Answer the questions below.
2.
(a) The area of a rectangular parking lot is 6370 m
If the width of the parking lot is 65 m, what is its length?

Answer:

3/8

Step-by-step explanation:

if u simplify you get half then add them the bigger dinominator is the bottom so only add the tops

Answer:

8%

Step-by-step explanation:

I=Pr

104=2600*r/2

r/2=104/2600

r=(104/2600)(2)

r=0.08=8%

Eliana must invest at a rate of 0.33% of simple interest to earn $104.

Given,

Eliana has $2600 to invest for 6 months.

If she needs the money to earn $104 in that time.

We need to find at what rate of simple interest must Eliana invest.

It is given as:

SI = PRT / 100

P = principal amount

R = rate

T = time in years.

Find the rate of interest.

We have,

Simple interest = PRT / 100

SI = $104

T = 6 months

Convert it into years.

12 months = 1 year

6 months = 6/12 years

T = 1/2 years

$104 = ($2600 x R x 1/2) / 100

104 = (2600 x R x 1/2) / 100

100 x 104 = 2600 x R x 12

R = (100 x 104 ) / (2600 x 12)

R = 104 / 312

R = 0.33 %

Thus the rate of simple interest is 0.33%

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The answer is -2 , 0, and 4

Answer:

  x = 7

Step-by-step explanation:

First, you look at the equation. Identify the locations of variable terms (both sides of the equal sign) and the constant terms (both sides of the equal sign).

If there are any parentheses, it is a good idea to use the distributive property to eliminate them. Here, there are none.

I like to start by subtracting the variable term with the smallest coefficient. Here, that is 3x, so we add -3x to both sides of the equation.

  3x -3x +1 = 5x -3x -13

  1 = 2x -13 . . . . . . . . . . . . combine like terms

Now, we have the only variable term on one side of the equal sign. We want it by itself, so we need to make the -13 go away. We do that by adding its opposite to both sides of the equation:

  1 +13 = 2x -13 +13

  14 = 2x . . . . . . . . . . . . combine like terms

Finally, we want the coefficient of 2 in the x-term to disappear. We make that happen by multiplying both sides of the equation by 1/2, the reciprocal of that coefficient.

  (1/2)(14) = (1/2)(2x)

  7 = x . . . . the solution

__

It is generally a good idea to check your work by seeing if your solution value satisfies the equation:

  3(7) +1 = 5(7) -13 . . . . put 7 where x is in the original equation

  21 +1 = 35 -13

  22 = 22 . . . . . . x = 7 is the solution

_____

Additional comment

By subtracting 3x from 5x, the result is 2x with a positive coefficient. We could solve the equation just as easily by subtracting 5x from 3x. That result would be ...

  -2x +1 = -13

Subtracting 1 would give

  -2x = -14

and you would multiply by -1/2 to get x=7. I personally like to avoid having this many minus signs show up in the problem. That is why I choose to subtract the x-term with the smallest coefficient.

Answer:

10

Step-by-step explanation:

Remember that the formula for the sum of an arithmetic series is:

[tex]S=\frac{k}{2}(a+x_k)[/tex]

Where k is the number of terms, a is the initial term, and x_k is the last term of the series.

We essentially want to find k, the number of terms, given that the sum S is equal to 105. So, substitute 105 into our equation:

[tex]105=\frac{k}{2}(a+x_k)[/tex]

To do so, we need to final term x_k. We don't know what it is yet, but that doesn't matter. All we need to do is to write it in terms of k. First, remember that the standard form for the explicit formula of an arithmetic sequence is:

[tex]x_n=a+d(n-1)[/tex]

Where a is the first term, d is the common difference, and n is the nth term.

From our sequence, we can see that the first term is -3.

Also, we can determine that our common difference is +3, since each subsequent term is 3 more than the previous one. -3+3 is 0, 0+3 is 3, 3+3 is 6, and so on.

Therefore, our explicit formula is:

[tex]x_n=-3+3(n-1)[/tex]

Therefore, our final term, x_k, will be if we substitute k for n. So, we can acquire the equation:

[tex]x_k=-3+3(k-1)[/tex]

Now that we know what x_k is, we can substitute that into our original equation:

[tex]105=\frac{k}{2}(a+x_k)[/tex]

Substitute the equation into x_k. Also, let's substitute -3 (our first term) for a. So:

[tex]105=\frac{k}{2}(-3+(-3+3(k-1)))[/tex]

And now, all we have to do is to solve for k.

First, distribute the 3:

[tex]105=\frac{k}{2}(-3+(-3+3k-3))[/tex]

Add within the parentheses:

[tex]105=\frac{k}{2}(3k-9)[/tex]

Multiply both sides by 2. This removes the fraction on the right:

[tex]210=k(3k-9)[/tex]

Distribute. We will get a quadratic:

[tex]210=3k^2-9k[/tex]

So, let's solve for k. Let's divide everything by 3:

[tex]70=k^2-3k[/tex]

Subtract 70 from both sides:

[tex]0=k^2-3k-70[/tex]

Factor. We can use -10 and 7. So:

[tex]0=(k-10)(k+7)[/tex]

Zero Product Property:

[tex]k-10=0\text{ or } k+7=0[/tex]

Solve for k for each equation:

[tex]k=10\text{ or } k=-7[/tex]

-7 doesn't make sense (we can't have -7 terms). Remove that solution. So, we are left with:

[tex]k=10[/tex]

Therefore, the number of terms we have in our series for our sum to be 105 is 10.

And we're done!

3xcubed y to the fifth over 2

Answer:

[tex]x^{20}[/tex]

Step-by-step explanation:

[tex](x^{2} )^{5}[/tex]·[tex](x^{5})^{2}[/tex]

[tex](x^{10} )[/tex] · [tex](x^{10})[/tex]

[tex]x^{20}[/tex]

Answer:

C. The student did not put the polynomial in standard form before naming it by the first term. It is a fourth-degree trinomial.

Step-by-step explanation:

A trinomial is a polynomial with three variables. The polynomial -2x³ + 5x⁴ - 3x has three variables hence it is a trinomial.

The degree of a polynomial is the highest degree of a variable in a polynomial equation.

The polynomial -2x³ + 5x⁴ - 3x can be arranged as The polynomial 5x⁴ - 2x³ - 3x, hence the variable with the highest degree is 5x⁴ which has a degree of 4.

Therefore The polynomial -2x³ + 5x⁴ - 3x  has a degree of 4

This means the polynomial -2x³ + 5x⁴ - 3x is a trinomial with a degree of 4

Answer:

1.5 per hour.

Step-by-step explanation:

By proportion that is 5.4 / 3.6

= 1.5 per hour.

Answer:

The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis.

Step-by-step explanation:

I had this question not to long ago and got it right

Answer:

58

Step-by-step explanation:

I have attached an image with this answer that will help you to visualise this question. I will now explain it.

The smaller number (Number 1) has 1 unit.

The bigger number (Number 2) has 1 unit, and 19.

If you add 19 to the smaller number, you will make two of the bigger number.

[tex]97+19=116[/tex]

This is equivalent to two of the bigger number. (Try to visualise it!)

Hence, divide it by 2 to get one of the bigger number.

[tex]116\div2=58[/tex]

Answer:

58

Step-by-step explanation:

The smaller number (Number 1) has 1 unit.

The bigger number (Number 2) has 1 unit, and 19.

If you add 19 to the smaller number, you will make two of the bigger number.

This is equivalent to two of the bigger number. (Try to visualise it!)

Hence, divide it by 2 to get one of the bigger number.

Step-by-step explanation:

yf.bfz

vcg ,kgu nkkgfgvvxvh

Answer:

37,  ABD = CBD = 44 degrees, and ABC = 88 degrees

38.  ABD = CBD = 24 degrees, and ABC = 48 degrees

39.  ABD = CBD = 65 degrees, and ABC = 130 degrees

40.  ABD = CBD =67 degrees, and ABC = 134 degrees

Step-by-step explanation:

Recall that when a segment bisects an angle, the angle is divided in equal parts then we have:

37.  

6 x + 14 = 3 x + 29

3 x = 19 - 14 = 15

x = 15/3

x = 5

then ABD = 6 (5) + 14 = 30 + 14 = 44 degrees

CBD must equal ABD , so CBD = 44 degrees

And the total angle ABC = 88 degrees

38.

3 x + 6 = 7 x - 18

24 = 4 x

x = 24/4 = 6

Then ABD = 3 (6) + 6 = 24 degrees. Also CBD = 24 degrees and ABC = 48 degrees

39.

- 4 x + 33 = 2 x + 81

- 6 x = 81 - 33

-6 x = 48

x = - 48/6

x = -8

Then ABD = -4 (-8) + 33 = 32 + 33 = 65 degrees

The also CBD = 65 degrees, and ABC = 130 degrees

40.

8 x + 35 = 11 x + 23

35 - 23 = 11 x - 8 x

12 = 3 x

x = 12/3

x = 4 degrees

Therefore:

ABD = 8 (4) + 35 = 32 + 35 = 67 degrees.

Then also CBD = 67 degrees, and ABC = 134 degrees

Answer:

t= -0.18

Step-by-step explanation:

Isolate t to get the unknown number:

(-4.5t)(49.5t) = 40

      Multiply (-4.5t)(49.5t):

                     (-4.5t)(49.5t) = -222.75t

      Now, write full equation:

          -222.75t = 40

      Isolate t by dividing -222.75 on both sides:

           [tex]\frac{-222.75}{-222.75}t=\frac{40}{-222.75}[/tex]

      Cancel out left hand side:

            [tex]t=\frac{40}{-222.75}[/tex]

      Simplify your answer:

              [tex]t=-0.17957351[/tex]

      Approximate to 2 decimals:

           [tex]t=-0.18[/tex]

Set [tex]y = f^{-1}(x)[/tex] and [tex]f(y) = x[/tex]

Interchange the variables [tex]x[/tex] and [tex]y[/tex]

[tex]3y + 28 = x\\3y = x - 28\\y = \frac{x - 28}{3} \\\\f^{-1}(x) = \frac{x - 28}{3}[/tex]

Answer:

153.2 =x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adjacent side/ hypotenuse

cos 40 = x/200

Multiply each side by 200

200 cos 40 = x/200 * 200

200 cos 40 =x

153.20888886=x

To the nearest tenth

153.2 =x

Answer:

AC = 153.2 m.

Step-by-step explanation:

cos(Ф) = adj / hyp

cos(40) = AC / 200

AC = cos(40) x 200

AC = 153.2 m

Divide 30 by 25% to find the full amount:

30/0.25 = 120

Now multiply the full amount by 40%:

120 x 0.40 = 30

When something varies directly as something else, their ratio of change always stays the same.

56 / 7 = 8

Therefore,

8 * 3 = 24

If x = 3 then y = 24

Given: 2/3 every 30 seconds

If we cut 2/3 in half, we get 1/3. This would also mean we cut the time in half 30 / 2 = 15 seconds

Therefore, 1/3 of the length every 15 seconds.

15 + 15 + 15 = 45 seconds to go the full length of the path

Complete Question

Find a particular solution to [tex]ty''-(1+t)y'+y=t^2e^t , t > 0[/tex]  

[tex]y_1 = 1 + t , \ y_2 = e^t[/tex]

Answer:

The solution is    [tex]y_p = -e^{2t} + t + \frac{3t^2}{2} + \frac{t^3}{2}[/tex]

Step-by-step explanation:

  Now the given equation is [tex]ty''-(1+t)y'+y=t^2e^t , t > 0[/tex]

             dividing through by  t

       We have  

         [tex]y'' - \frac{1 + t }{t}y' + \frac{1}{t} y = te^t \\\\ let's\ call\ it \ g(t)[/tex]

Now for the given initial value we can generate our Wronskian as follows

        [tex]W(y_1 ,y_2) = | \left y_1} \atop {y_1'}} \right. \left y_2} \atop {y_2'}} \right | = | \left {(1 + t)} \atop {1}} \right. \left e^t} \atop {e^t}} \right | = (1 + t )e^t - e^t = te^t[/tex]

Now applying  method of variation of parameters to obtain the particular solution

So here we assume that

          [tex]y_p = v_1 y_1 + v_2 y_2[/tex]

So

       [tex]v_1 = - \int\limits {\frac{y_2 (t) g(t)}{W(t)} } \, dt = - \int\limits {\frac{e^t te^t}{te^t} } = - \int\limits { e^t} } = -e^t[/tex]

And

    [tex]v_2 = - \int\limits {\frac{y_1 (t) g(t)}{W(t)} } \, dt = - \int\limits {\frac{(1 + t) te^t}{te^t} } = - \int\limits (1 + t) = t + \frac{t^2}{2}[/tex]

So

     [tex]y_p = -e^t * e^t + t + \frac{t^2}{2} * 1 + t[/tex]

     [tex]y_p  =  -e^{2t}   +  t +   \frac{3t^2}{2} + \frac{t^3}{2}[/tex]

Answer:

C. the number of non-guppies

Step-by-step explanation:

The number of non-guppies is the only variable the other two options have defined values.

Answer:

C, The number of non- guppies is the most important variable.

Step-by-step explanation:

The answer is the unknown variable that you're trying to find and the entire problem is to help you find the unknown.

Answer:

-19n^4 - 8m^2 - 12m^4n

Step-by-step explanation:

8m^2 + 12m^4n + 9mn

-

19n^4 9mn

------------------------------------------------------------------------

-19n^4 - 8m^2 - 12m^4n

Answer:

The answer is B.) -31m^4n-8m^2

Answer:

35:60 times

Step-by-step explanation:

The proportion of time in which the coin land on Heads is 0.58

A proportion is an equation in which two ratios are set equal to each other.

Now it is given that,

Number of times coins tossed = 60

Number of times coin landed on Heads = 35

Therefore, the proportion of time in which the coin land on Heads is given as,

Proportion of time the coin land on Heads = Number of times coin landed on Heads/Number of times coins tossed

⇒ Proportion of time the coin land on Heads = 35/60

⇒ Proportion of time the coin land on Heads = 7/12 = 0.58

Thus, the proportion of time in which the coin land on Heads is 0.58

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Answer:

A) 14

Step-by-step explanation:

x - 6 > 10

Add 6 to both sides.

x > 16

The solution is all numbers greater than 16.

In the choices, only 14 is less than 16.

Answer: A) 14

Answer:

a

Step-by-step explanation:

x-6 [tex]>[/tex] 10

14-6 [tex]>[/tex]10

8 is less than 10

Answer:

Step-by-step explanation:

Given function

Let's try point x = 0

So the vertex moves right

See attached

Answer:

Sound travels 2258 feet in 2 seconds while travelling through air.

Step-by-step explanation:

Answer:

a) 3.2 cm

b) 6.25 km

Answer:

After 12 games.

Step-by-step explanation:

Deanna's money after playing 12 games =

15 - (0.75 × 12) = 6$

Lisa's money after playing 12 games =

12 - (0.50 × 12) = 6$