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3 years ago

State whether -4^-2 and (-4)^-2 represent the same quantity

Mathematics

1 answer:

timofeeve [1]3 years ago

3 0

A negative exponent just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side. For instance, "x^-2" just means "x2, but underneath, as in 1/x^2.

-4^-2 means the power -2 is only applied to 4 and not the negative sign. -4^-2 = -(4^-2), which is equal to -1/16.

Whereas, (-4)^-2 means the power -2 affects on both negative sign and 4. For example, (-4)^2 is equal to (-4 * -4) which is just 16. Moving on, with (-4)^-2 equals to 1/(-4*-4) = 1/16.

//Hope this helps.

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3 years ago

A piece of steel pipe 12.5 feet long weighs 158 pounds. How much does a piece of the same steel pipe 18.75 feet long weigh?

jonny [76]

Answer:

18.75 feet of steel pipe weighs 237 pounds

explanation:

find out how much 1 feet weighs than u can find out how much 18.75 feet.

by doing it like this

158÷ 12.5

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1 feet equals 12.64 pounds

12.64× 18.75

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3 years ago

Read 2 more answers

Evan randomly selects 30 marbles from a bag. His data is given in the table.

Igoryamba

The probability of selecting a yellow marble is #of yellow marbles/total # of marbles= 6/30 or .2 or 20%

If there are 300 marbles in the bag, a good estimate for the total number of red marbles in the bag is 90.

9/30=.3 = the percentage of red marbles
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2 years ago

What is a solution to (x + 6)(x + 2) = 60?

Reika [66]

Solution of the equation $(x+6)(x+2)=60$ is x=4 and x=-12

Step-by-step explanation:

We need to solve the equation: $(x+6)(x+2)=60$

Solving:

$(x+6)(x+2)=60$

Multiplying terms on the left hand side

$x(x+2)+6(x+2)=60$

$x^2+2x+6x+12=60$

$x^2+8x+12=60$

$x^2+8x+12-60=0$

$x^2+8x-48=0$

Now factorizing:

$x^2+12x-4x-48=0$

$x(x+12)-4(x+12)=0$

$(x-4)(x+12)=0$

$(x-4)=0\,\,and\,\,(x+12)=0$

$x=4\,\,and\,\,x=-12$

So, solution of the equation $(x+6)(x+2)=60$ is x=4 and x=-12

Keywords: Solving Equations

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3 years ago

A state park charges an entrance fee based on the number of people in a vehicle. A car containing 2 people is charged $14, a car

Artyom0805 [142]

Answer:

Therefore $98 is be charged a bus containing 30 people.

Step-by-step explanation:

Given that,

A state park charges an entrance fee based on the number of people in vehicle.

Let the entry fee for the vehicle be E and entry fee for each person be x.

Then

C= E+(P×x)

C= Total charge in $

E= entry fee for a vehicle

P=No. of person

x= Entry charge per person.

Given A car containing 2 people charged $14

C=$14, P=2

∴14= E+(2× x)

⇒E+2x=14.....(1)

Again A car containing 4 people charged $20

C=$20, P=4

∴20= E+(4× x)

⇒E+4x=20.....(2)

Subtract (1) from (2), we get

E+4x-(E+2x)= 20-14

⇒E+4x-E-2x=6

⇒2x=6

⇒x=3

Putting the value of x in equation (1)

E+(2×3)=14

⇒E=14-6

⇒E=8

Therefore E=$8 and x=$3

Next we check whether our assumption is correct or wrong. Putting the value of E and x for third case

Here P= 8

Therefore C= E+(P×x)

= 8+(8× 3)

=8+24

=$32

Therefore our assumption is correct.

Now C=? , P= 30

The charged for the 30 people is

C= $[8+(30×3)]

=$[8+90]

=$98

Therefore $98 is be charged a bus containing 30 people.

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