[tex] {x}^{2} - 18 < 0[/tex]
​

Answer:

11.17 ft

Step-by-step explanation:

Since the swing hangs from a beam 10 feet high with the seat hanging 2 feet above the ground, the swing moves in an arc of radius r = 10 ft - 2 ft = 8 ft.

Now, since the swing moves back and forth from -130° to -50° to the horizontal, the length of arc L it moves in is given by

L = Δθ/360 × 2πr where  Δθ = change in angle of the swing = θ₂ - θ₁ where θ₁ =  -50° and θ₂ = -130°. So, Δθ = θ₂ - θ₁ = -130° -(-50°) = -130° + 50° = -80°.

Substituting r and  Δθ into L, we have

L = -80°/360° × 2π(8 ft)

= -8/36 × 16π ft

=  -32π/9 ft

= -100.53/9 ft

= -11.17 ft

Ignoring the negative sign, the length of arc L = 11.17 ft. So, the swing moves back and forth 11.17 ft

Answer:

9×10 to the power of -8

Step-by-step explanation:

Cause when we add power to the power we multiply them

For example [tex](2^{2} )^2[/tex] , we multiply the power so , 2×2= 4 so [tex](2^{2} )^2[/tex] = [tex]2^{4}[/tex]=16

Same here [tex]((9*10)^{-4} )^2[/tex] we multiply the powers so -4×2=-8

So [tex]((9*10)^{-4} )^2[/tex] =[tex](9*10)^{-8}[/tex] = 2.323×[tex]10^{-16}[/tex]

Answer: 1/7

Step-by-step explanation:

Answer:

(4,2) (11,3)

Step-by-step explanation:

Answer:

First box, fourth box, sixth box

Step-by-step explanation:

Positive in division means either both numbers are positive or negative

Answer:

[tex]5x-4y+4=0[/tex]

Step-by-step explanation:

Given: A point  which is perpendicular to the line .

To find: The equation of the line which passes through [tex](-4, -4)[/tex] and is perpendicular to the line [tex]4x+5y=5[/tex].

Solution:

We have, [tex]4x+5y=5[/tex].

Slope of the line [tex]4x+5y=5[/tex] is [tex]-\frac{4}{5}[/tex].

The line which passes through [tex](-4, -4)[/tex] is perpendicular to the line [tex]4x+5y=5[/tex].

Now, the product of the slopes of two perpendicular lines is [tex]-1[/tex].

Therefore, [tex]m\times-\frac{4}{5}=-1[/tex]

So, its slope is [tex]\frac{5}{4}[/tex].

Now, the equation of the line which passes through [tex](-4, -4)[/tex] and slope [tex]\frac{5}{4}[/tex] is:

[tex]y-(-4)=\frac{5}{4} [x-(-4)][/tex]

[tex]\Rightarrow y+4=\frac{5}{4} (x+4)[/tex]

[tex]\Rightarrow 4(y+4)=5(x+4)[/tex]

[tex]\Rightarrow 4y+16=5x+20[/tex]

[tex]\Rightarrow 5x-4y+20-16=0[/tex]

[tex]\Rightarrow 5x-4y+4=0[/tex]

Hence, the equation of the line that contains the point [tex](-4, -4)[/tex] and is perpendicular to the line [tex]4x+5y=5[/tex] is [tex]5x-4y+4=0[/tex].

Answer:

We are to find the number of different meals that are available when we select an appetizer, an entree and a dessert. Thus, the required number of different meals is 216.

Step-by-step explanation:

PLZZZZZZZZ GIVE ME BRAINLYIST

The required number of the combination is 384. Option C is correct.

A menu at a local diner has 12 appetizers, 8 entrees, and 4 choice of desserts. How many different meal combinations are possible when you select one appetizer, one entrée, and one dessert from the menu is to be determined.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In a combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

For  12 appetizers, 8 entrees, and 4 choices of desserts.
The number of  composite combinations that can be made = 12 * 4 * 8
                                                                                  = 384

The required number of the combination is 384. Option C is correct.

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Answer:

Sample Response: To use the distributive property, distribute multiplication by 2 to both terms inside the parentheses. The products are 2(11) and 2(y). The equivalent expression is 22 + 2y

Step-by-step explanation:

you're welcome

Answer:

Step-by-step explanation:

-2 - (-5) = 3

3 - (-4) = 7

6/18 = 1/3

The sequence of transformation that will map the circle would be:

D). Translate <3, 7> then dilate by a scale factor of 1/3

Dilation is denoted as the process in which an object gets expanded or widened.

Given that,

Center of circle A = (-5, -4)

Radius = 18

Center of circle M = (-2,3)

To find the dilation,

⇒ [tex]-2 - (-5) = 3[/tex]

⇒ [tex]3 - (-4) = 7[/tex]

= [tex]6/18[/tex]

[tex]= 1/3[/tex]

Therefore, the translation will happen with <3, 7> and the dilation in the scale factor being 1/3.

Thus, option D is the correct answer.

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4x+2=150 150-2=148 148/4= 37

Answer:

37

Step-by-step explanation:

first option, 37..................................................................................................................................................................................................................................................................................................

Answer:

200

Step-by-step explanation:

delta math

its 200.456 before rounding

Step-by-step explanation:

(125/5)×3=75

75 participate jogging

25×2=50

50 participate in cycling

Answer:

lower Right.

Step-by-step explanation:

Remark

The two angles share the same side of vertically opposite angles. That makes them supplementary which means the two angles add to 180 degrees.

Equation

4x + 8x + 12 = 180         Combine like terms on the left

Solution

Answer:

A=50.24 mm²

Step-by-step explanation:

A=3.14×4²

A=3.14×16

A=50.24 mm²

Answer:

55

Step-by-step explanation:

55 is your answer

Answer:

Step-by-step explanation:

Subtract

2

y

from both sides of the equation.

x

=

12

−

2

y

−

x

=

−

y

−

6

Replace all occurrences of

x

with

12

−

2

y

in each equation.

Tap for more steps...

−

12

+

2

y

=

−

y

−

6

x

=

12

−

2

y

Solve for

y

in the first equation.

Tap for more steps...

y

=

2

x

=

12

−

2

y

Replace all occurrences of

y

with

2

in each equation.

Tap for more steps...

x

=

8

y

=

2

The solution to the system is the complete set of ordered pairs that are valid solutions.

(

8

,

2

)

The result can be shown in multiple forms.

Point Form:

(

8

,

2

)

Equation Form:

x

=

8

,

y

=

2

Answer:

6 and 2

Step-by-step explanation:

6 times 2 is 12 and 6 plus 2 is 8

Answer:

The jelly beans cost $2.25 / pound

The trail mix costs $1.25 / pound

Step-by-step explanation:

I just took the test.

Answer:

C. 1796.08 [tex]in^2[/tex]

Step-by-step explanation:

Area of circle is [tex]\pi r^2[/tex], r is the radius

remember radius is from the center to the edge, so it is half the diameter

now we need to find the area of the large circle (table) minus the small circle (hole)

the radius of the large circle is 48/2 which is 24

the area is [tex]\pi 24^2[/tex] replacing r in the formula with 24, the radius. Using 3.14 as pi, the answer is 1808.64

the radius of the small circle is 4/2 which is 2

the area is [tex]\pi 2^2[/tex] so the calculated value would be 12.56

now subtract the area of the hole (small circle) from the area of the table (large circle)

1808.64 - 12.56 = 1796.08

and there's your answer

hope that helps, lmk if it doesn't :)

Answer:

Step-by-step explanation:

r₁ = radius of tabletop = 24 in

r₂ = radius of hole = 2 in

area of hole = πr₂² = 4π in²

area of tabletop = πr₁² - πr₂² = 576π - 4π = 572π ≈ 1796.08 in²

Answer:

B

Step-by-step explanation:

The solution is

Option A - True

The volume of the rectangular cargo is 2187 feet³

Option B - True

The volume of the rectangular cargo is 2187 feet³

Option C - True

The volume of the rectangular cargo is 2187 feet³

Option D - True

The volume of the rectangular cargo is 2187 feet³

What is the Volume of a Rectangle?

The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle

Volume of Rectangle = Length x Width x Height

Volume of Rectangle = Area of Rectangle x Height

Given data ,

Let the cargo hold be a rectangular prism

Now , the dimensions of the rectangular prism is

18 feet x 13.5 feet x 9 feet

And , the Volume of Rectangle = Length x Width x Height

Substituting the values in the equation , we get

Volume of Rectangle = 18 x 13.5 x 9

Volume of Rectangle = 2187 feet³

a)

The number of boxes = 6

The dimensions of the cargo be = 9 feet x 4.5 feet x 9 feet

So , the volume of the cargo = number of boxes x 9 x 4.5 x 9

On simplifying the equation , we get

Volume of the cargo = 6 x 364.5

Volume of the cargo = 2187 feet³

b)

The number of boxes = 81

The dimensions of the cargo be = 3 feet x 3 feet x 3 feet

So , the volume of the cargo = number of boxes x 3 x 3 x 3

On simplifying the equation , we get

Volume of the cargo = 81 x 27

Volume of the cargo = 2187 feet³

c)

The number of boxes = 24

The dimensions of the cargo be = 4.5 feet x 4.5 feet x 4.5 feet

So , the volume of the cargo = number of boxes x 4.5 x 4.5 x 4.5

On simplifying the equation , we get

Volume of the cargo = 24 x 91.125

Volume of the cargo = 2187 feet³

d)

The number of boxes = 12

The dimensions of the cargo be = 9 feet x 4.5 feet x 4.5 feet

So , the volume of the cargo = number of boxes x 9 x 4.5 x 4.5

On simplifying the equation , we get

Volume of the cargo = 12 x 182.25

Volume of the cargo = 2187 feet³

Hence , the volume of the rectangular cargo is 2187 feet³

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Answer:

There are no statements

Step-by-step explanation:

If you put up the statements, I'll edit my answer

Answer: [tex]-3\hat{i}-6\hat{j}+2\hat{k}[/tex]

Step-by-step explanation:

Given

[tex]\vec{a}=2\hat{i}+4\hat{j}-5\hat{k}\\\vec{b}=\hat{i}+\hat{j}+\hat{k}[/tex]

[tex]\vec{c}=\hat{j}+2\hat{k}[/tex]

The addition of the three is [tex]\vec{a}+\vec{b}+\vec{c}[/tex]

[tex]\vec{a}+\vec{b}+\vec{c}=(2\hat{i}+4\hat{j}-5\hat{k})+(\hat{i}+\hat{j}+\hat{k})+(\hat{j}+2\hat{k})[/tex]

[tex]\vec{a}+\vec{b}+\vec{c}=3\hat{i}+6\hat{j}-2\hat{k}[/tex]

vector opposite to the vector  [tex]\vec{a}+\vec{b}+\vec{c}\ \ \text{is}\ -(\vec{a}+\vec{b}+\vec{c})[/tex]

[tex]\therefore -(\vec{a}+\vec{b}+\vec{c})=-3\hat{i}-6\hat{j}+2\hat{k}[/tex]

Answer:

9)m≤54

11)x>30

13)y≤40

Step-by-step explanation:

9)m−18≤36

Add 18 to both sides.

m≤36+18

Add 36 and 18 to get 54.

m≤54

11)9x>270

Divide both sides by 9. Since 9 is positive, the inequality direction remains the same.

x=270/9

Divide 270 by 9 to get 30.

x>30

13)y/5≤8

Multiply both sides by 5. Since 5 is positive, the inequality direction remains the same.

y≤8×5

Multiply 8 and 5 to get 40.

y≤40

Answer:

Division to get 28

Step-by-step explanation:

Answer:

2.8 liters

She drank 2.8 liters all together.

Step-by-step explanation:

0.878+1.2+0.75= 2.8

Nicky drank a total of 2.828 liters of water throughout the day.

To find out how much water Nicky drank altogether, you can add up the amounts of water she drank throughout the day.

0.878 liters after breakfast.

1.2 liters after lunch.

0.75 liters before dinner

Adding these values together:

0.878 + 1.2 + 0.75 = 2.828

Therefore, Nicky drank a total of 2.828 liters of water throughout the day.

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Answer:

40 Square Units

Step-by-step explanation:

Easy way to find area: Diagonal 1 * Diagonal 2 divide by 2 = your answer

Diagonal 1 (AC) = 5 + 5 = 10

Diagonal 2 (BD) = 4 + 4 = 8

10 + 8 = 80, 80/2 = 40

Answer: 40 square units