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faust18 [17]
3 years ago
7

84/12 = 28/x 1. x=4 2. X=28

Mathematics
1 answer:
yan [13]3 years ago
5 0

Answer:

x = 4

Step-by-step explanation:

We can use cross products to solve

84/12 = 28/x

84 * x = 12 *28

Divide each side by 84

84x/84 = 12*28/84

x =4

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Identify the vertex, axis of symmetry, minimum or maximum, domain, and range of the function f(
alekssr [168]

Identify the vertex, axis of symmetry, minimum or maximum, domain, and range of the function ()=−(+)^−

<em><u>Answer:</u></em>

vertex = (-4, -5)

Axis of symmetry = -4

use the (-4, -5) to find the minimum value

Domain = ( - \infty, \infty ) , [ x | x\ is\ real ]\\\\Range = [ -5, \infty ), y\geq -5

<em><u>Solution:</u></em>

Given function is:

f(x) = (x+4)^2 - 5

The equation in vertex form is given as:

y = a(x-h)^2+k

Where, (h, k) is constant

On comparing give function with vertex form,

h = -4

k = -5

Vertex is (-4 , -5)

Axis of symmetry : x co-ordinate of vertex

Thus, axis of symmetry = -4

The coefficient of x^2 is positive in given function.

Thus the vertex point will be a minimum

Minimum\ value = f(\frac{-b}{a})

f(x) = x^2 + 8x + 16 - 5\\\\f(x) = x^2 + 8x + 11

f(x) = ax^2+bx+c

On comparing,

a = 1

b = 8

x = \frac{-b}{2a} = \frac{-8}{2 \times 1} = -4

f(-4) = (-4)^2 + 8(-4) + 11 = 16 - 32 + 11 = -5

Thus, use the (-4, -5) to find the minimum value

Domain and range

f(x) = (x+4)^2 - 5

The domain is the input values shown on the x-axis

The range is the set of possible output values f(x)

Therefore,

Domain = ( - \infty, \infty ) , [ x | x\ is\ real ]\\\\Range = [ -5, \infty ), y\geq -5

4 0
3 years ago
Select the equivalent expression. <br><br> A, B or C?
Alina [70]

Answer:

  A

Step-by-step explanation:

The relevant rules of exponents are ...

  (a^b)^c = a^(bc)

  a^-b = 1/a^b

__

  \left(\dfrac{2^{-10}}{4^2}\right)^7=\dfrac{2^{(-10)(7)}}{4^{(2)(7)}}=\dfrac{2^{-70}}{4^{14}}\\\\=\boxed{\dfrac{1}{2^{70}\cdot 4^{14}}}

6 0
3 years ago
Find the area of the shape
Gwar [14]

Answer:

3pi

Step-by-step explanation:

First find the area of the entire circle

A = pi r^2

A = pi * 2^2

A = 4 pi

We know that this is 3/4 of a circle so multiply the area by the fraction of the circle

3/4 * 4 pi

3 pi

4 0
3 years ago
Read 2 more answers
The 70th term of an arithmatic sequence is 121.5 the common difference is 1.5. Find a12. (write a rule to find a12)
Katen [24]

Answer:

a_{12} = 34.5

Step-by-step explanation:

The n th term of an arithmetic sequence is

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a_{70} = 121.5, then

a₁ + (69 × 1.5) = 121.5

a₁ + 103.5 = 121.5 ( subtract 103.5 from both sides )

a₁ = 18

Hence

a_{12} = 18 + (11 × 1.5) = 18 + 16.5 = 34.5

8 0
2 years ago
Read 2 more answers
Select all the values that make the inequality true​
elena55 [62]

Answer:8

Step-by-step explanation: it cannot be 2, 6, or 5 because they are all less than 7.

7 0
3 years ago
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