MATHEMATICS HIGH SCHOOL

State the x-coordinate of the x-intercept in quadrant II for the function below.f(x)=x^3-x^2-x+1

Answers

Answer 1

Answer:

The x-coordinate of the x-intercept in quadrant || for the given function is -1.

x = -1.

What are coordinates?

Coordinates are a set of values that helps to show the exact position of a point in the coordinate plane.

We have,

x-intercept in quadrant ||.

f(x) = x³ - x² - x + 1

x-intercept means y = 0 so,

f(x) = y

0 = x³ - x² - x + 1

We see that,

when x = -1 we get,

f(x) = -1 - 1 + 1 + 1 = 0

When x = 1 we get,

f(x) = 1 - 1 - 1 + 1 = 0

But we can not take x = 1 because in quadrant || x is a negative value.

Thus,

The x-coordinate of the x-intercept in quadrant || for the given function is -1.

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Answer 2

Answer:

ANSWER

The x-coordinate of the x-intercept of the function $f(x)=x^3-x^2-x+1$ is $-1$ .

EXPLANATION:

The x-intercept refers to the point where the function meets or cuts the x-axis.

At the x-intercept, $f(x)=0$ .

This means we have to equate the whole function to zero and solve for $x$ .

$x^3-x^2-x+1=0$

According to the rational roots theorem, the possible rational roots of the equation $x^3-x^2-x+1=0$ are $\pm 1$ .

We now plug in these possible rational roots to see which of them are real roots.

$f(1)=1^3-1^2-1+1$

$f(1)=1-1-1+1$

$f(1)=-1+1$

$f(1)=0$

Since $f(1)=0$ , $x=-1$ is a root.

By the factor theorem, $x+1$ is a factor of the function.

We now divide the polynomial function, $x^3-x^2-x+1=0$ by $x+1$ to find the remaining roots.

See long division in diagram.

This means that $f(x)=(x+1)(x^2-2x+1)$ .

$f(x)=(x+1)(x-1)^2$

$\Rightarrow (x+1)(x-1)^2=0$

Hence the roots are $x=1$ or $x=-1$

In the second quadrant the x-coordinate is negative

Therefore, the x-coordinate of the x-intercept of the function $f(x)=x^3-x^2-x+1$ is $-1$ .

See graph in attachment

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a triangle has area 49.5 cm^2. if the base of the triangle is 9 cm, what is the height of the triangle

Answers

The height of the triangle is 11 cm

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the height of the triangle be = h

The area of the triangle A = 49.5 cm²

The base of the triangle b = 9 cm

So , the area of the triangle is given by the equation ,

Area of the triangle = ( 1/2 ) x Length x Base

Substituting the values in the equation , we get

A = ( 1/2 ) x b x h

49.5 = ( 1/2 ) x 9 x h

Multiply by 2 on both sides of the equation , we get

9h = 99

Divide by 9 on both sides of the equation , we get

h = 99/9

h = 11 cm

Therefore , the value of h is 11 cm

Hence , the height of the triangle is 11 cm

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Area of a triangle = (height * base ) / 2

height = (Area * 2) / base
height = (49.5 * 2) / 9
height = 99 / 9
height = 10 cm²

many colleges determine the number of full time students ,f,by using the formula f=n/15, where n is the total number of credits for each given semester if students on a campus register for a total of 68235 credits how many full time equivalent students does the campus have.

Answers

If students on a campus register for 68,235 credits, many colleges will estimate
the number of full-time students by using the formula

f = n / 15 = 68,235 / 15 = 4,549 students

Which solid figure has one polygon base?A. pyramid
B. cone
C. cylinder
D. prism
Question #6TrueFalse
A rectangular prism with a height of 6 m, a length of 5 m, and a width of 4 m will have a different surface area than a rectangular prism with a height of 5 m, a width of 6 m, and a length of 4 m.
TrueFalse
Question #7MultipleChoice Score:
The volume of a rectangular prism is 288 ft3. If its height is 6 feet and its length is 8 feet, what is its width?
A. 6 feet B. 8 feet C. 9 feet D. 12 feet
Question #8MultipleChoice
A cube is 6 feet on each side. What is its volume?

Answers

Q1: The answer is A. pyramid.
A pyramid has one polygon base. A prism has two polygon bases. A cone has one circular base. A cylinder has two circular bases.

Q6: The answer is false.
Surface area of a rectangular prism is:
A = 2(wl + hl + hw)
A1 = 2(4*5 + 6*5 + 6*4) = 2(20+30+24) = 2*74 = 148
A2 = 2(6*4 + 5*4 + 5*6) = 2(24+20+30) = 2*74 = 148

Q7. The answer is A. 6 feet
The volume of rectangular prism is:
V = w * l * h
w = ?
So, just replace the knowing facts:
288 = w * 8 * 6
288 = w * 48
w = 288/48 = 6

Q8: The answer is 216 ft³
The volume of the cube is:
V = a³
Since a = 6, then:
V = 6³ = 216

Answer: #1 is pyramid

Step-by-step explanation: a pyramid can have any polygon as a base

God bless

Which inequality will have a shaded area below the boundary line? A. y - x > 5 B. 2x - 3y < 3 C. 2x - 3y < 7 D. 7x + 2y < 2 E. 3x + 4y > 12

Answers

Answer:
D. 7x + 2y < 2

Explanation:
The two general forma of the inequality are:
y < mx + c .........> In this case, shading is below the boundary line
y > mx + c .........> In this case, shading is above the boundary line

Since we are looking for the inequality with shading below the boundary line, therefore, we are looking for an y < mx + c format

Now, let's check the givens:
y - x > 5
Rearranging, we would get:
y > x + 5
The shading is above the boundary line. This option is incorrect

2x - 3y < 3
Rearranging, we would get:
2x - 3 < 3y
The shading is above the boundary line. This option is incorrect

2x - 3y < 7
Rearranging, we would get:
2x - 7 < 3y
The shading is above the boundary line. This option is incorrect

7x + 2y < 2
Rearranging, we would get:
2y < -7x + 2
The shading is below the boundary line. This option is correct

3x + 4y > 12
Rearranging, we would get:
4y > -3x + 12
The shading is above the boundary line. This option is incorrect

As a second solution, I attached the graphs of the 5 given functions.
Observing these graphs, we will find that the correct one is D

Hope this helps :)

When you change the inequality as the formula of y>ax+b, it is over the boundary line. While the formula is y<ax+b, it is below the boundary line. So we can get the answer is D.

Simplify the expression as much as possible: 6(31/5)(21/3)=

Answers

Final answer:

The expression 6(31/5)(21/3) can be simplified by doing the division first, then multiplication. The final answer is 260.4.

Explanation:

To simplify the expression 6(31/5)(21/3), we must first perform the operations inside the parentheses, the division operations, and then multiply the results together with the other number, 6.

First, perform the division operations in each set of parentheses: (31/5) equals 6.2 and (21/3) equals 7.

Then multiply these two results together: 6.2 times 7 equals 43.4.

Lastly, multiply this result by 6: 43.4 times 6 equals 260.4.

So the expression 6(31/5)(21/3) simplifies to 260.4.

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Anyone a math Genius?
simplify each radical expression.
-21_/27x^9

Answers

ok so according to comments, question is
$-21\sqrt{27x^(9)}$
remember that
$√(xy)$ = $√(x)$ times $√(y)$
and $\sqrt{yx^(2)}$ = $x√(y)$
so
$-21\sqrt{27x^(9)}$ = $-21√(27)\sqrt{x^(9)}$ = $-21√(9)√(3)\sqrt{x^(2)}\sqrt{x^(2)}\sqrt{x^(2)}\sqrt{x^(2)}√(x)$ = $-21(3)√(3)(x)(x)(x)(x)√(x)$ =
$-63x^(4)√(3)√(x)$ = $-63x^(4)√(3x)$

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