All categories

3 years ago

Find the equation of the line perpendicular to y= -2x+1 that also intersects the point (8, 2)

Mathematics

1 answer:

Kay [80]3 years ago

4 0

The slope of the perpendicular is the negative reciprocal of the original line, so m = -1/(-2) = 1/2.

The general line of slope m through (a,b) is

$y - b = m(x-a)$

So the line we seek is

$y - 2 = \frac 1 2 ( x - 8)$

$y = \frac 1 2 x - 2$

Answer: y = 1/2 x + -2

You might be interested in

Please answer this I don't understand how to do it thanks

Mars2501 [29]

Answer:

The answer is 8.6×10¹⁴

Step-by-step explanation:

You can evaluate it :

$(4.3 \times {10}^{8} ) \times (2.0 \times {10}^{6} )$

$= (4.3 \times 2.0) \times ( {10}^{8} \times {10}^{6} )$

$= 8.6 \times {10}^{8 + 6}$

$=8.6 \times {10}^{14}$

6 0

2 years ago

Read 2 more answers

Use the FOIL method to evaluate the expression

In-s [12.5K]

So u multiply each term in the first parentheses by each term in the second parentheses.

√5 √5 + 6√5-3√5 - 3x6
Now you multiply the numbers which will get u:
5+6√5 - 3√5 - 18
Then subtract:
-13 +3√5 that’s your answer

7 0

2 years ago

Considering only the values of β for which sinβtanβsecβcotβ is defined, which of the following expressions is equivalent to sinβ

-Dominant- [34]

Answer:

$\tan(\beta)$

Step-by-step explanation:

For many of these identities, it is helpful to convert everything to sine and cosine, see what cancels, and then work to build out to something. If you have options that you're building toward, aim toward one of them.

${\tan(\theta)}={\dfrac{\sin(\theta)}{\cos(\theta)}$ and ${\sec(\theta)}={\dfrac{1}{\cos(\theta)}$

Recall the following reciprocal identity:

$\cot(\theta)=\dfrac{1}{\tan(\theta)}=\dfrac{1}{ \left ( \dfrac{\sin(\theta)}{\cos(\theta)} \right )} =\dfrac{\cos(\theta)}{\sin(\theta)}$

So, the original expression can be written in terms of only sines and cosines:

$\sin(\beta)\tan(\beta)\sec(\beta)\cot(\beta)$

$\sin(\beta) * \dfrac{\sin(\beta) }{\cos(\beta) } * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) } {\sin(\beta) }$

$\sin(\beta) * \dfrac{\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} {\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}$

$\sin(\beta) *\dfrac{1 }{\cos(\beta) }$

$\dfrac{\sin(\beta)}{\cos(\beta) }$

Working toward one of the answers provided, this is the tangent function.

The one caveat is that the original expression also was undefined for values of beta that caused the sine function to be zero, whereas this simplified function is only undefined for values of beta where the cosine is equal to zero. However, the questions states that we are only considering values for which the original expression is defined, so, excluding those values of beta, the original expression is equivalent to $\tan(\beta)$ .

8 0

2 years ago

It takes a healthy bakery 10 hours to make 350 bagels what was the rate per hour

vladimir1956 [14]

The rate is 35 bagels per hour

8 0

3 years ago

Read 2 more answers

On a bicycle trail, the city is painting arrows like the one shown below: Upper pointing arrow with height of 11 and length of 9

Studentka2010 [4]

The image of the arrow is missing, so i have attached it.

Answer:

A_t = 69.5 cm²

Step-by-step explanation:

In a second image attached, I have divided the arrow into triangle and rectangle.

From the second image,

A1 is area of triangle while A2 is area of rectangle

Area of triangle is; A1 = ½bh

Our triangle base is given as 9 cm.

To get the height, we will subtract the rectangle height of 8 cm from the total arrow height.

Thus; height of triangle; h = 11 - 8 = 3cm

Thus;

A1 = ½ × 9 × 3

A1 = 13.5 cm²

Formula for area of rectangle is;

A2 = length × breadth

A2 = 8 × 7

A2 = 56 cm²

Thus, total area of arrow is;

A_t = A1 + A2 = 13.5 + 56

A_t = 69.5 cm²

8 0

2 years ago