1/5(2x-15)=1/10(4x-30)

The area of a shape is 100cm2 what is the area if the shape is dialated with a scale factor of 1/5

Sveta_85 [38]

Answer:

20cm squared

Step-by-step explanation:

8 0

3 years ago

hi, i dont undertand number 20 because i was absent in class today and i rerally need help, i will appraciate with the help, and

Mariulka [41]

Given:

The equation is,

$2\log _3x-\log _3(x-2)=2$

Explanation:

Simplify the equation by using logarthimic property.

$\begin{gathered} 2\log _3x-\log _3(x-2)=2 \\ \log _3x^2-\log _3(x-2)=2_{}\text{ \lbrack{}log(a)-log(b) = log(a/b)\rbrack} \\ \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \end{gathered}$

Simplify further.

$\begin{gathered} \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \\ \frac{x^2}{x-2}=3^2 \\ x^2=9(x-2) \\ x^2-9x+18=0 \end{gathered}$

Solve the quadratic equation for x.

$\begin{gathered} x^2-6x-3x+18=0 \\ x(x-6)-3(x-6)=0 \\ (x-6)(x-3)=0 \end{gathered}$

From the above equation (x - 6) = 0 or (x - 3) = 0.

For (x - 6) = 0,

$\begin{gathered} x-6=0 \\ x=6 \end{gathered}$

For (x - 3) = 0,

$\begin{gathered} x-3=0 \\ x=3 \end{gathered}$

The values of x from solving the equations are x = 3 and x = 6.

Substitute the values of x in the equation to check answers are valid or not.

For x = 3,

$\begin{gathered} 2\log _3(3^{})-\log _3(3-2)=2 \\ 2\log _33-\log _31=2 \\ 2\cdot1-0=2 \\ 2=2 \end{gathered}$

Equation satisfy for x = 3. So x = 3 is valid value of x.

For x = 6,

$\begin{gathered} 2\log _36-\log _3(6-2)=2 \\ 2\log _36-\log _34=2 \\ \log _3(6^2)-\log _34=2 \\ \log _3(\frac{36}{4})=2 \\ \log _39=2 \\ \log _3(3^2)=2 \\ 2\log _33=2 \\ 2=2 \end{gathered}$

Equation satifies for x = 6.

Thus values of x for equation are x = 3 and x = 6.

6 0

11 months ago

The sum of 5 consecutive integers is 100. What is the first number in this sequence?

yanalaym [24]

So we can call first number "n"

Then all five integers would be n, n+1, n+2, n+3, n+4

So sum of them would be 5n + 10 = 100

Now you can solve for n:

5n + 10 = 100

5n = 90

n = 18

Verify: 18 + 19 + 20 + 21 + 22 = 100. All good.

So answer is 18

5 0

2 years ago

ALGUEMMM ME AJUDAAA POR FAVORRR!!!!!!!!!!!!!!!!!!!

Amanda [17]

Answer:

50)

a. + 13

B. +10

C. -15

D. -5

Step-by-step explanation:

8 0

3 years ago

Emily thinks the perfect tomato sauce has 8 cloves of garlic in every 500 mL of sauce. Raphael's tomato sauce has 12 cloves of g

ivolga24 [154]

Answer:

Emiy would think that it is not the perfect tomato sauce because it has 12 cloves of garlic in every 900 mL of sauce and it should have 14.4 cloves of garlic in every 900 mL of sauce to be perfect.

Step-by-step explanation:

The statement indicates that for Emily the perfect tomato sauce have 8 cloves of garlic in every 500 mL. With that we can calculate the amount of cloves of garlic that a tomato sauce should have for Emily to consider it to be perfect using the rule of three:

8 cloves of garlic → 500 mL

x ← 900 mL

x= (8*500)/900= 14.4

According to this, the perfect tomato sauce would need to have 14.4 cloves of garlic in every 900 mL. As Raphael's tomato sauce only has 12, it means that Emily would think that it is not the perfect tomato sauce.

7 0

2 years ago