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The first term of an arithmetic progression of 4 terms and ratio equal to 4 whose sum is 100 is 19.

The first term of an arithmetic progression can be calculated using the following expression:

Sn = n/2 [2a + (n − 1)d]

Where;

100 = 2 [2a + (4 - 1)4]

100 = 4a + 24

4a = 100 - 24

a = 76/4

a = 19

Therefore, the first term of an arithmetic progression of 4 terms and ratio equal to 4 whose sum is 100 is 19.

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Answer:

3.94

Step-by-step explanation:

3.944     rounded to nearest hundredth  = 3.94    becuase the thousandth digit is <5  you do not change the hundredth

Answer:

57 f

Step-by-step explanation:

-16t² + vt + h

-16(4 s)² + (72 f/s)(4 s) + (25 f)

-256 + 288 + 25 = 57

Answer:

6x-5

Step-by-step explanation:

We have to find 2 sides added together, so we do (24x-20)/2=12x-10. (12x-10)/2=6x-5, so it is 6x-5.

Answer:

x=9

y=4

z=4

Step-by-step explanation:

9x-13=7x+5

9x-7x=5+13

2x=18

x=18/2=9

3y=12

y=12/3=4

11z-41=5z-17

11z-5z=-17+41

6z=24

z=24/6=4

The area of a circle is defined as [tex]\pi(r^{2})[/tex], where r = 4.3 here. 4.3^2 ≅ 18.49, so the area of the full circle is 18.49π.
The shaded section covers 12 degrees of the full 360 degrees in a circle, or 1/30th of the area. Therefore, the area of the shaded section is equal to [tex]\frac{18.49\pi}{30}[/tex], or about 1.936. In this question's context, that would be 1.936[tex]in^{2}[/tex].

Work Shown:

x = unknown number

4x = four times the unknown number

-8+4x = sum of -8 and the previous expression

-8+4x is the same as 4x+(-8) or 4x-8

Answer:

(3,0)

Step-by-step explanation:

Answer:

x = 1

y = -3

Step-by-step explanation:

cos(pi) = -1

so many ways :

sqrt(0.5/2) = sqrt(0.5/2 × 8/8) = sqrt(4/16)

= sqrt(0.5/2 × 18/18) = sqrt(9/36)

= sqrt(1/4) = 1/2

"nicest" approach (all integers) :

3x² = sqrt(9)

3x² = 3

x² = 3/3 = 1

x = 1

2y = sqrt(36)

2y = 6

y = 6/2 = 3

one of them has to be negative (because cos(pi) = -1), so it has to be y, because 3x² cannot be negative with real numbers.

so, y = -3

-1 × 3×1²/(2×-3) = sqrt(0.5/2) = 1/2

-1 × 3/-6 = 1/2

3/6 = 1/2

1/2 = 1/2

correct

The degree of a polynomial is the highest exponent of the algebraic expression.

[tex]6 {x}^{2} \: + \: {x}^{ \boxed{ \bold{9}}} \: + \: 5 {x}^{7} \: + \: 20 {x}^{6} [/tex]

The point at which three or more lines intersect is the point of concurrency.

The point were three lines meet or intersect is a point of concurrency.

In other words, a point of concurrency is where three or more lines intersect in one place.

This point of concurrency is a single point shared by three or more lines.

Perpendicular bisectors, and altitudes are concurrent in every triangle.

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Answer:

concurrency

Step-by-step explanation:

Look above for more

Answer:

Step-by-step explanation:

2x^3 + 5x^3 + 2 + 3 = 7x^3 + 5

Answer:

xy = - 8

Step-by-step explanation:

note that

(x - y)² = x² + y² - 2xy , that is

6² = 20 - 2xy

36 = 20 - 2xy ( subtract 20 from both sides )

16 = - 2xy ( divide both sides by - 2 )

- 8 = xy

[tex](x-y)^2=x^2-2xy+y^2[/tex]

Therefore

[tex]6^2=20-2xy\\36=20-2xy\\2xy=-16\\xy=-8[/tex]

Answer:

Step-by-step explanation:

_________________________________________________

initial number of sweets               |   18                   |      18

                                                       |                          |

Sue gives Tony x sweets              |   18 - x              |      18 + x

                                                       |                          |

Sue ,eats 5 of her sweets. and   |  18 - x - 5 =       |      (18 + x)/2 =

Tony ,eats half of his sweets        | 13 - x                |     9 + x/2

Answer:

1 solution

Key:

Assume x is the the range x > 0 ≥ 1, in other words, assume x is equal to 1.

Step-by-step explanation:

[tex]y = -x - 8x - 16\\= -x - 8x\\= 9x\\= 9x - 16[/tex]

They spend about three hours a day online

Step-by-step explanation:

n + 5 = -16

n = -21

The correct option is -21

Answer:

Step-by-step explanation:

B is at (-3,-2) Multiply by 3: (-9,-6)

O is at (2,-1)  Multiply by 3: (6,-3)

T is at (-3,3) Multiply by 3: (-9,9)

Hope this helps!!

Answer:

6+8x

Step-by-step explanation:

The vertices of ABCD after 90 degrees clockwise rotation about point C are: A' (0,6), B' (3,7), C' (4,6) and D' (4,3)

The image of the polygon ABCD is not given; however, the question can still be answered because the coordinates are known.

The vertices of polygon ABCD are given as:

A = (4, 6)

B = (5, 3)

C = (4, 2)

D = (1, 2)

The rule of rotation about point C is:

(x,y) = (a + b - y, x + b - a)

Where:

(a, b) = (4, 2) --- the point of rotation.

So, we have:

(x,y) = (4 + 2 - y, x + 4 - 2)

(x,y) = (6 - y, x + 2)

The above means that:

A' = (6 - 6, 4 + 2) = (0,6)

B' = (6 - 3, 5 + 2) = (3,7)

C' = (6 - 2, 4 + 2) = (4,6)

D' = (6 - 2, 1 + 2) = (4,3)

Hence, the image of the rotation and their vertices (i.e. coordinates) are:

A' = (0,6)

B' =  (3,7)

C' = (4,6)

D' =  (4,3)

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1 + 2 + 3 + 4 + 5 + 95 + 96 + 97 + 98 + 99. = 500

Answer:

500

Step-by-step explanation:

rearrange the sum as

(99 + 1) + (98 + 2) + (97 + 3) + (96 + 4) + (95 + 5)

= 100 + 100 + 100 + 1000 + 100

= 5 × 100

= 500

Graph is in attached image.

Answer:

36

Step-by-step explanation:

If x = 2 and y = -3...

xy^2=

(2)(-3)^2 =

-6^2 =

36

XY times 2=

(-6)(2) =

-12

Answer:

18

Step-by-step explanation:

First you must fill input the values into their variable counterparts:

xy^2 turns into: 2 * -3 ^2

Since there isn't a parenthesis around x AND y, the exponent only applies to the y value.

-3 ^2 = 9, so 2 x 9 = 18

xy^2 = 18 if x =2 and y = -3

Answer:

C

Step-by-step explanation:

Formula for the volume of a cone :

Volume (cone) = 1/3πr²h

===========================================================

Given :

⇒ r = 4 units

⇒ h = 21 units

============================================================

Solving :

⇒ Volume (cone) = 1/3 × π × (4)² × 21

⇒ Volume (cone) = 16 × 7 × π

⇒ Volume (cone) = 112π units²

Answer:

[tex]\sf C. \quad 112 \pi \:units^2[/tex]

Step-by-step explanation:

[tex]\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Given:

Substituting the given values into the formula:

[tex]\implies \sf Volume=\dfrac{1}{3} \cdot \pi \cdot 4^2 \cdot 21[/tex]

[tex]\implies \sf Volume=112 \pi \:units^2[/tex]

Answer:

Step-by-step explanation:

Answer:

22 3/4

Step-by-step explanation:

divide 1/4 which is 0.25, then add 3 to that, then multiply it by 7 which is 22.75

then convert it back into a fraction which is 22 3/4

Answer:

1/2  /   50% chance

Step-by-step explanation:

There are 10 yellow out of 20 (6 + 4 + 10 = 20) balls.

So, the probability is 10 / 20

Or, 1 / 2 (which is the same thing as 50% chance)

(chance = probability)