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3 years ago

Tropical islands have many rainstorms during the afternoon heat. One particular tropical island has a 79% chance of a

Mathematics

1 answer:

noname [10]3 years ago

6 0

Answer:

Step-by-step explanation:

I got it right on Edge.

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2.<br>√3x + 7 + √x + 1 =2

taurus [48]

Answer:

x = -1

Step-by-step explanation:

The usual approach to these is to square the radicals until they are gone.

$\displaystyle\sqrt{3x+7}+\sqrt{x+1}=2\\\\(3x+7) +2\sqrt{(3x+7)(x+1)}+(x+1) = 4\qquad\text{square both sides}\\\\2\sqrt{(3x+7)(x+1)}=-4x-4\qquad\text{subtract $4x+8$}\\\\(3x+7)(x+1)=(-2x-2)^2\qquad\text{divide by 2, square again}\\\\3x^2+10x +7=4x^2+8x+4\qquad\text{simplify}\\\\x^2-2x-3=0\qquad\text{subtract the left expression}\\\\(x-3)(x+1)=0\qquad\text{factor}\\\\x=3,\ x=-1\qquad\text{solutions to the quadratic}$

Each time the equation is squared, the possibility of an extraneous root is introduced. Here, x=3 is extraneous: it does not satisfy the original equation.

The solution is x = -1.

_____

Using a graphing calculator to solve the original equation can avoid extraneous solutions. The attachment shows only the solution x = -1. Rather than use f(x) = 2, we have rewritten the equation to f(x)-2 = 0. The graphing calculator is really good at showing the function values at the x-intercepts.

5 0

3 years ago

Suppose that $p$ and $q$ are positive numbers for which \[\log_9 p = \log_{12} q = \log_{16} (p + q).\] what is the value of $q/

SVEN [57.7K]

Given $p,q>0$ and $\log_9p=\log_{12}q=\log_{16}(p+q)=x$ (say).

Then,

$p=9^x\\ q=12^x\\ p+q=16^x$

From the above 3 equations,

$\frac{q}{p} =(\frac{12}{9} )^x\\ \frac{q}{p} =(\frac{4}{3} )^x\\ \frac{p+q}{p} =(\frac{16}{9} )^x\\ \frac{p+q}{p} =(\frac{4}{3} )^{2x}\\$

From the equations, we get

$\frac{p+q}{p}=(\frac{q}{p})^2\\ 1+\frac{q}{p}=(\frac{q}{p})^2\\ (\frac{q}{p})^2-\frac{q}{p}-1=0\\ \frac{q}{p}=\frac{1 \pm \sqrt{5}}{2}$

Since $p,q>0$ , the negative value is rejected.

$\frac{q}{p}=\frac{1 + \sqrt{5}}{2}$

3 0

3 years ago

Peggy wants to make 26

tekilochka [14]

If there are 26 bags EACH costing $9 then you would use equation A.
26 (The number of gift bags) x the price of each bag would cost close to $234. That would be the reasonable estimate and I hope this helps!

6 0

2 years ago

Please help if possible due today thank you so so much!!

LenKa [72]

It’s B, B is the answer

7 0

2 years ago

Read 2 more answers

If g(x) = 4 square root of x then g(45) is

AlladinOne [14]

Hi,

So we have g(x) = 4√(x). We're looking for g(45). Think of it like this: whatever number is in the place of x in g(x), just place that number AS x.

Therefore, we have :
g(45) = 4√(45) ⇒ (4) × (√(45)) ⇒ (4)(3√(5)) = 12√(5).

-Hope this helps!

5 0

3 years ago