All categories

3 years ago

Passes through (-4, 2 ) and parallel to y = 1/2x + 5

Mathematics

2 answers:

lord [1]3 years ago

7 0

Answer:

y = 1/2x + 4

Step-by-step explanation:

Lines that are parallel have the same gradient....in which its 1/2

Equation of the line that is parallel to y = 1/2x + 5 and passes through (-4,2)

(y - 2) = 1/2(x + 4)

2(y - 2) = x + 4

; 2y - 4 = x + 4

Equation of the line,

y = 1/2x + 4

kirill115 [55]3 years ago

3 0

Answer:

$\large\boxed{y=\dfrac{1}{2}x+4}$

Step-by-step explanation:

$\text{Let}\ k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\l\ \parallel\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\===========================\\\\\text{We have}\ k:y=\dfrac{1}{2}x+5\to m_1=\dfrac{1}{2}\\\\\text{Let}\ l:y=m_2x+b.\\\\l\ \parallel\ k\iff m_2=m_1\to m_2=\dfrac{1}{2}.\\\\l:y=\dfrac{1}{2}x+b\\\\\text{Put the coordinates of the given point (-4, 2) to the equation of a line:}\\\\2=\dfrac{1}{2}(-4)+b\\\\2=-2+b\qquad\text{add 2 to both sides}\\\\4=b\to b=4\\\\\text{Finally:}\\\\y=\dfrac{1}{2}x+4$

You might be interested in

Carmen is simplifying the expression (6.21 + 0.93) + 0.07 She recognizes that 0.93 and 0.07 will combine to equal 1, so she woul

almond37 [142]

For this case we have the following expression:
(6.21 + 0.93) + 0.07
We apply the associative property of the addition to rewrite the expression.
This property indicates that, when there are three or more terms in these operations, the result does not depend on the way in which the terms are grouped.
We have then:
6.21 + (0.93 + 0.07)
Answer:
6.21 + (0.93 + 0.07)
Associative property.

4 0

3 years ago

Read 2 more answers

1. In a circle with radius 6.5, an angle measuring 5.5 radians intercepts an arc. Find the length of the arc to the nearest 10th

mojhsa [17]

<h3>Answer:</h3>

[1] We know that,

<u>Length of arc(s) = r∅</u>

6.5 × 5.5
35.75 or 35.8 rounded.

[3] <u>Using section formula</u>,

Let A(-10, 10) and B(- 5, 5) ; m = 2, n = 3 and coordinates of the point be P(x,y)

So,

<u>P(x,y) = {mx2 + nx1/m + n},{my2 + ny1/m + n}</u>

{2 × - 5 + 3 × - 10/5},{2 × 5 + 3 × 10/5}
{- 10 + - 30/5},{10 + 30/5}
{- 40/5},{40/5}
{- 8, 8}

<u>Hence, Required coordinates are (- 8,8)</u>.

7 0

3 years ago

A field is to be fertilized at a cost of $0.12 per square yard. The rectangular part of the field is 110 yards long and the diam

Lera25 [3.4K]

see the picture in the attached figure

step 1

find the area of rectangle

A=110*43

A=4730 yd²

step 2

find the area of semicircles

we know that two semicircles is equal to one circle

Area of the circle=pi*r²

r=43/2

r=21.5 yd

A=pi*21.5²

A=462.25 *pi yd²-------->1,451.465 yd²

total area=area rectangle + area of circle

total area=4,730+1,451.465---------> 6,181.465 yd²

step 3

find the cost

$0.12 per square yard

6,181.465*0.12=$741.78

therefore

the answer is

$741.78

4 0

3 years ago

A manufacturing company produces two sizes of cylindrical containers that each have a height of 50 centimeters. The radius of Co

ira [324]

Answer:

Volume of B=62800 $cm^3$

Step-by-step explanation:

We are given

Height = 50 cm

Radius of A=16cm

Radius of Cylinder B is 25% more than that of A

Radius of B = 16 + $\frac{25}{100}*16$ cm =16+4= 20 cm

Volume of cylinder B = $pi*r^2*h$

= $3.14 * (20)^2*50$

=62800 $cm^3$

3 0

3 years ago

PLEASE SHOW WORK

Dmitrij [34]

Answer:

Below in bold

Step.-by-step explanation:

It consists of 5 isosceles triangles of equal sides 4 cm and vertex angles 360 / 5

= 72 degrees.

Area of 1 triangle = 1/2 * 4^2 *sin 72

Area of the whole pentagon = 5 * 1/2 *4^2 * sin 72

= 38.04 cm^2.

6 0

2 years ago