Which expressions are equivalent to (5⋅x)⋅3 ? Drag and drop the equivalent expressions into the box.
3⋅(5⋅x)
5⋅3+x⋅3
5⋅(x⋅3)
15x
5⋅3⋅x⋅3

Answer:

88 ft

Step-by-step explanation:  Start with the formula for the area of a rectangle:

A = L*W, where L is the length and W is the width.

Here, the width is W = 24 ft, and the area i s 480 ft^2.  Thus,

A = 480 ft^2 = L (24ft), which yields L = (480/24) ft = 20 ft.

The length of the fencing required is actually the perimeter of the yard, which is P = 2L + 2W.

Substituting 20 ft for L and 24 ft for W, we get:

P = perimeter of yard = amount of fending needed:

P = 2(20 ft) + 2(24 ft) = 88 ft

Ken would need 88 ft of fencing to enclose his entire yard.

Ken needs to buy 88 feet of fencing to enclose his rectangular yard, which has an area of 480 square feet and is 24 feet wide.

To find out how much fencing Ken would need to buy to enclose his rectangular yard, we first need to calculate the dimensions of the yard. We know the area of the yard is 480 square feet and the width is 24 feet.

To find the length, we use the following equation for the area of a rectangle (Area = length  imes width):

480 square feet = length x 24 feet

By dividing both sides by 24 feet, we obtain:

length = 480 / 24

length = 20 feet

Now, to calculate the total amount of fencing needed, we add together the lengths of all four sides:

Total fencing = 2  imes (length + width)

Total fencing =  2  imes (20 feet + 24 feet)

Total fencing = 2  imes 44 feet

Total fencing = 88 feet

Therefore, Ken needs to buy 88 feet of fencing to enclose his yard completely on all four sides.

Answer: the answer is 6ft

Step-by-step explanation:

3 times 1 times 2 = 6ft

Number of gallons of water would it take to fill the tank two-thirds full is,

⇒ 30 gallons

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

An aquarium tank is 3 feet long, 1 foot wide, and 2 feet high.

Hence, Volume of tank is,

⇒ V = 3 x 1 x 2

⇒ V = 6 feet³

Hence, Number of gallons of water would it take to fill the tank two-thirds full is,

⇒ 2/3 of 6

⇒ 4 feet³

⇒ 4 × 7.5

⇒ 30 gallons

Thus, Number of gallons of water would it take to fill the tank two-thirds full is,

⇒ 30 gallons

Learn more about the multiplication visit:

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Answer:

[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

The given ratio is [tex]\frac{18}{27}[/tex]

9 is the common factor of 18 and 27

divide numerator and denominator by 9

[tex]\frac{18/9}{27/9} =\frac{2}{3}[/tex]

hence [tex]\frac{2}{3}[/tex] is proportion with [tex]\frac{18}{27}[/tex]

Answer:

The altitude of the trapezoid is 60 feet.

Step-by-step explanation:

Trapezoid

Sum of the bases: B+b=280 feet

Area of the trapezoid: A=8,400 feet^2

Altitude of the trapezoid: h=?

The formula to calculate the area of a Trapezoid is:

A = (1/2) (B+b) h

Replacing the given values:

8,400 feet^2 = (1/2) (280 feet) h

(1/2) (280 feet) = (140 feet)

8,400 feet^2 = (140 feet) h

Solving for h: Dividing both sides of the equation by 140 feet:

8,400 feet^2 / (140 feet) = (140 feet) h / (140 feet)

60 feet = h

h = 60 feet

Answer: The altitude of the trapezoid is 60 feet.

Answer:

60

Step-by-step explanation:

Answer:

30°                                

Step-by-step explanation:

No. of sides in dodecagon = 12

No. of angles = 12

Since its regular, all sides and all angles are equal.

total rotational angle = 360°

since no. of angles = 12

and all angles are equal,

rotational angle at which, it will co - incide with itself = [tex]\frac{360}{12}[/tex]

                                                                                     = 30°

A regular dodecagon will be onto itself it is rotated about the central angle 30°.

Answer: 30°

Step-by-step explanation:

[tex]\frac{422}{8}=52.75mph[/tex]

A.

[tex]average=\dfrac{distance}{time}\\\\\text{We have}\\\\distance=422\ miles\\\\time=8\ hours.\\\\\text{Substitute:}\\\\\boxed{x=\dfrac{422\ miles}{8\ hours}=52.75\ mph}[/tex]

Answer:

v = 9

Step-by-step explanation:

Use the method of cross- multiplying

[tex]\frac{a}{b}[/tex] = [tex]\frac{c}{d}[/tex] ⇒ ad = bc

8v = 12 × 6

8v = 72 ( divide both sides by 8 )

v = 9

Answer:

[tex]v=9[/tex]

Step-by-step explanation:

The given equation is

[tex]\frac{v}{12}=\frac{6}{8}[/tex].

We multiply both sides of the equation by 12 to obtain,

[tex]12\times \frac{v}{12}=\frac{6}{8}\times 12[/tex].

This implies that;

[tex]v=\frac{3}{4} \times 12[/tex]

This gives

[tex]v=\frac{3}{1} \times 3[/tex]

[tex]v=3\times 3[/tex]

[tex]v=9[/tex]

Answer: C < B < A

Step-by-step explanation:

First, let's evaluate the growth rate of A from [1, 3]

[tex]f(x) = 200\bigg(\dfrac{3}{2}\bigg)^1[/tex]

    = 300

coordinate is (1, 300)

[tex]f(x) = 200\bigg(\dfrac{3}{2}\bigg)^3[/tex]

    = 675

coordinate is (3, 675)

Average growth rate (AGR) is: [tex]\dfrac{675-300}{3-1} = \dfrac{375}{2} = 187.5[/tex]

AGR (A) = 187.5

*************************************************************************************

Next, let's evaluate the growth rate of B from [1, 3]

The coordinates are already provided as (1, 120) and (3, 480)

Average growth rate (AGR) is: [tex]\dfrac{480-120}{3-1} = \dfrac{360}{2} = 180[/tex]

AGR (B) = 180

*************************************************************************************

Lastly, let's evaluate the growth rate of C from [1, 3]

f(x) = 600(1.2)ˣ

f(x) = 600(1.2)¹

     = 720

coordinate is (1, 720)

f(x) = 600(1.2)³

     = 1036.8

coordinate is (3, 1036.8)

Average growth rate (AGR) is: [tex]\dfrac{1036.8-720}{3-1} = \dfrac{316.8}{2} = 158.4[/tex]

AGR (C) = 158.4

It's going to be 7/10

Answer:

29.03 units

Step-by-step explanation:

x^2 = 10^2 + 19^2 - 2*19*20 cos 122

=   100 + 361 - 720 * -0.52992

= 842.54

x = 29.03

Answer:

Step-by-step explanation: To find a y intercept you must find what y is when x is 0 so because it already tells you on the table the y intercept is 4. To find slope take 2 x intercepts and 2 y intercepts. For this well take the 0,4 and 5,1. The take the y from both pairs and minus them so it will look like 4 minus 1. Then draw a line under the equation under this line do the same thing but with the x's from both pairs so 0-5 then you will get as a result of both -3/5 as your slope.

Answer:

slope: -3/5

y-intercept: (0, 4)

slope-intercept form: y = -3/5x + 4

Step-by-step explanation:

To find the slope of this line, you would take two points from the table and substitute their coordinates into the slope formula.

Slope formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

I'm going to use the points (0, 4) and (5, 1). You can really use any point from the table. Substitute these points into the formula to find the slope.

(0, 4), (5, 1) → [tex]\frac{1-4}{5-0} \rightarrow \frac{-3}{5}[/tex]

This means the slope of the line is -3/5.

The y-intercept will always have the value of x be 0 (so the point is solely on the y-axis), so by looking at the table we can see that the y-intercept is at (0, 4).

Since we have the slope and a point of the line, we must use point-slope form to find the equation of the line in slope-intercept form. Substitute in the point (0, 4) --you could use any point from the table-- and the slope -3/5 into the point-slope form equation.

point-slope form: y - y1 = m(x - x1) --you'll be substituting the point coordinates and slope into y1, x1, and m.

y - (4) = -3/5(x - (0))

Simplify.

y - 4 = -3/5x

Add 4 to both sides.

y = -3/5x + 4 is the equation of the line in slope-intercept form (you have both the slope and the y-intercept in this form).

Answer:

x= 0.4

Step-by-step explanation:

We need to solve and find the value of x

7 1/3x = 1.6 ÷ 6/11

Converting mixed fraction into improper fraction

22/3 x = 1.6 ÷ 6/11

Converting ÷ sign by X and reciprocating the term

22/3 x = 1.6 * 11/6

Now divide both sides by 3/22

x = 1.6 * 11/6 * 3/22

x = 1.6 * 1/2 * 1/2

x = 1.6/4

x = 0.4

S0, x= 0.4

Answer:

D

Step-by-step explanation:

note that the values in the domain map to the values in the domain as

- 1 → 2 ( that is 1 + 3 = 2 )

3 → 6 ( that is 3 + 3 = 6 )

5 → 8 ( that is 5 + 3 = 8 )

In each case 3 is added to the value in the domain(x) to obtain the value in the range ( y = f(x) )

Hence f(x) = x + 3 → D

Answer:

[tex]y=cos(x+\pi )[/tex]

Step-by-step explanation:

From the graph, we can see that y = -1 when x  = 0.

So to check whether which of the given options is the equation of the given graph, we will set our calculator to the radian mode and then plug the value of x as 0.

1. y = cos(x + pi/2) = cos(0 + pi/2) = 0

2. y = cos(x+2pi) = cos(0+2pi) = 1

3. y = cos(x+pi/3) = cos(0+pi/3) = 1/2 = 0.5

4. y = cos(x+pi) = cos(0+pi) = -1

Therefore, the equation of this graph is y = cos(x+pi) = cos(0+pi) = -1.

Answer:

21 students

Step-by-step explanation:

90 x .10 = 9

80 x .15 = 12

9 + 12 = 21 students

Answer:

3n+5

Step-by-step explanation:

Answer:

Opposite angles of a parallelogram are congruent.

Step-by-step explanation:

Given:

KLMN is a parallelogram.

KN ║ LM and KL ║MN.

To prove:

∠N ≅ ∠L

∠M ≅ ∠K

Proof:

∠N ≅ ∠L since the opposite angles of a parallelogram are congruent.

∠M ≅ ∠K since the opposite angles of a parallelogram are congruent.

Answer: Parallelogram KLMN Given

KL¯¯¯¯¯∥NM¯¯¯¯¯¯¯ and Kn---------llLM Definition of parallelogram

m∠K+m∠N=180°

m∠L+m∠M=180°

m∠K+m∠L=180° Same-Side Interior Angles Theorem

m∠K+m∠N=m∠K+m∠L

m∠L+m∠M=m∠K+m∠L Substitution Property of Equality

m∠N=m∠L

m∠M=m∠K Subtraction Property of Equality

∠N≅∠L

and ∠M≅∠K

Angle Congruence Postulate

Step-by-step explanation:

I took the test and got a 100

Answer: 252 feet tall

Step-by-step explanation:

1) make a proportion

x/18=140/10

2)solve

10x=140*18

x=140*18/10

x=14*18

x=252

3) Answer

The building is 252 feet tall

Answer:

2/5 * pi radians = 72 degrees

Step-by-step explanation:

To convert radians to degrees, we multiply by 180/pi

2 * pi/5 * 180/pi =

The pi/pi cancels leaving

2/5 * 180

360/5

72

2/5 * pi radians = 72 degrees

[tex]\dfrac{5x^4+10x^3-7x+1}{x+2}=(5x^4+10x^3-7x+1):(x+2)[/tex]

[tex]_+\begin{matrix}(5x^4&+&10x^3&-&7x&+&1)&:&(x+2)&=5x^3-7\\-5x^4&-&10x^3\end{matrix}\\\overline{_+\begin{matrix}\ \ =&&&&=&\ \ \ -&7x&+&1\\&&&&&&7x&+&14\end{matrix}}\\\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\ 15}[/tex]

[tex]\dfrac{5x^4+10x^3-7x+1}{x+2}=(5x^4+10x^3-7x+1):(x+2)=5x^3-7+R(15)\\\\5x^4+10x^3-7x+1=(x+2)(5x^3-7)+15[/tex]

Final answer:

Long division is a method used to divide two polynomials in algebra. It involves arranging the dividend and divisor, determining the term of the quotient, subtracting and repeating until there are no more terms left to bring down.

Explanation:

In algebra, long division is a method used to divide two polynomials. It is especially useful when the dividend (the polynomial being divided) has a higher degree than the divisor (the polynomial dividing the dividend).

Here's a step-by-step explanation:

Let me know if you need further assistance or if there's anything else I can help you with!

The amount that is direct-deposited bi-weekly is 404.30.

To calculate the bi-weekly direct deposit amount, we need to follow these steps:

1. Calculate the gross pay for a week:

 Gross pay per week = Hourly wage * Hours worked per week

 Gross pay per week = $8.60/hr * 32 hr/wk

 Gross pay per week = $275.20

2. Calculate the total deductions per week:

 Total deductions rate = FICA rate + federal tax rate + state tax rate

 Total deductions rate = 7.65% + 10.6% + 8.25%

 Total deductions rate = 26.5%

 Total deductions per week = Gross pay per week * Total deductions rate

 Total deductions per week = $275.20 * 26.5%

 Total deductions per week = $73.049

 3. Calculate the net pay for a week:

 Net pay per week = Gross pay per week - Total deductions per week

 Net pay per week = $275.20 - $73.049

 Net pay per week = $202.151

4. Calculate the bi-weekly net pay:

 Bi-weekly net pay = Net pay per week* 2

 Bi-weekly net pay = $202.151 * 2

 Bi-weekly net pay = $404.302

Since the net pay is calculated to the nearest cent, we can round the bi-weekly net pay to the nearest cent as well:

Bi-weekly net pay (rounded) = $404.30

Therefore, the amount that is direct-deposited bi-weekly is 404.30.

The answer is: $404.30.

Answer:

The right answer is 1 unit or A

Step-by-step explanation:

if the ∡E = ∡F = 90°, that means for that quadrilateral of BEGF, the other angles are ∡B = ∡G = 90°, which means is a square, meaning all its sides are equal, therefore

[tex]\bf y + 5 = 3y\implies 5=2y\implies \cfrac{5}{2}=y\implies 2\frac{1}{2}=y[/tex]

Answer:

A x 5

Step-by-step explanation:

Answer:

take all evaporation numbers and add them together to get the answer u r looking for

Step-by-step explanation:

Hey man, your answer is (A) I took the test!!!

The first 4 terms in the sequence are :

Firstly , let us learn about types of sequence in mathematics.

Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.

[tex]\boxed{T_n = a + (n-1)d}[/tex]

[tex]\boxed{S_n = \frac{1}{2}n ( 2a + (n-1)d )}[/tex]

Tn = n-th term of the sequence

Sn = sum of the first n numbers of the sequence

a = the initial term of the sequence

d = common difference between adjacent numbers

Geometric Progression is a sequence of numbers in which each of adjacent numbers have a constant ration.

[tex]\boxed{T_n = a ~ r^{n-1}}[/tex]

[tex]\boxed{S_n = \frac{a( 1 - r^n ) }{1 - r}}[/tex]

Tn = n-th term of the sequence

Sn = sum of the first n numbers of the sequence

a = the initial term of the sequence

r = common ratio between adjacent numbers

Let us now tackle the problem!

Given:

a = 4

r = 0.2

Solution:

[tex]T_n = a ~ r^{n-1}[/tex]

[tex]T_1 = 4 \times 0.2^{1-1} = 4 \times 1 = 4[/tex]

[tex]T_2 = 4 \times 0.2^{2-1} = 4 \times 0.2 = 0.8[/tex]

[tex]T_3 = 4 \times 0.2^{3-1} = 4 \times 0.04 = 0.16[/tex]

[tex]T_4 = 4 \times 0.2^{4-1} = 4 \times 0.008 = 0.032[/tex]

Therefore , the first 4 terms in the sequence are :

Grade: Middle School

Subject: Mathematics

Chapter: Arithmetic and Geometric Series

Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term