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3 years ago

Solve the following quadratic equations by completing the square. y^2-14y+48=0

Mathematics

1 answer:

NISA [10]3 years ago

5 0

Answer:

y = 6 or 8

Step-by-step explanation:

1. Subtract the constant:

y^2 -14y = -48

2. Add the square of half the y-coefficient:

y^2 -14y +49 = -48 +49

Write as a square, if you like:

(y -7)^2 = 1

3. Take the square root:

y -7 = ±√1 = ±1

4. Add the opposite of the constant on the left:

y = 7 ±1 = 6 or 8

The solution is y = 6 or y = 8.

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Given the flag ABCDE, determine the single rule (x,y) that creates the

cricket20 [7]

Answer:

(y, -x)

Step-by-step explanation:

Rotation of 90°

(Clockwise)

(x, y) ---> (y, -x)

Rotation of 90°

(CounterClockwise)

(x, y) --> (-y, x)

Rotation of 180°

(Both Clockwise and Counterclockwise)

(x, y) ---> (-x, -y)

Rotation of 270°

(Clockwise)

(x, y) ---> (-y, x)

Rotation of 270°

(CounterClockwise)

(x, y) ---> (y, -x)

6 0

3 years ago

A farmer estimated that there were 25 gallons of water left in a tank. If this is an underestimate by 16%, how much water was ac

djyliett [7]

Answer:

The actual water in the tank is 29.76 gallons.

Step-by-step explanation:

It is given that the farmer estimated amount of water is 25 gallons.

It is also given that he underestimate the water in tank by 16%.

Let the actual water in tank be x.

$(1-\frac{16}{100})x=25$

$(\frac{100-16}{100})x=25$

$84x=25\times 100$

$x=\frac{2500}{84}$

$x=29.7619$

$x\approx 29.76$

Therefore the actual water in the tank is 29.76 gallons.

8 0

3 years ago

A moving company charges a base fee of $280 for a move plus $50 per hour of time. If H represents the number of hours of time, a

Gekata [30.6K]

C = 280m + 50H
…………..

6 0

3 years ago

Charlie does a weekly exercise program consisting of cardiovascular work and weight training. Each week, he exercises for at lea

german

Answer:

$(x_1,y_1) = (0,9)$

$(x_2,y_2) = (6,3)$

$(x_3,y_3) = (6,12)$

Step-by-step explanation:

Given

x = hours spent on cardiovascular work

y = hours spent on weight training

From the first statement,

Each week: he spends at least 9 hours

This is represented as:

$Total \ge 9$

$x + y \ge 9$

From the second statement,

Each week: he spends a max of 12 hours on weights

This is represented as:

$Weight \le 12$

$y \le 12$

From the third statement,

Each week: he spends a max of 6 hours on cardio works

This is represented as:

$Cardio \le 6$

$x \le 6$

So, the inequalities are:

$x + y \ge 9$

$y \le 12$

$x \le 6$

See attachment for the graph where the solution are also highlighted

From the attachment, the solutions are:

$(x_1,y_1) = (0,9)$

$(x_2,y_2) = (6,3)$

$(x_3,y_3) = (6,12)$

8 0

3 years ago

3x = 2y. Is this equation a linear or non-linear relation? How do you know?

viktelen [127]

Answer:

linear equation
all variables are to the first power

Step-by-step explanation:

"Linear equation" is another way to say "first-degree equation." That is, the equation involves constants and variables to the first degree only. No term contains any product or ratio of variables.

A term is first degree when the sum of all of the exponents of the variables is 1, and all exponents are positive integers. That is, the only allowed exponent of the single variable in a term is 1.

Here, the term on the left side of the equal sign has x to the first power. The term on the right side of the equal sign has y to the first power. Both are linear terms, so this is a linear equation.

7 0

3 years ago