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kupik [55]
3 years ago
6

A grasshopper covered a distance of 5 yards in 9 equal hops.How many yards did the grasshopper travel on each hop?

Mathematics
2 answers:
Luda [366]3 years ago
5 0
5/9 = .55555555555 yards traveled per hop
15/9 = 1.6666667 feet per hop
Mashcka [7]3 years ago
4 0

For this case we can make the following rule of three:

5 yards ---------> 9 hops

x -------------------> 1 hop

From here, we must clear the value of x.

We have then:

x = \frac {5} {9}\\x = 0.56 \frac {yards} {hop}

Answer:

the grasshopper 0.56 yards travel on each hop


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Answer:

4x^2 -12x +9   ft^2

Step-by-step explanation:

The area of a square is

A = s^2 where s is the side length

A = (2x-3) ^2

A = (2x-3) (2x-3)

FOIL

first 2x*2x =4x^2

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inner -3*2x = -6x

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Add them together

4x^2 -6x-6x +9

Combine like terms

4x^2 -12x +9

The area is 4x^2 -12x +9 ft^2

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The correct answer to the question is

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In the question, the option

e. If is likely that between 35% and 41% percent of the driving population would be willing to pay higher gas prices to protect the environment , clearly depicts the definition of margin of error as it shows the expected variance from te real population

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Step-by-step explanation:

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A circle has the equation 2x²+12x+2y²−16y−150=0.
KonstantinChe [14]

Answer: B. The coordinates of the center are (-3,4), and the length of the radius is 10 units.

Step-by-step explanation:

The equation of a circle in the center-radius form is:

(x-h)^{2} +(y-k)^{2}=r^{2} (1)

Where (h,k) are the coordinates of the center and r is the radius.

Now, we are given the equation of this circle as follows:

2x^{2}+12x+2y^{2}-16y-150=0 (2)

And we have to write it in the format of equation (1). So, let's begin by applying common factor 2 in the left side of the equation:

2(x^{2}+6x+y^{2}-8y-75)=0 (3)

Rearranging the equation:

x^{2}+6x+y^{2}-8y=75 (4)

(x^{2}+6x)+(y^{2}-8y)=75 (5)

Now we have to complete the square in both parenthesis, in order to have a perfect square trinomial in the form of (a\pm b)^{2}=a^{2}\pm+2ab+b^{2}:

<u>For the first parenthesis:</u>

x^{2}+6x+b^{2}

We can rewrite this as:

x^{2}+2(3)x+b^{2}

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x^{2}+2(3)x+3^{2}=x^{2}+6x+9=(x+3)^{2}

<u>For the second parenthesis:</u>

y^{2}-8y+b^{2}

We can rewrite this as:

y^{2}-2(4)y+b^{2}

Hence in this case b=-3 and b^{2}=9:

y^{2}-2(4)y+4^{2}=y^{2}-8y+16=(y-4)^{2}

Then, equation (5) is rewritten as follows:

(x^{2}+6x+9)+(y^{2}-8y+16)=75+9+16 (6)

<u>Note we are adding 9 and 16 in both sides of the equation in order to keep the equality.</u>

Rearranging:

(x-3)^{2}+(y-4)^{2}=100 (7)

At this point we have the circle equation in the center radius form (x-h)^{2} +(y-k)^{2}=r^{2}

Hence:

h=-3

k=4

r=\sqrt{100}=10

8 0
3 years ago
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