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3 years ago

An expression is shown.

Mathematics

1 answer:

Colt1911 [192]3 years ago

5 0

Answer:

Step-by-step explanation:

(2x - 3) + [ 4x(3x + 2)]

2x - 3 + [ (4x*3x) + (4x*2) ]

2x - 3 + [ 12x² + 8x ]

2x - 3 + 12x² + 8x

12x² + 10x - 3

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Find the standard form of the equation of the circle with endpoints of a diameter at the points (3,8) and (-7,2)

poizon [28]

$(x+2)^{2}$ + $(y-5)^{2}$ = 34

The equation of a circle in standard form is

$(x-a)^{2}$ + $(y-b)^{2}$ = $r^{2}$

where (a , b) are the coordinates of the centre and r is the radius

The centre is at the midpoint of the endpoints and the radius is the distance from the centre to either of the 2 endpoints

Using the midpoint formula

midpoint = [ $\frac{1}{2}$ (x $x_{1}$ + $x_{2}$ , $\frac{1}{2}$ ( $y_{1}$ + $y_{2}$

where ( $x_{1}$ , $y_{1}$ =(3,8) and ( $x_{2}$ , $y_{2}$ =(-7,2)

centre = ( $\frac{1}{2}$ (3-7), $\frac{1}{2}$ (8+2)) = (-2,5)

Calculate r using the distance formula

r = √( $x_{2}$ - $x_{1}$ )²+( $y_{2}$ - $y_{1}$ )²)

= √((3+2)²+(8-5)²) = √(25+9) = √34 ⇒ r² =(√34)² = 34

equation of circle is : (x+2)²+(y-5)² = 34

8 0

3 years ago

1. When a cannonball is fired, the equation of its pathway can be modeled by h = -1612 + 128t.

sashaice [31]

Answer:

The maximum height of the ball is 256m

Step-by-step explanation:

Given the equation of a pathway modelled as pathway can be modeled by h = -16t² + 128t

At maximum height, the velocity of the ball is zero.

velocity = dh/dt

velocity = -32t + 128

Since v = 0 at maximum height

0 = -32t+128

32t = 128

t = 128/32

t = 4seconds

The maximum height can be gotten by substituting t = 4 into the modelled equation.

h = -16t² + 128t

h = -16(4)²+128(4)

h = -16(16)+512

h = -256+512

h = 256m

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3 years ago

Find the geometric mean of 8 and 13.

Doss [256]

Find the factors from the roots, then multiply the factors together.
y
=
x
2
−
21
x
+
104

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3 years ago

The graph of an exponential function has a y-intercept of 7 and contains the point (4,112). Construct the exponential function T

blondinia [14]

The exponential function that describes the graph is $y=7\cdot 2^x$

The standard form of an exponential function is expressed as $y=ab^x$

a is the y-intercept

(x, y) is the point on the graph

Given the following expression

a = 7

(x, y) = (4, 112)

Substitute the given values into the exponential equation

$y = ab^x\\112=7\cdot b^4\\b^4 = \frac{112}{7}\\b^4= 16\\b =\sqrt[4]{16}\\b = 2$

Get the required exponential equation

Recall that $y=ab^x$ , hence the required equation will be $y=7\cdot 2^x$

Learn more here: brainly.com/question/19245707

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2 years ago

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Oksanka [162]

Answer:

Step-by-step explanation:

The rate of charge is how often you are charged something. If x represents miles than every ? miles you are charged 2.5. The 3 at the end is the y intercept or the point where you start so no matter how many miles you go you automatically owe 3 dollars

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3 years ago