The membership fee at a sports club was $600 per year. Each year, the membership fee increased by 7%. The cost of membership, y, can be modeled by the equation y=600(1.07)^x, where x is the number of years.
How many years will it take for the cost of the membership to be $900?

Choose the answer that gives the correct logarithmic equation and answer.


x=log1.5(1.07)

x=6


x=log1.07(1.5)

x=6


x=log(1.51.07)

x=1


x=log(1.071.5)

x=1

Answer:

C)

Step-by-step explanation:

infinite number of solutions means the left side equals the right side of the equation

no solution means the left side does not equal the right side

x = {whatever} means there is one solution

Answer:1.85+x=5.30

Step-by-step explanation: ez

Answer:

1.85 + x = 5.30

Step-by-step explanation:

It started of at 1.85 meters

After awhile it has reached a height of 5.30

If x represents the meters the tree has grown then x + 1.85 will equal 5.30 as the tree started off at 1.85 meters and reached a height of 5.30

Answer:

[tex] \displaystyle \begin{cases} \displaystyle {x} _{1} = - p \\ \displaystyle x _{2} = - q \end{cases}[/tex]

Step-by-step explanation:

we would like to solve the following equation for x:

[tex] \displaystyle \frac{1}{p} + \frac{1}{q} + \frac{1}{x} = \frac{1}{p + q + x} [/tex]

to do so isolate [tex]\frac{1}{x}[/tex] to right hand side and change its sign which yields:

[tex] \displaystyle \frac{1}{p} + \frac{1}{q} = \frac{1}{p + q + x} - \frac{1}{x} [/tex]

simplify Substraction:

[tex] \displaystyle \frac{1}{p} + \frac{1}{q} = \frac{x - (q + p + x)}{x(p + q + x)} [/tex]

get rid of only x:

[tex] \displaystyle \frac{1}{p} + \frac{1}{q} = \frac{ - (q + p )}{x(p + q + x)} [/tex]

simplify addition of the left hand side:

[tex] \displaystyle \frac{q + p}{pq} = \frac{ - (q + p )}{x(p + q + x)} [/tex]

divide both sides by q+p Which yields:

[tex] \displaystyle \frac{1}{pq} = \frac{ -1}{x(p + q + x)} [/tex]

cross multiplication:

[tex] \displaystyle x(p + q + x) = - pq[/tex]

distribute:

[tex] \displaystyle xp + xq + {x}^{2} = - pq[/tex]

isolate -pq to the left hand side and change its sign:

[tex] \displaystyle xp + xq + {x}^{2} + pq = 0[/tex]

rearrange it to standard form:

[tex] \displaystyle {x}^{2} + xp + xq + pq = 0[/tex]

now notice we end up with a quadratic equation therefore to solve so we can consider factoring method to use so

factor out x:

[tex] \displaystyle x( {x}^{} + p ) + xq + pq = 0[/tex]

factor out q:

[tex] \displaystyle x( {x}^{} + p ) +q (x + p)= 0[/tex]

group:

[tex] \displaystyle ( {x}^{} + p ) (x + q)= 0[/tex]

by Zero product property we obtain:

[tex] \displaystyle \begin{cases} \displaystyle {x}^{} + p = 0 \\ \displaystyle x + q= 0 \end{cases}[/tex]

cancel out p from the first equation and q from the second equation which yields:

[tex] \displaystyle \begin{cases} \displaystyle {x}^{} = - p \\ \displaystyle x = - q \end{cases}[/tex]

and we are done!

Step-by-step explanation:

here is my answer.. i hope it can help.. correct me if im wrong..

Answer:

y= -3x + 5

Step-by-step explanation:

The slope of the line is m=−3

m=−3.

The equation of the line in the slope-intercept form is y=−3x+5y=−3x+5.

The equation of the line in the point-slope form is y−5=−3xy−5=−3x.

Answer:

A) The total length of each edging in her scale drawing would be 19.2 centimeters.

B) Square or rectangle

C) angle  α= 53.13 degrees

angle β=  36.87 degrees

height=  32 inches

base= 24 inches

hypotenuse 40 inches.

Step-by-step explanation:

Part A:

If the roll edging is 96 inches long and the scale chosen is

5inches = 1 cm

96inches /5= 19.2cm

The total length of each edging in her scale drawing would be 19.2 centimeters.

Part B:

The quadrilaterals such rectangle square right  trapezoid have a pair of 90 degrees angles.

If we choose a square shape then all sides must be equal. And we have a length of 19.2 centimeters.

Dividing 19.2 by 4  gives 4.8 cm for each side.

Figure A  shows a square and has 4 sides equal and 4 right angles.

If we choose a rectangle shape then 2 sides must be equal. We have a length of 19.2 centimeters.

Suppose the length is 2 times more than the width

which will give the dimensions as

2*2 x+ 2x= 6x   ( length and width denoted by x)

Dividing 19.2 by 6  gives 3.2 cm for each width and  6.4 for the lengths.

Figure B shows a rectangle  and has 2 sides equal and 4 right angles.

It depends on which quadrilateral you wish to choose.

Part C:

Using Pythagorus theorem if the base and altitude are given then the hypotenuse can be found out using the following formula.

c²= a² +b²

c²= 6.4² +4.8²

c²= 40.96+23.04= 64

c= √64 = 8

The third side must be equal to 8 centimeters.

Using the formula

Cos α= base / hypotenuse

Cos α=4.8/8

α= Cos (inverse) 4.8/8

α= Cos (inverse) 0.6

α= 53.13 degrees

So angle α= 53.13 degrees

All the angles in the triangle must be 180 degrees.

α + β +  90°= 180°

And angle β= 180-90-53.13= 36.869= 36.87 degrees

The actual dimensions of this triangle are

height= a= 6.4* 5= 32 inches

base= b= 4.8*5= 24 inches

hypotenuse= 8*5= 40 inches.

Answer:

its all black;-; that just color black

Step-by-step explanation:

how we going to see it if that is black

Answer:

SI = $1,200 ; A = $6,200

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 3%/100 = 0.03 per year,

then, solving our equation

I = 5000 × 0.03 × 8 = 1200

I = $ 1,200.00

The simple interest accumulated

on a principal of $ 5,000.00

at a rate of 3% per year

for 8 years is $ 1,200.00.

Answer:

no

Step-by-step explanation:

it's X= 0.5

group like terms

3x - 5x = 6 - 2 - 5

simplify the equation

-2x = -1

divide through by the coefficient of X

x = 0.5

Answer:

20%

Step-by-step explanation:

We were given a price at $50 on sale for $40. To get the markdown percentage, take the amount of money you've discounted the merchandise at and divide it by the sales price.

$50 sweaters, you can put them on sale for $40.

[tex]50 - 40 = 10[/tex]

The difference between these two prices is $10.

Now, we need to add the amount of which it was marked down

[tex]10 + 10 = 20[/tex]

Therefore, the watch has been marked down by 20%.

Answer:

x-15

Step-by-step explanation:

less than means it comes after

so the 15 is subtracted from x

x-15

Answer:

A. x - 15

Step-by-step explanation:

Answer:

Length of straw = 11 inch (Approx.)

Step-by-step explanation:

Given:

Length of cuboid = 9 inch

Width of cuboid = 5 inch

Height of cuboid = 4 inch

Find;

Length of straw

Computation:

Length of straw = Diagonal of cuboid

Diagonal of cuboid = √l² + b² + h²

Diagonal of cuboid = √9² + 5² + 4²

Diagonal of cuboid = √81 + 25 + 16

Diagonal of cuboid = √122

Diagonal of cuboid = 11.04

Length of straw = 11 inch (Approx.)

Answer: 1/5 or 20%

Step-by-step explanation:

4 red + 9 blue + 7 white = 20 total

neither blue nor white means it has to be red so 4/20 or 1/5

Answer:

25in (correct)

Answer:

88 centimeters

Step-by-step explanation:

8 times 11 is 88

The length of the path is 88 centimeters.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example: so

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Ayla uses 11 pieces of track, and each piece is 8 centimeters long, so the total length of the path is:

11 pieces of track x 8 centimeters per piece

= 88 centimeters

Therefore,

The length of the path is 88 centimeters.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ3

Answer:

y = -5x + 2

Step-by-step explanation:

y = -5x + b

2 = -5(0) + b

2 = 0 + b

b = 2

y = -5x + 2

Answer:

A and C

Step-by-step explanation:

Answer:

volume = ⅓×π×4²×9 = 48π sq. meters

Answer:

y=.5x-2

Step-by-step explanation:

If one line is perpendicular to another that means that their slopes are negative reciprocals

which means that the slope (or m in y=mx+b) is .5

so far we have

y=.5x+b

to solve for b we plug in (8,2)

2=.5(8)+b

2=4+b

-2=b

therefore our equation is

y=.5x-2

Answer:

hope it helps

stay safe healthy and happy.

Answer:

70.83

Step-by-step explanation:

srr if incorrect

Answer:

10

Step-by-step explanation:

Given:

[tex](3x+7)^2[/tex] is subtracted from 3.

To find:

The result of the given statement in the standard form of the polynomial.

Solution:

We need to find the result when [tex](3x+7)^2[/tex] is subtracted from 3.

So, the resulted polynomial can be written as:

[tex]P(x)=3-(3x+7)^2[/tex]

On simplification, we get

[tex]P(x)=3-((3x)^2+2(3x)(7)+(7)^2)[/tex]               [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]

[tex]P(x)=3-(9x^2+42x+49)[/tex]

[tex]P(x)=3-9x^2-42x-49[/tex]

[tex]P(x)=-9x^2-42x-46[/tex]

Therefore, the resulted polynomial in standard form is [tex]-9x^2-42x-46[/tex].

Answer:

The answer is d

Step-by-step explanation:

this is because a , b and c all have multiple x vales with more then one y value .

Answer:

24

Step-by-step explanation:

Because we have to look at the GREATEST common factor.

8 and 12 are factors but they are not the greatest.

24 is the greatest common factor they both share.