Help with this personal finance problem

1. Firstly, statement 1 is given in the question.

2. When two lines cut through two parallel lines, the alternate interior angles are congruent(equal)

So;

3. Given

4. PK = KT

Since K is the mid point of PT as stated in the question, then PK will be of equal length as KT.

5. Vertically opposite angles are equal.

So;

6. when two corresponding angles and the included side are respectively equal, a triangle is said to be congruent.

7. The Triangle Inequality theorem states that the sum of two sides of a triangle is greater than the third side.

8. CPCTC means that Corresponding Parts of Congruent Triangles are Congruent.

The corresponding sides of the two congruent triangles are;

So;

9. The final one is a conbination of CPCTC and Triangle Inequality theorem

The polynomial can be factorized in linear factors:

For (x^2) - 6x - 6 we use the general equation:

Then, our factors are:

The missing value for the letter B is 51.

Given,

A teacher gives pens and pencils to elementary students at an equal rate.

Pencil ; 21  33  45  B

Pen ; 63  A  135  153

We have to determine the missing value of B.

Here,

Ratio of pencil to pen for each student.

Each student get pencil and pen in the same ratio as 1/3

Then,

33/A = 1/3

33 × 3 = A

A = 99

Ratio = 33/99 = 1/3

45/135 = 1/3

B/153 = 1/3

3B = 153

B = 153/3 = 51

Ratio = 51/153

That is,

The missing value for the letter B is 51.

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The variable x has a value of 22.5 degrees

Angles are the measure of space when two or more lines intersect.

The figure represents the given parameter

On the figure, we have the following angle measures

AED = 2x

BEF = 4x

EBC = 6x

Using the above as a guide, we have the following angle measures

BAE = AED = 2x ---- Corresponding angles

BEA = 180 - BEF ---- Angle on a straight line

BEA = 180 - 4x

ABE = 180 - EBC ---- Angle on a straight line

ABE = 180 - 6x

The sum of angles in a triangle is 180

So, we have

BAE  + BEA + ABE  = 180

This gives

2x + 180 - 4x + 180 - 6x = 180

Evaluate the like terms

-8x = -180

Divide both sides by -8

x = 22.5

Hence, the measure of x is 22.5

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tank is 1/3 full

after he buys 9 gallons of gas it is 5/6

How many gallons can Jim's tank hold?

9 gallons = 1/2 tank

18 gallons is the capacity of the tank

Answer:

10 5/8

Step-by-step explanation:

First, we want to convert the mixed fraction to an improper fraction.

3 1/2 = 7/2

7 1/8 = 57/8

Now, we have to find the Least Common Denominator (LCD).

The LCD is 8.

We multiply the top and bottom by 4 because the denominator is 2, which multiplied by 4 is 8.

7  x  4  =  28
_               _
2  x  4  =   8

Now we have 28/8.

We add.

28/8 + 57/8 = 85/8.

85/8 simplified is 10 5/8.

Answer = 10 5/8

Hope this helps!

Btw, if this is correct, can I have Brainliest?

Thanks!

f(x) = 4 -2x^2

First we need to find f(6)

f(6) = 4 - 2( 6) ^2 = 4 - 2(36) = 4 - 72 = -68

Then we need to find

f(-6) = 4 - 2( -6) ^2 = 4 -2( 36) = 4 - 72 = -68

Now we find the average or mean slope

The mean slope is zero

Now f'(c) must equal 0

The derivative is -4x and evaluated at c

-4c

This must be equal to 0

-4c =0

Solving for c

c=0

From the statement, we know that:

• a jar contains 100 tickets for a drawing,

• among those tickets are 7 winning tickets.

We must find the odds in favour of winning.

The odds in favour of winning are:

Odds in favour = Number of successes : Number of failures

In this case, we have:

• Number of successes = 7,

• Number of failures = 100 - 7 = 93.

So we have:

7:93

Let's determine the cost of each banana based on the given data.

Number of Bananas Total Cost Price per Banana

4 $2.48 $0.62

8 $4.96 $0.62

12 $7.44 $0.62

lt appears that each banana cost $0.62.

Thus, buying 7 bananas, it'll cost:

7 x 0.62 = $4.34

The answer is letter C.

The statement which is true is Option(D) The output value of the function is 8 when the input value is -2.

An expression, rule, or regulation that establishes a relationship between one variable (the independent variable) and another variable (the dependent variable) is referred to as a function in mathematics.

Given function:

H(x) = -x + 6

In Option A, the input value is -2 so the output of the function will be,

H(x) = -x + 6 = -(-2) +6 = 2+ 6 = 8 ,which is not equal to the given output value 4.

Hence, the statement is false.

Similarly in Option B and C, the input values are 1 and x.

H(x) = -x + 6 = -1 +6 = 5 ≠ 7

H(x) = -x + 6 ≠ 6

The given output values are not equal to the output values calculated.

So both statements are false.

In Option D the input value is -2 and the output value is 8 which is a correct statement as calculated in Option A.

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Answer

The shoes cost $14.03 at Walmart.

Explanation

The markup, the selling price and the cost price are all related through the relation

For this question,

Markup percent = 65%

Selling Price = x = ?

Cost Price = $8.50

x - 8.5 = (0.65) (8.5)

x - 8.5 = 5.525

x = 8.5 + 5.525

x = $14.025

x = $14.03

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Given that the side of the square is 1.6 yards.

The area of the square is

Substitute a=1.6, we get

We need to convert yards to inches.

We know that

Taking square on both sides, we get

Multiplying by 2.56 on both sides, we get

Rounding to the nearest tenth, we get

Hence the area of the given square is 3317.8 square inches.

A function to represent the relation is  f = q × p, the quantity that maximizes value could only be when q = p, therefore p = 200 so, q = 200 too according to demand function q = 1200 - 5p.

In mathematics, the relationship between demand and its factors is represented by a demand function. The function demonstrates how elements like a product's own price, buyer income, and the cost of related products affect demand for a given good (substitutes and complements).

We can deduce from the equation how they influence a product's demand, whether positively or negatively, and how much.

A function for generated revenue is simply f = q × p

where f is the generated revenue and

q is the quantity and

p is the price.

The quantity that maximizes value could only be when q = p

Lets substitute the value of q in q = 1200 - 5p,

q + 5p = 1200

But q = p so

p + 5p = 1200

6p = 1200

p = 1200/6

p = 200

So when price is 200 the revenue will be maximized as the quantity is equal to as price.

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Answer:

x=-1

Step-by-step explanation:

make equation

-2x-3=x

-3=3x

-1=x

Answer:

x=-1

Step-by-step explanation:

-x+-x-1-1-1 = x

-2x-3=x

3x=-3

x=-1

The solution to the system of equations using Cramer's rule is given by the image at the end of the answer.

The solution of a system of equations using Cramer's rule is based on the use of determinants of matrices.

In the context of this problem, the system is:

The matrix for the system is:

M =

[1 2]

[-3 - 2]

The determinant of the matrix M of the system is given as follows:

|M| = -2 + 6 = 4.

(using the standard procedure to obtain the determinant of a 2 x 2 matrix).

To find the matrix for x, the x-coefficients are replaced by the right-side coefficients, that is, the results of the operations, hence:

Mx =

[8 2]

[12 - 2]

Then the determinant is:

|Mx| = 8(-2) - 2(12) = -16 - 24 = -40.

The solution for x is:

x = -40/4 = -10.

To find the matrix for y, the y-coefficients are replaced by the right-side coefficients, that is, the results of the operations, hence:

My =

[1 8]

[-3  12]

The determinant is:

|My| =  12 - (-3)(8) = 12 + 24 = 36.

Hence the solution is:

y = 36/4 = 9.

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The correct steps to transform x² + 10x + 24 = 0 into the form (x − p)² = q is a.

Step 1 x² + 10x + 24 − 1 = 0 − 1

Step 2 x² + 10x + 23 = −1

Step 3 (x + 5)² = −1 and

d.

Step 1 x² + 10x + 24 + 1 = 0 + 1

Step 2 x² + 10x + 25 = 1

Step 3 (x + 5)² = 1

Factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.

a² + b² + 2ab = (a + b)²

Given: x² + 10x + 24 = 0

= x² + 2x × 5 + 24

so b² has to equal 25 = 5²

Now, x² + 10x + 24 = 0

x² + 2x × 5 + 24 + 1 = 0 + 1

simplifying the above equation, we get

x² + 2x × 5 + 25 = 1

(x + 5)² = 1

Therefore, the correct answer is option

a.

Step 1 x² + 10x + 24 − 1 = 0 − 1

Step 2 x² + 10x + 23 = −1

Step 3 (x + 5)² = −1 and

d.

Step 1 x² + 10x + 24 + 1 = 0 + 1

Step 2 x² + 10x + 25 = 1

Step 3 (x + 5)² = 1

The complete question is:

Which of the following tables shows the correct steps to transform x² + 10x + 24 = 0 into the form (x − p)² = q?[p and q are integers] (5 points)

Select one:

a.

Step 1 x² + 10x + 24 − 1 = 0 − 1

Step 2 x² + 10x + 23 = −1

Step 3 (x + 5)² = −1

b.

Step 1 x² + 10x + 24 − 2 = 0 − 2

Step 2 x² + 10x + 22 = −2

Step 3 (x + 5)² = −2

c.

Step 1 x² + 10x + 24 + 2 = 0 + 2

Step 2 x² + 10x + 26 = 2

Step 3 (x + 5)² = 2

d.

Step 1 x² + 10x + 24 + 1 = 0 + 1

Step 2 x² + 10x + 25 = 1

Step 3 (x + 5)² = 1

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33. For this problem you have to sole the following system of equations.

x+y=531

5.75x+1.25y=2013.75

After you solve the system of equations you get that

x=300, y=231

Therefore 300 full-price tickets were sold.

34. Since water is not acid, you have to solve the following equation

0*Water + 0.40*50 = 0.30*(Water+50)

After you solve the equation you get

Water = 16.67

So, you have to add 16.67 ML of water.

and that's the solution for 34.

35.

The next problem is very easy, notice that 12/6 = 2 and 4/6 = 0.666666=0.67 , therefore the scale factor would be 6. And that would be it.

The range of the function, y = 16x, is 60, where y is 960.

The range of the function, y = 16x, are the possible values that x can assume to meet the value of y.

Usually, the range of a function is the output value.

Since the value of y = 960, the range of the function will be 60 (960/16).

The capacity of the dispenser = 960 ounces

The capacity of the juice containers = 16 ounces

The function that models the situation is y = 16x

Where y = 960

x = 60 (960/16)

Thus, the implication is that the range of the function or the number of 16-ounce containers that can fill the dispenser with a capacity of 960 ounces is 60.

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The probability of selecting or having a marble to be either a blue marble or a stone marble is 0.8076.

Given, a bag contains 6 blue glass marbles, 5 yellow glass marbles,

12 blue stone marbles and 3 yellow stone marbles.

Probability of selecting a marble and having that marble to be either blue marble or a stone marble = ?

we know that,

Glass marbles:

n(B) = 6 and n(Y)= 5

Stone marbles:

n(B) = 12 and n(Y) = 3

Probability = Number of favorable outcomes/Total number of outcomes.

Probability of selecting a marble and having that marble to be either blue marble or a stone marble:

total number of blue marbles = 18

total number of stone marbles = 15

total number of marbles in the bag = 26

⇒ 18+15-12/26

⇒ 33-12/26

⇒ 21/26

= 0.8076

Hence the probability of selecting a marble and having that marble be either a blue marble or a stone marble is 0.8076.

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The equation to solve:

We can subtract the like terms on the left hand side:

Now, we can divide both sides by 0.9 and solve for x. Shown below:

The answer is

Answer: x = 60

Step-by-step explanation:

   To solve for x, we will isolate the variable with simplifying and reverse operations.

   Given:

x - 0.1x = 54

   Subtract 0.1 from 1:

0.9x = 54

   Divide both sides of the equation by 0.9:

x = 60

Given:

5 tiels cover the area 90square inch.

bathroom floor area is 3024

1 tiles cover the area is 18 square inch.

Let n tiles cover 3,024 square inch then:

So 168 tiels required for cover the bathroom floor.

Answer:

105

Step-by-step explanation:

Let x, y and z be the 3 numbers in the order first, second and third

x + y + z = 180

Second number y is 3 times the smallest number and third number z is 7 times the smallest number. So smallest number has to be x

so y = 4x

z = 7x

x + y + z = x + 4x + 7x = 180

12x = 180

x = 15

Largest number = 7 x 15 = 105

To simplify the expression, we need to operate the like terms, then:

Therefore:

The domain of a function, are the values for which the function is defined on the x-axis,

Let the function:

denominator can't be

The experimental probability of rolling such that the number is more than 3 is 0.44.

The proportion of outcomes where a specific event occurs in all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.

When a dies is rolled 200 times, the results are:

Frequency     Outcome

     1                     32

     2                    36

     3                    44

     4                    20

     5                    30

     6                    38

Therefore,

The experimental probability that a number is more than 3 after rolling will be:

= The sum of outcome above 3 / total outcome

= ( 20 + 30 + 38 ) / ( 32 + 36 + 44 + 20 + 30 + 38 )

= 88/ 200

= 0.44

Hence, the probability that the number is more than 3 is 0.44.

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we know that

Erica

The sequence in minute is

15,30,60,120,240,480,960

This is a geometric sequence

where

r=30/15=2 ----> common ratio

the recursive formula For n>1 is equal to

Find out the explicit formula

where

a1=15

r=2

Naomi

we have the sequence in hours

3 3.5 4 4.5 5 5.5 6

This is an arithmetic sequence

where

d=3.5-3=0.5 ----> the common difference

the recursive formula For n> 1 is equal to

Find out the explicit formula

where

a1=3

d=0.5

substitute

Given:

The height of tallest man is 2510 mm.

Explanation:

The conversion unit for mm to meter is,

Determine the height in meters.

So height of tallest man Sultan Kosen is 2.510 meters.

Answer: 2.510 meters

Answer:

y = -800x + 294000

286,000

Step-by-step explanation:

To write the equation, you need the slope and the y-intercept.  

The slope is -800

You find the slope by the change in y over the change in x

[tex]\frac{288400 - 294000}{7 - 0}[/tex] = [tex]\frac{15600}{7}[/tex] = -800

Now we will find the y -intercept.  I will use the slope and the point (0, 294,000) to find this.  I could have used the other point given. They will both work.

slope (m) = -800

x = 0

y = 294000

y = mx + b

294000 = -800(0) = b

294000 = b

The equation is

y = mx + b

y = -800x + 294000

2014

y = -800x + 294000

y = -800(10) + 294000

y =-8000 + 294000

y  = 286,000