Write an equation of a parabola with a vertex at the origin and a directrix at y=5

Quinn got paid $121,560 in his first career and on switching, he made 55% less, i.e. he made 45% of his previous career.

This is because, if in a previous career he made 100%, then a 55% reduction in salary annually would mean, he is left with only 45%.

Let us suppose, previous salary as x

then, x= $121,560

so, 45% of x= 45% of $121,560

i.e. 45% of x= 45/100 x 121560

therefore, 45% of x= $54,702

Quinn makes $54,702 now.

Therefore, a reduction in 55% of earlier salary would mean that Quinn's salary reduced from $121,560 to $54,702

To know more about simple percentage solving, check out the solution below:

https://brainly.com/question/24304697

#SPJ12

If the swamp vehicle that travels at 3.2 miles per hour to travel across the swamp, then the time taken to travel from point Z to point Y is 1.56 hours

The speed of the swamp vehicle = 3.2 miles per hour

From the figure we can see the two triangles ΔXVM and ΔXYZ

Here we have to use the ratio of the two similar triangles

The ratio will be

VW/WX = YZ/ZX

Substitute the values in the equations

10/6 = YZ/3

We have to find the distance from point Z to point Y

YZ = (10/6)×3

= 5 Miles

We know

Speed = Distance / Time

Time = Distance / speed

= 5/3.2

= 1.56 hours

Hence, if the swamp vehicle that travels at 3.2 miles per hour to travel across the swamp, then the time taken to travel from point Z to point Y is 1.56 hours

The complete question is

You want to go on a swamp tour. How long does it take a swamp vehicle that travels at 3.2 miles per hour to travel across the swamp, from point Z to point Y ?

Learn more about speed here

brainly.com/question/7359669

#SPJ1

Point A

(-16, 20)

Point B

(-16, -14)

The Distance Formula itself is actually derived from the Pythagorean Theorem which is a

The distance would be 34 units

Using concept of Quadratic Equation we got that best ticket price is $16, maximum income is $19,200 and the corresponding number of tickets are 1200.

A Quadratic Equation is one of the following: f(x) = ax2 + bx + c, where a, b, and c are positive integers and an is not equal to zero. A parabola is basically a curve that represents the graph of a quadratic equation. Parabolas can open up or down, and their "width" or "steepness" can vary, but they all have the same basic "U" shape.

We know that,

No. of people who will buy tickets at $4 = 600

For each 20¢ decrease, additional no. of people buying tickets = 50

Revenue = (No. of tickets sold)(Pricing)

Revenue = (600+50x)(4+x)

= 50[tex]x^{2}[/tex] + 800x + 2400

Solving the quadratic equation we got,

x = -4 or -12

Since we're dealing with real-life entities such as money, we'll take the value of x as positive.

Taking x as 12 (higher value),

No. of tickets sold = 600 + 50x = 1200

Pricing = 4 + x = 16

Revenue = 1200×16 = $19,200

To know more about Quadratic Equations, visit:

https://brainly.com/question/1863222

#SPJ13

The probability of the marksman hitting the long-range target in 5 shots is 0.1429.

The geometric distribution is a Bernoulli experiment that predicts the likelihood of the first success after a certain number of failures. Negative-binomial and binomial distributions are two different forms of Bernoulli trials.

P = 0.268

x = 5

Use the geometric probability mass function below to calculate the probability:

P(X = x) = [tex](1 - P)^{(x-1)}[/tex]× P

P(X = x) = [tex](1 - 0.268)^{(3-1)}[/tex]× 0.268

P(X = x) = 0.1429

The probability that it takes 5 shots for the marksman to hit the long-range target is 0.1429.

Learn more about binomial distributions at

https://brainly.com/question/28823380?referrer=searchResults

#SPJ4

The identified acute angles in the diagram are: D. Angle WZY and angle WXY.

An acute angle can be described as any angle that has a degree measure that is below 90 degrees, in order words, it is smaller than a right angle.

For example, an acute angle is attached below, which is 62°, and it is less than a right angle or 90 degrees. Angles 30°, 45°, 60°, 75°, etc are all regarded as acute angles because they are less than a right angle or 90 degrees.

In quadrilateral WXYZ, the acute angles that are less than a right angle, and are below 90 degrees are: D. Angle WZY and angle WXY.

Learn more about acute angles on:

https://brainly.com/question/6979153

#SPJ1

the correct answer is a so write it

Answer:

1/26

Step-by-step explanation:

If the cards are all there, you can count there are 2 red threes. And there are 52 cards. The fraction is 2/52 or 1/26

The equation of the line that is parallel to k and passes through (-1, 3) is

- x + 2y = 7

The equation of a line can be represented in different form such as point slope form, slope intercept form and standard form.

Therefore, the equation of the line is parallel to k.

Parallel line shave the same slope.

Therefore, let's find the slope of k to find the slope of the equation of the line.

Hence, using (7, 2)(1, -1)

m = -1  - 2 / 1 - 7

m = - 3 / -6

m = 1/ 2

Therefore, the slope of the line is 1 / 2. Let's find the y-intercept using the point (-1, 3)

3 = 1 / 2(-1) + b

3 = - 1 / 2 + b

b = 3 + 1 / 2

b = 7 / 2

Hence, the equation is as follows;

y = 1  /2x + 7 / 2

2y = x + 7

2y - x = 7

- x + 2y = 7

learn more on equation of the line here: https://brainly.com/question/14200719

#SPJ1

By solving matrices  we get,

[tex]A+B= \left[\begin{array}{ccc}13&10\\4&7\\7&5\end{array}\right] , C-B=\left[\begin{array}{ccc}-8&1\\-7&4\\3&-5\end{array}\right] \\\\\\\\A+B+C = \left[\begin{array}{ccc}13&14\\2&12\\14&-6\end{array}\right][/tex]

A matrix is a rectangular array or table that contains numbers, symbols, or expressions that are arranged in rows and columns to represent a mathematical object or a characteristic of such an entity. As an illustration, consider a matrix with two rows and three columns.

Adding matrices, subtracting matrices, and multiplying matrices are the three algebraic operations that make up the majority of matrix operations. Array of numbers or expressions arranged in rows and columns is called a matrix. The field of mathematics has several useful uses for matrices.

Here the matrices A, B and C are given in the question, so we use matrix addition and matrix subraction operations to solve the question.  

When solving by using the matrices solving method we get

[tex]A+B=\left[\begin{array}{ccc}5&7\\-1&6\\3&-9\end{array}\right] +\left[\begin{array}{ccc}8&3\\5&1\\4&4\end{array}\right]= \left[\begin{array}{ccc}5+8&7+3\\-1+5&6+1\\3+4&-9+4\end{array}\right]=\left[\begin{array}{ccc}13&10\\4&7\\7&5\end{array}\right] \\[/tex]

[tex]C-B = \left[\begin{array}{ccc}0-8&4-3\\-2-5&5-1\\7-4&-1-4\end{array}\right] =\left[\begin{array}{ccc}-8&1\\-7&4\\3&-5\end{array}\right][/tex]

[tex]A+B+C= \left[\begin{array}{ccc}5+8+0&7+3+4\\-1+5+-2&6+1+5\\3+4+7&-9+4+-1\end{array}\right] = \left[\begin{array}{ccc}13&14\\2&12\\14&-6\end{array}\right][/tex]

To Know more about Matrices here :

https://brainly.com/question/18291235

#SPJ1

Answer:

126

Step-by-step explanation:

90 ÷ 10 = 9

9 × 4 = 36

90 + 36 = 126

Given a block play problem, the minimum number of blocks Agnes can use to build a tower is 3 or 1.

To calculate the average (mean) of a set of values, first divide by the number of values in the set. Therefore, the sum of the values in the set is equal to their average multiplied by the number of values in the set. The average number of blocks in each tower was 25, and since there were 5 towers, the total number of blocks used was 5 × 25 = 125. Yuri's Tower used 32 blocks, so the remaining towers used a total of 125 minus 32 = 93 blocks.

To find the minimum possible number of blocks for Agne's tower, let the other three towers use as many blocks as possible. Now we know that Yuri's tower used the most blocks and each tower used a different number of blocks. So the other 3 towers can use up to 31, 30 and 29 blocks respectively. The result was an absolute minimum number of blocks that Agnes could use, 93 - 31 - 30 - 29 = 3

By the way, the minimum number of blocks Agnes can use is not 93 - 32 - 32 - 32 = - 3 , but negative value is not possible. so, if everyone could use the same number of blocks. Agnes must have used at least one block, as it is possible to use a negative number of blocks.

To learn more about playing with blocks, visit:

https://brainly.com/question/13654367

#SPJ4

The number of copies that can be made would be: 35 copies

We would have to solve this problem through the use of cross multiplication

such that we have 20 copies = 8 dollars

unknown copies ? = 14 dollars

This can be re written to be arranged in the form

20 = 8 dollars

? = 14 dollars

we would have to cross multiply

14 x 20 = 8 x ?

280 = 8?

divide through by 14

? = 280 / 14

= 20

Hence the copies that would be made is 35 copies for 14 dollars at the local print shop

Read more on equations here:

https://brainly.com/question/13763238

#SPJ1

The greatest number of cards that April can place in a row , so that the two families have same number of cards in each row is  14.

In the question ;

it is given that

number of card that Bride's family has = 154

number of cards that Groom's family has = 140 cards.

So , to find the greatest number of cards that April can place in a row we need to find the GCF(154,140) ,

to find the GCF (154,140)

prime factorization of 154 = 2*7*11

prime factorization of 140 = 2*2*5*7

common factors = 2*7

Hence the GCF(154,140) = 14

Therefore , the greatest number of cards that April can place in a row , so that the two families have same number of cards in each row is  14.

Learn more about Greatest Common Factor here

https://brainly.com/question/11444998

#SPJ1

Given:

yearly salary=28,800

Required:

To calculate adjusted monthly income

Explanation:

student loan

250 dollar

The sum equivalent to 7√28x⁶+4√7x⁶ is :

18√7x⁶ .

Given ,7√28x⁶+4√7x⁶,

To find sum in simplest form ;

7√28x⁶+4√7x⁶

By splitting to factors,

= 7√(7*4)x⁶+4√7x⁶

= 7*2√7x⁶+4√7x⁶

= 14√7x⁶+4√7x⁶

By factoring out like terms,

= 2√7x⁶(7+2)

= 2√7x⁶(9)

= 18√7x⁶

Therefore  sum is =  18√7x⁶.

To learn more about algebraic equation refer to :

https://brainly.com/question/4344214

#SPJ13

If the point M (4,3) is translated using the rules (x, y) ⇒ (x, y-2),  then the coordinates of the M' = (4,1)

The point is M(4,3)

The translation rules is

(x, y) ⇒ (x, y-2)

The translation states that the movement of the graph either horizontally  or vertically. When we translate the graph, the shape and size will not change, only the coordinates of the graph changes.

We know the values of

x = 4

y = 3

Substitute the values in the equation

The coordinates of the M' = (x, y-2)

= (4, 3-2)

= (4,1)

Hence, if the point M (4,3) is translated using the rules (x, y) ⇒ (x, y-2),  then the coordinates of the M' = (4,1)

Learn more about translation here

brainly.com/question/12463306

#SPJ1

The powers of the imaginary number i have four possible values: 1, i, -1, and -i. Let's see some examples:

i⁰ = 1 (any number with the exponent 0 equals 1)

i¹ = i (any number with the exponent 1 is the number itself)

i² = -1 (this follows from the definition of the imaginary number, the square root of -1)

i³ = i² * i = -1 * i = -i

Now, the results start to repeat from 1 to -i:

i⁴= i² * i² = (-1) * (-1) = 1

i⁵ = i⁴ * i = 1 * i = i

i⁶ = i * i⁵ = i * i = i² = -1

i⁷ = i⁶ * i = -1 * i = -i

From that, we can follow the steps below to find the value of a power of i:

• divide the exponent by 4;

• if the rest of the division is 0, then the power equals ,i⁰ = 1,;

• if the rest of the division is 1, then the power equals ,i¹ = i,;

• if the rest of the division is 2, then the power equals ,i² = -1,;

• if the rest of the division is 3, then the power equals ,i³ = -i,.

So, for the power i⁶⁴⁹, the exponent is 649. Following the steps above, we find:

• 649/4, has a quotient of 162 and the, rest 1,. Therefore:

i⁶⁴⁹ = i¹ = i

Thus, i⁶⁴⁹ equals i.

We have:

These fractions are equal because the x is found by multiplying and it is as if we have this:

And as we already know:

The correct solution of the expressions are;

1. (14⁴)² × 14⁻⁶ / 14² = 1

2. 14⁻⁵ (14³)² 14⁻² = 1 / 14

3. (14³)⁴ (14⁻⁷)² = 1 / 196

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The expressions are,

1. (14⁴)² × 14⁻⁶ / 14²

2. 14⁻⁵ (14³)² 14⁻²

3. (14³)⁴ (14⁻⁷)²

Now,

The solutions of the expressions are find as;

1. (14⁴)² × 14⁻⁶ / 14² = 14⁸ × 14⁻⁶ / 14²

                            = 14⁸⁻⁶ / 14²

                            = 14² / 14²

                            = 14²⁻²

                            = 14⁰

                            = 1

And,

2. 14⁻⁵ × (14³)² × 14⁻² = 14⁻⁵ × 14⁶ × 14⁻²

                               = 14⁻⁵⁺⁶⁻²

                               = 14⁻¹

                               = 1 / 14

And,

3. (14³)⁴ (14⁻⁷)² = 14¹²  14⁻¹⁴

                     = 14¹²⁻¹⁴

                     = 14⁻²

                     = 1 / 14²

                     = 1 / 196

Therefore,

The correct solution of the expressions are;

1. (14⁴)² × 14⁻⁶ / 14² = 1

2. 14⁻⁵ (14³)² 14⁻² = 1 / 14

3. (14³)⁴ (14⁻⁷)² = 1 / 196

Learn more about the multiplication visit:

https://brainly.com/question/2811940

#SPJ1

The population mean, exists even comprehended as the average or mean of all values in a population, exist determined by summing all population values and dividing that total by the number of population values.

The population mean can be determined by dividing the total number of values in the given data/population by the sum of all values in the data/population. The whole sum of the numbers is referred to as summation. The sign μ stands for the population mean.

The population mean, also known as the average or mean of all values in a population, is determined by summing all population values (represented by the symbol X) and dividing that total by the number of population values (represented by the symbol N).

Therefore, the correct answer is option a. less than the population mean.

To learn more about population mean refer to:

https://brainly.com/question/28103278

#SPJ4

The equivalent expression for the indices is 17⁻⁷ × 17⁵ is  1/17²

Index is the power or exponent which is raised to a number or a variable e.g in number 3⁵, 5 is the index of 3. The 3 is called the base. The plural form of index is indices.

We have different  Laws of Indices, but the one applicable to this question is the product law and reciprocal law.

Product law: To multiply two variables or numbers with the same base, we need to add their powers and raise them to that base":   5² x 5³ = 5²⁺³ = 5 and  P⁴ + P⁶ = P¹⁰

Reciprocal Law: If the index is a negative value, then it can be shown as the reciprocal of the positive index raised to the same variable:

8⁻² = 1/8²   and b⁻⁶ = 1/b⁶      

Let's use the two laws to create an equivalent expression for 17⁻⁷ × 17⁵:

17⁻⁷ × 17⁵ = 17⁻⁷ ⁺ ⁵  = 17⁻²  = 1/17²

Therefore, the equivalent expression for 17⁻⁷ × 17⁵ is  1/17². The 1st option is the answer.

Learn more about indices on:

https://brainly.com/question/10339517

#SPJ1

Answer:29

Step-by-step explanation:

9+4 spots times five days

The parallel between 2 highlights is called eduidistand

pls provide the picture below, because of that its an incomplete answer

A function is called bijective if it is one-to-one and onto.

To check one to one, let x1 = x2 , where x1, x2 belongs to R.

so, we can say that:

and

Given the condition that x1 and x2 are not equal to 2. So, the above equation implies that

So, it is a one-to-one function.

For onto function, let y= (3x + 4) / (x-2). Now, interchange x and y, and solve the equation fo y:

Here, the domain of the inverse of the function is R - {3}. But the function is R - {2} => R. So, it is not onto.

thus, the given function is not a bijection.

From the ellipse equation

the length of the major axis is equal to 2a. By comparing this equation with the given one, we can note that

Then, the length of the major axis is 2x7 = 14