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3 years ago

Combine like terms. What is a simpler form of the expression? -3(-4y+3)+7y

Mathematics

1 answer:

kupik [55]3 years ago

8 0

Answer:

19y - 9

Step-by-step explanation:

-3(-4y + 3) + 7y =

Distribute the -3.

= 12y - 9 + 7y

Combine like terms: 12y + 7y

= 19y - 9

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The snack shop makes 3 mixes of nuts in the following proportions.

Julli [10]

Answer:

$A=\begin{bmatrix}6 & 5 & 3\\ 2 & 3 & 4\\ 2 & 2 & 3\end{bmatrix}$

$B=\begin{bmatrix}25\\ 18\\ 35\end{bmatrix}$

Step-by-step explanation:

It is given that the snack shop makes 3 mixes of nuts in the following proportions.

Mix I: 6 lbs peanuts, 2 lbs cashews, 2 lbs pecans.

Mix II: 5 lbs peanuts, 3 lbs cashews, 2 lbs pecans.

Mix III: 3 lbs peanuts, 4 lbs cashews, 3 lbs pecans.

they received an order for 25 of mix I, 18 of mix II, and 35 of mix III.

We need to find the matrices A & B for which AB gives the total number of lbs of each nut required to fill the order.

Mix I Mix II Mix III

peanuts 6 5 3

cashews 2 3 4

pecans 2 2 2

$A=\begin{bmatrix}6 & 5 & 3\\ 2 & 3 & 4\\ 2 & 2 & 3\end{bmatrix}$

$B=\begin{bmatrix}25\\ 18\\ 35\end{bmatrix}$

The product of both matrices is

$AB=\begin{bmatrix}6 & 5 & 3\\ 2 & 3 & 4\\ 2 & 2 & 3\end{bmatrix}\begin{bmatrix}25\\ 18\\ 35\end{bmatrix}$

$AB=\begin{bmatrix}6\cdot \:25+5\cdot \:18+3\cdot \:35\\ 2\cdot \:25+3\cdot \:18+4\cdot \:35\\ 2\cdot \:25+2\cdot \:18+3\cdot \:35\end{bmatrix}$

$AB=\begin{bmatrix}345\\ 244\\ 191\end{bmatrix}$

Therefore matrix AB gives the total number of lbs of each nut required to fill the order.

8 0

3 years ago

What is the 200 hundredth digit in 5/6

sladkih [1.3K]

5/6 = .83333333(repeating)

the 200th digit is 3

3 0

3 years ago

What is the absolute value equation for this graph?

tatyana61 [14]

Answer:

y = -|x +2| +4

Step-by-step explanation:

The parent function y=|x| is shifted to the left 2 units, so x is replaced by x+2. It is reflected across the x-axis, so is multiplied by -1: -|x+2|. It is shifted up 4 units, so has 4 added to it:

y = -|x+2| + 4

3 0

3 years ago

In the previous part, we obtained dy dx = 3t2 − 27 −2t . Next, find the points where the tangent to the curve is horizontal. (En

mina [271]

Answer:

(27.55, 7.22), (-11.3, 3.21).

Step-by-step explanation:

When is the tangent to the curve horizontal?

The tangent curve is horizontal when the derivative is zero.

The derivative is:

$\frac{dy}{dx} = 3t^{2} - 2t - 27$

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this question:

$3t^{2} - 2t - 27 = 0$

$a = 3, b = -2, c = -27$

Then

$\bigtriangleup = b^{2} - 4ac = (-2)^{2} - 4*3*(-27) = 328$

$t_{1} = \frac{-(-2) + \sqrt{328}}{2*3} = 3.35$

$t_{2} = \frac{-(-2) - \sqrt{328}}{2*3} = -2.685$

Enter your answers as a comma-separated list of ordered pairs.

We found values of t, now we have to replace in the equations for x and y.

t = 3.35

$x = t^{3} - 3t = (3.35)^{3} - 3*3.35 = 27.55$

$y = t^{2} - 4 = (3.35)^2 - 4 = 7.22$

The first point is (27.55, 7.22)

t = -2.685

$x = t^{3} - 3t = (-2.685)^3 - 3*(-2.685) = -11.3$

$y = t^{2} - 4 = (-2.685)^2 - 4 = 3.21$

The second point is (-11.3, 3.21).

8 0

3 years ago

the amount of gasoline used by a car varies jointly as the distance travelled and the square root of the speed.Suppose a car use

klemol [59]

Answer:

200 litres

Step-by-step explanation:

let g be gasoline used, d the distance travelled and s the speed, then the equation relating the quantities is

g = kd $\sqrt{s}$ ← k is the constant of variation

To find k use g = 25, d = 100 and s = 100, then

25 = k × 100 × $\sqrt{100}$ = k × 100 × 10 = 1000k ( divide both sides by 1000 )

0.025 = k

g = 0.025d $\sqrt{s}$ ← equation of variation

When d = 1000 and s = 64, then

g = 0.025 × 1000 × $\sqrt{64}$ = 0.025 × 1000 × 8 = 200

4 0

3 years ago