what is the domain of the function

Answer:

28 ft

Step-by-step explanation:

The height of the triangle = 15 ft

The least required area A = 210 ft^2

We know that the area of a triangle = 1/2bh

Where

b is the base

h is the height

Substituting, we have

210 = 1/2 x b x 15

210 = 15/2 x b

420/15 = b

b = 28 ft

Answer:

3x-2

Step-by-step explanation:

The algebraic expression is 3x -2.

Algebraic expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

We have to determine an algebraic expression for "2 less than the product of 3 and a number x"

Here, the product of 3 and a number x

⇒ 3x

Therefore, 2 is less than the product of 3, and a number x as

⇒ 3x -2

Hence, the algebraic expression is 3x -2.

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Answer:

2(2W+12) < 560

Step-by-step explanation:

Perimeter of a rectangular dog pen P = 2(L+W) where;

L is the length of the dog pen

W is the width of the dog pen

If Lyle wants to build a rectangular dog pen with a length that is 12 feet more than the width, then L = W+12

If Lyle can afford no more than 560 feet of fence, this means that the perimeter cannot be more than 560feet i.e P<560

The inequality to show that the perimeter of the dog pen can be no more than 560 feet is expressed as P < 2(L+W)

Substituting the given parameters;

2([W+12]+W)<560

2(2W+12)<560

Hence the inequality to show that the perimeter of the dog pen can be no more than 560 feet is 2(2W+12)<560

Answer:

$2.33

Step-by-step explanation:

To find how much strawberries cost per pint, we would divide the seven dollars by 3 which will tell us how much each pint costs. Hope this helps, have a great day!

Answer: x=1

Step-by-step explanation:

5x-4+2x=3

    +4       +4

5x+2x=7

7x=7

x=1

Answer:

x=1

Step-by-step explanation:

5x - 4 +2x =3

5x +2x =3 +4

7x =7

x=7 :7

x=1

Answer:

length =16

Step-by-step explanation:

area= breadth*length

length = 2 breadth    --equation 1        

(the length of the rectangle is twice the breadth)

128m^2= breadth*2 breadth

128m^2= 2 breadth^2

breadth^2= 128/2m^2

breadth^2=64m^2

taking square root on both sides

[tex]\sqrt{breadth^2}[/tex]=[tex]\sqrt{64m^2}[/tex]

[tex]\sqrt{breadth^2}[/tex]=[tex]\sqrt{(8m)^2}[/tex]

breadth= 8m   (cancelling square root with power 2

put breadth in equation 1

length= 2*8

length= 16

CHECK:

area of rectangle = breadth * length

area= 8*16

area=128

Answer:

See Below

Step-by-step explanation:

4) t = n -r  Solve for n

Add r to both sides

t = n -r

+r     +r

t +r = n

Or  n = t+r

7) [tex]\frac{f}{g}[/tex] = h    Solve for f

Multiply both sides by g to get rid of fraction

g/1 (f/g) = h(g)

f = hg

Answer:

pre-image coordinates (x,y) imagine coordinates (y,x)

Step-by-step explanation:

bascially just switch the x and y coordinates and keep the sign :)

Explicación paso a paso:

El tiempo necesario para completar la trayectoria se conoce como tiempo de vuelo.

Tiempo de vuelo = dónde;

U es la velocidad inicial del cuerpo = 47,5 m / s

es el ángulo de lanzamiento = 39,4 °

g es la aceleración debida a la gravedad = 9,81 m / s²

Sustituyendo los parámetros dados en la fórmula anterior, tendremos;

[tex]T = \dfrac{2(47.5)sin39.4^0}{9.81} \\\\T = \dfrac{95sin39.4^0}{9.81} \\\\T = \dfrac{95*0.6347}{9.81} \\\\T = \dfrac{60.2994}{9.81} \\\\T =6.1467 secs[/tex]

El tiempo necesario para completar la trayectoria es de 6.1467 segundos.

First, let's find the slope.

Slope = (7 - (-3)) / (2 - 0) = (7 + 3) / 2 = 10 / 2 = 5

So far our equation looks like: y = 5x + b

Leta plug one of the points into our equation to find b.

-3 = 5(0) + b

Simplify.

-3 = b

The equation is: y = 5x - 3

Answer choice B is correct.

Step-by-step explanation:

In an equilateral triangle, all the three sides are equal as well as all the angles are equal. Let the angles be x.

We know that the sum of angles of a triangle is equal to 180 degrees. It means that,

x+x+x=180

3x=180

x=60°

Hence, if a triangle is an equilateral triangle, then the triangle has exactly three 60°  angles. Hence, △ABC is an equilateral triangle

Answer:

6 months

Step-by-step explanation:

Answer:

1/10

Step-by-step explanation:

7000/70000=1/10

Answer:

Find the exact value using trigonometric identities.

Exact Form: 1/16

Decimal Form:

0.0625

Step-by-step explanation:

☽------------❀-------------☾

Hi there!

~

The absolute value is the distance from 0 to 2.5. In this case the absolute value from 0 to |2.5| is 2.5

❀Hope this helped you!❀

☽------------❀-------------☾

Steps to solve:

(4 + 5 + 3) + 8

~Add everything in parenthesis

12 + 8

~Add

20

Best of Luck!

[tex] \huge \purple {\tt {(4 + 5 + 3) + 8 =? }} [/tex]

By using parenthesis, we get

[tex] \huge \purple {\tt {12 + 8 = 20}} [/tex]

[tex] \huge \purple {\tt {20}} [/tex]

Answer:

the answer should be 0.96

Answer:

Earning on one shift = 4**5.25= 21

to earn 220 she had to do 220/21= 10.48 shifts

Answer:

Option (A)

Step-by-step explanation:

Let the equation of the linear function representing number of party guests (c) and total cost (p) is in the form of c = mp + b

m = Slope of the line

b = y-intercept

Choose the two ordered pairs from the table (3, 274) and (7, 306).

Slope of the function 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m = [tex]\frac{306-274}{7-3}[/tex]

m = 8

Since, equation of a line passing through (x', y') and slope m is,

y - y' = m(x - x')

Therefore, equation of a line passing through (3, 274) and slope = 8,

y - 274 = 8(x - 3)

y - 274 = 8x - 24

y = 8x + 274 - 24

y = 8x + 250

Since, y = p and x = c

Therefore, p = 8c + 250 will be the equation.

Option (A) is the answer.

Answer:ok

Step-by-step explanation: the answer is A

Answer:

∠ BOF = 32°

Step-by-step explanation:

Since AB is a straight line, then

∠ AOE + ∠ EOD + ∠ DOE = 180° , substitute values

90 + x + 8 + 2x - 8 = 180 , that is

3x + 90 = 180 ( subtract 90 from both sides )

3x = 90 ( divide both sides by 3 )

x = 30

Thus

∠ DOB = 2x - 8 = 2(30) - 8 = 60 - 8 = 52°

∠ COF = 4x - 24 = 4(30) - 24 = 120 - 24 = 96°

∠ AOC = ∠ DOB ( vertical angles ), thus

y = 52, then

∠ BOF = 180° - (96 + 52)° = 180° - 148° = 32° ( angles on a straight line )

Answer:

13,200

Step-by-step explanation:

6000/100=60

60x8=480

480x15=7,200

6,000+7,200=13,200

If the initial amount is $6000 , rate of interest 8% then after 15 years the amount willbe $19957.218.

Compound interest is the interest calculated on the principal and the aggregate interest. It may be copounded annually,semi annually, monthly, bimonthly,etc.

We have been given that the deposit is $6000,rate is 8% which is compounded monthly.

So effective rate of interest will be 8/1200=0.0067.

n will be 15*12=180

The sum after 15 years=6000[tex](1+0.0067)^{180}[/tex]

S=6000[tex](1+0.0067)^{180}[/tex]

Take log both sides.

log S=log 6000[tex](1+0.0067)^{180}[/tex]

log S=log 6000+log [tex](1+0.0067)^{180}[/tex]

log S=log 6000+180 log (1.0067)

log S=3.7781+180*0.0029

log S=3.7781+0.522

log S=4.3001

S=AL (4.3001)

S=19957.218

Hence if the initial amount is $6000 , rate of interest 8% then after 15 years the amount willbe $19957.218.

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Answer:

Answer:

Solve for x or y,  Ax + By = 0

x=1  y=unknown number.

Step-by-step explanation:

Answer:20

Step-by-step explanation:

You take 203 and subtract 3 since you know you have 3 pieces left over you then divide 209 by 10 and get 20!!

Answer:

20 people

Step-by-step explanation:

Did it in my head

Answer:

60 square unit

Step-by-step explanation:

side = √225.2 = 15

perimeter = side x 4

perimeter = 15 x 4 = 60 square unit

Answer:

f^-1(x)-(x/10)-(1/5).

Hope this helps!

Step-by-step explanation:

(See picture for explanation!)

Answer:

42

Step-by-step explanation:

D-42 on EDG.

A clock is constructed using a regular polygon with 60 sides. The polygon rotates each minute, making one full revolution each hour. The polygon has rotated 42 times after 7 minutes.

A polygon is known to be a plane figure with at least three equal sides and angles.

From the given information,

To estimate the revolution completed in 1 minute, we have:

[tex]\mathbf{= \dfrac{360 \ ^ 0}{60 \ ^ 0} }[/tex]

= 6° per minute

Now, to determine how much the polygon has rotated after 7 minutes, we have:

= (6° / minute) × 7 minutes

= 42°

Therefore, we can conclude that the polygon has rotated 42° in 7 minutes,

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Answer:

27.7

Step-by-step explanation:

For this problem, we will simply use standard rounding conventions to round the number to the nearest tenth.

If the number after the target, the hundreths place in this case, is between 0 and 4, we won't change the tenths place.  If the number is between 5 and 9, we will increment the tenths place by one.

So for our number, 27.68, 8 is between 5 and 9 so we will increment the tenths place by one for the round.

Hence, our rounded answer for the nearest tenth is 27.7.

Cheers.