if a jar of coins contains 40 half dollars and 200 quarters, what is the monetary value of the coins? (Show all work)

Quadratic equations are never used to solve word problems. True or false?

mel-nik [20]

Quadratic equations CAN be used to solve word problems so the answer to your question is false

7 0

2 years ago

What is the volume of a sphere that has a 12m diameter?

lesya [120]

Volume of Sphere = (4/3)*(pi)*(r^3)

r = (D/2) = 6 m

  =<span>(4/3)*(pi)*((6^3)

  = 904.7786.. m^3
I hope this helps.</span>

5 0

3 years ago

(-4, -7) and (-6, 9) in slope-intercept form. Show work

BigorU [14]

Answer:

Equation of line in slope-intercept form is: y = -8x-39

Step-by-step explanation:

Given points are:

(-4, -7) and (-6, 9)

The slope-intercept form is given by the equation

$y = mx+b$

Here m is the slope of the line and b is the y-intercept.

m is found using the formula

$m = \frac{y_2-y_1}{x_2-x_1}$

Here

(x1,y1) = (-4-7)

(x2,y2) = (-6,9)

Putting the values in the formula

$m = \frac{9+7}{-6+4} = \frac{16}{-2} = -8$

Putting slope in general equation

$y = -8x+b$

Putting (-6,9) in the equation

$9 = -8(-6)+b\\9 = 48+b\\b = 9-48\\b = -39$

Putting the value of b we get

$y = -8x-39$

Hence,

Equation of line in slope-intercept form is: y = -8x-39

5 0

2 years ago

Find parametric equations for the sphere centered at the origin and with radius 3. Use the parameters s and t in your answer.

sdas [7]

Radius, r = 3

The equation of a sphere entered at the origin in cartesian coordinates is

x^2 + y^2 + z^2 = r^2

That in spherical coordinates is:

x = rcos(theta)*sin(phi)
y= r sin(theta)*sin(phi)
z = rcos(phi)

where you can make u = r cos(phi) to obtain the parametrical equations

x = √[r^2 - u^2] cos(theta)
y = √[r^2 - u^2] sin (theta)
z = u

where theta goes from 0 to 2π and u goes from -r to r.

In our case r = 3, so the parametrical equations are:

Answer:
x = √[9 - u^2] cos(theta)
y = √[9 - u^2] sin (theta)
z = u

6 0

2 years ago

Read 2 more answers

The product of (3 − 4i) and____is 25.

LiRa [457]

$(3-4i)(a+bi)=25\qquad\text{use FOIL method}\\\\(3)(a)+(3bi)+(-4i)(a)+(-4i)(bi)=25+0i\\\\3a+3bi-4ai-4bi^2=25+0i\\\\3a+3bi-4ai-4b(-1)=25+0i\\\\3a+3bi-4ai+4b=25+0i\\\\(3a+4b)+(3b-4a)i=25+0i\\.\qquad\qquad\qquad\qquad\Downarrow\\\\3a+4b=25\ and\ 3b-4a=0\\\\3b-4a=0\qquad\text{add 4a to both sides}\\\\3b=4a\qquad\text{divide both sides by 3}\\\\b=\dfrac{4}{3}a\qquad\text{substitute it to the first equation}\\\\3a+4\left(\dfrac{4}{3}a\right)=25\\\\3a+\dfrac{16}{3}a=25\qquad\text{multiply both sides by 3}$

$9a+16a=75\\\\25a=75\qquad\text{divide both sides by 25}\\\\\boxed{a=3}\qquad\text{put the value of a to}\ b=\dfrac{4}{3}a:\\\\b=\dfrac{4}{3}(3)\\\\\boxed{b=4}\\\\Answer:\ \boxed{(3-4i)\underline{(3+4i)}=25}$

6 0

2 years ago