Help!! Direct and Inverse Variations

The loan amount at the end of 2 years is Rs. 12,127 .

In the given question we have, amount Rs. 11500 is borrowed by investor at the interest rate of 6% per annum.

compund interest is defined as the addition of interest to the principal of loan.

principal (P) = 11500

If interest is compunded quarterly then time(t) = 3 years = 12 , rate ( r%) = 6/4% = 2/3 %

Using the formula of Amount ,

Amount = P( 1 + r / 100) ᵗ

= 11500( 1 + 2/ 300)⁸

= 12127.83 ~ 12128

compound interest = Amount - principal =

12128- 11500 = Rs. 628

So, An investor has to pay total Rs. 12128 at the end of 2- year.

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The given quadrilateral PONY is rotated to 180° as P'O'N'Y' and its coordinates are:

So, rotate the given quadrilateral at 180° as follows:

Given quadrilateral: PONY

Rotate to 180° and plot as follows:

Quadrilateral after rotation: P'O'N'Y'

(Refer to the graph attached below)

Therefore, the given quadrilateral PONY is rotated to 180° as P'O'N'Y', and its coordinates are:

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Answer:

P': (2, -7)

O': (2, -3)

N': (6, -3)

Y': (5, -6)

Step-by-step explanation:

Answer: Cannot be factored

Step-by-step explanation:

= Factor Y^2x -y^x-20

= Cannot be factored

Answer:I think $1064

Step-by-step explanation:

First you multiply 1/5 by 420 and then add, so 1/5 x 420 = 84 & 420 + 84 = 504. Then you multiply 1/3 by 420 and also add, so 1/3 x 420 = 140 & 420 + 140 = 560. After you add both totals to get your final answer, so 504 + 560 = 1064. Her income each month is $1064.

Answer:

the shorter leg = 9mm

the longer leg = 12mm

the hypotenuse is 15mm

Step-by-step explanation:

x^2 +(x+3)^2 =(x+6)^2

x^2 + x^2 + 6x +9=x^2 + 12x +36

x^2-6x-27=0

(x+3)(3-9)=0

x=-3 (impossible) ... or x=9

The value of the variables x and y in each figure are 28 and 46.3 respectively.

Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line.

Therefore,

5x + 40 = 180,

5x = 180 - 40

5x = 140

x = 28

Also,

(3y-1 ) and 40 are corresponding angles, thus

40 + 3y - 1= 180 ,

3y = 180 - 40 + 1

3y = 139

y = 46.3

Thus, the value of the variables x and y in each figure are 28 and 46.3 respectively.

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If ∠4 ≅ ∠14, then the lines that must be parallel are a and b and so we can say that; a∥b, Converse of the Alternate Interior Angles Theorem

Interior angles are basically the pair of angles created on the inner side of the parallel lines and right on the opposite sides of the transversal when two parallel lines are intersected by a transversal .

We are told that ∠4 ≅ ∠14, which lines,

If a transversal connects two parallel lines, we know that the corresponding angles and vertically opposite angles are equivalent.

Thus, angle 4 is congruent to angle 14.

Therefore, we can deduce the following;

Angle 15 is a corresponding angle to angle 3 and so we can write that;

∠15 ≅ ∠3

Angle 15 is a vertically opposite angle to angle 13 and so we can write that; ∠15 ≅ ∠13

By transitive property of equality, we can say that;

∠3 ≅ ∠13    [Alternate interior angles]

Thus, we have  ∠4 ≅ ∠14

Therefore, we conclude that a∥b, Converse of the Alternate Interior Angles Theorem.

Hence, the correct answer would be an option (B).

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If sum of the measures of the angles in the triangle is 180 degrees then

measures of each angle is 60 degrees.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given,

The sum of the measures of the angles in the triangle is 180 degrees

By angle sum property,  sum of the measures of the angles in the triangle is 180 degrees

Let the measure of angle be x

x+x+x= 180 degrees

3x=180

Divide both sides by 3

x=180/3

x=60

Hence each angle measures 60 degrees.

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Using simple mathematical operations, the missing values are as follows:

(B) Dijon Mustard: 18g

(C) Barbeque sauce: 70g

(D) Worcestershire sauce: 10.35g

(E) Kosher salt: 1.5g

(F) Ground black pepper: 2.3g

(G) Crushed red pepper: 1.15g

So, we can calculate missing values as follows:

(B) Dijon Mustard: 18g

(C) Barbeque sauce: 70g

(D) Worcestershire sauce: 10.35g

(E) Kosher salt: 1.5g

(F) Ground black pepper: 2.3g

(G) Crushed red pepper: 1.15g

Therefore, using simple mathematical operations, the missing values are as follows:

(B) Dijon Mustard: 18g

(C) Barbeque sauce: 70g

(D) Worcestershire sauce: 10.35g

(E) Kosher salt: 1.5g

(F) Ground black pepper: 2.3g

(G) Crushed red pepper: 1.15g

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The rational roots of the given equation x(3x − 4) (x − 5) = 0 are x = 0, 4/3 and 5

What is Rational Number?

Numbers that may be expressed in the form p/q, where p and q are integers and q0, are considered rational numbers. Because fractions cannot have a negative numerator or denominator, they differ from rational numbers in this respect. Because of this, the numerator and denominator of a fraction are whole numbers (denominator 0), unlike in the case of rational numbers, when they are both integers.

So to convert a fractional to reduce form we have to divide by 10 to power how many digits thereafter decimal point, and make sure that numerator or denominator doesn't have common divisible.

x(3x − 4) (x − 5) = 0

So we can put every term equal to zero to find it's root.

1st case, x = 0

2nd, 3x-4 = 0

        3x = 4

         x= 4/3

3rd, x-5 = 0

        x = 5

Hence, the rational roots of the given equation are x = 0, 4/3 and 5

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Answer:

negative, as the points are slowly making their way "down" the graph :)

Answer:

Option D

Step-by-step explanation:

This is because it contains the sum of the same variable to different powers.

The capital letters of the word TRANSFORMATION are rotated 180 degrees, they generate the same letter are I, N, O and S.

It is possible to rotate clockwise or counterclockwise. If an item needs to be rotated, there are several methods for doing so:

When the capital letters of the word TRANSFORMATION are rotated 180 degrees, they generate the same letter: I, N, O and S.

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Answer:

48cm = 480mm

Step-by-step explanation:

1cm = 10mm

48cm = 48 X 10 mm

48cm = 480mm

Answer:

480mm

When converting from cm to mm, multiply by 10.

48 x 10 = 480

Answer: [tex]x=13, y=132[/tex]

Step-by-step explanation:

Using the same-side interior angles theorem, [tex]y=132[/tex].

Using the alternate interior angles theorem, [tex]5x-17=48 \implies x=13[/tex]

Answer:

x<6

Step-by-step explanation:

2x/3<4

2x<12

x<6

Answer:

x < 6

Step-by-step explanation:

[tex]\frac{2x}{3}[/tex] < 4 ( multiply both sides by 3 to clear the fraction )

2x < 12 ( divide both sides by 2 )

x < 6

Answer: (0,-2)

Step-by-step explanation: just multiply

The amount that Omar will pay when he bought 3.5k of onions are 8.90 per kilo is $31.15.

From the information given, Omah wants to know the total amount that he will pay for the onions. It's important to know the cost for each kilogram of onion and then multiply it but the number of kilograms that are bought.

In this case, Omar bought 3.5k of onions are 8.90 per kilo.

The amount that Omar will pay for the onions will be:

= Number of kilograms × Cost per kg

= 3.5 × 8.90

= $31.15

In conclusion, the amount is $31.15.

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The end behavior of the function is f(x) → -∞, as x→ -∞ and f(x) → -∞, as x→ +∞.

A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity.

The graph's final behavior is determined by a polynomial function's degree and leading coefficient.

For extremely big or very tiny values, the leading coefficient is more important than the other function coefficients. Therefore, it is sufficient to forecast the function's final behavior based on the sign of the leading coefficient.

The given function is -x⁴ -x³ +3x² +2x +6

The degree of the given function is even and the leading coefficient is negative. So,

End behavior is given by

f(x) → -∞, as x→ -∞

f(x) → -∞, as x→ +∞

The graph looks as follows:

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The probability that the divisor chosen is a perfect square is found to be 1/22 which is m:n.

Given: Randomly, a positive integer divisor of 12! is selected.

Prime factorization of 12! = 2¹⁰ × 3⁵ × 5² × 7¹ × 11

Total divisors of 12! = 11 × 6 × 3 × 2 × 2

The probability that the divisor chosen is a perfect square is given as:

(6 × 3 × 2)/(11 × 6 × 3 × 2 × 2)

= 1/22

=m/n

Therefore, the probability that the divisor chosen is a perfect square is found to be 1/22 which is m:n.

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Step-by-step explanation:

the answer is Y=-1/2×+5

Explanation:

You put the gradient in M for Y=M×+C (substitute) then you substitute the coordinates it has given you into the X and Y part of linear equation. (x,y)

Answer:

D

Step-by-step explanation:

Using the properties of conditional statements we can write the inverse of the statement as ": if the 2 smallest sides sum is not larger than the 3rd side, then it is not a triangle."

The statement  is given as if the sum of two sides is greater than the third side then it is a triangle.

Now for the inverse we have to convert the given line into double negative.

Hence we get:

If the 2 smallest sides sum is not larger than the 3rd side, then it is not a triangle

Conditional statements are part of mathematical reasoning, a vital skill that enables students to evaluate a given hypothesis without reference to a particular context or meaning. Simply put, when a scientific research or allegation is studied, the logic isn't truly founded on an individual's perspective. Deductions and evidence must have factual and scientific foundations.

the various types of conditional statements are:

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Answer: 31, 33, 35

Step-by-step explanation:

The vertex of the parabola is at (-2, 2), the line of symmetry of the parabola is at x = -2 and the parabola is open downwards

From the given parabola

The vertex of the parabola is at (-2, 2)

The vertex of the parabola is defined as the the point at the intersection of the parabola and its line of symmetry.

The line of symmetry is at x = -2

The parabola is open downwards

Hence, the vertex of the parabola is at (-2, 2), the line of symmetry of the parabola is at x = -2 and the given parabola is open downwards

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Answer:

Step-by-step explanation:

-8x-7=33

    +7 +7

-8x=40

x=-5

Answer:

y+1=-4(x+5)

Step-by-step explanation:

it changed to point slope form so now it’s different

the equation is y-y1=m(X-x1)

y-(-1)=m(x-(-5)

y+1=m(x+5)

Now to find slope y2-y1/x2-x1

-5+1/-4+5

-4/1

-4 is the slope so we just fill it in

y+1=-4(x+5)

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The diameter of the circle is 4.45 units.

What is circle?

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry. Also, it has rotational symmetry around the centre for every angle.

A line segment having both the endpoints on the circle and is the largest chord of the circle is called diameter.

Given,

the circumference of circle = 14 units

circumference = πd

14 = 3.14(d)

14/3.14 = d

d = 4.45

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The maximum area is 640,000.

Given fencing yards = 3200

let the length be x and the width be y

The parameter of the rectangle is given as;

2(L + B),that is

2(x + y) = 3200

x + y = 1600

y = 1600-x

let the area of the rectangle be A, then

A = x y

A = x(1600-x)

A = 1600x - x^2

finding the maximum derivative of A with respect of x

da/dx = 1600 - 2x

set da/dx to zero,

1600 - 2x = 0

1600 = 2x

x = 1600/2

x =800

substitute the value of x = 800 in to y

y = 1600 - 800

y = 800

The maximum area is 800 x 800

Therefore Maximum area = 640,000.

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