Simplify the expression. Write your answer as a power.
6^7•6^10 divided by 6^4•6^3

Answer:

y=-16

Step-by-step explanation:

2(y-4)-5(y+8)=0  (distribute the 2 and the negative 5)

2y-8-5y-40=0   (combine like terms)

-3y-48=0    (add 48 to both sides)

-3y=48     (divide both sides by -3)

y=-16

Hope this helps :)

The number of weeks after which they both have volunteered the same number of hours is 4 weeks. The amount volunteering time they'd have volunteered till that week is 16 hours.

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

Given that:

Let the number of weeks after which they both have volunteered the same number of hours be 'w' weeks.

Now, as Adrian volunteer 4 hours per week, then in w weeks, he'd have volunteered [tex]4 \times w[/tex] hours.

Also, as Cyrus already volunteered 8 hours, and then for w weeks, he volunteered 2 hours per week, so the number of hours he volunteered is: [tex]2 \times w + 8[/tex]

We had assumed that after w weeks, their volunteer time is same, so we can equate these amount of volunteering hours, as shown below:

[tex]4\times w= 2\times w + 8\\4w = 2w + 8[/tex]

(sign of multiplication is often hidden if there are non numeric symbols and numbers being multiplied are written together)

Subtracting 2w from both the sides, we get:

[tex]4w -2w = 8\\(4-2)w = 8\\2w = 8[/tex]

Dividing both the sides by 2, we get w on one side, rest of the constants on the other side, as:

[tex]\dfrac{2w}{2} = \dfrac{8}{2}\\\\w = 4[/tex]

Thus,  the number of weeks after which they both have volunteered the same number of hours is w = 4 weeks.

Now, evaluating any of those expressions to get the number of hours each of them volunteered till 4th week:

[tex]4w |_{w=4} = 4 \times 4 = 16 \: \rm hours\\2w +8|_{w=4} = 2(4) + 8 = 8+8 = 16 \: \rm hours[/tex]

(see, these are equal amount of time).

Thus, the number of weeks after which they both have volunteered the same number of hours is 4 weeks. The amount volunteering time they'd have volunteered till that week is 16 hours.

Learn more about forming equations here:

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Answer:

1st and 2nd options

Step-by-step explanation:

Using the method of completing the square to obtain standard form

(13)

Rearrange the given equation so x and y terms are together, that is

x² + 24x + y² + 30y + 353 = 0 ( subtract 353 from both sides )

x² + 24x + y² + 30y = - 353

To complete the square

add ( half the coefficients of the x/ y term)² to both sides

x² + 2(12)x + 144 + y² + 2(15)y + 225 = - 353 + 144 + 225

(x + 12)² + (y + 15)² = 16

(x + 12)² + (y + 15)² = 4² ← in standard form

with centre = (- 12, - 15 ) and radius = 4

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

(14)

As in number 13

x² - 22x + y² + 16y = - 181

Complete the square

x² + 2(-11)x + 121 + y² + 2(8)y + 64 = - 181 + 121 + 64

(x - 11)² + (y + 8)² = 4

(x - 11)² + (y + 8)² = 2² ← in standard form

with centre = (11, - 8 ) and radius = 2

Answer:

70

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

Answer:

3g

Step-by-step explanation:

We know that

20g = 8g + 4 * r

where r is the weight of a single red circle.

20g = 8g + 4 * r

12g = 4 * r

3g = r

Answer:

Hope this helps

Answer:

Middle and far right one

Step-by-step explanation:

X values cannot repeat

Answer:

SA = 615.44

Step-by-step explanation:

d = 14

r = d/2

r = 7

SA of a Sphere:

SA = 4πr²

SA = 4(3.14)(7²)

SA = 4(3.14)(49)

SA = 12.56(49)

SA = 615.44

Answer:

question? I don't understand

Answer:

7s + 10a

Step-by-step explanation:

I don't see a question so I just answered with a formula...

Answer:

172

Step-by-step explanation:

8/20 = x/430

8(430) = 3,440 = 20x/20

3,440/20  = 172

Ik it's complicated but you'll get it & your so very welcome.

Answer:

$39

Step-by-step explanation:

Answer:

12) complementary,   x=15

13) complementary, x = 35

x+ (x-20) = 90

x+x+20=90

2x=70

x=35

14) supplementary, x=31

2x+3x+25=180

5x=155

x=31

15) <1 = 130 degrees

 <2 = 50 degrees

<3 = 130 degrees

16) x=53

x+2x+21=180

3x=159

x=53

Answer:

The angle is equal to 45°, its complementary is equal to (90-45)°=45°, and its supplementar is equal to (180-45)°=135°

Step-by-step explanation:

Let the angle be equal to x°. We know that

[tex](180 - x) = 3(90- x)[/tex]

Therefore, solving for x, we have

[tex]180 - x = 270 - 3x \\ 2x = 90 \\ x = 45[/tex]

So the angle is equal to 45°, its complementary is equal to (90-45)°=45°, and its supplementar is equal to (180-45)°=135°

Answer:

x=1/3, x=-2/3

Step-by-step explanation:

9x^2 +6x -3x -2=0

6x and -3x add up to 3x. You need four terms to factor.

Then you factor=

3x(3x+2)-1(3x+2)=0

(3x-1)(3x+2)=0

Then you can make two equations

3x-1=0 and 3x+2=0 because to multiply to get 0, at least one will be 0.

3x-1=0

3x=1

x=1/3

3x+2=0

3x=-2

x=-2/3

So your answers are x=1/3, x=-2/3

hope this helps!

Answer:

the answer is B 1/x^2

Step-by-step explanation:

Answer:

B) 1/x²

Step-by-step explanation:

Answer:

I think its like a cartoon or something like that

https://hbomax-images.warnermediacdn.com/images/GXyniGAhmEcJZOgEAAABz/tileburnedin?size=1280x720&format=jpeg&partner=hbomaxcom&productCode=hbomax&host=artist.api.cdn.hbo.com&w=1200

there image I think

Answer:

do yourself a favor and download photomath. It'll save your life

Step-by-step explanation:

Step-by-step explanation:

To find the composite function, it says

[tex](f \: o \: g)(x)[/tex]

means we put the function g(x) into f(x) so that means it looks like

[tex]( \sqrt{x}) {}^{2} - 4[/tex]

Which equal

[tex]x - 4[/tex]

So that expression above is the answer.

To find the range we must find the range of the inner function ,(g(x) and then see which parts it corresponds of f(x).

The range of a g(x) which is a radical function is all real numbers.

The range of a f(x) which is a quadratic function is all real numbers greater than or equal to -4.

This means for our function to work we can use any numbers as long as it greater than -4.

So we would represent that as x is all real numbers as long as x is greater than or equal to -4

In interval notation this would be

[-4,+ infintiy)

q<13

Step-by-step explanation:

2q is less than 26 so 1q has to be less than half of 26 or 13.

q<13

Answer:

is 53

heart if it helped brain if im cooll

Answer:

37/20y

you find LCM first

Answer:

Budget= $1,100

Step-by-step explanation:

Giving the following information:

They spent $737 on equipment and 33% of the total budget on costumes.

If they spent all their budget on equipment and costumes, then the percentage spent on equipment was 67% (100 - 33).

Then, to calculate the total budget, we need to use the following formula:

Budget= 737 / 0.67

Budget= $1,100

Answer:

23 + [tex]\sqrt{29}[/tex] + [tex]\sqrt{58}[/tex]

Step-by-step explanation:

Answer:

152 pencils remain after 14 days of school.

Step-by-step explanation:

Replace x in this formula with 14 (14 days):

f(14) = 250 - 7(14) = 250 - 98 = 152

152 pencils remain after 14 days of school.

Answer:...

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

A

B

She can buy 5-6

C

Louis cannot purchase the bagels because she does not have enough money

Answer:

105

Step-by-step explanation:

To find area, you have to multiple the width by the height.

15*7=105.

Answer:

Area = 2307.9 cu.cm

Step-by-step explanation:

Height of the cylinder (h) = 15cm

radius (r) = 7 cm

we know ,

[tex]area \: of \: cyliner = \pi {r}^{2} \times h \\ \: \: \: \: = 3.14 \times {(7cm)}^{2} \times 15cm \\ \: \: = (3.14 \times 49 \times 15) {cm}^{3} \\ = 2307.9 {cm}^{3} [/tex]

Answer:

$969.04

Step-by-step explanation:

now at age of 18 Brad has 1500 * 1,065^18

at age of 21 he will have 1500 * 1,065^21

if he waits the difference will be 1500 * 1,065^21 - 1500 * 1,065^18 = $969.04

An amount of $292.5 will be more if the money is taken after 21st birthday that that in 18th birthday.

Simple interest is defined as the interest obtained over the principal amount on a certain rate.

Given that,

Principal amount, P = $1500

Rate of interest, r = 6.5% = 0.065

The final amount in a simple interest is,

A = P (1 + rt), where t is the number of years.

After 18 years,

Amount = 1500 [1 + (0.065 × 18)]

             = 1500 × 2.17

             = $3255

After 21 years,

Amount = 1500 [1 + (0.065 × 21)]

             = 1500 × 2.365

             = $3547.5

Difference = $3547.5 - $3255 = $292.5

Hence the difference of the amount is $292.5.

Learn more about Simple Interest here :

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#SPJ2

x = 5/2 or x = 1/3

C is the answer.

Answer:

x = 5/2 or x = 1/3

Step-by-step explanation:

Simplify  

( 2 x − 5 )( 3 x − 1 ) .

6 x 2 − 17 x + 5 = 0

Use the quadratic formula to find the solutions.

[tex]\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex] or [tex]\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]

Substitute the values  a = 6 ,  b = − 17 , and  c = 5  into the quadratic formula and solve for  x .

17 ±sqrt(-17)^2-4*(6*5)

_________________

2*6

Simplify.

x = 17 ± 13 /12

The final answer is the combination of both solutions.

x = 5 /2 ,  1 /3