If given the equation y = 3(x + 5)2 - 4, what is the vertex of the parabola

the sum of three number number in an artithmetic product is 21. if second number isreduced by 1 and third term is increased by 1

grin007 [14]

The three numbers will be 12, 7, 2 and 3, 7, 11.

<h3>What is a sequence?</h3>

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.

Let the three consecutive numbers be a, a + d, and a + 2d

The sum of three numbers which are consecutive terms of an A.P. is 21.

a + a + d + a + 2d = 21

3(a + d) = 21

a = 7 - d

If the second number is reduced by 1 and the third term is increased by 1 we obtain the geometric product.

Then the number will be a, a + d − 1, a + 2d + 1. Then we have

$\rm \dfrac{a + d - 1}{a} = \dfrac{a + 2d + 1}{a + d - 1}$

On simplifying, we have

36 = a (8 + d)

a² - 15a + 36 = 0

On factorizing, the value of a will be

a² - 15a + 36 = 0

a² - 12a - 3a + 36 = 0

(a - 12)(a - 3) = 0

a = 3, 12

If a = 12, then the value of d will be

d = 7 - 12

d = -5

If a = 3, then the value of d will be

d = 7 - 3

d = 4

Then the three numbers will be 12, 7, 2 and 3, 7, 11.

More about the sequence link is given below.

brainly.com/question/21961097

#SPJ1

7 0

2 years ago

Which phrase correctly represents the algebraic expression for 22-n?

Harrizon [31]

Answer:

D

Step-by-step explanation:

3 0

3 years ago

If cos(x) = Three-fourths and tan(x) < 0, what is cos(2x)?

makvit [3.9K]

Step-by-step explanation:

The value of sin(2x) is \sin(2x) = - \frac{\sqrt{15}}{8}sin(2x)=−

8

15

How to determine the value of sin(2x)

The cosine ratio is given as:

\cos(x) = -\frac 14cos(x)=−

4

1

Calculate sine(x) using the following identity equation

\sin^2(x) + \cos^2(x) = 1sin

2

(x)+cos

2

(x)=1

So we have:

\sin^2(x) + (1/4)^2 = 1sin

2

(x)+(1/4)

2

=1

\sin^2(x) + 1/16= 1sin

2

(x)+1/16=1

Subtract 1/16 from both sides

\sin^2(x) = 15/16sin

2

(x)=15/16

Take the square root of both sides

\sin(x) = \pm \sqrt{15/16

Given that

tan(x) < 0

It means that:

sin(x) < 0

So, we have:

\sin(x) = -\sqrt{15/16

Simplify

\sin(x) = \sqrt{15}/4sin(x)=

15

/4

sin(2x) is then calculated as:

\sin(2x) = 2\sin(x)\cos(x)sin(2x)=2sin(x)cos(x)

So, we have:

\sin(2x) = -2 * \frac{\sqrt{15}}{4} * \frac 14sin(2x)=−2∗

4

15

∗

4

1

This gives

\sin(2x) = - \frac{\sqrt{15}}{8}sin(2x)=−

8

15

6 0

2 years ago

Read 2 more answers

If f(x) and f⁻¹(x) are inverse functions of each other and f(x)=2x+5, what is f⁻¹(8)?

dexar [7]

Answer:

3/2.

Step-by-step explanation:

f(x)=2x+5 Finding the inverse:

y = 2x + 5

2x = y - 5

x = (y - 5)/2

So the inverse f-1(x) = (x - 5)/2

and f-1(8) = (8-5)/2

= 3/2.

3 0

3 years ago

Last year Baron Enterprises had $800 million of sales, and it had $270 million of fixed assets that were used at 65% of capacity

Svetllana [295]

Answer: B. $430.80

Step-by-step explanation:

Given : Last year Baron Enterprises had $800 million of sales.

It had $270 million of fixed assets that were used at 65% (=0.65) of capacity last year.

Now, the used asset = $0.65\times270=\$175.5$ million

Now, Baron Enterprises had $800 million of sales in $175.5 million of assets , if we use all of $270 million of fixed assets , then the sales will be :-

$\dfrac{800}{175.5}\times270=1230.76923077\approx1230.80\text{ million}$

Now, the increase in Baron's sales before it is required to increase its fixed assets = $\$1230.80-$800=\$430.80\text{ millions}$

Hence, the increase in Baron's ( in million ) sales before it is required to increase its fixed assets = $430.80

8 0

3 years ago