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8_murik_8 [283]

2 years ago

13

What is the equation of the following line written in slope-intercept form -2/3 and -1/-4? y = -11x - 7 y = -7x + 11 y = -7x - 1

1

1 answer:

Snowcat [4.5K]2 years ago

4 0

Answer:

$y=-7x-11$

Step-by-step explanation:

Given:

The two points on the line are $(-2,3)$ and $(-1,-4)$ .

The slope of the line joining two points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is given as:

$Slope,m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Here, $x_{1}=-2,y_{1}=3,x_{2}=-1,y_{2}=-4$

∴ $m=\frac{-3-4}{-1-(-2)}=\frac{-7}{-1+2}=\frac{-7}{1}=-7$

Equation of line with a point $(x_{1},y_{1})$ and slope $m$ is given as:

$y-y_{1}=m(x-x_{1})$

Plug in -2 for $x_{1}$ , 3 for $y_{1}$ and -7 for $m$ . This gives,

$y-3=-7(x-(-2))\\y-3=-7(x+2)\\y-3=-7x-(7\times 2)\\y-3=-7x-14\\y=-7x-14+3\\y=-7x-11$

Therefore, the equation of the line in vertex form is $y=-7x-11$ .

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The discriminant of a quadratic equation is 40. What is the nature of solutions?

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Answer:

It means that the roots of the quadratic equation are real and distinct

Step-by-step explanation:

Here, given the discriminant of the quadratic equation, we want to find out the nature of the solutions.

Mathematically, we can use to determine the nature of the discriminant.

By it’s formula;

D = b^2 - 4ac

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3 years ago

Type the correct answer in each box. A circle is centered at the point (5, -4) and passes through the point (-3, 2). The equatio

Galina-37 [17]

Answer:

$(x+ \boxed{-5})^2+(y+\boxed4)^2=\boxed{100}$

Step-by-step explanation:

Given:

Center of circle is at (5, -4).

A point on the circle is $(x_1,y_1)=(-3, 2)$

Equation of a circle with center $(h,k)$ and radius 'r' is given as:

$(x-h)^2+(y-k)^2=r^2$

Here, $(h,k)=(5,-4)$

Radius of a circle is equal to the distance of point on the circle from the center of the circle and is given using the distance formula for square of the distance as:

$r^2=(h-x_1)^2+(k-y_1)^2$

Using distance formula for the points (5, -4) and (-3, 2), we get

$r^2=(5-(-3))^2+(-4-2)^2\\r^2=(5+3)^2+(-6)^2\\r^2=8^2+6^2\\r^2=64+36=100$

Therefore, the equation of the circle is:

$(x-5)^2+(y-(-4))^2=100\\(x-5)^2+(y+4)^2=100$

Now, rewriting it in the form asked in the question, we get

$(x+ \boxed{-5})^2+(y+\boxed4)^2=\boxed{100}$

4 0

3 years ago

one rectangle measures 2 units by 7 units. a second rectangle measures 11 units by 37 units. are these two figures scaled versio

Amanda [17]

Answer: The both triangle are not scale version to each other.

Explanation:

It is given that the one rectangle measures 2 units by 7 units. a second rectangle measures 11 units by 37 units.

The two shapes are scaled version of each other if their corresponding sides are in same proportion. In other words the if two shapes scaled version of each then the shapes are similar.

The sides or first rectangle are 2 and 7. The measures of second rectangle are 11 and 37.

The proportion of small side is,

$\frac{2}{11}$

The proportion of large side is,

$\frac{7}{37}$

So,

$\frac{2}{11}\neq \frac{7}{37}$

Since the proportion are not equal, therefore both triangle are not scale version to each other.

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3 years ago