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2 years ago

A teacher graded s 27 tests in 3 hours. Do these quantities(number of tests graded in time) vary directly or inversely? Explain.

Mathematics

1 answer:

Gwar [14]2 years ago

3 0

Answer:

directly

Step-by-step explanation:

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A new car is purchased for 20700 dollars. The value of the car depreciates at 11% per year. What will the value of the car be, t

Mandarinka [93]

Answer:

The answer for that is 5744.61

4 0

3 years ago

A movie theater decreased the size of its popcorn bags by 20%. If the old bags held 15 cups of popcorn, how much do the new bags

vovikov84 [41]

Answer:

Your answer will be  $12$  cups of popcorn.

Step-by-step explanation:

To find out how much the new bags hold, you need to find out the discount.

$\frac{20}{100 } = .2$

$15 * .2 = 3$

We know that the discount is $3$ .

To figure out how much the new bags hold, subtract by the old bags.

$15 - 3 = 12$

The new bags hold 12 cups of popcorn. 

7 0

2 years ago

If x^2+1/x^2=3 find the value of x^2/(x^2+1)^2 Express answer as a common fraction. Thanks!!

timama [110]

$x^2+\dfrac1{x^2}=3\implies x^4+1=3x^2\implies x^4-3x^2+1=0$

By the quadratic formula,

$x^2=\dfrac{3\pm\sqrt5}2\implies x^2+1=\dfrac{5\pm\sqrt5}2$

Then

$(x^2+1)^2=\dfrac{25\pm10\sqrt5+5}4=\dfrac{15\pm5\sqrt5}2$

$\implies\dfrac{x^2}{(x^2+1)^2}=\dfrac{\frac{3\pm\sqrt5}2}{\frac{15\pm5\sqrt5}2}=\dfrac{3\pm\sqrt5}{15\pm5\sqrt5}$

Multiply numerator and denominator by the denominator's conjugate:

$\dfrac{3\pm\sqrt5}{15\pm5\sqrt5}\cdot\dfrac{15\mp5\sqrt5}{15\mp5\sqrt5}=\dfrac{45\pm15\sqrt5\mp15\sqrt5-25}{15^2-(5\sqrt5)^2}=\dfrac{20}{100}=\dfrac15$

3 0

3 years ago

our friend purchased a medium pizza for $10.31 with a 30% off coupon. What is the price of a medium pizza without a coupon?

makkiz [27]

Answer:

$7.22 or $7.217

Step-by-step explanation:

$7.22 would be the answer because 70% of 10.31 is what you are looking for which is 7.217 which is rounded to 7.22

3 0

3 years ago

Can anyone help me with this? im confused

kvasek [131]

Answer:

1,2,3 and 6 are similar triangles by AA similarity

Step-by-step explanation:

1) ∠DEC ≅ ∠FEG {Vertically opposite angles}

DC // GF

∠ECD ≅ ∠EGF {Alternate interior angles}

∠EDC ≅ ∠EFG {Alternate interior angles}

ΔDEC & ΔFEG are similar triangles by AA similarity

2)MN // QP

∠LQP ≅ ∠QMN {Corresponding angles }

∠LPQ ≅ ∠PNM {Corresponding angles}

ΔLQP & ΔLMN are similar triangles by AA similarity

3) In ΔSYE ,

∠S = 180 - 90 - 39

∠S = 51°

In ΔCHW,

∠H = 180 - 51 - 90

∠H = 39

ΔSYE and ΔCHW

∠S ≅ ∠W = 51°

∠Y ≅ ∠C = 90°

∠E ≅∠H = 39°

ΔSYE & ΔWCH are similar triangles by AA similarity

6) ∠P ≅ ∠Z {Given}

∠PXQ ≅∠ZXY {Vertically opposite angles}

ΔPXQ & ΔZXY are similar triangles by AA similarity

5 0

1 year ago