Michael is building a skateboard ramp He cannot decide how long the ramp should be so he draws the blueprint below. Michael draws a vertical line in the big triangle AAGH to form the AABC Michael determines the slope of both triangles to find out which ramp will be steeper​

Answer: x = 5

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

7 − 8(x − 3) = x − 14

7 + (−8)(x) + (−8)(−3) = x + − 14 (Distribute)

7+ (−8x) + 24 = x + (−14)

(−8x) + (7+24) = x − 14 (Combine Like Terms)

−8x + 31 = x − 14

−8x + 31 = x − 14

Step 2: Subtract x from both sides.

−8x + 31 − x = x − 14 − x

−9x + 31 = −14

Step 3: Subtract 31 from both sides.

−9x + 31 − 31 = −14 − 31

−9x = −45

Step 4: Divide both sides by -9.

−9x/−9 = −45/−9

x = 5

The exact length of the given curve is 62/3

We can calculate the above answer by following the steps given below,

We have been given the following values,

x = 1/3 √y (y - 3), 4 ≤ y ≤ 16

The curve is of the length, x = f(y) from y =a to y = b is given by:

x = 1/3 √y (y - 3)

x = 1/3 (- 3)

dx/dy = 1/3 [(3/2)- (3/2)]

= 1/3 [(3/2) - (3/2)]

= 1/2 [ - 1/]

= (y-1)/2√y = f'(y)

Now we will calculate the length of the curve

= [tex]\int\limits^a_b {\sqrt{1+f'(y)^{2} } } \, dy[/tex]

= [tex]\int\limits^a_b{\sqrt{1+ (\frac{y-1}{2\sqrt{y} } )^2} } \, dy[/tex]  (here a= 4, b=16)

= [tex]\int\limits^{16} _4 {\sqrt{1+ (\frac{y^2+2y-1}{4y} } )^} } \, dy[/tex]

= [tex]\int\limits^{16} _4 {\sqrt{\frac{4y+ y^2+ 2y-1}{4y} } } \, dy[/tex]

= [tex]\int\limits^{16}_4 {\frac{y+1}{2\sqrt{y} } } \, dy[/tex]

= [tex]\int\limits^{16}_4 {\frac{1}{2}\sqrt{y} } \, dy+ \int\limits^{16}_4 {\frac{1}{2\sqrt{y} } } \, dy[/tex]

= [1/3 (64-8)] +[4-2]

= (56/3)+2

= 62/3

Therefore the exact length of the curve that we get after solving the equation for curve is x = 1/3, 4 ≤ y ≤ 16, is 62/3.

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Answer:

The circumference of the wheel is 2 * pi * r = 2 * 3.14 * 225 mm = 1413.8 mm.

The number of arcs between each spoke is 25 - 1 = 24.

So, the arc length between each spoke is the circumference of the wheel divided by the number of arcs, which is 1413.8 mm / 24 = 58.91 mm.

Answer:I don’t onos

Step-by-step explanation:I don’t know

The statement and reasons are

The complete question is added as an attachment

With the given information and the image attached below, we can state that the two triangles are congruent by SAS,

Then go ahead to use the CPCTC to show that any of their corresponding parts are congruent as well.

Part of the proof is as follows:

Statement Reason

1. AB ≅ BC, AE ≅ FC 1. Given

2. AC ≅ AC 2. Reflexive property of congruence

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Mary and Jane have multiple ways to choose their subset of figurines for the comic book convention.

We know that Mary must include every figurine that Jane brings, so Mary must choose a subset of her collection that is at least x+1 figurines.

Since Mary must also choose at least one additional figurine, the total number of figurines that Mary can choose from is n-(x+1) + 1 = n-x

The total number of ways that Mary and Jane can choose their subsets is the product of the number of ways each can choose their subsets.

So, the number of ways is

(choose x out of n) * (choose x+1 out of n)

This is also known as binomial coefficient, which can be represented as nCx or (n x)

Hence the number of ways is

nCx * (n-(x))C(x+1)

Mary and Jane have multiple ways to choose.

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Answer:

4) 100

5) 120

Step-by-step explanation:

4) Number of sides in the polygon = n = 6

Sum of all the angles of n-sided polygon = (n -2)* 180

                                                                    = (6 - 2) *180

                                                                    = 4 * 180

                                                                    = 720

x + x + 9 + 90 + 120 +156 + 145 = 720

Combine like terms,

                             2x + 520  = 720

Subtract 520 from both sides,

                                           2x = 720 - 520

                                           2x = 200

Divide both sides by 2,

                                             x = 200÷2

                                             [tex]\sf \boxed{x = 100^\circ}[/tex]

5)    Sum of all the angles of 5 sided polygon = ( 5 - 2)*180

                                                                           = 3 * 180

                                                                            = 540

    x + x + x + x + 60 = 540

                    4x + 60 = 540

                            4x = 540 - 60

                             4x = 480

                               x = 480 ÷ 4

                               [tex]\sf \boxed{x = 120^\circ}[/tex]

Answer:

4.) You need 720 degrees sum for 6 sided polygon.

5.) You need 540 degrees for a 5 sided polygon.

Step-by-step explanation:

4.) -

120 + 156 + 145 + 90= 511

720 - 511 = 209.

209 - 9 = 200

200 / 2 = 100

X is equivalent to 100 Degrees

-

5.) -

Since X is the same for all sides we'll take 60 from 540 = 480

480 / 4 = 120

X = 120

For the given system of equations −x+4y = 8 & 2x+3y = −5

he proceed to the solution in following way,

Step 1:   Inv. of [tex]\left[\begin{array}{ccc}-1&4&\\2&3&\\&\end{array}\right][/tex] × [tex]\left[\begin{array}{ccc}8\\-5\\\end{array}\right][/tex]

Step 2:  -1/11 [tex]\left[\begin{array}{ccc}3&-4&\\-2&-1&\\\end{array}\right][/tex]

Step 3:  -1/11 [tex]\left[\begin{array}{ccc}-44\\11\\\end{array}\right][/tex]

Step 4:  [tex]\left[\begin{array}{ccc}-4\\1\\\end{array}\right][/tex]

Inverse matrix is a type of matrix which we get by taking the transpose of an adjoint matrix.

P⁻¹ = adj(P)/ |P|

|P| = Determinant of P

Property of inverse matrix,

P⁻¹×P = I

Given that,

system of equations

−x+4y = 8 & 2x+3y = −5

He multiplies the left side of the coefficient matrix by the inverse matrix

 Inv. of [tex]\left[\begin{array}{ccc}-1&4&\\2&3&\\&\end{array}\right][/tex]× [tex]\left[\begin{array}{ccc}-1&4&\\2&3&\\&\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right][/tex] = Inv. of [tex]\left[\begin{array}{ccc}-1&4&\\2&3&\\&\end{array}\right][/tex]× [tex]\left[\begin{array}{ccc}8\\-5\\\end{array}\right][/tex]

By using property of inverse matrix

[tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right][/tex] =  -1/11 [tex]\left[\begin{array}{ccc}3&-4&\\-2&-1&\\\end{array}\right][/tex]× [tex]\left[\begin{array}{ccc}8\\-5\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right][/tex] =   -1/11 [tex]\left[\begin{array}{ccc}-44\\11\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right][/tex] =   [tex]\left[\begin{array}{ccc}-4\\1\\\end{array}\right][/tex]

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Answer:

3(1-3x)

Step-by-step explanation:

factor out 3 from the expression

The equation to find the number of leaves which Aidan has now, n is given by 8 × 12 - 7 = n.

In Mathematics, an equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.

Next, we would write the equation that gives n, the number of leaves Aidan would have after collecting leaves for an art project as follows:

The number of leaves that Aidan collected from 8 different trees is equal to 8 leaves. Additionally, Aidan picks 12 leaves from each tree to have a total of 96;

n = 8 × 12 = 96.

Lastly, Aidan lost 7 leaves on his way home. Therefore, we would subtract 7 leaves from the total number of leaves that Aidan collected from 8 different trees;

n = 96 - 7 = 89 leaves.

In conclusion, the complete equation is represented by 8 × 12 - 7 = n.

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The number of each type of tickets which August sold is equal to: B. 20 students and 15 adults.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of adult tickets sold and number of student tickets sold, and then translate the word problem into an algebraic equation as follows:

Since Adults pay $7 a ticket while students pay $5 a ticket for a total cost of $205, an algebraic equation to model is given by;

7a + 5s = 205

For the sales of 35 tickets, we have:

a + s = 35      

Solving for a, we have the following:

7a + 5(35 - a) = 205

7a + 175 - 5a = 205

2a = 205 - 175

2a = 30

a = 30/2

a = 15 adult tickets.

For the number of student tickets, we have:

s = 35 - a

s = 35 - 15

s = 20 student tickets.

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Complete Question:

August is selling tickets for his school play.

-Adults pay $7 a ticket while students pay $5 a ticket.

-August sells 35 tickets and collects $205.

How many of each type of tickets did he sell?

A. 40 students and 32 adults

B. 20 students and 15 adults

C. 4 students and 5 adults

D. 15 students and 20 adults

For solving the equation we are using

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.

The equation is 2x = 13 - 5

here by subtracting 5 from 13 we get 8

so 2x = 8

or x = 4 (proved)

for solving the equation we are using

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Answer:

m is equal to [tex]34\sqrt{2}[/tex]

Step-by-step explanation:

We can use the cosine function to evaluate m.

Note that [tex]m[/tex] is the hypotenuse in this triangle.

[tex]cos(x)=\frac{A}{H}[/tex]

[tex]A[/tex] is the adjacent side

[tex]H[/tex] is the hypotenuse

Lets look at the 60 degree angle.

The side adjacent to it is [tex]17\sqrt{2}[/tex].

Therefore we can say that

[tex]cos(60)=\frac{17\sqrt{2} }{H}[/tex]

Lets solve for [tex]H[/tex].

[tex]cos(60)[/tex] is equal to [tex]\frac{1}{2}[/tex].

[tex]\frac{1}{2} =\frac{17\sqrt{2} }{H}[/tex]

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

[tex]1*H=17\sqrt{2}*2\\H=17\sqrt{2}*2\\H=34\sqrt{2}[/tex]

A protractor is used to measure angles in degrees (°). With the aid of a protractor, one may measure and calculate angles in terms of degrees.

Through the use of a protractor, angles are measured in degrees (°). In order to calculate or draw angles in terms of degrees, a protractor is a measuring tool that is utilised. Using a protractor, for instance, we can observe that the black arrow in the image below crosses the 90° line at 100°. Thus, the angle has a 100° measurement.

Generally speaking, supplementary angles are those where the total of two angles is greater than 180 degrees. A supplement to another angle is stated to exist for each of the angles. By deducting an angle's complement from 180 degrees, we can calculate its value.

A 113 degree angle's complement is a 67 degree angle.

Therefore, the answer is 67 degree.

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Answer:

Below

Step-by-step explanation:

96 heads out of 200 flips

96/200 = 48 %

Answer: 48%

Step-by-step explanation: 96 is 48% of 200, therefore the probability of landing on heads is 48%.

If you cannot vote, then you are under 18. If the next month is not March, then this month is not February. If you cannot afford a new laptop computer, then you do not have $400.

What is Inverse, Converse and Contrapositive Statement?

Inverse Statement: The inverse statement, denoted pq, assumes the inverse of each of the original statements (if not p, then not q).

Converse Statement: The converse statement is notated as q→p (if q, then p).In the original "if-then" statement, the original statements trade places.

Contrapositive Statement: The conditional statement's inverse is "If not Q, then not P."

1) The inverse statement would be,

If you cannot vote, then you are under 18.

2) The converse statement would be,

If the next month is not March, then this month is not February.

3)The Contrapositive statement would be,

If you cannot afford a new laptop computer, then you do not have $400.

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The solution is x minus 2 divided by 6 open parentheses x + 12 close parentheses.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The product of 8 and 3 equals 11. 8 + 3 is an expression.

Here,

=quantity x squared minus 100 over quantity x squared plus 2 x minus 120 divided quantity 6 x plus 60 over quantity x minus 2

=((x²-100)/(x²+2x-120))/((6x+60)/(x-2))

Let's simplify some of the factors:

x² - 100 = x² - 10²

= (x - 10)(x + 10)            

6x + 60 = 6 * x + 6 * 10

= 6 * (x+10)

x² + 2x - 120 =  x² + 12x - 10x - 12 * 10

= (x * x - 10 * x) + (12 * x - 12 * 10)

= x(x - 10) + 12(x - 10)

= (x - 10)(x + 12)

The solution is amount x minus 2 over 6 open parentheses x + 12 close parentheses.

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Step-by-step explanation:

last week = 15

this week 2o%

therefore =. last WK + this WK = 15×20÷100/1

= 300÷100/1=. 3

Diana scored 3point this week

The value of x for the given expression -2(4x+5.5) = 3/4x +27.6+5/4x is, 3.86

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given expression,

-2(4x+5.5) = 3/4x +27.6+5/4x

-8x -11  =  3/4x + 27.6 + 5/4x

-8x-2x = 27.6 + 11

-10x =  38.6

x  = -3.86

Hence, the value of x is -3.86

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So on solving the provided question, we can say that by unitary method saving = 25 - 7.3333333336 = $17.6666666664

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

by unitary method,

12 pack of can, costs = $2

cost of 3 12 pack can - $2 *3 = $6

12 pack can = 12 days

1 can = $2/12 = $0.1666666667

8 can = $0.1666666667*8 = $1.3333333336

original cost of 1 can = $1.25

ordinal cost of 20 cans = $1.25*20 = 25

sale cost of 20 cans = $1.3333333336 +  $6 = 7.3333333336

saving = 25 - 7.3333333336 = $17.6666666664

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Answer: 5-5x

Step-by-step explanation:

Answer: yes

Step-by-step explanation: a square is always a rectangle but a rectangle is only a square when all sides are equal

Answer:

Absolutely!

Step-by-step explanation:

Since a square has 4 right angles, it can also be classified as a rectangle.

Answer:

Step-by-step explanation:

Well as the chair of the fed i would need to mandate things to help have maximum employment fair stable prices and to help moderate long term interest rates. The monetary role im going to take is commodity based money.

let x = the number of 2-point baskets Anya made

y = the number of 3-point baskets Anya made

Equations:

x + y = 14

2x + 3y =

Multiply the 1st equation by 3 to get:

3x + 3y = 42

Subtract above equation by 2nd equation to get:

(3x-2x) + (3y - 3y) = 42 -30

x = 12

Anya made 12 2-point baskets.

Answer:  The ocean liner is approximately 5.2 miles from the fishing boat.

The teaspoons of strawberry syrup you would need if you used up all the milk is 6. 75 teaspoons

The question shows that the strawberry syrup recipe uses 3 teaspoons of strawberry syrup for every 8 ounces of milk.

Given that there are 18 ounces of milk left in the container, the number of teaspoons needed would be:

= ( Number of ounces left x teaspoons used ) / 8 ounces

= ( 18 x 3 ) / 8

= 6. 75 teaspoons

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The first part of question is:

A strawberry syrup recipe uses 3 teaspoons of strawberry syrup for every 8 ounces of milk.

No. of players and reporters in stadium = 275

No. of spectators and stadium workers in stadium = 42225

Seating Arrangement is a process of making a group of people sit as per a prefixed manner.

Given,

Stadium capacity = 42500

General capacity seating = 31750

Reserved Seating = 10475

Total spectator seating  = 31750 + 10475

                                        = 42225

No. of players, radio and newspaper reporters = 42500 - 42225

                                                                              = 275

There could be 275 players, news and radio reporters and 42225 spectators in addition to stadium workers, at the game.

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The volume of the baseball to the nearest cubic inch is 9 cubic inches.

A sphere is a three dimensional figure which consists of set of all the points which are at an equal distance from a point called the center of the sphere.

Volume is the space occupied by a three dimensional object.

Given that,

Radius of a baseball = 1 3/10 inches = (1 × 10 + 3) / 10 = 13/10 inches.

Also we know that,

Volume of a sphere = 4/3 π r³, where r is the radius.

Volume of the baseball = 4/3 π (13/10)³

                                       = 4/3 π (1.3)³

                                       = 4/3 π × 2.197

                                       = 2.9293 π

                                       = 2.9293 × 3.14

                                       = 9.198 cubic inches.

                                       ≈ 9 inches³

Hence the volume of the baseball is 9 cubic inches.

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If shelby is attending a school orchestra concert.   The two teacher are far apart by 35ft.

Using Pythagoreans theorem  formula to find the length

c² = √ a² -b²

Where:

c = Length of the hypotenuse

a = 45

b= 28

Let plug in the formula

c² = √45² - 28²

c² = √2025 -784

c² = √1241

c = 35ft

Therefore we can conclude that the two teacher are far apart by 35ft.

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Explanation:

The shorter side lengths 3 and 3 add to 3+3 = 6, which is not larger than the remaining side 9. This is why a triangle is not possible.

For a triangle to be possible, we need the sum of any two sides to be larger than the third side. Refer to the triangle inequality theorem.

I recommend making slips of paper that are 3 inches, 3 inches, and 9 inches long (or replace "inches" with "centimeters"). Then try to make a triangle with those slips of paper. You should find such a task is impossible: as mentioned, the 3 inch sides come up short when trying to attach to the 9 inch side.

The statement "It's not possible to build a triangle with side lengths of 3, 3, and 9" is true.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

A triangle cannot be formed with side lengths of 3, 3, and 9.

To form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

However, in this case, the sum of the lengths of any two sides is 3+3=6, which is less than the length of the third side, 9.

Therefore, it is not possible to form a triangle with side lengths of 3, 3, and 9.

Thus,

The statement "It's not possible to build a triangle with side lengths of 3, 3, and 9" is true.

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