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GuDViN [60]
3 years ago
14

Write as an exponent with the base of b:

="b^{n} b^{5}" alt="b^{n} b^{5}" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
goldfiish [28.3K]3 years ago
4 0
B^n+5
When multiplying exponents the numbers are added
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F $1 \le a \le 10$ and $1 \le b \le 36$, for how many ordered pairs of integers $(a, b)$ is $\sqrt{a + \sqrt{b}}$ an integer?
svetlana [45]
You have such entry data: 
1\ \textless \ a\ \textless \ 10 \\ 1\ \textless \ b\ \textless \ 36

Consider expression \sqrt{a+ \sqrt{b} }. If this expression becomes an integer, then b=4,9,16,25, because then \sqrt{b} = 2,3,4,5, respectively. In other cases \sqrt{b} is not integer and thus the expression \sqrt{a+ \sqrt{b} } also is not integer.

1. b=4, then \sqrt{a+ \sqrt{b} }=\sqrt{a+2}. Here a=2,7 (in other cases \sqrt{a+2} is not integer). When a=2, \sqrt{a+2}=\sqrt{2+2}=2 and when a=7, \sqrt{a+2}=\sqrt{7+2}=3.

2. b=9, then a=6 and \sqrt{a+ \sqrt{b} }= \sqrt{a+3}=\sqrt{6+3}=3.

3. b=16, then a=5 and \sqrt{a+ \sqrt{b} }= \sqrt{a+4}=\sqrt{5+4}=3.

4. b=25, then a=4 and \sqrt{a+ \sqrt{b} }=\sqrt{a+5}=\sqrt{4+5}=3.

Answer: (2,4), (7,4), (6,9), (5,16), (4,25).







3 0
3 years ago
1)
Irina-Kira [14]
1. 5x/2 +y=-3 
2. False
3. y= -5x-37  because y=mx-b
4. y= 1/5 x - 1 because y=mx-b  
M= the slope and b represents the intercept.
5 0
3 years ago
Aimee is shipping a care package to her friend in college, and she has a piece of cardboard with which to create a box. The dime
kow [346]

Answer:

x = 10 - 10sqrt(3)/3

Approximately 4.2265 cm

Volume = 1539.6 cm³

Step-by-step explanation:

Let the height be x

V = (20 - 2x)(40 - 2x)x

V = (800 - 80x - 40x + 4x²)x

V = 4x³ - 120x² + 800x

dV/dx= 12x² - 240x + 800 = 0

3x² - 60x + 200 = 0

x = [60 +/- sqrt(60² - 4(3)(200))]/6

x = [30 +/- 10sqrt(3)]/3

x = 10 +/- 10sqrt(3)/3

Approximately,

15.7735 and 4.2265

d²V/dx² = 24x - 240

For max, d²V/dx² < 0

So, x = 4.2265

V = (20 - 2x)(40 - 2x)x

Plug in x = 10 - 10sqrt(3)/3

V = 1539.600718

8 0
3 years ago
What is the equation in point slope form of the line passing through (1,9) and (-1,11)
irinina [24]

the answer to the question

7 0
3 years ago
Factor completely:<br><br> 1. 9x^2 + 3x − 90
malfutka [58]

Answer:

9x^2+3x-90

81x+3x-90

84x-90 final answer

Step-by-step explanation:

7 0
2 years ago
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