MATHEMATICS HIGH SCHOOL

If two lines are perpendicular and they are defined by the equations, y=2x-3 and y=ax+2, what is the value of a?

Answers

Answer 1

Answer:

Answer:

a = - $(1)/(2)$

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x - 3 ← is in slope- intercept form

with slope m = 2

given a line with slope m then the slope of a line perpendicular to it is

$m_(perpendicular)$ = - $(1)/(m)$ = - $(1)/(2)$

Thus the value of a in the equation y = ax + 2 is a = - $(1)/(2)$

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PLEASE HELP Polynomial Graph Studies Polynomials are great functions to use for modeling real-world scenarios where different intervals of increase and decrease happen. But polynomial equations and graphs can be trickier to work with than other function types. In mathematical modeling, we often create an equation to summarize data and make predictions for information not shown on the original display. In this activity, you’ll create an equation to fit this graph of a polynomial function. Part A Describe the type of function shown in the graph. Part B What are the standard form and the factored form of the function? Part C What are the zeros of the function? Part D Use the zeros to find all of the linear factors of the polynomial function. Part E Write the equation of the graphed function f(x), where a is the leading coefficient. Use the factors found in part D. Express the function as the product of its leading coefficient and the expanded form of the equation in standard form. Part F Use the y-intercept of the graph and your equation from part E to calculate the value of a. Part G Given what you found in all of the previous parts, write the equation for the function shown in the graph.

Answers

Answer:

Here's what I get

Step-by-step explanation:

Part A

The graph shows a polynomial of odd degree. It is probably a third-degree polynomial — a cubic equation.

Part B

The standard form of a cubic equation is

y = ax³ + bx² + cx + d

The factored form of a cubic equation is

y = a(x - b₁)(x² + b₂x + b₃)

If you can factor the quadratic, the factored form becomes

y = a(x - c₁)(x - c₂)(x - c₃)

Part C

The zeros of the function are at x = -25, x = - 15, and x = 15.

Part D

The linear factors of the function are x + 25, x + 15, and x - 15.

Part E

y = a(x + 25)(x + 15)(x - 15) = a(x + 25)(x² - 225)

y = a(x³ + 25x² - 225x - 5625)

Part F

When x = 0, y = 1.

1 = a[0³ +25(0)² - 225(0) - 5625] = a(0 + 0 - 0 -5625) = -5625a

a = -1/5625

Part G

$y = -(1)/(5625)( x^(3) + 25x^(2) - 225x - 5625)\n\ny = \mathbf{ -(1)/(5625) x^(3) - (1)/(225)x^(2) + (1)/(25) x + 1}$

Answer

Actually, the answer should be -0.0007(x+20)(x+5)(x-15)

Step-by-step explanation:

This is continuing off of the previous answer

PART C

The zeros should be (15,0), (-5,0), and (-20,0)

PART D

x - 15, x + 5, and x + 20

PART E

a(x - 15)(x + 5)(x + 20)

Standard: $a(x^(3) + 10x^(2) -275x-1500)$

PART F

The y-intercept is at (0,1), so we replace the x's with 0:

1 = $[(0)x^(3) +10(0)x^(2) -275(0)-1500]$ and this gives us (0+0-0-1500) which also equals -1500

Then we do $(1)/(-1500)$ which gives us -0.0006 repeating which rounds to -0.0007

a= -0.0007

PART G

Just place the numbers where they should go and your answer is

y =-0.0007(x + 20)(x + 5)(x - 15)

the placement for (x + 20) (x + 5) and (x - 15) doesn't matter as long as they are behind -0.0007

Need help.
I 2x +1 I < -4

Answers

the absolute value of a number is always positive. Therefore you cannot have an absolute value equal to a negative number.

the answer would be "no solution"

$| 2x +1 | < -4\n x\in\emptyset$

Solve the following problem: 28 – 18 – 10.
A. 10
B. 0
C. 18
D. 8

Answers

The value of the expression 28 -18 - 10 is 0.

What is subtraction?

Subtraction is a mathematical operation. Which is used to remove terms or objects in the expression.

Given that the expression is 28 - 18 - 10.

The problem is asking you to subtract 18 from 28, and then subtract another 10 from the result.

First, you can perform the operation 28 - 18, which gives you 10.

Then, you can subtract 10 from 10, which gives you 0.

So the final answer is 0, which is option B.

To learn more about subtraction;

brainly.com/question/2346316

#SPJ2

First;

28-18=10

After;

10-10=0

B.

Is 1 prime, composite, or neither?

prime
composite
neither

Answers

Answer: Neither prime nor composite

Step-by-step explanation: Since 1 divides into 1 exactly one time, 1 is the only factor of one. Prime numbers are numbers that only have two factors and composite numbers are numbers with more than two factors. Since 1 only has 1 factor, we will call it neither prime nor composite.

1 is neither prime nor composite

(x^2+1)(x-2)=x^3-2x^2+x-2
Solve for x

Answers

Step 1: Subtract x^3 from both sides.x^3−2x^2+x−2−x^3=x^3−2x^2+x−2−x^3−2x^2+x−2=−2x^2+x−2

Step 2: Add 2x^2 to both sides.−2x^2+x−2+2x^2=−2x^2+x−2+2x^2x−2=x−2

Step 3: Subtract x from both sides.x−2−x=x−2−x−2=−2

Step 4: Add 2 to both sides.−2+2=−2+20=0

Answer:All real numbers are solutions.

-1.5 __ -1.05
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