Express as a single logarithm. 3log 6x + 5log 6(x - 6)

Answer:

12 years old

Step-by-step explanation:

Let's call Sydney's age x and Sam's age 2x. We can write:

x + 2x = 36

3x = 36

x = 12 so the answer is 12 years old.

Answer: 14 cm

Step-by-step explanation:

let's total length = h

white = 1/4h

remain = h - 1/4h

=3/4h

blue = 1/2 of remaining

=1/2 of 3/4h

=3/8h

remain part black = 3/4h - 3/8h

=3/8h

according to the question

3/8h = 5 1/4 cm

h = 14 cm

length of the pipe is 14 cm

Answer:

The length of the pipe is 14.

Solution,

Let the total length be X cm

[tex]x - \frac{x}{4} -{ (x - \frac{x}{4} ) \times \frac{1}{2}} = 5 \frac{1}{4} \\ x - \frac{x}{4} - \frac{x}{2} + \frac{x}{8} = \frac{21}{4} \\ \frac{8x - 2x - 4x + x}{8} = \frac{21}{4} \\ \frac{3x}{8} = \frac{21}{4} \\ 3x \times 4 = 21 \times 8 \\ 12x = 168 \\ x = \frac{168}{12} \\ x = 14[/tex]

Hope this helps..

Good luck on your assignment..

Answer:

8

Step-by-step explanation:

when the valueof x is 8 then it is multiple of 3 and 11

#21285/3=7095

#21285/11=1935

I Hope this will be helpful for you.

Answer:

Step-by-step explanation:

Consecutive angles cut by a common transversal are supplementary. That means that

x + 87 =180             Subtract 87 from both sides.

x+87-87=180-87

x = 93

Answer:

k = -11

Step-by-step explanation:

Let [tex]p(x) = x^3-6x^2+kx+10[/tex]

And x+2 is a factor of p(x)

Let x+2 = 0 => x = -2

Putting in p(x)

=> p(-2) = [tex](-2)^3-6(-2)^2+k(-2)+10[/tex]

By remainder theorem, Remainder will be zero

=> 0 = -8-6(4)-2k+10

=> 0 = -8-24+10-2k

=> 0 = -22-2k

=> -2k = 22

Dividing both sides by -2

=> k = -11

Answer:

3

Step-by-step explanation:

The Absolute value of -3 is 3 because it's the distance away from 0. Both have the same distance away from 0.

The opposite number of the integer number negative 3 will be 3.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The number that produces zero when multiplied by an is known as the additive inverse of a number, or a, in arithmetic. The opposite, a shift in the sign, and negation are other names for this number.

The number is given below.

⇒ - 3

The opposite of the number negative 3 will be given as,

⇒ - (-3)

⇒ 3

The opposite number of the integer number negative 3 will be 3.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ5

Answer:

Step-by-step explanation:

A(-5,-2),B(-2,-2), C(-5,2)

find distance first:d=√(x2-x1)^2+(y^2-y1^2)

AB: 3

BC: 5

AC: 4

perimeter of triangle=3+5+4=12

compliment angle=90

90+34=124

5x+17+x+19=180

x=24

Answer:

B

Step-by-step explanation:

mean = average. to find it, add all terms, and then divide by the number of terms.

find the mean of group a:

(1+1.5+3+3.2+2.8+1.5+1.8+2.5+2.2)/9 = 2.16

find the mean of group b:

(2+2.5+3.2+3+1.8+2.4+3+1.5+1/8)/9 = 2.1694

group b is larger.

answer = b

Answer:

1386 in³

Step-by-step explanation:

Volume of the composite cone = volume of a hemisphere + volume of a cone

=>Find the volume of cone

Volume of cone = ⅓πr²h

π = 3.142

r = 7 in

h = =√(15² - 7²) [using Pythagorean theorem to solve for height given the slant height and radius]

h = √(225 - 49)

h = √176 ≈ 13 in

Volume of cone = ⅓*3.142*7²*13

= ⅓*2001.454 ≈ 667 in³

=>Find volume of hemisphere.

Volume of hemisphere = ½*volume of sphere = ½*4/3πr³ = ⅔πr³

π = 3.142

r = 7 in

Volume = ⅔*3.142*7³ ≈ 719 in³

Volume of composite figure = 667+719 = 1386 in³

Answer:

26

Step-by-step explanation:

Answer:

Its 26

Step-by-step explanation:

Correct on edg. 2021

Answer:

Step-by-step explanation:

Given the equations x^2 + y^2=25 ...1 and x^2/15-y^2/9=1,.. 2 to solve the systam of equation we will make  x^2 the subject of the formula from the first equation and substitute it into the second equation as shown;

Fom 1; x² = 25-y²... 3

Substituting equation 3 into 2 to get the resulting equation will give;

x²/15-y²/9=1

25-y²/15 - y²/9 = 1

The final expression gives the required equation.

Answer:

L/2

Step-by-step explanation:

If the width is half of its length, that means it is 1/2*L, as L is the length. This can be simplified into L/2, which is our answer.

Answer:L/2

Step-by-step explanation: The length is represented as L. So half the lenght is 1/2L which can also be represented as L/2. So the width is represented as L/2

Answer:

C. y=2x-48

Step-by-step explanation:

A. y=48x−2

B. y=48x+2

C. y=2x−48

D. y=2x+48

Profit per hotdog=$2

Quantity=x

Cost of hotdog, buns and mustard=$48

Find the equation profit earned by the hotdog stand for x hot dog sold

Total Profit(y)=(units profits*quantity)-cost

=$2*x-$48

y=2x-48

Answer:

C. y=2x−48

Step-by-step explanation:

did it on edge 2020

Answer:

When they create 3.44 products and make a revenue of $76.027, they will break even.

Step-by-step explanation:

To do this, simply graph the 2 equation in a graphing calculator and analyze the graph for where the 2 graphs intersect. Discard the negative intersection because we cannot have a negative production. You should see that your intersection point is (3.441, 76.027).

Answer:

1 - 8/9 + 4/9 = 9/9 -8/9 +4/9 = (9-8+4)/9 = 5/9

Step-by-step explanation:

Answer:

The answer is 5/9.

Step-by-step explanation:

First, you have to make all the denorminator of the fractions the same by multultiplying :

[tex]1 - \frac{8}{9} + \frac{4}{9} [/tex]

[tex] = \frac{1}{ 1} - \frac{8}{9} + \frac{4}{9} [/tex]

[tex] = \frac{1 \times 9}{1 \times 9} - \frac{8}{9} + \frac{4}{9} [/tex]

[tex] = \frac{9}{9} - \frac{8}{9} + \frac{4}{9} [/tex]

Next, you have to make it into 1 fraction and simplify :

[tex] \frac{9}{9} - \frac{8}{9} + \frac{4}{9} [/tex]

[tex] = \frac{9 - 8 + 4}{9} [/tex]

[tex] = \frac{5}{9} [/tex]

Answer:

1.) f(-2)=g(4)

2.) f(0) = g(-2)

3.) f(-4)=g(-2) and f(4)=g(4)

4.) -9

Step-by-step explanation:

Answer:

8,643

Step-by-step explanation:

The thousands digit is 8 so we know it is 8,000 The hundreds digit is 2 less than 8, so it's 6, giving us 8,600. The units digit is half the hundreds digit, so it is half of 6, or 3, now we have 8,603. Lastly, the tens digit is one greater than the units digit, so it is 4, leaving you with 8,643.

Answer:

7.5 hours

Step-by-step explanation:

distance = rate * time (d=rt)

First we find her average rate, or speed:

Now we take that rate and use our second distance to find the time:

d = rt

t = d/r = 350 miles / 46.6666 miles/hour = 7.5 hours

Answer:

D 0.6

Step-by-step explanation:

plato/edmentum

Answer: 0.6

Step-by-step explanation:

Answer:

( P^2) / K^2 = x

Step-by-step explanation:

P = K * sqrt ( x)

Divide each side by K

P/K = sqrt(x)

Square each side

( P^2) / K^2 = x

Answer:

The answer is

[tex]X = ({ \frac{K}{P} })^{2} [/tex]

[tex]P = \frac{K}{ \sqrt{x} } [/tex]

Cross multiply

that's

P√x = K

Divide both sides by P

That's

√x = K/P

Square both sides to make x stand alone

That's

(√X)² = ( K/P)²

We have the final answer as

[tex]X = ({ \frac{K}{P} })^{2} [/tex]

Hope this helps you

Answer:

Step-by-step explanation:

The claim being tested is that p not equals ≠ 0.877

A) This is the alternative hypothesis and it is a two tailed test. It means that it can be in either direction.

B)Given that z = 2.94, the p value would be determined from the normal distribution table. Since the curve is symmetrical and it is a two tailed test, the p for the left tail and the right tail would be considered. We will look at the area in both tails. Since it is showing in one tail only, we would double the area

From the normal distribution table, the area above the test z score in the right tail is 1 - 0.998 = 0.002

We would double this area to include the area in the left tail of z = - 2.94 Thus

p = 0.002 × 2 = 0.004

C) Since alpha, 0.01 > than the p value, 0.004, then we would reject the null hypothesis, H0

Answer:

first one

Step-by-step explanation:

Tracey bought 10 movies

some cost 13 and the others 16

Let x be the movies that cost 13 and y ones that cost 16

we can state that

since Tracey both ten

since the total price is 139

so the system is :

[tex]\left \{ {{13x+16y=139} \atop {x+y=10}} \right.[/tex]

Answer:

58000 x 15= 87000

Step-by-step explanation:

you just have to multiply it by 15

Answer:

667000

Step-by-step explanation:

Have to find what 15% of 580000 is first:

580000 x 0.15 (15% as decimal --> divide by 100) = 87000

Next add what 15% of 580000 is to 580000:

580000  + 87000 = 667000

Answer:

[tex]P(t)=256*e^{0.068185t}[/tex]

10 minutes for the population to double.

Step-by-step explanation:

The general formula for the population equation, P(t), is:

[tex]P(t)=A*e^{nt}[/tex]

We are given that for t =5 minutes and t = 2 minutes:

[tex]P(5)=360=A*e^{5n}\\P(20)=1,000=A*e^{20n}\\\\[/tex]

Solving for A and n:

[tex]ln(360)=ln(A)+5n\\ln(1,000)=ln(A)+20n\\ln(1,000)-4ln(360)=ln(A)-4ln(A)+20n-20n\\ln(A)=5.5455536\\A=256\\n=\frac{ln(360)-ln(256)}{5}\\n=0.068185[/tex]

The exponential equation that represents this situation is:

[tex]P(t)=256*e^{0.068185t}[/tex]

The population will double when P(t) = 512 bacteria:

[tex]512=256*e^{0.068185t}\\ln(2)=0.068185t\\t=10.17\ minutes[/tex]

To the nearest minute, it takes roughly 10 minutes for the population to double.

Answer:

a

Step-by-step explanation:

Well in the first you buy 5P+2B+3L

but then you buy 3P +1B+2L

and you add then up

Answer:

g=6

Step-by-step explanation:

We can start by multiplying both sides by 2

5(3g+2)=100

Now we can distribute the 5 by using the distributive property

15g+10=100

Then we subtract 10 from both sides

15g=90

Divide both sides by 15

g=6

Answer:

6

Step-by-step explanation:

5(3g + 2)/2 = 50              Multiply both sides by 2

5(3g + 2)  = 50*2 = 100   Remove the brackets

15g + 10 = 100                  Subtract 10     ***

15g+10-10 = 100 - 10         Collect like terms.

15g = 90                            Divide by 15   ***

15g/15 = 90/15

g = 6

I don't know how to cut this down so that it requires only 2 steps.  I guess that the two steps marked with *** are the 2 I would choose.

Answer:

Step-by-step explanation:

surface area of two trapezoids=2[(12+8)/2×3]=2[30]=60 cm²

surface area of side rectangles=10×8+10×12=10(8+12)=200 cm²

surface area of top=10×5=50 cm²

surface area of bottom=10×3=30 cm²

Total surface area=60+200+50+30=340 cm²

Answer:

Step-by-step explanation:

to find the surface area , you need to find the area of each side(face)

top: 5*10=50

the bottom of the shape: 3*10=30

the front face:10*8=80

the sides are trapezoid shapes with:different dimensions:

side :8,12 and eight of 3 ( the shape has 3 faces the same)

area=((12+8)/2)*3= 30 (30*3 faces or sides)

add the numbers: 50+30+80+(30*3)=250 cm^2

I hope it is right and good luck

Answer:

Step-by-step explanation:

The third one :

Answer:

solution,

[tex]x = \frac{far \: arc - near \: arc}{2} \\ \: \: \: \: = \frac{250 - (360 - 250)}{2} \\ \: \: \: \: \: = \frac{250 - 110}{2} \\ \: \: = \frac{140}{2} \\ \: \: = 70[/tex]

Hope this helps..

Good luck on your assignment

Answer:

Step-by-step explanation:

To calculate the perimeter we must add the lenghts of the sides :