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jarptica [38.1K]
3 years ago
11

A rectangle has an area of 48 in^2. Every dimension of the rectangleis multiplied by a scale factor, and the new rectangle has a

n area of 12 in^2. What is the scale factor?
Mathematics
1 answer:
jeka57 [31]3 years ago
5 0

Let the dimensions of the first rectangle be L and W.  Then L*W = 48 in^2.

If we multiply both dimensions of this first rectangle by scale factor f, we get

f*L * f^W = 12 in^2.  Our job is to determine the scale factor, f.

Note that f^2*L*W = 12 in^2, and that LW = 48 in^2.

Therefore, the above equation becomes f^2*(48 in^2) = 12 in^2.

Dividing both sides by (48 in^2), we get f^2 = 1/4.

Solving for the scale factor, we get f = √(1/4) = 1/2.

The scale factor is 1/2.

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Mr. Stanford’s greenhouse has the dimensions shown. The volume of the greenhouse is 90 cubic yards. Find the missing dimension o
bulgar [2K]

Answer:

h=10\ yd

Step-by-step explanation:

we know that

The volume of the triangular prism of the figure is equal to

V=Bh

where

B is the area of the triangular base

h is the height of the triangular prism

Find the value of B

B=\frac{1}{2}(6)(3)=9\ yd^{2}

we have that

V=90\ yd^{3}

substitute the values and solve for h

90=9h

h=90/9=10\ yd

5 0
3 years ago
Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2,700 grams and a standard deviation of 900
makkiz [27]

Answer:

the answers have been provided below

Step-by-step explanation:

Population z score is given as (x-μ)/sd For a 32 to 35 week gestation period

μ= 2700

Sd = 900grams

x = 2225

z = (2225-2700)/900

z = -0.527

For a 40 week gestation period.

μ = 3000

Sd = 465grams

x = 2525

z = (2525-3000)/465

Z = -1.022

In answer to the question:

a. The 33-week gestation period baby weighs 0.53 standard deviations below the mean.

b. The 40-week gestation period baby weighs 1.02 standard deviations below the mean.

c. -1.022 < -0.527. the 40 weeks gestation baby weighs less.

A. The baby born in week 40 does since its z-score is smaller.

6 0
3 years ago
The average low temperature is Springfield, Illinois in January is 5°C. The average low temperature in Winters Run, Alaska in Ja
nadezda [96]

Answer:

5 - (-8) = 13

3 0
3 years ago
Consider the function . find the vertical asymptote(s) of f(x). x = 0, –9 x = –9 x = 0, 9 x = 9
kondaur [170]

The vertical asymptote of f(x) is (A) x = 0, –9.

<h3>What is a function?</h3>
  • A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable).
  • Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.

To find the vertical asymptote of f(x):

The vertical asymptotes of a function are the zeroes of the denominator of a rational function

The function is given as: f(x) = \frac{(x-9)}{(x^{3} -81x)}

Set the denominator to 0:

  • x^{3} -81x=0

Factor out x:

  • x(x^{2} -81)=0

Express 81 as 9^2:

  • x(x^{2} -9^{2} )=0

Express the difference between the two squares:

  • x(x-9)(x+9)

Split, x=0 or x=-9 or x+9=0.

Solve for x:

  • x=0\\ or x=-9 or x+9=0.

Therefore, the vertical asymptote of f(x) is (A) x = 0, –9.

(See attachment for the graph of f(x))

Know more about functions here:

brainly.com/question/6561461

#SPJ4

The complete question is given below:

Consider the function f(x)=(x-9)/(x^3-81x) . find the vertical asymptote(s) of f(x).

A) x = 0, –9

B) x = –9

C) x = 0, 9

D) x = 9

3 0
2 years ago
Please help with graphing please
JulsSmile [24]
The solution is (3,4). It’s where the lines intersect
7 0
3 years ago
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