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WITCHER [35]
2 years ago
13

Write an equation for the sentence below.

Mathematics
1 answer:
Alex_Xolod [135]2 years ago
7 0

Answer:

3x - 23 = 2828

Step-by-step explanation:

I'll assume the question is supposed to read "The sum of three times a number (x) and −23 is 2828."

"three times a number (x)" can be written as 3x

"sum of three times a number (x) and −23" means 3x - 23

"is 2828"  = 2828

Put them together:

3x - 23 = 2828

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

<u>Not part of the question</u>

If you want to solve for x:

3x = 2805

x = 935

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Find the sum of the series given in sigma notation.
Kryger [21]

Answer:

Option b is correct 175

Step-by-step explanation:

n = 7

k = 6

3k -2 ------1

put k = 6 in above eq. for finding first term

  a1 = 3(6) - 2  = 18 - 2 = 16

put k = 7 in above eq. for finding first term

 a2 = 3(7) - 2 = 21 - 2 = 19

 a3 = 3 (8) - 2 = 24 - 2 = 22

16, 19 , 22, ...  //Arithmetic series formation

a1 = 16 , a2 = 19

d = a2 - a1 = 19 - 16 = 3 //Difference of first two terms

Using sum forumula for arithmetic series

sum = \frac{n}{2}(2a1 + (n-1)d)

      = \frac{7}{2}(2a1 + (7-1)d)

      = \frac{7}{2}(2(16) + (6)3)

      =  \frac{7}{2}(32 + 18)    

      =  \frac{7}{2}(50)

      = 7 * 25

      = 175




4 0
3 years ago
The sum of the squares of two consecutive negative integers is 61. Find the smaller of the two integers
Marysya12 [62]
x^2+(x+1)^2=61\\ x^2+x^2+2x+1-61=0\\ 2x^2+2x-60=0\ \ /:2\\ x^2+x-30=0\\ \Delta=1^2-4\cdot(-40)=1+120=121\ \ \Rightarrow\ \  \sqrt{\Delta} =11\\ \\ x_1= \frac{-1-11}{2} = \frac{-12}{2} =-6,\ \ \ \ x_2= \frac{-1+11}{2} = \frac{10}{2}=5\\ \\Ans.:x=-6
3 0
3 years ago
Need geometry help ASAP please!
tatiyna

Answer:

1. 121 π  unit²

2. 143°

3. 151 unit²

Step-by-step explanation:

1.

Area of a circle is given by the formula  A = πr²

where

A is the area,

r is the radius of the circle

From the given diagram, we can see that the radius is 11, hence the area will be:

A=\pi r^2\\A=\pi (11)^2\\A=121\pi

The answer is  121\pi units^2

2.

The unshaded secctor and the shaded sector equals the circle. We know that circle is 360°. The unshaded sector has an angle of 217°. So the shaded part will be 360 - 217 = 143°

The measure of the central angle of the shaded sector is 143°

3.

Area of a sector is given by the formula  A=\frac{\theta}{360}*\pi r^2

Where

\theta is the central angle of the sector (in our case it is 143°)

r is the radius (which is 11)

Plugging in all the info into the formula we have:

A=\frac{\theta}{360}*\pi r^2\\A=\frac{143}{360}*\pi (11)^2\\A=150.99

<em>rounding to the nearest whole number, it is </em>151 units^2

3 0
3 years ago
You observe the following pattern: J, K, N, B. What is the next letter in the sequence?
Nata [24]

Answer:

C. G

Step-by-step explanation:

4 0
3 years ago
What expression is equivalent to (9x^2 + 2x -7)(x - 4)
Dima020 [189]

Answer: C

Step-by-step explanation:

We can use the expanding rule to get that one if the expressions is

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

3 0
2 years ago
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