Use the Binomial Theorem and Pascal’s Triangle to write each binomial expansion.

Solve the matrix equation below

Ket [755]

Answer:

We need to distribute the values
Hence [-4 0: 0 - 2 ] +[0 -3: 5 -4] X + [ 0 -3: 5 -4 ] = [19 -27 : 10 -24]

6 0

3 years ago

Question 1:

Gala2k [10]

Answer:

Q. 1: g(x) is translated 6 units down from f(x).

Q. 2: $g(x) = 1.25 \times 10^{x}$

Step-by-step explanation:

Question 1: Let $y = f(x) = \frac{3}{4}x$ and $y = g(x) = \frac{3}{4}x - 6$ are two different functions.

Now, the value of y is decreased by 6 units in g(x) with respect to f(x).

Therefore, g(x) is translated 6 units down from f(x). (Answer)

Question 2: Let $f(x) = 10^{x}$ , then transformation of f(x) by a vertical stretch with factor 1.25 means the y-value will be increases by 1.25 times for the same value of x.

Therefore, the transformed function will be $g(x) = 1.25 \times 10^{x}$ . (Answer)

8 0

3 years ago

One number is 4 less than 3 times a second number. If 3 more than two times the first number is decreased by two times the secon

Natali5045456 [20]

The 1st number is x and the 2nd number is y:

x = 3y-4
3 + 2x - 2y = 11

The first equation says that x is equal to "3y - 4", so you can plug in "3y - 4" for x in the second equation:

3 + 2(3y - 4) - 2y = 11
3 + 6y - 8 - 2y = 11
-5 + 4y = 11
4y = 16
y = 4

Now that you have y, you can plug it into the 1st equation to get x:

x = 3y - 4
x = 3(4) - 4
x = 12 - 4
x = 8

So, the 1st number is 8 and the 2nd number is 4.

6 0

3 years ago

2. The area of the base of the cone is 64π cm2 and the altitude is 6 cm. Calculate the cone: (a) the length of the constituent;(

andriy [413]

Answer: We have to calculate the (i) volume and (ii) the surface area of the cone:

$\begin{gathered} A=\pi r^2+\pi rl\rightarrow(1) \\ \\ V=\pi r^2\frac{h}{3}\rightarrow(2) \end{gathered}$

The formula (1) is for the lateral surface of the cone and the formula (2) is for the volume of the cone, the unknowns are determined as follows:

$\begin{gathered} r=\sqrt{\frac{64\pi}{\pi}}=8cm \\ \\ r=8cm \\ \\ l=\sqrt{r^2+h^2}=\sqrt{(8cm)^2+(6cm)^2} \\ \\ l=\sqrt{100}=10 \\ \\ l=10 \end{gathered}$

Therefore the volume and the lateral surface area is calculated as follows:

$\begin{gathered} \begin{equation*} A=\pi r^2+\pi rl \end{equation*} \\ \\ A=\pi(8)^2+\pi(8)(10) \\ \\ A=144\pi cm^2\Rightarrow(x) \\ \\ \begin{equation*} V=\pi r^2\frac{h}{3} \end{equation*} \\ \\ V=\pi(8cm)^2\frac{6cm}{3} \\ \\ V=128\pi cm^3\Rightarrow(y) \end{gathered}$

Therefore x and y are the answers.

5 0

1 year ago

NO LINKS!! PLEASEE HELPP QUICK I POSTED THIS SO MANY TIMES AND NOBODY ANSWERS PLSSS HELP MEEE Write the slope-intercept inequali

miskamm [114]

Answer:

y ≤ -2x - 2

Step-by-step explanation:

Slope- intercept form is y = mx + b, m being the slope and b being the y-intercept.

The slope is the rise of the line over the run. We can choose two points that are exactly on the line. Let's try points (-1, 0) and (0, -2). The line slopes down, so we already know the slope is negative. From point (-1, 0), the line goes down 2 units and over 1 unit. So, the slope is - $\frac{2}{1}$ . We can also simply say that the slope is -2.

The line intersects with the y-axis at point (0, -2), so the y-intercept is -2.

Because the shading is on the left side of the line and the line is solid, we can tell that y is less than or equal to -2x - 2. So, the equation is-

y ≤ -2x - 2

8 0

3 years ago