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A rectangle has sides measuring (2x + 7) units and (5x + 9) units.

Part A: What is the expression that represents the area of the rectangle? Show your work. (4 points)

Part B: What are the degree and classification of the expression obtained in Part A? (3 points)

Part C: How does Part A demonstrate the closure property for polynomials? (3 points)

All the given equations have 2 real solutions except for equation 4 which has only one real root.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

The given quadratic equation

[tex]y = 12x^2 - 9x+ 4[/tex]

where, a = 12, b = -9 and c = 4

x = [tex]-b + \sqrt{b^2 - 4ac} /2a[/tex]

x = [tex]-(-9)+ \sqrt{(-9)^2 - 4(12)(4)} /2(12)[/tex]

x = 1.063 or -0.313

Second Equation

[tex]10x +y = -x^2 +2 \\y = x^{2} +10x - 2[/tex]

where, a = 1, b = 10, c = -2

substitute the values into the equation

x = [tex]-b + \sqrt{b^2 - 4ac} /2a[/tex]

[tex]-10 + \sqrt{10^2 - 4(1)(-2)} /2(1)[/tex]

x = 0.195 or -10.195

Third Equation

[tex]4y - 7 = 5x^2 - x +2 +3y[/tex]

[tex]y = 5x^{2} -x -5[/tex]

where, a = 5, b = -1, c = - 5

x = [tex]-b + \sqrt{b^2 - 4ac} /2a[/tex]

[tex]-(-1) + \sqrt{(-1)^2 - 4(5)(-5)} /2(5)[/tex]

x = 0.905 or -0.55

Fourth Equation

[tex]y = (-x +4)^2 \\y = x^{2} -8x +16[/tex]

where, a = 1, b = -8, c = 16

x = [tex]-b + \sqrt{b^2 - 4ac} /2a[/tex]

x = [tex]-(-8) + \sqrt{(-8)^2 - 4(1)(16)} /2(1)[/tex]

x = 4

Learn more about quadratic equations;

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Answer:

y = 12x2 - 9x + 4

✔ no

real solution(s)

4y - 7 = 5x2 - x + 2 + 3y

✔ no

real solution(s)

10x + y = -x2 + 2

✔ two

real solution(s)

y = (-x + 4)2

✔ one

real solution(s)

Step-by-step explanation:

hope this helps:)

Answer:

B) formation of a precipitate
E) change in color

Step-by-step explanation:

just did the assignment on e.d.g.e

Answer:

B and E is correct

Step-by-step explanation:

Answer:

Yes, I agree with Noah because the first lake has a smaller mean and MAD than the second

Step-by-step explanation:

Answer:

y = 3x -2

Step-by-step explanation:

General equation of a line in the slope intercept form is

y = mx + b ,

where m is the slope and b is the y-intercept ( where intercepts the y-axis)

y = 3x + b ,

because is given slope is m = 3

For point (x = -2, y = -8) we have

-8 = 3 (-2) + b

-8 = -6 + b

-8 + 6 = b

-2 = b

The equation of the line that passes through the point (-2,-8) and has a slope of 3 is

y = 3x -2

Answer:

Statement 1 - false

A function is one-to-one or many-to-one.

One-to-one means each value in the range (y-values) corresponds to exactly one value in the domain (x-values)

Many-to-one means some values in the range (y-values) correspond to more than one (many) value in the domain (x-values).

Therefore, as some y-values correspond to more than one x-value, this is a many-to-one function.

The true statement should be:

The relation is a function because some y-values correspond to more than one x-value.

Statement 2- true

The domain is the set of input values (x-values).  Therefore, the domain is 3 ≤ x ≤ 8 as the smallest x-value is 3 and the highest x-value is 8.

Statement 3 - true

The range is the set of output values (y-values).  Therefore, the range is {6, 7, 8, 10} as these are the y-values of the ordered pairs.

Answer:

24 books

Step-by-step explanation:

Books are valued at $10/3 books.  18 books would have a value of (18books)*($10/3books) = $60, and so on.

X books would have a value of X($10/3)=$80

X = ($80)*(3/$10)

X = 24 books

Answer:

A cube is a rectangular prism where all its sides are the same. The formula to find the surface area of a rectangular prism is A = 2wl + 2lh + 2hw, where w is the width, the l is the length, and the h is the height.

The surface area formula for a cube is 6l²

A cube has the following features:

The area of a face of a cube is:

Area = l²

Where l represents the side length

The surface area formula for a cube is then calculated using:

Surface area = 6 * Area of a face

So, we have:

Surface area = 6 * l²

Surface area = 6l²

Hence, the surface area formula for a cube is 6l²

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Generally, you'd see the equation of a circle organized in the following format:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

To determine the equation given the center and the radius:

We're given:

Plug the radius and center into the equation as r and (h,k):

[tex](x-(-1))^2+(y-(-8))^2=99^2\\(x+1)^2+(y+8)^2=9801[/tex]

[tex](x+1)^2+(y+8)^2=9801[/tex]

Answer:

All answers are bold and links are real photos  

BTW THE PHOTOS ARE IN ORDER OF THE ANSWERS

Brainlyist??

Step-by-step explanation:

Task 1

Part A

Tangent Line

Part B

PHOTO WITH LARGE CIRCLE AND LINE OUT SIDE BUT CONNECTED

Part C

2034.7

PHOTO WITH EQUATION

We calculate the point from the center of the earth to the satellite and because we have the radius we can subtract it getting the distance from the satellite to the earth.

Task 2

Gears

Part A

Approximately 10.47 inches

Part B

300°

Part C

Approximately 125.66 inches

Part D

The distance traveled increases by approximately 62.83 inches

Task 3

Circle Theorems

Part A

PHOTO WITH LINE THROUGH CIRCLE AND ONE 90 DEGREE ANGLE

Part B

Prove OC is perpendicular to AB

We know that ΔAEC≅AED by SSS criteria (SSS criteria is when all three sides of a triangle is equal making them congruent)

To prove this that they apply to the SSS criteria: m∠ADO=m∠BDO m∠ADO=90°=m∠BDO

Part C

A radius is perpendicular to a chord when the chord is equally divided in half by the radius.

PHOTO OF LINE THROUGH CIRCLE AND LINE DISTANCES

Part D

Prove OC is perpendicular to AB

AO=BO because AO and BO are both radii

OD≅OD by reflexive theorem

ΔADO≅ΔBDO because they are both right triangle with the hypotenuse and a side

AB≅BC means that OC is perpendicular to AB

Disclaimer: The images to part A and part C is the same.

Two theorems we are proving are:

Part A: The image is attached

Part B:

Let there be a circle with the center at O. Let AC be a chord. Let OE be a radius of the chord such that OE bisects AC at B, that is, AB = BC.

To prove: A line drawn from the center of the circle to bisect a chord is perpendicular to it.

Construction: We join OA and OB.

Proof:

In ΔOAB and ΔOCB,

OA = OC (Radius of the same circle)

AB = BC (Given, at B, the chord is bisected)

OB = OB (common side)

∴ ΔOAB ≅ ΔOCB [SSS axiom]

∴ ∠OBA = ∠OBC [Common parts of Congruent triangles]

Let ∠OBA = ∠OBC = x.

Since AC is a straight line,

∠OBA + ∠OBC = 180° [Linear pair]

or, x + x = 180°

or, 2x = 180°

or, x = 90°.

∴ ∠OBA = ∠OBC = 90°.

So, we can say that OB ⊥ AC, hence the theorem is proved.

Part C: The image is attached

Part D:

Let there be a circle with the center at O. Let AC be a chord. Let OE be a radius of the chord such that OE is perpendicular to AC at B, that is, AB ⊥ BC.

To prove: A line drawn from the center of the circle perpendicular to the chord bisects it.

Construction: We join OA and OB.

Proof:

In ΔOAB and ΔOCB,

OA = OC (Radius of the same circle)

∠OBA = ∠OBC = 90° (∵ OB ⊥ AC)

OB = OB (common side)

∴ ΔOAB ≅ ΔOCB [RHS axiom]

∴ AB = AC [Common parts of Congruent triangles]

So, we can say that OE perpendicular to the chord AC bisects it, hence the theorem is proved.

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Answer:

1. Growth

2. Growth

3. Decay

Answer:

44

Step-by-step explanation:

First remmember that all triangles will add up to equal 180 degrees

so we will have to subtract 180 by 92

whitch is 88

Now sence an isoclies are to equal sides we will have to divide 88 by 2

whitch is 44

Making 44 your answer.

Answer:

To create a "mini-triangle", we could use any number pairs (coordinates matter). We can use the side lengths of 4, 6, and 7 as they are the smallest pairs. It's a pretty easy concept which I'm sure you'll be able to grasp (I know you're smart! :) ). Ask your teacher if you have more questions. <3

Good luck!,

Answer:

Side Lengths of 4,6, & 7

Side Lengths of 8,9, &4

Step-by-step explanation:

According to the image given.

We must know that in order to be a triangle the following below must be include:

Note:

< ⇒ less than

> ⇒ greater than

= ⇒ equal

Solving all the given :

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

Side Lengths of 4,6, & 7

4 + 7 > 7

10 > 7

True

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

Side Lengths of 2,10,&3

2 + 3 > 10

5 <10

False

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

Side Lengths of 15, 7 , &8

7+8=15

15 = 15

False

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

Side Lengths of 1,4,&3

1+3>4

4=4

False

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

Side Lengths of 8,9,&4

8+4>9

12>9

True

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

Side Lengths of 6,7,&1

1+6=7

7=7

False

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

Kavinsky

Answer:

(1,12) ; (2,9) ; (3,6) ; (4,3) ; (5,0)

Step-by-step explanation:

You need to plug the x values into the equation.

Your equation: y=15-3x

Example:

Plug in 1

y=15-3

y=12

Plug in 2:

y=15-3(2)

y=15-6

y=9

Plug in 3:

y=15-3(3)

y=15-9

y=6

Plug in 4:

y=15-3(4)

y=15-12

y=3

Plug in 5:

y= 15-3(5)

y=15-15

y=0

Answer:

a- ounce glass of water.

Answer:

it falls left to right horizontal

pls give brainlyist

Step-by-step explanation:

Answer:

The line will fall (from left to right).

Step-by-step explanation:

If the slope of any line is negative then that line will go downwards or fall (from left to right). While if the slope were to be positive, that would mean the line will rise (from left to right).

Here is a picture to justify my answer ⤴⤴⤴

Hope this helps you :)

The difference between the polynomial is [tex]\rm 9x^3-5x^2-6x+10[/tex].

The subtract means to take away from a group or a number of things.

Lorne subtracted 6x3 – 2x + 3 from –3x3 + 5x2 + 4x – 7.

The difference between the expression is;

[tex]\rm ( 6x^3 - 2x + 3 )- (-3x^3 + 5x^2 + 4x - 7)[/tex]

[tex]\rm 6x^3 - 2x + 3 +3x^3 -5x^2 -4x +7\\\\9x^3-5x^2-6x+10[/tex]

Hence, the difference between the polynomial is [tex]\rm 9x^3-5x^2-6x+10[/tex].

To know more about subtraction click the link given below.

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Answer:

A on edge 2021

Step-by-step explanation:

I got it correct.

Rachel's beginning balance one year ago was $800.

Compound interest is applicable when there will be a change in the principle amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.

Given that,

The current balance is $836 which is the result of compound interest of 4.5 % annually.

The original amount was a priciple amount P on which interest was applied and the final amount $836 made.

Compound interest formula;

A = P[ 1 + RT/100]^T

Where A is the final amount and T is the time period.

Here,

A = 836 , R = 4.5% and T = 1 year.

So,

836 = P[1 + 4.5/100]^1

P = 836/1.045 = $800

Hence "Rachel's beginning balance one year ago was $800".

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Answer:

The slope is -8 and the y-intercept is 5

Answer:

see image

Step-by-step explanation:

You average the x's and average the y's.

This means add x+x and divide by 2. And add y+y and divide by 2. See image.

Answer:

an angle measuring 32 degrees has a complement that measures (2x-16) degrees. What is the value of x?

Step-by-step explanation:

let me know if its right

Answer:

Step-by-step explanation: y axis is 6units up (y=+6)

X axis is 2units to the right. (×=+2)

Answer:

x=6*4y=20

Step-by-step explanation:

the difference = x, six times = 6*, 4 times = 4y, number is 20 = 20

[tex]\\ \rm\dashrightarrow x^{\frac{2}{7}}[/tex]

[tex]\\ \rm\dashrightarrow x^{2(1/7)}[/tex]

[tex]\\ \rm\dashrightarrow \sqrt[7]{x^2}[/tex]

And

[tex]\\ \rm\dashrightarrow \sqrt[3]{2y}[/tex]

[tex]\\ \rm\dashrightarrow 2y^{\frac{1}{3}}[/tex]

Answer:

see below

Step-by-step explanation:

Problem-1:

[tex] {x}^{ \frac{2}{7} } [/tex]

remember that,

[tex]\displaystyle {x}^{ \frac{a}{b} } = \sqrt[b]{ {x}^{a} } [/tex]

here,

hence,

[tex] {x}^{ \frac{2}{7} } = \boxed{\sqrt[7]{ {x}^{2} } }[/tex]

Problem-2:

recall that,

[tex] \sqrt[n]{x} = {x}^{ \frac{1}{n} } [/tex]

therefore,

[tex] \sqrt[3]{2y} = (2y {)}^{ \frac{1}{3} } \implies \boxed{{2 }^{ \frac{1}{3} } {y}^{ \frac{1}{3} } }[/tex]

Answer:

2.27

Step-by-step explanation: