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3 years ago

what is the factorization of the trinomial below -x^2+x+42 A. (x+6)(x-7) B. -1(x+7)(x+6)C. -1(x-7)(x+6) D. (-x+6)(x+7)

Mathematics

2 answers:

IRISSAK [1]3 years ago

5 0

Answer:

-(x - 7)(x + 6)

Step-by-step explanation:

Step 1: Factor GCF

-1(x² - x - 42)

Step 2: Factor quadratic

-1(x - 7)(x + 6)

Firlakuza [10]3 years ago

4 0

Answer:

Step-by-step explanation:

-x²+x+42

=-(x²-x-42)

[7-6=1,7×-6=-42]

=-(x²-(7-6)x-42)

=-(x²-7x+6x-42)

=-[x(x-7)+6(x-7)]

=-(x-7)(x+6)

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NEED HELP PLEASE!!!! (10 PTS)

slavikrds [6]

Tigers:-

f(t) = 7(1 + 0.1)^2 where t = number of years

Eagle

g(t) = 15 + 2t

B after ten year number tigers = f(t) = 7(1 + 0.1)^10 = 18

number of eagles = 15 + 10(2) = 35

C when the number of tigers = number eagles the 2 functions will be equal;-

f(t) = g(t) that is:-

7* 1.1^t = 15 + 2t

solve for t

5 0

3 years ago

The fish population of Lake Collins is decreasing at a rate of 5% per year. In 2004 there were about 1,350 fish. Write an expone

ad-work [718]

Answer:

Part 1) The exponential function is equal to $y=1,350(0.95)^{x}$

Part 2) The population in 2010 was $992\ fish$

Step-by-step explanation:

Part 1) Write an exponential decay function that models this situation

we know that

In this problem we have a exponential function of the form

$y=a(b)^{x}$

where

y ----> the fish population of Lake Collins since 2004

x ----> the time in years

a is the initial value

b is the base

we have

$a=1,350\ fish$

$b=(100\%-5\%)=95\%=0.95$

substitute

$y=1,350(0.95)^{x}$ ----> exponential function that represent this scenario

Part 2) Find the population in 2010

we have

$y=1,350(0.95)^{x}$

For $x=(2010-2004)=6\ years$

substitute

$y=1,350(0.95)^{6}=992\ fish$

7 0

3 years ago

Multiply.

ANTONII [103]

The multiplication of the expression (x² + 3x + 2) (2x² + 3x + 1) is 2x⁴ + 9x³ + 14x² + 9x + 2

<h3>Multiplication</h3>

(x² + 3x + 2) (2x² + 3x + 1)

= 2x⁴ + 3x³ + x² + 6x³ + 9x² + 3x + 4x² + 6x + 2

collect like terms

= 2x⁴ + 3x³ + 6x³ + x² + 9x² + 4x² + 3x + 6x + 2

= 2x⁴ + 9x³ + 14x² + 9x + 2

Learn more about multiplication:

brainly.com/question/10873737

#SPJ1

8 0

2 years ago

Find the length of the curve given by ~r(t) = 1 2 cos(t 2 )~i + 1 2 sin(t 2 ) ~j + 2 5 t 5/2 ~k between t = 0 and t = 1. Simplif

xxMikexx [17]

Answer:

The length of the curve is

L ≈ 0.59501

Step-by-step explanation:

The length of a curve on an interval a ≤ t ≤ b is given as

L = Integral from a to b of √[(x')² + (y' )² + (z')²]

Where x' = dx/dt

y' = dy/dt

z' = dz/dt

Given the function r(t) = (1/2)cos(t²)i + (1/2)sin(t²)j + (2/5)t^(5/2)

We can write

x = (1/2)cos(t²)

y = (1/2)sin(t²)

z = (2/5)t^(5/2)

x' = -tsin(t²)

y' = tcos(t²)

z' = t^(3/2)

(x')² + (y')² + (z')² = [-tsin(t²)]² + [tcos(t²)]² + [t^(3/2)]²

= t²(-sin²(t²) + cos²(t²) + 1 )

................................................

But cos²(t²) + sin²(t²) = 1

=> cos²(t²) = 1 - sin²(t²)

................................................

So, we have

(x')² + (y')² + (z')² = t²[2cos²(t²)]

√[(x')² + (y')² + (z')²] = √[2t²cos²(t²)]

= (√2)tcos(t²)

Now,

L = integral of (√2)tcos(t²) from 0 to 1

= (1/√2)sin(t²) from 0 to 1

= (1/√2)[sin(1) - sin(0)]

= (1/√2)sin(1)

≈ 0.59501

8 0

3 years ago

A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot dogs and 2 bags of chips for $9.00. Another customer buy

stiv31 [10]

Answer: hot dog = $1.75

Step-by-step explanation:

Let h represent hot dogs and c represent bags of chips.

Customer 1: 4h + 2c = 9.00 → 3(4h + 2c = 9.00) → 12h + 6c = 27.00

Customer 2: 5h + 3c = 11.75 → -2(5h + 3c = 11.75) → -10h - 6c = -23.50

2h = 3.50

÷2 ÷2

h = 1.75

7 0

3 years ago