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2 years ago

Write the standard form of the equation: Slope= 3 y-intercept= -1

Mathematics

1 answer:

Amiraneli [1.4K]2 years ago

7 0

Answer:

y=3x-1

Step-by-step explanation:

y=mx+b

y=3x+b

y=3x-1

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Rewrite using a single positive exponent. 78 73

vivado [14]

Hey! I don’t know if this is what you mean.. but I tried to understand it.

78^1
73^1

Have a good day :)

3 0

2 years ago

Find the equation of a line through the coordinate (3,−2) and parallel to the line represented by y=12x−2.

denis-greek [22]

Answer:

Step-by-step explanation:

y + 2 = 12(x - 3)

y + 2 = 12x - 36

y =12x - 38

7 0

3 years ago

Please help me! Find the number x such that f(x) =1

STatiana [176]

Answer:

Step-by-step explanation:

We have the piecewise function:

$f(x) = \left\{ \begin{array}{ll} -\frac{1}{2}x-1 & \quad x \leq -2 \\ x & \quad x > -2 \end{array} \right.$

And we want to find x such that f(x)=1.

So, let's substitute 1 for f(x):

$1 = \left\{ \begin{array}{ll} -\frac{1}{2}x-1 & \quad x \leq -2 \\ x & \quad x > -2 \end{array} \right.$

This has two equations. So, we can separate them into two separate cases. Namely:

$1=-\frac{1}{2}x-1\text{ or } 1=x$

Let's solve for x in each case.

Case I:

We have:

$1=-\frac{1}{2}x-1$

Add 1 to both sides:

$2=-\frac{1}{2}x$

Let's cancel out the fraction by multiplying both sides by -2. So:

$2(-2)=(-2)\frac{-1}{2}x$

The right side cancels:

$-4=x\\$

Flip:

$x=-4$

So, x is -4.

Case II:

We have:

$1=x$

Flip:

$x=1$

This is the solution for our second case.

So, we have:

$x_1=-4\text{ or } x_2=1$

Now, can check to see if we have to to remove solution(s) that don't work.

Note that x=-4 is the solution to our first equation.

The first equation is defined only if x is less than -2.

-4 is less than -2. So, x=-4 is indeed a solution.

x=1 is the solution to our second equation.

The second equation is defined only if x is greater than or equal to -2.

1 is greater than or equal to -2. So, x=1 is also a solution.

Therefore, our two solutions are:

$x_1=-4\text{ or } x_2=1$

Out of our answer choices, we can pick D.

And we're done!

7 0

3 years ago

Question 2(Multiple Choice Worth 4 points) (08.02)A pair of equations is shown below. x + y = 5 y = one halfx + 2 If the two equ

8_murik_8 [283]

Answer:

$(2,3)$

Step-by-step explanation:

The first equation is $x+y=5$

The second equation is $y=\frac{1}{2}x+2$

When we graph these two equations, they will meet at a point which represent the solution of the two equations.

We can solve the two equations simultaneously to determine their point of intersection.

Let us substitute the second equation into the first equation to get;

$x+\frac{1}{2}x+2=5$

Multiply through by 2 to get;

$2x+x+4=10$

Group similar terms to obtain;

$2x+x=10-4$

Simplify;

$3x=6$

Divide both sides by 3;

$\Rightarrow x=2$

Put $x=2$ into the second equation;

$y=\frac{1}{2}(2)+2$

$\Rightarrow y=1+2$

$\Rightarrow y=3$

Therefore the graphs of the two functions intersect at (2,3)

See graph in attachment.

3 0

2 years ago

Explain why the exponents cannot be added in the product 12^3x11^3

frez [133]

Answer:

Step-by-step explanation:

Because 12 and 11 are not the same number it could be added it it were 11^3 and 11^4. But in this case it cannot.

4 0

2 years ago

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