All categories

2 years ago

Find the coordinate of point P that lies along the directed line segment from A (3, 4) to B (6, 10) and partitions the segment i

n the ratio of 3:2.
Type the coordinate in the decimal form

Mathematics

1 answer:

AveGali [126]2 years ago

8 0

$\bf \left. \qquad \right.\textit{internal division of a line segment}
\\\\\\
A(3,4)\qquad B(6,10)\qquad
\qquad 3:2
\\\\\\
\cfrac{AP}{PB} = \cfrac{3}{2}\implies \cfrac{A}{B} = \cfrac{3}{2}\implies 2A=3B\implies 2(3,4)=3(6,10)\\\\
-------------------------------\\\\
{ P=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)}\\\\
-------------------------------$

$\bf P=\left(\cfrac{(2\cdot 3)+(3\cdot 6)}{3+2}\quad ,\quad \cfrac{(2\cdot 4)+(3\cdot 10)}{3+2}\right)
\\\\\\
P=\left( \cfrac{6+18}{5}~~,~~\cfrac{8+30}{5} \right)\implies \left( \cfrac{24}{5}~~,~~\cfrac{38}{5} \right)\implies \left( 4\frac{4}{5}~~,~~7\frac{3}{5} \right)$

You might be interested in

EThe graph of a quadratic function passes through the points (6,0) and (p,0). The maximum point

MA_775_DIABLO [31]

Answer:

p = - 5

Step-by-step explanation:

The vertex of the function is (0.5, 30.25 )

Since the roots are (6, 0) and (p, 0) then the axis of symmetry is vertical

with equation x = 0.5

The axis of symmetry passes through the midpoint of the roots, thus

$\frac{6+p}{2}$ = 0.5 ( multiply both sides by 2 )

6 + p = 1 ( subtract 6 from both sides )

p = - 5

6 0

2 years ago

Look at the diagram.

azamat

Answer:

Option G

Step-by-step explanation:

Option F

m∠1 + 121 = 180 [Sum of linear angles = 180°]

True.

Option G

121 + m∠2 + 33 = 180

False. Because 121° is not an interior angle of the given triangle.

Option H

33 + m∠1 = 92

True.

Measure of exterior angle of a triangle is equal to the sum of he measure of the non adjacent interior angles.

Option J

121 + 92 + m∠3 = 360°

True.

Sum of the exterior angles of triangle is 180°.

5 0

2 years ago

Hi, can someone help with these two questions ASAP! (Ignore the multiple choice I circled, not sure if it’s correct)

Sindrei [870]

Answer:

1) D. $y = -\frac{3}{2}\cdot x^{12} -7\cdot x^{5}+\frac{2}{3}\cdot x -10$

2) E. The coefficient of $x$ is -16.

Step-by-step explanation:

1) A polynomial is an algebraic expression of the form $p(x) = \Sigma \limits_{i = 0}^{n} c_{i}\cdot x^{i}$ , where $n$ is the grade of the polynomial. In this case, the only equation that satisfies this definition is: