(-q^2 + 3q + 4) - (7q^2 + 7q)

Find the point that is 1/5 the way from A to B where<br> A(-7,4) and B(3, 10).

mestny [16]

Answer:

The coordinates of the point that is 1/5 the way from A to B is $(x,y) = (-5,\frac{26}{5})$

Step-by-step explanation:

Here, the given points are: A (-7,4) and B (3,10)

Let us assume the point M(x,y) on AB is such that

AM : AB = 1 : 5

⇒ AM : (AB - AM) = 1 : (5-1) = 1: 4

⇒ AM : MB = 1 : 4

Now, The Section Formula states the coordinates of point (x,y) on any line dividing the line in the ratio m1 : m2

$(x,y) = (\frac{m_2x_1+m_1x_2}{m_1+m_2} ,\frac{m_2y_1+m_1y_2}{m_1+m_2} )$

Here, in the given equation, m1: m2 = 1:4

So, the coordinates M(x,y) is given as:

$(x,y) = (\frac{(-7)(4) + 1 (3)}{1+ 4} ,\frac{4(4) + 1(10)}{1+4} )\\\implies (x,y) = (\frac{-28+3}{5} ,\frac{16+10}{5} ) = (\frac{-25}{5} ,\frac{26}{5} )\\\implies (x,y) = (-5,\frac{26}{5} )$

Hence, the coordinates of the point that is 1/5 the way

from A to B is $(x,y) = (-5,\frac{26}{5})$

5 0

3 years ago

I Need Number 4 &' 6

adoni [48]

4 is again c because you should put the 2 here 2a'2-1 so this is 2a'1 and this is 20 so
A2 is 20
Than you should again do this and find a3 ...

4 0

3 years ago

Y=-1/4x+6 when y equals 4

timofeeve [1]

Answer:

Step-by-step explanation:

Y = -1/4x+6, when y= 4

Same as saying

4 = -1/4x+6 , where y = 4

Multiply both sides by (4x+6)

4(4x+6) = -1

Opening the parentheses

16x + 24 = -4

16x = -4-24

16x = -28

Divide both sides by 16

X = -28/16

X = - 7/4

Ans = -7/4

8 0

3 years ago

Solve y=-3x² + 4.5x – 20<br> Use the Quadratic formula

statuscvo [17]

Answer:

$x=0.75 \pm 2.47067i$

Step-by-step explanation:

Quadratic Formula: $x=\frac{-b \pm \sqrt{b^2-4ac} }{2a}$

√-1 is imaginary number i

Step 1: Define

y = -3x² + 4.5x - 20

a = -3

b = 4.5

c = -20

Step 2: Substitute and Evaluate

$x=\frac{-4.5 \pm \sqrt{4.5^2-4(-3)(-20)} }{2(-3)}$

$x=\frac{-4.5 \pm \sqrt{20.25-240} }{-6}$

$x=\frac{-4.5 \pm \sqrt{-219.75} }{-6}$

$x=\frac{-4.5 \pm \sqrt{219.75}(\sqrt{-1} ) }{-6}$

$x=\frac{-4.5 \pm i\sqrt{219.75} }{-6}$

$x=\frac{4.5 \pm i14.824 }{6}$

$x=0.75 \pm 2.47067i$

7 0

3 years ago

GEOMETRY PEOPLE PLEASE HELP ME!!!!!!!!!!!!!!!!! I WILL GIVE BRAINLIEST!

IrinaVladis [17]

$\Delta KLJ\sim\DeltaNPM$ (AAA) Corresponding angles are congruent.

Therefore, the sides of the triangles are proportional:

$\dfrac{4x-4}{20}=\dfrac{30}{25}$ cross multiply

$25(4x-4)=(20)(30)$ use distributive property

$(25)(4x)+(25)(4)=600\\\\100x+100=600$ subtract 100 from both sides

$100x=500$ divide both sides by 100

$x=5$

--------------------------------------------------------------------------------------------

$\Delta PQR\cong\Delta STU$ (SAS)

If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

Therefore we have the equation:

$3y-2=y+4\qquad|+2\\\\3y=y+6\qquad|-y\\\\2y=6\qquad|:2\\\\y=3$

The perimeter of △PQR:

$P=4+6+3y-2=8+3y$

Substitute the value of y to the expression:

$P=8+3(3)=8+9=17\ ft$

7 0

3 years ago