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Tems11 [23]
2 years ago
5

Yuki's guppies have begun to have babies. She started with 5 guppies. One week later, Yuki counted twice as many guppies in the

fish tank. Each week afterwards, the number of guppies doubled. In how many weeks did Yuki have 160 guppies?
Mathematics
1 answer:
s2008m [1.1K]2 years ago
5 0
Week 1 = 5 guppies.
week 2 = 5x 2 = 10 guppies
week 3 = 10 x 2 = 20 guppies
week 4= 20 x 2 = 40 guppies
week 5 = 40 x 2 = 80 guppies
week 6= 80 x 2 = 160 guppies
Yuki had 160 guppies in 6 weeks.
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A stick of butter in the shape of a rectangular prism has a length of 8 inches, a width of 3 inches, and a height of 3 inches. W
SVEN [57.7K]

Answer:

72in^3

Step-by-step explanation:

the information we know about the shape of the stick of butter:  

length = 8in

width = 3in

height=3in

The formula for the volume of a rectangular prism is:

volume=length*width*height

we find the volume by multiplying ll the measurements of the stick.

So we substitute the values to find the volume and we get the following:

volume=8in*3in*3in\\volume=72in^3

the volume of the stick of butter is 72in^3

5 0
2 years ago
Which will result in a difference of squares? (–7x + 4)(–7x + 4) (–7x + 4)(4 – 7x) (–7x + 4)(–7x – 4) (–7x + 4)(7x – 4)
maw [93]

You can simply expand each product and see whether it gives you a difference of squares.


•  \mathsf{(-7x+4)\cdot (-7x+4)}

That's actually  \mathsf{(-7x+4)^2:}

     \mathsf{(-7x+4)^2}\\\\ \mathsf{=(-7x+4)\cdot (-7x+4)}\\\\ \mathsf{=(-7x+4)\cdot (-7x)+(-7x+4)\cdot 4}\\\\ \mathsf{=49x^2-28x-28x+16}

     \mathsf{=49x^2-56x+16}        <span>✖

which is not a difference of squares.

</span>————<span>—

</span>•  \mathsf{(-7x+4)\cdot (4-7x)}

     \mathsf{=(-7x+4)\cdot 4-(-7x+4)\cdot 7x}\\\\ \mathsf{=-28x+16-(-49x^2+28x)}\\\\ \mathsf{=-28x+16+49x^2-28x}

     \mathsf{=49x^2-56x+16}        ✖

which is not a difference of squares.

—————

•  \mathsf{(-7x+4)\cdot (-7x-4)}

     \mathsf{=(-7x+4)\cdot (-7x)-(-7x+4)\cdot 4}\\\\ \mathsf{=49x^2-28x-(-28x+16)}\\\\ \mathsf{=49x^2-\diagup\!\!\!\!\! 28x+\diagup\!\!\!\!\! 28x-16}\\\\ \mathsf{=49x^2-16}

     \mathsf{=(7x)^2-4^2}        <span>✔

That is a difference of two squares.

</span>————<span>—

</span>•  \mathsf{(-7x+4)\cdot (7x-4)}

     \mathsf{=(-7x+4)\cdot 7x-(-7x+4)\cdot 4)}\\\\ \mathsf{=-49x^2+28x-(-28x+16)}\\\\ \mathsf{=-49x^2+28x+28x-16}

     \mathsf{=-49x^2+56x-16}        <span>✖

</span>which is not a difference of squares.

—————

Only the  third option  will result in a difference of squares.


Answer:  (− 7x + 4) · (− 7x − 4).


I hope this helps. =)

8 0
2 years ago
Read 2 more answers
Match each function formula with the corresponding transformation of the parent function y = –x 2 – 1. 1. y = –x2 – 1 Translated
sweet [91]

Answer:

1. f₁(x)=-x²+2x-2

2. f₂(x)=-x²+6x-10

3. f₃(x)=-x²-2  

4. f₄(x)=-x²+10x-26

5. f₅(x)=-x²-2x-2

6. f₆(x)=-x²

Step-by-step explanation:

1. we have that f(x) is translated right by 1 unit , also

according to the graph f(x) has a vertex P(0,-1) then P₁ ( 1,-1) to f₁(x) therefore y-y₁ = -(x-x₁)² ⇒ y-y₁ = -(x-x₁)² ⇒ y+1 = -(x-1)² ⇒ y=-(x²-2x+1)-1 =-x²+2x-2

2. f(x) is reflected across the x-axis 3, same as in 1., P₂(3,-1) to f₂(x)

y+1 = -(x-3)² ⇒ y=-(x²-6x+9)-1 =-x²+6x-10

3. f(x) is translated down by 1 unit, P₃(0,-2) to f₃(x)

y+2 = -(x)² ⇒ y=-x²-2  

4. f(x) is reflected across the y-axis 5, P₄(5,-1) to f₄(x)

y+1 = -(x-5)² ⇒ y=-(x²-10x+25)-1 =-x²+10x-26

5. f(x) is translated left by 1, P₅(-1,-1) to f₅(x)

y+1 = -(x+1)² ⇒ y=-(x²+2x+1)-1 =-x²-2x-2

6. f(x) is translated up by 1 unit, P₆(0,0) to f₆(x)

y+0 = -(x+0)² ⇒ y=-x²

4 0
2 years ago
Which of the following best describes the slope of the line below?
Aleonysh [2.5K]

Answer:

it is undefined

Step-by-step explanation:

it is undefined because the vertical line touches the same x coordinate in the whole thing.

5 0
2 years ago
The profit earned by a hot dog stand is a linear function of the number of hot dogs sold. It costs the owner $48 dollars
Gekata [30.6K]

Answer:

Its the third one because, he gets $2 for each hot dog but we dont know ow many hot dogs are sold everyday. We also know that at the end of the day $48 is taken out for supplies to make the hot dogs.

Hope this helped! :3

4 0
2 years ago
Read 2 more answers
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