16) How many more line segments will be needed to be added to Step 3 to create Step 4 of the
sequence?
Step 1
Step 2
Step 3

Required equation of the parabola with origin as its vertex and directrix  

y = 1/2 is equal to x² = -2y.

As given in the question,

Let vertex of the parabola be ( h, k )

Vertex of the given parabola be at origin

⇒ ( h , k ) = ( 0 , 0 )

Directrix is y =1/2 above the vertex.

Focus is ( 0, -1/2)

Equation of the parabola is given by

Distance between focus to the vertex = distance between vertex to the directrix

( y - (1/2) )² = ( x - 0)² +  ( y - (-1/2) )²

⇒ y² - y + 1/4 = x² + y² + y + 1/4

⇒ -y = x² + y

⇒x² = -y - y

⇒ x² = -2y

Therefore, the equation of the parabola with vertex at origin and directrix y =1/2 is equal to x² = -2y .

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Answer:

w-10

Step-by-step explanation:

(3w-6)-(2w+4)

Take out the brackets:

3w-6-2w-4

Group the like terms:

3w-2w-6-4

Simplify:

w-10

The equivalent expression to (36 - y²) is (6 - y) (6 + y).

The correct answer option is option C

(36 - y²)

Check all options

A. (36 + 12y + y²)

No

B. (36 - 12y + y²)

No

C. (6 - y) (6 + y)

open parenthesis

= 36 + 6y - 6y - y²

= 36 - y²

Yes

D. (6 - y) (6 - y)

= 36 - 6y - 6y + y²

= 36 - 12y + y²

No

In conclusion, the expression (6 - y) (6 + y) is equivalent to (36 - y²)

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Answer: Gwen's breakfast in total was $8. Max's Breakfast in total is $8 as well. so their breakfast together is $16 in total

Answer:

their breakfast cost 16 dollars

Step-by-step explanation:

because you would do 2 times 2 which is 4 and 1 times 4 which is also 4 add those two together to get 8 and the double it because max got the same thing

if 40 is the least frequent multiple of two whole numbers. The higher number to lesser number ratio is 4:5. The two digits after that are 8 and 10.

Least Common Multiple is the meaning of the abbreviation LCM.

The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers.

It can also be computed using two or more numbers.

Finding the LCM of a given collection of numbers can be done in a variety of ways.

Utilizing the prime factorization of each number and then calculating the product of the greatest powers of the shared prime factors is one of the quickest techniques to determine the LCM of two numbers.

In mathematics, the least common multiple is sometimes referred to as LCM or the lowest common multiple.

The smallest number among all numbers is called the least common multiple of two or more numbers.

According to our question-

The number LCM is equal to 40.

4 × 5 × x = 40

20 × x = 40

20x=40

x=2

The larger number is equal to 4 x=4(2)=8.

The smaller value is =5x=5(2)=10.

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Complete question-

The least common multiple of two whole numbers is 40. The ratio of the greater number to the lesser number is 4:5. What are the two numbers?

Answer: y-3 = -4/5(x+0)

Step-by-step explanation:

formula

y-y1=m(x-x1)

y = y coordinate of the second point

y1 = y coordinate of point one

m = slope

x = x coordinate of the second point

x1 = x coordinate of point one

slope formula

y2-y1/x2-x1

-1-3/5-0

slope = -4/5

the 2 points on the graph are (0,3) (5,-1)

substitute and solve

y-3 = -4/5(x+0)

y-3=-4/5x

The result is 6-13/3×t after simplification by multiplying first and added the like term.

The procedure of calculation which we use in arithmetic. We perform our mathematical calculation by using particular operational properties such as addition, subtraction, multiplication and division.

we can simplify any expression by using the properties of addition, subtraction, multiplication or division depending on the statement given.

in the above expression 7×(1/3)t- [10×(2/3)t-6]

we simplify it (7/3)t- (20/3)t+6

                      -(13/3)t+6

             hence, 6-13/3t

hence, the result is 6-13/3×t

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Answer:88 i think

Step-by-step explanation:

The answers are ; a) -5/9, 6/10, -7/11, 8/12, b) f(n) = n/(n+4) and c) f(56) is positive.

A sequence is defined as an arrangement of numbers in a particular order.

A sequence is given ; -1/5, 2/6, -3/7, 4/8.....

Part A

From inspection of the sequence, the pattern is:

i) Add 1 to the numerator of the previous term.

ii) Add 1 to the denominator of the previous term.

iii) Make every other term negative.

Therefore, The next four terms are -5/9, 6/10, -7/11, 8/12

Part B

From inspection of the sequence, we can see that the numerator is the position of the term (n) in the sequence.  So when n = 1 the numerator is 1, when n = 2 the numerator is 2, etc.

The denominator is 5 more than the position of the term in the sequence.  So when n = 2 the denominator is 2 + 4 = 6, and when n = 4 the denominator is 4 + 4= 8.

Hence, the rule can be,

f(n) = n/(n+4)

If n is even, then f(n) is positive.

If n is odd, then f(n) is negative.

Part C

56 is an even number.

As the function f(n) is positive when n is even, the sign of f(56) is positive.

Therefore, the answers are ; a) -5/9, 6/10, -7/11, 8/12, b) f(n) = n/(n+4) and c) f(56) is positive.

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[tex]x^2 - y^2[/tex] when x = 1/2 and y = 1/4

[tex]\frac{1}{2} ^2 - \frac{1}{4} ^2\\\\=\frac{1}{4}-\frac{1}{16} \\\\= \frac{4}{16}-\frac{1}{16}\\ \\= 3/16[/tex]

Jenny needs to score 79 on final exam.

Total marks divide by total number subjects=Average

100+88+96+84+98+x=90*6

461+x=540

x=79

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Using translation concepts, the equation for the graph is b.

y = cos(x + π/2) + 1

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Suppose that we've got:

f(x) = a cos (bx - c) + d

Then, this function has:

Amplitude (the maximum distance of the graph from the middle line) = a

Period =[tex]\dfrac{2\pi}{b}[/tex]

Phase shift = [tex]\dfrac{c}{b}[/tex]

Maximum value: a + d

Minimum value: -a + d

In this problem, we have a cosine function

(zero at π/2, this is zero at the origin), shifted π/2 units to the right and 1 unit up.

Since the standard amplitude is between -1 and 1, here is between 0 and 2).

Hence the rule is given as follows:

b. y = cos(x + π/2) + 1

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The value of the given expression 6 3/5-2 7/10 is 39/10.

What is an expression?

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

Here, we have

Given: 6 3/5-2 7/10

We have to solve this expression and find the value of the given expression.

6 3/5-2 7/10 = 33/5 - 27/10

6 3/5-2 7/10 = (66-27)/10

6 3/5-2 7/10 = 39/10

Hence, the value of the given expression is 39/10.

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Answer:

265

Step-by-step explanation:

1590/6=265

265x1=265

Answer:

13

Step-by-step explanation:

w = -8 -5 =-13=13

"Define variables"

→ The number of student's tickets = a

→ The number of non-student tickets = b

→ the total cost represented = y

"Create an equation that models this situation"

→ y = $5 × a + $10 × b

"Rewrite the equation in slope intercept form"

→ y = $5 × a + $10 × b

→ y = 5a + 10b

→ 250 = 5a + 10b

To each side, add 4 positive unit tiles.

What is a one-variable linear equation and what does it look like?

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable.

The initial formula is:

3x - 4 = 2x + 5

Four positive unit tiles are added to each side, giving us:

3x - 4 + 4 = 2x + 5 + 4

3x = 2x + 9

which removes the independent elements off both sides of the equal sign and places them all on the right side (the +9 term), simplifying the initial equation. You'll see that the other choices don't produce this outcome.

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Answer:

second option or B

And to mark brainliest on answers when 2 people answer a crown button will appear on the bottom right and you click that

Step-by-step explanation:

-7+4x>-3

+7.     +7

4x>4
/4.  /4

x>1
So second option is correct

Hopes this helps sorry for late response I was eating

Number of yellow marbles for every 18 green marbles = 30 yellow marbles

The unitary method entails figuring out the value of a single unit from which we can extrapolate the values of all the required units.

According to the given information

Applying the unitary method

Number of yellow marbles for every 3 green marbles = 5

Number of yellow marbles for every One green marbles = [tex]\frac{5}{3}[/tex]

Number of yellow marbles for every 18 green marbles = [tex]\frac{5}{3}[/tex] × 18

So

Number of yellow marbles for every 18 green marbles = 30 yellow marbles

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Allison feeds 11 horses in a day.

Horses are herbivores and, as such, they need a very specific diet. They must consume lots of fiber to keep their extremely long and sensitive digestive tract working and they must eat little and often, almost all day long.

A horse's feed should consist primarily of grass or roughage. However, hay is insufficient to provide a complete nutritional profile. Important minerals and nutrients will be added by adding grains and concentrates, but calories will also be added. Roughage, feeds, and concentration types are listed below, from least to most "complete."

Given,

Allison feeds 2 quarter horses and 3 paint horses the same amount each day.

Therefore, she feeds 2*4+3 = 11 horses in a day.

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The required monthly payment is given as follows:

$644.22.

The monthly payment is defined by the equation presented 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]

The parameters are listed as follows:

For this problem, the values of these parameters are given as follows:

P = 120000, r = 0.05, n = 30 x 12 = 360.

Then:

r/12 = 0.05/12 = 0.004167.

Hence the monthly payment is obtained 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 = 120000\frac{0.004167(1.004167)^{360}}{(1.004167)^{360} - 1}[/tex]

A = $644.22.

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The total years taken to double the money according to Compounding will be 12.5  years.

What is compound interest?

Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.

Main body:

Given :

rate = 6%

amount = $900

Total amount = $1800

Compounded monthly,

so formula becomes,

Total amount = amount (1+r/1200)^12t

T = A[tex](1+r/1200)^{12t}[/tex]

1800 = 900 (1+6/1200)^12t

2 = (1+1/200)^12t

2 = 1.005^12t

taking log on both sides

log 2 = 12t *log 1.005

0.3/0.002 = 12t

t = 12.5 years

Hence the time taken to double the money is 12.5 years.

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Answer:

Center: (2,-1)

Radius: 4

Step-by-step explanation:

Circle equation: (x-h)^2 + (y-k)^2 = r^2

Finding the center:

Set to equaling 0 and solve for x and y

(x - 2)^2=0

(y + 1)^2=0

Finding the radius:

In the equation, because it's set to r^2, you would undo the square.

[tex]\sqrt{16}[/tex]=4

Answer:

y = 2x - 5

Step-by-step explanation:

slope = 1-(-3)/3-1

4/2 = 2

this is the m value, or value before x.

So far, this is what we have: y = 2x + b

To find b, we plug in one of the points we have, into the equation.

(in this case ill use (3, 1), where 3 is the x and 1 is the y)

So,

1 = 2(3) + b

1 = 6 + b

1 - 6 = b

-5 = b

Finally,

y = 2x - 5

Answer: 13

Step-by-step explanation:

Minus 29 from 42 to get 13

Answer:

13

Step-by-step explanation:

If you subtract 20 from 42, you will get your answer. Then you plug it into the equation to make sure it's correct.

42-29=13

29+13=42

42-13=29.

-Hope this helped

Answer:

14 4/5

Step-by-step explanation: 7 2/5 x 2 or 7 2/5

                                                                +7 2/5

                                                                  -------

                                                                   14 4/5

The compound inequality solved are:

x ≤ 2 and x > -5

x > 4 or x < -5.3

The graph of the number line is given above.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

-2 x ≤ 4 and 10 > -2x

x ≤ 4/-2 and 10/2 > -x

x ≤ -2 and 5 > -x

x ≤ 2 and x > -5

This means.

-5 < x ≤ 2

The number line can be graphed as,

<----__-5__-4__-3__-2__-1__0__1__2__3__4__5----->

             o---------------------------------------- o

10 < 3x - 2 or -3x - 2 > 14

10 + 2 < 3x or -3x > 14 + 2

12 < 3x or -3x > 16

x > 4 or -x > 16/3

x > 4 or x < -16/3

x > 4 or x < -5.3

x > 4 can be represented on a line graph as,

__-1__0__1__2__3__4__5__6__7--------->

                                     o----------------------->

x < -5.3 can be represented on a number graph as,

<---------8__-7__-6__-5__-4__-3__-2__-1__0__1__2__3__4---------->

<--------------------------o

Thus,

The compound inequality solved are:

x ≤ 2 and x > -5

x > 4 or x < -5.3

The graph of the number line is given above.

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The function f(x) = 14(0.87) has is a constant function has no growth or decay.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given a function f(x) = 14(0.87) Now it is a constant function as for every different values of x the function f(x) has same value and has no growth or decay.

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