All categories

3 years ago

Write 10x² + 3x -2=-1 in the form a(x+h)²+k clearly stating

Mathematics

1 answer:

Fofino [41]3 years ago

7 0

Answer:

Below in bold.

Step-by-step explanation:

10x² + 3x -2 = -1

10x^2 + 3x - 1 = 0 Taking 10 out from the first 2 terms:-

10(x^2 + 0.3) - 1 = 0 Completing the square:

10[(x + 0.15)^2 - 0.15^2] - 1 = 0

10[(x + 0.15)^2 - 0.0225] - 1 = 0

10(x + 0.15)^2 - 0.225 - 1 = 0

10(x + 0.15)^2 - 1.225 = 0 is vertex form.

The vertex (turning point is at (-0.15, -1.225).

y- intercept is at the point where x = 0,

- that is at y = 10(0.15)^2 - 1.225 = -1

So at (0, -1).

Solving for x:

10(x + 0.15)^2 - 1.225 = 0

(x + 0.15)^2 = 0.1225

x + 0.15 = +/- sqrt 0.1225

x = -0.15 +/- sqrt 0.1225

The roots are -0.5, 0.2

You might be interested in

Please help ONLY ONE QUESTION !!

xxTIMURxx [149]

Answer:

slope = - 4, y- intercept = 9

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 = - 4x + 9 is in slope- intercept form

with slope m = - 4 and y- intercept c = 9

A proportional relationship has the form

y = mx

y = - 4x + 9 is not in this form

Hence the relationship is not proportional

6 0

3 years ago

For the geometric sequence of a1=2 and r=2 find a5

Brrunno [24]

Answer:

$a_5 = 32$

Step-by-step explanation:

The nth term for the geometric sequence is given by:

$a_n = a_1 \cdot r^{n-1}$

where,

$a_1$ is the first term

r is the common ratio

n is the number of terms.

As per the statement:

For the geometric sequence of $a_1=2$ and r=2

We have to find $a_5$

for n = 5;

$a_5=a_1 \cdot r^{n-1}$

Substitute the given values we have;

$a_5 = 2 \cdot 2^4 = 2 \cdot 16$

⇒ $a_5 = 32$

Therefore, the value of $a_5$ is, 32

3 0

4 years ago

A need help Dilations-He Said, She Said (12/10)

Elodia [21]

Answer:

We conclude that the original triangle ΔDEF is dilated by a scale factor of 5/2 to get the image triangle ΔD'E'F'.

Therefore, 'Cárl' is correct. Hence, option 'a' is correct.

Step-by-step explanation:

Checking the location of the vertices of the original triangle ΔDEF

D(-2, 4)
E(2, 4)
F(0, 2)

Checking the location of the dilated vertices of the image triangle ΔD'E'F'

D'(-5, 10)
E'(5, 10)
F'(0, 5)

Notice that if we multiply the vertices of the original triangle ΔDEF by 5/2, we get the correct image vertices of image triangleΔD'E'F'

i.e.

D(-2, 4) → D'(5/2 (-2), 5/2 (4)) → D'(-5, 10)

E(2, 4) → E'(5/2 (2), 5/2(4)) → D'(5, 10)

F(0, 2) → E'(5/2 (0), 5/2(2)) → F'(0, 5)

Thus, we conclude that the original triangle ΔDEF is dilated by a scale factor of 5/2 to get the image triangle ΔD'E'F'.

Therefore, 'Cárl' is correct. Hence, option 'a' is correct.

6 0

3 years ago

Simplify -12x^4/x^4+8x^5

alexgriva [62]

Answer:

OPTION A: $\frac{12}{1 + 8x}$ , where $x \ne - \frac{1}{8}$ .

Step-by-step explanation:

Given: $\frac{- 12x^4}{x^4 + 8x^5}$

Taking $x^4$ common outside in the denominator, we get:

$= \frac{-12x^4}{(x^4)(1 + 8x)}$

$x^4$ will get cancelled on the numerator and denominator, we get:

$= \frac{-12}{1 + 8x}$

we know that the denominator can not be zero.

That means, 1 + 8x $\ne$ 0.

$\implies 8x \ne -1$

$\implies x \ne \frac{-1}{8}$

So, the answer is: $\frac{-12}{1 + 8x}$ , where $x \ne \frac{-1}{8}$ .

6 0

3 years ago

Freeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee points

masya89 [10]

Step-by-step explanation:

thank you very much.....

5 0

3 years ago