All categories

4 years ago

If s(x) = 2x2 + 3x - 4, and t(x) = x + 4 then s(x) · t(x) =

Mathematics

1 answer:

Paladinen [302]4 years ago

7 0

Answer:

$\large\boxed{s(x)\cdot t(x)=2x^3+11x^2+8x-16}$

Step-by-step explanation:

$s(x)=2x^2+3x-4,\ t(x)=x+4\\\\s(x)\cdot t(x)\\\\\text{use the distributive property:}\ a(b+c)=ab+ac\\\\s(x)\cdot t(x)=(2x^2+3x-4)(x+4)\\\\=(2x^2+3x-4)(x)+(2x^2+3x-4)(4)\\\\=(2x^2)(x)+(3x)(x)+(-4)(x)+(2x^2)(4)+(3x)(4)+(-4)(4)\\\\=2x^3+3x^2-4x+8x^2+12x-16\\\\\text{combine like terms}\\\\=2x^3+(3x^2+8x^2)+(-4x+12x)-16\\\\=2x^3+11x^2+8x-16$

You might be interested in

What that two numbers when multiplied give 600 and when added give 59

ozzi

Answer:

Step-by-step explanation:

Let the 2 numbers be x and y

From the problem we have that

x * y = 600 and x + y = 59

From x + y = 59 -> x = 59 - y

Plug x = 59 - y to x * y = 600 we have

(59 - y) * y = 600

-> 59y - y^2 = 600

-> -y^2 + 59y - 600 = 0

-> y = $(59 - \sqrt{1081})/2$ or $(59 + \sqrt{1081})/2$

Then we could plug the answers in and find x because x = 59 - y

8 0

3 years ago

On which number line do the points represent negative seven and one over two and +1? (4 points)

Veronika [31]

Answer:

A number line is used in the mathematical positioning of real numbers that include the numbers from positive infinity to negative infinity. This includes rational, irrational, fractions, and whole numbers. In this case, we are given with an expression that we have to reduce to lowest terms: negative seven and one over two and +1. The first one is equal to -7.5 while the other one is equal to +1. Positive numbers lie on the right side of zero (center of the line) while negative numbers lie on the left on the other hand. -7.5 lies between -8 and -7 while +1 lies exactly between 0 and 2. Both of which are positive numbers.

8 0

3 years ago

Gemma, a scuba diver, begins a dive on the side of a boat 4 feet above sea level. She descends 28 feet. Which integer represents

pantera1 [17]

That would be
4 feet - 28 feet = -24
The integer is -24

5 0

3 years ago

Read 2 more answers

I am having trouble with this could somebody give me a hand

MrRa [10]

check the picture below.

$\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+100}t\stackrel{\stackrel{c}{\downarrow }}{+12} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)$

$\bf \left( -\cfrac{100}{2(-16)}~~,~~12-\cfrac{100^2}{4(-16)} \right)\implies \left( \cfrac{25}{8}~~,~~12+\cfrac{625}{4}\right) \\\\\\ \left(\cfrac{25}{8}~,~\cfrac{673}{4} \right)\implies \left(\stackrel{\stackrel{\textit{took this long}}{\downarrow }}{3\frac{1}{8}}~~,~~\stackrel{\stackrel{\textit{went this high}}{\downarrow }}{168\frac{1}{4}} \right)$

5 0

4 years ago

Please help me!

MA_775_DIABLO [31]

Answer:

The answer is below

Step-by-step explanation:

a) The patio is in the form of a rectangle. The patio has a width of (x - 10) ft. Therefore given that the area of the patio is x² + 10x - 200, hence:

$Area=length*breadth\\\\x^2+10x-200=length*(x -10)\\\\x^2+20x-10x-200=length*(x -10)\\\\x(x+20)-10(x+20)=length*(x -10)\\\\(x-10)(x+20)=length*(x -10)\\\\length=x +20$

b) Area of original house = length of house * breadth of house

The length of house = length of patio = x + 20; breadth of house = x + 10; therefore:

Area of original house = (x + 20)(x + 10) = x² + 10x + 20x + 200

Area of original house = x² + 30x + 200

c) If the width is extended, hence:

$Area=length*breadth\\\\x^2+12x-160=(x+20)*width\\\\x^2+20x-8x-160=(x+20)*width\\\\x(x+20)-8(x+20)=(x+20)*width\\\\(x-8)(x+20)=(x+20)*width\\\\width=x-8\\\\Extended \ width=(x-8)-(x-10)\\\\Extended \ width=2\ feet$

7 0

3 years ago