Start with the graph of the function f(x) = x^2, which is a U-shaped curve opening upward.

Move the entire graph 3 units to the right. This means you shift the curve horizontally to the right by 3 units.

Flip the graph upside down by reflecting it in the x-axis. This means the U-shaped curve will now open downward.

Squish or compress the graph vertically by a factor of 3. This means the curve will become narrower and steeper.

Move the graph 3 units up. This means you shift the curve vertically upward by 3 units.

This results in a graph that is a downward-opening parabola centered at the point (3, 3), with a vertical compression and vertical translation.

The first image is y=x^2 the second is how it should look

Move the entire graph 3 units to the right. This means you shift the curve horizontally to the right by 3 units.

Flip the graph upside down by reflecting it in the x-axis. This means the U-shaped curve will now open downward.

Squish or compress the graph vertically by a factor of 3. This means the curve will become narrower and steeper.

Move the graph 3 units up. This means you shift the curve vertically upward by 3 units.

This results in a graph that is a downward-opening parabola centered at the point (3, 3), with a vertical compression and vertical translation.

The first image is y=x^2 the second is how it should look

a girl is 12years old now.what was her age x years ago?

6 is the correct answer

What is the equation, in slope-intercept form, of the line parallel to y = 5x + 2 that passes through the point with coordinates (-2, 1)? Show your work on the scratchpad. y = C G City 2 E X

**Answer:**

y = 5x + 11

**Step-by-step explanation:**

**Step 1: **When two lines are parallel, they have the same slope, as indicated by the following equation as m2 = m1, where

Thus, since the slope of line 1 is 5, the slope of line 2 is also 5.

**Step 2: **Now we can plug in (-2, 1) for x and y and 5 for m to solve for b, the y-intercept of the other line:

1 = 5(-2) + b

1 = -10 + b

11 = b

Thus, the equation of the line parallel to y = 5x + 2 and passing through (-2, 1) is y = 5x + 11

PLEASE HELPPP!!!!!!!!!

If tanA= 40/9 and sin B = 45/53

and angles A and B are in

Quadrant I, find the value of tan (A-B).

The **value** of tan (A-B) is equal to 715/2052.

To find the value of tan(A - B), we can use the trigonometric identity:

tan(A - B) = (tan(A) - tan(B))/(1 + tan(A)tan(B))

Given that tan(A) = 40/9 and sin(B) = 45/53, we can determine the values of cos(B) and tan(B) using the **Pythagorean **identity:

sin^2(B) + cos^2(B) = 1

cos(B) = sqrt(1 - sin^2(B))

cos(B) = sqrt(1 - (45/53)^2)

cos(B) = sqrt(1 - 2025/2809)

cos(B) = sqrt(784/2809)

cos(B) = 28/53

tan(B) = sin(B)/cos(B)

tan(B) = (45/53)/(28/53)

tan(B) = 45/28

Now we can **substitute **the values into the **formula **for tan(A - B):

tan(A - B) = (tan(A) - tan(B))/(1 + tan(A)tan(B))

tan(A - B) = (40/9 - 45/28)/(1 + (40/9)(45/28))

tan(A - B) = [(1120/252 - 405/252)] / (1 + (1800/252))

tan(A - B) = (715/252) / (2052/252)

tan(A - B) = 715/2052

Therefore, tan(A - B) is equal to 715/2052.

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find the equation of the line that passes through the points (-3,-7) (-3,10

The **equation **of the **line **that passes through point (-3,-7) and point (-3,10) is x = -3.

The formula for **equation** of **line **is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the **points **through which the line passes: (-3,-7) and (-3,10).

The two given points (-3, -7) and (-3, 10) have the **same x**-**coordinate **-3

Hence, the two lines lie on a **vertical line**.

since the slope of the vertical line is undefined.

The **equation **of the **line **passing through these two points is simply the equation of the vertical line:

x = -3

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at ghs the ratio of students to teachers is about 14.5 to 1 approximately how many teachers would there be if the school had an enrollment of 205 students

**Answer:**

14

**Step-by-step explanation:**

14.5 to 1

205/14.5 = 14

NO LINKS!! URGENT HELP PLEASE!!!!

Measuring a Pond: A surveyor is measuring the width of a pond. The transit is setup at point C and forms an angle of 37° from point A to point B. The distance from point C to point A is 54 feet and the distance from point C to point B is 72 feet. How wide is the pond from point A to point B?

**Answer:**

43.47 feet (2 d.p.)

**Step-by-step explanation:**

Points A, B and C form a **triangle**.

We have been given **sides a and b**, and their **included angle C**.

The **distance **between points A and B is **side c **of triangle ABC.

Therefore, we can solve this problem using the** Law of Cosines**, which relates the lengths of the sides of a triangle to the cosine of one of its angles.

[tex]\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines (for finding sides)} \\\\$c^2=a^2+b^2-2ab \cos (C)$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]

Given values:

a = side CB = 72 ftb = side CA = 54 ftC = angle ACB = 37°**Substitute **the given **values **into the** Law of Cosines** formula and solve for **side c**:

[tex]\implies c^2=72^2+54^2-2(72)(54)\cos(37^{\circ})[/tex]

[tex]\implies c^2=8100-7776\cos(37^{\circ})[/tex]

[tex]\implies c=\sqrt{8100-7776\cos(37^{\circ})}[/tex]

[tex]\implies c=43.4719481...[/tex]

[tex]\implies c=43.47\; \sf ft\;(2\; d.p.)[/tex]

Therefore, the **width **of the pond from point A to point B is **43.47 feet**, to two decimal places.

Gavin is working two summer jobs making $14 per hour tutoring and $13 per hour landscaping. Last week Gavin worked a total of 10 hours and earned a total of $137. Determine the number of hours Gavin worked tutoring last week and the number of hours he worked landscaping last week.

Solving a **system of equations **we can see that Gavin worked 7 hours tutoring.

Let's define the **variables**:

x = number of hours tutoring.

y = number of hours land scaping.

We know that he worked for 10 hours and earned $137, then we can write a **system of equations:**

x + y = 10

14x + 13y = 137

Isolating y on the first equation we get:

y = 10 - x

Replace that in the second one to get:

14x + 13*(10 - x) = 137

14x + 130 - 13x = 137

x = 137 - 130 = 7

He worked 7 hours tutoring.

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Can someone answer this question

**Answer:**

The function is given by p(x) = x^2 - 5x^2 + x + 15. The potential rational zeros of the function are given by the factors of the constant term (15) divided by the factors of the leading coefficient (1).

So the potential rational zeros are ±1, ±3, ±5, ±15.

The list of potential rational zeros of the function includes all of the options listed except option (b) -2. **Therefore, the answer is (b) -2.**

**Step-by-step explanation:**

12. Sasha surveys students from her homeroom about the number of

siblings each student has. The results are 1, 0, 2, 2, 3, 0, 1, 1, 4,

and 5. What is the mode(s) of the data? (CC.6.SP.5c)

C 1

(D) 1 and 2

in

(A) 1.5

B 0 and 2

The calculated value of the **mode(s)** of the **data **is (a) 1

From the question, we have the following parameters that can be used in our computation:

1, 0, 2, 2, 3, 0, 1, 1, 4, and 5

By definition, the mode of a **data **is the data that has the **highest frequency**

Using the above as a guide, we have the following:

The **data element **1 has the highest frequency of 3

Other data elements have **lesser** frequencies

Hence, the **mode(s)** of the **data **is (a) 1

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You roll a 6-sided number cube and toss a coin. Let event A = Toss a heads.

What outcomes are in event A?

What outcomes are in event AC?

1. Event A includes the **outcomes **of H and T,

2. while event AC includes all the possible outcomes of rolling a number cube, which are 1, 2, 3, 4, 5, and 6.

1. Event A is defined as tossing a heads on a coin, regardless of the outcome of rolling a **number cube**. Therefore, the outcomes in event A are H (heads) and T (tails), since either of these outcomes could occur when rolling a number cube and tossing a coin.

2. Event AC is the complement of event A, i.e., it is the set of outcomes that are not in event A. Since event A contains H and T, the outcomes in event AC are the remaining outcomes that are not in **event **A, which are all the **possible **outcomes when rolling a number cube: 1, 2, 3, 4, 5, and 6.

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50 Points! Multiple choice geometry question. Photo attached. Thank you!

The **measure**,

⇒∠s = 124 degree

In the given figure of **kite,**

PQRS,

Measure of angle p = 22 degree

And angle R is a **right angle**

Therefore,

∠R = 90 degree

Now we know that for a kite PQRS

Angle Q and Angle S are **equal **

Now consider,

Angle s is equal to x degree

Therefore,

∠S = ∠ Q = x degree

We know that,

For a kite the sum of **interior angle** is equal to 360 degree.

Therefore,

⇒ ∠P + ∠Q + ∠R + ∠S = 360

⇒ 22 + x + 90 + x = 360

⇒ 22 + x + 90 + x = 360

⇒ 2x = 248

⇒ x = 124 degree.

Thus,

Measure of** angle** s = 124 degree.

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24. Find RT.

13

Ø

S

P

X

11

20

RT =

Show work need bothof these problems

24. The **length **RT is 18 units

25. The **equation **of the **circle **graphed is x² + (y - 3)² = 16

The **length RT** can be calculated using the **intersecting secants **equation

So, we have

11 * (11 + x) = 9 * (9 + 13)

So, we have

11 + x = 18

This gives

RT = 18

The equation of the circleThe **equation **of the **circle **graphed is represented as

(x - a)² + (y - b)² = r²

Where, we have

Center = (a, b) = (0, 3)Radius, r = 4 unitsSo, we have

(x - 0)² + (y - 3)² = 4²

Evaluate

x² + (y - 3)² = 16

Hence, the **equation **of the **circle **graphed is x² + (y - 3)² = 16

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A straight line is given as 2 x+4 -2 y-5=-3 z-6 (a) Determine the vector equation of the straight line. (b) Find the intersection point between the straight line with the plane yz

**Answer:**

a) r(t) = (10, 5, -5) + (5, 5, 0)*t

b) ** (0, -5, -5)**

**Step-by-step explanation: **

**a) 2x + 4 -2y -5 = -3z -6 **

**2x - 2y +3z +5 =0**

**(10, 5, -5)**

**(15, 10, -5)**

**(5, 5, 0)**

r = (10, 5, -5) + (5, 5, 0)*t

**b) The yz plane is given by the equation x = 0.**

**x = 0 in the vector equation of a straight line if and only if t = -2, than r ( - 2) = (0, -5, -5) is the desired intersection point.**

Which equation is represented by the graph below?

16

&

T

&

4

Oy=e*+5

Oy=e* +4

Oy=Inx+4

2

1

-2 -1₁

7 ?

TY

1

2

3 4

The **exponential function** graphed in this problem is given as follows:

[tex]y = e^x[/tex]

How to define an exponential function?An exponential function has the **definition **presented according to the equation as follows:

[tex]y = ab^x[/tex]

In which the **parameters **are given as follows:

The graphed function has an intercept of 1, hence the** parameter a** is given as follows:

a = 1.

The function has the **base e**, hence it is given as follows:

[tex]y = e^x[/tex]

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A designer is making a sample design that will use 3 different kinds of tiles. The designer has 9 different kinds of tiles from which to choose. How many possible combinations of tiles can the designer choose? The designer will create a sample design by placing 3 tiles side by side. How many different sample designs can the designer make from the 3 chosen tiles?

The designer can choose from 84 possible **combinations **of tiles, and they can create 6 different sample designs using the 3 chosen tiles when placing them side by side.

To determine the number of possible combinations of tiles that the designer can choose, we can use the concept of combinations.

Since the designer has 9 different kinds of **tiles **and wants to choose 3 of them, we can calculate the number of combinations using the formula for combinations, which is [tex]nCr = n! / (r! \times (n - r)!).[/tex]

Number of combinations of tiles = 9C3 [tex]= 9! / (3! \times (9 - 3)!)[/tex]

Simplifying further:

[tex]9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1[/tex]

[tex]3! = 3 \times 2 \times 1[/tex]

[tex](9 - 3)! = 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1[/tex]

Plugging these values into the formula:

Number of combinations of tiles[tex]= 9 \times 8 \times 7 / (3 \times 2 \times 1 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1)[/tex]

Simplifying the expression:

Number of combinations of tiles = 84

The designer can choose from 84 possible combinations of tiles, and they can create 6 **different sample** designs using the 3 chosen tiles when placing them side by side.

Therefore, the designer can choose from 84 possible combinations of tiles.

Now, let's calculate the number of different sample designs the designer can make using the 3 chosen tiles.

Since the tiles are placed side by side, the order of the tiles matters.

To calculate the number of different arrangements, we can use the concept of **permutations**.

Number of sample designs = 3!

Calculating:

[tex]3! = 3 \times 2 \times 1 = 6[/tex]

Therefore, the designer can create 6 different sample designs using the 3 chosen tiles when placing them side by side.

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2. Convert the following into a single log statement from the many log statements to 1.

2 Log w+ log 7-3 log x-8 log y

NOTE: You must show this in at least two steps.

1st line should be to convert the 2 the 3 and the 8 only.

2nd line can be the final answer.

A single log statement from the many** log statements** to 1 is: [tex]log(7wy^{(-8)}/x^3)[/tex]

The exponent that indicates the power to which a base number is raised to produce a given number are called** logarithm.**

Use the logarithmic identity:

log[tex](a^n)[/tex] = n*log(a)

to **convert** the coefficients 2, 3, and 8:

log w + log 7 - 3log x - 8log y

= log w + log 7 - log [tex]x^3[/tex] - log [tex]y^8[/tex]

**Combine** the terms on the right-hand side using the logarithmic identity:

log(a) + log(b) = log(ab)

log w + log 7 - log[tex]x^3[/tex] - log [tex]y^8[/tex]

= log([tex]7wy^{-8}/x^3[/tex])

Therefore, the single log statement is from the many** **log statements to 1 is: log[tex](7wy^{-8}/x^3)[/tex]

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Can someone answer this question

8/5 is the **value **that is **not **one of the possible rational **zeros **of the given polynomial.

Using the **Rational Root **Theorem, we need to consider the **factors **of the constant term (-8) divided by the factors of the leading coefficient (5).

The **factors **of -8 are ±1, ±2, ±4, ±8.

The **factors **of 5 are ±1, ±5.

Since the **leading **coefficient of the given polynomial is **positive **(5), the negative factors can be ignored.

So, the **possible **rational **zeros **are:

1/1, 2/1, 4/1, 8/1, 1/5, 2/5, 4/5, 8/5

Now, we can **substitute **each of these **values **into the **polynomial **and see if any of them result in a zero.

Upon checking, we find that 8/5 is **not **a **zero **of the polynomial 5x³ - 2x² + 20x - 8.

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Lyndon is making a nylon case for his new snare drum which measures 14 inches in diameter

and is 6 inches deep. If the case fits snugly around the drum, how much nylon will Lyndon

need?

572 **square inche**s nylon will Lyndon need.

To determine how much nylon Lyndon will need to make a case for his snare drum, we need to calculate the surface area of the drum.

The surface area of a cylinder can be calculated using the formula:

**Surface Area** = 2π[tex]r^2[/tex] + 2πrh

where r is the radius of the base of the **cylinder **and h is the height of the cylinder.

Since the **diameter **of the drum is 14 inches, the radius is 7 inches.

The height of the drum is 6 inches.

So, the surface area of the drum is:

Surface Area = 2π[tex](7)^2[/tex] + 2π(7)(6)

Surface Area = 2π(49) + 2π(42)

Surface Area = 98π + 84π

Surface Area = 182π

Surface Area = 182 pi

Surface Area = 182 x 22/7

Surface Area = 572 squae inches

Therefore, Lyndon will need 182π square** **inches** **of nylon to make a case for his snare drum.

This is approximately 572 square inches when rounded to the nearest hundredth.

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How do you write 37 million as using the power of ten exponent

37 million can be written as 3.7 × 10⁶ in the **power **of ten **exponent **notation.

In **scientific **notation, a number is written as the **product **of a coefficient and a **power **of ten.

To convert 37 million to scientific notation, we need to move the decimal point to the left until we have a number between 1 and 10.

Starting with 37 million, we can move the **decimal** point **six places **to the left to obtain the number 3.7:

= 37,000,000 -> 3.7

Now, we **express **this number as a product of the coefficient (3.7) and 10 **raised **to the **power **of the number of places we moved the decimal point.

In this case, since we moved the decimal point six places to the left, the **exponent **of ten is 6:

37 million = 3.7 × 10⁶

Therefore, 37 million can be written as 3.7 × 10⁶ in the **power **of ten **exponent **notation.

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$16,000 is deposited into a savings account with an annual interest rate of 2% compounded continuously. How much will be in the account after 4 years? Round to the nearest cent.

The **amount** in the **account** after 4 years, rounded to the nearest cent, will be approximately $17,332.8.

Recall the **compounding** formula:

A = P * [tex]e^{rt}[/tex]

Where:

A = Final amount in the account

P = Initial **principal** (deposit)

e = **Euler's** number (approximately 2.71828)

r = Annual **interest** rate (as a decimal)

t = Time in years

Given:

Initial principal (P) = $16,000

Annual interest rate (r) = 2% = 0.02

time (t) = 4 years.

Substitute these values into the formula, we get:

A = $16,000 * [tex]e^{0.02 * 4}[/tex]

Using a calculator, we can calculate:

A = $16,000 * [tex]e^{0.08}[/tex]

A = $16,000 * 1.0833

A = $17,332.8

Therefore, the **amount in the account** after 4 years, rounded to the nearest cent, will be approximately $17,332.8.

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The number of miles on a car when the engine fails is normally distributed. The mean is 60,000 miles and the standar

deviation is 5000 miles. What is the probability the engine will not fail between 55,000 and 65,000 miles?

25%

40%

35%

32%

The **probability** that the engine will not fail between 55,000 and 65,000 miles, based on **normal distribution probabilities**, when the **mean** failure is 60,000 miles and standard deviation of 5,000 miles is e) 68%.

**Normal distribution probability** is a continuous probability distribution with **symmetrical values** that mostly cluster around the mean.

We can compute the normal distribution probability using the **normal distribution calculator**.

Mean number of miles when a car's engine fails = 60,000 miles

Standard deviation = 5,000 miles

Sample cutoff = between 55,000 and 65,000 miles

The **probability** of the engine fail between 55,000 and 65,000 miles = 0.6827.

= 68%.

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Question Completion:a) 25%

b) 40%

c) 35%

d) 32%

e) 68%

need help fast pls!!!

The **volume **of** solid figure** is,

⇒ V = 113 cm³

We have to given that;

A solid figure is shown with a **cylinder **and a cone.

Now, We know that;

Volume of cylinder = πr²h

And,

Volume of cone = πr²h / 3

Where, 'r' is **radius** and 'h' is height.

Here, **Height **of cylinder = 7 cm

And, Radius of cylinder = 4/2 = 2 cm

Hence, WE get;

Volume of cylinder = πr²h

Volume of cylinder = 3.14 x 2² x 7

Volume of cylinder = 87.9 cm³

And, Height of **Cone **= 6 cm

**Radius **of Cone = 4/2 = 2 cm

Hence, WE get;

Volume of Cone = πr²h/3

Volume of Cone = 3.14 x 2² x 6 / 3

Volume of Cone = 25.1 cm³

Thus, The **volume **of solid figure is,

⇒ V = 87.9 cm³ + 25.1 cm³

⇒ V = 113 cm³

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50 Points! Multiple choice algebra question. Photo attached. Thank you!

**Answer:**

d. 465 degrees (not my own answer, see below)

**Step-by-step explanation:**

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Nadeen bought a 91-day T-bill that has an interest rate of

4.30% p.a. and a face value of $5,000.

a) How much did she pay for the T-Bill?

b) After 40 days, Barbara sold the T-bill to her friend when the interest rate for this T-bill in the market increased to 5.30% p.a. What was her selling price?

The 91-day **T-bill **that Nadeen bought at an interest rate of 4.30% p.a. and face value of $5,000 indicates;

a) Nadeen paid about $4,946.24 for the T-bill

b) Barbara's selling price for the T-bill is about $4,962.74

What is a T-bill?A **Treasury** **bill** (**T-bill**), is a short-term obligation that is issued by the U.S. Department of Treasury and which is backed by the United States government, and has a **maturity** of less than a **year**. T-bills are low risk **investment** as they are backed by the credit and full faith of the U.S. government.

The formula for the **price** of the T-bill can be calculated with the formula;

Price = Face Value/(1 + (Interest Rate × Days to Maturity/360))

Plugging in the value from the question, we get;

Price = 5000/(1 + (0.043 × 91/360)) ≈ 4946.24

Therefore, Nadeen paid $4,946.24 for the T-billb) The **formula** for the **selling price** can be presented as follows;

Selling Price = Face Value/(1 + (Interest Rate × Remaining Days to Maturity/360))

Plugging in the known values, we get;

Selling Price = 5,000/(1 + (0.053 × (91 - 40)/360)) ≈ $4,962.74

Therefore, Barbara sold the T-bill to her friend for $4,962.74

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The sector of a circle has an area of 7π/5 square inches and central angle with

measure 56°.

What is the radius of the circle, in inches?

Answer:

3

Step-by-step explanation:

Area = 7pi/5

56/360 × pi r² = 7pi/5

Pi is canceled on both sides.

r² = 7/5 ÷ 56/360 = 9

r = root 9 = 3

4. Approximate the solution to this system of equations.

y = -2x+6

y = 4x - 1

The **solution** of the **system of linear equations**, is (1.167, 3.667).

Given that the **system of linear equations**, y = -2x+6 and y = 4x - 1, we need to find the **solution** for the same,

y = -2x+6............(i)

y = 4x - 1.......(ii)

**Equating** the equations since the LHS is same,

-2x+6 = 4x-1

6x = 7

x = 1.167

Put x = 1.16 to find the value of y,

y = 4(1.16)-1

y = 4.66-1

y = 3.667

Therefore, the **solution** of the **system of linear equations**, is (1.167, 3.667).

You can also find the solution using the **graphical** method,

Plot the equations in the graph, the point of the intersection of both the lines will be the solution of the **system of linear equations**, [attached]

Hence, the **solution** of the **system of linear equations**, is (1.167, 3.667).

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Find the area of this semi-circle with diameter 5cm.

Use the л (pi) button on your calculator and give your answer rounded to 2 decimal places.

No spam, please.

**Answer:**

**Step-by-step explanation:**

Help me please I need help asap

1. Area of the **smaller circle **is 100πcm²

2. **Area** of the bigger circle 800πcm²

The formula for the **circumference **of a **circle** is expressed as;

Circumference = 2πr

Substitute the values, we get;

20π = 2πr

Divide by the coefficient of r, we get;

r = 10cm

Now, area of a circle is expressed as;

**Area** = πr²

Substitute the value of the radius

Area = π × 10²

Find the square

Area = 100πcm²

Area of the big circle = 8(area of the small circle)

substitute the values

Area of the big circle = 8(100π)

expand the bracket

Area of the big circle = 800 πcm²

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The figure shows three tennis balls in a can with each tennis ball having a diameter of 2.5 inches. What is the total volume of the air space around the three tennis balls?

The total **volume **of the air **space **of **spherical **ball is A = 12.265625 inches³

Given data ,

Since each tennis **ball **has a diameter of 2.5 inches, the radius of each ball is 1.25 inches.

The air space around the balls can be thought of as a **cylinder **with a height equal to the diameter of one ball and a radius equal to the radius of one ball.

The height of the **cylinder **is 2.5 inches, and the radius is 1.25 inches.

The formula for the volume of a cylinder is:

V = πr²h

V = ( 3.14 ) ( 1.25 )² ( 7.5 )

V = 36.796875 inches³

where V is the volume, r is the radius, and h is the height.

So, the volume of the one ball is:

V₁ = ( 4/3 )π(1.25)³

V₁ = 8.177083 inches³

The total volume of three **balls **is = volume of 3 **spherical **balls

V₂ = 3V₁ = 3(8.177083) ≈ 24.53125 cubic inches

Therefore, the total volume of the air space around the three tennis **balls **is approximately A = 36.796875 inches³ - 24.53125 inches³

A = 12.265625 inches³

Hence , the **volume **of air space is A = 12.265625 inches³

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The proof shows that ABCD is a square. Which of the following is the missing

reason?

E

B

AC BD

mZDEC = 90°

The missing reason in the proof is "mZDEC = 90°" or "Angle DEC is a **right angle**."

The missing reason in the proof is the statement "mZDEC = 90°". This statement implies that the angle DEC is a right angle, which is a crucial piece of information in proving that ABCD is a** square**.

In a square, all angles are right angles, so if we can establish that an angle in the figure is 90°, we can conclude that the figure is a square. In this case, the angle DEC being 90° is the** key piece** of evidence that supports the claim that ABCD is a square.

The statement "mZDEC = 90°" indicates that the **measure** of angle DEC is 90 degrees. This is significant because it confirms that one of the angles in the figure is a right angle, meeting the definition of a square.

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