**Answer:**

**The variable x represents ****the number of fish tanks he/she sells****.**

**Explanation:**

Given that Eric's base salary is still $1400, but now he makes a commission of

$100 for each fish tank that he sells and Nancy now gets a base salary of $500 per month, but her commission has stayed the same at $250 per fish tank.

Eric's total income would be;

$1400 plus $100 times **the number of fish tanks he sells.**

and Nancy's total income would be;

$500 plus $250 times **the number of fish tanks she sells.**

Therefore, **the variable x represents ****the number of fish tanks he/she sells****.**

The number of fish tanks each of them sells will determine the total commission and also determines their total income.

Consider the following equation of the circle. Graph the circle

**Explanation**

Given the equation;

[tex](x+6)^2+(y+7)^2=4[/tex]Using a graphing calculator, the graph of the circle becomes;

**Answer:**

Luther made $9,000 in interest by placing $60,000 in a savings account with simple interest for 3 years. What was the interest rate?

**Answer:**

[tex]5\%\text{ or }0.05[/tex]

**Step-by-step explanation:**

Simple interest rate means if I have "**P**" amount that I initially deposited, then every year this amount increases by "**x%** **of P**" or the original amount I deposited. So it's increasing by the same amount each year, unlike **compound interest**.

The formula for calculating the amount of interest is: [tex]I=P*r*t[/tex]

Where, **r **is the **interest rate**, **t **is the time unit, and **P** is the initial amount.

In most cases the **t** will be expressed in **years, **and one thing to note is the **r** is the **interest rate** in **decimal form**, so [tex]30\%=0.30[/tex], we want to convert it to decimal form by dividing by 100

We know the amount of **interest**, as it's given to us as **9,000**, and the **principle amount or initial amount**, given to us as **60,000**, and also the **time** which is given to us as **3 years**.

So we know that:

[tex]I=9,000\\P=60,000\\t=3\\[/tex]

Plugging all these values into the equation we get:

[tex]9,000=60,000*3*r\\\\9,000=180,000*r\\\\\frac{9,000}{180,000}=r\\\\0.05=r[/tex]

as noted above, this **interest rate, "r"** is expressed in **decimal form**. Since we have to **divide by 100** to convert from** percentage** to **decimal**, we have to **multiply by 100** to convert from **decimal **to **percentage.**

this gives us: [tex]r=5\%[/tex]

please help! I do not understand and it is due tonight!!!!!!!

Consider that there are, generally, the following types of angles pairs,

1. Adjacent Angles: Angles that share a common side and are formed on the same vertex.

2. Complementary Angles: Angles that are adjacent and together form a right angle.

3. Supplementary Angles: Angles that are adjacent and whose sum of degree measures is 180 degrees.

a.

The adjacent angles to angle 4 are angles 1 and 3.

There are no complementary angles associated with angle 4.

The supplementary angles to angle 4, are angles 1 and 3.

Thus, the angle pairs that include angle 4 are,

[tex](\angle4\text{ and }\angle1),\text{ }(\angle4\text{ and }\angle3)[/tex]b.

The adjacent angles to angle 5 are angles 6 and 7.

There are no complementary angles associated with angle 5.

The supplementary angles to angle 5, are angles 6 and 7.

Thus, the angle pairs involving angle 5 are,

[tex](\angle5\text{ and }\angle6),\text{ }(\angle5\text{ and }\angle7)[/tex]1. The data set represents the number of cars in a town given a speeding ticketeach day for 10 days.2 4 5 5 7 7 8 8 8 121. What is the median? Interpret this value in the situation.*

**ANSWER:**

7

**STEP-BY-STEP EXPLANATION:**

We have the following data:

[tex]2,4,5,5,7,7,8,8,8,12[/tex]The median is the data value that separates the upper half of a data set from the lower half. Therefore:

In this case, being even, the two data are half, but since the value is the same, that is, 7, the median is equal to 7.

The interpretation of this value is in the middle of the 10 days (days 5 and 6), 7 would be the number of cars in a town given a a speeding ticket.

What is the answer to 2(7x-3)+9

**Answer:**

14x+3 is the answer I think

The solution to the given equation would be [tex]14x+3[/tex].

Hope this helps!

rThe number of dogs per household in a neighborhood is given in the probabilitydistribution. Find the mean and the standard deviation. Round to 1 decimal.# of Dogs012.34P(x)0.640.250.060.03.02a) What is the mean rounded to 2 decimal place?b) What is the standard deviation rounded to 2 decimal place?

[tex]\mu=\frac{x1+x1\ldots xn}{N}[/tex]

N = Number of data

x1...xn = Samples

[tex]s=\sqrt[]{\frac{\sum ^n_{n\mathop=1}(y-\mu)^2}{n-1}}[/tex]Let's calculate first:

[tex]\sum ^n_{n\mathop=1}yn=0.64+0.25+0.06+0.03+0.02=1[/tex]Now:

[tex]\sum ^n_{n\mathop=1}yn^2=(0.64)^2+(0.25)^2+(0.06)^2+(0.03)^2+(0.02)^2=0.477[/tex]So:

[tex]s=\sqrt[]{\frac{0.477-\frac{(1)^2}{5}}{5-1}}=0.2631539473\approx0.3[/tex]helppppppppppppp meeeeeeeeeeeeeeeeeeeeeeeeeee

**Answer:**

55.17

**Step-by-step explanation:**

[tex]P(0)=0.023(0)^3-0.289(0)^2+3.068(0)+55.170=55.17[/tex]

A football team was able to run the ball for 8 yards on their first play. On the second play they lost 12 yards. The third play they lost another 11 yards. What was their total yards they gained?

The total **yards **gained or lost is the **algebraic sum **so the **resultant **yards is -15 yards thus they **lose **15 yards.

**Arithmetic **operators are four **basic **mathematical operations in which summation, subtraction, division, and multiplication **involve**.,

**Subtraction** = Minus of any two or more numbers.

**Summation **= addition of two or more numbers or variable

Let's **consider **all **gained **yards by positive (+) and all lost yards by negative (-).

Given that,

In the **first play **= +8 yards (gain)

In **second play **= -12 yards (lost)

In the **third play **= 11 yards (Lost)

So total yards = +8 - 12 - 11 = -15 (Lost)

Therefore, the football team **lost **15 yards.

Hence "The total **yards **gained or lost is the **algebraic sum **so the **resultant **yards is -15 yards thus they **lose **15 yards".

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The radius, R, of a sphere is 4.8 cm. Calculate the sphere's volume, V. Use the value 3.14 for it, and round your answer to the nearest tenth. (Do not round any intermediate computations.) --0- V = 3 em Х 5 ?

The formula to calculate the volume of a sphere is given to be:

[tex]V=\frac{4}{3}\pi r^3[/tex]where r is the radius.

From the question, we have the following parameters:

[tex]\begin{gathered} \pi=3.14 \\ r=4.8 \end{gathered}[/tex]Therefore, the volume is calculated to be:

[tex]\begin{gathered} V=\frac{4}{3}\times3.14\times4.8^3 \\ V=463.0 \end{gathered}[/tex]**The volume is ****463.0 cm³****.**

Select True or False for each statement.

A right triangle always has obtuse exterior angles at two vertices.

**Answer:**

true

**Step-by-step explanation:**

it is true ........

Explanation:

A right triangle has exactly one angle that is 90 degrees. This is called a right angle.

The other two angles are acute, which means they are less than 90 degrees. An example would be 30 degrees and 60 degrees.

If 30 degrees is an interior acute angle, then 180-30 = 150 degrees is the exterior obtuse angle. Similarly, the adjacent angle to the 60 is 180-60 = 120 degrees.

This example shows we have two obtuse exterior angles. This applies to any right triangle, and not just this particular one.

There is a 5% chance that the mean reading speed of a random sample of 21

second grade students will exceed what value?

There is a 5% chance that** second **graders will be faster than 94.597 wpm.

Sample size = 21

**standard deviation** = 10 wpm

SE = 10/sqrt(21) = 2.18 as a consequence.

Let X be the average reading speed of 21 second-grade students. z = (X - 91)/2.18 Normal(91,2.18) (91,2.18).

If the 95th percentile of a standard **normal variable** z is 1.65 [5% probability], the outcome is 91 + 1.65 x 2.18 = 94.597.

So there's a 5% chance that the **average reading** speed of a random sample of 21 second-graders will be faster than 94.597 wpm.

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Function A gives the audience in millions

Using **function **concepts, it is found that:

**a) **The **meaning **of each expression is given as follows:

**b) **The **expression **is: A(4) = 1.3.

**c)** The **expression **is: A(2) = A(2.5).

In the context of this problem, the **format **of the function is:

A(t).

In which the **meaning **of each variable is given as follows:

Which gives the meaning of each expression in** item a**.

For **item b**, the **expression **is given as follows:

A(4) = 1.3.

As 4 hours after the episode premiered, the audience was of 1.3 million people.

For** item c**, the **expression **is given as follows:

A(2) = A(2.5).

As the audience after 2 hours = 120 minutes is the same as the audience half an hour = 30 minutes later.

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How long is the control line? I couldn’t figure this out

**Solution:**

Given the circle with center **A **as shown below:

The plane travels 120 feet counterclockwise from **B **to **C, **thus forming an arc **AC**.

The length of the arc **AC **is expressed as

Given that

[tex]\begin{gathered} L=120\text{ f}eet \\ \theta=80\degree \\ \end{gathered}[/tex]we have

[tex]\begin{gathered} L=\frac{\theta}{360}\times2\pi r \\ 120=\frac{80}{360}\times2\times\pi\times r \\ cross\text{ multiply} \\ 120\times360=80\times2\times\pi\times r \\ \text{make r the subject of the equation} \\ \Rightarrow r=\frac{120\times360}{2\times\pi\times80} \\ r=85.94366927\text{ fe}et \end{gathered}[/tex]**Hence, the length of the control line is ****85.94366927**** feet.**

** **

The equation for a line that has a y-intercept of -8 and passes through (-4,2) is y=-5/2x-8 True False

1) Let's verify whether that's true or not, plugging in that point into the equa

(-4,2)

[tex]\begin{gathered} 2=\frac{-5}{2}(-4)\text{ -8} \\ 2=10-8 \\ 2=2 \end{gathered}[/tex]Since this is an identity, in other words, the left side is equal to the right side then we can say that's true.

So that's true y=-5/2x-8 is the equation of the line that has in one of its points the y-coordinate y=-8

At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.042 for the estimation of a population

proportion? Assume that past data are not available for developing a planning value for p*. Round up to the next whole number.

The **sample size **should be taken as 545.6 to obtain a margin of error of 0.042 for the estimation of a population proportion.

**What is sample size?**

The process of deciding how many observations or replicates to include in a statistical sample is known as **sample size **determination. Any empirical study with the aim of drawing conclusions about a population from a **sample **must take into account the** sample size **as a crucial component. The **sample size** chosen for a study is typically influenced by the cost, convenience, or ease of data collection as well as the requirement that the **sample size** have adequate statistical power.

As given in the question,

Confidence level is 95% and the margin of error is 0.042

So,

1 - α = 0.95,

α = 0.05,

E = 0.042

planning value (p) = 0.5

To calculate **Sample size** the formula is:

[tex]n = \frac{p(1-p)(Z_{a/2})^2}{E^2}[/tex]

From the table we can find that:

[tex]Z_{a/2} = 1.96[/tex]

Putting the values given in the question in formula:

[tex]n = \frac{0.5(0.5)(1.96)^2}{(0.042)^2}[/tex]

[tex]n = \frac{(0.25)(1.96)^2}{(0.042)^2}[/tex]

[tex]n = \frac{(0.25)(3.841)}{0.00176}[/tex]

**n = 545.6**

Hence the **sample size** is 545.6

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Out of 450 applicants for a job, 249 are female and 59 are female and have a graduate degree. Step 1 of 2 : What is the probability that a randomly chosen applicant has a graduate degree, given that they are female? Express your answer as a fraction or a decimal rounded to four decimal places.

The **probability **that a randomly chosen **applicant **has a **graduate **degree, given that they are **female **is 0.236.

**Probability **refers to a possibility that deals with the occurrence of random events. The probability of all the **events **occurring need to be 1.

P(E) = Number of **favorable **outcomes / **total **number of outcomes

Given that 249 are **female **and 59 are female and have a graduate degree out of 450 applicants.

We are given following in the question;

M: **Applicant **is male.

G: Applicant have a **graduate **degree

F : Applicant is **female**.

The **Total **number of applicants = 450

Number of female applicants = 249

**Number **of female applicants have a **graduate degree **= 59

Therefore,

P(G/F) = P([tex]G^F[/tex])/P(F)

= 59/207 or 0.236

Hence, the **probability **that a randomly chosen **applicant **has a **graduate **degree, given that they are **female **is 0.236.

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A composite figure is created using asquare and a semicircle. What is the area ofthe figure?12 in200.52202.52204.52206.52

The area of the composite figure will be the sum of the area of the square and the area of the semicircle. The formula for determining the area of a square is expressed as

Area = length^2

From the diagram,

length = 12

Area of square = 12^2 = 144

The formula for determining the area of a semicircle is expressed as

Area = 1/2 * pi * radius^2

Radius = diameter/2

The diameter of the semicircle is 12. Thus,

radius = 12/2 = 6

pi = 3.14

Area of semicircle = 1/2 * 3.14 * 6^2 = 56.52

**Area of composite figure = 144 + 56.52 = 200.52 in^2**

**The first option is the correct answer**

Which equation is true when A.n = 1.2 B.

1.2n=10 n+1=1.2 C. 5+n=6.2 D. 10n=1.2

The **true equation **is **5 + n = 6.2.**

Here we have to find the equation for which n = 1.2.

So **the first equation **is

10n = 1.2

So for this, we get the value of n as:

n = 1.2/10

= 0.12

which is not equal to 1.2.

So it is not correct

The **second equation **is:

n + 1 = 1.2

n = 0.2

which is not equal to 1.2

So it is also not correct.

The **third equation **is:

5 + n = 6.2

n = 6.2 - 5

= 1.2

So it is correct.

The **fourth equation** is:

1.2n = 10

n = 10/1.2

= 8.33

Here n is not equal to 1.2

So it is also correct.

Therefore the **correct equation is 5 + n = 6.2.**

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16. The height, h, in feet of an object above the ground is given by h = -16t² +64t+190, t≥0, where t is the time in seconds. a) b) c) d) When will the object be 218 feet above the ground? When will it strike the ground? Will the object reach a height of 300 feet above the ground? Find the maximum height of the object and the time it will take.

the maximum height is 254 feet.

**Answer:**

a) 0.5 seconds and 3.5 seconds.

b) 5.98 seconds (2 d.p.)

c) No.

d) 254 feet at 2 seconds.

**Step-by-step explanation:**

Given equation:

[tex]h=-16t^2+64t+190, \quad t \geq 0[/tex]

where:

h is the height (in feet).t is the time (in seconds).Part aTo **calculate **when the object will be **218 feet** above the ground, substitute **h = 218** into the **equation **and **solve for t**:

[tex]\begin{aligned}\implies -16t^2+64t+190 & = 218\\-16t^2+64t+190-218& = 0\\-16t^2+64t-28 & = 0\\-4(4t^2-16t+7) & = 0\\4t^2-16t+7 & = 0\\4t^2-14t-2t+7 &=0\\2t(2t-7)-1(2t-7)&=0\\(2t-1)(2t-7)&=0\\\implies 2t-1&=0\implies t=\dfrac{1}{2}\\\implies 2t-7&=0 \implies t=\dfrac{7}{2}\end{aligned}[/tex]

Therefore, the object will be 218 feet about the ground at **0.5 seconds **and **3.5 seconds**.

The object strikes the **ground **when h is **zero**. Therefore, substitute **h = 0** into the **equation **and **solve for t**:

[tex]\begin{aligned}\implies -16t^2+64t+190 & = 0\\-2(8t^2-32t-95) & = 0\\8t^2-32t-95 & = 0\end{aligned}[/tex]

Use the **quadratic formula** to solve for t:

[tex]\implies t=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]

[tex]\implies t=\dfrac{-(-32) \pm \sqrt{(-32)^2-4(8)(-95)} }{2(8)}[/tex]

[tex]\implies t=\dfrac{32 \pm \sqrt{1024+3040} }{16}[/tex]

[tex]\implies t=\dfrac{32 \pm \sqrt{4064} }{16}[/tex]

[tex]\implies t=\dfrac{32 \pm \sqrt{16 \cdot 254} }{16}[/tex]

[tex]\implies t=\dfrac{32 \pm \sqrt{16} \sqrt{254} }{16}[/tex]

[tex]\implies t=\dfrac{32 \pm 4 \sqrt{254} }{16}[/tex]

[tex]\implies t=\dfrac{8\pm \sqrt{254} }{4}[/tex]

As t ≥ 0,

[tex]\implies t=\dfrac{8+ \sqrt{254} }{4}\quad \sf only.[/tex]

[tex]\implies t=5.98 \sf \; s \; (2 d.p.)[/tex]

Therefore, the object strikes the **ground **at **5.98 seconds **(2 d.p.).

Part c

To find if the object will reach a **height **of **300 feet** above the ground, substitute **h = 300 **into the **equation **and **solve for t**:

[tex]\begin{aligned}\implies -16t^2+64t+190 & = 300\\-16t^2+64t+190-300 & =0\\-16t^2+64t-110 & =0\\-2(8t^2-32t+55) & =0\\8t^2-32t+55& =0\end{aligned}[/tex]

Use the **quadratic formula** to solve for t:

[tex]\implies t=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]

[tex]\implies t=\dfrac{-(-32) \pm \sqrt{(-32)^2-4(8)(55)} }{2(8)}[/tex]

[tex]\implies t=\dfrac{32 \pm \sqrt{1024-1760} }{16}[/tex]

[tex]\implies t=\dfrac{32 \pm \sqrt{-736} }{16}[/tex]

[tex]\implies t=\dfrac{32 \pm \sqrt{16 \cdot -1 \cdot 46} }{16}[/tex]

[tex]\implies t=\dfrac{32 \pm \sqrt{16} \sqrt{-1} \sqrt{ 46}}{16}[/tex]

[tex]\implies t=\dfrac{32 \pm 4i\sqrt{ 46} }{16}[/tex]

[tex]\implies t=\dfrac{8\pm \sqrt{ 46} \;i}{4}[/tex]

Therefore, as t is a **complex number**, the object will **not **reach a height of 300 feet.

The **maximum height **the object can reach is the **y-coordinate** of the **vertex**.

Find the **x-coordinate** of the **vertex **and substitute this into the equation to find the maximum height.

[tex]\textsf{$x$-coordinate of the vertex}: \quad x=-\dfrac{b}{2a}[/tex]

[tex]\implies \textsf{$x$-coordinate of the vertex}=-\dfrac{64}{2(-16)}=-\dfrac{64}{-32}=2[/tex]

Substitute **t = 2** into the **equation**:

[tex]\begin{aligned}t=2 \implies h(2)&=-16(2)^2+64(2)+190\\&=-16(4)+128+190\\&=-64+128+190\\&=64+190\\&=254\end{aligned}[/tex]

Therefore, the **maximum height** of the object is **254 feet**.

It takes **2 seconds** for the object to reach its **maximum height**.

If XD = 2X – 6 and XV = 3x – 6 and WY and XV bisect at D, what is XV?

The diagonal WY bisects the diagonal XV at point D, which means that XV is divided into two equal line segments XD and XV.

[tex]XD=XV[/tex]Replace the equation above with the given expressions for both line segments:

XD= 2x-6

XV= 3x-6

[tex]2x-6=3x-6[/tex][tex]undefined[/tex]I'll give brainliest!

**Answer:**

24

**Step-by-step explanation:**

8y^0 + 2y^2 * x^-1

8(4)^0 + 2(4)^2 * 2^-1

8 + 2 * 16 * 2^-1

8 + 2 * 2^-1 * 16

8 + 2^1 - 1 * 16

8 + 16

24

Hope this helps! :)

please di it quickly I just need to confirm answer

**The Solution:**

Given:

[tex]\begin{gathered} V=(-5,3) \\ \\ W=(\frac{3}{2},-\frac{1}{2}) \end{gathered}[/tex]Required:

To find the value of **V - W**

[tex]V-W=\lbrace(-5-\frac{3}{2}),(3--\frac{1}{2})\rbrace=(-6\frac{1}{2},3\frac{1}{2})=(-\frac{13}{2},\frac{7}{2})[/tex]

Therefore, **the correct answer is [option 3]**

How do you find the square root of 18? Needs to be in decimal form and we cannot use calculators

Answer: [tex]\sqrt{18}\text{ = 4.25}[/tex]Explanation:

**Given:**

**To find:**

The root of 18 without using a calculator

There is a formula that gives an approximation of a square root without a calculator. This is given as:

[tex]\begin{gathered} \sqrt{N}\text{ = }\frac{N\text{ + M}}{2\sqrt{M}} \\ where\text{ N = is the number we want to find its root} \\ M\text{ = is a perfect square close the number we are to find} \\ That\text{ is a number we can find its root } \end{gathered}[/tex][tex]\begin{gathered} \text{N = 18} \\ M\text{ = 16 is the closest number to 18 we can find its root} \\ \\ substitute\text{ the values into the formula:} \\ \sqrt{18}\text{ = }\frac{18\text{ + 16}}{2\times\sqrt{16}} \\ \\ \sqrt{18}\text{ = }\frac{34}{2(4)} \end{gathered}[/tex][tex]\begin{gathered} \sqrt{18}\text{ = }\frac{34}{8} \\ \\ \sqrt{18}\text{ = 4.25} \end{gathered}[/tex]Evaluate. 12⋅(1/4+1/3)to the power of2+2/3 Enter your answer as a mixed number in simplest form by filling in the boxes.

12×(1/4+1/3)to the power of2+2/3 using **PEDMAS**and **INDICIES** rule gives 7^8/3

**lndicies** is expressed as **Ax^n**. Where **A** is the coefficient, **x** is the **base** and **n** is the **power** or **index**.

12×(1/4+1/3)to the power of2+2/3

Evaluating the **expression**

= (12×( 1/4+1/3))^2+2/3

using **PEDMAS**

= (12× 7/12)^8/3

opening the bracket, we therefore have

= 7^8/3

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the bearing of L from Q is 90° what is the bearing of Q for L

**Given:**

the bearing of L from Q is 90°

**Required:**

what is the bearing of Q for L

**Explanation:**

There is a 180 degree difference in bearing between two location(L from Q, Q from L)

If L from Q is 90 degree then

Q from L is

180-90=90degree

**Required answer:**

90 degree

someone please help…

Q.12 The **polynomials** are 2 and 3

**What is polynomial ?**

A **polynomial** is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example of a **polynomial **of a single indeterminate x is x² − 4x + 7.

Given, p(x) = -x² + x + 2

p has a degree 2

Let, a = 1 + i√2

b = 1 - i√2

a + b = 1 + i√2 + 1 - i√2

= 2

a * b = (1 + i√2) * (1 - i√2 )

= 1 - (i√2)²

= 1 - i²*2 (where, i² = -1)

= 1 + 2

= 3

Therefore, the **polynomial** are 2 and 3

Q.13 The polynomial is x³ + x

Given, Q(x) = x³ - 2x² - 1

Q has a degree of 3

=>(x - 0) (x - i) (x + i)

=>(x² - ix) (x + i)

=>x³ + x²i - ix² - i²x (where i² = -1)

=>x³ + x

Therefore, the **polynomial** is x³ + x

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Solve the problems.

Prove: BD = CD

The** Angle-Side-Angle (ASA) **criterion states that any two angles and the side included between them of one** triangle** are identical to the **corresponding angles** and the included side of the other triangle if two triangles are congruent. One of the requirements for two triangles to be congruent is angle side angle.

When two **parallel lines** are intersected by another line, comparable angles are the angles that are created in matching corners or corresponding corners with the **transversal.**

If the three sides and the three angles of both angles are equal in any orientation, two triangles are said to be **congruent.**

Given,

**M∠1 = M∠2**

(On joining BD and CD)

M∠ADB = M∠ADC

In ΔABD and ΔADC

M∠ADB = M∠ADC (Given)

M∠BAD = M∠DAC (Given)

AD = AD (Common Sides)

⇒ **ΔABD ≅ ΔADC **(**Angle Side Angle Property**)

So**, BD = CD** (**Corresponding sides **are equal to a Congruent Triangle)

Hence, proved that **BD = CD.**

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Hello me with part B pleaseeee

**Answer:**

0, 0, 0

**Step-by-step explanation:**

You want the **sum** of a **number** and its **opposite** for the numbers ...

** 3, 7.5, and -2 2/3**

The definition of the additive inverse (opposite) of a number is that it is the number that **produces 0** when summed with the original number.

Any number summed with its opposite will give **zero**.

The sums are ...

3 + (-3) =Simplify the trigonometric expression. cos(theta+pi/2)

We have to simplify the expression:

[tex]\cos (\theta+\frac{\pi}{2})[/tex]We could see it graphically:

We see that for any angle theta, the cosine of theta + pi/2 is equal to negative sin of theta.

Then we can write:

[tex]\cos (\theta+\frac{\pi}{2})=-\sin (\theta)[/tex]**The answer is -sin(theta).**

What is x2 + 6x complete the square

You have the following expression:

**x² + 6x**

In order to complete the square, take into account that 6 is two times the product of the first coeffcient by the second one in the binomial (a+ b)², then, you have:

6 = 2ab

a=1 because is the coeffcient of the term with x², then for b you obtain:

**b = 6/2(1) = 3**

the third term of the trynomial is the squared of b.

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