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3 years ago

What is the equation of the line that passes through point (1, 1) and is

Mathematics

1 answer:

kaheart [24]3 years ago

8 0

Answer:

Step-by-step explanation:

-y = -2x + 3

y = 2x - 3

y - 1 = 2(x - 1)

y - 1 = 2x - 2

y = 2x - 1

answer is B

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A 25% acid solution must be added to a 40% solution to get 240 liters of 30% acid solution. How many of each should be used ?

schepotkina [342]

Answer:

The number of liters of 25% acid solution = x = 160 liters

The number of liters of 40% acid solution = y = 80 liters

Step-by-step explanation:

Let us represent:

The number of liters of 25% acid solution = x

The number of liters of 40% acid solution = y

Our system of Equations =

x + y = 240 liters....... Equation 1

x = 240 - y

A 25% acid solution must be added to a 40% solution to get 240 liters of 30% acid solution.

25% × x + 40% × y = 240 liters × 30%

0.25x+ 0.4y = 72...... Equation 2

We substitute 240 - y for x in Equation 2

0.25(240 - y)+ 0.4y = 72

60 - 0.25y + 0.4y = 72

Collect like terms

- 0.25y + 0.4y = 72 - 60

0.15y = 12

y = 12/0.15

y = 80 Liters

Solving for x

x = 240 - y

x = 240 liters - 80 Liters

x = 160 liters

Therefore,

The number of liters of 25% acid solution = x = 160 liters

The number of liters of 40% acid solution = y = 80 liters

5 0

3 years ago

Circle B has a center at point (0, 2) and a point W on the circle at (3, 3). Which equation represents a line that is tangent to

Solnce55 [7]

According to the given information, the equation represents a line that is tangent to the circle and goes through the point W is given by:

y = -x + 6.

<h3>What is the equation of the circle?</h3>

The equation of a circle of center $(x_0,y_0)$ and radius r is given by:

$(x - x_0)^2 + (y - y_0)^2 = r^2$

In this problem, we have that the center is at point (0,2), hence:

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

It goes through point (3,3), hence:

$3^2 + (3 - 2)^2 = r^2$

$r^2 = 10$

Hence, the equation is:

$x^2 + (y - 2)^2 = 10$

<h3>What is the equation of the tangent line at point W?</h3>

It is given by:

$y - y(0) = \frac{dy}{dx}|_{W}(x - x(0))$

Applying implicit differentiation, we have that:

$2x + 2y\frac{dy}{dy} = 0$

$\frac{dy}{dx} = -\frac{x}{y}$

Point W(3,3), hence:

$(x_0, y_0) = (3,3)$

$\frac{dy}{dx} = -\frac{3}{3} = -1$

Hence the equation is:

y - 3 = -(x - 3).

y = -x + 6.

More can be learned about the equation of a tangent line at brainly.com/question/8174665

5 0

2 years ago

Factor the polynomial:<br> ab −3b+b^2−3a

Pavlova-9 [17]

ab(b-3)

ab-3b+b^2-3a

(-3a+ab)(-3b+b^2)

a(b-3) b(b-3)

ab(b-3)

8 0

3 years ago

Construct a 2 ×2 Matrix whose elements aij are given by a ij = i+j

beks73 [17]

Answer:

the required matrix is can be given as

8 0

3 years ago

Putting the other player's king in check is always a good move. true or false subject: chess

Elena-2011 [213]

Putting the other player's king in check is always a good move. true

<h3>What is chess?</h3>

The policies of chess allow a king to take an opponent's piece whilst in check, so long as that piece isn't always being defended.
At the equal time, a king in the test is usually forced to move.

The standard regulations of chess, a participant may not make any pass that places or leaves their king in the test.
A player may additionally pass the king, seize the threatening piece, or block the check with some other piece.
A king cannot look at the opposing king, considering this will vicinity the first king in check as well.

Learn more about chess here:-

#SPJ2

7 0

2 years ago