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Sedbober
1 month ago
15

Hank estimated width of the door to his classroom in feet. what is a reasonable estimate?

Mathematics
1 answer:
zzz [12.3K]1 month ago
5 0
<span>A typical door measures about 80 inches tall by 36 inches wide. The width in that pair is 36 inches, so Hank's reasonable estimate for the classroom door width would be 36 inches. Converting inches to feet uses 12 inches = 1 foot, and 36 ÷ 12 = 3, so the width is about 3 feet.</span>
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The number of rainbow smelt in Lake Michigan had an average rate of change of −19.76 per year between 1990 and 2000. The bloater
Zina [12379]

Answer:

x = 11.33 years

Step-by-step explanation:

The equation for rainbow smelt is Y1 = −19.76x + 227

For bloater fish, the equation is Y2 = –92.57x + 1052

To find where these populations are equal:

–19.76x + 227 = –92.57x + 1052

Combine like terms:

-19.76x + 92.57x = 1052 - 227

72.81x = 825

Now divide by 72.81:

x = 825 / 72.81

Thus,

x = 11.33 years

6 0
1 month ago
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Ms. Gallegos burns 236 calories riding her bike each hour. She wants to burn more than 590 calories riding her bike at the same
Svet_ta [12734]

Response:

354

Detailed explanation:

5 0
1 month ago
F(x) = -4x(2)+ 12x – 9
AnnZ [12381]

For this context, we examine the function:

f (x) = - 4x ^ 2 + 12x-9

y = 0 presented as:

-4x ^ 2 + 12x-9 = 0

The definition of the discriminant in a quadratic equation is provided by:

a = -4\\b = 12\\c = -9

Sentences correspond to the types of roots: Different real roots, equal real roots, or distinct complex roots

d = b ^ 2-4 (a) (c)

d> 0:Upon substituting the provided values, we arrive at

d = 0:

d

This indicates that there are two equal real roots.

To discover the intersections along the x-axis, we apply the quadratic formula:d = (12) ^ 2-4 (-4) (- 9)\\d = 144-144

d = 0

Plugging in the values yields: y = 0:

-4x ^ 2 + 12x-9 = 0

The intersection on the x-axis is

x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}

x = \frac {-12 \pm \sqrt {12 ^ 2-4 (-4) (- 9)}} {2 (-4)}\\x = \frac {-12 \pm \sqrt {144-144}} {- 8}\\x = \frac {-12 \pm0} {- 8}\\x = \frac {-12} {- 8}\\x = \frac {3} {2}

(\frac {3} {2}, 0)

5 0
8 days ago
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A has the coordinates (–4, 3) and B has the coordinates (4, 4). If DO,1/2(x, y) is a dilation of △ABC, what is true about the im
lawyer [12517]
A dilation represents a transformation D_{o,k}(x,y), centered at point O with a scale factor of k, which cannot be zero. This transformation keeps O fixed while transforming any other point P into its image P'. Points O, P, and P' are collinear.

In a dilation of D_{o, \frac{1}{2} }(x,y), the scale factor \frac{1}{2} maps the original figure to its transformed image in such a way that the distances from O to points of the image are half the distances from O to the original figure. Consequently, the image's size is also half that of the original figure.

Thus, <span>If D_{o, \frac{1}{2} }(x,y) represents the dilation of △ABC, then the properties of the image △A'B'C'</span> are:

<span>AB is parallel to A'B'.

D_{o, \frac{1}{2} }(x,y)=( \frac{1}{2}x, \frac{1}{2}y)

The distance from A' to the origin is half that from A to the origin.</span>
3 0
1 month ago
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Water leaves a spigot at a rate of 462 cubic inches per minute. How many cubic feet of water is this per hour? (Round your answe
tester [12383]

Answer:

16 cubic feet per hour

Step-by-step explanation:

This involves a straightforward conversion from inches to feet.

Step 1: Establish the conversion scale

---> the volume of water in 1 minute is 462 cubic inches

--->1 cubic foot = 1728 cubic inches

--->1 hour consists of 60 minutes,

Step 2: Determine the volume in feet per hour

Volume of water in one hour =  0.0347 x 462

---> the amount of water in 1 hour =  = 16.0314 cubic feet

---> Rounded to--> 16 cubic feet

Thus, 462 cubic inches per minute equates to 16 cubic feet of water on an hourly basis

5 0
18 days ago
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