Three vertices of a parallelogram are shown in the figure below. Give the coordinates of the fourth vertex. (7,2) (-4,0) (-6, -7)

Given:

Total invested amount = $9000

One account = 5%

Another account = 6%

Find-:

Invested amount of each equation

Explanation-:

Let in 5% account invested amount is x

then amount in 6% account is (9000-x)

Then,

Then the value of "x" is:

The "x" is:

The value of x is 3000 the mean amount in 5% invested amount is 3000.

6% invested amount is:

So each account invested amount is:

Answer: 120

Step-by-step explanation:

All angles in a triangle add up to 180. The third angle in the triangle is 60. A straight line is always 180, and line TU intersects it. So, subtract 60 from 180 and you get 120.

Answer:

120 degrees

Step-by-step explanation:

70 + 50 = 120 (exterior angle of a triangle)

Given:

Adrian initially has $52,000 and n denotes the number of years

Required:

Adrian's annual income, /(7), as a function of

the year?

Explanation:

Initially has $52,000, therefore

The salary is 1.05 times the previous year's salary.

Required answer:

Option D

Answer:  [tex]3\sqrt{2}+3\sqrt{5}[/tex]

===================================================

Work Shown:

[tex]\sqrt{3}\left(\sqrt{6}+\sqrt{15}\right)\\\\\sqrt{3}*\sqrt{6}+\sqrt{3}*\sqrt{15}\\\\\sqrt{3*6}+\sqrt{3*15}\\\\\sqrt{18}+\sqrt{3*3*5}\\\\\sqrt{9*2}+\sqrt{9*5}\\\\\sqrt{9}*\sqrt{2}+\sqrt{9}*\sqrt{5}\\\\3\sqrt{2}+3\sqrt{5}\\\\[/tex]

-------------------

Explanation:

I distributed and used the idea that sqrt(A*B) = sqrt(A)*sqrt(B) to combine square roots, but also to break them up when factor out the largest perfect square factor.

Optionally for the last step, you could factor out 3, but your teacher may want you to leave it like shown.

Explanation

Question 10

We are asked to write the quadratic eqation that has the solutions of x=3 and x =-7

To do so, we will make use of

So we will follow the steps below

substituting the above, we will have

Therefore, the quadratic equation is

The circumference of the circle is

Since P(t) models the number of people on a beach, t hours past midnight, hence P(10)=N means that there were N people on the beach at 10 am

The number of graduates in the sample that came from University A is:

35 + 90 + 35 = 160 graduates

let's recall the vertical line test, if a vertical line hits the graph or points twice, then is NOT a function.  Check the picture below.

A very easy way to find out if a graph is a function is to use the vertical line test.

Look at each graph and mentally draw a vertical line that goes through each of its points.

If that line goes through more than one point (2, 3, 4...) then that graph is not a function.

That's because a function, is an equation for which each input (x value) has exactly one output (y value). There cannot be two points of the same x value, with two different y values.

Given the function below,

Let us now plot the graph in order to obtain the end behaviours.

From the graph above, we can conclude that

Hence, the correct answer is Option D.

Answer:

1 is the answer

Step-by-step explanation:

a-b+c       Substitute values into the equation

4-2+(-1)

2+(-1)

2-1

1 Answer

The value of: 1) a - b + c is, 1 is the solution.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

a=4 b=2 and C=-1

now,

a-b+c      

Substitute values into the equation

we get,

4-2+(-1)

=2+(-1)

=2-1

=1  (Answer)

Hence, The value of: 1) a - b + c is, 1 is the solution.

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11 is the greatest number of bags that Jason can fill with equal number of raspberry and blackberry scones.

In this question we have been given Jason has 22 raspberry scones and 55 blackberry scones.

We need to find the maximum number of bags Jason can fill with equal number of raspberry scones and blackberry scones.

We will be using Greatest common factor (GCF) for knowing the number of bags.

22 = 2 × 11

and 55 = 5 × 11

So, the greatest common factor of 22 and 55 is 11

GCF(22, 55) = 11

Therefore, 11 is the greatest number of bags that Jason can fill with equal number of raspberry and blackberry scones.

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In a line plot the maximum value is the rightmost mark in the line plot; in this case the maximum capacity is 2 1/2. On the other hand the minimum value is the leftmost mark in the line plot, here the minimum is 1 1/2. Let's calculate the difference between them:

Therefore, the difference between the maxiimum and minimum capacity is 1.

Answer:

The solution to the inequality is;

Explanation:

Given the inequality;

Firstly, let's multiply both sides of the equation by 9;

Then we can multiply both sides by -1.

Note that when we multiply both sides by a negative number(-1) the sign will change;

So;

The solution to the inequality is;

Answer: 2%

Step-by-step explanation:

Exponential growth functions are of the form [tex]P(1+r)^t[/tex], where r is the rate of change. From the equation, we see that r=0.02, and converting this to a percentage, we get 2%.

Considering a parabolic equation with a vertex of (-7,-2) and directrix of x = -1. This is a horizontal parabola

The directrix of a parabola is a straight line perpendicular to the axis of symmetry of the parabola.

The directrix does not touch the parabola

A parabolic equation is also called quadratic equation.

Since the directrix is perpendicular to the axis of symmetry of the parabola it means that if:

The axis of symmetry says if the parabola is vertical or horizontal, when the axis of symmetry is parallel:

In the given problem, the directrix is given at x, the axis of symmetry is along the x direction and hence a horizontal parabola

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Answer: 1 minute

Step-by-step explanation:

First elevator's rate is 200 meters per second

Second's rate is 250

In one second, they would travel 450 meters

Answer:

Step-by-step explanation:  

The pancakes stall sells total 12 combinations of pancakes.

What is Combination?

Combinations are mathematical operations that count the number of potential permutations for a set of elements when the order of the selection is irrelevant.

According to the given data:

Savory pancakes can have 3 toppings in any combination.

Therefore, total number of savory pancake combinations = 3 x 2 x 1 = 6

For sweet pancakes jams can either have ice cream or fresh cream.

Therefore combinations with ice cream = 3

And combinations with fresh cream = 3

Hence total combinations for sweet pancakes = 3 + 3 = 6

Now, total pancakes combination = 6 + 6 = 12

So, the stall sells 12 combinations of pancakes.

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1.

Algebra:

Graph:

2.

Words:

x is greater than 3 or x is less than minus 2

Graph:

3.

Words:

x is greater than minus 1 and x is less than 2.

Algebra:

The solution of 3x−10>5 inequality is x>5 and is graphed with the image attached.

what is inequality?

Given inequality,

3x−10>5

3x>5+10

3x>15

x> (15/3)

x>5

The solution of 3x−10>5 inequality is x>5 and is graphed with the image attached.

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Answer:  If we take the aerobics class, then we will be in good shape for the ski trip

===============================================

Explanation:

The conditional statement in bold is of the form "If P, then Q" where

P and Q are placeholders for logical statements, in much a similar fashion that x = 2 has x as a placeholder for the number 2.

Answer:

f

Step-by-step explanation:

The sum of the interior angle of a polygon with 10 sides is equal to 1440°

If it can be expressed as 360n, then n is

Interior Angle Theorem asserts that the alternate interior angles that result when two parallel lines are cut by a transversal are equivalent.

If m2 + m28 = 180 then we get ∠2 + ∠8 = 180°

Lines that are parallel to one another on a plane do not intersect or meet at any point.  They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines.

Two lines are said to be parallel if a transversal and two matching angles it forms are congruent.

Verification of Parallel Lines

When two lines are intersected by a transversal and the opposing interior angles line up, the intersected lines are said to be parallel. Two lines are said to be parallel if they are divided by a transversal such that their opposing exterior angles are equivalent.

Therefore,

Given line m is parallel to line m

Interior Angle Theorem asserts that the alternate interior angles that result when two parallel lines are cut by a transversal are equivalent.

Alternate Exterior Angles are congruent if a transversal cuts two parallel lines. When a transversal cuts two parallel lines, the resulting angles are congruent.

Therefore, ∠2 = ∠6

∠2 + ∠4 = 180° ( Sum of the angles on a straight line is 180°)

∠6 + ∠8 = 180° ( Sum of the angles on a straight line is 180°)

∵  ∠2 = ∠6

∴ ∠6 + ∠8 = 180° ⇒ ∠2 + ∠8 = 180°

∠2 + ∠8 = 180° , Hence Proved.

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The coordinates of the point P lying between AB is found as (7, -2/5).

For the given question;

The two end coordinates are;

(x₁, y₁) = (8, 0)

(x₂, y₂) = (3, -2)

The ratio of the division is;

AP/PB = 1/4

OR

m:n = 1:4

The Formula for finding the coordinates of P for internally crossing is;

x = (mx₂ + nx₁)/(m + n)

y = (my₂ + ny₁)/(m + n)

Put the values;

x = (mx₂ + nx₁)/(m + n)

x = (1×3 + 4×8)/(1 + 4)

x = (3 + 32)/5

x = 7

Now for y coordinates.

y = (my₂ + ny₁)/(m + n)

y = (1×(-2) + 4×0)/(1 + 4)

y = -2/5

Thus, the coordinates of the point P lying between AB is found as (7, -2/5).

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Below is the figure of the triangle

We have three unkown variables which are x, y, and z

Firstly, let us find the unknown side z

To find z, we will be applying SOH CAH TOA

The longest side is z

The opposite sides is 39

Find x

X can be find by applying the SOH CAH TOA

Let z = opposite

let x = adjacent

Find y

let y = adjacent

x = Hypotenus

Applying SOH, CAH TOA

The standard form is 6x⁴+5x³-2x-15.

Here the term polynomial is characterized as an expression that is composed of variables, exponents, and constants, that are combined utilizing numerical operations such as subtraction,  addition, division, and multiplication. the standard form of a polynomial is :

P(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ +aₙ₋₂xⁿ⁻² + ………………. + a₁x + a₀  

Where aₙ, aₙ₋₁, aₙ₋₂, ……………………, a₁, a₀  are the coefficients of xⁿ, xⁿ⁻¹, xⁿ⁻², ….., x and are to a real number.

The polynomial given to us is (3x² + x − 5) (2x² + x + 3)

=3x²(2x² + x + 3) + x (2x² + x + 3) − 5 (2x² + x + 3)

= 6x⁴ + 3x³+9x²+2x³+x²+3x-10x²-5x-15

= 6x⁴+3x³+2x³+9x²+x²-10x²+3x-5x-15

= 6x⁴+5x³-2x-15

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We can find the unit price of a ticket by dividing the number of purchased tickets by the total price, like this:

Then, the unit price of the tickets is $0.15

The figure's perimeter and area would be as follows.

Perimeter = 21.19 cm

Area = 25.501 cm²

A Cartesian coordinate system in some kind of a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates, which are the signed distances from two fixed perpendicular lines that are aligned to the point and are both measured in the same length.

point of the coordinates are as follows:

A(2, 1)

B(8, 6).

C(10, 1)

We know that the formula for finding for the distance is:

d=√((x2 – x1)² + (y2 – y1)²).

For Point AB:

X₁ = 2

Y₁ = 1

X₂ = 8

Y₂ = 6

putting the values onto formula we get:

d=√((x2 – x1)² + (y2 – y1)²).

d=√((8 – 2)² + (6 – 1)²).

d=√((6)² + (5)²).

d=√(36 + 25).

d=√(61).

AB =7.81

For Point BC:

X₁ = 8

Y₁ = 6

X₂ = 10

Y₂ = 1

putting the values onto formula we get:

d=√((x2 – x1)² + (y2 – y1)²).

d=√((10 – 8)² + (1 – 6)²).

d=√((2)² + (-5)²).

d=√(4 + 25).

d=√(29).

BC = 5.38

For Point CA:

X₁ = 10

Y₁ = 1

X₂ = 2

Y₂ = 1

putting the values onto formula we get:

d=√((x2 – x1)² + (y2 – y1)²).

d=√((2 – 10)² + (1 – 1)²).

d=√((-8)² + (0)²).

d=√(64 + 0).

CA = 8

The perimeter of the given figure is:

Sum of all the sides.

AB + BC + CA

7.81 + 5.38 + 8

21.19 cm

Now finding the area of the tringle we use Pythagoras formula:

H² = P² + B²

P² = H²  - B²

P² = (7.81)²  - (5.38)²

P = 9.4837

We know that the area of the triangle is: = 1/2(base * Hight).

                                                                    = 1/2(5.38  * 9.48)

                                                                    = 25.501 cm²

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Answer:

The Answer is A

Step-by-step explanation: Edge