Been struggling on this for days, some help would be appreciated.

Solution

For this case we see that the focus is (0,-1)

And the directrix is y=1

So then we have a parabola that open downwards:

The vertex is given by V= (h,k)

The focus is given by: F = (h, k+p)

And the directrix is given by: y= k-p

So then replacing we got:

1 = k-p (1)

h = 0

k+p = -1 (2)

Using equation (1) we got k:

k = p+1

Replacing into second equation we got:

p+1+p = -1

2p = -2

p= -1

k = -1 +1= 0

Then the vertex is given by: V= (0, 0)

And the formula is given by:

And thats equivalent to :

the domain is the interval or set of all valid values for x (the input variable).

the range is the interval or set of all valid values for y or f(x) (the function result variable).

the functional result values for the first piece :

x - 4 for 0 <= x < 2

for x = 0 we get y = -4

for x = 2 we get y = -2

the range for this piece is [‐4, -2).

we use the round bracket to indicate -2 itself is not included, as we have x < 2 (and not x <= 2).

the functional result values for the second piece :

x² - 3x + 4 for 2 <= x < 4

for x = 2 we get 4-6+4 = 2

for x = 4 we get 16-12+4 = 8

the range for this piece is [2, 8)

again, because of x < 4 we use the ")" for 8 (not included).

the functional result values for the third piece :

5 for 4 <= x < 7

the range is simply [5) = [5] because the set contains only one element.

and 5 is already contained in the range of the second piece.

so, the range is just the combination of the ranges of the first 2 pieces :

[-4, -2) U [2, 8)

What is the slope of the line that passes through the points (9 , -10 ) and (14 , 5)? Write your answer in simplest form.

From inspection on the given problem:

To calculate the slope of the line passing through the given points, we must use the formula below:

Substitute the given values into the slope formula and solve for m:

[tex] \sf{m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{5 - (-10)}{14 - 9} = \dfrac{15}{5} = \pmb{3}}[/tex]

Therefore, the slope of the line that passes through the given points is 3.

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The cost for the lunches will be:

1 lunch = $2.50

2 lunches = $5

3 lunches = $7.50

4 lunches = $10

From the information, the cost of a school lunch is $2.50. Therefore, the cost of 1 lunch will be:

= 1 × $2.50

= $2.50

The cost of 2 lunches will be:

= 2 × $2.50

= $5.00

The cost of 3 lunches will be:

= 3 × $2.50

= $7.50

The cost of 4 lunches will be:

= 4 × $2.50

= $10

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By definition, [tex](f \circ g)(x)=\boxed{f(g(x))}[/tex]. So, if [tex]g(2)=6[/tex] and [tex]f(6)=17[/tex], then [tex](f \circ g)(2)=f(g(2))=f(6)=\boxed{17}[/tex].

Answer:

my answer would be m=-3/2

Step-by-step explanation:

given the coordinates

(0,0) - this is the origin and the first coordinate it will be treated as x1=0,y1=0

(-2,3)- this is the second given coordinate and will be treated as x2=-2,y2=3

To find the slope(m) we use the formula

m=y2-y1/x2-x1

m=3-0/-2-0

m=-(3/2)

m=-3/2

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The zero of the linear function will be at (1, 0).

A linear function is the one which can be represented in the form y = ax + b where a, b are coefficients and x, and y are independent and dependent variables respectively. The zero of a line is the point where the line crossed the x-axis which is also known as the x intercept. The equation of the line in slope intercept form is given as y = mx + c where m is the slope and c is the y intercept. The slope of line from points (0, 5) and (2, -5) can be found by m = -5 - 5/2 -0

m = -10/2

m = -5

Now, putting this and the point (0, 5) in y = mx + c we get

5 = -5×0 + c

=> c = 5

Now, equation of line is y = -5x + 5 and for x intercept we put y = 0

0 = -5x + 5

5x = 5

=> x = 1

=> (1, 0) which is the required point

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Ray is a part of a line that has a fixed starting point but no endpoints.

There is no end point of any of those rays.

The point V labeled in the diagram is not on any of those rays.

Ray is a part of a line that has a fixed starting point but no endpoints.

We have,

Four rays:

SP, SQ, SU, and SW

A ray has a starting point but does not have an endpoint.

There is no end point of any of those rays.

There are seven points in the diagram.

P, Q, S, V, T, U, and W.

We see that point V does not lie on any of the four rays.

Thus,

There is no end point of any of those rays.

The point V labeled in the diagram is not on any of those rays.

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The solution to the given expression is 10√5 - 4√10 which is the correct answer would be an option (C)

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

The given expression as:

⇒ √5(10 - 4√2)

Open the parentheses and apply the distributive property of multiplication to get,

⇒ 10√5 - 4√5√2

⇒ 10√5 - 4√(5 × 2)

⇒ 10√5 - 4√10

Therefore, the solution to the given expression is 10√5 - 4√10.

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We can see from the graph that there are 10 buildings that have 10-19 bricks and 2 buildings that have 50-59 bricks. So there are more buildings with 10-19 bricks in the neighborhood.

Answer: 10-19 bricks

From the given question,

There are given that two point, (-23, -14) and (-18, 2).

Now,

For finding the distance between two point,

Here use distance formula.

From the distance formula,

Where,

Put the all values into the above formula,

Then,

Then,

Hence, the distance of given

Answer:

slope = 5/2

Step-by-step explanation:

Locations of points: (-4 , -4) and (-2 , 1)

slope = rise / run

between two plotted points this means that:

slope = change in y / change in x

slope = (1 - (-4)) / (-2 - (-4))

slope = 5/2

If there are v vacant rooms, the number of occupied rooms is 300-v (in total there are 300 rooms).

As every occupied makes the hotel collect 125, the dollars the hotel generates are:

It means that the correct answer is the last option.

We are given the following product:

For "A" to be a polynomial the value of the first box "B" must be a constant or a term of the form:

We will use a constant. We will substitute the first box for "1":

For the second box, we need to use an exponent that is a positive whole number.

We will use 2:

With these values, the result of the product is a polynomial.

Given the function:

First part:

You need to substitute the following value of "x" into the function:

In order to find:

Then, substituting and evaluating, you get:

Second part:

Substitute this value of "x" into the function:

And then evaluate, in order to find:

You get:

Since the Radicand is negative, it is not a Real Number.

Therefore, the answers are:

First part:

A.

Second part:

B. The answer is not a real number.

The answer to question (a) that is if Ax = b has a solution and [tex]A^{T}[/tex] y = 0 then y is perpendicular to b

Answer to question (b) that is if [tex]A^{T}[/tex] y = c has a solution and Ax = 0 then x is perpendicular to c.

a) As Ax = b has a solution for x this means b lies in the column space of A. We also know that [tex]A^{T}[/tex] y = 0. This means y lies in the orthogonal complement of the column space of A or in the left null space of A. Therefore y is perpendicular to b

b) We see [tex]A^{T}[/tex] y = c has a solution. This tells us that c lies in the row space of A and also from the given Ax = 0 we can deduce that x lies in the null space of A or the orthogonal complement of row space of A. Therefore evidently  x will be perpendicular to c

Determine whether AT has a row space same as column space of A

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Verify each set

W ---------> are closed under addition

F ------> are closed under addition

I ------> are closed under addition

N ----> are closed under addition

Q ----> are closed under addition

The limit of xlnx when x is tending towards zero is zero.

What is limit in mathematics?

In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches a particular value. Without limits, it is impossible to perform calculus or mathematical analysis; limits are also necessary to compute continuity, derivatives, and integrals.

Given limit is:

[tex]\lim_{x \to 0} x lnX[/tex]

Considering f = x, and g = ln x

The limit of f and g are both zero or both ±∞, and the limit f′/g′ exists, then the limit f/g equals it.

The wrong in the expression x lnx is we are individually defining f and g doesn't meet the hypothesis. so, we write it as

[tex]\frac{lnx}{1/x}[/tex]

We now use L' Hospital rule with f(x) = lnx, g(x) = 1/x as

The limits

[tex]\lim_{x \to 0^+} lnx= - \infty[/tex], and

[tex]\lim_{x \to 0^+} \frac{1}{x}[/tex]

The limits  [tex]\lim_{x \to 0^+} \frac{f'(x)}{g'(x)}[/tex] exists as:

[tex]\lim_{x \to 0^+} \frac{1/x}{-1/x^2} = \lim_{x \to 0^+} -x = 0[/tex]

Hence the answer is 0.

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Answer:

$11.10

Step-by-step explanation:

Ez

There were 120150 federally insured bank in the year 1987. The slope of the graph of B is -326.6.

The provided function B(x) states the number of federally insured banks from 1982-2004.

The function B(x) is,

B(x) = -326.6t + 13783

Here t is representing the year,

This function is a linear function corresponding to an equation of line,

If according to the situation,

t = 0, signifies the year 1982,

Then the year 1983 should be represented by t = 1.

On continuing the pattern the year 1987 should be represented by t = 5.

So, the number of federally insured banks in year 1987 can be found by putting t = 5 in B(x),

B(5) = -326.6(5) + 13783

B(5) = 12150.

The number of banks federally insured in year 1987 is 12150.

The function is B(x)= -326.6t + 1783,

This is representing the point-slope form of the line,

y = mx + c,

On comparing the provided function with the standard equation we can see,

Slope m = -326.6

So the slope of the function is -326.6.

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Solution:

The growth rate is given below as

The initial population is

The exponential growth formula is given below as

Hence,

The final answer is

The population will exceed 1500 in approximately 26 years' time

Notice that:

Therefore:

Then a carat is greater.

Now, since:

Then:

Simplifying the above result we get:

Also, since:

then:

Simplifying the above result we get:

Answer:

A carat is greater.

and

and

Given:

To find:

The angle 7.

Explanation:

We know that,

The sum of the exterior angles is supplementary.

So, we can write

Therefore, angle 7 is 57 degrees.

Final answer:

Angle 7 is 57 degrees.

M is the midpoint of the line segment FG.

Being the midpoint means that M divides the line in two equal halves so you know that the distance between F and M is equal to the distance between M and G, symbolically:

FM=MG

And of you add them you'll be able to calculate the length of the whole line FG

34.

Given the expressions

FM= 5y+13

MG=5-3y

We know that FM=MG, so the first step is to replace this equivalency with the given expressions. This way you'll determine an equation with one unknown y.

Once you have the equation you can clear the value of y:

Pass all terms with the unknown to one side of the equation and all others to the other side:

y=-1

Now that you know the value of y, you can replace it in the given expressions to calculate the length of FG

The length of the line segment FG is 16 units.

a represents the initial value of the function. Since the function starts at 1900, the associated population value for this year should be the answer. The answer is 0.52.

SOLUTION

Using cosine rule it follows:

Simplify the equation for x

Therefore the required answer is