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2 years ago

Lateral surface for a triangular prism l=8 w=4 h=6

Mathematics

1 answer:

allochka39001 [22]2 years ago

4 0

Answer:

? i need help

Step-by-step explanation:

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The graph of a quadratic function passes through the points (-1,0), (-2,0), and (0,2). Write the quadratic function in general f

ddd [48]

Answer:

$f(x)=x^2+3x+2$

Step-by-step explanation:

step 1

we have the points

(-1,0), (-2,0), and (0,2)

Plot the points

using a graphing tool

see the attached figure

The graph of a quadratic function must be a vertical parabola open upward

The vertex is a minimum

The quadratic function in general form is equal to

$f(x)=ax^2+bx+c$

Substitute the value of x and the value of y of each given ordered pair in the general equation and solve for a,b and c

(0,2)

For x=0, y=2

substitute

$2=a(0)^2+b(0)+c$

$c=2$

(-1,0)

For x=-1, y=0

substitute

$0=a(-1)^2+b(-1)+2$

$0=a-b+2$ ----> $a=b-2$ ----> equation A

(-2,0)

For x=-2, y=0

substitute

$0=a(-2)^2+b(-2)+2$

$0=4a-2b+2$ ----> equation B

we have the system

$a=b-2$ ----> equation A

$0=4a-2b+2$ ----> equation B

substitute equation A in equation B

$0=4(b-2)-2b+2$

solve for b

$0=4b-8-2b+2$

$2b=6$

$b=3$

Find the value of a

$a=3-2=1$

therefore

The quadratic function in general form is equal to

$f(x)=x^2+3x+2$

see the attached figure N 2 to better understand the problem

7 0

3 years ago

The functions r and s are defined as follows.

Arlecino [84]

Answer:

r o s(3)=?

s(x)= x²-1

x=3

s(3)= 3²-1

s(3)= 9-1

s(3)=8

r(8)

r(x)= -2x-1

x=8

r(8)= -16-1

r(8)= -17

r(s(3))= -17

6 0

2 years ago

Tanya bought two adult tickets and one children's ticket to a movie for $15.90. Li bought four adult tickets and four children's

Fiesta28 [93]

The answer, hopefully you will understand

6 0

3 years ago

Please Help! The following is an isosceles trapezoid, find m < J

ra1l [238]

Answer:

The measure of angle J is 44°

Step-by-step explanation:

Isosceles Trapezoid

The isosceles trapezoid has its non-parallel sides of the same length, thus the angles they form with their respective parallel sides are congruent.

It means: Angle J is congruent with angle K and angle M is congruent with angle L

The sum of angles in a trapezoid is 180*(4-2)=360°

Thus:

$m\angle J+m\angle K+m \angle M+m\angle L = 360^\circ$

$7x+2+7x+2+25x-14+25x-14=360$

Joining like terms:

$64x-24=360$

Adding 24:

$64x=384$

Dividing by 64:

x=6°

Thus:

$m\angle J = 7*6+2=44^\circ$

$m\angle M = 25*6-14=136^\circ$

The measure of angle J is 44°

3 0

3 years ago

ABCDEFGHIJ is a regular decagon with a radius of 25.89 units. Find the area of ABCDEFGHIJ. Round the answer to the nearest tenth

Verdich [7]

Let's call the midpoint of GF M.
MF = 16/2 = 8
KF = 25.89
MK = sqrt(25.89^2 - 8^2)
MK = 24.62
MKF = 8 * 24.62 / 2 = 98.48 square units for one triangle
There are 20 of those triangles that make up the decagon.
Therefore the total area = 20(98.48) = 1969.6 which would be option C

6 0

3 years ago