All categories

4 years ago

Solve: x − 2 3 = 61 3 A) 42 9 B) 52 3 C) 6 D) 7

Mathematics

1 answer:

Zepler [3.9K]4 years ago

8 0

Answer:

Step-by-step explanation:

$x-\dfrac{2}{3}=6\dfrac{1}{3}\qquad\text{add}\ \dfrac{2}{3}\ \text{to both sides}\\\\x-\dfrac{2}{3}+\dfrac{2}{3}=6\dfrac{1}{3}+\dfrac{2}{3}\\\\x=6\dfrac{1+2}{3}\\\\x=6\dfrac{3}{3}\\\\x=7$

You might be interested in

A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum heigh

Stella [2.4K]

A parabola is a mirror-symmetrical U-shape.

The equation of the parabola is $\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}$
The focus is $\mathbf{Focus = (80, -1760)}$
The directrix is $\mathbf{y = \frac{1}{640}}$
The axis of the symmetry of parabola is: $\mathbf{x = 80}$

From the question, we have:

$\mathbf{Vertex: (h,k) = (80,10)}$

$\mathbf{Origin: (x,y) = (0,0)}$

The equation of a parabola is:

$\mathbf{y = a(x - h)^2 + k}$

Substitute the values of origin and vertex in $\mathbf{y = a(x - h)^2 + k}$

$\mathbf{0 = a(0 - 80)^2 + 10}$

$\mathbf{0 = a(- 80)^2 + 10}$

$\mathbf{0 = 6400a + 10}$

Collect like terms

$\mathbf{6400a =- 10}$

Solve for a

$\mathbf{a =- \frac{1}{640}}$

Substitute the values of a and the vertex in $\mathbf{y = a(x - h)^2 + k}$

$\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}$

The focus of a parabola is:

$\mathbf{Focus = (h, \frac{k+1}{4a})}$

Substitute the values of a and the vertex in $\mathbf{Focus = (h, \frac{k+1}{4a})}$

$\mathbf{Focus = (80, \frac{10+1}{4 \times -\frac{1}{640}})}$

$\mathbf{Focus = (80, -\frac{11}{\frac{1}{160}})}$

$\mathbf{Focus = (80, -11\times 160)}$

$\mathbf{Focus = (80, -1760)}$

The equation of the directrix is:

$\mathbf{y = -a}$

So, we have:

$\mathbf{y = \frac{1}{640}}$ ----- the directrix

The axis of symmetry is:

$\mathbf{x = -\frac{b}{2a}}$

We have:

$\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}$

Expand

$\mathbf{y = -\frac{1}{640}(x^2 -160x + 6400) +10}$

Expand

$\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x - 10 +10}$

$\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x }$

A quadratic function is represented as:

$\mathbf{y = ax^2 + bx + c}$

So, we have:

$\mathbf{a = -\frac{1}{640}}$

$\mathbf{b = \frac{1}{4}}$

Recall that:

$\mathbf{x = -\frac{b}{2a}}$

So, we have:

$\mathbf{x = -\frac{1/4}{2 \times -1/640}}$

$\mathbf{x = \frac{1/4}{1/320}}$

This gives

$\mathbf{x = \frac{320}{4}}$

$\mathbf{x = 80}$

Hence, the axis of the symmetry of parabola is: $\mathbf{x = 80}$

Read more about parabola at:

brainly.com/question/21685473

6 0

3 years ago

AB=6CM AC= 12cm <br> calculate the length of CD

Brrunno [24]

AB=6cm AC=12cm

AC² = AB + BC²

12² = 6² + CB²

CB² = 12² - 6²

CB² = 144 - 36

CB² = 108

CB = √ 108 cm.

sin 55° = CB / CD

0.81915 = √108 / CD

CD = 10.392 / 0.81915

CD = 12.686 cm

7 0

3 years ago

Read 2 more answers

Write a 2-digit number using digits 2,9,4 draw a quick picture to show the value of your number

larisa [96]

Get the app “Quizlet” search up your question and it will give you an answer!

3 0

3 years ago

The sum of two consecutive natural numbers is 525.<br> Find the numbers.

Luda [366]

Answer:

262 and 263 are consecutive natural numbers whose sum is 525.

Step-by-step explanation:

Natural number are a subset of real numbers consisting in positive integers (i.e. 1, 2, 3, 525) and two natural numbers are consecutive when distance between each other is equal to 1. ( $|x-y| = 1$ , $\forall\,x,y \in \mathbb{N}$ ) We can interpret the statement mathematically by means of the following expression: