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3 years ago

For which equation is x = 9 a solution?

2 answers:

8 0

Substitute the value of x = 9 to the equations:

$A.\ 3x-7=-34\\\\L_s=3\cdot9-7=27-7=20;\ R_s=-34\\\\L_s\neq R_s\\\\B.\ x-9=1\\\\L_s=9-9=9;\ R_s=1\\\\L_s\neq R_s\\\\C.\ \dfrac{x}{9}-8=9\\\\L_s=\dfrac{9}{9}-8=1-8=-7;\ R_s=9\\\\L_s\neq R_s\\\\D.\ 4x+5=41\\\\L_s=4\cdot9+5=36+5=41;\ R_s=41\\\\L_s=R_s$

Answer: D. 4x + 5 =41

irinina [24]3 years ago

7 0

Answer

<span>D. 4x + 5 = 41

</span><span> 4(9) + 5 = 41
36 + 5 = 41
41 = 41 (TRUE)</span>

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Find the area of the regular hexagon

earnstyle [38]

Answer:

Area = 166cm² (Approximately)

Step-by-step explanation:

To solve this, let's recall the formula for the area of a REGULAR Hexagon.

The area of a REGULAR Hexagon is expressed as:

A = (3√3 * a²) / 2

Where a is the length of one side of the Hexagon.

a= 8cm.

Area = (3√3 * 8²) / 2

Area = (3√3 * 64) / 2

Area = (192√3) / 2

Area = 332.55 / 2

Area = 166.28cm²

Area = 166cm² (Approximately)

3 0

3 years ago

Read 2 more answers

What is the area of kite ABCD?

Alex_Xolod [135]

Answer:

72 square cm

Step-by-step explanation:

Area for a kite can be found by A=pq/2

p = 9

q = 16

(9)(16) = 144

144/2 = 72

5 0

4 years ago

When results from a scholastic assessment test are sent to test-takers, the percentiles associated with their scores are also gi

hram777 [196]

Answer:

The correct option is (D).

Step-by-step explanation:

Percentiles are statistical measures that are used to interpret data. It represents the data value which is more that a specific percentage of the data set.

The <em>n</em>th percentile of a data set is the value that is more that <em>n</em>% of the data set.

⇒ It is provided that a test-taker's score was at the 94th percentile for their verbal grade.

This statement implies that the test taker scored a mark more than 94% of the other test-takers, i.e. he\she performed better than 94% of the other test-takers in the verbal grade.

⇒ Also the test-taker's score was at the 16th percentile for their quantitative grade.

This implies that the test taker scored a mark more than 16% of the other test-takers, i.e. he\she performed better than 16% of the other test-takers in the quantitative grade.

Thus, the correct option is (D).

8 0

4 years ago

I have calculus problems that I need help with.

aleksklad [387]

a. Note that $f(x)=x^ne^{-2x}$ is continuous for all $x$ . If $f(x)$ attains a maximum at $x=3$ , then $f'(3) = 0$ . Compute the derivative of $f$ .

$f'(x) = nx^{n-1} e^{-2x} - 2x^n e^{-2x}$

Evaluate this at $x=3$ and solve for $n$ .

$n\cdot3^{n-1} e^{-6} - 2\cdot3^n e^{-6} = 0$

$n\cdot3^{n-1} = 2\cdot3^n$

$\dfrac n2 = \dfrac{3^n}{3^{n-1}}$

$\dfrac n2 = 3 \implies \boxed{n=6}$

To ensure that a maximum is reached for this value of $n$ , we need to check the sign of the second derivative at this critical point.

$f(x) = x^6 e^{-2x} \\\\ \implies f'(x) = 6x^5 e^{-2x} - 2x^6 e^{-2x} \\\\ \implies f''(x) = 30x^4 e^{-2x} - 24x^5 e^{-2x} + 4x^6 e^{-2x} \\\\ \implies f''(3) = -\dfrac{486}{e^6} < 0$

The second derivative at $x=3$ is negative, which indicate the function is concave downward, which in turn means that $f(3)$ is indeed a (local) maximum.

b. When $n=4$ , we have derivatives

$f(x) = x^4 e^{-2x} \\\\ \implies f'(x) = 4x^3 e^{-2x} - 2x^4 e^{-2x} \\\\ \implies f''(x) = 12x^2 e^{-2x} - 16x^3e^{-2x} + 4x^4e^{-2x}$

Inflection points can occur where the second derivative vanishes.

$12x^2 e^{-2x} - 16x^3 e^{-2x} + 4x^4 e^{-2x} = 0$

$12x^2 - 16x^3 + 4x^4 = 0$

$4x^2 (3 - 4x + x^2) = 0$

$4x^2 (x - 3) (x - 1) = 0$

Then we have three possible inflection points when $x=0$ , $x=1$ , or $x=3$ .

To decide which are actually inflection points, check the sign of $f''$ in each of the intervals $(-\infty,0)$ , $(0, 1)$ , $(1, 3)$ , and $(3,\infty)$ . It's enough to check the sign of any test value of $x$ from each interval.