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3 years ago

Find the exact solution to the equation. 10- log base 4 (x+6)=9

1 answer:

4 0

This will require some solving.

$10 - \log_4(x + 6) = 9$
$log_4(x + 6) = 1$
$4^{\log_4(x + 6)} = 4$
$x + 6 = 4$
$\boxed{x = -2}$

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11. <br> Find the equation of the line that goes through the points (4, 4) and (8, 6).

Vladimir [108]

Answer:

4,8

Step-by-step explanation:

because the lins equation goes through in 6

6 0

2 years ago

Find the y- intercept of the following equation y = 6x + 10<br> Please help quick!

n200080 [17]

The slope is 6 and the y intercept is 10. Mark brainliest would be aporeciated

8 0

4 years ago

Yesterday, stanley's doughnut shop sold 2/3 as many chocolate doughnuts as cinnamon doughnuts. if they sold 7 1/4 trays of cinna

katovenus [111]

You figure out the amount of chocolate doughnuts sold by multiplying 2/3 by 7 1/4

first you change 7 1/4 to an improper fraction:
7 1/4= 29/4
now multiply 2/3×29/4 by multiplying the two numerators then putting that over the two denominators multiplied: (2×29)/(3×4)=58/12
now simplify:58/12=4 10/12= 4 5/6

the answer is Stanley's doughnut shop sold
4 5/6 trays of chocolate doughnuts

5 0

3 years ago

If cde is a straight angle, de bisects gdh, m gde = (8x-1), m edh = (6x-15), and m cdf= 43, find each measure.

Sergio [31]

Answer:

x = 7°

<GDH = 112°

<FDH = 192°

<FDE = 135°

Step-by-step explanation:

If DE bisects <GDH this means that <GDE = <EDH

Given <GDE = (8x+1)° and <EDH = (6x+15)° then;

8x+1 = 6x+15

8x-6x = 15-1

2x = 14

x = 7°

Since <GDH = <GDE + <EDH

<GDH = 8x-1+6x+15

<GDH = 14x+14

<GDH = 14(7)+14

<GDH = 98+14

<GDH = 112°

For <FDH,

Note that sum of angle on a straight line is 180°

<FDH = <FDG + <GDE + <EDH

<FDH = <FDG + <GDH

<FDG = 180-(43+8x+1)

<FDG = 180-44-8x = 136-8x

<FDH = 136-8x+112

<FDH = 248-8x

<FDH = 248-8(7)

<FDH = 248-56

<FDH = 192°

For <FDE;

<FDE = <FDG + <GDE

<FDE = 136-8x+8x-1

<FDE = 135°

7 0

3 years ago

Two cars are driving towards an intersection from perpendicular directions.

FrozenT [24]

For a better understanding of the solution provided here please find the diagram in the attached file.

In the diagram, A is the intersection. B is the position of the first car and C is the position of the second car. As can be clearly seen, as per the directions given in the question, the cars and the intersection make a right triangle.

The distance between the first car and the intersection is $x$ and the distance between the second car and the intersection is $y$ . The distance between the two cars is depicted by $s$ . As we can see, $s$ is the hypotenuse of the right triangle. At the given instance the distances are 8 meters and 6 meters respectively. Thus, by the Pythagorean Theorem the hypotenuse will be:

$s=\sqrt{8^2+6^2}= \sqrt{100}=10$ ...............(Equation 1)

Now, we know that at any instant the Pythagorean Theorem holds and so we will have, in general:

$s^2=x^2+y^2$

Now, implicitly differentiating the above formula with respect to time, we get:

$2s\frac{ds}{dt}=2x \frac{dx}{dt}+2y \frac{dy}{dt}$

This can be further simplified by dividing both the sides by the common factor 2 as:

$s\frac{ds}{st}=x \frac{dx}{dy}+y\frac{dy}{dt}$ .................(Equation 2)

As we can see from the questions and the diagram, $\frac{dx}{dt}=-2 m/s$ and $\frac{dy}{dt}=-9 m/s$ . The negative sign is there because the distances y and x are reducing as the cars approach the intersection.

Applying this knowledge to (Equation 2) along with the fact that as per (Equation 1), $s=10$ , we get (Equation 2) to become:

$10\times \frac{ds}{dt}=8\times -2+6\times -9=-70$

Therefore, $\frac{ds}{dt}= \frac{-70}{10}=-7 m/s$

Thus, the rate of change of the distance between the cars at the given instant (in meters per second) is $-7$ .

Therefore, out of the given options, option D is the correct one.

4 0

3 years ago