Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1,0, 3), (1,4,6), and (6,2,0).

Answer:

(4, -3)

Step-by-step explanation:

y = f(x -5) means y = f(x) shifted 5 units to the right. So the minimum point would shift 5 units to the right as well.

The area of the sector in radians is calculated as: B. 8π units squared.

The area of a sector where the central angle of the sector that is shaded in a circle is given in radians is calculated using the formula that is expressed as:

Area of sector = (1/2) × r²θ; where we have:

θ = the angle subtended at the center/central angle measure in radians

r = the radius of the circle

Given the following:

The shaded area is half of the circle. Its measure would be 180 degrees which when expressed in radians would be π.

Central angle measure in radians (θ) = π

Radius (r) = 4 units

Plug in the values into the area of sector formula

Area of sector = (1/2) × r²θ = (1/2) × (4²)(π)

Area of sector = (1/2) × (16)(π)

Area of sector = (1 × 16 × π)(2)

Area of sector = (16π)(2)

Area of sector = 8π units squared

In conclusion, the area of the shaded sector in the image given below is calculated as: B. 8π units squared.

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Answer:

C

Step-by-step explanation:

The average is the total of the scores divided by 5.  

128 x 5 Gives us the total scores of 640.  I know that one bowler had a score of 160.  I will subtract that from the total of 640.  640-160 = 480.  Since the 4 bowlers left, all had the same score, I will divide 480 by 4 to get 120

Answer:

47.25

Step-by-step explanation:

8.89 is about 9.

So, we have 9(5.25)=9(5)+9(0.25)=45+2.25=47.25

As slope is undefined, then the slope of the line is parallel to the x axis.

In this problem we have a line that passes through two points, the slope is determined by definition of secant line:

m = [- 9 - (- 6)]/(8 - 8)

m = - 3/0

As slope is undefined, then the slope of the line is parallel to the x axis.

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Answer:

3

Step-by-step explanation:

a = the other leg:

[tex]a^{2} =(2\sqrt{3} )^{2} -(\sqrt{3}) ^{2} =(4)(3)-3=12-3[/tex]

[tex]a^{2} =9[/tex]

[tex]a=\sqrt{9}[/tex]

[tex]a=3[/tex]

Hope this helps

The purpose of the graphic is to show the relationship between different educational qualifications and unemployment rate.

This is a situation in which employable individuals look for jobs and are unable to find one.

The key findings in this graphic is that the higher the level of education, the lesser the unemployment rate.

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The distance between the skate and point X is 16 feet

Given that the distance between point X and kite is 12 feet

and the distance between stake and kite is 20 feet

We need to find the distance between the stake and point X

Here,

Perpendicular = 12 feet

Hypotenuse = 20 feet

Base = ?

According to Pythagoras Theorem

(Hypotenuse)² =  (Perpendicular)²+(Base)²

(20)² = (12)² + (Base)²

∴ (Base)² = 400 - 144

∴ (Base)² = 256

∴ Base = 16 feet

Hence the distance between the Point X and the stake is 16 feet

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Shyam travel total  [tex]10km 317m[/tex]  distance ,when he travelled  [tex]8 km 52 m[/tex]  by bus and [tex]2 km 265 m[/tex]  by car .

How to find the total distance travel by Shyam ?

Shyam travelled distance by bus [tex]=8 km 52 m[/tex]

Shyam travelled distance by car [tex]=2 km 265 m[/tex]

Total distance travelled by shyam is

Total distance= distance travelled by car + distance travelled by bus

Total distance

[tex]=2 km 265 m+8 km 52 m\\=(2+8)km(265+52)m\\=10km317m[/tex]

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The equation becomes of the pressure is   P = 90 + 10 sin(π/36(t +4 ))

By observation the sine function should be of form P=  90 + 10 sin(ω(t − c)) as it oscillates about 90 and with a factor of 10. Let time be represented by the variable t in hours from 12.00 AM.

At 2:00 P.M. that is t= 14 hours the pressure is 100 mmHg

Substituting it in the equation we get,

100 = 90 + 10 sin(ω(t − c))

10 = 10  sin(ω(14 − c))

1 = sin(ω(14 − c))

ω(14 − c) = π/2                           -1)

At 2:00 A.M. that is t= 2 hours the pressure is 80 mmHg

80 = 90 + 10 sin(ω(t − c))

-10 = 10 sin(ω(2 − c))

3π/2 = ω(2 − c)                           -2)

dividing 2) with 1) we get

3 = (14 − c) /(2 − c)  

6 - 3c = 14 - c

2c = -8

c = - 4

Substituting the value of c in 1) we get,

ω(14 − (-4)) = π/2

ω18 =  π/2

ω = π/36

Thus the equation becomes  P = 90 + 10 sin(π/36(t +4 ))

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The inverse proportionality expression is y =40/x

If the variable y is inversely proportional to x, this is expressed as;

y = k/x

where

k is the constant of proportionality

If y = 5 and x = 8. then;

5 = k/8

k = 5 * 8

k = 40

Determine the inverse proportionality

Recall that y = k/x

y = 40/x

Hence the inverse proportionality expression is y =40/x

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Answer:

27.2

Step-by-step explanation:

V = (1/2)(2.6)(5.1)(4.1), which is 27.2 to the nearest tenth

The length of the third side of the triangle is 4. 33

We have the length of the two sides to be;

2 and 5

If the angle between them is 60 degrees, then the third side is the opposite side

To find the opposite side, we use the sin ratio, which is

sin 60 = opposite/hypotenuse

sin 60 = x/ 5

Cross multiply

sin 60 × 5 = x

x = 0. 8660 × 5

x = 4. 33

Thus, the length of the third side of the triangle is 4. 33

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The shape formed, when a prism with a heart-shaped base is sliced parallel to the base, will be congruent to its base. Hence, it will also be heart-shaped.

A prism is a polyhedron made up of n parallelogram faces that connect the n-sided polygon base, the second base, which is a translated duplicate of the first base, and the n faces. The bases are translated into all cross-sections that are parallel to them.

In the question, we are informed that a prism with a heart-shaped base is sliced parallel to the base.

We are asked what shape is formed.

From the above discussion, we know that the bases are translated into all cross-sections that are parallel to them, that is, all cross-sections parallel to the base, will be congruent to the base.

Thus, the shape formed, when a prism with a heart-shaped base is sliced parallel to the base, will be congruent to its base. Hence, it will also be heart-shaped.

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Answer:

Step-by-step explanation:

Heart Shaped

Answer:

V = 15 in.³

Step-by-step explanation:

The original cylinder has radius r and height h.

V = πr²h

Its volume is 30 in.³, so

πr²h = 30 in.³

The new cylinder has radius (1/2)r and height 2h.

Its volume is

V = π(r/2)²(2h)

V = πr² × 2h/4

V = πr²h/2

πr²h is the volume of the original cylinder, and it is 30 in.³.

V = 30 in.³/2

V = 15 in.³

Deposit $625 into a money market account with a 5% rate for 1 year would result in more money.

To do this, we make use of 1.50% interest rate

Here, we have:

Initial, a= 625

Rate, r = 1.5%

The exponential growth equation is

A(t) = a * (1 + r)^t

So, we have:

A(t) = 625 * (1 + 1.5%)^t

Evaluate

A(t) = 625 * 1.015^t

Hence, the exponential growth equation is A(t) = 625 * 1.015^t

Here, t = 25.

So, we have:

A(25) = 625 * 1.015^25

Evaluate

A(25) = 906.84

Hence, the value in 25 years is $906.84

#Investment A

a = 625

r = 1.5%

t = 5

So, we have:

A(5) = 625 * 1.015^5

Evaluate

A(5) = 673.3

#Investment B

a = 625

r = 5%

t = 1

So, we have:

A(1) = 625 * 1.5^1

Evaluate

A(1) = 937.5

By comparison, 937.5 is greater than 673.3

Hence, deposit $625 into a money market account with a 5% rate for 1 year would result in more money.

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The following equation represents the function g in function notation,

g(x) = 3x - 14 [Option (A)]

Definition of a Function

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. A function, in general, represents the idealized relationship between two changing quantities.

Given equation is,

y -3x = -14

⇒ y = -14 + 3x

or y = 3x - 14

Here, y stands for or represents the function g(x) which is a function of independent variable x.

Thus, the correct function notation is as follows,

g(x) = 3x - 14

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Answer:

The volume of the cylinder is smaller than the rectangular prism.

Step-by-step explanation:

The statements that are true about the domain and range of the functions f(x), g(x), and h(x) include:

It should be noted that a function simply means a relation between a set of inputs to a set of possible outputs.

In this case, f(x) has a domain of all real numbers as well as g(x) which also has a domain of all real numbers.

In conclusion, the correct options are A and D.

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Answer:

A and D

Step-by-step explanation:

Edge 2022

The expression that represents the volume of the composite figure is: 1/3(8)(6)(6) + (8)(6)(4).

The volume for the given composite figure = volume of the rectangular pyramid + volume of rectangular prism.

= 1/3(l)(w)(h) + (l)(w)(h)

Thus, with the given dimensions, plug in the values to get the expression represents the volume of the composite figure:

Volume = 1/3(8)(6)(6) + (8)(6)(4)

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The function represents a cosine graph with axis at y = - 1, period of 6, and amplitude of 2.5.

In this question we have a sinusoidal function, of which we are supposed to find the following variables based on given picture:

Then, we have the following results:

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Answer:

I have just wrote answers

Step-by-step explanation:

what is the best definition of luminous

Answer:

(2x-5)(2x-5), 81 meters

Step-by-step explanation:

All of the sides of a square are equal, so to find the area we need to multiply 2x-5 by 2x-5: (2x-5)(2x-5)

Using this equation we can plug in 7 for x:

(2(7)-5)(2(7)-5) =

(14-5)(14-5) =

9*9 = 81

Answer:

Step-by-step explanation:

jello :

3x=2(mod4)

multiply by ; 5

5×3x=5×2(mod4)

15x=10(mod4)

but : 15= -1 (mod4)   and 10= 2 (mod4)

-x=2 (mod4)

now multiply by ; -1 you have :  x= -2 (mod4)

-2=2(mod4)

conclusion : x=2 (mod4)  means : x=4k+2   k in Z

Answer:

17

Step-by-step explanation:

x+3x+x-7=78

5x-7=78

5x=78+7

5x=85

x=85/5

x=17

Answer:

The three numbers are 17, 10 and 51.

Step-by-step explanation:

Let the first, second, and third numbers be [tex]x[/tex], [tex]y[/tex], and [tex]z[/tex] respectively.

• From the question, we know:

sum of the numbers is 78.

∴ [tex]x + y + z = 78[/tex]   ----------(1st equation)

Let's express both [tex]x[/tex] and  [tex]z[/tex] in terms of [tex]\bf y[/tex] :

• We know that:

the third number is 3 times the first.

∴ [tex]z = 3x[/tex]

⇒ [tex]x = \frac{z}{3}[/tex]     ----------(2nd equation)

• We also know that:

the first number is 7 more than the second.

∴ [tex]\boxed{x = 7 + y}[/tex]

Substituting  [tex]x = \frac{z}{3}[/tex]  (from 2nd equation)

⇒ [tex]\frac{z}{3} = 7 + y[/tex]

⇒ [tex]\boxed{z = 21 + 3y}[/tex]

• We can now substitute  [tex]x = 7 + y[/tex]  and  [tex]z = 21 + 3y[/tex]  into the first equation:

[tex]x + y + z = 78[/tex]

⇒ [tex](7 + y) + y + (21 + 3y) = 78[/tex]

⇒ [tex]5y + 28 = 78[/tex]

⇒ [tex]5y = 50[/tex]

⇒ [tex]y = \bf 10[/tex]

∴ [tex]x = 7 + 10\\[/tex]

⇒ [tex]x = \bf 17[/tex]

[tex]z = 21 + 3(10)[/tex]

⇒ [tex]z = \bf 51[/tex]

∴ The three numbers are 17, 10 and 51.

The coefficients for the polynomial with degree 3, roots: x = 2, x =

-1, and x = 3, and with a leading coefficient of 1 is given as -4 and 6. Hence, the polynomial turns out as x³ + (-4)x² + x + 6.

It is given that the polynomial is of degree 3 and its roots are,

x = 2

x = -1

x = 3

Thus, the factors of the polynomial would be,

(x - 2), (x + 1), and (x - 3)

The polynomial an be written in terms of its factors, with a leading coefficient of 1, as follows,

(x - 2)(x + 1)(x - 3)

= (x² -2x + x -2)(x - 3)

= (x² -x -2)(x - 3)

= x³ - 3x² - x² + 3x - 2x + 6

= x³ - 4x² + x + 6

= x³ + (-4)x² + x + 6

Hence, the required coefficients of the polynomial are, (-4) and 6.

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Answer: 36

Step-by-step explanation:

If 5/6 = 180

lets find what 1/6 equals

To do this lets divide 180 by 5 to find 1/6

[tex]\frac{180}{5} =36[/tex]

Therefore, 1/6 = 36

We know 180/5 will give us the answer because 180 is already 5/6 of the total; dividing by 5 will give us 1/6 of the total. Ex: if we had 4/6 of the total, we would divide by 4 to find 1/6.

Anyways, we can check our answer by doing:

36*5 = 216 then taking 5/6 of 216, which should equal 180

[tex]216*\frac{5}{6} =180[/tex]

Therefore, we know 36 is the correct answer