100 ft per second into the equivalent speed of mph

Determine the form of the following quadratic equation, and identify the values for the key characteristic of the parabola revea

Liono4ka [1.6K]

Answer:

1) The equation is given in factored form

2) The key characteristics of the parabola are;

a. The parabola has 2 real roots and extends to infinity on both sides

b. The x-intercepts of the parabola are (1/2, 0) and (-6, 0)

c. The y intercept is (0, -6)

d. The vertex point is (-2.75, -21.125)

Step-by-step explanation:

The given equation is f(x) = (2·x -1)(x + 6)

Therefore the equation is given in factored form

The key characteristic of the parabola revealed from the form f(x) = (2·x -1)(x + 6) are;

1) Writing the parabola in the intercept form, a(x - p)(x -q) we have;

f(x) = (2·x -1)(x + 6) = 2·(x - 1/2)(x + 6)

p = 1/2, q = -6

Therefore;

Given that a is positive the parabola is concave upwards

2) a. The parabola has 2 real roots and extends to infinity on both sides

b. The x-intercepts of the parabola are p and q which are (1/2, 0) and (-6, 0)

c. The y intercept is a·(-p)·(-q) = 2×(-1/2)×6 = -6

The y intercept is (0, -6)

d. Expanding we get;

f(x) = 2·x² + 11·x - 6

From the

The vertex is h = -b/(2·a) = -11/(2×2) = -2.75

h(2.75) = 2×(-2.75)² + 11×(-2.75) - 6 = -21.125

Therefore, the function is symmetrical about the vertex point (-2.75, -21.125)

7 0

4 years ago

I don’t understand how to proof Cpctc or answer the questions

n200080 [17]

I think that first you need to understand what CPCTC is used for.

Let's start with the definition of congruent triangles.

Definition of congruent triangles
Two triangles are congruent if each side of one triangle is congruent to a corresponding side of the other triangle and each angle of one triangle is congruent to a corresponding angle of the other triangle.

A definition works two ways.
1) If you are told the sides and angles of one triangle are congruent to the corresponding sides and angle of a second triangle, then you can conclude the triangles are congruent.
2) If you are told the triangles are congruent, then you can conclude 6 statements of congruence, 3 for sides and 3 for angles.

Now let's see what CPCTC is and how it works.
CPCTC stands for "corresponding parts of congruent triangles are congruent."
The way it works is this. You can prove triangles congruent by knowing fewer that 6 statements of congruence. You can use ASA, SAS, AAS, SSS, etc. Once you prove two triangles congruent, then by the definition of congruent triangles, there are 6 congruent statements. That is where CPCTC comes in. Once you prove the triangles congruent, then you can conclude two corresponding sides or two corresponding angles are congruent by CPCTC. These two corresponding parts were not involved in proving the triangles congruent.

Problem 1.

Statements                                        Reasons
1. Seg. AD perp. seg. BC               1. Given
2. <ADB & <ADC are right angles     2. Def. of perp. lines
3. <ADB is congr. <ADC                 3. All right angles are congruent
4. Seg. BD is congr. seg CD           4. Given
5. Seg. AD is congr. seg. AD        5. Congruence of segments is reflexive
6. Tr. ABD is congr. tr. ACD           6. SAS
7. Seg. AB is congr. seg. AC        7. CPCTC

4 0

3 years ago

Solve x + 3y = 9<br> 3x − 3y = −13

Minchanka [31]

X + 3y = 9
3x - 3y = -13
--------------add
4x = - 4
x = -4/4
x = -1

x + 3y = 9
-1 + 3y = 9
3y = 9 + 1
3y = 10
y = 10/3

solution (-1,10/3)

5 0

3 years ago

Read 2 more answers

A. Graph D B. Graph C C. Graph B D. Graph A

Neporo4naja [7]

Answer:

The correct option is C

Step-by-step explanation:

The given equation is:

y ≥ 2x - 3

For x= 2

y = 2(2) - 3 = 1

For x=0

y = 2(0) - 3 = -3

WE have two point:

(2,1) and (0,-3)

Graph both points on the coordinate plane.

Join both points and extend the line to find the graph of the line y = 2x - 3

To find the area the represents y ≥ 2x - 3, consider any point, suppose (0,0)

Substitute (0,0) into y ≥ 2x - 3

0 ≥ 2(0) - 3

0 ≥ -3

Hence the equation satisfies.

Which means the area which has the point (0 , 0) shows the region for the equation y ≥ 2x - 3.

The graph is shown.

5 0

3 years ago

jessie hiked 5(1/2) miles on sunday and 6(3/4) miles on sunday .how many miles did jessie hike altogether ?

sladkih [1.3K]

Answer: 12 1/4 miles

Step-by-step explanation:

jessie hiked 5 1/2 + 6 3/4 = lets convert the integers in fractions

= 11/2 + 27/4 = common denominator is 4

22/4+27/4= 49/4 = 12 1/4 miles

7 0

3 years ago