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kompoz [17]
3 years ago
13

What is the product of -4 and 8.1? a) -32.4 b) -12.1 c)12.1 b) 32.4

Mathematics
1 answer:
Sergeeva-Olga [200]3 years ago
8 0

Option A

<u>Answer: </u>

The product of -4 and 8.1 is -32.4

<u>Solution: </u>

When we multiply a negative number with a positive number we get the resultant product as a negative number.

Here we have to multiply - 4 which is a negative number and 8.1 which is a positive number.

To simplify the multiplication calculation we can write 8.1 as 8+0.1 and then multiply 4 with both 8 and 0.1

-4 \times 8.1 = -4 \times (8+0.1)

⇒  -4 \times 8.1 = -4 \times 8 – 4 \times 0.1   [Multiplying 4 with 8 and 0.1]

⇒  -4 \times 8.1= -32 - 0.4

⇒  -4 \times 8.1= - 32.4

Thus the product of -4 and 8.1 is -32.4

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4 3/4 divided by 1 1/6
ozzi

Answer:

2\frac{13}{22}

Step-by-step explanation:

=\frac{19}{4}\div \frac{11}{6}

\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}

=\frac{19}{4}\times \frac{6}{11}

=\frac{19}{2}\times \frac{3}{11}

\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}

=\frac{19\times \:3}{2\times \:11}

\mathrm{Multiply\:the\:numbers:}\:19\times \:3=57

=\frac{57}{2\times \:11}

\mathrm{Multiply\:the\:numbers:}\:2\times \:11=22

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5 0
3 years ago
What is 19.2×10^8 minutes in hours
Nuetrik [128]

Hi!

19.2*10^8

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100,000,000*19.2

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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
Christopher mixes gallon of red paint with 5/8 gallon of blue paint to make
Cerrena [4.2K]

Answer:1 3/8

Step-by-step explanation:

1 gallon + 5/8 gallon = 1 5/8 gallon

1 5/8 gallon - 2/8 gallon = 1 3/8 gallon left of purple paint

7 0
3 years ago
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