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horrorfan [7]
3 years ago
14

HELP! If the area of a rectangle is 10x^2+3x-4 and the width is 2x-1, what is the side length of the rectangle?

Mathematics
1 answer:
faltersainse [42]3 years ago
3 0

Answer:

5x+4

Step-by-step explanation:

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Farmer bob's square plot ofland is slowly eroding away. Worried about the future of his farm. Farmer Bob measures the rate of er
kow [346]

Answer:

Option A.

Step-by-step explanation:

Area of a square is

A=x^2               .... (1)

where, x is side length.

The length of each side of his square plot is decreasing at the constant rate of 2 feet/year.

\dfrac{dx}{dt}=2

It is given that bob currently owns 250,000 square feet of land.

Fist find the length of each side.

A=250000

x^2=250000

Taking square root on both sides.

x=500

Differentiate with respect to t.

\dfrac{dA}{dt}=2x\dfrac{dx}{dt}

Substitute x=500 and \frac{dx}{dt}=2 in the above equation.

\dfrac{dA}{dt}=2(500)(2)

\dfrac{dA}{dt}=2000

Farmer bob is losing 2,000 square feet of land per year.

Therefore, the correct option is A.

7 0
3 years ago
A cone has a volume of 108 pi and a base diameter of 12. What is the height of the cone?
serious [3.7K]

Answer:

h  = 9 units of length

Step-by-step explanation:

Volume of a circular right cone is:

V(c)  = (1/3)*Area of the circular base * h

Where h is the height of the cone, then

V(c)  =  (1/3) * π * r² * h

And  we have that  V(c) = 108*π

Then:

108 * π  =  (1/3) * π * r² * h                  (1)

We know diameter of the circular base is 12 units, according to that

r =  d/2     ⇒  r = 12/2     r = 6 units

Then:

108 * π  [ cubic units ]  =  (1/3) * π * (6)² * h  [square units] [ units of length]

When simplifying we have to take into account that in order to keep last equation h needs to have units of length  

Therefore:

108  =  (1/3) * 36 * h

h = ( 108* 3 )/ 36

h  = 9 units of length

7 0
4 years ago
NEED HELP WITH A MATH QUESTION
Lady_Fox [76]

Answer:

\dfrac{18}{5}

Step-by-step explanation:

The picture shows three isosceles tirangles with the same legs. The base of each triangle is 12 units, 5x-3 units and 17 units.

Since the angles at vertex of each isosceles triangles are 27°, 28° and 29°, then the lengths of the bases satisfy the double inequality

15<5x-3<17

Add 3 to this inequality

15+3<5x-3+3<17+3

18<5x<20

Divide it by 5:

\dfrac{18}{5}

3 0
3 years ago
Find the slope of the line that passes through the points (−2/3, 3/4) and (5/6, −1/2).
EastWind [94]

Answer:

-\frac{5}{6}

Step-by-step explanation:

Use the slope formula :\frac{y2-y1}{x2-x1}

-1/2 is y2, 3/4 is y1, 5/6 is x2, and -2/3 is x1.

\frac{-1/2-3/4}{5/6-(-2/3)}

\frac{-5/4}{5/6+2/3}

\frac{-5/4}{9/6}

\frac{-5}{4} ÷ \frac{9}{6}

-\frac{5}{4} • \frac{6}{9}

-\frac{5}{2} • \frac{3}{9}

-\frac{15}{18}  

-\frac{5}{6}

Hope this helps! Let me know if I got it wrong.

5 0
3 years ago
The accompanying data represent the miles per gallon of a random sample of cars with a​ three-cylinder, 1.0 liter engine.a. Comp
Kobotan [32]

Answer:

1). Z score = 1.464733

Mean = 38.87917

Standard deviation = 3.609405

2). Quartiles:

Q1 = 37.025

Q2 = 38.450

Q3 = 40.800

3). IQR = 3.775

4).

CI (lower fence) = 37.4351

CI (upper fence) =  40.32323

5). There is outlier in the data set. Please see attached box plot for evidence.

Step-by-step explanation:

1). By Z score, we mean:

Z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}},

where:

x-bar ==> mean(g) = 38.87917

\mu = 37.80

standard deviation = 3.609405

sample size (n) = 24.

2). By quantile, we mean:

Q = L + (i*(n/4) - Cf)*c

Where L is the lower class limit of the quartile class

Cf is the cumulative frequency before the quartile class

c  is the class size.

3) . IQR = Q3 - Q1

4). CI = \mu \pm *Z_{\alpha/2} \frac{\sigma}{\sqrt{n}},

Where Z_{\alpha/2}  ==> 1.96

In order to replicate and obtain the result, please use the R code below:

g = c(31.5, 36.0, 37.8, 38.5, 40.1, 42.2,34.2, 36.2, 38.1, 38.7, 40.6, 42.5,34.7, 37.3, 38.2, 39.5,  

41.4, 43.4,35.6, 37.6, 38.4, 39.6, 41.7, 49.3)

boxplot(g)

Z = (mean(g) - 37.8)/(sd(g)/sqrt(length(g)))

mean(g)

quantile(g)

IQR(g)

CIl = mean(g) - 1.96*(sd(g)/sqrt(length(g)))

CIU = mean(g) + 1.96*(sd(g)/sqrt(length(g)))

4 0
3 years ago
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