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goldenfox [79]
3 years ago
10

when ashley buys 7 postage stamp booklets she gets 140 stamps.she get 60 stamps in three booklets. write an equation to find the

number of postage stamps, p , she gets in b booklets
Mathematics
1 answer:
Andreyy893 years ago
5 0
We can put this information into two equations:

7 booklets = 140 stamps
3 booklets = 60 stamps

Let us then focus on one equation to find the relationship:

7 booklets = 140 stamps

If we put that into a fraction, we get \frac{7}{140} or \frac{1}{20}.

This means that for every booklet, Ashley gets 20 stamps; or rather, each booklet has 20 stamps.

We can then see that this relationship holds true for the second equation as well:

\frac{3}{60} or \frac{1}{20}.

To write a general equation for this relationship using p for the number of postage stamps, and b for the number of booklets:

p = 20b

Where b is equal to p.
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<img src="https://tex.z-dn.net/?f=%20%5Clarge%5Cbegin%7Bbmatrix%7D%20%5Cbegin%7Barray%7D%20%7B%20l%20l%20%7D%20%7B%202%20%7D%20%
SVETLANKA909090 [29]

\huge \boxed{\mathbb{QUESTION} \downarrow}

\begin{bmatrix} \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \end{bmatrix} \begin{bmatrix} \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { - 1 } & { 1 } & { 5 } \end{array} \end{bmatrix}

\large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}

\begin{bmatrix} \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \end{bmatrix} \begin{bmatrix} \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { - 1 } & { 1 } & { 5 } \end{array} \end{bmatrix}

In matrix multiplication, the number of columns in the 1st matrix is equal to the number of rows in the 2nd matrix.

\left(\begin{matrix}2&3\\5&4\end{matrix}\right)\left(\begin{matrix}2&0&3\\-1&1&5\end{matrix}\right)

Multiply each element of the 1st row of the 1st matrix by the corresponding element of the 1st column of the 2nd matrix. Then add these products to obtain the element in the 1st row, 1st column of the product matrix.

\left(\begin{matrix}2\times 2+3\left(-1\right)&&\\&&\end{matrix}\right)

The remaining elements of the product matrix are found in the same way.

\left(\begin{matrix}2\times 2+3\left(-1\right)&3&2\times 3+3\times 5\\5\times 2+4\left(-1\right)&4&5\times 3+4\times 5\end{matrix}\right)

Simplify each element by multiplying the individual terms.

\left(\begin{matrix}4-3&3&6+15\\10-4&4&15+20\end{matrix}\right)

Now, sum each element of the matrix.

\large\boxed{\boxed{\left(\begin{matrix}1&3&21\\6&4&35\end{matrix}\right) }}

7 0
3 years ago
Among all pairs of numbers (x,y)such that 6x+2y=36 find the pair for which the sum of squares, x^2+y^2 is minimum.
lora16 [44]
First, we simplify 6x+2y=36 into 3x+y=18 by dividing by 2. This means that y=-3x+18.


The sum x^2+y^2 can be written as: x^2+y^2=(x+y)^2-2xy, 
<span>
from the binomial expansion formula: </span>(x+y)^2=x^2+2xy+y^2.
<span>
Thus, substituting </span>y=-3x+18 and simplifying we have<span>

</span>x^2+y^2=(x+(-3x+18))^2-2x(-3x+18)=(-2x+18)^2+6x^2-36x=4x^2-72x+18^2+6x^2-36x=10x^2-108x+18^2.

This is a parabola which opens upwards (the coefficient of x^2 is positive), so its minimum is at the vertex. To find x, we apply the formula -b/2a. Substituting b=-108, a=10, we find that x is 108/20=5.4.


At x=5.4, the expression 10x^2-108x+18^2, which is equivalent to x^2+y^2, takes it smallest value.

Substituting, we would find 10x^2-108x+18^2=10(5.4)^2-108(5.4)+18^2=291.6-583.2+324=32.4 This is the smallest value of the expression. 


For x=5.4, y=-3x+18=-3(5.4)+18=1.8.



Answer:   (5.4, 1.8)
8 0
3 years ago
I need help putting correct answers in the yellow boxes.
olasank [31]

Answer:

<u>-5 ± √5² - 4 · 1 · 4</u>

         2 · 1

Step-by-step explanation:

ax²+bx+c=0 (quadratic equation)

x=<u> -b ± √b² - 4ac</u>

           2a

a= 1

b= 5

c= 4

-<u>5 ± √5² - 4 · 1 · 4</u>

            2 · 1

7 0
2 years ago
Matt and Tikka thought of the same number. Matt added 7 to that number and then doubled the result. He got 26. Tikka did the sam
Reptile [31]

Answer:

19

Step-by-step explanation:

Matt ended up with 26.

We reverse the steps he did to get the original number that both people thought of.

26 / 2 = 13

13 - 7 = 6

6 is the original number.

Tikka did the same operations but in the reverse order so...

6 X 2 = 12

12 + 7 = 19

3 0
3 years ago
Factor out the greatest common factor 30c-45d
olga nikolaevna [1]
Simplifying
30c + -45d

Factor out the Greatest Common Factor (GCF), '15'.
15(2c + -3d)

Final result:
15(2c + -3d)
7 0
3 years ago
Read 2 more answers
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