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Marat540 [252]
3 years ago
7

Combine like terms (2+7x)(2-7x)=

Mathematics
1 answer:
Aleksandr [31]3 years ago
7 0

Answer: 4-49x²

Step-by-step explanation:

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Can anyone help me solve these math problems?
Veseljchak [2.6K]

Answer:

  1. x = 2
  2. r = 48
  3. 3536 ft
  4. √10
  5. 10°

Step-by-step explanation:

1. The Pythagorean theorem applies, so the sum of the squares of the legs is equal to the square of the hypotenuse.

  x² + (x+3)² = (√29)²

  2x² +6x +9 = 29 . . . . . . eliminate parentheses, collect terms

  2x² +6x -20 = 0 . . . . . . subtract 29

  x² +3x -10 = 0  . . . . . . . . divide by 2

  (x +5)(x -2) = 0 . . . . . . . . factor

x = -5 or +2 . . . . . . . . . . . . values that make the factors zero (-5 is extraneous)

The value of x is 2.

__

2. Even though the figure is drawn incorrectly the Pythagorean theorem still applies. (The second attachment shows the circle in the right place. The figure is not to scale.)

  14² + r² = (r+2)²

  196 + r² = r² +4r +4 . . . . eliminate parentheses

  192 = 4r . . . . . . . . . . . . . .subtract r²+4 from both sides

  48 = r . . . . . . . . . . . . . . . . divide by 4

The value of r is 48.

__

3. You will recognize that the triangle involving the distance above the ground, the distance along the ground, and the straight-line bullet path is an isosceles right triangle. So, the hypotenuse is √2 times the length of either leg. The path length of the bullet is ...

  (2500 ft)√2 ≈ 3536 ft

__

4. see below for the diagram

The length to the terminal point is found using the Pythagorean theorem:

  d = √(3² +(-1)²) = √10

The distance from the origin to the terminal point is √10 ≈ 3.16.

__

5. Angles "a" and "8a" total 90°, so we have ...

  a + 8a = 90°

  9a = 90° . . . . . . . . collect terms

  a = 10° . . . . . . . . . . divide by 9

The value of a is 10°.

8 0
3 years ago
What is the volume of the right prism?
Tasya [4]
Volume=legnth times widht times height
since this is a rectangle and multiplication is commutative

doesn't matter what order wr multiply
V=5*5*12
V=300 in^3
4 0
3 years ago
|20x|=2|2x+8|<br> please show all steps <br> and both answers
lukranit [14]

Step-by-step explanation:

20x = 4x +16

16x = 16

x=1

multiply the 2 into the absolute value bars. check if there are negatives. if there aren't, bars can be removed. solve as normal

7 0
3 years ago
I need help fast please!!
kaheart [24]

Solution set is: (7,\frac{13}{3})

Option B is correct

Step-by-step explanation:

We need to find the solution to system of equations

y=\frac{1}{3}x+2\\y=\frac{4}{3}x-5

Let:

y=\frac{1}{3}x+2\,\,\,eq(1)\\y=\frac{4}{3}x-5\,\,\,eq(2)

Putting value of y from eq(2) into eq(1)

\frac{4}{3}x-5=\frac{1}{3}x+2\\Combining\,\,like\,\,terms:\\\frac{4}{3}x-\frac{1}{3}x=2+5\\Taking\,\,LCM\\\frac{4x-1x}{3}=7\\\frac{3x}{3}=7\\x=7

So, value of x=7

Putting value of x into equation 1 to find the value of y:

y=\frac{1}{3}x+2\\y=\frac{1}{3}(7)+2\\y=\frac{7}{3}+2\\Taking\,\,LCM\\y=\frac{7+2*3}{3}\\y=\frac{7+6}{3}\\y=\frac{13}{3}

So, value of y = \frac{13}{3}

Solution set is: (7,\frac{13}{3})

Option B is correct

Keywords: System of equations

Learn more about system of equations at:

  • brainly.com/question/9045597
  • brainly.com/question/3739260
  • brainly.com/question/13168205

#learnwithBrainly

3 0
3 years ago
In 1928, when the high jump was first introduced as a women's sport at the Olympic Games, the winning jump for women was 70.0 in
sveta [45]

Answer: year 2194



Explanation:



1) Model the jump of the women:


i) initial jump = 70.0 in


ii) increase rate = 0.48% per year


iii) equation: h = 70.0(1 +0.0048)ⁿ


2) Model the jump of the men:


i) initial jump 86.5 inches.


ii) increase rate, 0.4%.


iii) equation: h = 86.5 (1 + 0.004)ⁿ


3) Equal the two equations (h = h) to find when the jumps will be equal:


i) 70.0(1 +0.0048)ⁿ = 86.5 (1 + 0.004)ⁿ


ii) 70.0(1.0048)ⁿ = 86.5 (1.004)ⁿ


ii) [1.0048ⁿ / 1.004ⁿ] = 86.5/70.0


iii) [1.0048/ 1.0040]ⁿ = 86.5/70.0


iv) n log (1.0048 / 1.0040) = log ( 86.5/70)


v) n = log (86.5/70) / log (1.0048/1.0040) ≈ 266


3) year = 1928 + 266 = 2194


That is in the year 2194

8 0
2 years ago
Read 2 more answers
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