All categories

3 years ago

What are the solutions to the equation?x² + 3x - 54

Mathematics

2 answers:

algol133 years ago

7 0

Answer:

x = - 9, x = 6

Step-by-step explanation:

Given

x² + 3x - 54

To find the solutions equate to zero

x² + 3x - 54 = 0 ← in standard form

(x + 9)(x - 6) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 9 = 0 ⇒ x = - 9

x - 6 = 0 ⇒ x = 6

Radda [10]3 years ago

4 0

Answer:

(x+6)⋅(x−9)

Step by Step

Factoring x2-3x-54

The first term is, x2 its coefficient is 1 .

The middle term is, -3x its coefficient is -3 .

The last term, "the constant", is -54

Step-1 : Multiply the coefficient of the first term by the constant 1 • -54 = -54

Step-2 : Find two factors of -54 whose sum equals the coefficient of the middle term, which is -3 .

-54 + 1 = -53

-27 + 2 = -25

-18 + 3 = -15

-9 + 6 = -3 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 6

x2 - 9x + 6x - 54

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-9)

Add up the last 2 terms, pulling out common factors :

6 • (x-9)

Step-5 : Add up the four terms of step 4 :

(x+6) • (x-9)

Which is the desired factorization

You might be interested in

A rectangular field is 75 yards wide and 105 yards long

nika2105 [10]

Answer:

width = 72 yards

length = 108 yards

Step-by-step explanation:

Given:

Width = 75 yards
Length = 105 yards

Area of the field with the given values:

$\begin{aligned}\textsf{Area of a rectangle}&=\sf width \times length\\& = \sf 75 \times 105\\& = \sf 7875\:\: yd^2\end{aligned}$

To maintain the same perimeter, but change the area, either:

decrease the width and increase the length by the same amount, or
increase the width and decrease the length by the same amount.

In geometry, length pertains to the longest side of the rectangle while width is the shorter side. Therefore, we should choose:

decrease the width and increase the length by the same amount.

Define the variables:

Let x = the amount by which to decrease/increase the width and length.

Therefore:

$\implies \sf width \times length < 7875\:\:yd^2$

$\implies (75-x)(105+x) < 7875$

Solve the inequality:

$\begin{aligned}(75-x)(105+x) & < 7875\\7875-30x-x^2 & < 7875\\-x^2-30x & < 0\\-x(x+30) & < 0\\x(x+30) & > 0\\\implies x & > 0 \:\: \textsf{ or }\:\:x < - 30\end{aligned}$

Therefore, as distance is positive only and the maximum width is 75 yd (since we are subtracting from the original width):

$\begin{cases}\textsf{width} = 75 - x\\\textsf{length} = 105 + x\end{cases}$

$\textsf{where } 0 < x < 75$

Therefore, to find the width and length of another rectangular field that has the same perimeter but a smaller area than the first field, simply substitute a value of x from the restricted interval into the found expressions for width and length:

Example 1:

Let x = 3

⇒ Width = 75 - 3 = 72 yd

⇒ Length = 105 + 3 = 108 yd

⇒ Perimeter = 2(72 + 108) = 360 yd

⇒ Area = 72 × 108 = 7776 yd²

Example 2:

Let x = 74

⇒ Width = 75 - 74 = 1 yd

⇒ Length = 105 + 74 = 179 yd

⇒ Perimeter = 2(1 + 179) = 360 yd

⇒ Area = 1 × 179 = 179 yd²

4 0

2 years ago

Read 2 more answers

What additional information would prove that LMNP is a rectangle?

eimsori [14]

Answer:

I just took the test and i know it is not A

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

A Sixteen Foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away fro

Romashka [77]

Answer:

-0.69 feet per second

Step-by-step explanation:

We have dx/dt = 2 ft/sec, and we want to determine dy/dt.

x and y are related by the Pythagorean Theorem.

x²+y²=16²

Differentiate both sides of this equation with respect to t to get

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

$2y\frac{dy}{dt} =-2x\frac{dx}{dt}$

Divide both sides by 2y

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

When x = 5 ft, we have

x²+y²=16²

5²+y²=256

y²=256-25=231

therefore

y= $\sqrt{213}$

$\frac{dy}{dt} =-\frac{5}{\sqrt{213}}\frac{2 ft}{sec}$

=-0.69

The top of the ladder is sliding down (because of the negative sign in the result) at a rate of -0.69 feet per second.

5 0

3 years ago

Read 2 more answers

Are the following points a function;

Firdavs [7]

No it is not a function because the x coordinate 0 has 2 y coordinates which is 4 and 5. a function means each x coordinate can only have one y coordinate

6 0

3 years ago

Two events, A and B, are independent. If P(A) = 0.3 and P(B) = 0.2, what is P(A and B)?

Flura [38]

Answer:0.06

Step-by-step explanation:

As the two events are independent

Therefore

$P(AandB) =P(A)\times P(B)$