Identify the vertex, the focus, and the directrix of the parabola with the given equation.

Draw the graph of the line that is perpendicular to Y= 4X +1 and goes through the point (2, 3)

spayn [35]

Given:

$\begin{gathered} y=4x+1 \\ \text{ point }(2,3) \end{gathered}$

To find:

Draw a graph of a line that is perpendicular to the given line and passing through a given point.

Explanation:

As we know that relation between two slopes of perpendicular slopes of lines:

$m_1.m_2=-1$

Slope of given line y = 4x + 1 is:

$m_2=4$

So, the slope of line perpendicular to given line is:

$m_2=-\frac{1}{4}$

Also, so line equation that is perpendicular to given line is:

$y=-\frac{1}{4}x+c...........(i)$

Also, the required line is passing thorugh given point (2, 3), i.e.,

$\begin{gathered} 3=-\frac{1}{4}(2)+c \\ c=3+\frac{1}{2} \\ c=\frac{7}{2} \end{gathered}$

So, line equation that is perpendicular to given line is:

$y=-\frac{1}{4}x+\frac{7}{2}$

The required graph of line is:

8 0

2 years ago

The quotient of x miles and 8 hours<br> is 55 miles per hour.

Dahasolnce [82]

X is equal to 440
440/8=55

3 0

3 years ago

The number of crayons in a box is forty

zzz [600]

2x-40=140
+40 +40
2x=180
————
2x
X=90

The correct answer would be 90 crayons

4 0

3 years ago

in a poll about work, 62% of respondents said that their jobs were sometimes or always stressful. twelve workers are chosen at r

Sladkaya [172]

The mean and standard deviation of number who find their jobs stressful are 7.44 and 1.6814 respectively.

Given,

number of workers chosen , n=12

percentage of respondents =62%

from given data the calculation are done according to binomial distribution,

then,

probability of respondents , $p=\frac{62}{100}=0.62$

a)calculating mean,

$\mu=n*p\\\\\mu=12*0.62\\\\\mu=7.44$

b)calculating standard deviation,

$\sigma=\sqrt{n*p*(1-p)}\\\\\sigma=\sqrt{12*0.62*(1-0.62)}\\\\\sigma=\sqrt{7.44(0.38)}\\\\\sigma=\sqrt{2.8272}\\\\\sigma=1.6814$

Thus, the mean and standard deviation of number who find their jobs stressful are 7.44 and 1.6814 respectively.

To learn more about binomial distribution refer here

brainly.com/question/15303817

#SPJ4

8 0

1 year ago

Need help with question 13B i can not figure it out please help.

Vsevolod [243]

Short Answer 10
The tough part is the number of drinks.
Let the number of them be x
4.5 x + 3 + (10/100) * (4.5x + 3) + (7/100) * (4.5 x + 3) ≤ 60

The tip is not included in the tax, and the tax does not include the tip. You can shorten this up quite a bit.
4.5 x + 3 + (10/100) * (4.5x + 3) + (7/100) * (4.5 x + 3) ≤ 60
(1 + 10/100 + 7 /100) (4.5x + 3) ≤ 60 Combine the tax, tip, scone and Lattes

(1.17) * (4.5x + 3) ≤ 60 Divide by 1.17
4.5x + 3 ≤ 60 / 1.17
4.5x + 3 ≤ 51.28 Subtract 3
4.5x ≤ 48.28 Divide by 4.5
x ≤ 48.28 / 4.5
x ≤ 10.72

Discussion.
There's a problem. He can't buy 0.72 of a Latte. He can only buy 10 of them. In this case we must round down so what happens if he buys 10 lattes? Does the price the taxes and the tip allow him to get another Latte? The answer should be no because then you would be 11 lattes and the tip and taxes would push you over 60 dollars. But be careful, sometimes things like this can alter you answer..

Answer: 10 <<<<

7 0

3 years ago