Solving Exponential Equations using Logarithms

Answer:

Step-by-step explanation:

Given the expressions f(x) =  |x| + 9 and g(x) = –6, sine f(x) contains the absolute value of a variable x, this absolute value can be negative and positive. Therefore f(x) can be expressed in two forms as shown;

f(x) = x+9 and f(x) = -x+9

If f(x) = x+ 9 and g(x) =  -6

(f + g)(x) = f(x)+ g(x)

(f + g)(x) = x+9+(-6)

(f + g)(x) = x+9-6

(f + g)(x) = x+3

Similarly, if f(x) = -x+ 9 and g(x) =  -6

(f + g)(x) = f(x)+ g(x)

(f + g)(x) = -x+9+(-6)

(f + g)(x) = -x+9-6

(f + g)(x) = -x+3

(f + g)(x) = 3-x

In  both expresson, we have bith x to be positive and negative, hence we can write the value of resulting x as an absolute value as shown;

(f + g)(x) = |x|+3

This shows that (f + g)(x)≥3 for all values of x

Answer:

Step-by-step explanation:

(0+2)/(0-10)= 2/-10 = -1/5

y - 0 = -1/5(x - 0)

y = -1/5x

solution is D

Answer:

Step-by-step explanation:

The formula for the dot product of vectors is

u·v = |u||v|cosθ

where |u| and |v| are the magnitudes (lengths) of the vectors. The formula for that is the same as Pythagorean's Theorem.

[tex]|u|=\sqrt{14^2+9^2}[/tex] which is [tex]\sqrt{277}[/tex]

[tex]|v|=\sqrt{3^2+6^2}[/tex] which is [tex]\sqrt{45}[/tex]

I am assuming by looking at the above that you can determine where the numbers under the square root signs came from. It's pretty apparent.

We also need the angle, which of course has its own formula.

[tex]cos\theta=\frac{uv}{|u||v|}[/tex] where uv has ITS own formula:

uv = (14 * 3) + (9 * 6) which is taking the numbers in the i positions in the first set of parenthesis and adding their product to the product of the numbers in the j positions.

uv = 96.

To get the denominator, multiply the lengths of the vectors together. Then take the inverse cosine of the whole mess:

[tex]cos^{-1}\theta=\frac{96}{111.64676}[/tex] which returns an angle measure of 30.7. Plugging that all into the dot product formula:

[tex]u*v=\sqrt{277}*\sqrt{45}cos(30.7)[/tex] gives you a dot product of 96

it is transformed [tex]|x|[/tex] function. moved down by and right by 1 unit,

so $y=|x-1|-1$

Answer:

X Intercept (-2,0), (-3,0) and Standard form y = -4x^2 - 20x - 24

Step-by-step explanation:

To write a polynomial in standard form, simplify, and then arrange the terms in descending order.

y = ax^2 + bx + c

y = (−4x−8) (x+3)

Expand (−4x−8) (x+3) using the FOIL Method

y = −4x ⋅ x − 4x ⋅ 3 − 8x−8 ⋅ 3

Simplify and combine like terms.

y = −4x^2 − 20x − 24

Hope this can help

Answer:

[tex]44^\circ[/tex]

Step-by-step explanation:

The angle measuring [tex]y^\circ[/tex] is formed by two secants intersecting at an exterior point.

The measure of that angle is half the difference between the big intercepted arc and the little intercepted arc.

y = 1/2 (m arc FKB - m arc CGJ)

Plug in the values you know.

56 = 1/2 (156 - m arc CGJ)

Multiply both sides by 2 to clear the fraction.

112 = 156 - m arc CGJ

Subtract 156.

-44 = - m arc CGJ

44 = m arc CGJ

The measure of the little intercepted arc is [tex]44^\circ[/tex].

Answer:

f(-1) = 12

Step-by-step explanation:

Using the graph for f(x)  let x=-1

Find the y value when x= -1

f(-1) = 12

Answer:

Approximately 66.4 Meters

Step-by-step explanation:

So we have a rectangle with a width of 18.8 meters and a diagonal with 23.7 meters. To find the perimeter, we need to find the length first. Since a rectangle has four right angles, we can use the Pythagorean Theorem, where the diagonal is the hypotenuse.

[tex]a^2+b^2=c^2[/tex]

Plug in 18.8 for either a or b. Plug in the diagonal 23.7 for c.

[tex](18.8)^2+b^2=23.7^2\\b^2=23.7^2-18.8^2\\b=\sqrt{23.7^2-18.8^2} \\b\approx14.4 \text{ meters}[/tex]

Therefore, the length is 14.4 meters. Now, find the perimeter:

[tex]P=2l+2w\\P=2(14.4)+2(18.8)\\P=66.4\text{ meters}[/tex]

Answer:

x=11 y=6

Step-by-step explanation:

making x the subject in the first equation we get

x=y+5 put that in the second equation we also get

2(y+5)-3y=4

2y+10-3y=4

-y=4-10

-y=-6

y=6 use that to also find x from the equation x=y+5 we get

x=6+5

x=11

therefore x=11 y=6

Answer:

down 8 units

Step-by-step explanation:

going from +6 to -2 goes down 8 units

Answer:

Step-by-step explanation:

f(x) + n - shift the graph n units up

f(x) - n - shift the graph n units down

f(x + n) - shift the graph n units to the left

f(x - n) - shift the graph n units to the right

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

We have y = 3/7x + 6. It has been changed to y = 3/7x - 2.

y = 3/7x + 6 → f(x) = 3/7x + 6

f(x) - 8 = (3/7x + 6) - 8 = 3/7x + 6 - 8 = 3/7x - 2

Answer: x = -2 , y = 3

Step-by-step explanation:

4x-y=-11

2x+3y=5

Solve 4x-y=-11 for y

Add -4x to both sides

4x-y+-4x=-11+-4x

-y=-4x-11

Divide both sides by -1

-y/-1=-4x-11/-1

y=4x+11

Substitute 4x+11 for y in 2x +3y=5

2x+3y=5

2x+3(4x+11)=5

Simplify both sides of the equation

14x+33=5

Add -33 to both sides

14x+33+-33=5+-33

14x=-28

Divide both sides by 14

14x/14=-28/14

x=-2

Substitute -2 for x in y= 4x+11

y=4x+11

y=(4)(-2)+11

Simplify both sides of the equation

y=3

Answer:

a. 5p+3

b. 26p + 6

Step-by-step explanation:

a.

Area = length × width

40p² + 24p = length × 8p

Factorise out 8p from both sides

8p(5p + 3) = length × 8p

Divide both sides by 8p

5p + 3 = length

b.

Perimeter = 2(length + width)

"" = 2(5p+3 + 8p)

"" = 2(13p + 3)

"" = 26p + 6

Answer: C

1/4

Step-by-step explanation:

Given a graph for the transformation of f(x) in the format g(x) = f(kx),

This means that for every value of x, f(x) will take the value it would have had at kx, that is, the graph of f(x) is stretched by a factor of 1/k in the direction of positive x-direction.

Therefore, the value of k will be 1/4.

Answer:

k=4

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Put -1 and 12 in the absolute value form and add them together. You'll get 13.

Number of  units separate the points is 13 units.

Given that;

Coordinate of first point = (5 , -1)

Coordinate of second point = (5 , 12)

Find:

Number of  units separate the points

Computation:

Number of  units separate the points = √(x1 - x2)² + (y1 - y2)²

Number of  units separate the points = √(5 - 5)² + (-1 - 12)²

Number of  units separate the points = √(-13)²

Number of  units separate the points = 13 units

Find out more information about 'Coordinate'.

https://brainly.com/question/4399730?referrer=searchResults

Answer:

The angle is determined by dividing 360 by the number of vertexes that it took to complete the circle. The tangent of the 100th triangle would be the same respectively.

Step-by-step explanation:

I remember learning this in kindergarten.

Answer:

The answer is 15%.

Step-by-step explanation:

The probability that:

       80% x 90% = 72%

        80% x (1 - 90%) = 8%

        (1 - 80%) x 25% = 5%

        1 - (72% + 8% + 5%) = 15%

[tex] {3x}^{2} - 4x - 12 = 0[/tex]

[tex]a = 3[/tex]

[tex]b = - 4[/tex]

[tex]c = - 12[/tex]

Formula:

[tex] \boxed{x = \dfrac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} }[/tex]

Replacing:

[tex]x = \dfrac{ -( - 4) \pm \sqrt{ { (- 4)}^{2} - 4(3)( - 12)} }{2(3)} [/tex]

Option: C).

Answer:  13.5 units³

Step-by-step explanation:

[tex]\dfrac{5}{2}\times \dfrac{27}{5}\quad =\dfrac{27}{2}\quad =\large\boxed{13.5\ units^3}[/tex]

Answer:

125

Step-by-step explanation:

So you can see that the sequence is all of the perfect cubes so knowing that the next perfect cube we have to find is 5's perfect cube which is 125.

Answer:

192

Step-by-step explanation:

Answer:

The capacity of the water bottle is 2.5 times greater than the mug.

Step-by-step explanation:

We know that the capacity of a water bottle and a mug is 7/8 litre:

[tex]bottle+mug=\frac{7}{8}[/tex]

But we also now that the mug's capacity is 1/4 litre, so the equation above becomes:

[tex]bottle + \frac{1}{4}=\frac{7}{8}[/tex]

Now we want to know how much greater the capacity of the bottle than the mug is. To do this we need to know first what's the capacity of the bottle.

So, we would have:

[tex]bottle=\frac{7}{8}-\frac{1}{4} \\\\bottle=\frac{7}{8}-\frac{2}{8}\\\\\\bottle=\frac{5}{8}[/tex]

Therefore the bottle has a capacity of 5/8 liter while the mug has a 2/8 liter one.

To know how much greater is the capacity of the water bottle than the mug we need to divide these two quantities, so we have:

[tex]\frac{5}{8}[/tex]÷[tex]\frac{2}{8}[/tex][tex]=\frac{5}{8}[/tex]×[tex]\frac{8}{2}[/tex][tex]=\frac{5}{2}=2.5[/tex]

Therefore the capacity of the water bottle is 2.5 times greater than the mug.

Answer:

Hey there!

The two lines in this graph are: y=-1/5x+2, and y=3x-2

Since y=-1/5x+2 is a dotted line, we know that we use the < or > symbols.

Since y=3x-2 is a straight line, we use the ≤ and ≥ symbols.

Thus, for area z, we have y<-1/5x+2, and y≥3x-2

Hope this helps :)

Answer:

$430

Step-by-step explanation:

Let the weekly income be x

Money spent on food= $86

% of weekly income spent on food = 20

20% of weekly income in terms = 20/100 * x = x/5

This, income is equal to $86 as given

thus,

x/5 = 86

x = 86*5 = 430

Thus, weekly income is $430.

Answer:

B and D

Step-by-step explanation:

I think this is the answer

Answer:1 3/7

Step-by-step explanation:When you multiply the nominator and 4you get 20.So it would 20/14 but if you find the simplest form of fraction you would get 1 3/7

Answer:

73.2

Step-by-step explanation:

you can find the answer using trigonometry relationship

sin31°=41/x

x=41/sin31°. sin31° is approximately equal to 0.56

x=41/0.56

x=73.2

Answer:

Her Verticle ramp support was 5.5 ft tall.

Step-by-step explanation:

In this type of question, you would need to use the saying "soh cah toa".

Soh Cah Toa is a saying that people use for Sin, Cosine, and tagent. Each of those mean

Sine: opposite/hypotenuse Cosine: Adjacent/hypotenuse and Tagent: Opposite/Adjacent

In this specific question to figure out how tall or high her support is or needs to be have to 20 degree  angle off the ground, you will need to use Sin which is opposite over Hypotenuse or x/16

To find the answer in your calculator you would do:

Sin(20)=x/16

First thing you do is the get the x on one side by itself so you would multiply 16 on both sides giving you:

16 × Sin(20)= x

You would then follow to put Sin(20) in your calculator giving you 0.34202014332

After that you multiply that number by 16

5.47232229321

Rounding to the nearest tenth you get answer:

5.5

Answer:

For mileages higher than 80 miles Company A  will charge less than Company B

Step-by-step explanation:

Hi, to answer this question we have to write an inequality:

Company A charges $111 and allows unlimited mileage.

Company A =111

Company B has an initial fee of $55 and charges an additional $0.70 for every mile driven

Company B = 55+0.70m

Where m is the number of miles.

Company A has to charge less than Company B

a<b

111 < 55+0.70m

Solving for m

111-55 < 0.70 m

56 < 0.70m

56/0.70 < m

80 < m  

For mileages higher than 80 miles Company A will charge less than Company B

Answer:

6:00 p.m.

hope this helps :)

Hi king,

Let's split it into two prisms.

[tex]V_{1}=5cm*10cm*3cm\\V_{1} =150cm^{3}[/tex]

[tex]V_{2}=5cm*10cm*(9cm-5cm)\\V_{2}=5cm*10cm*4cm\\V_{2} =200cm^{3}[/tex]

The prism in the picture:

[tex]V_{final}=150cm^{3} +200cm^{3} \\V_{final}=350cm^{3}[/tex]

Have a good day.