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VLD [36.1K]
3 years ago
11

NEED HELPPPPPPP!!!!!!! PLEASE!!!!!!!!

Mathematics
1 answer:
vagabundo [1.1K]3 years ago
4 0

Firstly, simplife the function -x^3-x^2+4x+4 in the following way:

-x^3-x^2+4x+4=-(x^3+x^2)+4(x+1)=-x^2(x+1)+4(x+1)=(x+1)(4-x^2)=(x+1)(2-x)(2+x)=-(x+2)(x+1)(x-2).

There are three x-intercepts: x=-1; x=2 and x=-2 (therefore, options A and D are incorrect).

Since before brackets is sign "-", you should state that graph starts down on the left (you can check this substituting smaller negative number than -2 into function expression. For example, if x=-10, then f(-10)=-(-10+2)(-10+1)(-10-2)=-(-8)(-9)(-12)>0) and goes up on the right (you can check this substituting greater positive number than 2 into function expression. For example, if x=10, then f(-10)=-(10+2)(10+1)(10-2)=-(12)(11)(8)<0).

Answer: correct choice is B.

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Can someone finish the whole thing ??
Romashka-Z-Leto [24]
<h3>Answer:    y = (3/2)x + 0</h3>

This is the same as  y = (3/2)x

=============================================================

Work Shown:

Find the slope of the line through (x1,y1) = (-2,-3) and (x2,y2) = (2,3)

m = (y2 - y1)/(x2 - x1)

m = (3 - (-3))/(2 - (-2))

m = (3 + 3)/(2 + 2)

m = 6/4

m = 3/2

The slope is the fraction 3/2. This is going to be in front of the x, or to the left of the x.

----------

Plug m = 3/2 and (x1,y1) = (-2,-3) into the point slope formula. Solve for y.

y - y1 = m(x - x1)

y - (-3) = (3/2)(x - (-2))

y + 3 = (3/2)(x + 2)

y + 3 = (3/2)x + (3/2)(2)

y + 3 = (3/2)*x + 3

y + 3 - 3 = (3/2)*x + 3 - 3

y = (3/2)x + 0

The y intercept is zero. This matches up with the fact the graph crosses the y axis at y = 0.

3 0
3 years ago
The distance between two cities is 180km. The distance was covered by a car at the rate of 50km/h, by a bus 45km/h, by a truck a
Gennadij [26K]

Answer:

The speed and time are directly proportional in that the higher the speed the lesser the time and vice versa.

The constant is the total distance which is 180 km

Step-by-step explanation:

Step one:

given data

The distance between the  two cities is 180km

1.The distance was covered by a car at the rate of 50km/h

The time taken will be

velocity= distance/time

time= distance/velocity

time= 180/50

time= 3.6 hours

2.The distance was covered by a bus 45km/h

The time taken will be

velocity= distance/time

time= distance/velocity

time= 180/45

time= 4 hours

3.The distance was covered by a bicycle at 25km/h

The time taken will be

velocity= distance/time

time= distance/velocity

time= 180/25

time= 7.2 hours

7 0
3 years ago
Let $f(x) = x^2$ and $g(x) = \sqrt{x}$. Find the area bounded by $f(x)$ and $g(x).$
Anna [14]

Answer:

\large\boxed{1\dfrac{1}{3}\ u^2}

Step-by-step explanation:

Let's sketch graphs of functions f(x) and g(x) on one coordinate system (attachment).

Let's calculate the common points:

x^2=\sqrt{x}\qquad\text{square of both sides}\\\\(x^2)^2=\left(\sqrt{x}\right)^2\\\\x^4=x\qquad\text{subtract}\ x\ \text{from both sides}\\\\x^4-x=0\qquad\text{distribute}\\\\x(x^3-1)=0\iff x=0\ \vee\ x^3-1=0\\\\x^3-1=0\qquad\text{add 1 to both sides}\\\\x^3=1\to x=\sqrt[3]1\to x=1

The area to be calculated is the area in the interval [0, 1] bounded by the graph g(x) and the axis x minus the area bounded by the graph f(x) and the axis x.

We have integrals:

\int\limits_{0}^1(\sqrt{x})dx-\int\limits_{0}^1(x^2)dx=(*)\\\\\int(\sqrt{x})dx=\int\left(x^\frac{1}{2}\right)dx=\dfrac{2}{3}x^\frac{3}{2}=\dfrac{2x\sqrt{x}}{3}\\\\\int(x^2)dx=\dfrac{1}{3}x^3\\\\(*)=\left(\dfrac{2x\sqrt{x}}{2}\right]^1_0-\left(\dfrac{1}{3}x^3\right]^1_0=\dfrac{2(1)\sqrt{1}}{2}-\dfrac{2(0)\sqrt{0}}{2}-\left(\dfrac{1}{3}(1)^3-\dfrac{1}{3}(0)^3\right)\\\\=\dfrac{2(1)(1)}{2}-\dfrac{2(0)(0)}{2}-\dfrac{1}{3}(1)}+\dfrac{1}{3}(0)=2-0-\dfrac{1}{3}+0=1\dfrac{1}{3}

6 0
3 years ago
3 1/3 divided by 1 1/4 =
lora16 [44]

Answer:

3/8

Step-by-step explanation:

3 1/3 = 10/3

1 1/4 = 5/4

Remember when dividing by a fraction you can also multiply by its reciprocal meaning flip the numerator and denominator.

so

(3 1/3) / (1 1/4) = (10/3) / (5/4) = (10/3) x (4/5) which is the same as (3/10) x (5/4)

= (3 x 5) / (10 x 4) = 15 / 40

the numerator and denominator have a common factor of 5 so divide the  numerator and denominator by 5

15 / 40 = 3/8

3 0
3 years ago
HELP PICTURE IS SHOWN
Marrrta [24]
C hope it helps .....................
6 0
3 years ago
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