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iragen [17]
3 years ago
12

Please help me with these questions

Mathematics
1 answer:
d1i1m1o1n [39]3 years ago
5 0

Problem 5)

The bases are the same, so we add the exponents when multiplying something like this out. We have -5+7 = 2 as the final exponent meaning that 5^2 = 25

<h3>Answer: Choice B) 25</h3>

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

Problem 6)

We can multiply the exponents (t^8)^2 = t^(8*2) = t^16

Or we can expand out (t^8)^2 to get (t^8)*(t^8), then add the exponents from here to get t^(8+8) = t^16. Either way we get the same answer

<h3>Answer: Choice C) t^16</h3>

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

Problem 7)

The negative exponent indicates we will apply the reciprocal to get that exponent to a positive number. The rule is x^(-k) = 1/(x^k)

So 5^(-4) = 1/(5^4) = 1/625 and (t^3)^(-4) = t^(3*(-4)) = t^(-12) = 1/(t^12)

Put together, we end up with 1/(625t^12)

<h3>Answer: Choice C) 1 over 625t^12</h3>
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Janet can plant nine feet of carrots in 15 minutes while her daughter Amy can plant 17 feet of carrots in half an hour.
Lena [83]

Answer:

Step-by-step explanation:

In order to find who is more efficient at planting carrots, we want to put both ratios in terms of the same amount of time.

For simplicity, lets see how many carrots each can make in 1 hour.

Janet:\\9ft \: in \: 15 \:minutes

\frac{9ft}{15min} = \frac{xft}{60min}\\x = \frac{60*9}{15} = 36

Janet can plant 36 feet of carrots in one hour

Amy:\\\frac{17ft}{30min} = \frac{xft}{60min}\\x = \frac{17*60}{30} = 34

Amy can plant 34 feet of carrots in one hour

So, Janet can plant carrots more quickly

6 0
3 years ago
Solve for the smallest value of $x$ such that $24x^2 + 17x - 20 = 0.$ Express your answer as a simplified common fraction.
Gala2k [10]
X=5/8 or x=-4/3 
here is the work if needed...
24x^2+17x-20=0
Step one: Factor left side of equation.
(8x-5)(3x-4)=0
Step two: Set factor equal to 0.
8x-5=0 or 3x-4=0
x=5/8 or x=-4/3
4 0
3 years ago
The hypotenuse of a right triangle is 13.0, and one leg is 9.0 units shorter than the other. Find the dimensions of the figure (
Darina [25.2K]
Let, one leg be x units. 
since the other leg is 9.0 units shorter than the other, 
the measure of the other leg =x-9 
hypotenuse =13.0 units 
According to Pythagorean theorem, the square of the hypotenuse is equal to the sum of squares of the other two sides.  
x^2 +(x-9)^2 =13^2 
x^2 + x^2 -18x +81 = 169 
2x^2-18x-88=0 
Divide the whole equation by 2 
x^2 - 9x -44 =0  
Let's use the quadratic formula to find the roots. 
formula: x= [-b ± sqrt(b^2-4*a*c)]/2*a  
a=1 b=-9 c=-44 
x= [9±sqrt(81+176)]/2
 =[9±sqrt(257)]/2
 =[9±16.03]/2
 =25.03/2 or -7.03/2
 length of a triangle cannot be negative,
 Therefore, x=25.03/2 =12.52 
 one leg =12.5 units
 other leg =12.52-9 =3.5 units
4 0
3 years ago
Pleeeeeseee have to finish before 3:00
aleksley [76]

Answer:

175.9

Step-by-step explanation:

AL=2πrh=2·π·4·7≈175.92919 rounded to the nearest tenth would be 175.9

5 0
3 years ago
Sorry to waste time, but could you help? 5/3(4/3a+9b+2/3a) simplified, take your time! I’m not the best at math so :p
mixas84 [53]

Answer:

sorry I'm not that good at math either it's complicated

Step-by-step explanation:

5

3

(

4

3

⋅

5 0
3 years ago
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