Why is the metric system called a decimal system of measurement

Answer:

  θ = 60°

Step-by-step explanation:

The cross sectional area of the trapezoid shape will be that of a trapezoid with bases of 10 cm and (10 cm + 2·(10 cm)·cos(θ)) and height (10 cm)·sin(θ).

That area in cm² is ...

  A = (1/2)(b1 +b2)h = (1/2)(10 + (10 +20cos(θ))(10sin(θ)

  A = 100sin(θ)(1 +cos(θ))

A graphing calculator shows this area to be maximized when ...

  θ = π/3 radians = 60°

_____

A will be maximized when its derivative with respect to θ is zero. That derivative can be found to be 2cos(θ)² +cos(θ) -1, so the solution reduces to ...

  cos(θ) = 1/2

  θ = arccos(1/2) = π/3

ACD and ACE are supplementary angles that need to equal 180 degrees

ACE = 180 -100 = 80 degrees.

For this case we have by definition that, a flat angle is the space included in an intersection between two straight lines whose opening measures 180 degrees. So, the angle between A and B is 180 degrees.

If we are told that the ACD angle is 100 degrees, then the DCB angle should be 80 degrees.

The angle ACE is opposite by vertex to the angle DCB, then it is also 80 degrees; since by definition, two angles opposed by the vertex are congruent or equal.

Answer:

80 degrees

Answer:

x =23/14

If we want to change it to a mixed number

x = 1 9/14

Step-by-step explanation:

42x – 5 = 64

Add 5 to each side

42x – 5+5 = 64+5

42x = 69

Divide each side by 42

42x/42 = 69/42

x = 69/42

Divide the top and bottom by 3

x =23/14

If we want to change it to a mixed number

x = 1 9/14

Answer:

d)4

Step-by-step explanation:

Answer:  101 revolutions

Step-by-step explanation:

Answer:  The total number of revolutions is 101.

Step-by-step explanation:  Given that the wheels on Jason's dirt bike measure 19 inches in diameter.

We are to find the number of revolutions that the wheels make when Jason rides for 500 feet.

We know

1 foot = 12 inches.

So, 500 feet = 12 × 500 = 6000 inches.

Now, diameter of the wheels is given by

d = 19 inches.

So, the circumference of the wheels will be

[tex]C=\pi d=3.14\times19=59.66~\textup{inches}.[/tex]

Therefore, to ride 500 feet, The number of revolutions that the wheels make is given by

[tex]n=\dfrac{6000}{59.66}=100.56989...[/tex]

Rounding to the nearest whole number, the required number of revolutions will be 101.

Thus, the total number of revolutions is 101.

Answer:

  -8, 0

Step-by-step explanation:

The floor and ceiling functions have equal values for any integer argument. Their value is that integer.

Among your answer choices, the integers are -8 and 0.

Answer:

-8 and 0 or A and D

Step-by-step explanation:

Just took it on Edge 2020

Answer:

It doesn't. x = 22 271 201

Step-by-step explanation:

You are going to need a calculator no matter how you do it.

[tex]x =19 169 000 \times e^{0.15}[/tex]

(a) The direct method

[tex]x = 19 169 000\times 2.718 281 828^{0.15} = 19 169 000 \times 1.161 834 243 = 22 271 201[/tex]

(b) The indirect method

[tex]\ln \left (19 169 000\times 2.718 281 828^{0.15} \right ) = \ln(19 169 000) + 0.15 = 16.768 805 + 0.15 = 16.918 804\\\\e^{16.918 804} = 22 271 201[/tex]

Answer:

| x - 0 | ≤ 2

Step-by-step explanation:

Given,

The ideal temperature of the freezer = 0° F,

Also, it can fluctuate by 2° F,

Thus, if x represents the temperature of the freezer,

Then, there can be two cases,

Case 1 : x > 0,

⇒ x - 0 ≤ 2

Case 2 : If x < 0,

⇒ 0 - x ≤ 2,

⇒ -( x - 0 ) ≤ 2,

By combining the inequalities,

We get,

| x - 0 | ≤ 2,

Which is the required inequality.

Answer:

sqrt(5)

Step-by-step explanation:

Honestly think this person means to find the magnitude of the vector.  You can use dot product here, the vector with itself... But that isn't the last step.

v dot v=4+1=5

and so |v|=sqrt(5)

Answer: both are 21/29

Step-by-step explanation:

Use SOHCAHTOA so the opposite/hypotenuse for P is 21/29 and the adjacent/hypotenuse for Q is also 21/29

Answer:

720

Step-by-step explanation:

Answer:

720

Step-by-step explanation:

We are given the following permutation problem to solve:

[tex] _ 6 P _ 6 [/tex]

We know that the number of possibilities to choose an ordered set of [tex] r [/tex] objects from a total of [tex]n[/tex] objects is given by:

[tex] _ n P _ r = \frac { n ! } { ( n - r ) ! } [/tex]

Substituting the given values, n = 6, r = 6:

[tex] _ 6 P _ 6 = \frac { 6 ! } { ( 6 - 6 ) ! } [/tex] = 720

The best and most correct answer among the choices provided by the question is B.) 23,000

Hope this helps :)

Answer:

B).  (2, –23)

Well this person made it easy by literally saying the answer...

Step-by-step explanation:

Hope this helps!!  Also heart and rate if you found this answer helpful!!

The correct option is, (B) (2, –23).

Learn more about  coordinates here:

https://brainly.com/question/17206319

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So the series looks something like this:

[tex]\Sigma_{n=4}^{\infty}\frac{n-1}{16} \\

\frac{1}{16}\Sigma_{n=4}^{\infty}n-1[/tex]

If [tex]\lim_{n\rightarrow\infty}\neq[/tex] than [tex]\Sigma{a_n}[/tex] diverges. So we must apply limit infinity property:

[tex]\lim_{n\rightarrow\infty}(ax^n+\dots+bx+c)=\infty, a>0[/tex] and n is odd.

So...

[tex]\lim_{n\rightarrow\infty}n-1=\infty[/tex]

The series diverges.

Hope this helps.

r3t40

Answer:

the one that equals to 7

Step-by-step explanation:

Answer: The answer is B   2x2 - 3x+3

Step-by-step explanation:

3x-2 = 5x-14

Subtract 3x from each side:

-2 = 2x -14

Add 14 to each side:

12 = 2x

Divide both sides by 2:

x = 12/2

x = 6

Answer:

i believe the answer is 9/18

Answer:

B

Step-by-step explanation:

We will use substitution method after writing 2 equations to solve for number of glass items.

Let number of glass items be g and number of plastic items be p

"The number of plastic items is 30 less than nine times the number of glass items":

We can write the equation as  [tex]p=9g-30[/tex]

"The recyclables are 85% plastic":

This means that plastic (p) is 0.85 of  the total (p+g). Thus we can write equation as  [tex]p=0.85(p+g)[/tex]

We can substitute the expression for p in first equation into 2nd and solve for g:

[tex]p=0.85(p+g)\\(9g-30)=0.85((9g-30)+g)\\9g-30=0.85(10g-30)\\9g-30=8.5g-25.5\\0.5g=-25.5+30\\0.5g=4.5\\g=\frac{4.5}{0.5}\\g=9[/tex]

The number of glass items is 9

Answer:

b. 9

Step-by-step explanation:

x : glass items

9x - 30 : plastic items

(the equation will be set equal to [tex]\frac{15}{85}[/tex] because 85% of the recyclables are plastic, so that means 15% must be glass.)

[tex]\frac{x}{9x-30} =\frac{15}{85}[/tex]

[tex]85x=135x-450[/tex]  (now subtract 135x from each side to isolate x to one side of the equation)

[tex]-50x=-450[/tex] (divide each side of the equation by -50 to isolate x)

[tex]x=9[/tex]

Final answer:

Using the Rational Root Theorem, the polynomial equation 2x⁴+ 4x³-6x²+15x-12=0 has 12 distinct possible rational roots, where factors of the constant term are divided by factors of the leading coefficient.

Explanation:

To determine the number of possible rational roots for the polynomial equation 2x⁴+4x³−6x²+15x−12=0, we can use the Rational Root Theorem. This theorem states that if the polynomial has any rational roots, they must be of the form ±p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

The constant term in this case is -12, and its factors are ±1, ±2, ±3, ±4, ±6, and ±12. The leading coefficient is 2, and its factors are ±1 and ±2.

Thus, the possible rational roots are combinations of the factors of -12 divided by the factors of 2, giving us ±1, ±2, ±3, ±4, ±6, and ±12 combined with ±1 and ±2. So, our possible rational roots are: ±1/1, ±2/1, ±3/1, ±4/1, ±6/1, ±12/1, ±1/2, ±2/2, ±3/2, ±4/2, ±6/2, and ±12/2 which simplifies to ±1/1, ±2, ±3, ±4, ±6, ±12, ±1/2, ±3/2, and ±6/2.

After simplification, there is a total of 12 distinct possible rational roots, corresponding to option D.

Answer:

b

Step-by-step explanation:

Using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (4, 1)

d = [tex]\sqrt{(4+1)^2+(1-4)^2}[/tex]

  = [tex]\sqrt{5^2+(-3)^2}[/tex]

  = [tex]\sqrt{25+9}[/tex] = [tex]\sqrt{34}[/tex] → b

ANSWER

Point-slope form:

[tex]y - 3 = -\frac{3}{5} (x + 2)[/tex]

Slope-intercept form:

[tex]y= -\frac{3}{5} x + \frac{9}{5}[/tex]

EXPLANATION

The graphed line passes through

[tex](-2,3) \: \: and \: \: (3,0)[/tex]

The slope of this line is determined using

[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]

We substitute the points to get;

[tex]m = \frac{0 - 3}{3 - - 2} [/tex]

[tex]m = -\frac{3}{5} [/tex]

The point-slope formula is:

[tex]y-y_1 = m(x - x_1)[/tex]

Substitute the first point and slope to get:

[tex]y - 3 = -\frac{3}{5} (x - - 2)[/tex]

[tex]y - 3 = -\frac{3}{5} (x + 2)[/tex]

To find the slope-intercept form, we expand to get:

[tex]y= -\frac{3}{5} x - \frac{6}{5} + 3[/tex]

[tex]y= -\frac{3}{5} x + \frac{9}{5} [/tex]

Answer:

Slope

[tex]m=-\frac{3}{5}[/tex]

point-slope form

[tex]y=-\frac{3}{5}(x-3)[/tex]

slope-intersection form

[tex]y=-\frac{3}{5}x+1.8[/tex]

Step-by-step explanation:

The equation of a line in the point-slope form has the following formula:

[tex]y-y_0 = m (x-x_0)[/tex]

Where m is the slope and [tex](x_0, y_0)[/tex] is a point belonging to the line.

The equation of a line in the slope-intersection form has the following formula:

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

Where b is the intersection of the line with the y axis.

To calculate the slope of the line knowing 2 points we use the following formula:

[tex]m=\frac{y_1-y_0}{x_1-x_0}[/tex]

In this case:

[tex]x_0 =3\\y_0=0\\x_1=-2\\y_1=3[/tex]

So

[tex]m=\frac{3-0}{-2-3}[/tex]

[tex]m=-\frac{3}{5}[/tex]

So the equation of a line in the point-slope form

[tex]y-0 =-\frac{3}{5}(x-3)[/tex]

[tex]y=-\frac{3}{5}(x-3)[/tex]

The equation of a line in the slope-intersection form is:

[tex]y-0=-\frac{3}{5}(x-3)[/tex]

[tex]y=-\frac{3}{5}(x-3)[/tex]

[tex]y=-\frac{3}{5}x+\frac{9}{5}[/tex]

[tex]y=-\frac{3}{5}x+1.8[/tex]

with [tex]b=1.8[/tex]

Q1: The solution of a system of two linear equations in two variables is the point where their graphs intersect. At that point, the (x, y) pair satisfies both equations.

__

Q2: There will be no solution when the lines representing the equations do not intersect. That will only happen when they are parallel. (We say the equations are "inconsistent.")

There will be infinitely many solutions when the lines overlap. That is, the equations for them are essentially the same equation. (We say the equations are "dependent.")

__

Q3: Elimination is easiest when the coefficients of one of the variables are opposites of each other, or if one is a factor of the other. Substitution is easiest if one of the equations is easily put in the form x = ( ) or y = ( ).

If neither or both conditions hold, the choice is by student preference. (In this latter case, solution using Cramer's rule may be simplest.)

Answer:

  183.7 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the relation between the hypotenuse and opposite side in a right triangle is ...

  Sin = Opposite/Hypotenuse

For the first observation, the angle is 45° and the length of the hypotenuse of the triangle is given as x. For the second observation, the opposite side (building height) is the same, the angle is 60°, and the hypotenuse is 150 ft.

We can multiply the above equation by "Hypotenuse" to get an expression for "Opposite".

  Opposite = Sin×Hypotenuse

For our two observations, this becomes ...

  sin(45°)·x = (building height) = sin(60°)·(150 ft)

Dividing by the coefficient of x, we have ...

  x = (150 ft)·sin(60°)/sin(45°) ≈ 183.7 ft

Answer:

B: 183.7

Step-by-step explanation:

First we need to find our values

A = 45°

B = 180 - 60 = 120

a = 150

Then we can solve for x using this formula x = a * sin(B)/sin(A).

x = 150 * sin(120)/sin(45)

x = 150 * √6/2

x = 75√6

x = 183.71173

Answer:

(5sqrt(2), 45 deg)

(-5sqrt(2), 225 deg)

Step-by-step explanation:

(x,y)=(5,5)

So theta=arctan(5/5)=arctan(1)=45 degrees

Now r! r=sqrt(x^2+y^2)=sqrt(5^2+5^2)=sqrt(50)=sqrt(25)sqrt(2)=5sqrt(2)

So one polar point is (5sqrt(2) , 45 degrees)

Now if we do 180+45=225 degrees... this puts us in the 3rd quadrant... to get back to quadrant 1 we just take the opposite of our r

so another point is (-5sqrt(2) , 225 degrees)

Answer:

A

Step-by-step explanation:

y = 2x² + 8x + 3

Complete the square:

y = 2(x² + 4x) + 3

y = 2(x² + 4x + 4) + 3 - 2(4)

y = 2(x + 2)² - 5

So the vertex is at (-2, -5).  The graph must be Graph A.

Graph A has its vertex at (-4, -5). Then the correct option is A.

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

The parabolic expression is given below.

y = 2x² + 8x + 3

y = 2(x² + 4x) + 3

y = 2(x² + 4x + 4) - 8 + 3

y = 2(x + 4)² -5

The vertex of the parabola is at (-4, -5).

Graph A has its vertex at (-4, -5). Then the correct option is A.

Then the graph of the parabola is given below.

More about the parabola link is given below.

https://brainly.com/question/8495504

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Answer:

d

Step-by-step explanation:

y=mx+b

Answer:

  D.  y = 3x+1

Step-by-step explanation:

A -- this describes the inverse function rule (x and y are interchanged).

B -- this describes one point that is described by the function rule, but does not cover the remaining infinite number of points.

C -- there is no variable y in the right side of the rule, so this would give f(1) = 3x+1, f(2) = 3x+1, and so on. The value will always be "3x+1" for any function argument. This is not the same as the given function rule.

D -- y (or any other variable except x) can stand in for f(x), so this is the same as y = f(x). It is another way to write the function rule.

Answer: C (600 - 28w < 300)

I know this because: I took the E2020 test

Answer:

Answer: C (600 - 28w < 300)

Step-by-step explanation:

One grey side or one gray side?

P(one grey side) = 1/6

ANSWER

The correct answer is C

EXPLANATION

We want to find the value of

[tex] - \frac{3}{8} \times \frac{8}{15} [/tex]

This is the same as:

[tex] - \frac{3}{8} \times \frac{8}{3 \times 5} [/tex]

We cancel out the common factors to get:

[tex]- \frac{1}{1} \times \frac{1}{1 \times 5} [/tex]

We simplify to get:

[tex] - \frac{1}{5} [/tex]

The correct answer is C

Answer:

Part 1) The  lateral area of the cone is [tex]LA=2\pi\ cm^{2}[/tex]

Part 2) The lateral surface area of the cylinder is [tex]LA=36\pi\ cm^{2}[/tex]

Part 3) The surface area of the crayon is [tex]SA=41.50\pi\ cm^{2}[/tex]

Step-by-step explanation:

Part 1) Find the  lateral area of the cone  

The lateral area of the cone is equal to

[tex]LA=\pi rl[/tex]

we have

[tex]r=1\ cm[/tex]

[tex]l=2\ cm[/tex]

substitute

[tex]LA=\pi (1)(2)[/tex]

[tex]LA=2\pi\ cm^{2}[/tex]

Part 2) Find the lateral surface area of the cylinder

The lateral area of the cylinder is equal to

[tex]LA=2\pi rh[/tex]

we have

[tex]r=1.5\ cm[/tex]

[tex]h=12\ cm[/tex]

substitute

[tex]LA=2\pi (1.5)(12)[/tex]

[tex]LA=36\pi\ cm^{2}[/tex]

Part 3) Find the surface area of the crayon

The surface area of the crayon is equal to the lateral area of the cone, plus the lateral area of the cylinder, plus the top area of the cylinder plus the bottom base of the crayon

Find the area of the bottom base of the crayon

[tex]A=\pi[r2^{2}-r1^{2}][/tex]

where

r2 is the radius of the cylinder

r1 is the radius of the cone

substitute

[tex]A=\pi[1.5^{2}-1^{2}][/tex]

[tex]A=1.25\pi\ cm^{2}[/tex]

Find the area of the top base of the cylinder

[tex]A=\pi(1.5)^{2}=2.25\pi\ cm^{2}[/tex]

Find the surface area

[tex]SA=2\pi+36\pi+2.25\pi+1.25\pi=41.50\pi\ cm^{2}[/tex]

Answer:

2

36

41.5

Step-by-step explanation:

just got it all right even though I guessed soooo, yay

Step-by-step explanation: