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3 years ago

The number is odd. the number is more than 7 times 3. the number is less than 5 times 5. the myster number is what?

Mathematics

2 answers:

Diano4ka-milaya [45]3 years ago

6 0

23 thx my bestie @djalleman1

Ksju [112]3 years ago

4 0

23 is your answer i think

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Identify an equation in point-slope form for the ine parallel to y = -2/3 x+8 that

zlopas [31]

Answer:

$y +5 = -\frac{2}{3}(x - 4)$

Step-by-step explanation:

Given

$y = -\frac{2}{3}x + 8$

Point (4,-5)

Required

Determine the line equation

From the question, we understand that the line is parallel to $y = -\frac{2}{3}x + 8$

This implies that they have the same slope, m

A linear equation is:

$y = mx + b$

Where

$m = slope$

By comparison: $y = mx + b$ and $y = -\frac{2}{3}x + 8$

$m = -\frac{2}{3}$

Next, we determine the line equation using:

$y - y_1 = m(x - x_1)$

Where

$(x_1,y_1) = (4,-5)$ and $m = -\frac{2}{3}$

$y - (-5) = -\frac{2}{3}(x - 4)$

$y +5 = -\frac{2}{3}(x - 4)$

Hence,

<em>Option C is correct</em>

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4 0

3 years ago

Find the integral <br> ∫√(9+x)/(9-x)

densk [106]

I suppose you mean

$\displaystyle \int \frac{\sqrt{9+x}}{9-x} \, dx$

Substitute y = √(9 + x). Solving for x gives x = y² - 9, so that 9 - x = 18 - y², and we have differential dx = 2y dy. Replacing everything in the integral gives

$\displaystyle \int \frac{2y^2}{18 - y^2} \, dy$

Simplify the integrand by dividing:

$\dfrac{2y^2}{18 - y^2} = -2 + \dfrac{36}{18 - y^2}$

$\implies \displaystyle \int \left(\frac{36}{18-y^2} - 2\right) \, dy$

For the first term of this new integral, we have the partial fraction expansion

$\dfrac1{18 - y^2} = \dfrac1{\sqrt{72}} \left(\dfrac1{\sqrt{18}-y} + \dfrac1{\sqrt{18}+y}\right)$

$\implies \displaystyle \frac{36}{\sqrt{72}} \int \left(\frac1{\sqrt{18}-y} + \frac1{\sqrt{18}+y}\right) \, dy - 2 \int dy$

The rest is trivial:

$\displaystyle \sqrt{18} \int \left(\frac1{\sqrt{18}-y} + \frac1{\sqrt{18}+y}\right) \, dy - 2 \int dy$

$= \displaystyle \sqrt{18} \left(\ln\left|\sqrt{18}+y\right| - \ln\left|\sqrt{18}-y\right|\right) - 2y + C$

$= \displaystyle \sqrt{18} \ln\left|\frac{\sqrt{18}+y}{\sqrt{18}-y}\right| - 2y + C$

$= \boxed{\displaystyle \sqrt{18} \ln\left|\frac{\sqrt{18}+\sqrt{9+x}}{\sqrt{18}-\sqrt{9+x}}\right| - 2\sqrt{9+x} + C}$

6 0

2 years ago

Which number is closest to the square root of 71 ?

eduard

Answer:8.4 or 8 depends on the rounding

Step-by-step explanation:

8 0

3 years ago

Sharon hits a golf ball off the ground. The function h represents the height of the golf ball, in feet, t seconds after it is hi

Ulleksa [173]

Answer:

The golf ball will be on the ground at 0 and 6 seconds.

Step-by-step explanation:

Just took the test on Plato

6 0

3 years ago

Consider the algebraic expression (a+b)^10

yawa3891 [41]

Answer:

210, a⁵b⁵

Step-by-step explanation:

The coefficient of a⁶b⁴ is 210

The term in the expansion having the greatest coefficient is a⁵b⁵ with a coefficient of 252

8 0

3 years ago