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Alexus [3.1K]
3 years ago
8

Zach has a terrarium with the dimensions of 20 by 8 and the terrarium was filled with 3 inches of sand.Zach gets a new terrarium

that is larger with the dimensions of 10 by 24.Zach moved the existing sand in the new terrarium. How deep is the sand in the new terrarium
Mathematics
1 answer:
Vladimir79 [104]3 years ago
7 0

Answer: the sand in the new terrarium is 2 inches deep.

Step-by-step explanation:

Zach has a terrarium with the dimensions of 20 by 8 and the terrarium was filled with 3 inches of sand. It means that the volume of sand that this terrarium contains is

20 × 8 × 3 = 480 inches³

Zach gets a new terrarium that is larger with the dimensions of 10 by 24. If Zach moved the existing sand in the new terrarium and the height of the sand is represented by h, then the volume of sand into he new terrarium is

10 × 24 × h = 240h

Since the volume of sand in both terrariums is equal, then

240h = 480

h = 480/240

h = 2 inches

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What equals 5 in multiplication and -4 in addition
kirill [66]

Answer:

  • -2 +i
  • -2 -i

Step-by-step explanation:

There is no pair of real numbers that have a total of -4 and a product of 5. The complex numbers (-2+i) and (-2-i) will meet your requirements.

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If the numbers of interest are 'a' and 'b', they will be zeros of the quadratic whose factored form is ...

  (x -a)(x -b) = 0

Expanding that, we find an opportunity to use the given sum and product numbers:

  x² -(a+b)x +ab = 0

  x² -(-4)x +5 = 0

Rewriting this in vertex form gives ...

  (x² +4x +4) +1 = 0

  (x +2)² +1 = 0

We can find the values of x by subtracting 1 and taking the square root.

  (x +2)² = -1

  x +2 = ±√(-1) = ±i

  x = -2±i

The two numbers of interest are -2+i and -2-i.

4 0
2 years ago
Construct a circle of any radius, and draw a chord on it. Then construct the radius of the circle that bisects the chord. Measur
Nady [450]

Answer:

Part A: See the image attached. The angle between the radius and the chord will always be 90 degree if the radius is perpendicular to the chord

Part B: There are many ways to prove this and here is mine

Prove OC is perpendicular to AB

We know that ΔAEC≅AED by SSS criteria (SSS criteria is when all three sides of a triangle is equal making them congruent)

to prove this that they apply to the SSS criteria:

m∠ADO=m∠BDO

m∠ADO=90°=m∠BDO

Part C: See the image attached. A radius is perpendicular to a chord when the chord is equally divided in half by the radius.

Part D: There are many ways to prove this and here is mine

Prove OC is perpendicular to AB

AO=BO because AO and BO are both radii

OD≅OD by reflexive theorem

ΔADO≅ΔBDO because they are both right triangle with the hypotenuse and a side

AB≅BC means that OC is perpendicular to AB

If you are still confused then I recommend watching these vdos by khan academy about proving perpendicular radius bisector: https://youtu.be/2NgzruZ4_5c

https://youtu.be/TgDk06Qayxw

Hope this helped bye:)

4 0
3 years ago
What is - 1 .2 % as a fraction and decimal
inysia [295]
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8 0
3 years ago
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Students in a statistics class are conducting a survey to estimate the mean number of units students at their college are enroll
Katena32 [7]

Answer:

( 11.7 , 12.7 )

Step-by-step explanation:

The provided information is:

Sample mean = \bar{X} = 12.2

Standard deviation = \sigma=1.6

Sample size = n = 49

Significance level = \alpha=0.05

Thus, the 95% confidence interval is:

\bar{X}\pm Z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\\=12.2\pm Z_{0.05/2}\frac{1.6}{\sqrt{49}}\\=12.2\pm 1.96\times0.2286\\=12.2\pm 0.4480\\=(11.7.12.7)

8 0
3 years ago
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