What is the solution to the system of equations graphed below? Please Help (:

A rectangular prism must have a base with an area of no more than 27 square meters. The width of the base must be 9 meters less

Leona [12618]

Answer:

The upper limit for the height of the prism is $12\ m$

Step-by-step explanation:

Let

x------> represent the height of the prism

It is known that

the area of the base of the prism must not exceed

$A=L*W$

$A\leq 27\ m^{2}$

thus

$L*W\leq 27$ -------> inequality A

$W=x-9$ ------> equation B

$L=W+6$ -----> equation C

Insert equation B into equation C

$L=(x-9)+6$

$L=x-3$ ------> equation D

Substituting equations B and D into inequality A

$(x-3)*(x-9)\leq 27$ -------> using a graphing tool to solve the inequality

The resultant solution for x lies in the interval----------> $[0,12]$

consult the attached figure

but bear in mind that

The width of the base must be $9$ meters shorter than the height of the prism

thus

the solution for x is confined to the interval ------> $(9,12]$

The maximum height of the prism equals $12\ m$

8 1

1 month ago

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landon owns a hybrid SUV that can travel 400 miles on a 15-gallon tank of gas.Determine how many miles he can travel on a 6 gall

tester [12383]

From another answer, "There are various methods to calculate this. One approach is:

With a range of 400 miles on a 15-gallon fuel tank,
400 / 15 results in 26.66666666666667 miles for every gallon (it seems odd, but we'll reach a concise outcome shortly)
Thus, 26.66666666666667 multiplied by 6 gallons equals 160 miles.

Final result: Landon's SUV can go 160 miles using 6 gallons."

7 0

1 month ago

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At what rate would you need to invest $12000 and make $2880 after 8 years?

PIT_PIT [12445]

Answer:

$3\%$

Step-by-step explanation:

We start with the fact that

The formula for simple interest is represented by

$I=P(rt)$

where:

I denotes the Final Interest Value

P indicates the Principal amount to be invested

r specifies the interest rate

t refers to the Number of Time Periods

For this scenario, we have

$t=8\ years\\ P=\$12,000\\I=\$2,880\\r=?$

We can substitute these values into the formula mentioned above

$2,880=12,000(8r)$

Next, we solve for t

$2,880=96,000(r)$

$r=2,880/96,000$

$r=0.03$

Convert to a percentage format

$0.03*100=3\%$

4 0

1 month ago

Juan drove 126 miles in 3 hours. If he continued at the same rate, how long would it

babunello [11817]

Answer:

If he were to drive for 9 hours, he would cover 378 miles

6 0

16 days ago

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Consider sampling heights from the population of all female college soccer players in the United States. Assume the mean height

Leona [12618]

Answer:

B).35

Step-by-step explanation:

The Central Limit Theorem asserts that for a normally distributed variable X, with mean $\mu$ and standard deviation $\sigma$ , sample means' distribution with a size n can be closely approximated by a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .