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4 years ago

Which pair of points represents the solution set of this system of equations? y = x2 − 6x + 8 2y + x = 4

Mathematics

1 answer:

astra-53 [7]4 years ago

6 0

Try this

2y+x=4 Y=(4-x)\2 (4-x)/2=x2-6x+8

Hope this helps

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For the equation ae^ct=d, solve for the variable t in terms of a,c, and d. Express your answer in terms of the natural logarithm

saveliy_v [14]

We have been given an equation $ae^{ct}=d$ . We are asked to solve the equation for t.

First of all, we will divide both sides of equation by a.

$\frac{ae^{ct}}{a}=\frac{d}{a}$

$e^{ct}=\frac{d}{a}$

Now we will take natural log on both sides.

$\text{ln}(e^{ct})=\text{ln}(\frac{d}{a})$

Using natural log property $\text{ln}(a^b)=b\cdot \text{ln}(a)$ , we will get:

$ct\cdot \text{ln}(e)=\text{ln}(\frac{d}{a})$

We know that $\text{ln}(e)=1$ , so we will get:

$ct\cdot 1=\text{ln}(\frac{d}{a})$

$ct=\text{ln}(\frac{d}{a})$

Now we will divide both sides by c as:

$\frac{ct}{c}=\frac{\text{ln}(\frac{d}{a})}{c}$

$t=\frac{\text{ln}(\frac{d}{a})}{c}$

Therefore, our solution would be $t=\frac{\text{ln}(\frac{d}{a})}{c}$ .

5 0

3 years ago

What key features will all continuous exponential functions have?

Hoochie [10]

Answer:

The graph passes through the point (0,1)
The domain is all real numbers.
The range is y>0.
The graph is increasing.
The graph is asymptotic to the x-axis as x approaches negative infinity.
The graph increases without bound as x approaches positive infinity.
The graph is continuous.

7 0

3 years ago

Please help me?i don’t want to fail

Kobotan [32]

Answer:

-4x-(-5x)=1

the slope is 6

you start at the 0 axis and go up 3 on the y.Once you did that you want to go up 2 on the y axis then 3 to the right on the x axis,then go up 2 then 3 to the right.

Step-by-step explanation:

8 0

2 years ago

Simplify -3x³y²(-4x²y•y•y•y•y)²

AnnZ [28]

$-3x^3y^2(-4x^2 \underbrace{y\cdot y\cdot y\cdot y}_{y^4})^2\\\\=(-3)(-4)(x^3x^2)(y^2y^4)\\\\=12x^{3+2}y^{2+4}\\\\=\boxed{12x^5y^6}\\\\Used:\\\\a^n\cdot a^m=a^{n+m}$

3 0

3 years ago

Read 2 more answers

A kangaroo hops 2 kiliometers in 3 minutes. At this rate: How far does the kangaroo travel in 6 minutes?

Bess [88]

Answer:

4km

Step-by-step explanation:

4 0

3 years ago