What is the volume of the square pyramid with base edges 12 cm and height 12 cm?

The terms of an arithmetic sequence are generated by adding a fixed term [tex]r[/tex] every time.

So, we start with [tex]a_1=15[/tex], and we continue with [tex]a_2=15+r[/tex], [tex]a_3=15+2r[/tex] and so on.

As you can see, the general rule is [tex]a_n = 15+(n-1)r[/tex]

With this information, we can derive [tex]r[/tex], knowing that

[tex]a_{100} = 307 = 15+99r \iff 99r = 292 \iff r = \dfrac{292}{99}[/tex]

So, the sum of the first 100 terms is

[tex][tex]\displaystyle \sum_{i=0}^{99} 15+i\dfrac{292}{99} = \displaystyle \sum_{i=0}^{99} 15 + \displaystyle \dfrac{292}{99}\sum_{i=0}^{99} i = (15\cdot 99) + \dfrac{292}{99}\dfrac{99\cdot 100}{2} = 1485 + \dfrac{490342}{99}[/tex]

Answer:

Option A

A B C D

Step-by-step explanation:

Line of symmetry means that line which cut anything into two two halves.

It could horizontal, vertical and diagonal.

A - vertical line of symmetry

B - horizontal line of symmetry

C - horizontal line of symmetry

D - horizontal line of symmetry

And it is an example of Spherical symmetry:

If the organism is cut through its centre, the resulting parts look the same.

The correct option is a.

The list given entirely contain letters with line symmetry. Line symmetry means that one half of an image or shape exactly matches the other half.

The question asks about line symmetry in letters. Line symmetry, also known as reflection symmetry or mirror symmetry, means that one half of an image or shape exactly matches the other half along a line of symmetry.

Looking at the options given:

a. A, B, C, D—B, C and D have horizontal line of symmetry; A has vertical line of symmetry.

b. W, X, Y, Z—X, W and Y have line symmetry, but Z do not.

c. L, M, N, O—M and O have line symmetry, but L and N do not.

d. S, T, U, V—T, U and V have line symmetry, but S do not.

Therefore, only option a is correct. Since, the list given entirely contain letters with line symmetry.

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Answer:

896 cm³

Step-by-step explanation:

the linear ratio = 1 : 2

The volume ratio = 1³ : 2³ = 1 : 8

The volume of the car is 8 times the volume of the two wheeler

volume = 112 × 8 = 896 cm³

Answer:

B) translated 6 units to the right then translated 9 units up

Step-by-step explanation:

Just use the graph to follow each translation until you get thee right answer, or you can count how many spaces are from the pre-image to the image. Just make sure to always use the same point.

The transformation from figure A to figure A' are:

Translating 6 units to the right.

Translated 9 units up.

Option B is the correct answer.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

We will take two coordinates from the figure.

Figure A has the coordinates:

(-5, -2) and (-4, -2)

And,

Figure A' has the coordinates:

(1, 7) and (2, 7)

Now,

Translating 6 units to the right.

(-5, -2) = (-5 + 6, -2) = (1, -2)

And,

(-4, -2) = (-4 + 6, -2) = (2, -2) _____(1)

Again,

Translated 9 units up.

(1, -2) = (1, -2 + 9) = (1, 7)

And,

(2, -2) = (2, -2 + 9) = (2, 7) ______(2)

From (1) and (2) we see that,

Figure A to Figure A'.

Translating 6 units to the right.

Translated 9 units up.

Thus,

The transformation from figure A to figure A' are:

Translating 6 units to the right.

Translated 9 units up.

Learn more about translation here:

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Answer:

1.7

Step-by-step explanation:

Of means multiply and is means equals

W = 5% *34

Change to decimal form

W = .05 *34

W =1.7

Answer:

$5093.37

Step-by-step explanation:

To get Rebecca's available credit we need to take all of her payments and purchases and previous balance.

Previous balance = $398.64

Purchases = $1,257.99

Payment = $250

Credit Line = $6,500

Now first we add together her purchases and previous balance.

398.64 + 1,257.99

This will give us:

$1,656.63 Total deductions.

Now we subtract that to her credit line.

$6500.00 - $1656.63

$4843.37

Now we take her payment and add it to her credit line.

$4843.37 + $250

$5093.37

So Rebecca's available credit is $5093.37.

Answer:

(b) 12; (a) 75%

Step-by-step explanation:

For b, convert the percentage to a SIMPLIFIED FRACTION [3⁄20 = 15%]. After you get your fraction, multiply it by 80 to get 12.

For a, it gives you your number already, but kind of turned around. This time, they want to to figure out what percentage of 48 will give you 36. Simply divide 36 by 48 to get your answer.

I am joyous to assist you anytime.

Answer:

"The number c is a​ zero the polynomial function y=​P(x) if and only if x-c is a​ factor of the polynomial​ P(x)."

Step-by-step explanation:

We have been given some statements with blank spaces:

"The number c is a​ _______ of the polynomial function y=​P(x) if and only if x-c is a​ _______ of the polynomial​ P(x)."

Now we need to fill those blank spaces by suitable words.

We know that if x=5 is some root (zero or solution) of the polynomial function then (x-5) works as factor.

So using that logic, we can fill the blanks spaces as:

"The number c is a​ zero the polynomial function y=​P(x) if and only if x-c is a​ factor of the polynomial​ P(x)."

Answer:

 I am 86% sure that it is The number c is zero the polynomial function y=​P(x) if and only if x-c is a​ factor of the polynomial​ P(x)

    Hope this helped!

Answer:

The answer is C because when you substituted the coordinate pairs into the equation, both sides are equal which tells you that they're a solution to the equation.

Explanation:

All you do is substitute. (x,y)

A:

Substitute

1 = 4(2) - 7

Multiply the number inside the parentheses by the outside number.

1 = 8 - 7

Subtract to get your solution.

1 = 1

Both sides equal to each other so this means that this is a solution to the equation.

B:

Substitute

9 = 4(4) - 7

Multiply the number inside the parentheses by the outside number.

9 = 16 - 7

Subtract to get your solution.

9 = 9

Both sides equal to each other so this means that this is also a solution to the equation.

D:

Both ordered pair is a solution to the equation.

Answer:

 1           1

------ + -------    

r^7      s^12

Step-by-step explanation:

r^(-7) + s^(-12) can be re-written as

 1           1

------ + -------    by putting to use the rule:

r^7      s^12

                1

x^(-a) = ----------

              x^a

For this case, we must simplify the following expression:

[tex]r ^ {- 7} + s ^ {- 12}[/tex]

By definition of power properties we have to:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

So, rewriting the expression we have:

[tex]\frac {1} {r ^ 7} + \frac {1} {s ^ {12}}[/tex]

Answer:

[tex]\frac {1} {r ^ 7} + \frac {1} {s ^ {12}}[/tex]

Option D

Final answer:

The property illustrated in the equation is the Commutative Property of Addition. It states that the order in which numbers are added does not affect the sum.

Explanation:

The equation showcases the Commutative Property of Addition. This property asserts that altering the order of addends doesn't impact the sum. Specifically, the given equation, 6 + 4 + 3, demonstrates this property as it equals 6 + 3 + 4. In essence, rearranging the sequence of addends doesn't alter the total, underscoring the flexibility of addition. This fundamental property simplifies mathematical operations, allowing for easier manipulation and calculation of sums, regardless of the order in which numbers are combined.

The Commutative Property of Addition plays a pivotal role in arithmetic, streamlining calculations and enhancing mathematical efficiency.

Answer:

Hello thank you for your question! The answer to your problem is 2.993

Enjoy Brainly ,

Homepage10

Step-by-step explanation:

Answer: 8 cm

Step-by-step explanation: its 8

it would be A i hope i helped

The least possible side effect of anabolic steroids among the choices provided is the first choice which is Brain and liver cancer.

Anabolic steroids are synthetic variations of the male hormone. The proper term for these compounds is anabolic-androgenic steroids.

"Anabolic" refers to muscle building, and "androgenic" refers to increased male characteristics.

Irritability and aggression increase when anabolic steroids are used in high doses.

The least possible side effect of anabolic steroids among the choices provided is the first choice which is Brain and liver cancer.

Learn more about anabolic steroids ;

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the answer is twenty-four

Answer:  f(t) is shifted 20 units to the left and 7 units down

Step-by-step explanation:

The general form of a sin function is: y = A sin (Bx - C) + D

y = sin (5t)

f(t) = sin (5t + 20) -7

I believe it is because it would be he most simplistic answer to be honest because for example 10,8 it is the same as 5,4 so u would put 5,4 because it is simplified so put (2.1,0) as your answer

The ordered pair that is a solution to the equation represented by the graph is (-2.5, 3).

Here's my reasoning:

- The graph intersects the x-axis at (2.1, 0): This means that any point on the x-axis, including (2.1, 0), has a y-value of 0. However, this doesn't guarantee that (2.1, 0) is a solution to the equation itself.

- The graph passes through the point (-2.5, 3): This means that the equation of the graph must yield a y-value of 3 when x = -2.5. Therefore, (-2.5, 3) is a solution to the equation.

The other points are not on the graph itself:

- (0, 0.6) is above the x-axis but not on the graph's line.

- (-1, 1.8) is also above the x-axis but not on the graph's line.

Therefore, the only ordered pair that is a solution to the equation represented by the graph is (-2.5, 3).

Answer:

y = 4

or

y - 4 = 0(x - 3)

Step-by-step explanation:

The points (-2,4) and (3,4) have the same y-value. Because of this, the slope of the line will be 0 and the line will be horizontal. This means the line will have the equation y = b where b is the y-coordinate. The equation of the line is

y = 4.

In point slope form, the equation will have m = 0.

y - 4 = 0(x -3)

Step-by-step explanation:

13x=7

It would be fractional

The equation to find the number of 13-foot pieces from a 7-foot piece of wood is explained step-by-step.

The equation to calculate the number of 13-foot pieces that can be cut from a 7-foot piece of wood is:

Number of pieces = Total length of wood / Length of each piece

Plugging in the values:

Answer:

x = -1/7

Step-by-step explanation:

Work is in attached sheet :)

Answer:

-1/7 or -0.14

Step-by-step explanation:

Answer:

Faster plane --> 600km/hr

Slower Plane --> 500km/hr

Step-by-step explanation:

Use inequality: 1800/r = 1800/(r-100) + 3/5 and solve to get r = 600, so the plane which is r -100 is 500 km/hr.

Answer: The first answer choice

Step-by-step explanation:

Answer:

776.46 m

Step-by-step explanation:

According to the scenario it is a question of right angle triangle

To find the height of the plane above the ground we will use trigonometry identity.

here Ф = 15°

        opposite = height

        hypotenuse = 3000m

Plug values in the formula above

height = sin(15)(3000)

           = 776 .46 m

(make sure your calculator is in degree mode)

Answer:

776.46 m

Step-by-step explanation:

The angle of elevation is 15 degrees which is measured from the horizontal.

The height above the ground is the opposite side of the triangle, the hypotenuse is the 3000 m and the angle of elevation is 15 degrees.

The sine ratio is the one one that ties the relationship;

Therefore;

sin 15 = x/3000

x = sin 15 × 3000

   = 776.46 m

Answer:

Melissa will be able to hold 8 1/4 containers of rice.  

Step-by-step explanation:

1 pound= 16 oz

132/16= 8.25

Answer:

Step-by-step explanation:

Let's work in pounds everywhere.  Convert 132 oz of rice into lb:

132 oz          1 lb

----------  ·  ------------  =  8.25 lb

     1            16 oz

Melissa will be able to fill 8 1-lb containers with rice, but will have 0.25 lb left over.

If she wants 10 lb of rice and is curious regarding how many oz that would be, take this 10 lb and multiply it by the conversion factor shown above:

10 lb        16 oz

--------  ·  ---------  =  160 oz

   1           1 lb

Twenty students are male.

Hope this helps.

Answer: [tex]46x^2+73x+15[/tex]

Step-by-step explanation:

The area of a rectangle can be calculated with the formula:

[tex]A=lw[/tex]

l: the length of the rectangle.

w: the width of the rectangle.

The area of the remaning wall after the mural has been painted, will be the difference of the area of the wall and the area of the mural.

Knowing that the dimensions of the wall are [tex](6x+7)[/tex] by [tex](8x+5)[/tex], its area is:

[tex]A_w=(6x+7)(8x+5)\\\\A_w=48x^2+30x+56x+35\\\\A_w=48x^2+86x+35[/tex]

As they are planning that the dimensions of the mural be [tex](x+4)[/tex] by [tex](2x+5)[/tex], its area is:

[tex]A_m=(x+4)(2x+5)\\\\A_m=2x^2+5x+8x+20\\\\A_m=2x^2+13x+20[/tex]

Then the area of the remaining wall after the mural has been painted is:

[tex]A_{(remaining)}=A_w-A_m\\\\A_{(remaining)}=48x^2+86x+35-(2x^2+13x+20)\\\\A_{(remaining)}=48x^2+86x+35-2x^2-13x-20\\\\A_{(remaining)}=46x^2+73x+15[/tex]

The answer is 143312

Answer:

it is  143312                                    

Answer:

30

Step-by-step explanation:

1/2 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

1/3 3 6 9 12 15 18 21 24 27 30

1/5 5 10 15 20 25 30

Answer:

If your definition of "Cover" is to fill it in, than there is no longer a hole.

If your definition of "Cover" is to simply "cover" the hole and not filling it, there is still a 12 feet hole.

Unless your perspective is that there is no hole simply because it was Covered.

Step-by-step explanation: Try again

the hole would be over 9000 deeper