Principal amount: $1,000
Interest rate: 10%
Time: 12 months

The average rate of change of the function in the interval [5, 11] is -82.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂),

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

Given:

The table of values is shown in the image.

The average rate of change of the function in the interval [5, 11],

= the slope of the function in the interval  [5, 11].

= (-623 + 131) / (11 - 5)

= -492/6

= -82

Therefore, -82 is the slope.

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Answer:

x < -3

Step-by-step explanation:

Inequality form: x < -3

Interval Notation: (-[tex]\infty}[/tex],-3)

Answer:2nd one

Step-by-step explanation: look carefully at the problem and you will see one thing that makes the only possible solution graph #2 I dont want to give you the answer just look carefully at the problem.

The value of y in  [tex]x^\frac{1}{2} - 3y^\frac{1}{4} + 2 = 0[/tex]  is y = 1.189 for the quadratic-like equation.

Any equation of the form  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

The equation [tex]x^\frac{1}{2} - 3y^\frac{1}{4} + 2 = 0[/tex] is not a traditional quadratic equation, but it can be solved using numerical methods or by using a change of variables.

1) One possible method to solve the equation is to use the Newton-Raphson method, which is an iterative numerical method for finding the roots of a function. This method involves finding a first approximation for the root and then using that approximation to improve the estimate in each iteration until the root is found to a desired level of accuracy.

2) Another possible method is to change the variables to make the equation a traditional quadratic equation. For example, one could substitute  [tex]y\frac{1}{4} = x[/tex] and then solve for x. This would result in the equation [tex]x^{2} - 3x + 2 = 0[/tex], which can be solved using the quadratic formula.

Let us substitute [tex]y\frac{1}{4} = x[/tex]

Then we have x² - 3x + 2 = 0

On solving

⇒ x² -2x -  1x + 2

⇒ x² -2x -  1x + 2

⇒ x(x - 2) -1(x + 2)

⇒ (x - 2)(x - 1)

Thus, x = 1 and x = 2

Solving for y

[tex]y^{\frac{1}{4}} = 2[/tex]

y = [tex]\sqrt[4]{2}[/tex]

y = 1.189

[tex]1.189^{1/2} = 1.09[/tex]

Thus, the value of y in  [tex]x^\frac{1}{2} - 3y^\frac{1}{4} + 2 = 0[/tex]  is y = 1.189 for the quadratic-like equation.

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Answer:

x = -3

y = -4

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}6x-y=-14\\2x-3y=6\end{cases}[/tex]

Multiply the second equation by -3:

[tex]\implies 2x(-3)-3y(-3)=6(-3)[/tex]

[tex]\implies -6x+9y=-18[/tex]

Add this to the first equation to eliminate the term in x:

[tex]\begin{array}{crcrcl}\vphantom{\dfrac12}& 6x & - & y & = & -14\\\vphantom{\dfrac12}+ & (-6x & + & 9y & = & -18)\\\cline{2-6}\vphantom{\dfrac12}&&&8y&=&-32\\\cline{2-6}\end{array}[/tex]

Solve the equation for y:

[tex]\implies 8y=-32[/tex]

[tex]\implies y=-4[/tex]

Substitute the found value of y into one of the original equations and solve for x:

[tex]\implies 2x-3(-4)=6[/tex]

[tex]\implies 2x+12=6[/tex]

[tex]\implies 2x=-6[/tex]

[tex]\implies x=-3[/tex]

Therefore, the solution to the given system of equations is (-3, -4).

Answer:

Step-by-step explanation:

The given equations to us are ,

In elimination method we eliminate any variable and then find the find the value of second unknown variable. Using that value we can find the value of 1st variable.

Multiply equation 1 by 3 ,

3(6x-y)=-14*3

18x - 3y = -42 ..... (3)

Now subtract equation 2 and 3 to eliminate y as,

2x - 3y - (18x -3y) = 6 -(-42)

2x -3y -18x +3y = 6+42

-16x = 48

x = 48/-16 = -48/16

x = -3

Substitute this value in equation 2 ,

2*(-3) -3y = 6

-6-3y =6

-3y =6+6

-3y = 12

y = -4

And we are done!

The triangle is congruent by the Angle side Angle property.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.

The Angle side Angle Congruence Theorem (ASA) defines two triangles to be congruent to each other if the included two angles and one side of one are congruent to the included angle and corresponding two sides of the other triangle.

The three parameters that are congruent are:-

BV ≅ BV ( common side)

∠1 ≅ ∠2  ( Bisector)

∠3 ≅ ∠4  ( Bisector)

Hence, the two triangles are congruent with each other.

The question on geometry is attached with the answer below.

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Just enter each value of x into the formula f(x) = x - 4. For example, f(x) = 2 - 4 = -2 when x = 2.

A general rule is that the algebraic expression should take any of the following forms: addition, subtraction, multiplication, and division. to ascertain x's value.

Finding the value of f(x) =... or y =... that corresponds to a given value of x is the definition of function evaluation. Simply swap out all instances of x with the value that has been allocated to x to do this. For instance, if f(4) is to be evaluated, then x has been given the value of 4.

Separate the variable. In this instance, you transfer the constant term across the equal sign by doing the reverse operation on both sides and adding 1 to isolate the variable term. Isolate the variable further, then simplify.

Given,

f(x)=x-4

⇒ when x = -2,

⇒ f(x) = -2 -4 = -6

When x = -1,

⇒ f(x) = -1 -4 = -5

When x = 0

⇒ f(x) = 0 -4 = - 4

When x = 1

⇒ f(x) = 1 -4 = -3

When x = 2

⇒ f(x) = 2 -4 = - 2

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Answer:

About $0.08 per an oz

Step-by-step explanation:

Number of outcomes are in R​,

⇒ n (R) = 8 / 19

And, Number of outcomes are not in R,

⇒ n (R') = 11 / 8

A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Given that;

You take a random token from a bag that contains 8 red, 7 green, and 4 blue tokens.

Hence, Number of outcomes are in R​,

⇒ ⁸ C ₁ / ¹⁹C₁

⇒ 8 / 19

⇒ n (R) = 8 / 19

And, Number of outcomes are not in R,

⇒ 1 - 8/19

⇒ 11 / 8

⇒ n (R') = 11 / 8

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as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

[tex]\stackrel{f(x)}{y}~~ = ~~\cfrac{x+5}{x+7}\hspace{10em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~\cfrac{y+5}{y+7}} \\\\\\ xy+7x=y+5\implies xy-y+7x=5\implies xy-y=5-7x \\\\\\ \stackrel{\textit{common factoring}}{y(x-1)=5-7x}\implies y=\cfrac{5-7x}{x-1}=f^{-1}(x) \\\\[-0.35em] ~\dotfill\\\\ f^{-1}(-8)~~ = ~~\cfrac{5-7(-8)}{(-8)-1}\implies f^{-1}(-8)=\cfrac{61}{-9}\implies f^{-1}(-8)=-6\frac{7}{9}[/tex]

One learning aid that  provides an interactive​ walk-through for solving the particular problem you are working on is "view an example"

It is also known as teaching aids, which are an essential part of any classroom. Teaching aids can help students improve their reading comprehension skills, illustrate or reinforce a skill or concept, differentiate instruction, and relieve anxiety or boredom by presenting information in a new and exciting way.

Teaching aids also engage students' other senses because there are no restrictions on what aids can be used to supplement a lesson. As technology advances, so do teaching aids, which are now classified as audio aids, visual aids, mechanical teaching aids, audio-visual aids, and more.

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Answer:

2A=B

Step-by-step explanation:

use ratio of axis to solve the scale. verify to second axis.

x axis: 4 A to 8 B

set Ratio A/4 = B/8 and solve

2A = B or A = (1/2)B

verify to sefond axis.

y axis: 3A to 6 B

A/3 = B/6

2A = B or A = (1/2)B

Answer: No. It is positive

Step-by-step explanation:

I am assuming 10.75 is the sum and you are not missing another additive. A positive sum holds a value equal to or over zero while a negative sum is less than zero on the number line.

Answer:

14,35,42,63,77

Step-by-step explanation:

Actually how to get the output you follow the rule;

n×7

the first will be;2×7=14

the second will be; 5×7=35

the third will be; 6×7=42

the forth will be; 9×7=63

the fifth will be; 11×7=77

To save $10,000 over two years, you would need to deposit $20,407 per month in an account earning 4.7% interest (compounded monthly).

Divide the capital by the cost of borrowing, the length of time, and certain other considerations to arrive at simple interest. Simple return = principal + interest + hours is the commercial formula. This method allows it easiest to calculate interest. The most basic technique to figure the interest is as a portion of the outstanding amount. He will only pay his share of the 100% interest, for example, if he borrowed $100 from a partner and agrees to repay the loan th with 5% interest. $100 (0.05) = $5. When you keep borrowing, you must pay interest, and when you give it out, you must lend money.

given

Future Value = Current Value x (Present Value + Interest Rate) (Years/frequency of payments per year)

FV = (-15,000 x [1+8%]^

[4/1])

PV is adverse because you are redistributing funds.

FV = $20,407

Calculator for Finances: Enter PV of -15,000 as

Make 4 N.

Set 8 as I/Y CPT FV and 0 as PMT

$20,407

To save $10,000 over two years, you would need to deposit $20,407 per month in an account earning 4.7% interest (compounded monthly).

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Answer:

[tex]\frac{61}{10}[/tex]

Step-by-step explanation:

14/5=28/10

By changing the denominator so that they are equal, you can now add the two fractions together.

(28/10)+(33/10)=61/10

Hope this helped! :)

Finance amount: The amount you can finance for a new car with a monthly payment of $240, for 60 months (5 years), depends on several factors, including the loan interest rate, the down payment, and the value of the car.

Estimated percentage rate: The interest rate for a new car loan with a credit score between 601-660 typically ranges from 5% to 10%.

Amount of interest you will pay for the loan: The amount of interest you will pay for the loan can be calculated by multiplying the loan amount by the interest rate and the number of months.

For example, if you finance $20,000 at a 7% interest rate for 60 months, the total interest paid over the life of the loan would be $3,140.

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The quadrilateral exists not a parallelogram.

The formula to calculate the distance between two points is equal to

[tex]$$d=\sqrt{(y 2-y 1)^2+(x 2-x 1)^2}$$[/tex]

We have Q(-10,-2), R(1,-1)

substitute the values in the above equation, we get

[tex]& d=\sqrt{(-1+2)^2+(1+10)^2} \\[/tex]

simplifying the equation, we get

[tex]& d=\sqrt{(1)^2+(11)^2} \\[/tex]

d = √122 units

Find the distance TS

the formula to calculate the distance between two points is equal to [tex]$d=\sqrt{(y 2-y 1)^2+(x 2-x 1)^2}$[/tex]

we have

T(-11, -8), S(1, -7)

substitute the values in the above equation, we get

[tex]$d=\sqrt{(-7+8)^2+(1+11)^2}$[/tex]

simplifying the equation, we get

[tex]$d=\sqrt{(1)^2+(12)^2}$[/tex]

d = √145 units

We know that the opposite sides of QR and TS exist.

The opposing sides of a parallelogram are congruent, but in this case, QR TS.

√122 units ≠ √145 units

Therefore, the quadrilateral exists not a parallelogram.

The complete question is:

Determine whether the quadrilateral is a parallelogram using the indicated method Q(-10,-2), R(1,-1), S(1,-7), T(-11,-8) (Distance Formula)

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Step-by-step explanation:

remember, y = f(x)

so, the question is really for what x is y = 1 ?

and what is the y-value for x = -1 ?

a)

when we imagine a horizontal line through y = 1, at what points (x-value) does this line cross the function graph ?

as we can see, at x = -2 and x = 2.

pick one for your answer.

b)

now we imagine a vertical line through x = -1.

at what point (y-value) does this line cross the function graph ?

as we can see, at y = 4.

f(-1) = 4

Without the cost of the electrical power, the cash cost of production would be $104,040 + $2460 = $106,500 per year.

What is the addition?

Addends are the numbers being added, and the result or the final answer we get after the process is called the sum.

The cost of raw materials can be calculated as follows:

Caprolactam: 1.02 tons per ton of product * 60 tons of product per year = 61.2 tons of caprolactam per year

Cost of caprolactam: 61.2 tons per year * $1700 per ton = $104,040 per year

The cost of utilities can be calculated as follows:

Fuel gas: 9 MMBtu per ton of product * 60 tons of product per year = 540 MMBtu per year

Cost of fuel gas: 540 MMBtu per year * $4.50 per MMBtu = $2460 per year

Cooling water: not a cost as it's a utility not charged

Electrical power: 130 kWh per ton of product * 60 tons of product per year = 7800 kWh per year

Cost of electrical power: Not specified, we need the cost per kWh to calculate it.

Hence, without the cost of the electrical power, the cash cost of production would be $104,040 + $2460 = $106,500 per year. If we had the cost of electrical power, we could add it to this amount to get the complete cash cost of production.

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Answer: x = 7

Step-by-step explanation:

The right angle is equal to 90 degrees

Therefore (5x - 8) + (4x + 35) is equal to 90 degrees

5x - 8 + 4x + 35 = 90

5x + 4x + 35 - 8 = 90

9x + 27 = 90

     - 27    -27 (subtract 27 from both sides)

9x = 90 - 27

9x/9 = 63/9 (divide both sides by 9)

x = 7

Check

5(7) - 8 + 4(7) + 35 = 90

35 - 8 + 28 + 35 = 90

Answer:

Step-by-step explanation:

ur mom

Answer:

6

Check if you have written the function equation properly. If you have, this is the answer

Step-by-step explanation:

Average rate of change is the first differential of the function

Given function is f(x) = 6x + 5

Rate of change = f'(x) = d/dx(6x) + d/dx(5)

= 6 + 0

= 6

The average rate of change(slope) is a constant throughout all values of the function and so also between[4, 7]

The total angle made at the center of the pie chart is 360°

An angle is formed when two lines come together at a point. The distance between these two rays, known as the "opening," is measured as a "angle." This character represents it. Degrees and radians are frequently used to quantify an angle's circularity or rotation. Angles frequently appear in daily life.

In geometry, an angle is made when two rays are connected at their ends. These rays are known as the sides or arms of the angle. Continue reading to find out more about an angle's many parts.

Two rays form an angle when they come together at a point. The symbol represents a "angle," which is the phrase used to describe the "opening" between these two rays.

Number of students playing volley Ball = 48

Total number of students = 50 +48 +60 + 22 = 180

The measure of central angle representing the students playing volley Ball = 48 180 x 360° = 96°

:. The angle made by the volleyball playing student is 96°

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Given question is incomplete , the complete question is given below

The table shows the number of students of a school who play different games.

Game                     football         volleyball       cricket      basketball

No. of                          50                  48                 60                22

students

When the data shown in the table above is presented in a pie chart, what will be the measure of the central angle of the sector representing the students playing Volley Ball?

The rate of change of the area of the triangle after two seconds have passed is 16 cm².

Right angled triangle are those triangle for which one of the angle is 90 degrees.

Area of a right angled triangle = [tex]\frac{1}{2}[/tex] × base × height

Given that, the lengths of the right sides of a right triangle were 12 cm and 16 cm.

Initial area of the triangle = [tex]\frac{1}{2}[/tex] × 12 × 16

                                          = 96 cm²

The first side is increasing at a rate of 2 cm/sec and the second side is decreasing at a rate of 1 cm/sec.

After 2 seconds, length of base = 12 + (2 × 2) = 16 cm

After 2 seconds, length of height = 16 - (2 × 1) = 14 cm

Area of the triangle after 2 seconds = [tex]\frac{1}{2}[/tex] × 16 × 14

                                                            = 112 cm²

Rate of change of area = 112 cm² - 96 cm² = 16 cm²

Hence the rate of change of area is 16 cm².

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Answer:

Step-by-step explanation:

I think it 5

Answer:

Step-by-step explanation:

The number that goes under the radical sign in 17.

The answer is [tex]\sqrt{17}[/tex]

use the distance formula to calculate the distance between to two points.

Distance (d) = √(3 - -1)² + (-1 - -2)²

= √(4)² + (1)²

= √17

The value regarding the probability shows that n is 5, p is 0.4 and q is 0.6.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur.

a)n=5

P=40%=0.4

q=1-p=1-0.4=0.6

b)p(x)= nc x p x q^n-x

p(x=3)=5C3×0.4^3×0.6^2

=0.2304

C) E(x)=np=5×0.4=2

Expected number of applications that will need research is 2

d)or(at least the expected number of applications)=p(x≥2)=1-p(x<2)

=1-{p(x=0)+p(x=1)

=1-{5C0×0.4^0×0.6^5 +5C1×0.4^1×0.6^4}

=1-0.3370

=0.6630

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Therefore , the solution of the given problem of quadratic equation comes out to be quadratic equation., cubic equation and leading coefficient is 1.

For one-variable equations, the quadratic result x = ax2 + b + c=0 is used in regression modeling. The First Thesis basic Algebra asserts that there is just one solution because this equation has a second order. Both straightforward and complex solutions can be found. A "quadratic solution," as the name suggests, consists of four variables. This suggests that there might be a single squared word.

Here,

Given :

=> x² + 2x -5 its degree is 2

hence quadratic equation.

=> 4x³ -8 its degree is 3

hence cubic equation

=> 2x⁴ - 7x² -5x + 1 its degree is 4

hence its an degree 4 equation.

leading coefficient of:

=> x³ + 5x² + 28 -x

leading coeffcient is = 1

Therefore , the solution of the given problem of quadratic equation comes out to be quadratic equation., cubic equation and leading coefficient is 1.

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The sum of two even integers or two odd integers is always even. However, the sum of an even and an odd integer is always odd.

The sum of two even integers or two odd integers is always even because an even integer is a multiple of two. Therefore, if two even integers are added together, the sum will also be a multiple of two (an even integer). Similarly, an odd integer is a multiple of two plus one, so when two odd integers are added together, the sum will be a multiple of two plus two (an even integer). On the other hand, the sum of an odd and an even integer is always odd because an even integer is a multiple of two and an odd integer is a multiple of two plus one. Therefore, when an even and an odd integer are added together, the sum will be a multiple of two plus one (an odd integer).

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