What will be the successor of the greatest 7-digit number and the predecessor of the smallest 8-digit number? Is there any relation between these two numbers? If yes, state the relation.

    Given ,

To Find : Maximum number of small cube shaped boxes that can fit in the cuboid

Volume of the Cuboid = [tex]2(lb+bh+lh)[/tex]

Volume of the cuboid = [tex]2(70X40+40X40+70X40)[/tex]

                                      = [tex]14400cm^{3}[/tex]

Now to find the volume of a cube,

[tex]V = a^{3}[/tex]

[tex]V = 10X10X10[/tex]

[tex]V = 1000cm^{3}[/tex]

Number of boxes that can fit in a cuboid = [tex]\frac{14400}{1000}[/tex]

                                                                    = [tex]14boxes[/tex]

Hence , the number of cube shaped boxes that can fit in a cuboid are 14

Answer:

4 1/8 m^2

Step-by-step explanation:

Given data

Length = 2 1/4 meters

Width= 1 7/8 meters

Area= Length* Width

Area=  2 1/4  * 1 7/8

Convert from mixed to simple fraction

Area= 9/4+ 15/8

Area= 18+ 15/8

Area= 33/8

Convert back to  mixed fraction

Area= 4 1/8 m^2

Answer:

P=3000$

T=2 years

R=1.6% per annum

Now,

interest=(3000×2×1.6)/100=96$

Amount=P+interest=3096$

Hence,Conan needs to pay back 3096$ and the interest is 96$

5 * root(x ^ 2, 3) is the equivalent expression.

Simply multiplying the radicands and placing the result behind the radical sign is all that is required to multiply two square roots. The square root of the product of the radicands, in other words, is equal to the product of two square roots.

Only if the numbers under the radical sign are equal can you add or subtract square roots themselves. The original number will still be in the radical sign after adding or subtracting the coefficients (numbers in front of the radical sign). Implement the suggested action.

5 * root(x ^ 2, 3) is the equivalent expression.

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Answer:

A=-1, B=2

Step-by-step explanation:

2a + 3b=4 equation 1

a-b=-3 equation 2

a=-3+b isolate a in equation 2

2(-3+b) + 3b=4. Substitute value of a in equation 2 (-3+b) into a value of  equ 1

-6+2b+3b=4

5b=10

b=2

solve for a:

a-b=-3

a-(2)=-3

a-2=-3

a=-1

The exponential function f so that the slope of a line from the point (0, f(0)) to the point (2, f(2)) is equal to 12 is defined as follows:

f(x) = 5^x.

The general format of an exponential function is given as follows:

y = ab^x.

In which:

The slope of a line, given two points, is given by the division of the change in the output by the change in the input of these two points.

Considering that the slope of points (0, f(0)) and (2, f(2)) is equals to 12, we have that:

[f(2) - f(0)]/(2 - 0) = 12

f(2) - f(0) = 24.

One case that satisfies this involves these two following points.

Hence the parameter a is given as follows:

a = 1.

When x = 2, y = 25, meaning that the parameter b is calculated as follows:

b² = 25

b = 5.

Hence the exponential function is:

f(x) = 5^x.

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According to the following graph, the reflection point of (-3,4) across the line y = 2 is (-3,0).

The term reflection point in math is defined as

Here we need to find the reflection point of (-3, 4) across the line y = 2.

Here first we have t plot the point on the graph, and then we have to plot the line equation y = 2 on the graph,

Here in order to find the reflection of a point along the x-axis, then we have to keep the abscissa constant and see the reflection of ordinate along the x-axis.

Based on these rule, the resulting graph is obtained as follows.

Through the graph we have identified that the resulting reflection point is (-3,0).

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Answer:

130°

Step-by-step explanation:

All the interior angles should add up to 540 degrees because it's a pentagon

∠T ≅∠S, so ∠T is also 115°

∠P and ∠R are both 90°

Add everything up and solve for ∠Q:

115 + 115 + 90 + 90 + m∠Q = 540

410 + m∠Q = 540

m∠Q = 130°

Composite numbers are whole numbers that contain more than two elements.. Examples of composite numbers include 36 and 42. These numbers are divisible by more than just 1 and themselves. 36 is divisible by 1, 2, 3, 4, 6, 9, 12, and 18. 42 is divisible by 1, 2, 3, 6, 7, 14, and 21.

Example 1: To find the factors of 36

Step 1: Start by dividing 36 by 2, which gives us 18.

Step 2: Divide 18 by 2, which gives us 9.

Step 3: Divide 9 by 3, which gives us 3.

Step 4: Divide 3 by 3 which gives us 1.

Step 5: The factors of 36 are 1, 2, 3, 4, 6, 9, 12, and 18.

Example 2: To find the factors of 42

Step 1: Start by dividing 42 by 2, which gives us 21.

Step 2: Divide 21 by 3, which gives us 7.

Step 3: Divide 7 by 7 which gives us 1.

Step 4: The factors of 42 are 1, 2, 3, 6, 7, 14, and 21.

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Answer:

168 - 147 = 21

21/168 = 12.5

Answer:

The lines t and u are perpendicular.

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(4-11)/(8-3)

m=-7/5

----------------------

m=(y2-y1)/(x2-x1)

m=(9-4)/(8-1)

m=5/7

Perpendicular lines have negative reciprocal slopes.

The triangles are not similar

Answer:

5x-7-5+X=5-x-5+X

or,6x-12=0

or,6x=12

or,X=12/6

:.X=2

The solution of the pair of equations y = 0 and y = -3 is y = -3/2.

The given pair of equations is:

y = 0

y = -3

We can solve this pair of equations using elimination. To do this, we first add the two equations together, which gives us:

y + y = 0 + (-3)

2y = -3

We then divide both sides by 2 to get the solution for y:

2y/2 = -3/2

y = -3/2

Therefore, the solution of the pair of equations y = 0 and y = -3 is y = -3/2.

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Answer:

0.12

Step-by-step explanation:

Rise/run

Answer:

B is the answer

Step-by-step explanation:

When you add AOB and NOM its 90 degrees. AOB is 29 + NOM that is 61. 61 + 29 = 90 degrees. Since complementry angles are 90 degrees, it is correct! Pls tell me if its correct or not!

Answer:

B is the answer

Step-by-step explanation:

ADD-

AOB and NOM

=90 degrees

AOB =29

add "NOM"

NOM= 32

=61.

61 + 29 = 90 degrees.

Complementary angles are 90 degrees

Answer:

9/7, 1/6, -3, 4/5

Step-by-step explanation:

Use the [tex]gradient =\frac{rise}{run}[/tex] formula to solve this.

4: [tex]gradient = \frac{14-5}{8-1} = \frac{9}{7}[/tex]

5: [tex]gradient = \frac{10-9}{2-(-4)} = \frac{1}{6}[/tex]

6: [tex]gradient = \frac{-5-4}{6-3} = \frac{-9}{3} = -3[/tex]

7: [tex]gradient = \frac{-1-(-5)}{7-2} = \frac{4}{5}[/tex]

Answer: x= 9.2

Scale Factor is 2.5

Step-by-step explanation:

1. Divide 17.5 by 7 to find scale factor

2. So 17.5/7=2.5

3. Divide 23 by 2.5 to find x

4. So 23/2.5=9.2

Answer:

Scale Factor: 2.5

x = 9.2

Step-by-step explanation:

So, the simple way to find this is by first figuring how much the new triangle has shrunk. Since they gave you both the bottom numbers, all you have to do is divide 17.5 by 7 to give you the scale factor of 2.5. You will use this scale factor to divide the 23 and get your answer of 9.2.

I hope this helps!

After simplification the correct matching is

1) 9i - A)[tex]\sqrt{-81}[/tex]

2) 5i[tex]\sqrt{2}[/tex] - C) [tex]\sqrt{-50}[/tex]

3) 12[tex]\sqrt{6}[/tex] - B) 4[tex]\sqrt{54}[/tex]

4) 6i[tex]\sqrt{7}[/tex] - D) [tex]\sqrt{-252}[/tex]

What is simplification?

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

Here to convert radical to simplified form we need to simplify them then

A)=> [tex]\sqrt{-81}[/tex] = [tex](\sqrt{i*9*9} })[/tex] =  9i

B) =>  [tex]4\sqrt{54} = 4\sqrt{9*6}= 4\sqrt{3^2*6}= 4*3\sqrt{6} = 12\sqrt{6}[/tex]

C) => [tex]\sqrt{-50} = \sqrt{i^2*25*2}=\sqrt{i^2*5^2*2}=5i\sqrt{2}[/tex]

D) => [tex]\sqrt{-252} = \sqrt{i^2*36*7}=6i\sqrt{7}[/tex]

Hence the correct matching is

1) 9i - A)[tex]\sqrt{-81}[/tex]

2) 5i[tex]\sqrt{2}[/tex] - C) [tex]\sqrt{-50}[/tex]

3) 12[tex]\sqrt{6}[/tex] - B) 4[tex]\sqrt{54}[/tex]

4) 6i[tex]\sqrt{7}[/tex] - D) [tex]\sqrt{-252}[/tex]

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To simplify a square root, simply factor the number and extract the roots of any perfect squares found from the radical sign.

Simplify a radical expression that use the Product Property.

To convert radicals to simplified forms, we must first simplify them.

A) = [tex]\sqrt{-81}[/tex]

   = ([tex]\sqrt{i*9*9}[/tex] )

   =  9i

B) = 4[tex]\sqrt{54}[/tex]

    = 4[tex]\sqrt{9*6}[/tex]

    = 4[tex]\sqrt{3^{2}*6 }[/tex]

    = 4*3√6

    = 12√6

C) = [tex]\sqrt{-50}[/tex]

    = [tex]\sqrt{i^{2}*25*2 }[/tex]

    = [tex]\sqrt{i^{2}*5^{2}*2 }[/tex]

    = 5i√2

D) = [tex]\sqrt{-252}[/tex]

    = [tex]\sqrt{i^{2}*36*7 }[/tex]

    = 6i√7

As a result, the correct match is

1) 9i - A) [tex]\sqrt{-81}[/tex]

2) 5i - C) [tex]\sqrt{-50}[/tex]

3) 12 - B) 4[tex]\sqrt{54}[/tex]

4) 6i - D)[tex]\sqrt{-252}[/tex]

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On solving the provided question, we can say that vectors are -  4 miles E: <4, 0>; 4 miles SE: <2√2, -2√2>; 7 miles S: <0, -7>; 6 miles SW: <-3√2, -3√2>; 2 miles E: <2, 0>

In mathematics, a vector is a quantity with magnitude and direction but no location. Acceleration and velocity are two examples of such numbers. A thing with both magnitude and direction is called a vector. A vector can be conceptualised geometrically as a directed line segment, the length of which corresponds to the magnitude of the vector, and the direction of which is denoted by an arrow. Size and direction are two independent characteristics of a quantity or phenomena known as a vector. The phrase also describes how these numbers are represented mathematically or geometrically. In nature, vectors may be found in electromagnetic fields, weight, momentum, force, and velocity.

4 + 4 + 7 + 6 + 2 = 23 miles.

vectors are -

4 miles E: <4, 0>

4 miles SE: <2√2, -2√2>

7 miles S: <0, -7>

6 miles SW: <-3√2, -3√2>

2 miles E: <2, 0>

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a=12,d=17-12=5

nth term =a+(n-1)d

36th term=12+(36-1)5

=12+(35×5)

12+175

36th term=187

Answer: 187

Step-by-step explanation: 17 - 12 = 5 and 22 - 17 = 5

aₙ = a₁ + (n - 1) d

where a₁ = 12, n = 36, d = 5

a₃₆ = 12 + (36 - 1) 5

a₃₆ = 12 + 35 × 5

a₃₆ = 12 + 175

a₃₆ = 187

187 is the 36th term

Answer: 80 degrees

Step-by-step explanation:

Answer:

the remaining angle of triangle is 80° by the sum of triangle is 180.

The shape of a decagon will remain the same when it is rotated through

its angle of rotational symmetry.

The rotation about the center will carry a regular decagon back to itself is 36°.

Note the following

The angle of rotational symmetry of a decagon is the smallest angle that a decagon can be rotated by such that the image formed by the rotation coincide with the preimage;

A decagon has 10 sides, the interior angle of a regular decagon is given as follows;

Each interior angle =  (n-2)*180/10 = 144⁰

A decagon has a reflective symmetry, therefore, the lines of symmetry joining opposite vertices are straight lines.

The number of diagonals in a decagon = 5

Rotating through the vertex and opposite vertex of the diagonals gives the number of image of the rotation that is similar to the preimage of a decagon as ten.

Therefore, a rotation of  (360/10) = 36⁰, about the center will carry a regular decagon back to itself.

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Answer:1

Step-by-step explanation:

because 1 devided by 3 is 3 and 1 devided by 25 is 5

Answer:

The answers are B ) A Symbol used to represent an unknown value and C ) Can be changed from one value to another