MATHEMATICS HIGH SCHOOL

Gym A charges a registration fee of $74 plus $33 per month for members. Gym B charges a registration fee of $164 plus $18 per month for members. After how many months would the total cost at Gym A and Gym B be the same for members?

Answers

Answer 1

Answer:

Answer:

The total charge at Gym A and Gym B would be the same at 6 months

Step-by-step explanation:

The model for the charges of both Gyms is made of the registration fee plus a variable quantity per month.

Let's call m the number of months for members.

Gym A charges $74 plus $33 per month, thus:

$C_a=74+33m$

Gym B charges $164 plus $18 per month, thus:

$C_b=164+18m$

We want to find out the number of months needed for both charges to be the same, thus:

$74+33m=164+18m$

Subtracting 74 and 18m:

$33m-18m=164-74$

Simplifying:

$15m=90$

Dividing by 15:

$m=90/15=6$

m=6

The total charge at Gym A and Gym B would be the same at 6 months

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Write each sum as a product of the GCF of the two numbers : 75 and 90

Answers

find factors and group common ones
75=3*5*5
90=2*3*3*5
common gropu is 3*5=15

75=15*5
90=15*6
ab+ac=a(b+c)
a is GCF
75+90
5(15)+5(6)=5(15+6)

If x2=y3, what is the value of z does x3z=y9?

Answers

If x² = y³ , for what value of z does $x^(3z)$ = $Y^(9)$ ?

Answer:

z= 2

Step-by-step explanation:

To solve the question given, we will follow the steps below;

$X^(3z)$ = $Y^(9)$ -----------------------------------------------------------------(1)

but applying the law of indices mᵃᵇ = (mᵃ)ᵇ

then

$Y^(9)$ = $(Y^(3))^(3)$

replace $Y^(9)$ by $(Y^(3))^(3)$ in equation (1)

$X^(3z)$ = $Y^(9)$

$X^(3z)$ = $(Y^(3))^(3)$ --------------------------------------------------------------------(2)

but from the question x² = y³

replace y³ by x² in equation (2)

$X^(3z)$ = $(Y^(3))^(3)$

$X^(3z)$ = $(X^(2))^(3)$

$X^(3z)$ = $X^(6)$

3z = 6

divide both-side of the equation by 3

3z/3 = 6/3

On the left-hand side of the equation, 3 at the numerator will cancel-out 3 at the denominator leaving us with just z while on the right-hand side of the equation 6 will be divided by 3

z= 2

What is the LCD of 8 5/12 and 3 5/8?

Answers

The lowest common denominator of those two numbers is 12.

8 5/12 = 8 10/24
3 5/8 = 3 15/24

Answer:

Step-by-step explanation:

Which are all the solutions of 5sinθ-4=2sinθ-4, where 0≤θ≤2π

Answers

5sinx-4 =2sinx-4
5sinx-2sinx= 4-4
3sinx=0
sinx=(0÷3)
sinx = 0
x = sin^-1 (0)
x= 0 degrees

And also x = (180- 0 ) = 180 degrees

so x; has 2 answers within the above given interval.

They are;
x= 0 degrees and x=180 degrees

What two numbers have a sum of 17 and a difference of 3

Answers

(7 & 10), bc 10-7=3 and 10+7=17

Select all the true statements.- 1.9 is to the left of -1.48.
-1.9 is to the right of -1.48.
1.9 is closer to 0.
-1.48 is closer to 0.
-1.48 is less than – 1.9.
-1.48 is greater than -1.9.