step-by-step explanation:

x^2+5x-9-(7x+4)

x^2+5x-9-7x-4

x^2-2x-9-4

x^2-2x-13

Okay this is the answer I hope this help

If Angela spent $95 to buy 7 cakes for her office party, and she then cut each cake into quarters and each quarter into further 3 pieces, of which Kevin ate 5 pieces, then Angela had spent $5.65 on just the share of the cake that Kevin had.

As per the question statement, Angela spends $95 to buy 7 cakes for her office party, and she then cuts each cake into quarters and each quarter into further 3 pieces, of which Kevin ate 5 pieces.

We are required to calculate the amount Angela had spent on just the share of the cake that Kevin had.

To solve this question, first let us calculate the total number of pieces, did Angela cut all the 7 pieces of the cake into.

Considering one piece, that it was first cut into a quarter and then each quarter into further 3 pieces, one single piece out of original 7 pieces was cut into a total of [(4 * 3) = 12] pieces.

Therefore, all the 7 original pieces were altogether cut into a total of

[(7 * 12) = 84] pieces.

Now, since Angela spent $95 to buy the original 7 pieces,

Or, Angela actually spent $95 to buy 84 pieces of cake,

Then, 1 piece of the 84 costs $(95/84) = $1.13.

Now, since Kevin ate 5 such pieces of the 84, those 5 pieces cost

$(1.13 * 5) = $5.65.

Therefore, Angela had spent $5.65 on just the share of the cake that Kevin had.

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Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:

23

Step-by-step explanation:

An integer is a whole number that can be positive, negative, or zero, without any fractional or decimal parts.

The given expressions for three consecutive integers are:

Give that twice the first number is 20 more than the second:

\(2x = (x + 1) + 20\)

Solve this equation for x:

\(\begin{aligned}2x &= (x + 1) + 20\\2x&=x+1+20\\2x&=x+21\\2x-x&=x+21-x\\x&=21\end{aligned}\)

The expression for the largest integer is (x + 2).

Therefore, to find the largest number, substitute the found value of x into this expression:

\(\begin{aligned}\sf Largest\;number&=(x+2)\\&=21+2\\&=23\end{aligned}\)

Therefore, the largest number is 23.

Answer:

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

126/3=42

126-42=84

84/4=21

63 are dogs

42 are cats

and 21 are rabbits

Answer:

you see

Step-by-step explanation:

Answer: 156.38 m

Step-by-step explanation:

Using the arc length formula, the answer is \(2\pi(8^2) \cdot \frac{140}{360} \approx 156.38\)

Answer:

I am confident the answer is H.

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2.

The five regular polyhedra, also known as the Platonic solids, are the only convex polyhedra where all faces are congruent regular polygons, and the same number of polygons meet at each vertex.

The five regular polyhedra are:

1. Tetrahedron: It has four triangular faces, and three triangles meet at each vertex.

2. Cube: It has six square faces, and three squares meet at each vertex.

3. Octahedron: It has eight triangular faces, and four triangles meet at each vertex.

4. Dodecahedron: It has twelve pentagonal faces, and three pentagons meet at each vertex.

5. Icosahedron: It has twenty triangular faces, and five triangles meet at each vertex.

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that:

"for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2".

For regular polyhedra, each face has the same number of sides (n) and each vertex is the meeting point of the same number of edges (k). Therefore, we can rewrite Euler's formula for regular polyhedra as:

V - E + F = 2  

=>  kV/2 - kE/2 + F = 2  

=>  k(V/2 - E/2) + F = 2

Since each face has n sides, the total number of edges can be calculated as E = (nF)/2, as each edge is shared by two faces. Substituting this into the equation:

k(V/2 - (nF)/2) + F = 2  

=>  (kV - knF + 2F)/2 = 2  

=>  kV - knF + 2F = 4

Now, we need to consider the conditions for a valid polyhedron:

1. The number of faces (F), edges (E), and vertices (V) must be positive integers.

2. The number of sides on each face (n) and the number of edges meeting at each vertex (k) must be positive integers.

Given these conditions, we can analyze the possibilities for different values of n and k. By exploring various combinations, it can be proven that the only valid solutions satisfying the conditions are:

(n, k) pairs:

(3, 3) - Tetrahedron

(4, 3) - Cube

(3, 4) - Octahedron

(5, 3) - Dodecahedron

(3, 5) - Icosahedron

Therefore, there exist only five regular polyhedra.

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Answer:

Joff-tchoff-tchoffo-tchoffo-tchoff!

Tchoff-tchoff-tchoffo-tchoffo-tchoff!

Joff-tchoff-tchoffo-tchoffo-tchoff!

Step-by-step explanation:

Answer:

"Joff-tchoff-tchoffo-tchoffo-tchoff!

Tchoff-tchoff-tchoffo-tchoffo-tchoff!

Joff-tchoff-tchoffo-tchoffo-tchoff!"

Answer:

no

Step-by-step explanation:

every triangles degrees equal 180.

78+21=99

180-99=81

the smaller triangle

21+80= 101

180-101=79

so the degrees are different

Based on the distribution of data, the box and whisker plot displays the results of the scientific test for two classes. It is incorrect to say that both sections have the same value for the third quartile.

The formulation of partial differential equation solutions uses distribution generalized functions. The likelihood of a specific value or range of values for a variable is known as the probability distribution. Cumulative distribution function, where the likelihood of a value not exceeding a certain value depends on that value. A list of the values recorded in a sample, or a frequency distribution. In coding theory, there are two types of distribution: inner and outer. distribution of a portion of a manifold's tangent bundle.Term distribution: the state of having all members of a category present. The distributive law from elementary algebra is generalized by the property of binary operations known as distributivity. the distribution.

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Answer: 9.5112

Step-by-step explanation:

There are 0.2642 gallons in a liter. So, in 36 liters, there are \(36(0.2642)=9.5112 \text{ gal }\)

Answer:

2 forms

Step-by-step explanation:

hope this helps <3

\( \sf \longrightarrow \: \frac{8}{5} \div 6 \\ \)

\( \sf \longrightarrow \: \frac{5}{8} \times 6 \\ \)

\( \sf \longrightarrow \: \frac{5 \times 6}{8} \\ \)

\( \sf \longrightarrow \: \frac{30}{8} \\ \)

\( \sf \longrightarrow \: \frac{8}{30} \\ \)

\( \sf \longrightarrow \: 0.26 \\ \)

_____________________________

Answer

Edge length of the cube = 1.067 units

Explanation

The volume of a cube of edge length, L units, is given as

Volume = L³

For this question,

Volume = 1.216 cubic units

L = edge length = ?

Volume = L³

1.216 = L³

We can rewrite this

L³ = 1.216

Take the cube root of both sides

∛(L³) = ∛(1.216)

L = 1.067 units

Hope this Helps!!!

Answer:

0.4, 40%

Step-by-step explanation:

Step-by-step explanation:

The way you can think about volume is that we have some cross sectional area times the height of the solid.

27.

The volume of a square based pyramid is

\(v = {s}^{2} ( \frac{h}{3} )\)

where h is the height of the pyramid

s is the side length of the square base.

S=7

h=12

\(v = {7}^{2} ( \frac{12}{3} ) = 49 \times 4 = 196\)

28. The volume of a rectangular prism

\(v = l \times w \times h\)

where l is length

w is width

h is height

\(v = 11 \times 11 \times 8 = 968\)

29.

Use the same formula in 27

\(v = 100(3) = 300\)

30.

Volume of a Cylinder is

\(v = \pi {r}^{2} h\)

where r is the radius of the circle

where h is the height

r is half of the diameter

The diameter is 22, thus the radius is 11.

\(v = {11}^{2} (8)(\pi)\)

\(v = 968\pi\)

pi is approximately 3.14

\(v = 3041.06\)

31. Volume of A Sphere

\( \frac{4}{3} \pi {r}^{3} = v\)

The radius is half of diamter, thus r=7

\( \frac{4}{3} \pi( {7}^{3} ) = 1436.76\)

Answer:

x < -3 or x > 2

Step-by-step explanation:

x² + x - 6 > 0

Convert the inequality to an equation.

x² + x - 6 = 0

Factor using the AC method and get:

(x - 2) (x + 3) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x - 2 = 0

x = 2

x + 3 = 0

x = -3

So, the solution is x < -3 or x > 2

The size of the angle between AH and the plane ABCD is approximately 74.4°, rounded to one decimal place.

To find the size of the angle between AH and the plane ABCD in the given cuboid, we can use the concept of three-dimensional geometry.

First, let's consider the right triangle BCA. The given angle BCA is 48°, and we know that the length of AB is 7.3 cm. Using trigonometric functions, we can find the length of BC:

BC = AB * sin(BCA)

BC = 7.3 * sin(48°)

BC ≈ 5.429 cm

Now, let's look at the right triangle BAH. The length of AH is given as 8.1 cm. We can find the length of BH by subtracting BC from AB:

BH = AB - BC

BH ≈ 7.3 - 5.429

BH ≈ 1.871 cm

Next, let's consider the right triangle ABH. We want to find the angle BAH, which is the complement of the angle between AH and the plane ABCD. We can use the cosine function to find the angle BAH:

cos(BAH) = BH / AH

cos(BAH) ≈ 1.871 / 8.1

BAH ≈ arccos(1.871 / 8.1)

BAH ≈ 74.4°

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The equation of a straigth line is

y = mx + c

m = slope

from the question slope = 9

our points are (5,4)

y - y1 = m(x - x1)

x1 = 5 and y1 = 4

y - 4 = 9(x - 5)

y - 4 = 9 * x - 9 *5

y - 4 = 9x - 45

y = 9x -45 + 4

y = 9x - 41

The answer is y = 9x - 41

Answer:

1

Step-by-step explanation:

We can see that 7 is equal to 6, as opposite angles are the same.

We can also see that 2 is also 6, as corresponding angles are equivalent.

Therefore, 3 is also congruent to 6, as it is equal to 2.

Hope that this helps!

Answer:

10A+7B should be D or it changed but the answer is 10A+7B

Explanation to Answer

it is correct have a good day

Answer:

10A = 7B

Step-by-step explanation:

It is the correct answer on A P E X

Answer:

The table with (-3, 2), (0, 2), etc.

Every input has exactly one output.

Hope this helps :)

The correct solution set for the given graph include the following: D. {infinite set of points on the line}.

In Mathematics, a quadrant can be defined as the area that is occupied by the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of a cartesian coordinate.

This ultimately implies that, there are four (4) major quadrants in any graph and these include the following:

Generally speaking, the solution set of a graph simply refers to all of the points that lie on its line. By critically observing the graph of lines a and b, we can reasonably infer and logically deduce that they both have the same slope, solution set, as well as increasing and decreasing infinitely.

In this context, the correct solution set lies in both Quadrant II and Quadrant III because both lines move towards negative and positive infinity i.e [-∞, ∞].

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