what is the instantaneous rate of change at x=2 of the function f given by

Answer:

A

Step-by-step explanation:

diameter

The another name for the chord that passes through the center of the circle is the diameter.

The correct option is (A).

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.

As per the given data:

We have to find out the alternate name for a chord that passes through the center of a circle out of the given options.

Diameter:

It's a chord that passes through the center and touches the ends of the circumference of the circle.

Hence, this is correct.

Circumference:

It's the length of the boundary of a circle, hence this cannot be a chord.

This is incorrect.

Center:

It's a point and a chord is a line, hence this cannot be true.

Radius:

A radius is not a chord, as it does not touch the endpoints on the circumference of the circle.

The another name for the chord that passes through the center of the circle is the diameter.

Hence, The another name for the chord that passes through the center of the circle is the diameter.

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The algebraic form of the statement is b/4 + 7 = 2 and the value of b is -20.

Given the statement; the quotient of a number b and four plus seven is two.

First, we convert the statement into an algebraic equation.

Now, combine the terms and equality sign.

b/4 + 7 = 2

Next, solve for the numerical value of b.

b/4 + 7 = 2

Subtract 7 from both sides

b/4 + 7 - 7  = 2 - 7

Simplify the left-hand side

b/4 = 2 - 7

Subtract 7 from 2

b/4 = -5

Next, multiply both sides by 4

b/4 × 4 = -5 × 4

b = -5 × 4

b = -20

Therefore, the numerical value of b is -20.

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The factor is -3x(x - 4) and value of x is 4.

Define Algebraic Expression

An expression that includes variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.)

Define Factorization

Factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

Given expression,

-3x² + 12x

Take -3x common

⇒ -3x(x - 4)

Now, if you want to find the value of x then write it in standard form like this

-3x(x - 4) = 0

Now, find x

x - 4 = 0

x = 4

Hence, the factor is -3x(x - 4) and value of x is 4.

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Answer:   The final balance is $9,013.73.

The total compound interest is $7,513.73.

Step-by-step explanation:

The eigenvalues of A are 5 and 10.

What is  eigenvalues ?

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that, when the linear transformation is applied to it, changes at most by a scalar factor. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by lambda.

The eigenvalues of the 2 x 2 matrix are described by the following characteristic polynomial:

[tex]$$t^2-{tr}(A) \cdot t+{det}(A)=0$$[/tex]

The roots of the characteristic polynomial are deflned by the quadratic formula:

[tex]t=\frac{{tr}(A) \pm \sqrt{[{tr}(A)]^2-4-{det}(A)}}{2} \text { (2) }$$[/tex]

If we know that [tex]${tr}(A)=15$[/tex]and [tex]${det}(A)=50$[/tex], then the elgenvalues of A are:

[tex]$$\begin{aligned}& t=\frac{15 \pm \sqrt{15^2-4 \cdot(50)}}{2} \\& t_1=10 \vee t_2=5\end{aligned}$$[/tex]

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An equation for this line in the point-slope form will be y-7 = -2(x + 4).

What is the Point-slope form?

The equation of the straight line has its slope and given point. If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation. Point-slope is a specific form of linear equations in two variables:

y - y₁ = m(x - x₁)

Which is the required equation of a line in a point-slope form.

We need to find the equation of the line that passes through (-4, 7) and whose slope is -2.

Well, we will simply plug m = -2, x₁= -4, and y₁  = 7 into point-slope form.

y-y₁ = m(x-x₁)

Now substitute;

y-7 = -2(x - (-4))

y-7 = -2(x + 4)

Therefore, an equation for this line in the point-slope form will be y-7 = -2(x + 4).

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Answer:

3x + y = 4

Step-by-step explanation:

The standard form of an equation can be written as: ax + by = c

The equation is currently written in slope-intercept form.

In order to turn it into standard form, we must have both x and y on one side of the equation. So...

y = -3x + 4 Add 3x to both sides

3x + y = 4

Therefore the standard form of the equation y = -3x + 4 is 3x + y = 4

The fencing needed to enclose the garden is equal to the perimeter of the rectangle and it will be 5x + 56.

The perimeter of the rectangle: The sum of all the sides of the rectangle will be known as the perimeter of the rectangle.

Let L be the length and W be the width of the rectangle.

Then the perimeter of the rectangle will be

The perimeter of the rectangle = Sum of all the sides

If the gardener fences in the total rectangular area shown in the illustration instead of just the square area, he will need twice as much fencing to enclose the garden.

From the diagram, the length is 28 + x. And the width is x. Then the perimeters of the rectangle will be

P = 28 + x + 28 + x + x + x + x

P = 56 + 5x

The fencing needed is equal to the perimeter and will be 5x + 56.

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Answer:

(- 3, - 7 )

Step-by-step explanation:

given

y = x - 4 ← substitute y = - 7 into the equation and solve for x

- 7 = x - 4 ( add 4 to both sides )

- 3 = x

then point is (x, y ) = (- 3, - 7 )

Answer:

(-3, -7)

Step-by-step explanation:

y=-7

y=x-4

-7 = x - 4  ==> since y=-7 and y=x-4, -7 = x-4

-7 + 4 = x - 4 + 4  ==> solve for x by adding 4 on both sides

-3 = x

x = -3

x=-3, y=-7 ==> (-3, -7)

groceries has a higher population mean annual credit card charge

What is population mean?

A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic. In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study.

The population mean can be calculated by the sum of all values in the given data/population divided by a total number of values in the given data/population.

Given that Bank of America’s Consumer Spending Survey collected data on annual credit card  charges in seven different categories of expenditures: transportation, groceries, dining out,  household expenses, home furnishings, apparel, and entertainment (US Airways Attache,  December 2003).

Sample size n =42

Mean difference d = 850

Std dev s = 1125

Point estimate of the difference is 0

95% confidence level would be

= 0A ± tcritical * stderrror

=  A ± 2.021*173.59

= (-350.83 , 350.83)

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Answer:

y = x + 2

Step-by-step explanation:

Use the slope-intercept form:

y=mx+b

M represents the slope of the line

B represents the y-intercept

The equation is y = (5/3)x. Then the cost of the 12 yards of fabric will be $20. Then the correct option is B.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

The two points are (3, 5) and (6, 10).

Let 'x' be the number of yards of fabric and 'y' be the cost in dollars. Then the equation is given as,

(y - 5) = [(10 - 5) / (6 - 3)](x - 3)

y - 5= (5/3)x - 5

y = (5/3)x

The cost of the 12 yards of fabric is given as,

y = (5/3) × 12

y = 5 × 4

y = $20

The equation is y = (5/3)x. Then the cost of the 12 yards of fabric will be $20. Then the correct option is B.

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Step-by-step explanation:

(3-2)^2+y^2=4

(9-4)+y^2=2^2

the power of y and 2 should be cut now

5+y=2

5-2=y

3=y

y=3

:. the area of enclosed by a circle is 3 cm

Answer:

Step-by-step explanation:

Given,

[tex]P = $400 find I\\R = 9%\\\\T = 0.25 years[/tex]

[tex]T=0.25[/tex](Remember 9% = .09 in decimal form)

So We convert it into a decimal form

[tex]\frac{9}{100} =0.09[/tex]

Now we find the Interest,

[tex]I=PRT\\[/tex][tex]I = 400X0.09X0.25\\I=36X0.25\\I=9$[/tex]

9$ is the answer

The value of x in the linear inequality 5/8x - 1 ≥ 9 is x ≥ 16

Linear inequalities are inequalities that involve at least one linear algebraic expression, that is, a polynomial of degree 1 is compared with another algebraic expression of degree less than or equal to 1. There are several ways to represent various kinds of linear inequalities.

The inequality given is

5/8x - 1 ≥ 9

5/8x ≥ 9 + 1

5/8x ≥ 10

5x ≥ 10 * 8

5x ≥ 80

x ≥ 16

The value of x is greater than or equal to 16

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Answer:

f(x) / g(x) = x - 1   where x ≠ -1.

Step-by-step explanation:

f(x) / g(x) =   x² - 1 / x + 1

                = (x + 1)(x - 1) / (x + 1)

                = x - 1.

The angle whose tangent is 456/321 is 54.85°

The tangent of an angle in trigonometry is the ratio of the lengths of the adjacent side to the opposing side. In order for the value of the cosine function to not be 0, it is the ratio of the sine and cosine functions of an acute angle.

The Tangent Formula is given as:

Tan A = Opposite Side/Adjacent side

In terms of sine and cosine, tangent may be represented as:

Tan A = Sin A / Cos A

We know that the sine of an angle is equal to the length of the opposite side divided by the length of the hypotenuse side whereas the cosine of the angle is the ratio of the length of the adjacent side to the ratio of the hypotenuse side.

That is, Sin A = Opposite Side/ Hypotenuse Side

Cos A = Adjacent Side/ Hypotenuse Side

Therefore, tan A = Opposite Side/ Adjacent Side

[tex]tan^{-1} (1.42056)[/tex] =54.85°

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(x/5)-10 where x is "number"

The solution to the equation are x=a

The given equation is sin (2x) = a and 0 < x < pi/2

Sin(2x) = sin x, 0≤x≤2п  ........................... (eq. 1)

Using the trigonometrical formula,

sin(2x) = sin xcosx

Let us subtract the formula from equation 1

2sinxcosx = sinx

Therefore, 2sinxcosx-sinx = 0

Let us remove common terms to get

sinx(2cox-1)=0

Now, sinx=0

x= 0, [tex]\pi[/tex], [tex]2\pi[/tex]

Also, 2cos x =1

This means that cos x = 1/2

By implication, x=cos⁻¹(1/2)

That is to say that x= [tex]\frac{\pi }{3} , \frac{5\pi }{3}[/tex]

In conclusion, the value of [tex]\pi[/tex] is a as a single integer

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Therefore the balance after a year comes out to be $3552.80 and the balance comes out to be after compounded annually is $3552.50

Compound interest is the interest on savings that is computed using both the original principal and the interest accrued over time.

It is believed that Italy in the 17th century was where the idea of "interest on interest" or compound interest first emerged. It will accelerate the growth of a sum more quickly than simple interest, which is only applied to the principal sum.

Money multiplies more quickly through compounding, and the higher the

Here,

The Liam deposits $3,500 in a saving account that pays 1.5% interest,

Thus rate=1.5% and principle amount =3500

Therefore it is compounded quartely ,

The balance after year=

C=P[tex]e^{rt}[/tex]

C=3500*[tex]e^{1.5*4}[/tex]

C=3552.80

Therefore the balance after a year comes out to be $3552.80

Therefore the balance comes out to be after compounded annually is

$3552.50

So there is only $0.30 difference between the amounts

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The angles GBD, GBD and G measures 90 , 90, 52 degree respectively.

GB is the diameter given.

AD is the tangent given.

The tangent makes 90 degree angle with diameter.

hence the angle GBD will be : 90°

Similarly, GBA will also be 90°

The angle GBA is given as 38°

Hence the angle G will be = 90 - 38 =52

All points in a plane that are at a specific distance from a specific point, the centre, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant. The radius of a circle is the separation between any point on the circle and its centre.

The radius must typically be a positive integer. A degenerate situation is a circle with radius equal to zero (one point). Except when otherwise specified, this article discusses circles in Euclidean geometry, namely the Euclidean plane.

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Answer:

Let X be the amount Jaheem invested in the first money market, and Y be the amount he invested in the second money market. We can set up the following system of equations to represent the given information:

X + Y = 10000 (1)

0.125X + 0.0825Y = 925 (2)

We can solve this system of equations using any method of your choice, such as elimination or substitution.

Using elimination, we can multiply equation (1) by 0.125 and equation (2) by 10,000 to eliminate Y:

1.25X + 1250Y = 1250000

125X + 82500Y = 9250000

Subtracting the first equation from the second gives us:

124X + 82350Y = 8037500

Y = (8037500 - 124X)/82350

Substituting this expression for Y into equation (1) and solving for X gives us:

X + (8037500 - 124X)/82350 = 10000

X = $7,500

Therefore, Jaheem invested $7,500 in the first money market and $2,500 in the second money market.

Step-by-step explanation:

SELF EXPLANATORY

If the discriminant, b² - 4ac is positive

From the question, we have the following equation of discriminant

The discriminant (d) is calculated as

d = b² - 4ac

The solutions of a quadratic equation are dependent on the following conditions

This means that "d > 0, the quadratic equation has 2 different real solutions" implies that the discriminant is positive

Hence, the complete statement is (b) positive

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Answer:

17

Step-by-step explanation:

Using PEMDAS:

5² + 2(-8 ÷ 2)​

5² + 2(-4)

25 - 8

17

Carrie made a mistake in her step 3.

She was suppose to change the inequality symbols to the opposite after dividing by a negative number.

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.

Carrie is trying to solve this inequality.

2x - 5 < 11 + 6x

add 5 t both sides of the inequality

2x - 5 + 5 < 11 + 5 + 6x

2x < 16 + 6x

subtract 6x from both sides of the inequality

2x - 6x < 16 + 6x - 6x

-4x < 16

divide both sides by -4

-4x / -4 < 16 / -4

x > - 4

Therefore, She made a mistake in the step 3.

If she is dividing both sides of an inequality by a negative number, the inequality sign will change to the opposite.

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Before the change maple tree was 240 cm longer than cherry tree when the heights of a maple tree and a cherry tree currently have a ratio of 5:2. if the maple tree grew 20 centimeters, and 20 centimeters was cut off the top of the cherry tree, the ratio of their heights would be 3:1.

One quantity can be expressed as a fraction of another using a ratio, which is a number. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given,

Current ratio = 5:2

Let y equal the height of the cherry tree, and x represent the height of a maple tree.

x/y = 5/2

New ratio = 3:1

x+20/y-20 = 3/1

Cross multiplying,

x + 20 = 3(y - 20)

x = 3(y - 20) -20

Equating values in x/y = 5/2

3(y-20) - 20/y = 5/2

5y = 2(3y - 60) -20

5y = 6y - 160

y = 160

Now, for value of x,

Equating values in x = 3(y - 20) -20

x = 3(160 - 20) - 20

x = 480 - 60 - 20

x = 400

For the height,

400 - 160

240

Before the change maple tree was 240 cm longer than cherry tree when the heights of a maple tree and a cherry tree currently have a ratio of 5:2. if the maple tree grew 20 centimeters, and 20 centimeters was cut off the top of the cherry tree, the ratio of their heights would be 3:1.

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Answer:

The ordered pair that satisfies the system of equations is (7, -1)

Step-by-step explanation:

⭐What is a system of equations?

When we solve for an ordered pair that satisfies the system of equations, we are finding at what point do the equations intersect.

⭐How can we solve a system of equations?

For this problem, I find elimination to be the easiest. I will demonstrate how to use elimination to solve this system of equations.

⭐What is the elimination method?

We have the system: [tex]{ x+7y = 0\\\\2x - 8y = 22[/tex]. Let's eliminate the variable "x".

To do so, multiply the first equation by -2, then add both equations.

[tex]-2(x+7y = 0)\\-2x -14y = 0[/tex]

Now add this new equation with the second equation. This eliminates the x variable.

[tex]-2x - 14y = 0 \\+2x -8y = 22\\\\-22y = 22\\y = -1[/tex]

∴ y = -1

Next, we need to solve for the x variable. To do so, substitute the y variable into one of the equations we added and solve for x.

I will substitute y into the equation [tex]2x - 8y = 22[/tex], but you can also substitute it into [tex]-2x-14y = 0[/tex]

[tex]2x - 8y = 22[/tex]

[tex]2x-8(-1) = 22[/tex]

[tex]2x + 8 = 22[/tex]

[tex]2x = 14[/tex]

[tex]x = 7[/tex]

∴ The ordered pair that satisfies the system of equations is (7, -1)

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The vertex form of the equation is in the form of y = a(x-h)^2 + k.

Step 1: Use the formula below to solve for a.

a = -1/4 * (4 - 12) = -1

Step 2: Use the formula below to solve for h.

h = -b/(2a) = 12/(2(-1)) = -6

Step 3: Use the formula below to solve for k.

k = f(h) = -(-6)^2 + 12(-6) - 4 = 36

Therefore, the vertex form of the equation is y = -(x+6)^2 + 36.

A vertex, or particular point, is a place where two or more lines or edges meet in a mathematical object. Angles, polygons, polyhedra, and graphs are where vertices are most frequently seen. Nodes and vertices in a graph are the same thing.

Recall that a parabola's General Form is y = ax2 + bx + c. The x-coordinate of the vertices, which is x = - b/2a, must first be discovered in order to find the vertex from this form. You will use this number to replace x in the parabola equation once you have determined the x-coordinate of the vertex.

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