6³ . 2⁶ |Which expressions are equal to 2³ ? |126 23 . 33 26. 33 123

Find the missing side length assuming lines that appear to be tangent are tangent. Show work on piece of paper.

KIM [24]

Answer:

20

Step-by-step explanation:

Since the line of length 16 is a tangent to the circle, then the angle between it and the radius is right.

? is the hypotenuse of the right triangle formed.

Using Pythagoras' identity on the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

?² = 12² + 16² = 144 + 256 = 400 ( take the square root of both sides )

? = $\sqrt{400}$ = 20

3 0

3 years ago

Dilate the given points distance from the origin (x,y) (0.8x, 0.8y) . The point (-10,-20) becomes & point (15,25) become

dalvyx [7]

Answer: The point (-10,-20) becomes (-8,-16) & point (15,25) becomes (12,20).

Step-by-step explanation:

When a point (x,y) is dilated by a scale factor k from the origin, then the new points become

$(kx,ky).$

The given rule of dilation : (x,y) →(0.8x, 0.8y)

The first point is (-10,-20), so its image will be

$(-10,-20)\to (0.8\times-10,0.8\times-20)=(-8,-16)$

So, the point (-10,-20) becomes (-8,-16).

The second point is (15,25), so its image will be

$(15,25)\to (0.8\times15,0.8\times25)=(12,20)$

So, the point (15,25) becomes (12,20).

Hence, the point (-10,-20) becomes (-8,-16) & point (15,25) becomes (12,20).

8 0

3 years ago

What is the first step to solve the following system of equations using substitution?

Akimi4 [234]

Answer:

Step 1: Solve one of the equations for one of the variables. Let's solve the first equation for x

Thus, option A) is true.

The solution to the system of equations be:

$x = 4, y = 5$

Step-by-step explanation:

It is important to remember that when we solve the system of equations, the first step we need to do is to solve one of the equations for one of the variables.

Given the system of equations

$x - y = -1$

$2x - y = 3$

Step 1: Solve one of the equations for one of the variables. Let's solve the first equation for x

$x-y=-1$

Add y to both sides

$x-y+y=-1+y$

$x=-1+y$

Thus, option A) is true.

NOW LET US SOLVE THE REMAINING PORTION

$\mathrm{Subsititute\:}x=-1+y$ to solve for y

$\begin{bmatrix}2\left(-1+y\right)-y=3\end{bmatrix}$

$-2+y=3$

$y=5$

For x = -1 + y

substitute y = 5

$x=-1+5$

$x=4$

Thus, the solution to the system of equations be:

$x = 4, y = 5$

3 0

2 years ago

A bacteria culture starts with 12,000 bacteria and the number doubles every 50 minutes.

Vlada [557]

Answer:

a) $y=12000(2)^{\frac{t}{50}}$

b) Approx. 27,569 bacteria

c) About 103 minutes

Step-by-step explanation:

a)

This will follow exponential modelling with form of equation shown below:

$y=Ab^{\frac{t}{n}}$

Where

A is the initial amount (here, 12000)

b is the growth factor (double, so growth factor is "2")

n is the number of minutes in which it doubles, so n = 50

Substituting, we get our formula:

$y=Ab^{\frac{t}{n}}\\y=12000(2)^{\frac{t}{50}}$

b)

To get number of bacteria after 1 hour, we have to plug in the time into "t" of the formula we wrote earlier.

Remember, t is in minutes, so

1 hour = 60 minutes

t = 60

Substituting, we get:

$y=12000(2)^{\frac{t}{50}}\\y=12000(2)^{\frac{60}{50}}\\y=12000(2)^{\frac{6}{5}}\\y=27,568.76$

The number of bacteria after 1 hour would approximate be 27,569 bacteria

c)

To get TIME to go to 50,000 bacteria, we will substitute 50,000 into "y" of the equation and solve the equation using natural logarithms to get t. Shown below:

$y=12000(2)^{\frac{t}{50}}\\50,000=12,000(2)^{\frac{t}{50}}\\4.17=2^{\frac{t}{50}}\\Ln(4.17)=Ln(2^{\frac{t}{50}})\\Ln(4.17)=\frac{t}{50}*Ln(2)\\\frac{t}{50}=\frac{Ln(4.17)}{Ln(2)}\\\frac{t}{50}=2.06\\t=103$

After about 103 minutes, there will be 50,000 bacteria

4 0

3 years ago

everyday a person uses about 90 liters of water at home 6 gallons is about 23 liters about how many liters of water does a perso

Trava [24]

Answer:

90 liters

Step-by-step explanation:

It's given in the question!

3 0

1 year ago

6³ . 2⁶ |Which expressions are equal to 2³ ? |126 23 . 33 26. 33 123​

6³ . 2⁶ |Which expressions are equal to 2³ ? |126 23 . 33 26. 33 123