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3 years ago

Which graph represents the solution to the inequality 3 + 5/2x ≥ 2 − 132?

Mathematics

1 answer:

Leno4ka [110]3 years ago

6 0

Answer:

Option D.

Step-by-step explanation:

We have the inequality:

3 + (5/2)*x ≥ 2*x - 13/2

First, let's try to isolate x in one side of the inequality:

3 + (5/2)*x ≥ 2*x - 13/2

(5/2)*x ≥ 2*x - 13/2 - 3

(5/2)*x - 2*x ≥ - 13/2 - 3

Now all the terms with an x are in the left, and the terms without are in the right.

We can rewrite this inequality as:

(5/2)*x - (4/2)*x ≥ - 13/2 - 6/2

(1/2)*x ≥ -19/2

Now, multiplying both sides by 2 we get:

2*(1/2)*x ≥ (-19/2)*2

x ≥ - 19

So the graph will be a solid point in x = -19, and a ray that extends to the right (the values that are larger than -19)

The correct option is the last graph, option D.

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The manufacturer of a weight-training bench spends $15 to build each bench and sells them for $32. The manufacturer also has fix

nasty-shy [4]

Answer:

Step-by-step explanation:

C(x) = 15x + 25,500....cost function

R(x) = 32x .....revenue function

break even point (when they are equal)....so set them equal and solve for x

15x + 25,500 = 32x

25,500 = 32x - 15x

25,500 = 17x

25,500 / 17 = x

1500 = x.......so the break even point is when 1500 benches are sold

15x + 25,500 = 32x =

15(1500) + 25,500 32(1500) =

22,500 + 25,500 48,000

48,000

and after selling 1500 benches, they will both equal $48,000

7 0

3 years ago

The nation of Finlandia has 120,000 people. Of these, 20,000 are children under 16, 72,000 have jobs, 8,000 don't have jobs but

stepan [7]

Answer: labor force participation rate =60%

unemployment rate = 6.67%

Step-by-step explanation:

The labor force participation rate is computed as

$\text{labor force participation rate}=\dfrac{\text{Total employed persons}}{\text{Total population}}$

i.e. $\text{labor force participation rate}= \dfrac{72000}{120000}$

$= 0.6\ or\ 60 \%$

The unemployment rate is computed as:

$\text{unemployment rate}=\dfrac{\text{Number of personsdon't have jobs }}{\text{Total population}}\\\\\text{unemployment rate}=\dfrac{8000}{120000}\\\\\text{unemployment rate}=0.0667\ or\ 6.67\%$

Hence, labor force participation rate =60%

unemployment rate = 6.67%

6 0

2 years ago

There are 3 islands A,B,C. Island B is east of island A, 8 miles away. Island C is northeast of A, 5 miles away and northwest of

Nostrana [21]

Answer:

The bearing needed to navigate from island B to island C is approximately 38.213º.

Step-by-step explanation:

The geometrical diagram representing the statement is introduced below as attachment, and from Trigonometry we determine that bearing needed to navigate from island B to C by the Cosine Law:

$AC^{2} = AB^{2}+BC^{2}-2\cdot AB\cdot BC\cdot \cos \theta$ (1)

Where:

$AC$ - The distance from A to C, measured in miles.

$AB$ - The distance from A to B, measured in miles.

$BC$ - The distance from B to C, measured in miles.

$\theta$ - Bearing from island B to island C, measured in sexagesimal degrees.

Then, we clear the bearing angle within the equation:

$AC^{2}-AB^{2}-BC^{2}=-2\cdot AB\cdot BC\cdot \cos \theta$

$\cos \theta = \frac{BC^{2}+AB^{2}-AC^{2}}{2\cdot AB\cdot BC}$

$\theta = \cos^{-1}\left(\frac{BC^{2}+AB^{2}-AC^{2}}{2\cdot AB\cdot BC} \right)$ (2)

If we know that $BC = 7\,mi$ , $AB = 8\,mi$ , $AC = 5\,mi$ , then the bearing from island B to island C:

$\theta = \cos^{-1}\left[\frac{(7\mi)^{2}+(8\,mi)^{2}-(5\,mi)^{2}}{2\cdot (8\,mi)\cdot (7\,mi)} \right]$

$\theta \approx 38.213^{\circ}$

The bearing needed to navigate from island B to island C is approximately 38.213º.

8 0

3 years ago

A certain number is the same as the square root of the product of 8 and the number find the number

Rudik [331]

So, we have x=√8x. The square root is a number times itself, so x=√x*x. That means that 8 is x.

6 0

3 years ago

The sum of two polynomials is –yz2 – 3z2 – 4y + 4. If one of the polynomials is y – 4yz2 – 3, what is the other polynomial? –2yz

marishachu [46]

The first polynomial is $y -4yz^2-3$ and let the second polynomial be P(y,z).

If the sum of two polynomials is $-yz^2-3z^2-4y+4$ , then $y-4yz^2-3+P(y,z)=-yz^2-3z^2-4y+4$ .

Take the first polynomial from the left side to the right side:

$P(y,z)=-yz^2-3z^2-4y+4 -(y-4yz^2-3),\\ P(y,z)=-yz^2-3z^2-4y+4 -y+4yz^2+3,\\ P(y,z)=3yz^2-3z^2-5y+7$ .

Answer: the second polynomial is $3yz^2-3z^2-5y+7$ .

3 0

3 years ago

Read 2 more answers