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Oksi-84 [34.3K]
3 years ago
12

.

Mathematics
2 answers:
Lena [83]3 years ago
7 0
The answer is 30 I believe
andrezito [222]3 years ago
5 0

Answer:

30 calories.

Step-by-step explanation:

First we need to know how many is one gram so do 180/30 to get 6. Then, since we are looking for the amount in 5 grams, multiply 6 by 5 to get 30.

Therefore, there are 30 calories in 5 grams.

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A bacteria culture contains 1500 bacteria initially and doubles every hour. (a) Find a function N that models the number of bact
Tpy6a [65]

Answer: a) N(t)=1500(2)^t

b) 25165824000

Step-by-step explanation:

The exponential equation for growth is given by :-

y= ab^t , where a= initial value , b =multiplicative growth factor and t = time.

Given : A bacteria culture contains 1500 bacteria initially and doubles every hour.

i.e. a = 1500 and b= 2

Then, the function N that models the number of bacteria after t hours will be :

N(t)=1500(2)^t

To find , the number of bacteria after 24 hours , we put t= 24 in above equation , we get

N(24)=1500(2)^{24}\\\\=1500(16777216)=25165824000

Hence, the number of bacteria after 24 hours is 25165824000.

7 0
3 years ago
Use Cramer Rule to solve the following system: 8x−5y=70 and 9x+7y=3
nlexa [21]

Answer:

(x,y) = (5,-6)

Step-by-step explanation:

\underline{\textbf{Determinant of a matrix.}}\\\\\text{For a}~ 2 \times 2 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2\\b_1&b_2 \end{vmatrix} = a_1b_2 - a_2b_1\\\\\\\text{For a}~ 3 \times 3 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2&a_3\\ b_1&b_2&b_3\\ c_1&c_2&c_3 \end{vmatrix} = a_1\begin{vmatrix} b_2&b_3\\c_2&c_3 \end{vmatrix} - a_2 \begin{vmatrix} b_1&b_3\\c_1&c_3 \end{vmatrix}+ a_3 \begin{vmatrix} b_1&b_2\\c_1&c_2 \end{vmatrix}\\\\\\

                     ~~~~~~~~~~~~~~~~~~=a_1(b_2c_3-b_3c_2) -a_2(b_1c_3-b_3c_1) +a_3(b_1c_2-b_2c_1)

\underline{\textbf{Cramer's Rule to solve a system of two equations.}}\\\\\text{Consider the system of two equations:}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_1x + b_1 y= c_1\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_2x +b_2 y = c_2\\\\\text{Here,}\\\\x = \dfrac{D_x}{D}= \dfrac{\begin{vmatrix} c_1&b_1\\c_2&b_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\\\ y= \dfrac{D_y}{D}= \dfrac{\begin{vmatrix} a_1&c_1\\a_2&c_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\

\underline{\textbf{Solution:}}\\\\~~~~~~~~~~~~~~~~~~~~~~~8x-5y = 70~~~~~~...(i)\\\\~~~~~~~~~~~~~~~~~~~~~~~9x +7y = 3~~~~~~~...(ii)\\\\\text{Applying Cramer's rule:}\\\\x = \dfrac{D_x}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 70& -5 \\3&7 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{70(7) -(-5)(3)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{490+15}{56+45}\\\\\\~~=\dfrac{505}{101}\\\\\\~~=5

y = \dfrac{D_y}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 8& 70 \\9&3 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{(8)(3) -(70)(9)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{24-630}{56+45}\\\\\\~~=-\dfrac{606}{101}\\\\\\~~=-6

\textbf{Hence, the solution to the system of equation is}~ (x,y) = (5,-6)

7 0
2 years ago
Please help me with this . I can’t fail geometry I need your help please<br> Please
krok68 [10]

Answer:

31

Step-by-step explanation:

m<ACB is half of the angle AOB  so u divide 62/2 and the answer is31

3 0
3 years ago
type the correct answer in each box. Use numerald instead of words. If necessary, use/ for the fraction bar​
Olegator [25]

Answer:

I just really don't kniwwww

7 0
3 years ago
What is the solution to this equation -8 and one third y equals 2
omeli [17]
I hope this helps you

6 0
3 years ago
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