What is the relationship between the number of sides of the base of a prism and the number of lateral faces?
A . The number of sides of the base of a prism is less than the number of lateral faces. B. The number of sides of the base of a prism and the number of lateral faces is equal. C. The number of sides of the base of a prism is greater than the number of lateral faces.
C . There is no consistent relationship between the number of sides of the base of a prism and the number of lateral faces.

Answer:

b = 40 and -40

General form of Perfect square trinomial is

a

2

+

2

a

b

+

b

2

Therefore from

16

x

2

−

b

x

+

25

a

2

=

√

16

x

2

,

b

2

=

25

, then

a

=

±

4

x

,

b

=

±

5

take consideration a=4x and b=-5 (different sign), then

−

b

x

=

2

(

4

x

)

(

−

5

)

−

b

x

=

−

40

x

b

=

40

The perfect square is

(

4

x

−

5

)

2

=

16

x

2

−

40

x

+

25

.

if we consider a=4x and b=5 (same sign), then

−

b

x

=

2

(

4

x

)

(

5

)

−

b

x

=

40

x

b

=

−

40

The perfect square is

(

4

x

+

5

)

2

=

16

x

2

+

40

x

+

25

.

The first solution

(

4

x

−

5

)

2

is the best solution after comparing the expression given.

Answer:

B. Square

Step-by-step explanation:

Finding the side lengths :

Side 1

⇒ d₁ = √(-4 - 0)² + (8 - 8)²

⇒ d₁ = √16

⇒ d₁ = 4

=============================================================

Side 2

⇒ d₂ = √(-4 + 4)² + (8 - 4)²

⇒ d₂ = √16

⇒ d₂ = 4

===========================================================

Side 3

⇒ d₃ = √(-4 - 0)² + (4 - 4)²

⇒ d₃ = √16

⇒ d₃ = 4

============================================================

Side 4

⇒ d₄ = √(0 - 0)² + (8 - 4)²

⇒ d₄ = √16

⇒ d₄ = 4

As all sides of the figure are equal, and it creates 4 right angles, it is a square.

Answer:

>

Step-by-step explanation:

Cause 750 was the least they could raise

Answer:

>=

Step-by-step explanation:

>= because the teacher wants AT LEAST 750. at least meaning you can raise 750 or MORE

Answer:

198 cm^3

Step-by-step explanation:

volume = 22/7 * 3^2 * 7

volume = 22/7 * 7 * 3^2

volume = 22 * 3^2

volume = 22 * 9

volume = 198

Answer:

1150.35 ft^3

Step-by-step explanation:

4/3πr^3 is the equation to find the volume of a sphere.

we know the radius is 6.5 feet so all we have to do is input it and calculate.

please give brainliest!

hope this helps

Answer:

4/25

Step-by-step explanation:

Let's make the units the same :

2 kg = 2000 g

Now lets simplify this fraction :

Divide top and bottom by 2 until you can't :

320/2000 = 160/1000

160/1000 = 80/500

80/500 = 40/250

40/250 = 20/125

Now we divide top and bottom by 5 as 2 is not a factor of 125 :

20/125 = 4/25

This is our final answer

Hope this helped and brainliest please

Answer:

[tex]y=\frac{1}{2} x[/tex]

Step-by-step explanation:

The equation of a line through two points can usually (except when the line is a vertical line) be written in slope intercept form,  [tex]y=mx+b[/tex] , where "m" is the slope of the line, and "b" is the y-intercept of the line.

To find "m", use the formula for slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\dfrac{(3)-(-2)}{(6)-(-4)}[/tex]

[tex]m=\dfrac{3+2}{6+4}[/tex]

[tex]m=\dfrac{5}{10}[/tex]

[tex]m=\dfrac{1}{2}[/tex]

So, the slope is 1/2 and we know that the equation for the line that passes through these two points should look like: [tex]y=\frac{1}{2} x+b[/tex]

To find "b", substitute one of the known points, and solve for "b":

[tex]y=\frac{1}{2} x+b[/tex]

[tex](3)=\frac{1}{2} (6)+b[/tex]

[tex]3=3+b[/tex]

Subtracting 3 from both sides to isolate the "b"...

[tex](3)-3=(3+b)-3[/tex]

[tex]0=b[/tex]

So, the y-intercept is 0.  Substituting into our line equation, [tex]y=\frac{1}{2} x+(0)[/tex] which simplifies to [tex]y=\frac{1}{2} x[/tex]  

Answer:

A. (AAA)

Step-by-step explanation:

.....(AAA) "does not work because it can produce similar but not congruent triangles"

.....(AAS) "If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent."

.....(ASA)"triangles are congruent if any two angles and their included side are equal in the triangles."

Hope This Helped

Answer:

50.27

Step-by-step explanation:

area for a circle is (pie)r^2

r^2=16

16xpie=50.27

The value of "x" and "y".

Let's solve "x" first.

Given is a supplementary angle so it should add up to 180°

[tex]x=180-123[/tex]

[tex]\large\boxed{x=57°}[/tex]

Now, we can solve "y"

Given is an isosceles triangle so the opposite sides will be equal.

[tex]57+57[/tex]

[tex]114°[/tex]

Angle sum of triangle is 180° so, it should add up to 180°

[tex]y=180-114[/tex]

[tex]\large\boxed{y=66°}[/tex]

Therefore, the correct answer is option C

Step-by-step explanation:

v = Victor's age

m = Maria's age

v = 3m

v - 10 = 7(m - 10)

3m - 10 = 7m - 70

60 = 4m

m = 15

v = 3m = 3×15 = 45

Victor is 45 years old. Maria is 15 years old.

Answer:

The slope of the line is:  

              [tex]-\frac{3}{4}[/tex]

Slope of a parallel line is the same:

             [tex]-\frac{3}{4}[/tex]

Slope of a perpendicular line, invert the sign and fraction:

              [tex]\frac{4}{3}[/tex]

Hope this helps

The correct function that matches the data in the graph is  a(n) = 46-(n-1)-4 (option C)

The only way is to verify the function matches the data by replacing n.

For example, we know at 5 seconds the temperature is 30. Let's use 5 (n) to verify the function.

This option matches the value of the temperature.

Learn more about function in: https://brainly.com/question/12431044

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Answer:

h = -5

Step-by-step explanation:

1) Subtract 7th from both sides

6h = 7h + 5

6h - 7h= 7h + 5 - 7h

2) Simplify

- Combine like terms

6h - 7h = 7h + 5 - 7h

-h = 7h + 5 - 7h

- Combine like terms

-h = 7h + 5 - 7h

-h = 5

3) Divide both sides by the same factor

-h = 5

-h/-1 = 5/-1

4) Simplify

Cancel terms that are in both the numerator and denominator

h/-1 = 5/-1

h = 5/-1

Divide the numbers

h = 5/-1

h = -5

Answer:

The answer is H=-5

Step-by-step explanation:

Using translation concepts, it is found that function g(x) is given by:

g(x) = x + 8.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, function g(x) is a translation 8 units left of f(x) = x, hence x -> x + 8 and:

g(x) = f(x +8) = x + 8.

More can be learned about translation concepts at https://brainly.com/question/4521517

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Answer:

42.25π m²

Step-by-step explanation:

Let's solve!

⇒ Take the radius of the lawn to be 'r'

===========================================================

Then, area of the path equals :

⇒ Area of (lawn + path) - Area of lawn

⇒ π (r + 2)² - πr² = 30π

⇒ πr² - πr² + 4πr + 4π = 30π

⇒ 4πr = 26π

⇒ r = 6.5 m

===========================================================

Area of the lawn :

⇒ Area = πr²

⇒ Area = π × (6.5)²

⇒ Area = 42.25π m²

The probability of all heads, all tails, exactly two tails, exactly one head will be 1/8, 1/8, 3/8, and 3/8 respectively.

The complete question is given below.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

Then the total number of the event will be

Total event = 2³

Total event = 8 {HHH, HHT, HTH, THH, HTT, THT, HHT, TTT}

Then the probability of all heads will be

⇒ 1/8

Then the probability of all tails will be

⇒ 1/8

Then the probability of exactly two tails will be

⇒ 3/8

Then the probability of exactly one head will be

⇒ 3/8

More about the probability link is given below.

https://brainly.com/question/795909

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Answer:

let n be the number then the sum of this number and 7 is n +7 and 3 times this sum is 3(n +7) 5 times the number less thirteen is 5n − 13

Step-by-step explanation:

Answer:

3 1/2 or said as 3.5 cups is equal to 1 pound

Step-by-step explanation:

1 Pound brown sugar is equivalent to ___3 1/2 or 3.5 __ cups

Hope This Helped

Answer:

1 and 4

Step-by-step explanation:

(x²+1)(x²-4)  = x^4 -3x²-4

The green blank is 1 and the blue/purple is 4.

Hope this helped and brainliest please

Here the set given is

So the set should be

The set elements are

{..,1,2,3}

Answer:

{ ..., 0, 1, 2, 3}

Step-by-step explanation:

Set notation is used in math to list numbers, objects or outcomes.

It uses curly brackets called "braces". Objects placed within the braces are the elements of the set.

Given set notation:   { x | x ∈ I, x ≤ 3 }

The ∈ symbol means "is an element of".

Therefore, x ∈ I means that x is an element of the set of integers. (Integers are whole numbers that can be positive, negative, or zero).

The ≤ symbol means "less than or equal to".

Therefore, x ≤ 3 means that x is less than or equal to 3.

Therefore, the given set notation means:

x is an element of the set of integers less than or equal to 3

The listing method of set notation simply lists the numbers in the set.

The three dots "..." means it is infinite (goes on forever).

Therefore:

{ x | x ∈ I, x ≤ 3 } = { ..., 0, 1, 2, 3}

Multiplication is the process of multiplying. Jay lost 30 pounds in a period of 6 months.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

A.) The newly recorded temperature in January will be six times the temperature in February, therefore, we can write,

January = 6 × February = 6×(-3°F) = -18°F

Hence, the newly recorded temperature in January will be equal to -18°F.

B.) Change in water level on each day of the drought was equal to -4 inches, while the drought lasted for 1 week(7days), Thus, the net change in water level can be written as,

net change = 7 × -4 = -28inches

Hence, the net change in the water level during the drought was equal to -28 inches.

C.) Jay went on a diet for six months and lost 5 pounds each month, therefore, the net change in the weight will be equal to,

Net Change = 6 × 5 = 30 pounds

Hence, Jay lost 30 pounds in a period of 6 months.

Learn more about Multiplication:

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Answer:

C

Step-by-step explanation:

equate d to 4 and solve for t , that is

- 9x² + 40 = 4 ( subtract 40 from both sides )

- 9x² = - 36 ( divide both sides by - 9 )

x² = 4 ( take square root of both sides )

x = [tex]\sqrt{4}[/tex] = 2

It takes 2 seconds for the skateboarder to be 4m from bottom of hill

Step-by-step explanation:

y + 4 = -4(x - 2) = -4x + 8

y - 4 = -4x

-4x - y = -4

4x + y = 4

Answer:one pen = $1.50

Step-by-step explanation:

See picture for the math if that helps

Using p for pens, h for highlighter,

A for first equation

B for second equation

I used equation A to reduce to a usable substitute by dividing all by 3

And then isolating “h”.

Now substitute the value of “h” into equation B and solve for “p”

P=$1.50

To check your work, substitute p ($1.50) into equation B and solve for “h”

h=$4.00

Now substitute the p and h values into either equation A or B and solve, they equal the numbers given

Answer: move up or add 7 in positive direction

Answer:

A , C , E , F

Step-by-step explanation:

If you have to write the solution, just tell me.

Answer:

see explanation

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k )² = r²

where (h, k ) are the coordinates of the centre and r is the radius

given

x² + y² - 8x + 8y + 23 = 0

collect the x and y terms together and subtract 23 from both sides

x² - 8x + y² + 8y = - 23

using the method of completing the square

add ( half the coefficient of the x / y terms )² to both sides

x² + 2(- 4)x + 16 + y² + 2(4)y + 16 = - 23 + 16 + 16

(x - 4)² + (y + 4)² = 9 ← in standard form

with centre = (4, - 4 ) and r = [tex]\sqrt{9}[/tex] = 3

this is shown in graph b