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3 years ago

Determine which of the following statements is true for the function g(x) = 4x^5 - 3x^6 + 2x^3 - 1.

Mathematics

1 answer:

jonny [76]3 years ago

8 0

Answer:

Option D. As x increases, y decreases. As x decreases, y decreases

Step-by-step explanation:

we have the function

$g(x)=4x^{5}-3x^{6}+2x^{3}-1$

we know that

g(x) is a polynomial of sixth degree

The value of the function will approach the same negative infinity for large positive or negative x. That infinity is determined by the sign of the coefficient of the 6th-degree term, which is negative.

therefore

As x increases -----> The value of y decreases

As x decreases ----> The value of y decreases

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Solve for the zeros of the quadratic function f(x) = 9x² + 6x + 1.

Nezavi [6.7K]

Answer:

$\large\boxed{x=-\dfrac{1}{3}}$

Step-by-step explanation:

$f(x)=9x^2+6x+1\\\\\text{The zeros are for}\ f(x)=0\\\\9x^2+6x+1=0\\\\9x^2+3x+3x+1=0\\\\3x(3x+1)+1(3x+1)=0\\\\(3x+1)(3x+1)=0\\\\(3x+1)^2=0\iff3x+1=0\qquad\text{subtract 1 from both sides}\\\\3x=-1\qquad\text{divide both sides by 3}\\\\x=-\dfrac{1}{3}$

8 0

3 years ago

Based on the side lengths given (a, b, and o, which triangles are right triangles?

Cloud [144]

Answer:

2 & 3

Step-by-step explanation:

Pythagorean Theorem is $a^2+b^2=c^2$ .

If the values given in each option satisfy the theorem, the sides will make a right triangle.

<h3>For Option One:</h3>

$4^2+6^2=8^2\\=> 4^2=16\\=> 6^2=36\\=>8^2 =64\\16+36=64\\\boxed{52\neq 64}$

The sides would not make a right triangle.

<h3>For Option Two:</h3>

$6^2+8^2=10^2\\=> 6^2 = 36\\=> 8^2=64\\=> 10^2=100\\36+64=100\\\boxed{100=100}$

The sides would make a right triangle.

<h3>For Option Three:</h3>

$5^2+6^2=\sqrt{61}^2\\ => 5^2=25\\=>6^2=36\\=>\sqrt{61}^2=61\\ 25+36=61\\\boxed {61=61}$

The sides would make a right triangle.

<h3>For Option Four:</h3>

$6^2+9^2=12^2\\=> 6^2=36\\=>9^2=81\\=>12^2=144\\36+81=144\\\boxed{117\neq 144}$

The sides would not make a right triangle.

The correct answer should be options two and three.

6 0

2 years ago

Salve this proportion 15/35=g/7

labwork [276]

G is equivalent to 3

4 0

3 years ago

Please help worth 25 points

wariber [46]

Answer:

h=6 feet

Step-by-step explanation:

Given: 1. The base of a rectangle is three feet longer than its height.

2.Are of the rectangle=54 square meters

Let us say the rectangle has height h and base(breadth) b.

Since, the base of the rectangle is three feet longer than the height, we have b=h+3.

Also, Area of the Rectangle= hb

therefore, 54=h(h+3)

54= h2+ 3h

h2+3h-54=0 (Subtract 54 from both the sides)

To find the value of h we have to solve the quadratic equation.

[We have the equation in the form ax2+bx+c=0, to factorise the equation-

Step1. Find two numbers such that their multiplication is equal to ac and their addition is equal to b.

Step2. Replace b with these numbers.

Step3. Simplify the equation]

So, h2+3h-54=0

h2+9h-6h-54=0

h(h+9)-6(h+9)=0

(h+9)(h-6)=0

Which gives-

h= -9 or h= 6

As h is the height of the rectangle, h can not be -9.

so h=6 feet

and b=h+3=9 feet

So the dimensions of the rectangle are 6 feet for the height and 9 feet for the base.

5 0

2 years ago

<img src="https://tex.z-dn.net/?f=f%20%2B%20523.89%20%20%3D%20812.57" id="TexFormula1" title="f + 523.89 = 812.57" alt="f + 523

Evgesh-ka [11]

Answer:

D.f=288.68

Step-by-step explanation:

f+ 523.89 = 812.57

subtract 523.89 from both sides

f+ 523.89-523.89 = 812.57-523.89

f = 288.68

8 0

3 years ago

Read 2 more answers