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3 years ago

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Natalie and John are both saving coins in jars for a rainy day. Natalie currently has 1 1!8 jars of coins, and John has 9/14 of

a jar of coins. If John gives all his coins to Natalie, how many jars of coins would she have all together?

2 answers:

Leokris [45]3 years ago

8 0

Natalie will have 10/14 coins

d1i1m1o1n [39]3 years ago

8 0

Answer:

1 43/56

Step-by-step explanation:

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What is the exponent in the power of 10?

Arisa [49]

X^10 the exponent would be 10

4 0

3 years ago

Simplify the given expression. (18+ - 8)2

JulsSmile [24]

Answer:

20

Step-by-step explanation:

Our expression:

2 * (18 + - 8)

Plus then minus (+ -) is the same as just minus ( - )

Some examples:

1 + (+ 1) = 2

1 + (- 1) = 0

1 - (+ 1) = 0

1 - (- 1) = 2

Thus, 18 + - 8 is the same as 18 - 8

2 * (18 + - 8) =

= 2 * (18 - 8) =

= 2* (10) =

= 2 * 10 =

= 20

Answer: 20

6 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

1 year ago

The areas of two similar triangles are 9cm2, and 49cm2. One of the sides of the first triangle is 2cm. What is the length of the

BlackZzzverrR [31]

Answer:

4 2/3 cm

Step-by-step explanation:

When we have area, it is the related to the scale factor by the scale factor squared

Area large/ area of small = 49/9

Take the square root

sqrt(49/9) = 7/3

The scale factor is 7/3 large to small

The small side is 2 cm

large 7 x cm

-------- = ------ = -----------

small 3 2 cm

Using cross products

7*2 = 3x

Divide by 3

14/3 = 3x/3

14/3 = the large side

4 2/3 cm

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3 years ago

What is the distance between the points (2, 5) and (5,9)?

RSB [31]

3 if by the x axis 4 if by the y axis

5 0

3 years ago