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aleksandrvk [35]
3 years ago
11

Find the slope of the line through the points (4, 4) and (-1, 5).

Mathematics
1 answer:
Phoenix [80]3 years ago
4 0
<span>We write pattern linear function
f(x) = ax + b

</span><span>Both points must be in one straight line so they can be used to lay the system of equations .
Points A=(4,4), B = (-1,5)
                x  y            x  y

</span>\left \{ {{f(x)=ax + b  (Point A)} \atop {f(x) = ax +b (PointB)}} \right.  \\  \\  \left \{ {{4 =a*4 + b} \atop {5=a*(-1)+b}} \right.  \\  \\  \left \{ {{b= 4 -4a} \atop {5 = -a + (4 - 4a)}} \right. \\  \\   \left \{ {{b = 4 - 4a} \atop {5 - 4 = - 5a }} \right.  \\  \\  \left \{ {{b = 4 - 4a} \atop {a = -  \frac{1}{5} }} \right.  \\  \\  \left \{ {{ b = 4 - 4*(- \frac{1}{5} )= 4 +  \frac{4}{5} = 4,8} \atop {a = -  \frac{1}{5} }} \right.

<span>We insert the calculated a and b in the equation f(x) = ax + b

</span>y = -  \frac{1}{5} x + 4,8

<span>Since a> 0, the function is decreasing</span>
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Help whit that 3 questions please and thanks
Serjik [45]

Answer:

80.

4s+5c=46\\3s+c=22

81. Each apple cost $0.50

82. One pound of chocolate = $3

Step-by-step explanation:

80.

Let sold of 1 senior citizen ticket be "s", and

cost of 1 child ticket be "c"

First Day, 4 senior citizen ticket and 5 child tickets sold, equaled $46, so the equation we can write is:

4s+5c=46

Second Day, 3 senior citizen ticket and 1 child ticket sold, equaled $22, so the equation we can write is:

3s+c=22

So, the system of equation (2 equations) written above can be solved simultaneously to find our answer.

4s+5c=46\\3s+c=22

81.

Let price of 1 apple be "a" and price of 1 banana be "b"

Since 3 apples and 2 banana cost $2, so we can write:

3a + 2b = 2

Then,

4 apples and 4 bananas cost $3, so we can write:

4a + 4b = 3

We can solve for the variable b in equation 1. Shown below:

3a + 2b = 2\\2b=2-3a\\b=\frac{2-3a}{2}

Now we put this value of b into equation 2 and solve for cost of 1 apple, a. Shown below:

4a+4b=3\\4a+4(\frac{2-3a}{2})=3\\4a+4-6a=3\\2a=1\\a=\frac{1}{2}\\a=0.5

So each apples cost $0.5

82.

Let 1 pound of chocolate be cost "c"

Let 1 pound of peanut be cost "p"

4 lb of chocolate and 2 lb of peanut = $16, thus we can write:

4c + 2p = 16

Next,

2 lb of chocolate and 3 lb of peanut costed $12, so we can write:

2c + 3p = 12

We solve first equation for p:

4c + 2p = 16\\2p=16-4c\\p=\frac{16-4c}{2}\\p=8-2c

Now, we put this expression for p into equation 2 and solve for c:

2c + 3p = 12\\2c + 3(8-2c) = 12\\2c+24-6c=12\\4c=12\\c=3

So, 1 pound of chocolates cost $3

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D

Step-by-step explanation:

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Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 16 min to 72 min​
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Answer:

2/9

Step-by-step explanation:

16/72 is the same thing as 2/9, just simplified. If you make 16 to 72 in a fraction you get 16/72. You divide them with their GCF which is 8. 16 divided by 8 is 2 and 72 divided by 8 is 9. Therefore the answer is 2/9.

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