The width of a 2-by-4 piece of wood is actually 3 1/2 inches. Find the total width of 30 2-by-4s laid side by side. Simplify your answer.

Answer:

121° and 59°

Step-by-step explanation:

We'll assign the two angles 'a' and 'b'. Since they are supplementary, this means they add to 180°. We can model this peoblem with the expressions:

a + b = 180° and a - b = 62°

Let's use the second equation to find a substitution for a:

a - b = 62°

a = 62° + b

Now substitute this in the first equation and solve:

(62° + b) + b = 180°

62° + 2b = 180°

2b = 118°

b = 59°

59° + 62° = 121° this is angle a

Answer:

Point form:

(2, 9)

Equation form:

x = 2,y = 9

Step-by-step explanation:

The correct option is (C) The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).

Given that the following table represents  the linear function f(x), and the equation represents the linear function g(x) :

x                   0                     2                          4

f(x)                1                      9                         17

and g(x) = 3x + 1 .........(1)

We have to compare the y-intercepts and slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.

From the graph, we note that (0, 1), (2, 9) and (4, 17) are three points on the line graph of function f(x).

We know that, the slope of any line having two points (a, b) and (c, d) on it is given by

m = d-b/c-a

So, the slope of the line of f(x) is

m = 9-1/2-0

m = 8/2

⇒ m = 4

Since the line of f(x) passes through the point (0, 1), so its equation will be

f(x) -1 = m(x-0)

⇒ f(x) -1 = 4(x-0)

⇒ f(x) -1 = 4x

⇒ f(x) = 4x+1 ........... (2)

The slope-intercept form of the equation of a line is y = mx + c, where m is the slope and c is the y-intercept of the line.

Comparing equation (2) and (1) with the slope-intercept form, we get

slope of f(x) = 4  and  y-intercept of f(x) = 1 and

slope of g(x) = 3  and  y-intercept of g(x) = 1.

Thus, the slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).

Option (C) is CORRECT.

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The correct option regarding the linear regression equation is:

No, the equation is not a good fit because the sum of the residuals is a large number.

To find the equation, we need to insert the points (x,y) in the calculator.

In possession of the equation, the residuals are given by the difference of the predicted values(with the equation) and the actual values.

The model represents a good fit if the sum of the residuals is close to 0.

For this problem, the sum of the residuals is given by:

90 - 50  - 100 - 100 + 150 - 50 = -60.

The sum is a large number, hence the model is not a good fit.

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The simplified value of the expression 1/2 / ( x² - y²) - 5/2(x² - y²) is -2/x² + 2/y²  .

Like terms in an algebraic expression is defined as those terms that have same variable and that variable has the same power .

For Example : 5y,2y are like terms .

In the given question 1/2 / ( x² - y²) - 5/2(x² - y²) the first term is a complex fraction,

[tex]=\frac{\frac{1}{2} }{(x^{2}-y^{2} ) } -\frac{5}{2(x^{2} -y^{2}) }[/tex]

Simplifying the complex fraction we get ,

= 1/2(x² -y²) -5/2(x² -y²)

= 1/(2x² - 2y²) -5/(2x² -2y²)

On further simplifying

= 1/2x² -1/2y²- 5/2x²  +5/2y²

On combining the like terms of x² and y².

= 1/2x² - 5/2x² -1/2y²  +5/2y²

taking LCM of like terms as 2x² and 2y².

=(1-5)/2x²+(-1+5)/2y²

= (-4)/2x² + 4/2y²

=-2/x² + 2/y²

Therefore , the simplified value of the expression 1/2 / ( x² - y²) - 5/2(x² - y²) is -2/x² + 2/y²  .

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The solution of the given system of equations is (1, 3)

We can solve a system of equations using:

- graphical method

- elimination method

- substitution method

The given system of equations:

y = 4 - x    ....... (1)

3x + y = 6  ....... (2)

To use elimination method, add x to both sides of equation (1)

x + y = 4 ....... (3)

Substract equation (3) from equation (2)

3x + y = 6

x + y = 4   –

2x       = 2

 x       = 1

Substitute x = 1 into equation (1)

y = 4 - x

  = 4 - 1 = 3

Thus the solution is (1,3)

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The total of Sam's liabilities are $5225.

A liability is an obligation of an individual towards his creditors arising out of some transactions. Bank loans, credit card bills, accounts payable , accrued expenses are examples of liabilities.

Given that Sam has a car that is worth $8,500. However, he still owes $4,750 on the car. He also has $1,500 in his savings account, a comic book collection worth $900 and owes $475 on his credit card.

Irrespective of his assets and savings Sam still owes $4750 on the car and $475 in his card card , therefore these are his liabilities.

Total liabilities of Sam = $4750+$475 = $5225

Therefore, total of Sam's liabilities are $5225

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marshal just stoopid.. that simple

anyway marshal divided it by 100 instead of 104, the answer of it divided by 104 is 243.547509615

On combining the like terms of the expression y²/2 + y/3 + y²/3 - y/5 the simplified value is  5y²/6 +2y/15.

In an algebraic expression Like terms are  defined as those terms that have same variable and that variable has the same power .

For Example : 5a,9a are like terms .

In the given question

=y²/2 +y/3 +y²/3 -y/5

On combining the like terms , one with y² and other with y.

We get;

=y²/2 +y²/3 +y/3  -y/5

Taking LCM of like terms with y² as "6"

and LCM of like terms with y as "15".

We get ;

=(3y²+2y²)/6 +(5y-3y)/15

=5y²/6 +2y/15

Therefore , On combining the like terms of the expression y²/2 + y/3 + y²/3 - y/5, the simplified value is  5y²/6 +2y/15.

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We can see that there is no element which is common Hence, they are mutually exclusive events.

Let A be the event of getting a sum of 7 on dice.

Let B be the events of getting a sum of 6 on dice.

A={ (1,6), (2,5), (3,4), (4,3), (5,2) }

B = { (1,5) , (2,4), (3,3),  (4,2), (5,1), }

Mutaullty exclusive events are those when there is no common event between two events.

Where there is empty set of intersection.

But we can see that there is no element which is common

So, n(A∩B) = ∅

Hence, they are mutually exclusive events.

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Answer:

Solutions below.

Step-by-step explanation:

a) To solve this question, we can use the formula.

Average Cost per Bracelet = Total Price ÷ Number of Bracelets.

Toy Barn

Average Cost = $5.40 ÷ 6 = $0.90 per bracelet

Dollar Deals

Average Cost = $10.50 ÷ 11 = $0.95 per bracelet (rounded off to 2 decimal places)

b) The better deal comes with a lower price per bracelet, in this case, Toy Barn has a better deal.

Part a - C = 120 + 5x

Part b - A = [120 + (5 x (x)] / x

Part c - The number of hours you must play before the average cost per hour drops to $10 per hour is 15 hours.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Membership fees = $120

Cost per hour = $5

x = number of hours

The equation that represents the total cost:

C = 120 + 5x

The equation that represents the average cost per hour:

A = [120 + (5 x (x)] / x

From the graph, we can assume that the y-axis indicates the average cost per hour and the x-axis indicates the number of hours.

We see that in 16 hours the average cost per hour is $10 so the number of hours to play before the average cost per hour drops to $10 per hour is 15 hours.

Thus,

Part a - C = 120 + 5x

Part b - A = [120 + (5 x (x)] / x

Part c - The number of hours you must play before the average cost per hour drops to $10 per hour is 15 hours.

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Ava's age = b

Ava's sister's age = 2b -9

Answer -

1/2x + 5 = 7

1x/2 + 5 = 7

1x/2 + 5 = 7

x/2 + 5 = 7

x/2 + 5 = 7

x/2 + 2.5/2 = 7

X = 4

The term is 0.04

The geometric sequence given is

0.004, __, 0.4, 4....

Now let us find the value of r which is the factor between the terms, called the common ratio.

r = [tex]\frac{0.04}{0.004}[/tex] = [tex]\frac{0.4}{0.04}[/tex]

 = 10

General form= [tex]a_{n}[/tex] =[tex]a_{1}[/tex]×[tex]r^{n-1}[/tex]

The geometric series

           [tex]a_{n}[/tex] = 0.004× [tex]10^{n-1}[/tex]

Therefore to find the second number of the sequence is

          [tex]a_{2}[/tex]  = 0.004 × [tex]10^{2-1}[/tex]

               = 0.004 × 10

               = 0.04

Therefore the missing term of a geometric sequence is 0.04.

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244140625 x^{54} value of the Algebraic functions .

What is Algebraic functions?

Evaluate the exponent

= [tex]\frac{5^{7} . 125^{3} }{25^{2} } . x^{54}[/tex]

Evaluate the exponent

= [tex]\frac{78125 . 125x^{3} }{25^{2} } . x^{54}[/tex]

Multiply the numbers

= [tex]\frac{78125 . 1953125 }{25^{2} } . x^{54}[/tex]

Evaluate the exponent

= [tex]\frac{152587890625}{25^{2} } . x^{54}[/tex]

Cancel terms that are in both the numerator and denominator

= [tex]\frac{152587890625}{625} . x^{54}[/tex]

= [tex]\frac{152587890625}{625} . x^{54}[/tex]

= 244140625 x^{54}

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Answer:

780 ≥ 58.53x + 566.83

Step-by-step explanation:

He has $780 that he can spend, so the total must be less than or equal to 780.

Let x = number of biking outfits.

Costs:

Bicycle: $490.50

Reflectors: 4 × $14.98 = $59.92

Gloves $16.44

Outfits: $58.53x (The cost of x outfits is 58.53x)

The total he spends is:

490.5 + 59.92 + 16.44 + 58.53x =

= 58.53x + 566.86

This total has to be less than or equal to $780.

58.53x + 566.86 ≤ 780

This can be written as

780 ≥ 58.53x + 566.83

   For numbers 5 and 20 the value of the geometric mean of these numbers is

Gm (5, 20) = 10

      The definition of geometric mean is a calculation that is performed on a set of numbers which consists of calculating the square root of the product between them, the equation is as follows:

Gm (a,b) = √ab

  Then in our case that we have the values 40 and 15, these are equivalent to the variables a and b

  We substitute and solve for the square root

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Answer:

24

Step-by-step explanation:

3a/6 = 12

3a = 6 * 12

3a = 72

a = 72/3

a = 24

Check:

3*24/6 = 12

72/6 = 12

We have proved that , the ΔXWZ is congruent to ΔZYX i.e., ΔXWZ ≅ ΔZYX

It is given that XY ║ WZ and XW ║ YZ.

We have to prove that ΔXWZ is congruent to ΔZYX i.e., ΔXWZ ≅ ΔZYX.

What is the SSS rule of congruency of triangles ?

SSS axiom states that if two triangles have three pairs of congruent sides, then the triangles are congruent.

As per the question ;

XY ║ WZ and XW ║ YZ

So , using this data we can conclude that ;

XY = XW and WZ = YZ

The two triangles are ΔXWZ and ΔZYX

So ,

XY = XW (from given data)

and

WZ = YZ (from given data)

and

XZ = XZ (common)

∴ Both triangles are congruent to each other ;

i.e.,

ΔXWZ ≅ ΔZYX

by using the SSS axiom.

Thus , the ΔXWZ is congruent to ΔZYX i.e., ΔXWZ ≅ ΔZYX

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Solving the problem with the arithmetic progression, the 32nd term of the sequence is 558.

Arithmetic progression is a sequence of numbers in which the next term is depicted by adding a fixed number 'd' to the preceding term. The series is in arithmetic progression.

We all know the formula for arithmetic progression is,

aⁿ = a + ( n-1 ) d

where d = difference between two corresponding terms, n = no. of term, a = first term

We have to find the 2nd term, and it's, a³⁸ = 3 + ( 38 - 1)( 18 - 3 ) = 3 + 37× 15 = 3 + 555 = 558.

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Answer:

i think the answer may be possibly 86%

Answer:

Calm down, I gotcha!

Step-by-step explanation:

4 7/12+ 2 3/4+ 7 5/12=14.75

Considering the definition of an equation and the way to solve it, the money earned by Adriano's online business this month is $1,150.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

In this case, you know that every month, Adriano receives a subscription fee of $5 from each of the subscribers to his website. Then, the amount of money earned by Adriano's online business each month will be represented by the following equation:

Money earned by Adriano's online business each month= $5x

where x is the number of subscribers on the website.

On the other hand, you know:

Then, the number of subscribers this month can be calculated as:

Number of subscribers this month = 200 + 40 - 10

Number of subscribers this month = 230

So, the amount of money earned by Adriano's online business this month is calculated by substituting this value in the equation above:

Money earned by Adriano's online business this month= $5×230 subscribers

Money earned by Adriano's online business this month=$1,150

Finally, the money earned by Adriano's online business this month is $1,150.

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The scalar multiplication [tex]k(\overrightarrow{a}+\overrightarrow{b})=k\overrightarrow{a}+k\overrightarrow{b}[/tex]has been proved.

Scalar Multiplication Property:

Basically a scalar means the real number.

The scalar multiplication property states that the product of a sum or difference of a number is equal to the sum or difference of the products.

The general form of scalar multiplication as follows:

k (A + B) = kA + k B

where

k is the scalar.

Given,

Let

[tex]\overrightarrow{a}= < x_1,y_1 >[/tex]

and

[tex]\overrightarrow{b}= < x_2,y_2 >[/tex]

Then we have to prove the following scalar multiplication property,

[tex]k(\overrightarrow{a}+\overrightarrow{b})=k\overrightarrow{a}+k\overrightarrow{b}[/tex]

We know that,

"The vector is an object that has both a magnitude and a direction. And  vector as a directed line segment, whose length is the magnitude of the vector and with an arrow indicating the direction."

Here we have two vectors like [tex]\overrightarrow{a},\overrightarrow{b}[/tex].

Now we need to use the definition of the scalar multiplication property,

Then, the LHS of the expression is written as,

[tex]\implies k(\overrightarrow{a}+\overrightarrow{b})[/tex]

Apply the values of the vectors then we get,

=> k(<x₁, y₁> + <x₂, y₂>)

When we expand the terms then we get,

=> k<x₁, y₁> +  k<x₂, y₂>

And it can be written as,

[tex]\implies k\overrightarrow{a}+k\overrightarrow{b}[/tex]

Therefore, the scalar multiplication property has been proved.

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Answer:

Option 2 [tex]x[/tex] = 15, [tex]y[/tex] = 3

Step-by-step explanation:

Vertical angles are equivalent. Thus [tex]4x+10y[/tex] = 90. To solve for [tex]x[/tex], we set [tex]6x[/tex] = 90, since adjacent angles equal 180. This gives us 15 as x. Plugging 15 into the first equation we get that y is equal to 3.

Answer:

8:30 a.m.

Step-by-step explanation:

The total time it takes for Lyle to reach his friend's house is 720/80 + 1 + 0.25 * 2, which is 9 + 1.5 = 10.5 hours

The latest possible time that Lyle would be able to leave his house to reach on time is 8:30 a.m.

Answer:

y = 3x + 1

y = -x + 5

Step-by-step explanation:

Take the system of equations and substitute (1 ,4) in any one of the equations. If both the sides are justified, then (4,1) is the solution to that pair of equations.

  1) y = -3x  - 1   ---------(I)

     y = -x + 5

Substitute (1,4) in equation (I)

        4 = -3*1 - 1

        4 = -3-1

        4 ≠ -4

So, (1, 4) is not a solution.

2) y = 3x + 1   ---------------(II)

   y = - x + 5

Substitute (1 ,4) in equation (II)

      4 = 3*1 + 1

       4 = 3 + 1

       4 =  4

(1 ,4) is the solution for this system of equation.

Answer:

Needs alot of steps which you can try

Step-by-step explanation:

Sum of interior angles=exterior angle

Eg, left side 60°+90° = the exterior (big angle outside triangle)

All of the lines are straight so you can find angles using (angles on a straight line) so 180°- the angle known when your solving

There is also opposites angles which are equal, you can search it up

From the given vertices, the area of the polygon is 28.

The rectangle is a quadrilateral.  The classification for quadrilaterals is given by the length of sides and angles. For a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

A rectangle is a geometric figure that has 4 sides called: base and height. Due to its characteristics, the rectangle presents two bases (B) and two heights (H).

The area of a rectangle is given by the multiplication between the base and the height.

First, you should plot the points, then see image 1.

From the figure, it is possible to see that the bases ( AB and CD) = 5-3=2

and heights (AC and BD) =-7-(-7)=7+7=14. Thus,

A= B*H= 2*14=28

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