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Leni [432]
3 years ago
5

3 times a number X subtracted from 18 is less than -90 write an inequality for the statement above

Mathematics
1 answer:
emmainna [20.7K]3 years ago
5 0
18-3x<-90. Hope this helps! :)
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Please someone help me to prove this. ​
morpeh [17]

Answer:  see proof below

<u>Step-by-step explanation:</u>

Use the Double Angle Identity: sin 2Ф = 2sinФ · cosФ

Use the Sum/Difference Identities:

sin(α + β) = sinα · cosβ + cosα · sinβ

cos(α - β) = cosα · cosβ + sinα · sinβ

Use the Unit circle to evaluate: sin45 = cos45 = √2/2

Use the Double Angle Identities:   sin2Ф = 2sinФ · cosФ

Use the Pythagorean Identity: cos²Ф + sin²Ф = 1

<u />

<u>Proof LHS → RHS</u>

LHS:                                  2sin(45 + 2A) · cos(45 - 2A)

Sum/Difference: 2 (sin45·cos2A + cos45·sin2A) (cos45·cos2A + sin45·sin2A)

Unit Circle:    2[(√2/2)cos2A + (√2/2)sin2A][(√2/2)cos2A +(√2/2)·sin2A)]  

Expand:        2[(1/2)cos²2A  + cos2A·sin2A + (1/2)sin²2A]

Distribute:              cos²2A   + 2cos2A·sin2A + sin²2A  

Pythagorean Identity:    1 + 2cos2A·sin2A

Double Angle:                1 + sin4A

LHS = RHS:  1 + sin4A = 1 + sin4A   \checkmark

6 0
3 years ago
Jensen is building a snow fort. Each block in the fort weighs about 1 kilogram. Jensen hopes to make about 40 blocks for the for
babymother [125]

Answer: 13,333 snowflakes

Step-by-step explanation:

For this exercise let be "x" represents the number of snowflakes that will be in the fort.

According to the information given in the exercise, the weight of one block is 1 kilogram. Knowing that the fort must have 40 blocks, the total weight is:

total\ weight=(1\ g)(40)\\\\total\ weight=40\ g

 Since each snowflake weighs 3* 10^{-3} grams, need to divide the total weight calculated above by the weight of a snowfake.

Therefore, through this procedure you get the following result:

x=\frac{40\ grams}{3 * 10 ^{-3}\ grams}\\\\x\approx13,333

Therefore, the there will be 13,333 snowflakes in the fort.

5 0
3 years ago
Montel can't keep up with the demand for the latest best-selling book. He had to order more copies twice this week. On Monday he
zhannawk [14.2K]
96+264 = 360
360 \ 24 = 15

Therefore he received 15 boxes
6 0
3 years ago
Read 2 more answers
29. March sales accounted for 1/7 of the total number of jazz records sold all year. About how many jazz records were sold all y
enot [183]

The March sales of Jazz records is an illustration of proportions, and the number of jazz records sold all year is 7x

<h3>How to determine the total number of sales?</h3>

The sales in March is given as:

Proportion = 1/7

Let the actual number of sales in the month of March be x, and the total sales in the year be y.

So, we have:

1/7 * y = x

Make y the subject

y =7x

Hence, the number of jazz records sold all year is 7x

Read more about proportions at

brainly.com/question/1781657

#SPJ1

8 0
2 years ago
Given that
valentina_108 [34]

Answer: x= -3.25

Step-by-step explanation:

R=4x+6y   11=4x+6(4)     11=4x+ 24     11-24=4x   -13=4x  -13/4=x  x=-3.25

11=4(-3.25)+ 6(4)  11= -13+24

6 0
3 years ago
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