Express the number CMLXXVI in our numeration sytem.

Answer:

52,047.96

Step-by-step explanation:

Answer:

[tex]y(t) =10t[/tex]

Step-by-step explanation:

The summary of the given parameters are:

[tex]a = 0[/tex] --- initial savings

[tex]m = 10[/tex] --- monthly savings

[tex]t \to[/tex] months

Required

The linear function

The linear function is calculated using:

y(t) = Initial Savings + Monthly Savings * Months

So, we have:

[tex]y(t) =a + m*t[/tex]

[tex]y(t) =0 + 10*t[/tex]

[tex]y(t) =10t[/tex]

Answer:

[tex] \rm \displaystyle y _{ \rm tangent} = - \frac{8}{5} x - \frac{5}{2} a[/tex]

[tex] \rm \displaystyle y _{ \rm normal} = \frac{5}{8} x - \frac{765}{128} a[/tex]

Step-by-step explanation:

we are given a equation of parabola and we want to find the equation of tangent and normal lines of the Parabola

finding the tangent line

equation of a line given by:

[tex] \displaystyle y = mx + b[/tex]

where:

to find m take derivative In both sides of the equation of parabola

[tex] \displaystyle \frac{d}{dx} {y}^{2} = \frac{d}{dx} 16ax [/tex]

[tex] \displaystyle 2y\frac{dy}{dx}= 16a[/tex]

divide both sides by 2y:

[tex] \displaystyle \frac{dy}{dx}= \frac{16a}{2y}[/tex]

substitute the given value of y:

[tex] \displaystyle \frac{dy}{dx}= \frac{16a}{2( - 5a)}[/tex]

simplify:

[tex] \displaystyle \frac{dy}{dx}= - \frac{8}{5}[/tex]

therefore

[tex] \displaystyle m_{ \rm tangent} = - \frac{8}{5}[/tex]

now we need to figure out the x coordinate to do so we can use the Parabola equation

[tex] \displaystyle ( - 5a {)}^{2} = 16ax [/tex]

simplify:

[tex] \displaystyle x = \frac{25}{16} a[/tex]

we'll use point-slope form of linear equation to get the equation and to get so substitute what we got

[tex] \rm \displaystyle y - ( - 5a)= - \frac{8}{5} (x - \frac{25}{16} a)[/tex]

simplify which yields:

[tex] \rm \displaystyle y = - \frac{8}{5} x - \frac{5}{2} a[/tex]

finding the equation of the normal line

normal line has negative reciprocal slope of tangent line therefore

[tex] \displaystyle m_{ \rm normal} = \frac{5}{8}[/tex]

once again we'll use point-slope form of linear equation to get the equation and to get so substitute what we got

[tex] \rm \displaystyle y - ( - 5a)= \frac{5}{8} (x - \frac{25}{16} a)[/tex]

simplify which yields:

[tex] \rm \displaystyle y = \frac{5}{8} x - \frac{765}{128} a[/tex]

and we're done!

( please note that "a" can't be specified and for any value of "a" the equations fulfill the conditions)

Answer:

In attachment

Step-by-step explanation:

For answer refer to attachment .

Answer:

B) 8 and 24.

Step-by-step explanation:

Just by looking at the answer choices, since one number must be three times the other, we can determine that the correct answer is B.

Regardless, let's work this out mathematically. Let the first number be a and the second number be b.

Their difference is 16. Hence:

[tex]a-b=16[/tex]

The first number is three times the second number. So:

[tex]a=3b[/tex]

Substitute:

[tex]3b-b=16[/tex]

Solve for b. Subtract:

[tex]2b=16[/tex]

And divide both sides by two:

[tex]b=8[/tex]

So, the second number is 8.

And since the first number is three times the second, the first number is 24.

Our answer is B as expected.

Answer:

volume is the product of the 3 dimensions. so devide the volume by the height and by the length to get just the width

1176 / 14 / 8

= 10.5

Answer:

75

Step-by-step explanation:

this problem statement tries to confuse us. there is no pi involved - also because there are no round surfaces and edges involved.

what do you think the surface area of such a 4-sided pyramid consists of ?

think !

there are the 4 walls or sides. and then there is the bottom too (if you lift the pyramid up, yes, the "floor" or bottom also belongs to the surface area).

each "wall" or side is actually a triangle.

and the bottom is a square.

what is the area of a triangle (At) ?

At = base length × height / 2 = 3×11/2 = 33/2 in²

what is the area of a square (As) ?

it is a special form of a rectangle, where length = width.

the area of a rectangle (Ar) = length × width.

and the area of a square (As), where length = width is

As = side length × side length = length² = 3² = 9 in²

our pyramid now has 4 "walls", all of the same size, so we need 4 times the area of such a single triangle.

and then add the bottom area.

=> the pyramid surface area (Ap) is

Ap = 4 × At + As = 4×33/2 + 9 = 132/2 + 9 = 66+9 = 75 in²

Answer:

521.1 mm²

Step-by-step explanation:

The shape is made up of a semicircle and a trapezoid.

Area of the shape = area of the semicircle + area of the trapezoid

= ½(πr²) + ½(a + b)*h

Where,

r = radius of the semicircle = ½(20) = 10 mm

a = 20 mm

b = 32 mm

h = height of trapezoid = 14 mm

Plug in the values

Area of the shape = ½(π*10²) + ½(20 + 32)*14

= 157.1 + 364

= 521.1 mm²

Answer:

A. (-6,0)

Step-by-step explanation:

The point on the y-axis lies on the line that passes through point C and is perpendicular to line AB is (-6, 0). Therefore, option C is the correct answer.

Given that, on a coordinate plane, line AB goes through (-2, 4) and (2, -8). Point C is at (6, 4).

The slope of a line is defined as the change in y-coordinate with respect to the change in x-coordinate of that line.

The slope is represented by the letter m, and is given by, m = tan θ = (y2 - y1)/(x2 - x1)

Now, slope of line AB with (x1, y1) = (-2, 4) and (x2, y2) = (2, -8) is

Slope = m = (-8-4)/(2(-2)

= -12/4

= -3

Slope perpendicular to AB = -1/m = -1/(-3)

=1/3

Put m=1/3 and C(6, 4) in y=mx+c, we get

4 = 1/3 (6) + c

⇒ c = 4-2

⇒ c = 2

Substitute m=1/3 and c = 2 in y = mx+c

That is, y = x/3 + 2

⇒ 3y = x+6

Point on the y-axis lies is 3(0) = x+6

⇒ x=-6

So, the coordinate is (-6, 0)

The point on the y-axis lies on the line that passes through point C and is perpendicular to line AB is (-6, 0). Therefore, option C is the correct answer.

To learn more about the slope of a line visit:

https://brainly.com/question/16180119.

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Answer:

I don't no answer sorry

Step-by-step explanation:

you follow me

Answer:

where is the question

Step-by-step explanation:

send question

Answer:

The answer is B: 67/10x + 9

Step-by-step explanation:

I did the test

Answer:

9

Step-by-step explanation:

the 2 angles create a right angle ( indicated by the little square.)

right angles have a measure of 90 degrees

hence, 90 = 72 + 2x

( note that we just created an equation that we can use to solve for x )

we now solve for x using the equation we created.

90 = 72 + 2x

step 1 subtract 72 from each side

90 - 72 = 18

72 - 72 cancels out

we now have 18 = 2x

step 2 divide each side by 2

18 / 2 = 9

2x / 2 = x

we're left with x = 9

Answer:

90

Step-by-step explanation:

there is 6 sides of box

2 bigger and 4 smaller

area of bigger side is 5×5 = 25 this is the area of one side as we have 2 sides so are of both sides is 25 + 25 = 50

now come to the smaller sides ( we have 4 here)

are of one side is 2× 5 = 10

so are of all 4 sides is 10× 4 = 40

now we get area of 4 smaller sides and 2 bigger sides

total area of box is 40+ 50 = 90

hope you understand

Answer:

D

Step-by-step explanation:

If you look at the centerand radius of a circle (those are the two most important things when defining a circle), you will see, they shrank by a factor of two, so since it affected both x and y, it had to be from the origin.

Answer:

it's answer is 4:1

Because length of small intestine is 6 m and length of large intestine is 1•5m

So 6/1•5 =4:1

Answer:

126 cm^3

Step-by-step explanation:

Use volume formula (Bh=V): 21×6=126

The volume of the pentagonal prism is 126 cm³

Pentagonal prism has two pentagonal bases, top and bottom and five rectangular sides.

Volume of the pentagonal prism = Area of the pentagon• height of the prism

Given:

Area of the pentagon = 21 cm²

Height of the prism = 6 cm

The volume of pentagonal prism = Area of the pentagon * Height of the prism

The volume of pentagonal prism = 21 cm² × 6 cm = 126 cm³

Therefore, the volume of pentagonal prism is 126 cm³

Learn more about the volume of pentagonal prism here:

https://brainly.com/question/31028600

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Answer:  -47/36  

Step-by-step explanation:

3/2y-14/3x

as x=3 and y=6

3/2(6)-14/3(3)

3/12-14/9

1/4-14/9

9-56/36

-47/36

Answer:

- 5

Step-by-step explanation:

[tex]\frac{3}{2}y-\frac{14}{3}x[/tex]

[tex]\frac{3}{2}(6)-\frac{14}{3}(3)[/tex]

9 - 14

- 5

Answer:

The answer is 30/10

Step-by-step explanation:

30 divided by 10 is 3.

Answer:

C

Step-by-step explanation:

I found the slope which is 28-22 / 1.5-1 = 12

I plug in the hours to 12x+10 and it matched

It sounds like Joe calculated 5/400 = 0.0125

He divided in the wrong order. It should be 400/5 = 80 since we divide distance over time to get the speed (or rate).

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

In terms of x and y, we basically are saying

slope = rise/run

slope = (change in y)/(change in x)

slope = (change in distance)/(change in time)

slope = (400 km)/(5 hrs)

slope = 80 km per hour is the speed

Answer: x=9 is an extraneous solution

Step-by-step explanation:

Given

Function is [tex]f(x)=\sqrt{x-5}[/tex]

for function to exist

[tex]\Rightarrow x-5\geq 0\\\Rightarrow x\geq 5[/tex]

Therefore, 9 satisfies the  above equation. It is it's extraneous solution.

Answer:i dont know

Step-by-step explanation:lol

Answer:

tmabm queria saber

Step-by-step explanation:

Answer:

y=-1/2x+7

Step-by-step explanation:

I think its that

Answer:

y = (1/2) x + 3

Step-by-step explanation:

The equation of linear functions is y = m x + b

In this case, we know m = 1/2 , and have point (4,5). We only need to find our y-intercept or b value.

What we can do is substitute what we know into our formula which will give us variable b, or the y-intercept. That will look like:

5 = (1/2) * 4 + b

5 = 2 + b

3 = b

So, the equation is y = (1/2) x + 3 :)

Answer:

Mean 1.580666667 1.769333333

Standard Deviation 0.890741799 1.123161779

Step-by-step explanation:

When we run the commands in the R software we get the graphs as follows.

The commands were

qqnorm(c(0.32,0.52,0.77,0.81,0.96,1.2,1.31,1.43,1.62,1.87,1.95,2.1,2.48,3,3.37))

and

qqnorm(c(0.47,0.59,0.81,0.9,1.18,1.2,1.35,1.51,1.74,1.89,2.05,2.2,2.81,3.09,4.75))

We can plot the graphs in any other plotting software .

The results would be same .

We see there's a slight difference between the two graphs.

One curve goes above ( Minneapolis) for  0.4 and the other ( for St Paul) is below 0.4

Answer:

np

Step-by-step explanation:

3.14(rs + r2)

3.14 (r= 2 x s= 3 + r =2 x 2)

3.14 ( 6+4)

3.14 (10)

3.14 x 10 = 31.4 units ² I guess

Answer:

Step-by-step explanation:

L : y = -4x + 3

with a slope of -4.

Any line perpendicular to L will have a slope m such that

m ( -4) = -1, or m = 1/4

Any line perpendicular to L passing through point (a,b) will therefore have the form

P : (y-b) = (x-a)/4

When (a,b) = (8,1) as given, then substitute in P to get

P : (y-1) = (x-8)/4

y=x/4 -2 + 1

y = x/4 -1

Answer:

False

Step-by-step explanation:

There is 3 feet in every yard so if we multiply by 3, we get 9. This is more than 8 so it is NOT equal to 3 yards.

Best of Luck!

A plane is an undefined term of geometry.

The statement that explains the difference is (c) A plane does not have a formal definition, and a ray is described through undefined terms.

In geometry, a plane do not have a particular definition.

The definition of a plane is depedent on the example or concept that is being describe.

A ray on the other hand is defined as a function of the undefined terms of geometry.

Hence, the statement that explains the difference between a plane and a ray is (c)

Read more about rays and planes at:

https://brainly.com/question/14366932

Answer:

Yes it's a right triangle

Step-by-step explanation:

IF it's a right triangle

a² + b² will equal c²

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

25.5² = 650.25

12² + 22.5² = 650.25

Therefor this IS a right triangle