Which expression can be used to approximate the expression below, for all positive numbers a, b, and x, where a Not-equals 1 and b Not-equals 1? log Subscript x Baseline x StartFraction log Subscript b Baseline x Over log Subscript b Baseline a EndFraction StartFraction log Subscript b Baseline a Over log Subscript b Baseline x EndFraction StartFraction log Subscript a Baseline b Over log Subscript x Baseline b EndFraction StartFraction log Subscript a Baseline x Over log Subscript b Baseline x EndFraction.

Hi there!

[tex]\large\boxed{b = \frac{a}{ac - 1}}[/tex]

We can begin by making each fraction have a common denominator:

If we make each have a common denominator of ab, we get:

[tex]\frac{b}{ab} + \frac{a}{ab} = c[/tex]

Simplify:

[tex]\frac{a + b}{ab} = c[/tex]

Multiply both sides by ab:

[tex]a + b = cab[/tex]

Move b to the opposite side:

[tex]a = cab - b[/tex]

Factor out b:

[tex]a = b(ac - 1)[/tex]

Divide by (ac - 1):

[tex]\frac{a}{ac - 1} = b[/tex]

Answer:

4-t

Step-by-step explanation:

We use the second equation and  r = 4-t

every time we see r in the first equation replace it with 4-t

Answer:

Step-by-step explanation:

We need to first find the perimeter of this oddly-shaped rink. We have a rectangle for which we are enclosing 3 of its sides, and the fourth "side" is a half-circle. Let's find the perimeter (or circumference) of the circle, divide it in half because we have half a circle, then add in the remaining 3 sides from the rectangle, shall we?

C = πd. The diameter of the circle is the same as the shorter length in the rectangle, 26. Therefore,

C = (3.14)(26) so

C = 81.64 m for a whole circle, and for half of that circle, the circumference is

C = 40.82 m

Now we can find the perimeter of the rink:

40.82 + 61 + 26 + 61 = p so

p = 188.82 m

If the fencing costs $6.20 per meter and we have 188.82 m, then the total cost is

[tex]cost=\frac{6.20dollars}{meter}*188.82meters[/tex]. The label "meter" cancels out, leaving us with

cost = $1170.82

Answer:

x = 19

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp /adj

tan ? = 17/50

Taking the inverse tan of each side

tan ^-1 (tan ?)) = tan^-1 (17/50)

? =18.77803

To the nearest degree

x = 19

Answer:

2x + 3 = 3x + 1

x = 2

hope that helps ✌

Answer:

The original price is 80

The new price is 48

Step-by-step explanation:

Let x be the original price

x - .4x = new price

.6x = new price

.4x = markdown

.4x= 32

.4x/.4 = 32/.4

x =80

The original price is 80

.6x = new price

.6(80) =  48

Answer:

x = - 10, x = 10

Step-by-step explanation:

Given

x² - 100 = 0 ( add 100 to both sides )

x² = 100 ( take the square root of both sides )

x = ± [tex]\sqrt{100}[/tex] = ± 10

solutions are x = - 10, x = 10

Answer:

Step 1 is justified by the Distributive Property.

Step 4 is justified by the Symmetric Property

Step-by-step explanation:

Given the equation solved by Nigel expressed as

4(5x−12)−7x=5x.

First, we need to expand the bracket using the distributive property

4(5x−12)−7x=5x.

4(5x)-4(12) -7x = 5x

20x - 48 - 7x = 5x

Hence Step 1 is justified by the Distributive Property.

Next is to collect the like terms;

20x - 7x - 48 = 5x

Take the difference

13x - 48 = 5x

Next is to subtract 13x from both sides according to the symmetric property

13x - 48 - 13x = 5x - 13x

Hence Step 4 is justified by the Symmetric Property

The resulting equation will be

0-48 = -8x

Divide both sides by -8

-48/-8 = -8x/-8

6 = x

Hence the correct justifications are Step 1 is justified by the Distributive Property AND Step 4 is justified by the Symmetric Property

Answer:

50

Step-by-step explanation:

Answer:

3 + b/6 = 5

solve it too?

b/6 = 2

b = 12

Answer:

is it like

3x+6=5

to solve this

3x+6=5

collect like terms

3x= -6+5

3x= -1

divide both side by 3

3x/3=-1/3

x= -0.3

Answer:

please

Step-by-step explanation:

follow me

please

please

please

Answer:

-3

Step-by-step explanation:

Answer:

Rate of change, is also another word for slope.

Slope --> y2 - y1 / (x2-x1)

Assuming the table is already in xy, the cords are in xy form too.

1) (8,8)

2) (11,10)

Plug points into slope eq

--> 10 - 8 = 2

----> 11 - 8 = 3

2/3 Is the slope/rate of change.

Answer:

38,250

Step-by-step explanation:

Its a 15% discount so youre only paying 85% of the original 45,000. You then multiply 45,000 by .85 to find what youre paying because the decimal version of 85% is .85. You can find the decimal version of a percentage by dividing the percentage by 100; 85/100=.85. Once you multiply 45,000 by .85 you get 38,250.

Answer:

The angle θ = 312°.

Step-by-step explanation:

0° < θ < 360°

If cos θ = 2/3 and tan θ < 0

As cos θ is positive and tan θ is negative so the angle is in fourth quadrant.

cos θ = 2/3

θ = 312°

Answer:

50%

Step-by-step explanation:

1. determine the monthly interest rate

monthly interest rate = interest / loan amount

monthly interest = 25 / 600 = 4.17%

2, multiply the monthly interest rate by 12 to determine the annual interest rate

Annual interest = 4.17 x 12 = 0.5 = 50%

Answer:

Hello! the answer is CD is 17,0 (-2,19)

Answer:

Step-by-step explanation:

Use the Pythagorean theorem to find the length of the missing side that is 1/2 the side of the missing heptagon. You have to assume that the figure is a regular heptagon, something you should point out to your teacher. Math really requires well qualified diagrams.

c^2 = a^2 + b^2

c = 2.77

a = 2.5

b = 1/2 the side of the heptagon.

2.77^2 = 2.5^2 + b^2

7.6729 =6.25 + b^2

7.5629 - 6.25 = b^2

b^2 = 1.4229

b = sqrt(1.4229)

b = 1.1928

But the side is twice that long

s = 2.3857

Now draw another line from the side you just found. It will be the same length as 2.77. It's a radius of the circumcircle.

Area of the triangle so formed is

Area = 1/2 * b * h

b = 2.3857

h = 2.5

Area = 1/2 * 2.5 * 2.3857

Area = 2.982

There are 7 such triangles.

Answer: 7 * 2.982

Answer: 20.87

You want to pull out the square roots of each term since they are both perfect squares.

Factor using the difference of squares formula: a2-b2=(a+b)(a-b)

This formula allows the middle term to cancel out.

=x2 - 49

=(x + 7)(x - 7)

ANSWER: (x + 7)(x - 7)

Hope this helps! :)

Not the best way to do it, but it should look something like this.

Answer:

b. 40m

Step-by-step explanation:

[tex]length \: of \: x \\ {x}^{2} = {8}^{2} + {6}^{2} \\ {x}^{2} = 64 + 36 \\ {x}^{2} = 100 \\ \sqrt{ {x}^{2} } = \sqrt{100} \\ x = 10m[/tex]

[tex]x = 10m \\ 4x = 4 \times 10 \\ 4x = 40m[/tex]

Answer:

C) x=2

[tex]3x+8=4x+6[/tex]

[tex]8-6=4x-3x[/tex]

[tex]x=2[/tex]

~OAmalOHopeO

3x + 8 = 4x + 6

3x - 4x = 6 - 8

-x = -2

x = 2

Answer:

Gradient of line t is -1/5

Step-by-step explanation:

[tex]{ \sf{m _{s} \times m _{t} = - 1}} \\ { \sf{5 \times m _{t} = - 1 }} \\ { \sf{m _{t} = - \frac{1}{5} }}[/tex]

Answer:

39°

Step-by-step explanation:

The angle adjacent to 115° in the lower triangle = 180° - 115° = 65°

angle on circle in lower triangle

= 180° - (65 + 76)°  ← angle sum in triangle

= 180° - 141° = 39°

Angles on the circle subtended from the same arc are congruent, then

shaded angle = 39°

Answer:

17.1

Step-by-step explanation:

tan(35)=12/x, x=17.1

Answer:

x ≈ 17.1

Step-by-step explanation:

The angle is 35 degrees, so we do tan(35)

Which equals the side divided by x.

tan(35) = 12 / x

So x ≈ 17.1

Answer: V=9.4 cm^3

Step-by-step explanation:

[tex]V=\pi r^2h\\V=\pi (1)^2(3)\\V=9.4cm^3[/tex]

Answer:

the answer is

tan (B)=p/b

=5/12

Answer: C)5/12

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

1. We can clearly see that the "rise" is 5 and the "run" is 2, which cancels out both A. and D.

2. The line is dashed, which therefore cancels out both C. and D.

3. Just by canceling out those two can help you see that B fits what is seen in this figure because option A. has the wrong amount of "rise" over "run".

The linear inequality can be obtained from the given graph (the nature

of the line and the feasible (shaded) region).

Response:

[tex]B. \ y < -\dfrac{5}{2} \cdot x - 2[/tex]

The given points in the graph are;

(-2, 3), and (0, -2)

The slope of the line is therefore;

[tex]Slope = \dfrac{-2 - 3}{0 - (-2)} = \mathbf{-\dfrac{5}{2}}[/tex]

The equation of the line is therefore;

[tex]y - 3 = \mathbf{ -\dfrac{5}{2} \cdot (x - (-2))}[/tex]

[tex]y = -\dfrac{5}{2} \cdot x - 5 + 3 = -\dfrac{5}{2} \cdot x - 2[/tex]

[tex]y = \mathbf{-\dfrac{5}{2} \cdot x - 2}[/tex]

Given that the left side (below the line of the equation of the graph) is

shaded and the line of the graph is a broken line, the correct option is

therefore;

[tex]B. \ y < -\dfrac{5}{2} \cdot x - 2[/tex]

Learn more about the graph of inequalities here:

https://brainly.com/question/19251897