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3 years ago

X=4y+7 2x-6y=12 System of equations using substitution

Mathematics

1 answer:

Sonja [21]3 years ago

7 0

Answer:

x=3, y=-1

Step-by-step explanation:

We are already given an equation solved for x, making substitution much easier. We know x=4y+7, meaning we can put 4y+7 whenever we see x in the second equation

2x-6y=12

We substitute 4y+7 in place of x

2(4y+7)-6y=12

Now we only have one variable to work on, distribute the 2

8y+14-6y=12

Combine similar terms, 8y-6y=2y

2y+14=12

Subtract 14 from both sides

2y=-2

y=-1

Now we plug in -1 for y in the first equation to find x

x=4(-1)+7

x=-4+7

x=3

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The students in Mr. Wilson's Physics class are making golf ball catapults. The

Mnenie [13.5K]

Answer:

Part a) About 48.6 feet

Part b) About 8.3 feet

Part c) The domain is $0 \leq x \leq 48.6\ ft$ and the range is $0 \leq y \leq 8.3\ ft$

Step-by-step explanation:

we have

$y=-0.014x^{2} +0.68x$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

where

x is the ball's distance from the catapult in feet

y is the flight of the balls in feet

Part a) How far did the ball fly?

Find the x-intercepts or the roots of the quadratic equation

Remember that

The x-intercept is the value of x when the value of y is equal to zero

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-0.014x^{2} +0.68x=0$

$a=-0.014\\b=0.68\\c=0$

substitute in the formula

$x=\frac{-0.68(+/-)\sqrt{0.68^{2}-4(-0.014)(0)}} {2(-0.014)}$

$x=\frac{-0.68(+/-)0.68} {(-0.028)}$

$x=\frac{-0.68(+)0.68} {(-0.028)}=0$

$x=\frac{-0.68(-)0.68} {(-0.028)}=48.6\ ft$

therefore

The ball flew about 48.6 feet

Part b) How high above the ground did the ball fly?

Find the maximum (vertex)

$y=-0.014x^{2} +0.68x$

Find out the derivative and equate to zero

$0=-0.028x +0.68$

Solve for x

$0.028x=0.68$

$x=24.3$

<em>Alternative method</em>

To determine the x-coordinate of the vertex, find out the midpoint between the x-intercepts

$x=(0+48.6)/2=24.3\ ft$

To determine the y-coordinate of the vertex substitute the value of x in the quadratic equation and solve for y

$y=-0.014(24.3)^{2} +0.68(24.3)$

$y=8.3\ ft$

the vertex is the point (24.3,8.3)

therefore

The ball flew above the ground about 8.3 feet

Part c) What is a reasonable domain and range for this function?

we know that

A reasonable domain is the distance between the two x-intercepts

$0 \leq x \leq 48.6\ ft$

All real numbers greater than or equal to 0 feet and less than or equal to 48.6 feet

A reasonable range is all real numbers greater than or equal to zero and less than or equal to the y-coordinate of the vertex

we have the interval -----> [0,8.3]

$0 \leq y \leq 8.3\ ft$

All real numbers greater than or equal to 0 feet and less than or equal to 8.3 feet

8 0

3 years ago

Mrs. Hinely grows roses. There are 6 roses on each of her 10 rose bushes. How many roses in all are on Mrs. Hinely's rose bushes

diamong [38]

In order to find the total number of roses, we can use multiplication. Since there are 6 roses on each bush, we can say that the answer is: 6+6+6+6+6+6+6+6+6+6. Since multiplication is a way to quickly add the same number, we can use 6*10. This becomes 60.

Good luck :D

8 0

3 years ago

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What is 7/8+14/16+4/5

Jlenok [28]

Answer:

The answer is 2.55

Step-by-step explanation:

3 0

3 years ago

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4f + 5, when f = 3<br> URGENT LOTS OF POINTS ASAP!!!

umka2103 [35]

Answer:

Step-by-step explanation:

4(3) + 5 = ?

12 + 5 = 17

5 0

1 year ago

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If the diagonal of a square is 12 to the square root of two then what is the area of the square

erastovalidia [21]

Answer:

Let there be a square ABCD with diagonal AC=12 root 2 cm

Since angles of a square are all 90 degrees

pythagoras theoream

AB^2+BC^2=AC^2

Since all sides of square are equal

2AB^2=(12 root 2)^2

2AB ^2=144*2

AB^2=144

AB= root 144=12 cm

area of square = s^2 =12^2 = 144cm^2

hope it helps

Step-by-step explanation:

3 0

3 years ago