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3 years ago

Factor the four-term polynomial ab + ac - 4b - 4c

Mathematics

1 answer:

Troyanec [42]3 years ago

5 0

A b + a c - 4 b - 4 c = a ( b + c ) - 4 ( b + c ) =
= (b + c) (a - 4)

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A florist arranges 4 flower arrangements in 92 minutes.

Black_prince [1.1K]

Answer:

$\boxed {\boxed {\sf 9 \ arrangements }}$

Step-by-step explanation:

Let's set up a proportion using the following setup:

$\frac{arrangements}{minutes} =\frac{arrangements}{minutes}$

We know that the florist can arrange 4 in 92 minutes.

$\frac{4 \ arrangements}{92 \ minutes} = \frac{arrangements}{minutes}$

We don't know how many the florist can arrange in 207 minutes, so we say x arrangements can be completed in 207 minutes.

$\frac{4 \ arrangements}{92 \ minutes} = \frac{ x \ arrangements}{ 207 \ minutes}$

$\frac{4}{92} =\frac{x}{207}$

Solve for x by isolating it on one side of the proportion.

x is being divided by 207. The inverse of division is multiplication. Multiply both sides of the proportion by 207.

$207*\frac{4}{92}=\frac{x}{207}*207$

$207*\frac{4}{92}=x$

$207*0.0434782609=x$

$9=x$

The florist can arrange 9 arrangements in 207 minutes.

5 0

3 years ago

Which of the sets of equations represent the two lines graphed?

Oksi-84 [34.3K]

Answer:

B) y = x + 2 and y = -x - 4

Step-by-step explanation:

Let the equation of a straight line with x-intercept 'a' and y-intercept 'b' be

$\frac{x}{a} + \frac{y}{b} = 1$

The line with positive slope has x-intercept a=-2 and y-intercept b=2.

Its equation is:

$\frac{x}{ - 2} + \frac{y}{2} = 1$

Multiply through by 2

$- x + y = 2$

Solve for y,

$\boxed {y = x + 2}$

For the line with a negative slope,

the x-intercept is a=-4 and the y-intercept is b=-4

Its equation is

$\frac{x}{ - 4} + \frac{y}{ - 4} = 1$

Multiply through by -4

$x + y = - 4$

Solve for y

$\boxed {y = - x - 4}$

4 0

3 years ago

Evaluate by distributing and find the expression

Elden [556K]

Answer:

Step-by-step explanation:

3 0

3 years ago

Find all solutions in the interval [0, 2π) for 2 sin^2 x = sin x

Ede4ka [16]

Answer:

Step-by-step explanation:

2 sin²x=sin x

2 sin² x-sin x=0

sin x(2 sin x-1)=0

sin x=0

x=0,π

2 sin x-1=0

2 sin x=1

sin x=1/2= sin π/6,sin (π-π/6)

x=π/6,5π/6

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3 years ago

HELLLLLLLLLLLLLLLLLLLLLLPPPPPPPPPPPPPP!!! 98POINTS

Mnenie [13.5K]

Answer:

$1699.25

Step-by-step explanation:

Data:

Cost = $314 000

Down payment = 18 %

Term = 20 yr

i = 5 %/yr

Calculations:

(a) Down payment

Down payment = 314 000 × 0.18

= $56 520

(b) Amount financed

Cost = $314 000

-Down payment = 56 520

Financed = $257 480

(c) Monthly payments

The formula for the monthly payment (P) on a loan of A dollars that is paid back in equal monthly payments over n months, at an annual interest rate of i % is

$P = A(\frac{i}{1-(1+i)^{-n}})$

We must express the interest rate on a monthly basis.

I = 5 %/yr = 0.41 667 %/mo = 0.004 1667

n = 2 × 12 = 240 mo

$P = 257 480(\frac{0.004 1667}{1 - (1+0.004 1667)^{-240}})$

$P = \frac{1072.83}{1- (1.004 1667)^{-240}}$

$P = \frac{1072.83}{1 - 0.368 645}$

$P = \frac{1072.83}{0.631 355}$

P = $1699.25

Carlos' monthly mortgage payment will be $1699.25.

8 0

3 years ago