gina wilson unit 3 homework 1

Using elimination method, the solution of the given system of equations is (-3, -23/4)

A system of equations can be solved using:

The given system of equations is:

5c - 4t = 8   ...... (1)

14 + 4t = 3c  ...... (2)

Re-arrange equation (2) to

-3c + 4t = -14  ........ (3)

To eliminate variable t, add equation (1) to equation (3):

5c  - 4t = 8

-3c + 4t = -14 +

2c         = -6

 c         = -3

Substitute c = -3 into equation (1)

5c  - 4t = 8

5 . (-3) - 4t = 8

-15 - 4t = 8

Add 15 to both sides:

-4t = 23

   t = -23/4

Hence, the solution is (-3, -23/4)

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In the account of Rodney's will have the higher ending balance after 1 year.

Given that:

Rodney invests a sum of money, P, into an account that earns interest at a rate of r, compounded yearly.

Gerald invests half that amount into an account that pays twice Rodney’s interest rate.

To find:

Which of the accounts will have the higher ending balance after 1 year?

So, according the question

We have,

For Rodney,

p = Principle = P

r = Interest rate = r

t = time expressed in year = 1 year

n = Number of periods in a year = 1

We, know that the formula to calculate the compound interest for new balance of Rodney ,

    B = [tex]p (1 + \frac{r}{n} )^{nt}[/tex]

Now, putting the values,

    B = [tex]p (1 + \frac{r}{n} )^{nt}[/tex]    

    B = [tex]P(1+\frac{r}{1} )^{1\times 1)[/tex]

    B = [tex]P (1 + r )[/tex]  

    B = P + Pr

Now, For Gerald,

p = Principle = P/2 ( Invest half of the money from Rodney )

r = Interest rate = 2r ( Twice the rate of Rodney's)

t = time expressed in year = 1 year

n = Number of periods in a year = 1

We know that the formula to calculate the compound interest for new balance of Gerald ,

    B = [tex]p (1 + \frac{r}{n} )^{nt}[/tex]

Now, putting the values,

    B = [tex]p (1 + \frac{r}{n} )^{nt}[/tex]    

    B = [tex]\frac{P}{2} (1+\frac{2r}{1} )^{1\times 1)[/tex]

    B = [tex]\frac{P}{2} (1+ 2r)[/tex]  

    B = [tex]\frac{P}{2}[/tex] + Pr

Now compare the amounts of their accounts, so we can say that the amount of Rodney's account will have the higher ending balance after 1 year.

So, In the account of Rodney's will have the higher ending balance after 1 year.

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The explicit formula for the given sequence is a(n) =  -5 + (-1)(n - 1).

What is termed as recursive definition?

A recursive function is one that iterates or uses its very own previous term to determine subsequent terms, resulting in a series of terms.

The recursive formula for an arithmetic sequence is as follows.

a(1) = -5 and a(n) = a(n-1) -1

Remember that this formula provides us with two types of data.

Let's look for a formal formula again for sequence.

1) Remember that we can use the standard explicit form to represent a sequence in which the first term is A & common difference is B:  

A + B(n - 1)

2) As a result, the sequence's explicit formula is a(n) = -5 + (-1)(n - 1).

Thus, by the use of recursive definition, the explicit formula for the sequence is a(n) =  -5 + (-1)(n - 1).

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The amount of Rs8550 will be equal to 60 pounds.

The rate at which one currency will be exchanged for another is known as the exchange rate in the world of finance. The most frequent types of currencies are national currencies.

Given that $5 = 4 pounds and Rs 342 = $3, the amount RS 8550 will be calculated as below:-

$5 = 4 pounds

$1 = 4 / 5 pounds  .............................( 1 )

Rs 342 = $3

$1 =  342 / 3 RS  ..............................( 2 )

From the two equations:-

342 / 3 RS = 4 / 5 pounds

1 RS = ( 3 / 342 ) x  ( 4 / 5 )

8550 RS = ( 8550 x 3 x 4 ) / ( 342 x 5 )

8550 RS = 60 pounds

Therefore, the amount of Rs8550 will be equal to 60 pounds.

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When there qre 240scoops and that there are 12 gumdrops per scoop, the number of gumdrop is 20 per scoop.

From the information, it was stated that there are 240scoops and that there are 12 gumdrops per scoop.

Therefore, the number in each scoop will be

= Total scoops /Number of gumdrop

= 240 / 13

= 20

Therefore, there are 20 gumdrops.

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There are 240scoops. If there are 12 gumdrops per scoop how much is each scoop

Answer:57

Step-by-step explanation:180-123 I hope i have helped u have a wonderful day or night!

The number of batches of muffins and bread to be made in order to maximize the profits is 16 and 2.

Considering the x to be the number of batches of bread and y be the number of batches of muffins.

In the problem, it is mentioned that the preparation of both the bread and muffin takes 4 hours and 0.5 hours since the maximum preparation time is 16 altogether

The inequality equation for it will be  [tex]4x+0.5y\leq 16[/tex]

For baking the bread and  muffin it takes 1 hour and 0.5 hours, the maximum baking  time all together is  10

The inequality equation for it will be  [tex]x+0.5y\leq 10[/tex]

The profit  got from one batch of bread if  35 $ and from one batch of muffins is 10$

 f(x,y)= 35x+ 10y

for f(0,0)= 0, f(0,20)= 200, f(2,16)= 230 , f(4,0) =140

So it requires 2 batches of bread and  16 batches of muffins.

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A bakery is making whole-wheat bread and apple bran muffins. For each batch of break they make $35 profit. For each batch of muffins, they make $10 profit. The break takes 4 hours to prepare and 1 hour to back. The muffins take 0.5 hours to prepare and 0.5 hours to bake. The maximum preparation time available is 16 hours. The maximum bake time available is 10 hours. Let x = # of the batches of bread and y = # of batches of muffins. What constraints can be used to find the number of batches of bread and muffins that should be made to maximize profits?

The two-column proof are:

The angle WXV is congruent to angle YXZ

Triangle WXV congruent triangle YXZ

In this question, we are given;

X as the midpoint of line segment WY and line segment VZ

Therefore, it is correct for us to conclude that;

segment XZ is congruent to segment XV, segment XW is congruent to segment XY

Thus, angle WXV is congruent to angle YXZ

Triangle WXV congruent triangle YXZ

We then conclude that;

VW = ZY

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According to the question, to calculate the probability of the event which states that to draw a card from the standard deck but the condition is getting either ace or heart.

The total number of the playing cards are [tex]52[/tex]

And total number of heart cards are [tex]13[/tex]

And total number of ace cards are [tex]4[/tex]

Therefore, the total number of favorable outcomes in which either heart or ace can be drawn: [tex]4+13[/tex]

As per question, the probability can be written as:

P(h or a) = P(a) + P(h) - P( a and h)

[tex]= \frac{4}{52} +\frac{13}{52} -\frac{1}{52} = \frac{16}{52} = \frac{4}{13} = 30.8%[/tex]

Hence, the probability of getting either an ace or heart card is [tex]\frac{4}{13}[/tex].

The given event is not mutually exclusive because it has [tex]30.8[/tex] percent which is not close to tenth of a percent.

What are mutually exclusive events?

Mutually exclusive events are those events which cannot happen at the same time. For instance, in any event nobody can run forward or backward together at the same time.

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The height of the flagstaff by suing trigonometric ratios is found to be 27 m.

Given,

Height of the ladder, AD = 18 m

The distance to the point below the top of a vertical flagstaff where the ladder reaches, CD = 18m

Angle of elevation of flagstaff from the foot of the ladder, ∠ CAB = 60 °

Δ ACD is isosceles triangle.(Image is attached)

∠ ACB = ∠ CAD = 30 °

In △ ABD, by using the trigonometric ratios, we get that:

Sin 30 ° =  BD / AD

1 / 2 = BD / 18

BD = 9 m

So, the height of the flagstaff will be:

BC = BD + DC =9 + 18 = 27 m

Therefore, we get that, the height of the flagstaff by using trigonometric ratios is found to be 27 m.

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The roots of the equation will be imaginary. Then the number of real solutions will be zero.

The discriminant represents the types of the root. And the discriminant (D) of the equation ax² + bx + c = 0 is given as

D = b² - 4ac

The type of roots will be given below.

The equation is given below.

x² + 4x + 5 = 0

The discriminant of the given equation will be

D = 4² - 4 x 1 x 5

D = 16 - 20

D = - 4

D < 0

The roots of the equation will be imaginary. Then the number of real solutions will be zero.

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Given numbers[tex]\sqrt{14} , \sqrt{5/2} , \sqrt{9/16} , 1, 11[/tex]  in decreasing order are as follows:

[tex]11, \sqrt{14} , \sqrt{5/2}, 1, \sqrt{9/16}[/tex] .

As given in the question,

Given numbers are as follow : [tex]\sqrt{14} , \sqrt{5/2} , \sqrt{9/16} , 1, 11[/tex]

Approximate value of all given numbers

[tex]\sqrt{14} =3.74\\\\\sqrt{5/2}= 1.58\\ \\\sqrt{9 /16} = 0.75\\ \\1 =1.00\\\\11=11.00[/tex]

Arrange the given numbers in decreasing order :

11 > 3.74 > 1.58 > 1 > 0.75

[tex]\implies 11 > \sqrt{14} > \sqrt{5/2} > 1 > \sqrt{9/16}[/tex]

Therefore, given numbers[tex]\sqrt{14} , \sqrt{5/2} , \sqrt{9/16} , 1, 11[/tex]  in decreasing order are as follows:  [tex]11, \sqrt{14} , \sqrt{5/2}, 1, \sqrt{9/16}[/tex] .

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The number of students that did major in the north is 300 and the number of student that do major in the south is 700.

At the north campus of a performing arts school, 30% of the students are music majors.

At the south campus, 80% of the students are music majors.

let

x = number of student at the north campus before the merger

Therefore,

1000 - x = number of students at the south campus before the merger

Hence, the equation for the music majors in the merger is as follows:

0.3x + 0.8(1000 - x) = 0.65(1000)

0.3x + 800 - 0.8x = 650

-0.5x = 650 - 800

-0.5x = -150

divide both sides by -0.5

x = -150 / -0.5

x = 300

Therefore, the number of students that did major in the north is 300 and the number of student that do major in the south is 700.

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"If the congruent sides in one isosceles triangle have the same measure as the congruent sides in another isosceles triangle, then the triangles are congruent."

The given statement true.

When two angles become congruent, their degree measures are the same. The reverse of something like the Isosceles Triangle Theorem asserts that the sides of a triangle opposing congruent angles are also congruent.

If two two triangles are congruent, then perhaps the sides opposite the congruent angles are equal, in accordance with the isosceles triangle theorem converse.

Mathematics is defined by theorems. A theorem is a proposition that has been proven true by a rigorous proof, which is a type of logical argument.

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Trent writes 10×6=60, then in multiplication equation 10 represents the quantity of muffin boxes, 6 represents the numbers of muffins in each box and 60 represents the full numbers of muffins.

According to the statement

We have to find that the multiplication equation.

So, For this purpose, we know that the

The linear equation is defined as an equation that is written in the form of Ax+By=C.

From the given information:

Given,

Trent writes 10×6=60,

Here,

10 represents the quantity of muffin boxes

And

6 represents the numbers of muffins in each box

Then

60 represents the overall numbers of muffins

Hence, Trent writes 10×6=60, then within the multiplication equation 10 represents the amount of muffin boxes, 6 represents the numbers of muffins in each box and 60 represents the full numbers of muffins.

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Mr. Wong paid 63.75 for the car rental.

The cost of rental car will be added one time to the total rent. The cost of trip will be calculated based on the distance covered.

So, forming the equation -

Total cost = 30 + 45 × 0.75

Performing multiplication on Right Hand Side of the equation to find the cost of business trip based on miles distance traveled

Total cost = 30 + 33.75

Performing addition on Right Hand Side of the equation to find the total cost based on one time rent of car and distance traveled

Total cost = 63.75

Hence, the total cost of car rental on business trip is 63.75.

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The exponential function is y=2000(4/5)ˣ. 0.8 is the decay factor and 0.2 is the decay rate.

Given that,

The exponential function is y=2000(4/5)ˣ.

Parts of exponential function.

The general equation for an exponential growth function is :

y=a(b)ˣ

a is the initial value.

1. If b>1, growth. Then b is growth factor. r is the growth rate is b=1+r.

2. If 0<b<1, decay. Then b is decay factor. r is the decay rate is b=1-r.

Now, from the given y=2000(4/5)ˣ.

2000 is the initial value.

4/5=0.8 which is 0<0.8<1

So, 0.8 is the decay factor.

Decay rate r is

b=1-r

r=1-b

r=1-0.8

r=0.2

Therefore, 0.8 is the decay factor and 0.2 is the decay rate.

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Using an inequality, Plan 1 is more economical than Plan 2 given that the number of monthly phone calls is greater than 200.

If Plan 1 charges 31$ per month for unlimited calls, then the total cost per month of using Plan 1 is also 31$.

Plan 1 = 31$

If Plan 2 charges 13$ per month plus 0.09$ per call, we can express the total cost per month of using Plan 2 as:

Plan 2 = 13 + 0.09x

where x is the number of monthly phone calls

Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.

If Plan 1 is more economical than Plan 2 then the monthly cost of Plan 1 is less than the monthly cost of Plan 2.

Plan 1 < Plan 2

31 < 13 + 0.09x

Solving for x.

31 - 13 < 13 + 0.09x - 13

18 < 0.09x

200 < x

x > 200

the number of monthly phone calls > 200

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Answer:

Proportion says that two ratios (or fractions) are equal.

La proporción dice que dos razones (o fracciones) son iguales.

( translated )

Answer:

No solution is what I got if you solve for x

Step-by-step explanation:

Hope this helps!!

Answer: It is irrelevant if multiplying or dividing decimal numbers. For addition and subtraction it is not sufficient: you need to line up the decimal points as well as the digits according to their place values. If you intend to simply align the decimal points then you may as well not bother.

Step-by-step explanation:

Answer: 18 Days

Step-by-step explanation: 30x18=540

The sum of the annual salary and the annual contribution toward health insurance from the employer is $36,420.

Given,

Imagine that an employer purchases a health insurance plan that costs $365 per month, but requires that the employee pay $35 per month toward the cost of the plan.

The employee's salary is $36,000 per year.

We need to find what is the sum of the annual salary and the annual contribution toward health insurance from the employer.

We divide the total value by the number of items.

Example:

$120 = 5 items

1 items = 120 / 5 = $24

We have,

Health insurance plan costs = $365

Employee pay = $35 per month.

The employee's salary = $36,000 per year.

The sum of the annual salary and the annual contribution toward health insurance from the employer;

=  $36,000 + $35 x 12 months

= $36,000 + $420

= $36,420

Thus the sum of the annual salary and the annual contribution toward health insurance from the employer is $36,420.

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The expression which represents the function evaluation (f -g)(x) according to the task content is; (f -g)(x) = 2x³ +5x² -8x -4.

It follows from the task content that the required function evaluation required is; (f -g)(x).

Given;

f(x) = 2x³ +5x² - 6x - 7

g(x)=2x-3

To find;

(f-g)(x).

Since; (f -g)(x) = f(x) - g(x), the resulting expression for (f -g)(x) is;

(f -g)(x) = 2x³ +5x² -6x -7 -2x +3

Collect like terms;

(f -g)(x) = 2x³ +5x² -6x -2x -7 +3

Hence, (f -g)(x) = 2x³ +5x² -8x -4

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The translation vector will be as follows:

(x, y) → (x - 3, y + 5)

Regina travelled 3 blocks west and 5 blocks north.

The interpretation vector is the distance through which a particle should be moved (made an interpretation of) to be in the following unit cell. The image for an interpretation vector is television. The television ought to be indicated toward the finish of the math.

The distance that an atom must travel in order to transfer to the following unit cell is known as the translation vector. A translation vector is denoted by the letter Tv. At the conclusion of the geometry, the Tv should be provided. Real or fake atoms shouldn't follow a Tv, but symmetry information and other things are acceptable.

Let us consider the direction similar to map where north is positive y-axis , east is positive x-axis , west is negative x-axis and south is negative y-axis.

Therefore the translation vector will be as follows:

(x, y) → (x - 3, y + 5)

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x = 29 is the value of x.

To find the value of x:

So,

Now, rounding to the nearest tenths gives x = 29.

Therefore, x = 29 is the value of x.

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O( 0,0 ) A(9 , 0 ) D( 0,3 ) ( 9, 2) , ( 6 , 3 ) that are vertices of the feasible region.

What do math vertices mean?

The line 2x + 6y = 30

when x = 9 , 18 + 6y = 30

                     y = 2

So B = ( 9, 2)

So, C= ( b , 3 )

then , we can show O( 0,0 ) A(9 , 0 ) D( 0,3 )

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