All categories

2 years ago

What is the solution set to the inequality

Mathematics

2 answers:

creativ13 [48]2 years ago

5 0

$(4x - 3)(2x - 1) \geqslant 0 \\ \Leftrightarrow \begin{cases}4x - 3 \geqslant 0 \\ 2x - 1 \geqslant 0\end{cases}\: \vee \:\begin{cases}4x - 3 \leqslant 0 \\2x - 1 \leqslant 0 \end{cases} \\ \Leftrightarrow \begin{cases}x \geqslant \frac{3}{4} \\ x \geqslant \frac{1}{2} \end{cases}\: \vee \:\begin{cases}x\leqslant \frac{3}{4} \\x \leqslant \frac{1}{2} \end{cases} \\ \Leftrightarrow x \geqslant \frac{3}{4} \: \vee \: x \leqslant \frac{1}{2} \\ \Rightarrow The\: third\: option$

Grace [21]2 years ago

5 0

Answer:

Option C.

Step-by-step explanation:

The given inequality is

$\left(4x-3\right)\left(2x-1\right)\geq 0$

We know that if $ab\geq 0$ , then either both a and b are positive or both are negative.

Case 1: If both factors are positive.

$\left(4x-3\right)\geq 0\Rightarrow x\geq \frac{3}{4}$

$\left(2x-1\right)\geq 0\Rightarrow x\geq \frac{1}{2}$

Using these two equation we get

$x\geq \frac{3}{4}$

Case 2: If both factors are negative.

$\left(4x-3\right)\leq 0\Rightarrow x\leq \frac{3}{4}$

$\left(2x-1\right)\leq 0\Rightarrow x\leq \frac{1}{2}$

Using these two equation we get

$x\leq \frac{1}{2}$

From case (1) and (2) we get the solution set for the given inequality.

$\{x|x\leq \frac{1}{2}\text{ or }x\geq \frac{3}{4}\}$

Therefore, the correct option is C.

You might be interested in

Deyonne made 25% more cookies than Cameron. They sold cookies for $0.50 each. Let x represent the number of cookies Cameron made

Juli2301 [7.4K]

First we define the varible to use:
x = represent the number of cookies
Cameron:
The amount of cookies he made was:
x
Deyonne:
We can rewrite the amount in different ways:
x + 0.25x
1.25x
Then, the total revenue is:
0.50 * (x + (x + 0.25x))
We rewrite:
0.50 * (x + 1.25x)
0.50 * (2.25x)
Answer:
The following expressions represent possible revenue from the sales:
F. 0.50 (2.25x
C. 0.50 (x + 1.25x)
A. 0.50 [x + (x + 0.25x)]

5 0

3 years ago

Accounting procedures allow a business to evaluate their inventory costs based on two methods: LIFO (Last In First Out) or FIFO

ivanzaharov [21]

Answer: The FIFO method result in lower cost of inventory than the LIFO method.

Step-by-step explanation:

In the FIFO method old inventories are used to determine cost of goods sold (COGS), which result to less income because COGS is lesser, while it is greater in LIFO.

However, in LIFO, old and outdated inventories are valued lower than the present price. It not a good indicator of ending inventory value.

B. To calculate the degree of freedom of the inventory sample given: 1. 225221, 2. 119100, 3. 100113, 4. 212200, 5. 248245.

STEP 1. Find the mean or average of the samples.

Let x be the sample average, and N the sample size which is 5

x = 225221 + 119100 + 100113 + 212200 + 248245/5 = 180975.8

STEP 2. Degree of freedom Df is given as Df = N - 1

Remember, N is the sample size given as 5.

Df = 5 - 1 = 4.

CONCLUSION:

This shows that four numbers from the samples given have the freedom to vary as long as the average remains 180975.8.

8 0

2 years ago

Select the correct answer from each drop-down menu. A parabola is given by the equation y = x2 − 2x − 3. The directrix of the pa

choli [55]

Answer:

Part 1) The directrix of the parabola is y=-4.25

Part 2) The focus of the parabola is F(1,-3.75)

Step-by-step explanation:

we have

$y=x^{2}-2x-3$

This is a vertical parabola open upward

we know that

If a parabola has a vertical axis, the standard form of the equation of the parabola is

$(x - h)^{2}=4p(y - k)$

where

p≠ 0

The vertex of this parabola is at (h, k).

The focus is at (h, k + p).

The directrix is the line y = k - p.

The axis is the line x = h.

step 1

Convert the equation of the parabola in standard form

$y=x^{2}-2x-3$

$y+3=x^{2}-2x$

$y+3+1=x^{2}-2x+1$

$y+4=x^{2}-2x+1$

$y+4=(x-1)^{2}$

$(x-1)^{2}=(y+4)$ ----> equation in standard form

The vertex is the point (1,-4)

4p=1 ------> p=1/4

step 2

Find the directrix of the parabola

The directrix is the line y = k - p

we have

k=-4

p=1/4

substitute the values

y = k - p

y=-4-(1/4)=-17/4

y=-4.25

step 3

Find the focus of the parabola

we know that

The focus is at (h, k + p).

we have

h=1

k=-4

p=1/4

substitute

F(1,-4+1/4)

F(1,-3.75)

4 0

3 years ago

Alicia is making headbands using ribbon she would like to make to make 12headbands each one requires 15.5 inches of ribbon she e

Umnica [9.8K]

Do 15.5×12
then you will know how much ribbon you need. Hope that helps!

6 0

3 years ago

A candy store sells 7 packs of bubble gum for $29.33. How much would it cost to buy 3 packs?

alexira [117]

Hi there,

Recall how 7 packs for gum sell for $29.33.

Before we can calculate how much it would cost to sell 3 packs of gum, we must calculate how much it would first cost to sell 1 pack of gum.

The cost of 1 pack of gum is the current total cost divided by the total amount of gum packs you receive at that price.

In this case, the total cost is $29.33, and we receive 7 gum packs at that price.

Therefore, the cost of 1 pack of gum is $\frac{29.33}{7}$ , which equates to $4.19.

We now know that each pack of gum costs $4.19.

Hence, 3 packs of gum would cost three times that price.

$4.19 * 3 = 12.57$

The cost of 3 packs of gum is $12.57.

Hope that helps!

5 0

3 years ago

Read 2 more answers