Given:NP=MP,NP PL prove NPL≈MPL

Answer:

y = 1/3x + 8/3

Step-by-step explanation:

The slope of a line that is perpendicular to the line y = -1/3x + 7 is the negative reciprocal of the slope of the given line, which is -3. So, the slope of the perpendicular line is 1/3.

The point where the perpendicular line intersects the given line is also the point where the two lines intersect, which is (4,2) in this case. So, we can use this point to find the equation of the perpendicular line using the point-slope form of a line:

y - y1 = m(x - x1)

where m is the slope of the line and (x1,y1) is a point on the line.

In our case, the equation of the perpendicular line is:

y - 2 = 1/3(x - 4)

We can simplify this equation to obtain:

y = 1/3x + 8/3

Therefore, the equation of the perpendicular line is y = 1/3x + 8/3.

Alyssa has the money of worth $660

Eric has the money of worth $245

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

Let x be the amount Alyssa has.

Let y be the amount  Eric has.

alyssa has $75 less than three times eric

=> x= 3y - 75

Together they have $905

=> x + y =905

Substitute x

=> 3y - 75  +y = 905

    4y = 905 +75 = 980

    y = 980 /4 = 245

x= 3y - 75  = 3(245) - 75 = 660

Alyssa has  $660

Eric has  $245

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The equations found for the number of tickets sold when 22 tickets are sold on Monday and 30 per day after are sold by Madelyn, and 53 tickets are sold on Monday and 20 per day after that are;

Tickets sold by Madelyn is; y = 22 + 30·x

Tickets sold by Kaia is; y = 53 + 20·x

A system of equation obtained from the details in the question can be presented as follows

y = 22 + 30·x...(1)

y = 53 + 20·x...(2)

The appropriate method for solving the system is to equate equivalent values of one of the variable obtained from each equation in the system.

The solution of the system of equation is; x = 3.1, which indicates that it takes about 3.1 days for the number of tickets sold by Madelyn and Kaia to be equivalent.

An equation consists of two expressions that are joined by the 'equals to' (=) sign.

The number of tickets for the Winter Dance Madelyn sold = 22

Number of tickets per day Madelyn sold after that = 30 per day

Number of tickets Kaia sold on Monday = 53

Number of tickets per day Kaia sold after that = 20 per day

Let x represent the number of days since Monday, and let y represent the number of tickets sold

Therefore;

The number of tickets Madelyn sold, y = 22 + 30·x

The number of tickets Kaia sold, y = 53 + 20·x

The system of equations from the specified information is the equation for the number of tickets Madelyn sold and the number of tickets Kaia sold combined, which can be presented as follows;

y = 22 + 30·x...(1)

y = 53 + 20·x...(2)

The method of solving the equations is by plugging in the value of y from equation (1) in equation (2), as follows;
22 + 30·x = 53 + 20·x

30·x - 20·x = 53 - 22 = 31

10·x = 31

x = 31 ÷ 10 = 3.1

The meaning of the solution of the system of equation, x = 3.1, is that the number of days for the number of tickets sold by Madelyn and Kaia to be the same is about 3 days

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The measure of angle EHF is 63°

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

m∠EHG is a right angle.

This means,

m∠EHG = 90°

m∠EHF + m∠FHG = 90

m∠EHF + 27 = 90

m∠EHF = 90 - 27

m∠EHF = 63°

Thus,

The value of m∠EHF is 63°.

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1. In the simple interest equation, 687.5 = 550(1 + 0.05t), A. The value 550 represents the initial balance in the account, which means the account started with $550.

2. The account balance of a savings account opened with an initial deposit of $425.00, after 9 years if the account earns 2.7% simple interest annually, is C. $528.28.

3. The formula for the arithmetic sequence which begins with 56, 59, 62, 65, 68, … is C. f(n) = 56 + 3(n).

4. The equation, 816 = 600(1 + 9r), represents the amount of money earned on a simple interest savings account, where r is A. r = 0.04.

The simple interest system operates without compounding the interest.

Compounding implies that interest attracts interest.

1) 687.5 = 550(1 + 0.05t)

Principal = $550

Final amount after t years = $687.50

Simple interest rate = 0.05 or 5%

Time, t = [$687.5/$550 - 1]/0.05

= 5 years

2) Principal = $425.00

Time = 9 years

Simple interest rate = 2.7%

Amount after 9 years = $528.28 ($425 x 1 + (9 x 2.7%)

f(n) = 56 + 3(n)

Where n = 1:

f(n) = 56 + 3(1)

= 56 + 3

= 59

Where n = 2:

f(n) = 56 + 3(2)

= 56 + 6

= 62

4) Principal = $600

Amount after 9 years = $816

Simple interest rate = r

r = ($816/$600 - 1)/9

= 0.04

= 4%

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Answer:

Answer below

Step-by-step explanation:

1. The value 550 represents the initial balance in the account, which means the account started with $550.

2. (C) 528.28

425.00 x  2.7% x 9 = 103.275

Then we add 103.275 to the initial deposit of $425.00

425.00 + 103.275 = 528.275

Therefore the answer is (C) 528.28

3. The answer for this one is (A) f(n) = 56 + 3(n − 1)

So, as we can see the first value is 56 and the common difference is 3 and the rule for the nth term is [tex]a_{n} =a_{1} +d(n-1)[/tex] .

Therefore, its 56 + 3(n − 1)

4. For this one we solve for r and using a calculator its (A) r = 0.04

5. Oh also he doesn't have this one but its (C) 102

An auditorium has 30 seats in the first row, 38 seats in the second row, 46 seats in the third row, and so on. How many seats are in the 10th row?

60

93

102

110

As we can see the common difference is 8.

Then we use the rule for nth term which is [tex]a_{n} =a_{1} +d(n-1)[/tex]

[tex]a_{n} =30+8(n-1)[/tex]

[tex]a_{n} =30+8n-8[/tex]

[tex]a_{n} =22+8(10)[/tex]

[tex]a_{n} =22+80[/tex]

[tex]a_{n} = 102[/tex]

So therefore, the answer is (C) 102.

Answer:

New price = 0.06 x Original price

New price $1,968

The number of adult tickets  which were sold that day as calculated from the given data  is 29.

First, we must assign variables to what our "unknowns" are. Assume there are "A" number of adult tickets and "C" number of child tickets. To solve this problem, we will use two equations.

To begin, each adult ticket costs $8.90, and each kid ticket costs $5.30. When the sales totals for both types of tickets are added together, the total sale is $928.

This is represented by the following equation,

$8.90A + $5.30C = $928

Next, we know that multiplying the number of child tickets by three equals the number of adult tickets:

3 * C = A

Now we can answer our first problem by substituting 3 * C for A.

8.9 (3C) + 5.3C = 928

26.7C + 5.3C = 928

32C = 928

C = 29

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The original attendance of the video game club was 28.57 members.

To determine the original attendance of the video game club, you can use the following formula:

Original attendance = (Number of members lost) / (Percent of group that left)

Plugging in the values from the problem, we get:

Original attendance = (8 members) / (28%)

To solve this equation, you need to convert the percent to a decimal by dividing it by 100. This gives us:

Original attendance = (8 members) / (0.28)

Then, you can solve the equation by dividing the number of members lost by the decimal equivalent of the percent:

Original attendance = 28.57 members

Therefore, the video gaming club had 28.57 members when it first started.

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Parent function is represented by the graph is

B. The quadratic parent function

What is Parent function?

A parent function in mathematics is the most basic function within a family of functions that nonetheless upholds the definition of the entire family. For instance, displaystyle y=x2 is the simplest function in the family of quadratic functions with the general form displaystyle y=ax2+bx+c.

A parent function is an equation in the simplest form of a family of functions. There are many forms of parent functions such as: Linear functions: f(x)=x f ( x ) = x , where the degree of the function is 1 and represents a straight line.

The simplest parabola is y = x2, whose graph is shown at the right. The graph passes through the origin (0,0), and is contained in Quadrants I and II. This graph is known as the "Parent Function" for parabolas, or quadratic functions.

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Answer:

-5/3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)  ==> (x1, y1), (x2, y2) are the coordinates and

                                   m is the slope

  (x1, y1), (x2, y2)  ==> (x1=-4, y1=7), (x2=5, y2=-8)

m=(-8-7)/(5-(-4))  ==> plug in known values

m=(-15)/(5+4)  ==> simplify

m=-15/9

m=-5/3

The prices for filling a cavity can vary greatly depending on the dental practice. The interquartile range of $74 for 10 randomly selected dental practices in California is an indication of the amount of price variation for this procedure.

1. To find out how much prices for filling a cavity vary, an insurance company randomly selects 10 dental practices in California and asks for the cash (non-insurance) price for this procedure.

2. The insurance company then computes the interquartile range of the prices for each practice.

3. The interquartile range of $74 indicates the amount of price variation for filling a cavity at the 10 randomly selected dental practices in California.

The prices for filling a cavity can vary greatly depending on the dental practice. The interquartile range of $74 for 10 randomly selected dental practices in California is an indication of the amount of price variation for this procedure.

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Answer: x= -64

Step-by-step explanation: simplifying both sides of the equation

The number of quizzes still need to be graded is 17quizzes.

There are many different ways to define an equation. In terms of algebra, an equation is a claim that demonstrates the equality of two mathematical expressions.

For instance, the two equations 5x + 4 and 16, which are separated by the 'equal' sign, make up the equation 5x + 4 = 16.

Algebraic equations in mathematics frequently have one or more variables.

It is given that,

grades of the teacher out of 48 quizzes before school = 16

grades of the teacher of the remaining quizzes after school = 15

Let us assume 'X' as the number of quizzes still need to be graded.

then X= 48-16+15

          =48-31

          =17

Hence, The number of quizzes still need to be graded is 17quizzes.

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The number of quizzes still need to be graded is 17 quizzes.

   then X= 48-=48-31

    =17

Hence, The number of quizzes still need to be graded is 17 quizzes.

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The value of the numerical expression 70 / (7 - 2) will be 14. Then the correct option is B.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The numerical expression is given below.

⇒ 70 / (7 - 2)

Simplify the expression, then we have

⇒ 70 / (7 - 2)

⇒ 70 / 5

⇒ 14

The worth of the mathematical articulation 70/(7 - 2) will be 14. Then the right choice is B.

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The correct expression is given below.

70 / (7 - 2)

a. Harold's monthly payment is given as follows: $164.13.

b. The total amount paid is given as follows: $9,847.8.

c. The finance charge is of: $847.8.

The monthly payment formula is defined as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which the parameters are listed as follows:

The values of these parameters for this problem are given as follows:

P = 9000, r = 0.036, n = 5 \times 12 = 60.

Then:

r/12 = 0.036/12 = 0.003.

Then the monthly payment is calculated as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 9000\frac{(0.003)(1.003)^{60}}{(1.003)^{60} - 1}[/tex]

A = $164.13.

Then the total amount paid is of:

Total = 60 x 164.13 = $9,847.8.

Meaning that the finance charge is given as follows:

9847.8 - 9000 = $847.8.

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Harvey's mistake in this scenario is that he put the pigs on a bed of straw that could infect their belly buttons. Additionally, he did not ensure that they consume colostrum in the first hours of life.

When we have a pregnant sow and we have to manage the postpartum procedure, we must make sure of different necessary procedures so that the piglets are well and their lives are not at risk in the following hours or days.

Among the procedures necessary for the piglets to be well are breathing, feeding and hygiene. In detail, once the piglet is extracted from its mother, we must make sure that it is breathing correctly. Secondly, we must clean it properly and make sure that its navel is completely clean to avoid infections. Finally we must give colostrum as food within the following hours after birth.

Additionally, we must place it in a clean place where it is not exposed to possible bacteria or infections, so the option of putting it on a bed of straw would be ruled out due to hygiene for the pig.

According to the above, Harvey's mistake was that he did not clean the piglets when they were born, did not give them colostrum, and put them on straw. Actually, he made three mistakes.

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The range of the square footage values for the given mean , standard deviation and  95% confidence interval is equal to (1257.26 , 508.74).

As given in the question,

Sample size 'n' = 2

Sample mean '[tex]\bar{x}[/tex]' = 883 sq ft

Standard deviation 'σ' = 270 sq ft

95% confidence interval.

95% confidence interval = 1 - 0.95

                                        = 0.05

Critical value for 95% is [tex]Z_{0.05}[/tex] = 1.96

Population mean for the given confidence interval is given by :

= [tex]\bar{x}[/tex] ± [tex]Z_{0.05}[/tex] (σ / √n)

= 883 ± 1.96 ( 270 / √2)

= 883 ± 374.26

= ( 1257.26 , 508.74 )

Therefore , the range of the square footage values for the 95% confidence interval is equal to ( 1257.26 , 508.74 ).

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Answer:

2xy + 3x + 6y + 9

Step-by-step explanation:

2y times x = 2xy

3 times x = 3x

2y times 3 = 6y

3 times 3 = 9

Answer:

All Real Numbers

Step-by-step explanation:

I assume you are solving for x.
The Interval Notation would be: (-∞,∞)

The null and different hypotheses for hypothesis test are

[tex]H_{0}[/tex] : P =0.63 against [tex]H_{1}[/tex] p [tex]\neq[/tex] 0.63

Null hypotheses

Given that:

sample size (η)= 196

sample proposition (p^) = 114/196

Let p denote the population proportion of people who use a loyalty card.

The percentage of shoppers use loyalty cards in their stores has remittent from sixty-three in 2014. [That is, whether or not the proportion has shifted from zero to 1] .63]

Hence, the null and alternative hypothesis are

[tex]H_{0}[/tex] : P =0.63 against [tex]H_{1}[/tex] p [tex]\neq[/tex] 0.63

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Answer:

volume of cube= l^ 3

=(4x)^3

=64x^3 cubic units

Bob pays $22 per month as 39 is joining fee which is only for first month

What is an example of a slope intercept form?

Slope-Intercept Form Examples

Example 1: Assuming a line has a slope of 1/2 and intersects the y-axis at (0, -3). Find the line's equation. Y = x/2 - 3 is the solution to the line's equation. Example 2: Using the horizontal line slope intercept formula, determine the equation at which the y-axis intersects (0, 8).

How is a slope equation solved?

Write the equation of the line in slope-intercept form to determine the slope from the equation. Utilize inverse procedures to find y, then write it as y=mx+b. Since the slope is the x variable's coefficient, or the number before x, you can thus readily see the slope.

Given that:

y=22m+39

Slope of the function is 22 and it is membership fee of a month .

If bob wants to increase membership for a months , he has to pay 22 extra and joining fee of 39

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Answer:

60

Step-by-step explanation:

?=60, multiply each side of the ratio by 10 to get the answer

6×10:1×10

60:10

Answer:12

Step-by-step explanation:

270/3=90, this is the amount it costs for 1 person to go

1080/90=12

12 people can go for $1080

Observing the information provided and using concept of central tendency parameters of statistics, The central tendency which we can immediately determine is median.

A field of mathematics that deals with gathering, analyzing, interpreting, and presenting vast amounts of numerical data.

The statistical test that determines whether a single result accurately represents a whole distribution is known as measure of central tendency.

total students = 40.

half = 20 students.

20 have scores below 77% and 20 have above 77%.

Thus, We can immediately determine that the median of score is 77%.

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The expression that represents c in terms of A, h, and d would be c = (2A/h) - d.

What is the area of the trapezium?

The formula for the area of a trapezium is A = h(c + d)/2, where h is the height of the trapezium, c is the length of one of the bases, and d is the length of the other base.

To find an expression for c in terms of A, h, and d, we can start by rearranging the formula to solve for c:

A = h(c + d)/2

2A = h(c + d)

2A/h = c + d

c + d = 2A/h

Then, we can subtract d from both sides of the equation to solve for c:

c = (2A/h) - d

Hence, the expression that represents c in terms of A, h, and d would be c = (2A/h) - d.

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The expression that represents c in terms of A, h, and d would be c = (2A/h) - d.

What is the area of the trapezium?

The formula for the area of a trapezium is A = h(c + d)/2, where h is the height of the trapezium, c is the length of one of the bases, and d is the length of the other base.

To find an expression for c in terms of A, h, and d, we can start by rearranging the formula to solve for c:

A = h(c + d)/2

2A = h(c + d)

2A/h = c + d

c + d = 2A/h

Then, we can subtract d from both sides of the equation to solve for c:

c = (2A/h) - d

Hence, the expression that represents c in terms of A, h, and d would be c = (2A/h) - d.

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Answer: -26 feet

Step-by-step explanation:

Answer:

Step-by-step explanation:

The coordinate location of the hill halfway between them is  (1, -1).

Jack's house is located at the point (-2, 3) and Jill's house is located at the point (4, -5).  They plan to meet up at the hill located halfway between there two houses.

The coordinate location of the hill can be calculated as follows:

using mid point formula,

(x, y) = (x₁ + x₂ / 2, y₁ + y₂ / 2)

using the end points (-2, 3) and (4, -5)

(x, y) = (-2 + 4 / 2, 3 - 5 / 2)

(x, y) = (2 / 2. -2 / 2)

(x, y) = (1, -1)

Therefore, the coordinate location of the hill is (1, -1).

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Answer:

144cm²

Step-by-step explanation:

If the square is perfectly even on all sides, the you first need to divide 48 by 4, as a square has 4 sides.

48/4 = 12cm

Then, to find the area, you need to multiply 12 by 12.

12 cm x 12 cm = 144cm²

Hope this helps :)