Completed in 1863 , the dome is one of the most recent additions to the United States Capitol. It is supported by 36 iron ribs and has 108 windows, divided equally among three levels.
a. Excluding the spire of the dome, how many horizontal and vertical planes of symmetry does the dome appear to have?

The sum of the polynomial is equal to -10x^3 + 2x^2 + 7x + 8.

In mathematics, polynomials refers to an algebraic equation which have more than two terms, the terms are usually same variable but the exponents tends to increase the number of terms.

An algebraic equation with the highest power as two is generally called parabolic equation/ When the power goes above two they are called polynomial.

addition of polynomials is achieved by adding like terms together. the like terms as in the question include similar alphabet and same exponents

( -4x^3 + 10x^2 + 6 ) - ( 6x^3 + 8x^2 - 7x - 2 )

terms with x^3: -4 - 6 = -10

terms with x^2: 10 - 8 = 2

terms with x:  0 - ( - 7 ) = 0 + 7 = 7

constant terms : 6 - ( - 2 ) = 6 + 2 = 8

constant terms refers to terms that does not have x

writing the equation together with their terms gives -10x^3 + 2x^2 + 7x + 8. Hence we can conclude that addition of polynomials involves addition performed considering the terms by adding like term.

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Answer:

please upload a picture of your question

the length of the stringer for the staircase of 6 steps is 199.74 cm.

The sum of the squares of the two sides (a and b) equals to the square of the hypotenuse (c). In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.

According to the question,

Each step is 28 cm long that is the length of one step of the staircase. And 18 cm high which is the height of the step at 90-degree angle thus forming a right-angle triangle and the stringer acts as a hypotenuse. Therefore, we can use Pythagoras theorem to find the length of the stringer of one step.

Length=a=28 inch

Breadth=b=18 inch

Applying the Pythagoras theorem, we get

28²+18²= (length of the stringer)²

28²+18²= = 1108  

Now, √1108 = 33.29

to find the length of 6 steps multiply 33.29 with 6

33.29*6 = 199.74

Therefore, the length of the stringer for the staircase of 6 steps is 199.74 cm.

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Answer:

199.7 cm

Step-by-step explanation:

The area of the rectangle according to the given length and width is 107.58m².

The formula of the area of a rectangle: l × w

Now, substitute the values in the formula:

Therefore, the area of the rectangle is 107.58m².

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The property that justifies the following statement, if 12=2 x+8 and 2x+8=3y, then 12=3y is the transitive property.

Transitive property is one of the properties of equality which states that if there is an equality sign between two values or numbers and one of these numbers is equal to a third numerical value then the other number is also equal to that third numerical value.

Therefore this property can be described as,

if x = y and y = a, then x = a

The transitive property also justifies that if two values x and y are not equal, but y is equal to a, then x cannot be equal to a. That is if x ≠ y, but y = a, then x ≠ a.

So, according to the transitive property, the statement, If 12=2x+8 and 2x+8=3y, then 12=3y is valid.

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Answer:

159 minutes

Step-by-step explanation:

y = .11x + 3

$3 initial fee to start the scooter

$0.11 per minute

y = the total bill price of the scooter ride

x = the total minutes of the ride

plug in what we know : $20.49 for the whole ride

20.49 = 0.11x + 3

SOLVE !! 20.49 - 3 = 0.11x

17.49 = 0.11x

17.49 / 0.11 = x

x = 159 minutes

check answer if you want

20.49 = 0.11 (159) + 3

20.49 = 17.49 + 3

20.49 = 20.49

Answer: a₁=31    a₁₁=-9

Step-by-step explanation:

[tex]\displaystyle\\\left \{ {{a_4=19} \atop {a_7=7}} \right. \\\\a_n=a_1+(n-1)d\\\\\left \{ {{a_1+(4-1)d=19} \atop {a_1+(7-1)d=7}} \right. \\\\\left \{ {{a_1+3d=19\ \ \ \ (1)} \atop {a_1+6d=7\ \ \ \ \ (2)}} \right.[/tex]

Subtract equation (2) from equation (1):

[tex]3d=-12[/tex]

Divide both parts of the equation by 3:

[tex]d=-4[/tex]

Thus,

[tex]a_1+(3)(-4)=19\\a_1-12=19\\a_1-12+12=19+12\\a_1=31\\a_{11}=a_1+(11-1)d\\a_{11}=31+(10)(-4)\\a_{11}=31-40\\a_{11}=-9[/tex]

Answer:

a = 43

d = -6

[tex]\sf a_{11} = -17[/tex]

Step-by-step explanation:

Arithmetic sequence:

 Use the formula to find the nth term:

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

Here, a is the first term, n is the number of terms and d is the common difference.

[tex]\sf a_4 = 19\\\\a+(4-1)*d = 19\\\\a + 3d = 19 -------------------(i)[/tex]

        [tex]\sf a_7 = 7\\\\a + 6d = 7 ------------------(ii)\\[/tex]

Subtract equation (i) from (ii) and thus 'a' will be eliminated and we can find the value of 'd'.

     (ii)       a + 6d = 7

     (i)        a + 4d = 19

                -    -     = -    

                       2d = -12

                          d = -12/2

                          [tex]\sf \boxed{\bf d = -6}[/tex]

Now, plugin d = -6 in any of the two equations. We are substituting the 'd' value in equation (i)

  a + 4*(-6) = 19

  a - 24      = 19

               a = 19 + 24

               [tex]\sf \boxed{\bf a = 43}[/tex]

[tex]\sf a_{11} = a + 10d[/tex]

      = 43 + 10*(-6)

      = 43 - 60

[tex]\sf \boxed{\bf a_{11} = -17 }[/tex]

Step-by-step explanation:

= 16 a^6=16a divide for 16

a^6=a there are only two solutions 1 and 0 cause:

1^6=1 and 0^6=0

In the formula V = (1/3)πr²h , (A)V/3πr² is the expression equal to h.

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily

Here given that,

V= (1/3)πr²h

V/3πr² = (1/3)πr²h/3πr²         (divided both sided with 3πr²)

V/3πr² = h or h = V/3πr²

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Range - { 1 , 0, 1 , 3 , 2 } is relation is a function.

What is domain and range ?

Definitions of domain and example?

The domain is the set of x -coordinates, {0,1,2} , and the range is the set of y -coordinates, {7,8,9,10} .

function. (1,1),(2,0),(3,1),(4,3),(0,2)

Domain - { 1,2, 3 , 4 , 0 }

Range - { 1 , 0, 1 , 3 , 2 }

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explanation up top:) that's the explanation I hope you understand

The number of maximum cupcakes and cookies sold is 6 and 5 respectively.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

Alexandra sell cupcakes for 3.25 each and donuts for 1.25 each.

let x be the number of cupcakes purchased and y be the number of donuts purchased.

Now, Alexandra has 25 to spend and must buy a minimum of 11 cupcakes and donuts altogether.

So, x+ y ≥11

and, 3.25x + 1.25y ≤ 25.

Thus, x= 5.625 and y= 5.375

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Answer:

Step-by-step explanat

36=10x-4

40=10x

10x=40

x=40/10

x=4

Based on the fact that the force needed to move object is directly proportional to the weight of the objects, the force needed to move and object that is 900 pounds is 3 newtons of force.

When things are directly proportional, it means that they increase by a given amount together and also decrease by the same amount.

If 4 Newtons are needed for 1,200 pounds, the newtons needed for 1 pound is:
= 4 / 1,200

= 1/300 newtons

If there are 900 pounds to be moved, the newtons needed are:

= 1/300 x 900

= 3 newtons of force

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 The result of the evaluation of the series described by 1/2, 3/2, 5/2, . . . . . . . , 15/2 is:

∑ = 28

A series is the summation of a set of numbers or sequences.

The sigma notation is a mathematical operation used to determine the final value of the sum of "n" terms consecutively, when dealing only with numbers without variables this is known as an arithmetic series.

The equation for this type of problem is:

∑ = n(a1 + an)/2

 Our values are:

1/2, 3/2, 5/2, . . . . . . , 15/2

∑ = 7(1/2 + 15/2)/2

∑ = 7(8)/2

∑ = 28

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The required difference in the size between the two garden is 20x. Option A is correct.

Given that,
Sonya has two rectangular gardens. The larger garden is four times as wide and five times as long as the smaller one. If the area of the smaller one is x, what is the difference in size between the two gardens is to be determined.

The rectangle is 4 sided geometric shape whose opposites sides are equal in length and all angles are about 90°.

Here,
length and width of the small rectangular garden is l and b
Let the are of the small garden be x = lw
Now according to the question
Length of the larger garden = 5l
And the width of the larger garden = 4w
Now the area of the larger garden = 5l * 4w
                                                          = 20lw
                                                          = 20x

Thus, the required difference in the size between the two gardens is 20x. Option A is correct.

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The equation to represent the number of people that can attend the event will be 18500 +/- 1200.

Based on the information, equation to represent the number of people that can attend the event will be 18500 +/- 1200.

The maximum number will be:

= 18500 + 1200

= 19700

The minimum number will be:

= 18500 - 1200

= 17300

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The Conjecture is : "the sum of the measures of the interior angles of a triangle is 180° ".

The interior angle of any triangle is defined as the angle which is inside the triangle. In the other words if the triangle has the point within the angle it is in the interior of the angle. A triangle has three internal angles. The interior angles are always less than 180.

According to triangle Angle Sum theorem, the measurement of the sum of all interior angles of a triangle is always equals to 180°. That means, For a given triangle say ΔABC if ∠A, ∠B and ∠C are the interior angles then their sum i.e. ∠A + ∠B + ∠C = 180°.

Thus according to this we can make the conjecture about the sum of measures of the interior angles of a triangle.

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The required estimate of the destination on the map is 800,000 kilometers.

Given that,
The scale on a map is stated as 1: 100 000 on the map, Jennifer estimates that the distance to her destination is 8 cm. If she is correct in her estimate, how many kilometers is it to her destination is to be determined.

The scale factor is defined as the ratio of modified change in length to the original length.

Here,
1 cm = 100, 000 km
Multiply both sides by 8
8cm = 800,000 kilometers.

Thus, the required estimate of the destination on the map is 800,000 kilometers.

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Answer:

5x-4

Step-by-step explanation:

Product of a number, x , and 5  = 5x

   subtract 4      5x -4

Answer:

98.5%

Step-by-step explanation:

1000 cubic centimeters = 1 litre

(3 decimal spaces to the left)

985 cubic centimeters = .985 liters (almost 1 litre)

.985 = 98.5% (2 decimal spaces to the right)

Answer:

-0.625

Step-by-step explanation:

A fraction is the numerator (top) divided by the denominator (bottom).  In this case it is -5 divided by 8.  Put that into a calculator and you will get -0.625.

Answer:

49/2 or 24 1/2

Step-by-step explanation:

Divide both sides by 2 to get x by itself.

Answer:

x = 7

Step-by-step explanation:

➟ x² = 49

in order to find the value of x will have to take square root of both side

➟ [tex] \sf \sqrt{x} = \sqrt{49} [/tex]

Calculate

➟ [tex] \sf \: x = 7[/tex]

The expression 7m+3n best represents a simpler form of 4m+3(m+n).

The Simplified Algebraic Expression is defined as the expression that do not have any like terms and also it cannot be simplified further.

For Example : 2x+5y+6x , the simplified form will be 8x+5y as it cannot be simplified further.

In the given question,

=4m+3(m+n)

=4m+3m+3n    ...(multiplying 3 with m and n)

Now Combining the like terms ,

We get ;

=7m+3n

Therefore , the expression that best represents a simpler form of 4m+3(m+n)  is 7m+3n.

The correct option is (A) 7m+3n.

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The correct location of the system of equations are;

Single solution;

y = 11 - 2•x

4•x - y = 7

x + y = 15

2•x - y = 15

No solution;

2•x + y = 7

-4•x = 2•y + 14

x = 12 - 3•y

3•x + 9•y = 24

Infinite solution;

2•x + y = 7

-6•x = 3•y - 21

The possible system of equations and their solution are presented as follows;

System of equations

Solution;

4•x - y = 7

Therefore;

11 - 2•x = 4•x - 7

6•x = 18

x = 3; Single solution;

System of equations

Solution;

2•x + y = 7 gives;

y = 7 -2•x

-4•x = 2•y + 14 gives;

y = -2•x - 7

7 -2•x = -2•x - 7

0 = 14, no solution

System of equations

Solution;

x = 12 - 3•y gives;

3•x + 9•y = 24 gives;

x = (24 - 9•y) ÷ 3 = 8 - 3•y

Which gives;

12 - 3•y = 8 - 3•y

System of equations

Solution;

2•x + y = 7 gives;

y = 7 - 2•x

-6•x = 3•y - 21 gives;

3•y = 21 - 6•x

y = 7 - 2•x

7 - 2•x = 7 - 2•x Infinitely many solutions

System of equations

Solution;

x + y = 15 gives;

y = 15 - x

2•x - y = 15 gives;

y = 2•x - 15

Which gives;

15 - x = 2•x - 15

3•x = 15 + 15 = 30

x = 30 ÷ 3 = 10 Single solution

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The solution to the functional notations would be either yes or no if the function on the left hand side and right hand side are the same. Hence we would have:

c. No:   f ( x )   ≠    f ( -x )

d. Yes:   ( - x )  = - f ( x )

Function notation is way of writing functions so that they can easily be understood in the mathematical sense. This method is applied in the question to help read the meaning in the question without much explanations.

Given data

f ( x )  =  x^3

f ( -x )  =  - x^3

c. No   f ( x )   ≠    f ( -x )

f ( x )  =  x^3   and f ( -x )  =  - x^3

f ( x ) is not equal to f ( -x )

plugging the values for the left hand side of the equation gives

x^3

and plugging the values for the right hand side of the equation gives

- x^3

since the left hand side of the equation is not equal to the right hand side of the equation it means that the both sides of the equation are not equal hence equation sated in c is not correct

f ( x )  ≠    f ( -x )  ( take note of the sign )

d. Yes   ( - x )  = - f ( x )

( - x ) is equal to - f ( x )

This represents odd functions where the negative sign persists at the left hand side and the right hand side of the equation. Odd function do appear for functions which have negative signs and have odd exponents  too.

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ok so the answer is

i might be wrong but

6+7+8+9 = 30

so 9

All the three equations represent the same function as they equal x² + 6x - 16.

It should be noted that the function that Corey wrote is:

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

y = x² - 2x + 8x - 16

y = x² + 6x - 16

Kimberly wrote y = x² + 6x - 16

Joshua wrote (x + 3)² - 25

= (x + 3)(x + 3) - 25

= x² + 3x + 3x + 9 - 25

= x² + 6x - 16

In conclusion, the three equations represent the same function as they equal x² + 6x - 16.

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Step-by-step explanation:

Let's denote the length of the rectangle to be L and the width to be W.

The first sentence tells us that the length, L, is "4 less than twice the width". "4 less than" implies we subtract 4 from some quantity. What is that quantity? Well that's "twice the width." We can rewrite this sentence in terms of L and W as: L = 2W - 4.

Now we know the length of the rectangle in terms of the width.

The area of a rectangle is given by A = L x W. Using this equation, we can substitute our values for area and length:

A = L x W

96 = (2W - 4) x W

From this we can solve for W and subsequently solve for L using algebra:

96 = (2W - 4) x W

96 = 2W^2 -4W

96 = 2(W^2 - 2W)

48 = W^2 - 2W

W^2 - 2W - 48 = 0

(W - 8)(W + 6) = 0

W = 8 or W = -6

Since W is the side-length of a rectangle, we can disregard the negative solution. Therefore W = 8 ft.

If W = 8, then L = 2W - 4 = 2(8) - 4 = 12 ft.

Lastly, we know the Perimeter of a rectangle is given as P = 2L + 2W. Substituting into this equation we solve for the perimeter:

P = 2L + 2W = 2(12) + 2(8) = 40 ft.

The width of the rectangle will be 38 inches.

Let W be the rectangle's width and L its length. The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be

Perimeter of the rectangle = 2(L + W) units

If the length of a rectangle is four less than twice its width and the perimeter is 220 inches.

L = 2W - 4

Then the equation is given as,

P = 2(L + W)

220 = 2W - 4 + W

110 = 3W - 4

3W = 114

W = 38 inches

The width of the rectangle will be 38 inches.

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