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3 years ago

10 - 2.5x > 35I need help

Mathematics

2 answers:

kvasek [131]3 years ago

8 0

Answer:

x<-10

Step-by-step explanation:

10-2.5x>35

2.5x>10-35

2.5x>-25

x>-25/2.5

x>-10

x<-10

erica [24]3 years ago

8 0

Answer:

x < -10

Step-by-step explanation:

-2.5x > 35-10

-2.5x > 25

-2.5x > 25/-2.5

x > -10

You have to switch the sign because you divided it by negative

x<-10

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Determine the domain of the function (fog) (x) where f(x) = 3x-1/x-4 and g(x)=x+1/x

Mrac [35]

Answer:

$(-\infty,0)\cup(0, \frac{1}{3})\cup (\frac{1}{3},\infty)$

Step-by-step explanation:

The given functions are $f(x)=\frac{3x-1}{x-4}$ and $g(x)=\frac{x+1}{x}$ .

We now composed the two functions to find:

$(f\circ g)(x)=f(g(x))$

$\implies (f\circ g)(x)=f(\frac{x+1}{x})$

$\implies (f\circ g)(x)=\frac{3(\frac{x+1}{x})+1}{\frac{x+1}{x}-4}$

$\implies (f\circ g)(x)=\frac{4x+3}{1-3x}$

This function is defined if the denominator is not zero.

$1-3x\ne0$

$x\ne\frac{1}{3}$

We write this in interval notation as:

$(-\infty,\frac{1}{3})\cup (\frac{1}{3},\infty)$

We need to be cautious here as x=0 is not in the domain of g(x).

Therefore the domain of $(f\circ g)(x)$ is

$(-\infty,0)\cup(0, \frac{1}{3})\cup (\frac{1}{3},\infty)$

4 0

3 years ago

A rectangle has a length of 34 inches less than 5 times it’s width. If the area of the rectangle is 867 square inches, find the

pshichka [43]

Length of the rectangle is 51 inches

Solution:

Given that

Length of the rectangle in 34 miles less than 5 times its width

Area of rectangle = 867 square inches

Need to determine length of the rectangle.

Let assume width of the rectangle be represented by variable x.

So 5 times width of the rectangle =5x

34 inches less than 5 times width of the rectangle = 5x – 34

As Length of the rectangle in 34 miles less than 5 times its width

=> Length of the rectangle = 5x – 34

The formula for rectangle is given as:

$\text { area of rectangle }=length \times width$

As given that Area of rectangle = 867 square inches

$\begin{array}{l}{=>867=(5 x-34) \times(x)} \\\\ {=>5 x^{2}-34 x-867=0}\end{array}$

On solving quadratic equation by using quadratic formula

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

In our case a = 5, b = -34 and c = -867

On substituting value of a, b and c in quadratic formula we get

$\begin{array}{l}{x=\frac{-(-34) \pm \sqrt{(-34)^{2}-4 \times 5 \times(-867)}}{2 \times 5}} \\\\ {=>x=\frac{34 \pm \sqrt{18496}}{10}=\frac{34+136}{10}} \\\\ {=>x=\frac{34+136}{10}=17 \text { or } x=\frac{34-136}{10}=-10.2}\end{array}$

Since x represents width, it cannot be negative, so x = 17

Length of the rectangle = 5x – 34 = 5(17) – 34 = 51

Hence length of the rectangle is 51 inches

5 0

3 years ago

Solve the following quadratic equation for all values of x in simplest form. (x-4)^2=33

Brrunno [24]

$\huge\text{$x=\boxed{\sqrt{33}+4,\ -\sqrt{33}+4}$}$

To solve for $x$ , we need to isolate it on one side of the equation.

Take the square root of both sides, making sure to use both positive and negative roots.

$\begin{aligned}(x-4)^2&=33\\x-4&=\pm\sqrt{33}\end{aligned}$

$\sqrt{33}$ cannot be simplified, so we'll leave it as-is.

Add $4$ to both sides to fully isolate $x$ .

$x=\pm\sqrt{33}+4$

Expand the solution by making two solutions, one where $\sqrt{33}$ is positive and one where it's negative.

$x=\sqrt{33}+4,\ x=-\sqrt{33}+4\\x=\boxed{\sqrt{33}+4,\ -\sqrt{33}+4}$

5 0

3 years ago

Read 2 more answers

Standard slope intercept form simplify all fractions 2y-4x=-16

Shtirlitz [24]

Answer: y= 2x-8

Step-by-step explanation:

2y-4x=-16

2y=-16+4x

y=-8+2x

y= 2x-8

4 0

3 years ago

Tickets to the zoo cost $12 for adults and $8 for children. The school has a budget of $240 for the field trip. An equation repr

Oxana [17]

Answer:

18 children

Step-by-step explanation:

Given

$240 = 12x +8y$

Required (missing part of the question):

Number of children that will be able to go to the zoo if 8 adult tickets are purchased

The graph is missing. However, the question can be solved without the graph.

From the question and equation, we can deduce the following:

x represents adults
y represents children

So, when 8 adult tickets were sold.

This means

$x = 8$

Substitute 8 for x in $240 = 12x +8y$

$240= 12 * 8 + 8y$

$240= 96+ 8y$

Subtract 96 from both sides

$240 - 96 = 96 - 96 + 8y$

$144 = 8y$

$8y = 144$

Solve for y

$y= \frac{144}{8}$

$y= 18$

This means that 18 children will be able to go

5 0

3 years ago

10 - 2.5x > 35I need help​

10 - 2.5x > 35I need help