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4 years ago

what is the slope intercept form of the linear equation with a graph that passes through (-2,2) and is perpendicular to the grap

h of y=1/3x+9

Mathematics

1 answer:

gtnhenbr [62]4 years ago

6 0

$\text{The slope-intercept form}\ y=mx+b.\\\\Let\\k:y=m_1x+b_1\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\\------------------------\\\text{Let}\ k:y=\dfrac{1}{3}x+9\ \text{and}\ l:y=mx+b\\\\l\ \perp\ k\iff\dfrac{1}{3}m=-1\qquad|\cdot3\to m=-3\\\\l:y=-3x+b\\\\\text{Substitute the coordinates of the point (-2, 2) to the equation}\\\text{of the line}\ l:\\\\2=-3(-2)+b\\2=6+b\qquad|-6\\-4=b\to b=-4\\\\\boxed{Answer:\ y=-3x-4}$

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Find the other x-intercept for the parabola defined by this equation y=2x2+3-2

ASHA 777 [7]

Answer:

( $\frac{1}{2}$ , 0 )

Step-by-step explanation:

To find the x- intercepts let y = 0, that is

2x² + 3x - 2 = 0

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × - 2 = - 4 and sum = + 3

The factors are + 4 and - 1

Use these factors to split the x- term

2x² + 4x - x - 2 = 0 ( factor the first/second and third/fourth terms )

2x(x + 2) - 1 (x + 2) ← factor out (x + 2) from each term

(x + 2)(2x - 1) = 0

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = $\frac{1}{2}$

The x- intercepts are (- 2, 0 ), ( $\frac{1}{2}$ , 0 )

8 0

3 years ago

In what career would you most likely apply concepts from geometry?

Nitella [24]

Answer:

- Architect

- Cartographer and Photogrammetrist

- Drafter

- Mechanical Engineer

- Surveyor

- Urban and Regional Planner

Step-by-step explanation:

Architects utilize geometric principles while designing layouts for their ongoing projects, which can include buildings, electrical systems, and plumbing architecture.

Cartographers utilize geographic data to create or update maps for use in education, as well as environmental presentations.

Using the same geometric knowledge and applications as architects and engineers, drafters create design plans with the use of computer-aided design (CAD) software.

Mechanical engineers, some of the most diversified engineers, use a multitude of geometric concepts to design mechanical devices, or update existing structures.

Surveyors use geometry to take exact measurements of boundaries for different types of property.

Urban and regional planners rely on the same geometry practices used by surveyors when examining the positives and negatives of introducing new and updated plans for a community.

* Not my own words. This is the website if you need more info;

https://study.com/articles/jobs_that_involve_geometry.html

8 0

3 years ago

Read 2 more answers

The distance between Henry's house and his school is 648 feet. How many yards are equivalent to 648 feet?

vlabodo [156]

Answer:

216 yards

Step-by-step explanation:

There are 3 feet in a yard, so the number of yards is equal to the number of feet divided by 3.

648/3 = 216

5 0

4 years ago

Read 2 more answers

What is the cell doing during the Sphase of interphase?

Studentka2010 [4]

Answer:

Synthesis or replication of DNA

Step-by-step explanation:

You can remember that because synthesis starts with an S

3 0

3 years ago

Louis built a swimming pool. The depth of the swimming pool is 5 feet. What is the volume of water that it will take to fill the

julia-pushkina [17]

Answer:

For a rectangular prism-like swimming pool: $V = w\cdot l \cdot h$ . $V = 360\,ft^{3}$ when $h = 5\,ft$ , $l = 12\,ft$ and $w = 6\,ft$ .

Step-by-step explanation:

Let assume that swimming pool has a rectangular base and depth is the same at any point at the bottom. In addition, let $w$ and $l$ be the width and length of the swimming pool. Then, the volume needed to fill the swimming pool is:

$V = w\cdot l \cdot h$ , where $h$ is the depth of the pool.

Let be $h = 5\,ft$ , $l = 12\,ft$ and $w = 6\,ft$ . The volume of the swimming pool is:

$V = (6\,ft)\cdot (12\,ft)\cdot (5\,ft)$

$V = 360\,ft^{3}$

3 0

4 years ago