What is the vertex? <br> What is the domain? <br> What is the range

Solve the equation using the zero-product property. (2x − 8)(7x + 5) = 0 x = –2 or x = 7 x = 4 or x = x = 4 or x = x = –4 or x =

aliya0001 [1]

$(2x-8)(7x+5)=0\iff2x-8=0\ \vee\ 7x+5=0\\\\2x-8=0\qquad\text{add 8 to both sides}\\2x=8\qquad\text{divide both sides by 2}\\\boxed{x=4}\\\\7x+5=0\qquad\text{subtract 5 from both sides}\\7x=-5\qquad\text{divide both sides by 7}\\\boxed{x=-\dfrac{5}{7}}$

5 0

3 years ago

Which equation has a graph that goes through the points (4, -6) and (0, 6)?

Ugo [173]

Answer:

$y = -3x + 6\\$

Step-by-step explanation:

Find the gradient of the equation

$\frac{Difference in y}{Difference in x} \\\\\frac{6 - - 6}{0 - 4} = \frac{12}{-4} = -3$

The equation will have the gradient -3x

Use the general equation of a line, and substitute the coordinates in to find the y-intercept.

$y = x + c\\ y = -3x + c\\$

(4, -6)

$-6 = -3(4) + c\\ -6 = -12 + c\\ -6 + 12 = c\\ c = 6$ $6 = -3(0) + c\\ 6 = 0 + c\\ c = 6$

(0, 6)

$6 = -3(0) + c\\ 6 = -0 + c\\ c = 6$

The equation of the line is

$y = -3x + 6\\$

4 0

3 years ago

A pet supplier has a stock of parakeets of which 20% are blue parakeets. A pet store orders 3 parakeets from this supplier. If t

Levart [38]

Answer:

0.384

Step-by-step explanation:

pet supplier has a stock of parakeets of which 20% are blue parakeets

20/100 = 0.2 blue parakeets (success)

1-0.2 = 0.8 not parakeets (not success)

A pet store orders 3 parakeets from this supplier

we need to find the chance of getting exactly one blue from 3 parakeets

$P(x=1)=nCr (p)^r(q)^{n-r}$

n=3, r=1, p = 0.2 , q=0.8

$P(x=1)=3C1 (0.2)^1(0.8)^{2}$

0.384

5 0

3 years ago

A 6th grade teacher can grade 25 homework assignments in 20 minutes. Is this working at a faster rate or slower rate than gradin

antoniya [11.8K]

This work is faster rate than grading 36 assignments in 30 minutes because :

25 ÷ 20 = 1.25
1.25 hw assignment per minute

36 ÷ 30 = 1.2
1.2 hw assignments per minute

3 0

3 years ago

A light bulb factory produces 922 light bulbs every hour. Approximately 3.34% of the light bulbs are defective, and do not work.

Nikitich [7]

Answer:

The value is $\sigma = 5.46$