Ask question

Ask question

All categories

2 years ago

9

Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determin

e two values of xx that support your conclusion.
-10x=-80

1 answer:

Serga [27]2 years ago

6 0

Answer:

One Solution

$x = 8$

Step-by-step explanation:

Given

$-10x = -80$

Required

Determine the number of solution and the value of x

The equation is a linear equation and they have just one solution

Solving further [Divide both sides by -10]

$\frac{-10x}{-10} = \frac{-80}{-10}$

$x = \frac{-80}{-10}$

$x = 8$

Hence;

<em>x has only one value</em>

You might be interested in

Write an expression that represents the volume of a rectangular prism (box) with length 2003-02-02-00-00_files/i0260000.jpg, wid

k0ka [10]

h=5 in

w-6 in

l=12 in

SA/V=2*12*6+2*6*5+2*12*5/12*6*5

817:180

This is just an example do not use this exact equation and number! Hope it helps. : )

3 0

2 years ago

A boat tour guide expects his tour to travel at a rate of x mph on the first leg of the trip. On the return route, the boat trav

Georgia [21]

<em><u>The intervals included in solution are:</u></em>

$\frac{1}{x} + \frac{1}{x}-10\ge \frac{2}{24}\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:0$

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

Given that,

A boat tour guide expects his tour to travel at a rate of x mph on the first leg of the trip

On the return route, the boat travels against the current, decreasing the boat's rate by 10 mph

The group needs to travel an average of at least 24 mph

<em><u>Given inequality is:</u></em>

$\frac{1}{x} + \frac{1}{x} - 10\geq \frac{2}{24}$

<em><u>We have to solve the inequality</u></em>

$\frac{1}{x} + \frac{1}{x} - 10\geq \frac{2}{24}\\\\\frac{2}{x} - 10\geq \frac{2}{24}$

$\mathrm{Subtract\:}\frac{2}{24}\mathrm{\:from\:both\:sides}\\\\\frac{2}{x}-10-\frac{2}{24}\ge \frac{2}{24}-\frac{2}{24}\\\\Simplify\\\\\frac{2}{x}-10-\frac{2}{24}\ge \:0$

$\frac{2}{x}-\frac{10}{1}-\frac{2}{24} \geq 0\\\\\frac{ 2 \times 24}{x \times 24} -\frac{10 \times 24}{1 \times 24} - \frac{2 \times x }{24 \times x}\geq 0\\\\\frac{48}{24x}-\frac{240x}{24x}-\frac{2x}{24x}\geq 0\\\\Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions\\\\\frac{48-240x-2x}{24x}\geq 0\\\\Add\:similar\:elements\\\\\frac{48-242x}{24x}\ge \:0$

$\mathrm{Multiply\:both\:sides\:by\:}24\\\\\frac{24\left(48-242x\right)}{24x}\ge \:0\cdot \:24\\\\Simplify\\\\\frac{48-242x}{x}\ge \:0\\\\Factor\ common\ terms\\\\\frac{-2\left(121x-24\right)}{x}\ge \:0\\\\\mathrm{Multiply\:both\:sides\:by\:}-1\mathrm{\:\left(reverse\:the\:inequality\right)}$

When we multiply or divide both sides by negative number, then we must flip the inequality sign

$\frac{\left(-2\left(121x-24\right)\right)\left(-1\right)}{x}\le \:0\cdot \left(-1\right)\\\\\frac{2\left(121x-24\right)}{x}\le \:0\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\\\frac{\frac{2\left(121x-24\right)}{x}}{2}\le \frac{0}{2}\\\\Simplify\\\\\frac{121x-24}{x}\le \:0$

$\mathrm{Find\:the\:signs\:of\:the\:factors\:of\:}\frac{121x-24}{x}\\$

This is attached as figure below

From the attached table,

$\mathrm{Identify\:the\:intervals\:that\:satisfy\:the\:required\:condition:}\:\le \:\:0\\\\0$

<em><u>Therefore, solution set is given as</u></em>:

$\frac{1}{x} + \frac{1}{x}-10\ge \frac{2}{24}\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:0$

8 0

2 years ago

Read 2 more answers

Jamie made the tree diagram below to show the different choices he has for ordering a pizza for lunch. According to the tree dia

USPshnik [31]

Sizes = Small, Medium and Large, so they has 3 choices for size.

Crust = Thin or thick for each size, so they have 2 choices for crust.

Topping = Tomato or meatball for each one, so they have 2 choices for toppings.

The answer would be:

<span>Three choices for size, two choices for crust, and two choices for topping</span>

8 0

2 years ago

Read 3 more answers

On Monday, the closing value of a share of stock in Company ABC, was 74.01. On Tuesday, it closed at 73.67, and on Wednesday, it

Elenna [48]

Answer:

$957.71$

Step-by-step explanation:

Given: On Monday, the closing value of a share of stock in Company ABC, was $74.01$ . On Tuesday, it closed at $73.67$ , and on Wednesday, it closed at $74.32$ . On Thursday, the change in stock value was $-1.48$ . And, on Friday, Company ABC's stock gained $0.89$ points.

To Find: One shareholder owns $13$ shares of Company ABC's stock. What was the total value of their stock in this company at the close of Tuesday.

Solution:

Closing value of Shares of company ABC on Monday $=74.01$

Closing value of Shares of company ABC on Tuesday $=73.67$

Closing value of Shares of company ABC on Wednesday $=74.32$

on Thursday change in stock value was $-1.48$

Closing value of Shares of company ABC on Thursday $=72.84$

on Friday comapny's stock gained $0.89$ points

Closing value of Shares of company ABC on Friday $=73.73$

As one shareholder owns $13$ shares of company

Total value of shares on Tuesday is

$=\text{number of shares}\times\text{closing stock value on tuesday}$

$=13\times73.67$

$=957.71$

Hence total value of shareholder's share on close of Tuesday is $957.71$

6 0

2 years ago

Read 2 more answers

The table shows y as a function of x. Suppose a point is added to this table. Which choice gives a point that preserves the func

Hunter-Best [27]

Answer:

<em>A) (-5,7)</em>

Step-by-step explanation:

<u>Functions and Relations</u>

A set of values A can have a relation with another set B as long as at least one element of A has at least one image in B. Functions are special relations where each element of A (the domain of the function) has one and only one image on B (the range of the function).

By looking at the options, we can see that x=9, x=-8, and x=-1 already have defined values in Y, so if we define another value for any of them the relation will stop being a function. The only possible choice to preserve the function is the option

$\boxed{A)\ (-5,7)}$

8 0

2 years ago