The width of a rectangle measures (9.6w+4.7x) centimeters, and its length
measures (7.8w - 2.1x) centimeters. Which expression represents the perimeter,
in centimeters, of the rectangle?

The equation of the parabola whose focus is at (3, 0) and directrix at x = - 3 is y² = 12 · x. (Correct choice: D)

In this problem we need to determine the equation of a parabola based on the information of the focus and the directrix. The vertex form of the parabola is described below:

4 · p · (x - h) = (y - k)²

Where p is the distance from the vertex to the focus. The coordinates of the vertex is the midpoint of the line segment of the least distance between the directrix and the focus.

First, determine the coordinates of the vertex:

(h, k) = 0.5 · (- 3, 0) + 0.5 · (3, 0)

(h, k) = (0, 0)

Second, calculate the distance from the vertex to the focus:

p = 3 - 0

p = 3

Third, write the vertex form of the parabola:

y² = 12 · x

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Answer:

$22,106.28

Step-by-step explanation:

[tex]CI=P(1+(\frac{r}{12}) )^{12t}[/tex], where [tex]P[/tex] is the principal, [tex]r[/tex] is the interest rate in decimal form, and [tex]t[/tex] is the time in years.

[tex]CI=\$11000.00(1+(\frac{0.07}{12}) )^{12(10)}[/tex]

[tex]CI=\$22106.28[/tex]

Answer:

Step-by-step explanation:

87

99

128

Answer:

  3

Step-by-step explanation:

You want the value of f(2) for the graphed function.

The value of the function f(a) is the y-coordinate of the point that has 'a' as its x-coordinate.

Finding the function value requires you locate x=a on the horizontal axis. Where the graph crosses that vertical line, the y-coordinate is the function value.

Here, the vertical line x=2 meets the function graph at the dot with coordinates (2, 3). The y-value there is 3, so ...

  f(2) = 3

Answer:  [D]:  " 3 " ;  [that is; f(2) = 3 ].
____
We are asked to:

Evaluate the given function for f(2) ; within the given image.

By examination of the graph, we can verify that the graph is, in fact, a function—by using the vertical line test.
  We find that no value for x shares more than one y-value; which means that the graph is a function.

____

Note that for a function:   f(x) = y .  

So;  To find f(2) :
____
Note:  f(2)  =  the "[ y - coordinate/corresponding value for y ]" ;  

                       ⇒  when " x = 2 ".

So; looking at the graph:   We see that when  " x = 2 " ;  →  " y = 3 " .
        → {Examine the co-ordinate/point:  (2, 3) —that is part of the graph.}

So;  f(2) = 3 ;  which is Answer choice:  [D]:  " 3 ."
______

Hope this is helpful to you.  Best wishes!
______

The actual end-of-year payment or present value of this ordinary annuity is equal to $1,482.

For the rate of interest, we have:

Rate of interest, r = APR/12

Rate of interest, r = 0.12/12

Rate of interest, r = 0.01

Next, we would calculate the present value of this ordinary annuity by using this formula:

Present value, PV = [P ÷ [1 - (1 + r)^{-n}]/r]

Where:

Substituting the given parameters into the formula, we have;

Present value, PV = 4,500 ÷ ((1 - (1 + 0.12)^(-4))/(0.12))

Present value, PV = 4,500 ÷ ((1 - (1.12)^(-4))/(0.12))

Present value, PV = 4,500 ÷ ((1 - 0.635518078)/(0.12))

Present value, PV = 4,500 ÷ ((0.364481922)/(0.12))

Present value, PV = 4,500/3.0373

Present value, PV = $1,481.58 ≈ $1,482.

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The weight of Luna is 82 pounds , the correct option is (d) .

In the question ,

it is given that

Kira has three dogs Luna , Cooper and Daisy .

let the weight of cooper be c .

given Cooper weighs 25 pounds less than Daisy

which is c = daisy - 25

So , daisy = c + 25

and Luna weighs 20 pounds less than three times Cooper ,

which is Luna = 3c - 20

Given the combined weight is = 175 pounds

Cooper + Daisy + Luna = 175

c + c + 25 + 3c - 20 = 175

5c + 5 = 175

5c = 175 - 5

5c = 170

c = 170/5

c = 34

So, Luna = 3c - 20 = 102 - 20 = 82 pounds .

Therefore , The weight of Luna is 82 pounds .

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Step-by-step explanation:

The base of the separated triangle is (x+5) - (2x - 4) = x + 5 - 2x + 4 = 9 - x

So, area of the separated triangle would be:-

1/2 * b* h

or, 1/2 * (9-x)* (x+3)

or, (6x + 27 - x² )/2

Total area of trapezium = (6x + 27 - x²)/2 + (2x-4)(x + 3)

or, 60 = (6x + 27 - x²)/2 + 2x² + 2x - 12

or, 60 = (6x + 27 - x² + 4x² + 4x - 24)/2

or, 120 = 10x + 3x² + 3

or, 0 = 3x² + 10x + 3 - 120

hence, 3x² + 10x - 117 = 0 (proved)

Again,

Use quadratic formula to figure out value of x.

(It woun't be a natural number)

Write the value of x with only one digit after it's decimal.

The coordinate of point B is such that M (1,-8) is the midpoint of A(-6,-12) and B will be (5,-2).

A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).

The coordinate of midpoint between two points  (x₁, y₁) and (x₂, y₂) is given by,

( (x₁ + x₂)/2 ,(y₁+ y₂)/2)

Given that, M is the midpoint of A and B.

Let's say the coordinate of point B is B(x,y).

Then,

1 = (-3 + x)/2

x = 2 + 3 = 5

And,

(-6 + y)/2 = -4

y = -8 + 6 = -2

Hence "The coordinate of point B is such that M (1,-8) is the midpoint of A(-6,-12) and B will be (5,-2)".

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The  simple or compound interest will be

a. $120

b. $12,000

c. $15,000

d. $18,000

e. Option B is better as it is giving us more interest.

Formula of total simple interest is

SI = (P * R * T) /100  where

P = initial principal balance

r = annual interest rate

t = time (in years)

Formula of compound interest is

C.I.= P × [tex](1 + r/n)^{nt}[/tex] - P  where

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

a. By applying the formula given above we will get

SI = (3000 * 0.4 * 10) / 100

SI = $120

b. Formula to find total value is P * R * T. By applying this we will get

I = 3000 * 0.4 * 10

I = $12,000

c.  By putting values in the formula we will get

CI = 3000 * [tex](1 + 0.2)^{10}[/tex] - 3000

CI = 18000 - 3000

CI = $15,000

d. formula to find total compound value is P * [tex](1 + r/n)^{nt}[/tex]. By applying this in the formula we get

A = 3000 [tex]( 1 + 0.2 )^{10}[/tex]

A = $18,000

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Step-by-step explanation:

please remember you middle school and high school classes, homework and exams.

here on college level this is just meant as a quick reminder.

so, what exactly don't you understand, please, so that I can provide specific guidance ?

6

the vertex : the turn-around point, where the parabola curve changes its tendency : (-3, 0.5)

axis of symmetry : since the parabola opens downwards, the axis of symmetry (it is like a mirror for one half of the curve to the other half) is a vertical line going right through the vertex : x = -3

y-intercept is the y-value when x = 0 : (0, -4)

x-intercepts are the x-values when y = 0 :

(-4, 0) and (-2, 0)

max or min : there is only one identifiable extreme value, it is at the vertex, of course, and is clearly a maximum :

at x = -3 the max value of the function is 0.5

the optimal value is the y-coordinate of the vertex (the function value between the 2 x-intercepts) : 0.5

4

y = 0.5x + 6 is linear. why ? because the highest exponent of x is 1. that creates a proportional relationship between x and y meaning y only increases with x in a constant manner.

y = 2x² + 5 is quadratic. why ? because the highest exponent of x is 2. this squares things, in other words, it makes them quadratic.

the graph as third item in the list is neither. the functional value gets exponentially bigger, the closer x gets to 0.

this looks like y = -1/x = x^(-1)

the graph as forth item in the list is a parabola again, and as such it is quadratic.

The revolution per minute done by the wheel of a bicycle is 16.9 rev/min.

Velocity is the rate at which a moving object's direction changes as perceived from a certain vantage point and measured by a particular unit of time. Kinematics, the area of special relativity that investigates how bodies move, starts with the fundamental idea of speed.

In order to be explained, the scientific vector quantity known as velocity needs to have both a magnitude and a direction.

As per the given information in the question,

Diameter of wheel = 20 inch

Radius, r = 10 inch

The velocity of the bicycle, v = 13 mi/h.

Revolution, R = v²/r

R = 13²/10

R = 16.9 rev/min

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The constant of proportionality in the equation y = 11x is  11 , the correct option is (a) .

in the question ,

it is given that

the equation is y = 11x

also given that the equation is proportional relationship ,

we need to find constant of proportionality .

we know that the proportional equation is written as y = k*x

where k is the constant of proportionality , on comparing it with the equation y = 11x

, we get k = 11 ,

So , the constant of proportionality is = 11 .

Therefore , The constant of proportionality in the equation y = 11x is  11 .

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The size of the moose population, 65 + (48-14)=99.

acc to our question-

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After simplifying an equation the value of x is x = 3.

What is solving an equation?

Unifying Principle for Equation Solving

By deleting parenthesis and grouping like terms, each side of the equation can be made simpler.

The variable term on one side of the equation can be separated using addition or subtraction.

To find the variable, use multiplication or division.

Consider, the given equation

     5(2x - 4) = 10

      10x - 20 = 10                                  Removing parenthesis

10x -20 + 20 = 10 + 20                         Adding 20 on both sides

              10x = 30                                 Simplifying

                  x = 3                                    Dividing both sides by 10

Hence, the value of x is, x = 3.

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The addition property used by Bill in finding the actual December temperature is the commutative property of addition.

According to the question,

We have the following information:

Bill claims that he found the actual December temperature by adding either -5 + 3 or 3 +-5.

We know that are five properties of addition: closure property, commutative property, associative property, additive identity property of addition and additive inverse property.

The commutative property of addition means that if two numbers are added and their order is inversed then  the result of addition will always be the same.

For example, we get -2 by adding -5+3 and 3+(-5). The change in order of digits does not affect the final result.

Hence, the addition property used by Bill in finding the actual December temperature is the commutative property of addition.

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The number of people that are seated in the buses is 425

From the information, there are 5 buses and there are 85 people in each. Therefore, the total number of people will be:

= 85 × 5.

= 425

Since 3/5 of those people are seated, the number of people seated will be:

= Fraction of those seated × Total number of people.

= 3/5 × 425

= 255

Therefore, there are 255 people.

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The missing side length of  triangle XYZ is 7.

Given,

Triangle ABC and triangle XYZ are similar.

Length of AB = 4

Length of BC = 8

Length of AC = x

Length of XY = 24

Length of YZ = 48

Length of XZ = 42

We have to find the missing length x.

Here,

Triangle ABC and triangle XYZ are similar.

So,

AB : XY = BC : YZ = AC : XZ

Then,

Take AB : XY = AC : XZ

= 4 : 24 = x : 42

= 4 × 42 = 24x

x = 4 × 42 / 24

x = 42/6

x = 7

That is,

The missing side length of  triangle XYZ is 7.

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Equation of a line that has a slope of 4 and passes through point (1, 6) is  y = 4x + 2 . Hence, C is the correct option.

To represent the standard form of equation of a line are:

Slope-intercept form:

y = mx + c

Here m represent the slope of the given line and c is the y intercept.

Intercept form:

x/a + y/b = 1

Generic way of representing the straight line, i.e. Ax+By+C = 0

x/(-C/A) + y/(-C/B) = 1

Hence a = -C / A and b = – C / B

Normal form:

The equation of the line whose length of the normal from the origin is p and the angle made by the normal with the positive x-axis is given by α is given by:

x cos α+y sin α = p

General equation of the line is represented in the form:-

y - y1 = m (x-x1) ,

Where x1, y1 represents a point on the line whereas,

m represents the slope of the line.

    = (1 , 6) point on the line

    = Slope (m) = 4

Putting all the required values in general equation:-

y - 6 = 4 ( x-1 )

Hence, we get y = 4x + 2

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The expressions are:

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

15 x squared minus 18 end quantity over 6.

= 15x² - 18 / 6

= 3(5x² - 6)/ 6

= (5x² - 6)/ 2

and, 5 x squared minus 18 end quantity over 2

= 5x² - 18/2

and, 5 x squared minus 6 end quantity over 2

= 5x² -6 /2

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Answer:

21 + 3x

Step-by-step explanation:

Its simple really. Just expanding the brackets by bringing the 3 inside the bracket :

3 × 7 = 21

3 × x = 3x

So our answer will 21 + 3x

Hope this helped and have a good day

Answer:

[tex]y=x+1[/tex]

Step-by-step explanation:

I am assuming that, given the nature of the curve, you know what a derivative is, and you know how to compute the derivative of the ratio of two functions.

[tex]f'(x) = \frac1{(\sqrt x)^2}[(2x+0)\sqrt x-(x^2+1)(\frac1{2\sqrt x})][/tex]

Could be rewritten in a nicer form? Probably, do we care? No, let's just evaluate it for [tex]x=1[/tex]:

[tex]f'(1)=\frac11 [(2)(1)-(1+1)\frac12]=1[2-1]=1[/tex]

We're almost done. We got the point, we have the slope, we can rewrite the tangent line as

[tex]y-y_0=f'(x_0)(x-x_0)\\y-2=1(x-1) \rightarrow y=x+1[/tex]

Answer:

y=4x+1

Step-by-step explanation:

Our slope is 4/1 or 4, so we know 4x is our slope. Then our y intercept is at (0,1), so we know our b=1. So we know our equation is y=4x+1.

-Hope this helped.

Answer:

B

Step-by-step explanation:

The Linear equation used is x -y = 1; to find the age of Isabelle's age.

What is Linear Equation?

An equation is said to be linear if the maximum power of the variable is consistent Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present. A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

A linear equation is an algebraic equation in which each term has an exponent of 1, and which, when plotted on a graph, always yields a straight line. It is called a "linear equation" for this reason.

Let the age of Ben be x;

Let the age of Amara be y;

According to the question:

It is given that:

Ben is one year younger than Amara. That means we have to form a linear equation such that Amara is one year older than Ben.

So,

We have assumed the Age of Ben is x;

we have assumed the Age of Amara is y;

So, According to the question,

Framing the linear equation,

x -1 =y;

⇒x -y = 1;

Hence, We can find the age of Isabelle using the linear equation: x -y = 1;

where x is ben's age;

where y is Amara's age.

Therefore, The Linear equation used is x -y = 1; to find the age of Isabelle's age.

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The value of P(1.17 <= Z <= 2.26 ) is 0.1091

From the question, we have

Z value for 1.17 is 0.8790

Z value for 2.26 is 0.9881

P(1.17 <= Z <= 2.26 ) = 0.9881 - 0.8790 = 0.1091

Probability:

Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

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Answer:

  XY is tangent to circle Z

Step-by-step explanation:

You want to know if segment XY, measuring 3.6 units, is tangent to circle Z at point X. Segment YZ has length 1.8 units outside the circle, which has radius 2.7 units.

If the triangle XYZ is a right triangle, then we have ...

  XY² +XZ² = YZ²

  3.6² +2.7² = (1.8 +2.7)²

  12.96 +7.29 = 20.25 . . . . . true

Segment XY is a tangent.

If segment YZ is extended across the circle, the lengths of the segments from Y to the circle intersection points are 1.8 and (1.8 +2·2.7) = 7.2. The relation between the secant and the "tangent" will be ...

  3.6² = (1.8)(7.2) . . . . . true

This means XY is a tangent.

The composition f(4) has a value of -27

The definition of the functions is given as

f(x) = -2x^2 + 5

Rewrite the above function properly

So, we have the following representation

f(x) = -2x² + 5

To find the function f(4), we set the value of x in the equation f(x) = -2x² + 5

This is represented by

Calculate f(x), when x = 4

Substitute 4 for x in the equation f(x) = -2x² + 5

So, we have the following equation

f(4) = -2(4)² + 5

Evaluate the exponents

This gives

f(4) = -2 * 16 + 5

Evaluate the products

This gives

f(4) = -32 + 5

Evaluate the sum

f(4) = -27

Hence, the value of the function is -27

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wa can rewrite it as 12/1 which is A

Answer:

B. -6.08 x 10^-8