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2 years ago

If f (x) = StartRoot one-half x minus 10 EndRoot + 3, which inequality can be used to find the domain of f(x)?

Mathematics

2 answers:

Margaret [11]2 years ago

8 0

Answer:

C. One-half x minus 10 greater-than-or-equal-to 0

Step-by-step explanation:

just olya [345]2 years ago

7 0

The inequality that represents the domain of the function is $\frac 12x - 10 \ge 0$

<h3>How to determine the domain?</h3>

The function is given as:

$f(x) = \sqrt{\frac 12x - 10} + 3$

Set the radicand greater than or equal to 0

$\frac 12x - 10 \ge 0$

Multiply through by 2

x - 20 ≥ 0

Add 20 to both sides

x ≥ 20

Hence, the domain of the function is x ≥ 20

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Frank was skiing down big bear mountain. He finished 22% of his skiing in the morning. Then he still had 23.4 miles left. How ma

gtnhenbr [62]

Answer: 6.6 miles

Step-by-step explanation:

Since he finished 22% of his skiing in the morning, that means he still has 78% (100% - 22%) of his skiing left.

The remaining 78% is equivalent to 23.4 miles. We need to know the total miles of the skiing. This will be:

78% of x = 23.4

0.78 × x = 23.4

0.78x = 23.4

x = 23.4 / 0.78

x = 30 miles

Since the total skiing is 30 miles and he has 23.4 miles left, the miles covered in the morning will be:

= 30 - 23.4

= 6.6 miles

8 0

3 years ago

Is 152 prime composite or neither

Nitella [24]

Its a prime number the factor of it are 1,2,4,19,38,76,152.

7 0

3 years ago

Solve each inequality, and then drag the correct solution graph to the inequality.

Nesterboy [21]

The correct solution graph to the inequalities are

$4(9x-18)>3(8x+12)$ → C

$-\frac{1}{3}(12x+6) \geq -2x +14$ → A

$1.6(x+8)\geq 38.4$ → B

(NOTE: The graphs are labelled A, B and C from left to right)

For the first inequality,

$4(9x-18)>3(8x+12)$

First, clear the brackets,

$36x-72>24x+36$

Then, collect like terms

$36x-24x>36+72\\12x >108$

Now divide both sides by 12

$\frac{12x}{12} > \frac{108}{12}$

∴ $x > 9$

For the second inequality

$-\frac{1}{3}(12x+6) \geq -2x +14$

First, clear the fraction by multiplying both sides by 3

$3 \times[-\frac{1}{3}(12x+6)] \geq3 \times( -2x +14)$

$-1(12x+6) \geq -6x +42$

Now, open the bracket

$-12x-6 \geq -6x +42$

Collect like terms

$-6 -42\geq -6x +12x$

$-48\geq 6x$

Divide both sides by 6

$\frac{-48}{6} \geq \frac{6x}{6}$

$-8\geq x$

∴ $x\leq -8$

For the third inequality,

$1.6(x+8)\geq 38.4$

First, clear the brackets

$1.6x + 12.8\geq 38.4$

Collect likes terms

$1.6x \geq 38.4-12.8$

$1.6x \geq 25.6$

Divide both sides by 1.6

$\frac{1.6x}{1.6}\geq \frac{25.6}{1.6}$

∴ $x \geq 16$

Let the graphs be A, B and C from left to right

The first graph (A) shows $x\leq -8$ and this matches the 2nd inequality

The second graph (B) shows $x \geq 16$ and this matches the 3rd inequality

The third graph (C) shows $x > 9$ and this matches the 1st inequality

Hence, the correct solution graph to the inequalities are

$4(9x-18)>3(8x+12)$ → C

$-\frac{1}{3}(12x+6) \geq -2x +14$ → A

$1.6(x+8)\geq 38.4$ → B

Learn more here: brainly.com/question/17448505

8 0

2 years ago

Item Value

7nadin3 [17]

Answer:

TRUE

Step-by-step explanation:

HOPE THIS HELPED!!

7 0

3 years ago

Solve the equation for the bold variable (h)

Aleonysh [2.5K]

This is the formula for the surface area of a cylinder including the ends, like the total surface area of a can of peas.

S = 2·π·r² + 2·π·r · H

Divide each side by 2·π·r :

S/2·π·r = r + H

Subtract r from each side :

H = (S/2·π·r) - r

H = (S - 2·π·r²) / (2·π·r)

8 0

3 years ago

Read 2 more answers