All categories

3 years ago

Which of these equations is in slope intercept form?

Mathematics

1 answer:

AVprozaik [17]3 years ago

8 0

Answer:

$y = \frac{1}{2} x + 6$

Step-by-step explanation:

Remmeber that the slope-intercept form is:

$y = mx + b$

You might be interested in

Meghan has a beginning balance of $750 in her checking account. She writes a check for $150 and has a debit transaction of $135.

tatuchka [14]

Her new balance is her new balance would be 435
heres my math
750-150-135=435

8 0

3 years ago

Read 2 more answers

What is the equation of a circle with center -4, 7 and radius 6

Kitty [74]

Answer:

$( x + 4 )^2 + ( y - 7 )^2 = 36$

Step-by-step explanation:

Use the circle equation, $( x - h )^2 + ( y - k )^2 = r^2$

Plug in the center and radius:

$( x + 4 )^2 + ( y - 7 )^2 = 6^2$

Simplify:

$( x + 4 )^2 + ( y - 7 )^2 = 36$

So, the equation is $( x + 4 )^2 + ( y - 7 )^2 = 36$

4 0

2 years ago

Which expression is equivilent to 3x/x+1 divided by x+1?

Sveta_85 [38]

Step-by-step explanation:

$\frac{3x}{x + 1} \div (x + 1) \\ \\ = \frac{3x}{x + 1} \times \frac{1}{(x + 1) } \\ \\ = \frac{3x}{ {(x + 1)}^{2} }$

6 0

3 years ago

TWO EASY QUESTIONS 8TH GRADE MATH

Sophie [7]

9.
<2 and <6 are right angles by the definition of perpendicular lines.
Since corresponding angles are congruent, m || n.

11.
In a triangle, the measures of the three angles add to 180 degrees.
If one angle is a right angle, then that angle measures 90 degrees. The other two angle measures plus 90 degrees add to 180 degrees, so the other two angle measures add to 90 degrees. In a right triangle there is a right angle and two other angles that are complementary.

Now look at your problem.
One angle is a right angle.
The other two angles are complementary, so their measures add to 90 deg.

8x + 2 + 9x + 3 = 90

17x + 5 = 90

17x = 85

x = 5

3 0

2 years ago

Complete the square and write in standard form. Show all work.What would be the conic section:CircleEllipseHyperbolaParabola

mote1985 [20]

ANSWER

This is an ellipse. The equation is:

$\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1$

EXPLANATION

We have to complete the square for each variable. To do so, we have to take the first two terms and compare them with the perfect binomial squared formula,

$(a+b)^2=a^2+2ab+b^2$

For x we have to take 16x² and -32x. Since the coefficient of x is not 1, first, we have to factor out the coefficient 16,

$16x^2-32x=16(x^2-2x)$

Now, the first term of the expanded binomial would be x and the second term -2x. Thus, the binomial is,

$(x-1)^2=x^2-2x+1$

To maintain the equation, we have to subtract 1,

$16(x^2-2x+1-1)=16((x-1)^2-1)=16(x-1)^2-16$

Now, we replace (16x² - 32x) from the given equation by this equivalent expression,

$16(x-1)^2-16+9y^2+72y+16=0$

The next step is to do the same for y. We have the terms 9y² + 72y. Again, since the coefficient of y² is not 1, we factor out the coefficient 9,

$9y^2+72y=9(y^2+8y)$

Following the same reasoning as before, we have that the perfect binomial squared is,

$(y+4)^2=y^2+8y+16$

Remember to subtract the independent term to maintain the equation,

$9(y^2+8y)=9(y^2+8y+16-16)=9((y+4)^2-16)=9(y+4)^2-144$

And now, as we did for x, replace the two terms (9y² + 72y) with this equivalent expression in the equation,

$16(x-1)^2-16+9(y+4)^2-144+16=0$

Add like terms,

$\begin{gathered} 16(x-1)^2+9(y+4)^2+(-16-144+16)=0 \\ 16(x-1)^2+9(y+4)^2-144=0 \end{gathered}$

Add 144 to both sides,

$\begin{gathered} 16(x-1)^2+9(y+4)^2-144+144=0+144 \\ 16(x-1)^2+9(y+4)^2=144 \end{gathered}$

As we can see, this is the equation of an ellipse. Its standard form is,

$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$

So the next step is to divide both sides by 144 and also write the coefficients as fractions in the denominator,

$\begin{gathered} \frac{16(x-1)^2}{144}+\frac{9(y+4)^2}{144}=\frac{144}{144} \\ \\ \frac{(x-1)^2}{\frac{144}{16}}+\frac{(y+4)^2}{\frac{144}{9}}=1 \end{gathered}$

Finally, we have to write the denominators as perfect squares, so we identify the values of a and b. 144 is 12², 16 is 4² and 9 is 3²,

$\frac{(x-1)^2}{(\frac{12}{4})^2}+\frac{(y+4)^2}{(\frac{12}{3})^2}=1$

Note that we can simplify a and b,

$\frac{12}{4}=3\text{ and }\frac{12}{3}=4$

Hence, the equation of the ellipse is,

$\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1$

3 0

1 year ago