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3 years ago

How to solve 45y to the second power plus 15y minus 10 ?

Mathematics

1 answer:

Lerok [7]3 years ago

4 0

Answer:

Either y = $\frac{-2}{3}$ or, y = $\frac{1}{3}$

Step-by-step explanation:

We have to solve the following quadratic equation

45y² + 15y - 10 =0

Now, dividing both sides with 5 we get, 9y² + 3y -2 =0

Hence, to solve the above equation we have to factorize the left-hand part of the equation.

So, 9y² + 3y - 2 =0

⇒ 9y² +6y -3y -2 =0

⇒ (3y +2) (3y -1 ) =0

⇒ Either (3y +2) =0 or (3y -1) =0

⇒ Either y = $\frac{-2}{3}$ or, y = $\frac{1}{3}$ (Answer)

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BigorU [14]

Answer:

Step-by-step explanation:

So basically you need to use the pythagorean thrm. Essentially, the diagonal and the width and length create a triangle, the diagonal being the hypothenuse. So the formula goes as $\sqrt[]{a^{2} +b^{2} }$ . the variable "a" being the length and the variable "b" being the width. So plug it in and there you have your answer!

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3 years ago

Find the slope and y-intrcept of y=5/3x -4

natima [27]

Answer:

Slope: 5/3

y-intercept: (0, -4)

Step-by-step explanation:

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y is your output.

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3 years ago

Solve for b. 35b=14 Simplify your answer as much as possible.

ELEN [110]

Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

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

$0.028x=0.68$

$x=24.3$

Alternative method

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

BRAINLIESTT ASAP! PLEASE HELP ME :)

Yuki888 [10]

Let's say we placed dominoes close together such that they only fell over one way: to the right hand side. Let's call the dominoes A and B.

Domino A is to the left of domino B. If we push over domino A, then it will hit domino B to cause it to fall over as well. We have a mini chain reaction of sorts. The fall of A triggers the fall of B, but not the other way around.

For this problem, we can think of domino A as "Jillian gets a raise" and domino B as "she will buy a new car". The raise causes her to get a new car, but not vice versa.

Since we're told in the last sentence she definitely got the raise, this must mean she will definitely get the new car.

In terms of symbols, the law of detachment is stated as

If P, then Q
P is true
Therefore Q is true

Side note: some books might use the term "modus ponens" instead of "law of detachment". They're the same thing.

3 0

3 years ago