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3 years ago

Indicate all possible values for the variable in each of the expressions: sqrt(2x+2)+sqrt(6-4x)

Mathematics

1 answer:

IrinaK [193]3 years ago

3 0

Answer:

Given expression:

$\sqrt{2x+2}+\sqrt{6-4x}$

The first root is valid when:

2x + 2 ≥ 0 ⇒ 2x ≥ - 2 ⇒ x ≥ - 1

The second root is valid when:

6 - 4x ≥ 0 ⇒ 4x ≤ 6 ⇒ x ≤ 1.5

So the variable x can get values within interval:

-1 ≤ x ≤ 1.5 or
x = [-1, 1.5]

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For the years from 2002 and projected to 2024, the national health care expenditures H, in billions of dollars, can be modeled b

dmitriy555 [2]

Answer:

2019.

Step-by-step explanation:

We have been given that for the years from 2002 and projected to 2024, the national health care expenditures H, in billions of dollars, can be modeled by $H = 1,500e^{0.053t}$ where t is the number of years past 2000.

To find the year in which national health care expenditures expected to reach $4.0 trillion (that is, $4,000 billion), we will substitute $H=4,000$ in our given formula and solve for t as:

$4,000= 1,500e^{0.053t}$

$\frac{4,000}{1,500}=\frac{ 1,500e^{0.053t}}{1,500}$

$\frac{8}{3}=e^{0.053t}$

$e^{0.053t}=\frac{8}{3}$

Take natural log of both sides:

$\text{ln}(e^{0.053t})=\text{ln}(\frac{8}{3})$

$0.053t\cdot \text{ln}(e)=\text{ln}(\frac{8}{3})$

$0.053t\cdot (1)=0.9808292530117262$

$\frac{0.053t}{0.053}=\frac{0.9808292530117262}{0.053}$

$t=18.506212320$

So in the 18.5 years after 2000 the expenditure will reach 4 trillion.

$2000+18.5=2018.5$

Therefore, in year 2019 national health care expenditures are expected to reach $4.0 trillion.

7 0

4 years ago

Solve 5h + 2(11 - h) = -5 (Find h. Explain each step please.)

pav-90 [236]

Answer:

h = -9

Step-by-step explanation:

Distribute the 2 to the parentheses:

5h + 2(11 - h) = -5

5h + 22 - 2h = -5

Add like terms:

3h + 22 = -5

3h = -27

h = -9

7 0

4 years ago

Read 2 more answers

The diagonals of a parallelogram are 24 meters and 40 meters and

Naddika [18.5K]

Answer:

28 m

Step-by-step explanation:

The longer side can be found using the Law of Cosines. The semi-diagonals are of length 12 and 20 m, and the angle between them facing the long side is 180° -60° = 120°.

c^2 = a^2 +b^2 -2ab·cos(C)

c^2 = 12^2 +20^2 -2·12·20·cos(120°) = 144 +400 +240 = 784

c = √784 = 28

The longer side is 28 meters.

8 0

3 years ago

Answer this quickly plx

Natalija [7]

Answer:

10x+200 $\leq$ 375

Step-by-step explanation:

subtract 200 from both sides

10x $\leq$ 175

divide both sides by 10

x $\leq$ 17.5 cars

Jesse must wash atleast 17.5 cars to afford the bike.

5 0

3 years ago

If 2n + 3(2- 2n) = 14 what is the value of n? (Please give the correct answer, I will give brainliest)

allochka39001 [22]

Answer:

n = -2

Step-by-step explanation:

Eliminating parentheses, you have ...

2n +6 -6n = 14

Combining terms and subtracting 6, you get ...

-4n = 8

Dividing by the coefficient of n gives ...

n = -2

_____

Check

2(-2) +3(2 -2(-2)) = 14

-4 +3(2+4) = 14

-4 +3(6) = 14

-4 +18 = 14 . . . . answer checks OK

5 0

3 years ago