Find the slope of the line shown below

(a) 20% of $224,000 is $44,800.

(b) 3 points on a $224,000 mortgage is $6,720.

(c) $44,800 + $6,720 is $51,520. So the total down payment and closing costs are $51,520.

(d) The mortgage amount is $224,000 - $51,520 = $172,480.

(e)

Monthly payment = $172,480 * (7%/12%)(30 years) = $1,234.15

Total interest paid over 30 years = $172,480 * 7% * 30 years = $243,720

A recursive definition for the set S of ordered pairs of positive integers (a,b) where a is a factor of b can be given as follows:

1. The ordered pair (1, b) is in S for all positive integers b.

2. If a is a factor of b, then (a, b) is in S if and only if (a, b/a) is in S.

The first rule establishes the base case for the recursion, stating that (1, b) is in S for all b. The second rule provides the recursive step, stating that (a, b) is in S if and only if (a, b/a) is in S, where b/a is an integer division of b by a, and a is a factor of b. This recursive definition ensures that all pairs (a, b) in S have a as a factor of b.

Answer:

1.  Not true, so (5,2) is not a solution

2. Not true, so (-3,-6) is not a solution.

3. Not true, so (0, [tex]\frac{2}{3}[/tex]) is not a solution.

Step-by-step explanation:

Substitute 5 for x and 2 for y

1 - y > x - 6

1 - 2 > 5 - 6

-1 > -1

This is not true. -1 is not greater than -1

y < x - 1

Substitute -3 for x and -6 for y

2 - y [tex]\leq[/tex] 2x

2 - (-6) [tex]\leq[/tex] 2(-3)

8 [tex]\leq[/tex] -6  

This is not true. 8 is not less than -6.

y [tex]\geq[/tex] x

Substitute 0 for x and [tex]\frac{2}{3}[/tex]

3 - [tex]\frac{1}{2}[/tex] x + 3y < 8

3 - [tex]\frac{1}{2}[/tex] (0) + 3([tex]\frac{2}{3}[/tex]) < 8

3 - 0 + [tex]\frac{6}{3}[/tex] < 8

3 + 2 < 8

6 < 8

This is true. 6 is less than  8

y [tex]\geq[/tex] 1

[tex]\frac{2}{3}[/tex] [tex]\geq[/tex] 1

This is not true. [tex]\frac{2}{3}[/tex] is not greater than or equal to one.  

The ordered pair has to be a solution for both equations for the ordered pair to be a solution for the system.

Helping in the name of Jesus.

The value of (2x^4+x^3-x^2+3)+(4x^4-2x^3-x^2+10x+2) is 6x⁴-x³-2x²+10x+5

Expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)

Adding two expressions together requires to collect like terms. like terms are terms with similar variable. For example, in 2x²+6x+x² , x² and 2x² are like terms.

Therefore, 2x⁴+x³-x²+3 + 4x⁴-2x³-x²+10x+2 can be simplified as;

2x⁴+4x⁴+x³-2x³-x²-x²+10x+2+3

= 6x⁴-x³-2x²+10x+2

therefore, the value of 2x⁴+4x⁴+x³-2x³-x²-x²+10x+2 is 6x⁴-x³-2x²+10x+5.

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Step-by-step explanation:

a 1/15 for getting 0

b 2/14 for getting u

c 2/210 or 3/210

Answer:

Step-by-step explanation:

To find the average mass of the six people, we need to divide the total mass by the number of people.

The total mass of the six people is 1/2 tonne, which is equivalent to 500 kg (since 1 tonne = 1000 kg).

So, the average mass of the six people is:

500 kg / 6 = 83.33 kg (rounded to two decimal places)

Therefore, the average mass of each person is approximately 83.33 kg.

The expression is equal to 2 is 5 x (one-third x 6) ÷ 5. The correct option is C.

A mathematical expression is the collection of mathematical symbols that results from the proper combination of numbers and variables using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions.

Can be simplified each of the expressions see if them equals 2:

4 x (one-half x 6) ÷ 3 = 4 x 3 ÷ 3 = 4

6 ÷ (one-fourth x 3 x one and one-fourth) = 6 ÷ (3/4 x 5/4) = 6 ÷ (15/16) = 96/15 ≠ 2

5 x (one-third x 6) ÷ 5 = 5 x 2 ÷ 5 = 2

10 − (one-fifth x 10) + 1 = 10 - 2 + 1 = 9 ≠ 2

Therefore, the correct option is c. 5 x (one-third x 6)

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Oliver withdraws an amount of $285.10 from his saving account and the interest is $26.60

Compound interest is a type of interest that is paid on the closing balance at the end of the previous year, which includes the interest paid in previous years.

His saving account earns 1.8% annually

The interest Oliver could have earned in five months:

Monthly interest = Annual interest ÷ 12

Monthly interest = 1.8% ÷ 12

Monthly interest = 0.018 ÷ 12 = 3/2000

A = P(1 + r)n

After five months = Principle × (1 + interest)ⁿ

After five months = 285.10 × (1 + 0.018)⁵

After five months = 311.70

Interest earned = 311.70 - 285.10 = $26.60

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Answer:

140

Step-by-step explanation:

First you want to add up the numbers inside of the hexagon and set them equal to 720. Your starting equation should be 3x+240=720. Then your going to subtract 240 from each side giving you 3x=480. Next divide each side by 3 giving you x=160. Plug 160 in for x and you should get 160-20= 140.

Answer:

140

Step-by-step explanation:

First you want to add up the numbers inside of the hexagon and set them equal to 720. Your starting equation should be 3x+240=720. Then your going to subtract 240 from each side giving you 3x=480. Next divide each side by 3 giving you x=160. Plug 160 in for x and you should get 160-20= 140.

The expression 8x^3/2 × -7x^2/3 can be simplified to give

To reduce the given expression, we can employ the principles of exponents and carry out the multiplication.

The given expression is:- 8x^(3/2) * (-7x^(2/3))

Utilizing this property, combining two terms with exponents entails adding the exponents when they feature the same bases. Thus, we establish:

8 * (-7) = -56 (coefficient multiplication)

x^(3/2 + 2/3) results in x^(13/6) (exponent addition)

Bringing it all together, we have:

8x^(3/2) * (-7x^(2/3)) = -56x^(13/6)

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The area under the curve is 522 units².

The area under the curve is calculated by integrating the function and finding the definite integra as shown below.

f(x) = 8x + 10

The integra of the function;

f(x)' = 4x² + 10x

Find the definite integra at the boundaries, x = 19 and x = 22

f(19)' = 4(19)² + 10(19)

F(19)' = 1,634

f(22)' = 4(22)² + 10(22)

F(22)' = 2,156

Area = 2,156 - 1,634 = 522 units²

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The equation to find the total number of lessons is T = 6 + 12 = 18, and the ratio to find the total cost of the lessons is c:T = 72:18 or  4:1.

The equation to find the total number of lessons (T) can be written as:

T = number of salsa lessons + number of rumba lessons

Substituting the given values, we get:

T = 6 + 12 = 18

The ratio to find the total cost of the lessons (c) can be written as:

c = cost per lesson x total number of lessons

Substituting the given values, we get:

c = $4 x 18 = $72

Therefore, the equation to find the total number of lessons is T = 6 + 12 = 18, and the ratio to find the total cost of the lessons is c:T = 72:18 = 4:1.

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The percent error is 25%

The first step is to calculate the error

= 5 - 4

= 1

The percent error can be calculated as follows

= 1/4 × 100

= 0.25 × 100

= 25%

Hence the percent error is 25%

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The length of the side DC is 10.099 units.

Similar triangles are those triangles whose corresponding sides are in the same ratio. And the corresponding angles measure the same. It is denoted by the ‘~’ symbol.

Given that DE is parallel to AB. Therefore, the two triangles, ΔCDE and ΔABC are similar to each other.

For a similar triangle, the ratio of the corresponding sides are in the same ratio, therefore, it can be written as,

DC/AC = DE/AB = CE/BC

Take the first two terms,

DC/AC = DE/AB

DC × AB = DE × AC

As the length of AB is the same as the length of DC,

DC × DC = DE × AC

DC² = 6 units × 17 units

DC² = 102 units²

DC = 10.099 units

Hence, the length of the side DC is 10.099 units.

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The complete question with the image of the triangle is mentioned below.

Question: In the diagram below, DE is parallel to AB. if the length of AB is the same as the length of DC, AC=17, and DE=6, find the length of DC.

For the function in the graph the range is option B: 40≤f≤100.

The collection of all potential output values (y-values) that a function could produce is known as the function's range. It is, in other words, the entire set of values that the function is capable of accepting as its input changes across its domain. The collection of all potential output values (y-values) that a function could produce is known as the function's range. It is, in other words, the entire set of values that the function is capable of accepting as its input changes across its domain.

The range of the function is the output values, or the y-coordinates of the function.

For the given graph, the output of the function is from 40 to 100 thus, the range is:

40≤f≤100

Hence, for the function in the graph the range is option B: 40≤f≤100.

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Complete paragraph proof would be detailed proof.

Given that M is the midpoint of PK and PK ⊥ MB, we need to prove that △PKB is isosceles.

Proof,

Since M is the midpoint of PK, PM ≅ KM.

Also, since PK ⊥ MB, we have ∠PMB and ∠KMB are right angles.

Since right angles are congruent, we have ∠PMB ≅ ∠KMB.

Now, by the SAS congruence theorem, we have △PMB ≅ △KMB because they share side MB, and PM ≅ KM and ∠PMB ≅ ∠KMB.

Thus, we have BP ≅ BK because corresponding parts of congruent triangles are congruent.

Therefore, △PKB has two congruent sides and isosceles by definition.

Hence, we have proven that △PKB is isosceles.

Correct Question :

Complete the paragraph proof. Given: M is the midpoint of PK PK ⊥ MB Prove: △PKB is isosceles It is given that M is the midpoint of PK and PK ⊥ MB. Midpoints divide a segment into two congruent segments, so PM ≅ KM. Since PK ⊥ MB and perpendicular lines intersect at right angles, ∠PMB and ∠KMB are right angles. Right angles are congruent, so ∠PMB ≅ ∠KMB. The triangles share MB, and the reflexive property justifies that MB ≅ MB. Therefore, △PMB ≅ △KMB by the SAS congruence theorem. Thus, BP ≅ BK because . Finally, △PKB is isosceles because it has two congruent sides.

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Answer:

1) Michele

2) f(t)

3) Elisa's puppy

4) g(x)

Step-by-step explanation:

This is because Michele's situation has a rate of change of -10, f(t) has -6.2, Elisa's puppy's situation has a rate of change of +5, and g(x) has 8.1

Hence,

-10 < -6.2 < 5 < 8.1

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If Thabang and Ndivhu decided to share their money according to hours, then Thabang will receive R240.

Thabang worked for 3 hours and Ndivhu worked for 2 hours.

Together, they worked for a total of 5 hours. They were paid R400 for their work,

So, we calculate their hourly-rate by dividing the total amount by the total number of hours worked;

⇒ Hourly rate = (Total amount paid)/(Total number of hours worked),

⇒ Hourly rate = R400/5,

⇒ Hourly rate = R80 per hour,

Now, we find amount Thabang will receive if it is decided to share the money according to "hours-worked".

Thabang worked for 3 out of the total 5 hours, so he should receive 3/5 of the total amount paid,

⇒ Amount Thabang will receive = (Hours Thabang worked / Total hours worked) × Total amount paid,

⇒ Amount Thabang will receive = (3/5) × R400,

⇒ Amount Thabang will receive = R240,

Therefore, Thabang will receive R240 if they decided to share their money according to hours worked.

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The given question is incomplete, the complete question is

Thabang and his friend Ndivhu share a job of cleaning a neighbors yard and they were paid R400, Thabang worked 3 hours and Ndivhu worked for 2 hours. Determine the amount Thabang will receive if they decided to share their money according to hours​.

The value of h is ( -1/3, -2/3)

Quadratic equation is a type of equation in which the highest power of variable is 2. A quadratic equation is represented as ax²+bx + c = 0

Solving, 9h²+9h = -2

9h²+9h+2 = 0

9h² +6h +3h +2 = 0

(9h²+6h) ( 3h +2) = 0

3h( 3h + 2)+1 ( 3h+2) = 0

(3h+2)(3h+1) = 0

Therefore ;

3h+2 = 0

3h = -2

h = -2/3 or

3h+1 = 0

3h = -1

h = -1/3

therefore the value of h is ( -1/3, -2/3)

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ANSWER:

They have $1,100 altogether.

EXPLANATION:

- Originally, Mike had $500, while Joel had $600. That adds up to $1,100, and it makes Joel have $100 more than Mike.

- Half of Joel’s $600 is $300, which he gave to Mike. That makes Joel now have $300 himself.

- Adding $300 to Mike’s $500 is $800, which means Mike now has $800.

- $800 (Mike’s new amount) minus $300 (Joel’s new amount) is $500, which works because Mike now has $500 more than Joel.

-$300 + $800 is, of course, still $1,100.

Answer:

[tex] - 9 {g}^{3} + {g}^{2} + 10g - 5[/tex]

Answer:

x = 115°

Step-by-step explanation:

The interior angle adjacent to the 115° angle measures:

180° - 115° = 65°

x is an exterior angle, so x = 65° + 50°

x = 115°

Answer:

115

Step-by-step explanation:

X has to be supplementary to that adjacent angle, so first the angle next to the 115 has to be defined. 180-115 (as the must be supplementary) is 65. 65+ 50= 115, which should be x. The 2 opposite angles will equal the opposite outside angle. Hope this helps!

The distance from the ball to the center of the green (CD) is approximately 13.2 yards.

Given:

AB = 110 yards (distance from marker to center of the green)

BC = 45 yards (distance from marker to golfer's ball)

angle BAC = 115° (angle formed when golfer turns towards the ball)

To find CD (distance from ball to center of the green):

Apply the cosine function to angle BAC:

cos(115°) = AB/BC  (∵cos θ = Adjacent side/ Hypotenuse)

Substitute the given values:

cos(115°) = 110/45

Calculate cos(115°):

cos(115°) ≈ -0.2924 (rounded to four decimal places)

Multiply both sides by BC to solve for AB:

AB = BC * cos(115°)

AB ≈ 45 * -0.2924

AB ≈ -13.16 yards (rounded to two decimal places)

Note: (The AB is negative, as the ball is moving in the opposite direction of the golfer's turn.)

CD = |AB| ≈ 13.16 yards (rounded to two decimal places)

CD ≈ 13.2 yards (rounded to one decimal point)

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The market's required rate of return for Samsung's common stock is 5.53%, rounded to two decimal points

What is meant by the rate of stock?

The rate of stock refers to the price at which a particular stock is being bought or sold in the stock market, which can vary based on supply and demand.

What is decimal?

A decimal is a number system that uses the base 10 and includes a decimal point to separate the integer part from the fractional part. It is commonly used in mathematics and everyday life for expressing fractions, percentages, and monetary values.

According to the given information

We can use the constant-growth dividend discount model to calculate the market's required rate of return for the stock. The model is:

Current stock price = Dividend next year / (Required rate of return - Dividend growth rate)

We know the current stock price is $216, the dividend next year is $1.14, and the dividend growth rate is 5%. We need to solve for the required rate of return.

216 = 1.14 / (r - 0.05)

Multiplying both sides by (r - 0.05), we get:

216(r - 0.05) = 1.14

Expanding the left side, we get:

216r - 10.8 = 1.14

Adding 10.8 to both sides, we get:

216r = 11.94

Dividing both sides by 216, we get:

r = 0.0553 or 5.53%

Therefore, the market's required rate of return for Samsung's common stock is 5.53%, rounded to two decimal points

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The market's required rate of return for Samsung's common stock is 5.53%, rounded to two decimal points

What is meant by the rate of stock?

The rate of stock refers to the price at which a particular stock is being bought or sold in the stock market, which can vary based on supply and demand.

What is decimal?

A decimal is a number system that uses the base 10 and includes a decimal point to separate the integer part from the fractional part. It is commonly used in mathematics and everyday life for expressing fractions, percentages, and monetary values.

According to the given information

We can use the constant-growth dividend discount model to calculate the market's required rate of return for the stock. The model is:

Current stock price = Dividend next year / (Required rate of return - Dividend growth rate)

We know the current stock price is $216, the dividend next year is $1.14, and the dividend growth rate is 5%. We need to solve for the required rate of return.

216 = 1.14 / (r - 0.05)

Multiplying both sides by (r - 0.05), we get:

216(r - 0.05) = 1.14

Expanding the left side, we get:

216r - 10.8 = 1.14

Adding 10.8 to both sides, we get:

216r = 11.94

Dividing both sides by 216, we get:

r = 0.0553 or 5.53%

Therefore, the market's required rate of return for Samsung's common stock is 5.53%, rounded to two decimal points

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if Dwayne made 10 hours of long-distance calls at a rate of $0.10 per minute, his bill for that month would be $60. However, if the rate is different, the bill will be different as well.

The cost of long-distance calls can vary depending on the service provider and the country being called. Without that information, it's difficult to give an accurate answer to this question.

Assuming a standard rate of $0.10 per minute for long-distance calls, we can calculate Dwayne's bill as follows:

10 hours = 600 minutes (since there are 60 minutes in an hour)

600 minutes x $0.10 per minute = $60

Therefore, if Dwayne made 10 hours of long-distance calls at a rate of $0.10 per minute, his bill for that month would be $60. However, if the rate is different, the bill will be different as well.

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Answer:

Step-by-step explanation:

By the law of cosines, [tex](59.7)^2=52^2+41^2-2\cdot 52 \cdot 41 \cos(\angle R).[/tex]

Thus, after solving for [tex]\cos(\angle R)[/tex], we get [tex]\cos(\angle R) = 0.1925211.[/tex] So taking the inverse cosine then yields [tex]\boxed{\angle R = 1.377 \text{ rad}}.[/tex]

Answer:

Step-by-step explanation:

By the law of cosines, [tex](59.7)^2=52^2+41^2-2\cdot 52 \cdot 41 \cos(\angle R).[/tex]

Thus, after solving for [tex]\cos(\angle R)[/tex], we get [tex]\cos(\angle R) = 0.1925211.[/tex] So taking the inverse cosine then yields [tex]\boxed{\angle R = 1.377 \text{ rad}}.[/tex]

Answer:

1)   13    **Explained below **

2)   4    **Explained below **

3)   6

4)   8

5)   15

6)   2.64575    **Explained below **

Step-by-step explanation:

All 6 problems can be solved using the Pythagorean theorem using the following two rules

If x is the hypotenuse and a, b are the shorter sides then
[tex]x = \sqrt{a^2 + b^2}[/tex]

If x is one of the shorter sides and a (or b) is the other shorter side and c is the hypotenuse then

[tex]x = \sqrt{c^2 - a^2\\[/tex]  if a is the other shorter side

[tex]x = \sqrt{c^2 - b^2\\[/tex]  if b is the other shorter side

I will just demonstrate for  #1 , #2 and #6. You can figure out the reasoning behind the rest.

#1. x is the hypotenuse, 5 and 12 are legs(shorter sides)

[tex]x = \sqrt{5^2 + 12^2}\\\\x = \sqrt{25 + 144}\\\\x = \sqrt{169}\\\\x = 13\\\\[/tex]

# 2. x is one of the shorter sides (leg)

5 is the hypotenuse and 3 is the other shorter side

[tex]x = \sqrt{5^{2} - 3^{2}}\\\\x = \sqrt{5^{2} - 3^{2}}\\\\x = \sqrt{25 - 9}\\\\x = \sqrt{16}\\\\x = 4[/tex]

#6  hypotenuse is 4, short side = 3

[tex]x = \sqrt{4^{2} - 3^{2}}\\\\x = \sqrt{4^{2} - 3^{2}}\\\\x = \sqrt{16 - 9}\\\\x = \sqrt{7}\\\\x = 2.64575\\\\[/tex]

To produce 60 liters of a 55% acid solution, we would need 40 liters of the 50% acid solution and 20 liters of the 65% acid solution.

Let number of liters of 50% acid solution needed be = "x", and

Let number of liters of 65% acid solution needed to produce 60 liters of a 55% acid solution. be = y,

To solve for x and y, we can use the following system of equations:

The "total-volume" of the solution is 60 liters,

⇒ x + y = 60,    ...equation(1)

We know that, the total amount of acid in the solution is equal to the concentration of the final solution times its volume;

⇒ 0.50x + 0.65y = 0.55(60)     ...equation(2),

On simplifying equation(2),

We get,

⇒ 0.50x + 0.65y = 33,

From equation(1), we have ⇒ x = 60 - y,

Now, we substitute "x" into the second equation and solve for y)

⇒ 0.50(60 - y) + 0.65y = 33,

⇒ 30 - 0.50y + 0.65y = 33,

⇒ 0.15y = 3,

⇒ y = 20

So, we need 20 liters of the 65% acid solution.

⇒ x + y = 60,

⇒ x + 20 = 60,

⇒ x = 40,

Therefore, we need 40 liters of the 50% acid solution and 20 liters of the 65% acid solution to produce 60 liters of a 55% acid solution.

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If P(A)= [tex]\frac{2}{3}[/tex], P(B) = [tex]\frac{1}{4}[/tex] and P(A and B)= [tex]\frac{2}{7}[/tex], then the events A and B are dependent.

By comparing the probability of events A and B intersection (P(A and B)) to the product of their individual probabilities (P(A) * P(B)), we can find out whether the events are independent or dependent.

Condition of independent events,

If P(A) * P(B) = P(A and B)

Condition of dependent events,

If P(A) * P(B) ≠ P(A and B)

Given,

P(A) = [tex]\frac{2}{3}[/tex]

P(B) = [tex]\frac{1}{4}[/tex]

P(A and B) = [tex]\frac{2}{7}[/tex]

Calculating P(A) * P(B) and compare it to P(A and B):

P(A) * P(B) = [tex]\frac{2}{3}[/tex] * [tex]\frac{1}{4}[/tex] = [tex]\frac{2}{12}[/tex] = [tex]\frac{1}{6}[/tex]

Since P(A and B) ≠ P(A) * P(B), therefore events A and B are dependent.

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