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3 years ago

WRITE THE SUM OF THE NUMBERS AS THE PRODUCT OF THEIR GCF AND ANOTHER SUM 40+25

1 answer:

4 0

The greatest common factor (GCF) of 40 and 44 is 4.

Explanation:

44 = 4 x 11

40 = 4 x 10

44 + 40 = (4 x 11) plus (4 x10) = 4 times (11+ 10)

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Ms. Li spent $840 on a vacation. She spent 2/3 of the amount on a plane ticket and 1/2 of the remaining amount on food. How much

olya-2409 [2.1K]

$\bf 840\cdot \cfrac{2}{3}\impliedby \textit{on the plane ticket}
\\\\\\
\left( 840\cdot \cfrac{2}{3} \right)\cdot \cfrac{1}{2}\impliedby \textit{ on food}$

4 0

3 years ago

Which expression is equal to 3/5?

MaRussiya [10]

Answer:

An expression that is equal to 3/5 is 3÷5.

Step-by-step explanation:

3/5 is really 3 things are being split amongst 5 things/groups. When you split things .up, it's division. Therefore, the expression would be 3÷5

3 0

3 years ago

Read 2 more answers

Connor went to the county fair with $32.50 in his pocket. He bought a hot dog and a drink for $4.50 and then

Alekssandra [29.7K]

Answer:

The answer is 14.

Step-by-step explanation:

4.50 + 2.00x ≤ 32.50

32.50 - 4.50 = 28

28 / 2.00 = 14

The total number of tickets he can buy is 14.

5 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

1/2 + 5/3 - 1 ------------------ 3/4

Sav [38]

Hey there :)

$\frac{ \frac{1}{2}+ \frac{5}{3} -1 }{ \frac{3}{4} }$
↓ Is the same as
$\frac{1}{2} + \frac{5}{3} -1$ ÷ $\frac{3}{4}$

Since it is a division by fraction, we can multiply by what is called the reciprocal
( The attached picture might help you )
( $\frac{1}{2} + \frac{5}{3} - 1$ ) × $\frac{4}{3}$
↓ For this part, we need the common denominator, which is 6
$\frac{1(3)}{2(3)}+ \frac{5(2)}{32)} \frac{1(6)}{1(6)}$ × $\frac{4}{3}$

$\frac{3}{6}+ \frac{10}{6} - \frac{6}{6}$ × $\frac{4}{3}$
$\frac{7}{6}$ × $\frac{4}{3}$
$\frac{14}{9} = 1\frac{5}{9}$
↑
Your final answer

7 0

3 years ago