Give three examples of equations where there will be no solution.

Hat is the equation of the quadratic function with a vertex at (2,–25) and an x-intercept at (7,0)?

Novosadov [1.4K]

Answer:

y = x² - 4x - 21

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (2, - 25), thus

y = a(x - 2)² - 25

To find a substitute (7, 0) into the equation

0 = a(7 - 2)² - 25 = a(5)² - 25 = 25a - 25 ( add 25 from both sides )

25a = 25 ( divide both sides by 25

a = 1, thus

y = (x - 2)² - 25 ← in vertex form

Expand and simplify

y = x² - 4x + 4 - 25

y = x² - 4x - 21 ← in standard form

8 0

3 years ago

Mrs. Martini is 6 years more than 3 times as old as Tony. Eight years ago, she

zalisa [80]

Mrs Martini age is 42 years and Tony age is 12 years

Step-by-step explanation:

The given is:

Mrs. Martini is 6 years more than 3 times as old as Tony
Eight years ago, she was 2 years less than 9 times as old as he was then

Assume that Tony is x years old now

∵ Mrs. Martini is 6 years more than 3 times as old as Tony

∵ Tony is x years old

- Multiply the age of Tony by 3 and add 6 to the product

∴ The age of Mrs Martini = 3 x + 6

8 years ago

- Subtract 8 from the age of each one

Tony age = (x - 8)

Mrs Martini age = (3 x + 6) - 8 = 3 x + 6 - 8 = 3 x - 2

∵ Eight years ago, Mrs Martini was 2 years less than 9 times as old

as Tony was then

- Multiply Tony age by 9 and subtract 2 from the product

∵ Tony age from 8 years ago = x - 8

∵ Mrs Martini age from 8 years ago = 3 x - 2

∴ 9(x - 8) - 2 = 3 x - 2

- Simplify the left hand side

∴ 9 x - 72 - 2 = 3 x - 2

- Add like terms

∴ 9 x - 74 = 3 x - 2

- Subtract 3 x from both sides

∴ 6 x - 74 = -2

- Add 74 to both sides

∴ 6 x = 72

- Divide both sides by 6

∴ x = 12

∵ x represents the age of Tony

∴ Tony is 12 years old

∴ 3 x + 6 is the age of Mrs Martini

- Substitute x by 12

∵ 3(12) + 6 = 36 + 6 = 42

∴ Mrs Martini is 42 years old

Mrs Martini age is 42 years and Tony age is 12 years

Learn more:

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6 0

2 years ago

Given the polynomial bellow which statement is true?

lions [1.4K]

Answer:

I think its A

Step-by-step explanation:

I factored the polynomial and its factors turned out to be (x-1)(x^2-2x-4), which eliminated the possibilities of 2 and 3. Then i replaced the (-1) in the place of the x and it turned out to be equal to 2, making the first statement true.

5 0

2 years ago

Vernon's work for finding the value of x is shown below. Lines A C and B D intersect at point E. Angle A E D is (16 x + 8) degre

Marta_Voda [28]

Answer:

<em>No, he should have set the sum of ∠AED and ∠DEC equal to 180°, rather then setting ∠AED and ∠DEC equal to each other</em>

Step-by-step explanation:

Find the diagram attached

If line AC and BD intersects, then m<AED + m<DEC = 180 (sum of angle on a straight line is 180 degrees)

Given

m<AED = 16x+8

m<DEC = 76 degrees

16x + 8 + 76 = 180

16x + 84 = 180

16x = 180-84

16x = 96

x = 96/16

x = 6

Hence the value of x is 6

Hence the correct option is <em>No, he should have set the sum of ∠AED and ∠DEC equal to 180°, rather then setting ∠AED and ∠DEC equal to each other</em>

5 0

2 years ago

Read 2 more answers

The Toblerone candy comes in a package like the triangular prism. The bases of the triangles are 2 inches with a height of 2.5 i

castortr0y [4]

Answer: 50 cubic in .

Step-by-step explanation: 10x2= 20 and then 20x2.5=50

6 0

2 years ago