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2 years ago

Match each operation involving f(x) and g(x) to its answer.

Mathematics

1 answer:

galben [10]2 years ago

8 0

F(x)=1-x² and g(x)=√(11-4x)

(g+f)(2)=>

1-(2)²+√(11-4(2))

=√3-3

(f/g)(-1)

(1-(-1)²)/(√(11-4(-1))

=0

(g-f)(-1)

√(11-4*-1)-(1-(-1)²

=√15

(g×f)(2)

1-(2)²×√(11-4(2))

-3√3

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Shawn has 4 nickles. How many walnuts can he buy if he spends all 4 nickels?

Roman55 [17]

Answer:

This really depends.

Step-by-step explanation:

If a walnut costs 10 cents, he can buy 2 walnuts.

If a walnut costs 5 cents, he can buy 4.

If a walnut costs 20 cents, he can buy 3.

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2 years ago

Two boats depart from a port located at (–8, 1) in a coordinate system measured in kilometers and travel in a positive x-directi

miss Akunina [59]

Answer:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

Step-by-step explanation:

1st boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=1\\ \\b=-2a$

Equation:

$y=ax^2 -2ax+c$

The y-coordinate of the vertex:

$y_v=a\cdot 1^2-2a\cdot 1+c\Rightarrow a-2a+c=10\\ \\c-a=10$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-2a\cdot (-8)+c\\ \\80a+c=1$

Solve:

$c=10+a\\ \\80a+10+a=1\\ \\81a=-9\\ \\a=-\dfrac{1}{9}\\ \\b=-2a=\dfrac{2}{9}\\ \\c=10-\dfrac{1}{9}=\dfrac{89}{9}$

Parabola equation:

$y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}$

2nd boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=0\\ \\b=0$

Equation:

$y=ax^2+c$

The y-coordinate of the vertex:

$y_v=a\cdot 0^2+c\Rightarrow c=-7$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-7\\ \\64a-7=1$

Solve:

$a=-\dfrac{1}{8}\\ \\b=0\\ \\c=-7$

Parabola equation:

$y=\dfrac{1}{8}x^2 -7$

System of two equations:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

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2 years ago

Read 2 more answers

Karina solves the system using linear combination and arrives at the equation 116y = 96.28. She then solves this equation for y.

igomit [66]

116y =96.28
116y = 96.28
---- ---------
116 116

y = .83

5 0

1 year ago

Here are two column vectors f=[4/1] g=[5/3]

Murljashka [212]

Answer:

Vectors a, b, c, d and e are drawn on an isometric grid. ... 5. Here are two column vectors. *= (3) 9= (). Work out 3f - 2g. [2]. 3. (1)-(3) =).

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2 years ago

Which number has the greatest absolute value? <br> a. 0 <br> b. 10 <br> c. –10 <br> d. –20?

Triss [41]

Keep in mind, absolute values are always positive, even when they say negative.That is because the absolute value of a number is just the distance that number is from 0. Example : -5 and 5...they are both 5 spaces from 0...doesn't matter if it is negative or positive, it is still 5 spaces.

|0| = 0
|10| = 10
|-10| = 10
|-20| = 20

so ur answer is : | -20 |

6 0

2 years ago