What is the area of the two-dimensional cross section that is parallel to face ABC ?



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A right triangular prism containing dashed lines representing the hidden edges. The prism is resting on a triangular face, which is labeled D E F and contains right angle E. Side E F is labeled twelve feet. The top of the prism is labeled A B C and contains right angle B. Side A B is labeled five feet and side A C, which is the hypotenuse of the right triangular face, is labeled thirteen feet. The height of the prism is side C F labeled seventeen feet.

Answer:

[tex]2^53^5[/tex]

Step-by-step explanation:

So if we compare [tex]2^5 \cdot 3^7[/tex] to [tex]2^7 \cdot 3^5[/tex], we should see the most amount of factors of 2 that they have in common is 5 and the most amount of factors of 3 that they have in common is 5.

If you aren't sure on the number of factors of 2 and 3 they have in common you could write it all out:

[tex]2^53^7=(2)(2)(2)(2)(2)\cdot\text{ }(3)(3)(3)(3)(3)(3)(3[/tex]

[tex]2^73^5=(2)(2)(2)(2)(2)(2)(2)\text{ }(3)(3)(3)(3)(3)[/tex]

So if I were able to circle each pair of 2's they had in common I would circle 5 pairs.

If were able to circle each pair of 3's they had in common I would circle 5 pairs.

Answer:

  11, 7, 44

Step-by-step explanation:

Let x represent the first number. Then the second is (x-4) and the third is (4x). Their sum is ...

  x +(x -4) +(4x) = 62

  6x = 66 . . . . . . . . . . . . add 4, collect terms

  x = 11 . . . . . . . . . divide by 6

  x -4 = 7 . . . . . . . find the second number

  4x = 44 . . . . . . . find the third number

The three numbers are 11, 7, and 44.

Answer:

3.876943x10^9

7.317x10^-4

Step-by-step explanation:

3,876,943,000

Put the decimal at the end

3,876,943,000.

Move it so only 1 number is before the decimal

3.876943000

We moved it 9 places, so that is the exponent

We moved it to the left, so the exponent is positive

The three zeros at the end can be dropped because they are the last numbers to the right of the decimal

3.876943x10^9

0.0007317

Move it so only 1 number is before the decimal

00007.317

We moved it 4 places, so that is the exponent

We moved it to the right, so the exponent is negative

The four zeros at the left can be dropped because they are the last numbers to the left of the whole number

7.317x10^-4

Answer: y = -1/4x - 4

Step-by-step explanation:

y = (-1/4)x + 2 (This is the first linear function.)

(4,3) has slope of (-1/4)x  or (1/-4)x

4(y2) - 4(y1= the new y  -1(x2) -3(x1) = new x which leads to (0,-4) so y-intercept = -4

so all in all, y = (-1/4)x -4 is the answer

Hopefully, you're able to understand this. It's difficult to explain through typed words rather than visually and through a written example.

Same y intercept as x+4y=8 through (4,3)

Y intercept is when x=0, so 4y=8, so y=2 and the y intercept is (0,2)

Answer for y intercept:  (0,2)

So we need the line through (0,2) and (4,3).  Point-point form says the line through (a,b) and (c,d) is

(c-a)(y-b) = (d-b)(x-a)

(4 - 0)(y - 2) = (3 - 2)(x - 0)

4y - 8 = x

Answer for the line:  x - 4y = -8

Check:

(0,2) is on the line: 0-4(2)  = -8 check

(4,3) is on the line 4 - 4(3) = -8 check

Answer:

The required standard form of  ellipse is [tex]\frac{x^2}{25}+\frac{y^2}{34}=1[/tex].

Step-by-step explanation:

The standard form of an ellipse is

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

Where, (h,k) is center of the ellipse.

It is given that the center of the circle is (0,0), so the standard form of the ellipse is

[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]             .... (1)

If a>b, then coordinates of vertices are (±a,0), coordinates of co-vertices are (0,±b) and focus (±c,0).

[tex]c^2=a^2-b^2[/tex]            .... (2)

If a<b, then coordinates of vertices are (0,±b), coordinates of co-vertices are (±a,0) and focus (0,±c).

[tex]c^2=b^2-a^2[/tex]            .... (3)

It is given that co-vertex of the ellipse at (5, 0); focus at (0, 3). So, a<b we get

[tex]a=5,c=3[/tex]

Substitute a=5 and c=3 these values in equation (3).

[tex]3^2=b^2-(5)^2[/tex]

[tex]9=b^2-25[/tex]

[tex]34=b^2[/tex]

[tex]\sqrt{34}=b[/tex]

Substitute a=5 and [tex]b=\sqrt{34}[/tex] in equation (1), to find the required equation.

[tex]\frac{x^2}{5^2}+\frac{y^2}{(\sqrt{34})^2}=1[/tex]

[tex]\frac{x^2}{25}+\frac{y^2}{34}=1[/tex]

Therefore the required standard form of  ellipse is [tex]\frac{x^2}{25}+\frac{y^2}{34}=1[/tex].

Answer:

The correct answer is option B.  

m<3 = m<6

Step-by-step explanation:

From the figure we an see that, a and b are parallel lines and line t is the traversal on the lines.

To find the correct option

From the given figure we get

Corresponding angles are,

<1 & <5,  <2&<6, <2&<7 and <4 &<8

Alternate interior angles are,

<3 & <6  and <4 &<5

Alternate interior angles are equal.

m<3 = m<6

Therefore the correct answer is optionB

Let x = amount of 16% alloy, and y = amount of 30% alloy he should use.

Mixing the alloys will result in a compound weighing x + y = 100 grams.

For each gram of the 16% alloy used, 0.16 gram of titanium is contributed; similarly, for each gram of the 30% alloy used, there's a contribution of 0.3 gram. He wants to end up with an alloy of 23% titanium, or 23 grams (23% of 100), so that 0.16x + 0.3y = 23.

Solve the system:

[tex]x+y=100\implies y=100-x[/tex]

[tex]0.16x+0.3y=23\implies 0.16x+0.3(100-x)=23\implies7=0.14x[/tex]

[tex]\implies\boxed{x=50}\implies\boxed{y=50}[/tex]

To find the x intercepts, we need to put the standard form equation into factored form.

Which two numbers multiply to -8 and add to -2?

[tex]-4*2=-8[/tex]

[tex]-4+2=-2[/tex]

So the factored form is

[tex](x-4)(x+2)[/tex]

That means the x intercepts are at [tex]x=4,-2[/tex]

So now we have the x intercepts.

To find the vertex, we need to convert the standard form equation into vertex form.

The formula of vertex form is [tex]y=a(x-h)^2+k[/tex]

Since the a value in the standard form equation is 1, the a value in vertex form is also one.

The h value can be found using the formula [tex]h=\frac{-b}{2a}[/tex]

Which comes out to [tex]\frac{2}{2}[/tex] or 1.

To find the k value, we can just plug in what we got for h back into the equation.

[tex](1)^2-2(1)-8=-9[/tex]

So the vertex is [tex](1,-9)[/tex].

This also means the axis of symmetry is [tex]x=-1[/tex]

Finally, to find the y intercept, we plug in 0 for x and solve.

[tex](0)^2-2(0)-8=-8[/tex]

So the y intercept is [tex](0,-8)[/tex].

Answer:

root 6

Step-by-step explanation:

pi*r^2 = A

6*pi*r^2 = 6A

6*r^2 = new radius squared

root 6 * r = new radius

The correct answer is option 1) The radius is multiplied by [tex]\sqrt{6}[/tex]

[tex]A = \pi r^2[/tex]
where A is the area and r is the radius.
If the area is multiplied by 6, we can represent this with the following equation:
A' = 6A
where A' is the new area and let r' be its radius.
[tex]A' = \pi (r')^2[/tex]
Substituting this into the equation for the new area gives us:
[tex]\pi (r')^2 = 6*(\pi r^2)[/tex]
To solve for r', we can divide both sides of the equation by [tex]\pi[/tex]:
[tex](r')^2 = 6r^2[/tex]
Next, take the square root of both sides to solve for r':
[tex]r' = \sqrt{6}r[/tex]
Therefore, the new radius r' is the original radius r multiplied by [tex]\sqrt{6}[/tex].

Answer:

  2

Step-by-step explanation:

Only graph 2 shows a function that passes the horizontal line test. The other graphs will cross a horizontal line multiple times, meaning the function does not have an inverse.

Answer:

Step-by-step explanation:

A function is invertible if its bijective: injective and surjective at the same time. But, graphically exist the horizontal line test to know if the function is injective,  i.e., one to one: one element of the domain has a unique element in the image set.

So, in this case, the only function that can be cut once by a imaginary horizontal line is graph number 2. If we draw a horizontal line in other options, it will cut them in more than one point, meaning that they are not injective, therefore, not invertible.

[tex]|\Omega|={_{20}C_3}=\dfrac{20!}{3!17!}=\dfrac{18\cdot19\cdot20}{2\cdot3}=1140\\|A|=1\\\\P(A)=\dfrac{1}{1140}\approx0.09\%[/tex]

Answer:

0.014%

Step-by-step explanation:

To calculate the probability that she chooses that exact songs for the piano recital, you just first calculate the probability of her choosing one of them:

[tex]Probability of 1=\frac{1}{20}=.05[/tex]

This is 5%, now you multipy this with the probability of the second song after this one, since there is one less song, the total number of outcomes should be reduced to 19:

[tex]Probability of 2nd=(.05)(\frac{1}{19}[/tex]

[tex]Probability of 2nd=(0.05)(0.052}[/tex]

[tex]Probability of 2nd=0.002[/tex]

This would be .26%

To calculate the probability of the third song being chosen after the first two, we have 2 less outcomes possibles, so the total number of possibilities now is reduced to 18.

[tex]Probability of 3rd=(.0026)(\frac{1}{18}[/tex]

[tex]Probability of 3rd=(.0026)(0.055)[/tex]

[tex]Probability of 3rd=0.00014[/tex]

The probability of Noam choosing the three songs would be: 0.014%

Answer:

I think that the first one is not a rhombus but the last two are.

Answer:

Each part is solved and working is shown  

Step-by-step explanation:

1)

[tex]-6\displaystyle\frac{4}{9}-3\displaystyle\frac{2}{9}-8\displaystyle\frac{2}{9}\\\\= -\displaystyle\frac{58}{9}-\displaystyle\frac{29}{9}-\displaystyle\frac{74}{9}\\\\= -\displaystyle\frac{161}{9}\\=-17\displaystyle\frac{8}{9}[/tex]

2)

[tex]-12.48-(-2.99) -5.62\\=-12.48 + 2.99 -5.62 \\=-15.11[/tex]

3)

[tex]-19\displaystyle\frac{2}{9}-4\displaystyle\frac{1}{9}+3\displaystyle\frac{4}{9}\\\\= -\displaystyle\frac{173}{9}-\displaystyle\frac{37}{9}+\displaystyle\frac{31}{9}\\\\= -\displaystyle\frac{179}{9}\\=-19\displaystyle\frac{8}{9}[/tex]

4)

[tex]-353.92 - (-283.56) - 131.29\\= -353.92 + 283.56 - 131.29\\= -201.65[/tex]

5)

[tex]83\displaystyle\frac{1}{5}-108\displaystyle\frac{2}{5} + 99\displaystyle\frac{1}{5}\\\\= \displaystyle\frac{416}{5}-\displaystyle\frac{542}{5}+\displaystyle\frac{496}{5}\\\\= -\displaystyle\frac{370}{5}\\= 74[/tex]

Answer:

Step-by-step explanation:

Answer:

Option A) [tex]\frac{4x+3y}{3x-4y}[/tex]

Step-by-step explanation:

The given expression is:

[tex]\frac{\frac{x}{3}+\frac{y}{4}}{\frac{x}{4}-\frac{y}{3}}[/tex]

Taking LCM in upper and lower fractions, we get:

[tex]\frac{\frac{x}{3}+\frac{y}{4}}{\frac{x}{4}-\frac{y}{3}}\\\\ =\frac{\frac{4x+3y}{12}}{\frac{3x-4y}{12}}\\\\\text{Cancelling out the common factor 12, we get:}\\\\ =\frac{4x+3y}{3x-4y}[/tex]

Therefore, the option A gives the correct answer.

Final answer:

To find the probability, we use the Poisson probability formula with a mean of three. The probability of exactly four births is 0.168, the probability of at least four births is 0.361, and the probability of more than four births is 0.193.

Explanation:

To find the probability in each case, we will use the Poisson probability formula since the number of births per minute in a country follows a Poisson distribution with a mean of three.

(a) Exactly four births in a minute:

The probability of exactly four births in a minute can be calculated using the Poisson probability formula:

P(X = 4) = (e⁻³* 3⁴) / 4! = 0.168

(b) At least four births in a minute:

The probability of at least four births in a minute is the complement of the probability of having three or fewer births in a minute:

P(X ≥ 4) = 1 - P(X ≤ 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)) = 1 - (0.049 + 0.147 + 0.221 + 0.222) = 0.361

(c) More than four births in a minute:

The probability of more than four births in a minute is the complement of the probability of having four or fewer births in a minute:

P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)) = 1 - (0.049 + 0.147 + 0.221 + 0.222 + 0.168) = 0.193

Answer:

The answer is

C.) BE

AD/AG=BE/BH

Answer:

Option C

Step-by-step explanation:

We have to find the value in the blank space

We are given that AC,DF and GI are parallel

We know that by middle splitting theorem

We have

[tex]\frac{JD}{AD}=\frac{JE}{BE}[/tex]

Because AC is parallel to DF and A and B are the mid points of JD and JE

[tex]\frac{JD}{GD}=\frac{JE}{EH}[/tex]

Because DF is parallel to GI

Divide  equation one by equation second then we get

[tex]\frac{GD}{AD}=\frac{EH}{BE}[/tex]

Adding one on both sides then we get

[tex]\frac{GD}{AD}+1=\frac{BE}{EH}+1[/tex]

[tex]\frac{GD+AD}{AD}=\frac{BE+EH}{BE}[/tex]

[tex]\frac{AG}{AD}=\frac{BH}{BE}[/tex]

Because BE+EH=BH and AD+GD=AG

Reciprocal on both sides then we get

[tex]\frac{AD}{AG}=\frac{BE}{BH}[/tex]

Hence, option C is true.

Answer:

4

(We didn't even need to use (9,6) )

Step-by-step explanation:

The slope-intercept form a line is y=mx+b where m is the slope and b is the y-intercept.

We are given the line we are looking for has the same y-intercept as x+2y=8.

So if we put x+2y=8 into y=mx+b form we can actually easily determine the value for b.

So we are solving x+2y=8 for y:

x+2y=8

Subtract x on both sides:

  2y=-x+8

Divide both sides by 2:

   y=(-x+8)/2

Separate the fraction:

  y=(-x/2)+(8/2)

Reduce the fractions (if there are any to reduce):

y=(-x/2)+4

Comparing this to y=mx+b we see that b is 4.

So the y-intercept is 4.

Again since we know that the line we are looking for has the same y-intercept, then the answer is 4 since the question is what is the y-intercept.

4

Answer:

-3 is the value of k in g(x)=kf(x)

Step-by-step explanation:

Both functions cross nicely at x=-3 so I'm going to plug in -3 for x:

g(x)=kf(x)

g(-3)=kf(-3)

To solve this for k we will need to find the values for both g(-3) and f(-3).

g(-3) means we want the y that corresponds to x=-3 on the curve/line of g.

g(-3)=-3

f(-3) means we want the y that corresponds to x=-3 on the curve/line of f.

f(-3)=1

So our equation becomes:

g(-3)=kf(-3)

-3=k(1)

-3=k

So k=-3.

This is about interpretation of graphs.

Option C is correct.

We see that the best point for that is where x = -3.

we can rewrite them as;

x = -3, f(-3) = 1 and x = -3, g(-3) = -3

-3 = k(1)

Thus; k = -1/3

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Answer:

  loss of $12,481.38

Step-by-step explanation:

It is usually a good idea to follow directions. (See attached.)

The sum of the three profit values is -$12,481.38, indicating a loss in the 3-year period.

Answer:

[tex]cosZ=\frac{3}{5}[/tex]

Step-by-step explanation:

Cos of an angle by definition of its ratio is side adjacent/hypotenuse.  The side adjacent to angle Z cannot be the hypotenuse, so it has to be 6.  The hypotenuse is 10.  Therefore,

[tex]cosZ=\frac{6}{10}=\frac{3}{5}[/tex]

Look at the table for the people that used Lithium.

There are 18 relapses, 6 No relapses with a total of 24 people.

The relative frequency for relapse, would be dividing the number of relapses by the total number of people.

This would be D. 18 / 24 = 75%

Answer:

  D.  they are parallel​

Step-by-step explanation:

A plane can be defined by a point and a direction vector that is perpendicular to the plane. If two planes have the same direction vector (perpendicular line), then they are either the same plane or they are parallel.

If two planes are perpendicular to the same line, then they must also be parallel to each other.

If two planes are perpendicular to the same line, then they are also parallel to each other. This is because any line that intersects two parallel planes will be perpendicular to both planes.

To illustrate this, imagine two planes, A and B, that are perpendicular to the same line, L. If we draw a line, M, that intersects both planes, then M will be perpendicular to both planes A and B. This is because lines A and B are parallel to each other, and any line that intersects two parallel lines will be perpendicular to both lines.

Therefore, if two planes are perpendicular to the same line, then they must also be parallel to each other. The answer is D. they are parallel.

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Answer: $80

Step-by-step explanation:

Given : Interest amount : [tex]T=\$40[/tex]

The rate of interest : [tex]r=10\%=0.1[/tex]

Time period : [tex]t=5[/tex] years

The simple interest formula is

[tex]l=prt[/tex], where l represents simple interest on an amount p for t years at a rate of r where r is expressed as a decimal.

Substitute all the values in the  formula , we get

[tex]40=p(0.1)(5)\\\\\Rightarrow\ p=\dfrac{40}{0.1\times5}=80[/tex]

Hence, the amount of money p that will generate $40 in interest at a 10% interest rate over 5 years= $80

The amount of money (p) required to generate $40 in interest at a 10% interest rate over 5 years is $80.

Given the parameters:

Simple interest l = $40

Interest rate r = 10% = 10/100 = 0.10

Time t = 5 years

To determine the amount of money (p) that will generate $40 in interest at a 10% interest rate over 5 years, we use the simple interest formula:

I = P × r × t

Solve for p:
P = I / rt

Plug in the values

P = $40 / ( 0.10 × 5 )

P = $40 / 0.5

P = $80

Therefore, the value of the principal is $80.

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I hate rounding.

Let's call the diagonal x.  It's the hypotenuse of the right triangle whose legs are the rectangle sides.

According to the problem we have a length x-4 and a width x-5 and an area

82 = (x-4)(x-5)

82 = x^2 - 9x + 20

0 = x^2 - 9x - 62

That one doesn't seem to factor so we go to the quadratic formula

[tex]x = \frac 1 2(9 \pm \sqrt{9^2-4(62)}) = \frac 1 2(9 \pm \sqrt{329})[/tex]

Only the positive value makes any sense for this problem, so we conclude

[tex]x = \frac 1 2(9 \pm \sqrt{329})[/tex]

That's the exact answer.  Did I mention I hate rounding?  That's about

x = 13.6 meters

Answer: 13.6

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It's not clear to me this problem is consistent.  By the Pythagorean Theorem the diagonal satisfies

[tex]x^2 = (x-4)^2 + (x-5)^2[/tex]

which works out to

[tex]x=9 \pm 2\sqrt{10}[/tex]

That's not consistent with the first answer; this problem really has no solution.  Tell your teacher to get better material.

To find the length of the diagonal, we can use the formula for the area of a rectangle and quadratic equation. By substituting the given values and solving for D, we can find the length of the diagonal.

To solve this problem, we can use the formula for the area of a rectangle: length * width = area. Let's represent the length of the rectangle as L, the width as W, and the diagonal as D. According to the problem, L = D - 4 and W = D - 5, and the area is given as 82 m2. We can substitute these values into the formula and solve for D.

L * W = area

(D - 4) * (D - 5) = 82

Expanding and rearranging the equation, we get:

D2 - 9D - 82 = 0

Next, we can solve this quadratic equation either by factoring or by using the quadratic formula. After finding the value of D, we can round it to the nearest tenth to obtain the length of the diagonal.

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Answer: 25%

Step-by-step explanation:

Given : A rectangular dartboard has an area of 648 square centimeters.

The triangular part of the dartboard has an area of 162 square centimeters.

If we assume that the dart lands in the rectangle, then the probability that it lands inside the triangle will be :-

[tex]\dfrac{\text{Area of triangular part}}{\text{Area of rectangular dart board}}\\\\=\dfrac{162}{648}=0.25[/tex]

In percent, [tex]0.25\times100=25\%[/tex]

Hence, the required probability = 25%

Answer:

No they will not have to install a rest platform.

The ramp will be 29.88 feet long so they will not have to install a rest platform.

Step-by-step explanation:

Answer:

Find the explicit from for the sequence [tex]t_n=t_{n-1}+4,t=6[/tex]:

[tex]a_n=4n+2[/tex]

This next question I edited a bit.  Your question just says find the four terms.  I'm assuming they meant the first four. I also changed the c to an [tex]a[/tex].

Find the first four terms of the sequence given by: [tex]a_n=n a_{n-1}-3,a_1=2[/tex]:

a) 2,1,0.-3

You might want to read that second question again because there is errors in the question or things that don't really make sense.  I made my own interpretation of the problem based on my own mathematical experience.

Step-by-step explanation:

So your first question actually says that you can find a term by taking that term's previous term and adding 4.

So more terms of the sequence starting at first term 6 is:

6,10,14,18,....

This is an arithmetic sequence.  When thinking of arithmetic sequences you should just really by thinking about equations of lines.

Let's say we have this table for (x,y):

x  |   y

----------

1      6

2    10

3     14

4     18

So we already know the slope which is the common difference of an arithmetic sequence.

We also know point slope form of a line is [tex]y-y_1=m(x-x_1)[/tex] where m is the slope and [tex](x_1,y_1)[/tex] is a point on the line.  You can use any point on the line. I'm going to use the first point (1,6) with my slope=4.

[tex]y-6=4(x-1)[/tex]

[tex]y=6+4(x-1)[/tex]    :I added 6 on both sides here.

[tex]y=6+4x-4[/tex]     :I distribute here.

[tex]y=4x+2[/tex]        :This is what I get after combining like terms.

So [tex]a_n=y[/tex] and [tex]x=n[/tex] so you have:

[tex]a_n=4n+2[/tex]

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

The first four terms of this sequence will be given by:

[tex]a_1,a_2,a_3,a_4[/tex]

[tex]a_1=2[/tex] so it is between choice a, c, and d.

[tex]a_n=na_{n-1}-3[/tex]

To find [tex]a_2[/tex] replace n with 2:

[tex]a_2=2a_{1}-3[/tex]

[tex]a_2=2(2)-3[/tex]

[tex]a_2=4-3[/tex]

[tex]a_2=1[/tex]

So we have to go another further the only one that has first two terms 2,1 is choice a.

Answer: Second Option

68%

Step-by-step explanation:

First we calculate the Z-scores

We know the mean and the standard deviation.

The mean is:

[tex]\mu=27[/tex]

The standard deviation is:

[tex]\sigma=3[/tex]

The z-score formula is:

[tex]Z = \frac{x-\mu}{\sigma}[/tex]

For x=24 the Z-score is:

[tex]Z_{24}=\frac{24-27}{3}=-1[/tex]

For x=30 the Z-score is:

[tex]Z_{30}=\frac{30-27}{3}=1[/tex]

Then we look for the percentage of the data that is between [tex]-1 <Z <1[/tex] deviations from the mean.

According to the empirical rule 68% of the data is less than 1 standard deviations of the mean.  This means that 68% of pizzas are delivered between 24 and 30 minutes

Answer:

  see below

Step-by-step explanation:

The applicable rules of logarithms are ...

  log(a^b) = b·log(a)

  log(a/b) = log(a) -log(b)

___

The expression can be rewritten as ...

[tex]\log{\dfrac{\sqrt[3]{2-x}}{3x}}=\log{\sqrt[3]{2-x}}-\log{3x}=\dfrac{1}{3}\log{(2-x)}-\log{(3x)}[/tex]

The expression can be written as a sum or difference as:

[tex]$$\boxed{\frac{1}{3} \log(2-x) - \log(3x)}$$[/tex]

To write the expression [tex]$\log(\frac{\sqrt[3]{2-x}}{3x})$[/tex] as a sum or difference, we can use the following logarithmic identities:

[tex]$\log(a/b) = \log(a) - \log(b)$[/tex]

[tex]$\log(a^n) = n \log(a)$[/tex]

First, we can use the first identity to split the logarithm of the fraction into two logarithms:

[tex]$$\log(\frac{\sqrt[3]{2-x}}{3x}) = \log(\sqrt[3]{2-x}) - \log(3x)$$[/tex]

Next, we can use the second identity to expand the logarithm of the cube root:

[tex]$$\log(\sqrt[3]{2-x}) = \log((2-x)^{1/3}) = \frac{1}{3} \log(2-x)$$[/tex]

Substituting this back into the first expression, we get:

[tex]$$\log(\frac{\sqrt[3]{2-x}}{3x}) = \frac{1}{3} \log(2-x) - \log(3x)$$[/tex]

Therefore, the expression can be written as a sum or difference as:

[tex]$$\boxed{\frac{1}{3} \log(2-x) - \log(3x)}$$[/tex]

Read more about logarithms at: https://brainly.com/question/30226560

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Answer:

y-7 = 1/2x point slope form

y = 1/2x+7  slope intercept form

Step-by-step explanation:

y=-2x+9

This equation is in the form y= mx +b so the slope is -2

We want a line perpendicular

Take the negative reciprocal

m perpendicular is - (-1/2)

m perpendicular = 1/2

We have a slope of 1/2 and a point.  We can use point slope form

y-y1 = m(x-x1)

y-7 = 1/2(x-0)  point slope form

y-7 = 1/2x

Adding 7 to each side

y-7+7 =1/2x +7

y = 1/2x+7  slope intercept form