Find the measures of the interior angles that maximize the area of an isosceles trapezoid
where the length of the non-parallel sides are each 4 inches and the length the shorter of
the two bases is 6 inches.

Answer:

m/5=15

Step-by-step explanation:

Since Jack was solving m/5 problems per day, the equation to solve this would be the one given above.

The equation that represents the situation is m = 75x.

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

If Jack solved m math problems in 5 days by solving the same number of problems every day, then he solved m/5 problems per day.

Now suppose Jack was solving 15 problems per day.

We want to find out how many problems he had to solve in total, so we can set up an equation using these two pieces of information:

15x = m/5

Here, x represents the number of days Jack took to solve all the problems.

We can solve for m by multiplying both sides of the equation by 5:

75x = m

So the equation we get is:

m = 75x

Therefore, this equation relates the total number of math problems Jack had to solve (m) to the number of days he took to solve them (x), given that he solved 15 problems per day.

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Answer:

D.  984

Step-by-step explanation:

The are of the trapozoid is 1/2(B1+B2)+h

Answer:

208.3

Step-by-step explanation:

Since the numbers are decreasing as multiples, its a geometric progression.

[tex]S_{n}=\frac{a(1-r^{n} )}{1-r} ; r\neq 1 \ and\ r \ is\ less\ than\ 1\\common\ ratio=\frac{20}{50}=\frac{2}{5}\\ S_{10}=\frac{125(1-(2/5)^{10} )}{1-(2/5)} \\=208.3[/tex]

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Explanation:

The first two rows are already done. They have X's for every month to indicate a monthly payment regularly throughout the year without any extra conditions/requirements.

The third row will have exactly 4 copies of X in it. Two of them are already placed for January and April. The other two payments are in July and October. Notice the months are spaced 3 apart and how 12/4 = 3.

The fourth row will have X's across every cell in the same way the first row does since the internet bill is monthly. The same applies to the cell phone bill and food rows.

Something like the car loan will only have 2 copies of X in that row. Semiannual means twice a year, aka every 6 months. One copy of X is already placed for us in this row. This is in January (month 1). Six months later in month 1+6 = 7 (July) is when the next car loan payment occurs.

Lawn care will have X's only for the months of April through September; any other month won't have an X.

Day care will have X's for February, April, June, August, October, December. We start with February and alternate each month to fill out the rest of the year. This is due to the phrasing "every other month".

The gym membership will have one X for July only, since it's an annual payment.

Answer:

Step-by-step explanation:

m∠ABC + m∠BAC + m∠ACB = 180°

a + 2a + 6a = 180°

9a = 180°

a = 20°

m∠ABC = 20°

m∠BAC = 2 × 20° = 40°

m∠ACB = 6 × 20° = 120°

$15

Explanation:

For each lawn he mows = $5

He should mow 6 lawns but did only 3 lawns as other 3 he forgot to mow.

earned:

Answer:

f(3) = 9

Step-by-step explanation:

From the table, when can see that when x is 3, f(x) is 9.

Therefore, f(3) = 9

Answer:

[tex]f(3)[/tex]=9

Step-by-step explanation:

[tex]f(x)[/tex] is x times a function.

so if you look at the table on the 'x' side and go down the table until you reach '3' and see what number on the 'f(x)' side corresponds with it, you will see '9'

so [tex]f(3) = 9[/tex]

and that means your answer is D

Answer:

the price of the adult's ticket is 14 and the price of the child's ticket is 6

Step-by-step explanation:

[tex]let \: x \: = adult \\ y = child \\ 4x + 3y = 74 - - - - 1\\ 2x + 5y = 58 - - - - - 2 \\ multiplying \: - - 2 \: by \: two \\ 4x + 10y = 116 - - - - 3 \\ eqn3 - eqn1 \\ 4x - 4x + 10y - 3y = 116 - 74 \\ 7y = 42 \\ y = \frac{42}{7} \\ y = 6 \\ putting \: the \: value \: of \: y \: into \: eqn2 \\ 2x + 5(6) = 58 \\ 2x = 28 \\ x = \frac{28}{2} \\ x = 14[/tex]

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Answer:

C.When the heart is starved of oxygen

Answer:

m = 4

(0, 1)

y = 4x + 1

Step-by-step explanation:

Slope using first two points (-2, 7) & (-1, -3):

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

[tex]m=\frac{-3+7}{-1+2} =\frac{4}{1}[/tex]

m = 4

Y-intercept, b: (0, 1)

Equation:

y = mx + b

y = 4x + 1

Answer:

x = 110

Step-by-step explanation:

find the number : x

that must be added : +

to :

40/100 * 225 + x = 200

2/5 * 225 + x = 200

90 + x = 200

x = 200 - 90

x = 110

Answer:

318

Step-by-step explanation:

300 + (300 * 6%) = Answer

300 + (300 * 0.06) = 318

Answer:

x=16ft 2x+4=36

Step-by-step explanation:

perimeter o rectangle=2(l+b)

2(2x+4+x)=104

4x+8+2x=104

x=16ft,2x+4=36ft

Answer:

[tex]x=6-\sqrt{ -100}/2=3-5i=3.0000-5.0000i\\x=6+\sqrt{-100} )/2=3+5i=3.0000+5.0000i[/tex]

Step-by-step explanation:

Step 1: Trying to factor by splitting the middle term

The first term is,  x²  its coefficient is  1 .

The middle term is,  -6x  its coefficient is  -6 .

The last term, "the constant", is  +34

Step-1 : Multiply the coefficient of the first term by the constant   1 • 34 = 34

Step-2 : Find two factors of  34  whose sum equals the coefficient of the middle term, which is   -6 .

     -34    +    -1    =    -35

     -17    +    -2    =    -19

     -2    +    -17    =    -19

     -1    +    -34    =    -35

     1    +    34    =    35

     2    +    17    =    19

     17    +    2    =    19

     34    +    1    =    35

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step 1:

 x² - 6x + 34  = 0

Parabola, Finding the Vertex:

 Find the Vertex of   y = x^2-6x+34

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   3.0000  

Plugging into the parabola formula   3.0000  for  x  we can calculate the  y -coordinate :

 y = 1.0 * 3.00 * 3.00 - 6.0 * 3.00 + 34.0

or   y = 25.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x2-6x+34

Axis of Symmetry (dashed)  {x}={ 3.00}

Vertex at  {x,y} = { 3.00,25.00}

Function has no real roots

Solve Quadratic Equation by Completing The Square

Solving   x2-6x+34 = 0 by Completing The Square .

Subtract  34  from both side of the equation :

  x2-6x = -34

Now the clever bit: Take the coefficient of  x , which is  6 , divide by two, giving  3 , and finally square it giving  9

Add  9  to both sides of the equation :

 On the right hand side we have :

  -34  +  9    or,  (-34/1)+(9/1)

 The common denominator of the two fractions is  1   Adding  (-34/1)+(9/1)  gives  -25/1

 So adding to both sides we finally get :

  x2-6x+9 = -25

Adding  9  has completed the left hand side into a perfect square :

  x2-6x+9  =

  (x-3) • (x-3)  =

 (x-3)2

Things which are equal to the same thing are also equal to one another. Since

  x2-6x+9 = -25 and

  x2-6x+9 = (x-3)2

then, according to the law of transitivity,

  (x-3)2 = -25

We'll refer to this Equation as  Eq. #2.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-3)2   is

  (x-3)2/2 =

 (x-3)1 =

  x-3

Now, applying the Square Root Principle to  Eq. #2.2.1  we get:

  x-3 = √ -25

Add  3  to both sides to obtain:

  x = 3 + √ -25

In Math,  i  is called the imaginary unit. It satisfies   i2  =-1. Both   i   and   -i   are the square roots of   -1

Since a square root has two values, one positive and the other negative

  x2 - 6x + 34 = 0

  has two solutions:

 x = 3 + √ 25 •  i

  or

 x = 3 - √ 25 •  i

Solve Quadratic Equation using the Quadratic Formula

2.3     Solving    x2-6x+34 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     1

                     B   =    -6

                     C   =   34

Accordingly,  B2  -  4AC   =

                    36 - 136 =

                    -100

Applying the quadratic formula :

x = 6 ± √ -100/2

In the set of real numbers, negative numbers do not have square roots. A new set of numbers, called complex, was invented so that negative numbers would have a square root. These numbers are written  (a+b*i)

Both   i   and   -i   are the square roots of minus 1

Accordingly,√ -100  =

                   √ 100 • (-1)  =

                   √ 100  • √ -1   =

                   ±  √ 100  • i

Can  √ 100 be simplified ?

Yes!   The prime factorization of  100   is

  2•2•5•5

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 100   =  √ 2•2•5•5   =2•5•√ 1   =

               ±  10 • √ 1   =

               ±  10

So now we are looking at:

          x  =  ( 6 ± 10i ) / 2

Two imaginary solutions :

x =(6+√-100)/2=3+5i= 3.0000+5.0000i

 or:

x =(6-√-100)/2=3-5i= 3.0000-5.0000i

Two solutions were found :

x =(6-√-100)/2=3-5i= 3.0000-5.0000i

x =(6+√-100)/2=3+5i= 3.0000+5.0000i

Answer:

The opposite sides in a rectangle are equal.

Step-by-step explanation:

If all sides were equal, you would have a square.

If the opposite sides were not parallel, you would not have 4 sides that meet at 90 degrees.

All angles in a rectangle are 90 degrees.

Answer:

The opposite sides in a rectangle are equal.

Step-by-step explanation:

hope this helps  hope you get it correct

Answer:

A. 5/1

C. -0.02

D. 4.177777....

Step-by-step explanation:

Rational numbers can be written as a ratio of numbers, such as 5/1. As decimals, the numbers either

*** "terminate" the decimal has a certain number of digits and then stops, such -0.02, this can be written as a ratio -2/100 which is -1/50

OR

*** "repeats" , such as 4.17777... which can also be written as a ratio, 4.1777... = 188/45

7/0 is undefined and the pi numbers are irrational, the digits of the decimal do not repeat and do not ever end, therefore NOT rational.

Answer:

Step-by-step explanation:

So you have a constant value of 5 dollars and a variable value of 1.50 dollars. some equation of these numbers equals 23 dollars. That equation is

23=5+(1.50n) where n is the number of booster packs.

Answer:

$23 = $5 + 1.5x

Step-by-step explanation:

We can make a format to find the equation.

Total = base fee + $ per pack

Let x = the number of packs

Therefore, the equation will be like this:

$23 = $5 + 1.5x

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Answer:

d=1

Step-by-step explanation:

d=2*r

r=(1/2)

d=2*(1/2)=1

Answer:

Step-by-step explanation:

General form of the linear differential equation can be written as:

[tex]\frac{dy}{dx}+P(x)y=Q(x)[/tex]

For this case, we can rewrite the equation as:

[tex]\frac{dy}{dx}+\frac{1}{2x}y=\frac{\sqrt{x}}{x}[/tex]

Here [tex]P(x) =\frac{1}{2x}; Q(x)=\frac{\sqrt{x}}{x}[/tex]

To find the solution (y(x)), we can use the integration factor method:

[tex]Fy(x)=\int Q(x)Fdx+C \rightarrow F=e^{\int P(x)dx[/tex]

Then [tex]F=e^{\int \frac{1}{2x}dx}=e^{\frac{1}{2}\ln|x|\right}=\sqrt{|x|}[/tex]

So, we can find:

[tex]y\sqrt{|x|}=\int \frac{\sqrt{x}\sqrt{|x|}}{x}dx+C[/tex]

Suppose that [tex]x\in \double R[/tex], then [tex]\sqrt{|x|}=\sqrt{x}[/tex] , and we find:

[tex]y\sqrt{x}=x+C \rightarrow y(x)=\sqrt{x}+\frac{C\sqrt{x}}{x}[/tex]

To check our solution is right or not, put your y(x) back to the ODE:

[tex]y' = \frac{1}{2\sqrt{x}}-\frac{C}{2\sqrt{x^{3}}}[/tex]

[tex]2xy'=\frac{x-C}{\sqrt{x}}[/tex]

[tex]2xy'+y=\frac{x-C}{\sqrt{x}}+\sqrt{x}+\frac{C\sqrt{x}}{x}=2\sqrt{x}[/tex]

(it means your solution is right)

Answer:

Positive

Step-by-step explanation:

The graph goes up (puff puff positive)

Answer:

60 feet?

Step-by-step explanation:

The area covered with grass, in square feeet, is the area of the shape of the yard.

The area of a yard can be calculated by determining the shape of the yard, and using the appropriate area formula of the shape to find the area of the yard.

Image of the yard is missing. However, assuming the yard is a rectangular shape with a dimension of 10 ft by 6 ft, therefore:

The square feet of grass Russell has = area of rectangle = (10)(6) = 60 ft²

In summary, the area covered with grass, in square feeet, is the area of the shape of the yard.

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Answer:

Bus B

Step-by-step explanation:

For both buses, the slope is the speed.

Bus A: y = 125/2 x

m = 125/2 = 62.5

Bus A travels at 62.5 mph

For Bus B, wee look at the graph.

When x = 3, y = 200.

m = 200/3 = 66.666...

Bus B travels at 66.7 mph

Answer: Bus B

Answer:

I believe its b

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

2 is in the ones place

4 is in the tens

1 is in the hundreds

6 is in the thousands

9 is in the ten thousands

Answer:

The number that is in the ten thousands is 9, whose value is 90,000.

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I hope help you :)

Kind regards, Antonio.

Answer:

D=9×30 and B=4x+20°=9.-30 B a 420

Using the expected value of a discrete distribution, it is found that:

a) His expected value is of -$2.5.

b) The fair price of a ticket is of $0.5.

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

In this problem, the distribution for the net value of the ticket is:

Item a:

The expected value is given by:

[tex]E(X) = 497\frac{1}{1000} - 3\frac{999}{1000} = -2.5[/tex]

His expected value is of -$2.5.

Item b:

With an unknown ticket price, the distribution is:

The game is fair if E(X) = 0, hence:

[tex]\frac{500 - x}{1000} - \frac{999x}{1000} = 0[/tex]

0.5 - x = 0

x = 0.

The fair price of a ticket is of $0.5.

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[tex]\cos \angle H =\dfrac{\text{Base}}{\text{Hypotenuse}}= \dfrac{IH}{GH}=\dfrac{28}{53}[/tex]