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4 years ago

Which line contains the point (1,-3)

1 answer:

4 0

There are infinitely many lines that have the point (1,-3).

A line can be expressed as:

y=mx+b, where m=slope and b=y-intercept..

Our only restriction is that it passes through (1,-3) so

-3=1m+b

So as long as the sum of the slope and the y-intercept is equal to -3, that is one of the infinite number of lines that passes through (1, -3)

So we could also say b=-3-m then our infinite lines are:

y=mx-3-m, now any real value of m creates a specific line that passes through the point. ie the first few are

y=x-4, y=2x-5, y=3x-6 or even y=x√2-3-√2

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A carpenter is making a rectangular form for a concrete pad she wants the length of the path to be 11 feet more than the width o

Basile [38]

Answer:

Length = 16 or -5 feet.

Width = 5 or -16 feet.

Step-by-step explanation:

Let the length of the concrete pad = l

Let the width of the concrete pad = w

Given the following data;

Area of concrete pad, a = 80ft²

Translating the word problem into an algebraic equation, we have;

$l = 11 + w$

We know that, the area of rectangle, A = length * width

$A = l*w$

Substituting the values into the equation, we have;

$80 = (11 + w)w$

Expanding the bracket, we have;

$80 = 11w + w^{2}$

$w^{2} + 11w - 80 = 0$

*Solving the quadratic equation by using factorization method*

$w^{2} + 16w - 5w - 80 = 0$

$w(w + 16) - 5(w + 16) = 0$

$(w - 5)(w + 16) = 0$

Width, w = 5 feet or w = -16 feet.

Therefore, the width of the concrete pad is 5 feet or -16 feet.

To find its length, l;

$l = 11 + w$

When w = 5 feet

$l = 11 + 5$

Length, l = 16 feet

When w = - 16 feet

$l = 11 + (-16)$

$l = 11 - 16$

Length, l = -5 feet.

Hence, the dimensions of the concrete pad is 16 by 5 feet or -5 by -16 feet.

6 0

3 years ago

Please hellp I’m really confused

Viefleur [7K]

Answer:

Start at the origin and plot the points.

Step-by-step explanation:

For A, start at the origin and then go 4 units to the left.

For B, start at the origin and then go 4 units up.

For D, start at the origin and then go 4 units to the right.

For C, start at the origin and then go 4 units down.

6 0

2 years ago

Read 2 more answers

Mario has $150 to spend on food for a party. He ordered pizzas that cost $8 each and bottles of soda that cost $2 each which ine

White raven [17]

Answer:

8p + 2s <= 150

Step-by-step explanation:

Let p = number of a pizza.

Let s = price of a bottle of soda.

The inequality is

8p + 2s <= 150

7 0

3 years ago

Find an equation of the sphere which contains points A(1, 3, 2) and B(4, 3, 7) and the distance between A and B is equal to the

Marina86 [1]

Answer:

The answer is 8.5=(x-2.5)^2+(y-3)^2+(z-4.5)^2

Step-by-step explanation:

First we need to find diameter of the sphere. The distance point A and point B is:

$d=\sqrt{(4-1)^2+(3-3)^2+(7-2)^2} \\d=\sqrt{3^2+0^2+5^2} \\d=\sqrt{34} \\d=5.83$

d/2=r=2.92

radius of the sphere is 2.92 units

and the center of the sphere is:

C=((4+1)/2,(3+3)/2,(7+2)/2)

C=(2.5,3,4.5)

We can write the equation of the sphere as:

$r^2=(x-2.5)^2+(y-3)^2+(z-4.5)^2\\8.5=(x-2.5)^2+(y-3)^2+(z-4.5)^2$

4 0

3 years ago

PLZ HELP I'M SO CONFUSED AND THIS IS TIMED

alexandr402 [8]

Value of x is 30°

Answer:

Solution given:

x°+(5x)°=180°[being straight line which sum of angle is 180°]

adding like terms

(6x)°=180°

dividing both side by 6

(6x)°/6=180°/6

x=30°

5 0

2 years ago

Read 2 more answers