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2 years ago

Help me plzzz!!!!!!!!!!!

Mathematics

1 answer:

Romashka-Z-Leto [24]2 years ago

6 0

Lets take a quick look at the rate of change in the graph. Apologies for how blurry the image is, but we can see for every minute 3 gallons of water gets poured in the tank. So, the answer would be 3!

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<img src="https://tex.z-dn.net/?f=4%20%20%20%7B%7D%5E%7Bx%20%7D%20%20%2B%206%20%7B%7D%5E%7Bx%7D%20%3D%209%20%7B%7D%5E%7Bx%7D%20%

Nookie1986 [14]

So, the value of x is 1.19

The question is an exponential equation

<h3>What is an exponential equation?</h3>

An exponential equation is a mathematical expression between two quantities in which one variable is raised to a power of the other variable.

Since $4^{x} + 6^{x} = 9^{x}$ ,

Dividing through by 4ˣ, we have

$\frac{4^{x} }{4^{x} } + \frac{6^{x} }{4^{x} } = \frac{9^{x} }{4^{x} } \\1 + (\frac{6}{4})^{x} } = (\frac{9}{4})^{x} } \\1 + (\frac{3}{2})^{x} } = (\frac{3^{2} }{2^{2} })^{x} } \\1 + (\frac{3}{2})^{x} } = (\frac{3}{2})^{2x} }$

Let y = (3/2)ˣ

So,

1 + y = y²

y² - y - 1 = 0

Using the quadratic formula to find y,

$y = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}$

where a = 1 b = -1 and c = -1

Substituting the values of the variables into the equation, we have

$y = \frac{-(-1) +/- \sqrt{(-1)^{2} - 4\times 1 \times (-1)} }{2\times 1}\\= \frac{1 +/- \sqrt{1 + 4} }{2}\\= \frac{1 +/- \sqrt{5} }{2}\\= \frac{1 - \sqrt{5} }{2} or \frac{1 + \sqrt{5} }{2}\\= \frac{1 - 2.236}{2} or \frac{1 + 2.236}{2}\\= \frac{- 1.236}{2} or \frac{3.236}{2}\\= -0.618 or 1.618$

Since y = (3/2)ˣ

Takung logarithm of both sides, we have

㏒y = ㏒(3/2)ˣ

㏒y = x㏒(3/2)

x = ㏒y/㏒(3/2)

x = ㏒y/㏒1.5

Since we do not have logarithm of a negative number, we use y = 1.618.

So, x = ㏒y/㏒1.5

x = ㏒1.618/㏒1.5

x = 0.2090/0.1761

x = 1.19

So, the value of x is 1.19

Learn more about exponential equation here:

brainly.com/question/11832081

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5 0

1 year ago

First and second place in the contest use a ratio to share a cash prize when first place pays $100 second please pay $60 how muc

Talja [164]

100/60 = x/36

Cross Multiply

3600 = 60x

x = 60

First place pays $60 when second place pays $36.

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✉️ If any further questions, inbox me! ✉️

4 0

3 years ago

9.5 is what percent of 500?

natta225 [31]

9.5% of 500 = 47.5

9.5% × 500 =

(9.5 ÷ 100) × 500 =

(9.5 × 500) ÷ 100 =

4,750 ÷ 100 =

47.5;

3 0

2 years ago

Analyzing the Discrim

ANEK [815]

The values of x that will give the quadratic equation no real number solutions are -5 and 9

<h3>What are real roots of a quadratic equation?</h3>

Real roots of a quadratic equation are values of x, whose numbers can be represented on a number line.

Analysis:

We have - $x^{2}$ +3x +c = 0

$b^{2}$ - 4ac is called the discriminant of a quadratic equation.

if $b^{2}$ - 4ac < 0, then the quadratic equation has no real root.

where a = -1, b = 3 c = c

$(3)^{2}$ -4(-1)c < 0

9 + 4c < 0

4c < -9

c < -9/2

Which means values lower than -9/2 would give the solution no real root.

From, the options, only -5 would give no real solution, since it is lower than -9/2.

Learn more about real roots of a quadratic equation: brainly.com/question/7784687

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3 0

1 year ago

€

Ksju [112]

Answer:

(-9.5, 6.75)

Step-by-step explanation:

I inputted both equations on the desmos website and they met at this point

8 0

3 years ago