A construction uses beams that are 2,3, or 4 meters long. The measure of each beam must be converted to centimeters. Write a function to describe the situation. Find a reasonable domain and range for the function. (Hint 1 m = 100 cm)

Answer:-3

Step-by-step explanation:

The minimum value of a function can be obtained from its derivative

The point on the x-axis that makes [tex]\overline{AC}[/tex] + [tex]\overline{BC}[/tex] minimum is the point [tex]\underline{(9, \, 0)}[/tex]

Reason:

Let (d, 0) represent the coordinate of the point, on the x-axis, we have;

[tex]\overline{AC}[/tex]² = (4 - d)² + (-5)²

[tex]\overline{AC}[/tex] = √((4 - d)² + (-5)²)

[tex]\overline{BC}[/tex]² = (12 - d)² + 3²

[tex]\overline{BC}[/tex] = √((12 - d)² + 3²)

[tex]\overline{AC}[/tex]² + [tex]\overline{BC}[/tex]² = L =  4² + (-5 - d)² + 12² + (3 - d)²

When [tex]\overline{AC}[/tex] + [tex]\overline{BC}[/tex] is minimum, we have;

[tex]\lim_{n \to \infty} a_n \dfrac{d}{dd} (\overline{AC} + \overline{BC}) = \dfrac{d}{dd} \left(\sqrt{ (4 - d)^2 + (-5)^2)} + \sqrt{ (12 - d)^2 + 3 ^2)} \right) = 0[/tex]

Which gives;

[tex]\dfrac{d}{dd} \left(\sqrt{ (4 - d)^2 + (-5)^2)} + \sqrt{ (12 - d)^2 + 3 ^2)} \right) = \dfrac{2 \cdot d - 24}{2 \cdot \sqrt{d^2-24 \cdot d + 153} } + \dfrac{2 \cdot d - 8}{2 \cdot \sqrt{d^2 - 8\cdot d + 41} }[/tex]

Therefore;

[tex]\dfrac{2 \cdot d - 24}{2 \cdot \sqrt{d^2-24 \cdot d + 153} } + \dfrac{2 \cdot d - 8}{2 \cdot \sqrt{d^2 - 8 \cdot d + 41} } = 0[/tex]

[tex]\dfrac{2 \cdot d - 24}{2 \cdot \sqrt{d^2-24 \cdot d + 153} } =- \dfrac{2 \cdot d - 8}{2 \cdot \sqrt{d^2 - 8 \cdot d + 41} }[/tex]

Squaring both sides and cross multiplying gives;

16·d² - 528·d + 3456 = 0

Which gives;

16·(d - 24)·(d - 9) = 0

Therefore, d = 24, and d = 9

The point (9, 0), is closer to the given points than the point (24, 0), therefore;

The point on the x-axis that makes [tex]\overline{AC}[/tex] + [tex]\overline{BC}[/tex] minimum is the point [tex]\underline{(9, \, 0)}[/tex]

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Answer:

what are the answer

Step-by-step explanation:

Answer:

(4, 1)

Step-by-step explanation:

Method elimination would be good for this system

2x - y = 7 ........ (1)

x + y = 5 ......... (2)

(1) + (2)

3x = 12 ⇒ x = 4

4 + y = 5 ⇒ y = 1

(4, 1)

Answer:

x=9

Step-by-step explanation:

FE is 3x-7

since ΔABC≅ΔDEF the equivalent of FE is CB, or BC...which is 20

3x-7=20

3x=27

x=9

Answer:

8 $5 bills and 5 $1 bills

Step-by-step explanation:

5x8=40, which would be $40

1x5=5, which would be $5

$40+$5=$45

hope this helps! :)

Answer:

it's not possible. I've tried every way, r these the right amounts?

Answer:

4x + 2 = 30

Step-by-step explanation:

To find the perimeter of a triangle, add up the length of all three sides of the triangle.

Here, the sides of the triangle are "x+6", "x+6", and "2x-10". When you add up all three sides of the triangle, it should be equal to the perimeter, 30. So:

(x+6) + (x+6) + (2x-10) = 30

We can simplify this equation:

(2 * (x+6)) + (2x-10) = 30

2x + 12 + 2x - 10 = 30

4x + 2 = 30

Answer D: 4x + 2 = 30

Answer:

(2x-5)+(x+25)+x

4x+20

Step-by-step explanation:

Simplify the expression.

Answer:

(f+g)(2)=5

Step-by-step explanation:

Subsitute 2 in for x in both functions. Then add the answers of the functions together.

Answer:

30 + 2x = 5x  i hope this helps

Answer:

513.95402 I think lol

 4.1     7776 = 25•35

(7776)2 = (25•35)2 = 210 • 310  4.2     343 = 73 (343)2 = (73)2 = 76

Answer:

D) (1,1)

Step-by-step explanation:

You can find the solution by plugging the x-value of each coordinate into the equation. It will be a solution if the y-value of the equation equals the y-value of the coordinate.

For example:

y = 3x -2

y = 3(1) - 2

y = 3-2

y = 1

1 = 1

(1, 1) are the coordinates that are on the given line.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given a equation y = 3x -2

To find which coordinates will satisfy the equation:

For coordinates (2, 0)

at x = 2, y should be zero

y = 3 * 2 -2

y = 4

Not satisfied

For coordinates(-3, 0)

at x = -3, y should be 0

y = 3 * -3 - 2

y = -9 -2

y = -11

Not satisfied

For coordinates(0, 2 )

at x = 0, y should be 2

y = 3*0 -2

y = -2

Not satisfied

For coordinates(1, 1)

at x = 1, y should be 1

Y = 3*1 - 2

y = 3 - 2

y = 1

satisfied

Therefore, (1, 1) are the coordinates that are on the given line.

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Answer:

c ≤ 6

Step-by-step explanation:

Lets make our equation!

2.5 per chore thats our slope

+3 she starts with 3 dollars

y = 2.50x +3

Substitute y for 17!

17 = 2.5x +3

Subtract 3!

14 = 2.5x

Divide both sides by 2.5!

x = 5.6

5.6 --> 6

x = 6

Turn it into an inequality!

c ≤ 6

Consider Brainliest! Hope I helped!

Answer:

Exponetial Growth

Answer: The correct answer would be 164(c)

Step-by-step explanation:

You are Miguel Cervantes de Navas y Colon, captain in the Royal Spanish

Army in Sevilla in the year 1842. Outside your barracks window is a stack of

cannonballs, as shown in the illustration. On an idle afternoon you decide to

calculate the number of cannonballs in the stack. What is the number of

cannonballs?

650 is the number of cannonballs.  It typically fires a projectile propelled by an explosive chemical.

A cannon constitutes a large-caliber gun that belongs to the artillery category. It typically fires a projectile propelled by an explosive chemical. Prior to the development of smokeless powder in the late 19th century, gunpowder (sometimes known as "black powder") served as the main propellant.

Depending on their intended purpose on the battlefield, different types of gun combine and balance these characteristics to differing degrees. Cannons differ in gauge, effective range, mobility, rate of fire, angle of fire, and firepower. A large artillery weapon is a cannon.

By utilizing the formula of a square pyramid,

n(n+1)(2n+1)/6

12(12+1)(2(12)+1)/6

12(13)(25)/6

2*13*25

=650

Therefore, 650 is the number of cannonballs.

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Given:

The American marriage rate R,  x years after 1960 is defined by the function

[tex]R(x)=-0.0065x^2 +0.23x + 8.47[/tex]

To find:

The year in which the marriage rate is the highest.

Solution:

We have,

[tex]R(x)=-0.0065x^2 +0.23x + 8.47[/tex]

It is a quadratic function with negative leading coefficient. So, it is a downward parabola and vertex of downward parabola is maximum.

If a quadratic function is [tex]f(x)=ax^2+bx+c[/tex], then

[tex]Vertex=\left(\dfrac{-b}{2a},f(\dfrac{-b}{2a})\right)[/tex]

In the given function,

[tex]a=-0.0065,b=0.23,c=8.47[/tex]

Now, x-coordinate of vertex is

[tex]-\dfrac{b}{2a}=-\dfrac{0.23}{2(-0.0065)}[/tex]

[tex]-\dfrac{b}{2a}=-\dfrac{0.23}{-0.013}[/tex]

[tex]-\dfrac{b}{2a}\approx 17.69[/tex]

It means the marriage rate is highest after 17 years of 1960.

[tex]1960+17=1977[/tex]

Therefore, the marriage rate is highest in year 1977.

Answer:

64 cups

Step-by-step explanation:

Answer:

The number of liters of the 45% acid solution = 10 liters

The number of liters of the 70% acid solution is = 40 liters

Step-by-step explanation:

How many liters each of a 45% acid solution and a 70% acid solution must be used to produce 50 liters of a 65% acid solution? (Round to two decimal places if necessary.)

Let x be the number of liters of the 45% acid solution

The number of liters of the 70% acid solution is y

x + y = 50

x = 50 - y

Also

How many liters each of a 45% acid solution and a 70% acid solution must be used to produce 50 liters of a 65% acid solution?

We have:

45% × x + 70% × y = 65% × 50

0.45x + 0.70y = 0.65 × 50

0.45x + 0.70y = 32.5

We substitute x = 50 - y in the equation

0.45(50 - y) + 0.70y = 32.5

= 22.5 - 0.45y + 0.70y = 32.5

= - 0.45y + 0.70y = 32.5 - 22.5

= 0.25y = 10

Divide both sides by 0.25

= y = 10/0.25

y = 40 liters

x = 50 - y

x = 50 - 40

x = 10 liters

Hence,

The number of liters of the 45% acid solution = 10 liters

The number of liters of the 70% acid solution is = 40 liters

Answer:

(3)¼×¾

Step-by-step explanation:

3⁴/⁴

hope its write

Answer:

[tex]\frac{13}{4}[/tex] · [tex]\frac{15}{4}[/tex]

Step-by-step explanation:

Focusing on the first fraction, in order to simplify it, you have to multiply the denominator by the whole number; 4 x 3 is 12. You add the product to the numerator, so 12 + 1 would be 13. Therefore, the first fraction simplified would be [tex]\frac{13}{4}[/tex].

We can apply the same procedure to the next fraction, so 3 x 4 is 12, and 12 + 3 is 15. [tex]\frac{15}{4}[/tex] would be your answer.

Hope this helps! :)

Answer:

0.76

Step-by-step explanation:

Hundredth is just the 2nd decimal point

Answer:

1) C

2) O

3) P

4) T

5) I

6) C

7) P

8) S

9) A

10) L

11) T

12) E

13) L

Step-by-step explanation:

Answer:

It’s 17.6

Step-by-step explanation:

Answer:

The equation of line n is;

y = -3x - 23

Step-by-step explanation:

Here, we want to find the equation of line n

For the alternate interior angles to be congruent after drawing the transversal, then both lines must be parallel

If the two lines are parallel, then their slopes are equal

To get the slope of line m, we compare the equation of line m to the standard form

The equation of line m is y = -3x + 8

if we compare this with the standard form which is y = mx + c

Then the slope of line m is -3 and since they are parallel lines, the slope of line n is -3 too

So now, we need to get the equation of line n

It passes through (-4,-11)

What we have already is;

y = -3x + c

we need to get the y-intercept to write the complete equation

To get the y-intercept we simply substitute for (-4,-11)

Thus, we have

-11 = -3(-4) + c

-11 = 12 + c

c = -11-12 = -23

The equation of line n is;

y = -3x - 23

Answer:

C and D

Step-by-step explanation:

Answer:

around 15.3

Step-by-step explanation:

3^2 + 15^2=c^2

Answer:

Step-by-step explanation:

Formula:

a^2 + b^2 + c^2

3^2 + 15^2 + c^2 = To find hypotenuse

3 • 3 + 15 • 15 = -c^2

9 + 225 = -c^2

234 = c^2

square root of 234 = 15.2970585408

c = 15.2970585408

The roof is 15.2970585408

Answer:

Easy lol mzvcn=48

Step-by-step explanation:

Answer:

Tristan will need 32 feet of material for the perimeter of the garden.

Step-by-step explanation:

Given that

Area of square garden = A = 64 square feet

Perimeter = P = ?

We know that for calculation of perimeter, length of side of square is required which is not directly given in the question. The area will be used to calculate length of side and then length will be used to calculate the perimeter.

So,

[tex]Area = A = s^2[/tex]

s is for side

Putting the value of area

[tex]64 = a^2[/tex]

Taking square root on both sides

[tex]\sqrt{s^2} = \sqrt{64}\\s = 8\ feet[/tex]

The length of side is 8 feet.

Perimeter will be:

[tex]P = 4*s\\P = 4*8\\P = 32\ feet[/tex]

Hence,

Tristan will need 32 feet of material for the perimeter of the garden.

Answer:

1000000

Step-by-step explanation:

I'm not sure what you meant by "scientific notation". So uhh, I only solved the 1.0 times 10^6,

10^6=10×10×10×10×10×10

10^6=1000000

(Fun fact. If you ever see a power of 10, you don't actually need to solve it. Look at the power, and add the same amount of 0's. For example 10^2. Power sign is 2. 2 trailing 0's.)