15 ( y - 4 ) - 2 (y - 9 ) + 5 (y + 6) = 0

The equivalent expression of [tex]\log_c(\frac{x^2 - 1}{5x})[/tex] is [tex]\log_c(x^2 - 1) - \log_c(5x)[/tex]

The logarithmic expression is given as:

[tex]\log_c(\frac{x^2 - 1}{5x})[/tex]

The law of logarithm states that:

log(a) - log(b) = log(a/b)

This means that the expression can be split as:

[tex]\log_c(\frac{x^2 - 1}{5x}) = \log_c(x^2 - 1) - \log_c(5x)[/tex]

Hence, the equivalent expression of [tex]\log_c(\frac{x^2 - 1}{5x})[/tex] is [tex]\log_c(x^2 - 1) - \log_c(5x)[/tex]

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Answer:

33 1/3

Step-by-step explanation:

divide 2/3 which is 0.66... then multiply that by 5 which is 3.33...

then multiply 6 times 5 which is 30, then add 30 and 3.33... which is 33.33...

in fraction form that is 33 1/3

========================================================

Explanation:

Focus on the bottom most triangle. The upper angle of this triangle is 360/5 = 72 degrees. This is because the regular pentagon is split into five congruent (aka identical) triangles.

Each of the triangles are isosceles. Let x be the measure of the base angles.

Use the rule that adding the three angles of a triangle gets us 180

angle1+angle2+angle3 = 180

x+x+72 = 180

2x+72 = 180

2x = 180-72

2x = 108

x = 108/2

x = 54 is the answer

----------------------

Another way to get the answer:

i = interior angle of a regular polygon with n sides

i = 180(n-2)/n

i = 180(5-2)/5

i = 180(3)/5

i = 540/5

i = 108

Each interior angle of a regular pentagon is 108 degrees.

Angle x marked in blue is half that, so it is 108/2 = 54 degrees

----------------------

A third method:

E = exterior angle of a regular polygon with n sides

E = 360/n

E = 360/5

E = 72 degrees is the measure of each exterior angle

i = 180 - E

i = 180-72

i = 108 is the measure of each interior angle.

To wrap things up, we follow the same exact steps at the end of the 2nd section to get 108/2 = 54 as our answer.

Answer:

a.240.15

Step-by-step explanation:

a.240.15

b.12.0075

c.252.1575

Answer:

Option A ----> -5

Step-by-step explanation:

Slope of a graph is given by the equation :

[tex]\frac{dy}{dx}[/tex] where d means change in .

Lets take the y-intercept (0,2) and (-1,7)

Change in y = 5

Change in x = -1

5/-1 = -5

Our answer will therefore Option A ---> -5

Hope this helped and brainliest please

Answer:

THE ANSWER IS A

Step-by-step explanation:

CORRECT IF I WRONG

9880 different possibilities are there in Sally's new combination option second 9880 is correct.

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

We have:

Total unique numbers consists in a Sally locker = 3

From the digits 0 to 39

Total numbers = 40

Apply combination formula:

= C(40, 3)

= 40!/(3!37!)

= 9880

Thus, 9880 different possibilities are there in Sally's new combination option second 9880 is correct.

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Answer:

16 new releases and 22 classic movies.

The arithmetic sequence that has a common difference of -5 from the options given is: A. 8, 3, -2, -7...

The common difference of an arithmetic sequence is determined as: a term - previous term.

For the sequence, 8, 3, -2, -7,.. the common difference is:

-7 - 2 = -2 - 3 = 3 - 8 = -5.

Therefore, the arithmetic sequence with a common difference of -5 is: A. 8, 3, -2, -7...

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Answer:

4 kg

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Add to find total mass:

2.5 + 3.5 + 3.5 + 5 + 5.5 = 20

Since there is a total of 5 bags and want to evenly distribute divided by 5,

20 / 5 = 4

The solids have the same volume.

Volume is the measure of the capacity that an object holds.

Volume of triangular prism be

= Base area * height

= 12*10

=120 cm³

Volume of rectangular prism be,

=10*3*4

=120 cm³      

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The return on equity for  the firm is 18.75%.

Return on equity=Return on assets +[ (Debt/Equity ratio)×(Return on assets-Return on debt)]

Let plug in the formula

Return on equity=.15+ [(.75)× (.15-.10)]

Return on assets=.15+ (.75×0.05)

Return on assets=.15+0.0375

Return on equity=0.1875×100

Return on equity=18.75%

Therefore the return on equity ratio is 18.75%.

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Answer:

if ur in college then how do u not know this

Step-by-step explanation:

use ur brain

Answer:

761.25 m³

Step-by-step explanation:

l = 15 , w = 14.5 , h = 3.5

Volume of a rectangular prism is given by the formula :

V = lwh

V = 15 × 14.5 × 3.5

V = 761.25

Units will be m³

I am attaching an image for visual understanding

Hope this helped and brainliest please.

The residuals of the linear regression equation are 0.329, -0.346, 0.064, -0.326,  0.049, -0.286,  -0.161, 0.214, 0.429 and 0.059

The regression equation is given as:

y = 0.005x + 3.111

Next, we calculate the predicted values (y) at the corresponding x values.

So, we have:

y = 0.005 * 4 + 3.111 = 3.131

y = 0.005 * 3 + 3.111 = 3.126

y = 0.005 * 5 + 3.111 = 3.136

y = 0.005 * 3 + 3.111 = 3.126

y = 0.005 * 8 + 3.111 = 3.151

y = 0.005 * 15 + 3.111 = 3.186

y = 0.005 * 10 + 3.111 = 3.161

y = 0.005 * 15 + 3.111 = 3.186

y = 0.005 * 6 + 3.111 = 3.141

y = 0.005 * 6 + 3.111 = 3.141

The residuals are then calculated using:

Residual = Actual value - Predicted value

So, we have:

y = 3.46 - 3.131 = 0.329

y = 2.78 - 3.126 = -0.346

y = 3.2 - 3.136 = 0.064

y = 2.8 - 3.126 = -0.326

y = 3.2 - 3.151 = 0.049

y = 2.9 - 3.186 = -0.286

y = 3 - 3.161 = --0.161

y = 3.4 - 3.186 = 0.214

y = 3.57 - 3.141 = 0.429

y = 3.2 - 3.141 = 0.059

Hence, the residuals of the linear regression equation are 0.329, -0.346, 0.064, -0.326,  0.049, -0.286,  -0.161, 0.214, 0.429 and 0.059

See attachment for the residual plot.

The residual plot shows that the linear model from the regression calculator is a good model because the points are not on a straight line

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274

hope that helps

:D

btw i used long division

By applying definitions of trigonometric reasons, Pythagorean theorem and a trigonometric expression, the value of the sin 2θ is equal to - (5/18) · √11.

In this question we must take into accounts the definitions of the trigonometric reasons sine and secant and the Pythagorean theorem as well.

If sec θ < 0 and csc θ > 0, then sin θ > 0 and cos θ < 0, the angle is in the second quadrant (0.5π < θ < π, x < 0, y > 0) and we have the following expression:

sec θ = r/x

[tex]\frac{r}{x}= -\frac{6\sqrt{11}}{11}[/tex]

Then x = - 11, r = 6√11 and the value of y is:

[tex]y = \sqrt{r^{2}-x^{2}}[/tex]

y = 5√11

By trigonometric expressions we have this formula for sin 2θ:

sin 2θ = 2 · sin θ · cos θ

sin 2θ = 2 · (y/r) · (x/r) = (2 · x · y)/r²

sin 2θ = [2 · (- 11) · (5√11)]/396

sin 2θ = - (5/18) · √11

By applying definitions of trigonometric reasons, Pythagorean theorem and a trigonometric expression, the value of the sin 2θ is equal to - (5/18) · √11.

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Answer: 433.5 square miles or 433 1/2 square miles

Step-by-step explanation

[tex]SA = 6x^{2}[/tex]

[tex]SA = 6 *(8.5)^{2} \\\\SA = 6*72.25\\\\SA = 433.5[/tex]

Answer:

O (5,-3.5)

Step-by-step explanation:

The factored form of the quadratic equation  x² - 2x - 3 = 0 is (x - 3)(x + 1)

The quadratic equation can be factored as follows;

x² - 2x - 3 = 0

Therefore, let's find the numbers we can multiply to get -3 and add to get -2.

x² + x - 3x - 3

x(x + 1) - 3(x + 1)

Therefore,

(x - 3)(x + 1)

Therefore, the factored form of x² - 2x - 3 = 0 is (x - 3)(x + 1)

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Answer:

8

Step-by-step explanation:

Answer:

25°

Step-by-step explanation:

hope it helps you solve the question

Answer:

  a.  y = -1/2x - 2

Step-by-step explanation:

The correct answer choice can be determined by finding the slope of the line. The slope is the ratio of rise to run.

__

The x-intercept is 4 units left of the y-axis. As the line "runs" those 4 units, it "rises" -2 units to intercept the y-axis at -2. The slope of the line is ...

  m = rise/run = -2/4 = -1/2

In the slope-intercept form of the equation of a line, the slope is the coefficient of x. This information is sufficient to let us choose the first answer choice.

__

The slope-intercept equation is ...

  y = mx +b . . . . . . . slope m, y-intercept b

We know the slope is -1/2, and the y-intercept is where x=0, at y=-2. Then the equation is ...

  y = -1/2x -2 . . . . . matches choice A

_____

Additional comment

When answering multiple-choice questions, you only need to do enough work to tell which answers are not viable.

When we plot the points, we see that the line has negative slope. (eliminates choice C). The slope is shallow, rather than steep (the x-intercept is farther from the origin than the y-intercept), so the magnitude of the slope is less than 1 and choices B and D are eliminated.

Answer:

2 is the absolute mean deviation

Step-by-step explanation:

absolute mean deviation is

the average of the differences of the data from the average

8, 8, 4, 12

1. take the average

8+8+4+12=32 -> 32/4 = 8

2. subtract each number from this average

8 - 8 = 0

8 - 8 = 0

4 - 8 = 4 (there are no negative answers)

12 - 8 = 4

3. take the average of these subtractions

0+0+4+4=8 -> 8/4 = 2

4. answer: 2 is the absolute mean deviation

Answer:

C. 5/12

Step-by-step explanation:

Finding the missing side :

Taking the tan ratio :

Answer:

Step-by-step explanation: