Part A: The length of two sides of a triangle are:

Side 1:

Side 2:

The perimeter of the triangle is

Part A: What is the total length of the two sides, 1 and 2, of the triangle? Show your work. (7 points)

Part B: What is the length of the third side of the triangle? Show your work. (7 points)

D. This is an experiment because it is applying a treatment

Experiments and observational studies are both ways to find new information about a hypothesis but in different ways.

Vocabulary

First, to understand the question, let's define the key terms.

These definitions eliminate the answer choices A and C because both of them match the incorrect definition of the term.

Experiment vs. Observational Study

Now, we need to figure out if this specific example is an experiment or an observational study. In this case, the nutritionist is giving a treatment of vitamins. This means that this cannot be an observational study because the scientist is interfering with people. It has to be an experiment because there is a specific treatment being applied.

The result of expanding the trigonometry expression [tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex] is [tex]cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

The expression is given as:

[tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex]

Express [tex]\sin^2(\theta)[/tex] as [tex]1 - \cos^2(\theta)[/tex].

So, we have:

[tex]\sin^2(\theta) * (1 + \cos(\theta)) = (1- \cos^2(\theta)) * (1 + \cos(\theta))[/tex]

Open the bracket

[tex]\sin^2(\theta) * (1 + \cos(\theta)) = 1 + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

Express 1 as cos°(Ф)

[tex]\sin^2(\theta) * (1 + \cos(\theta)) = cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

Hence, the result of expanding the trigonometry expression [tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex] is [tex]cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

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a) Triangle A is rotated 90 degrees anticlockwise about (-1,0) to give triangle A'.

Triangle A' is then reflected in the line y=0 to give triangle A''.

b) Rotation

a) Triangle A is rotated 90 degrees anticlockwise about (-1,0) to give triangle A'. Triangle A' is then reflected in the line y=0 to give triangle A''.

b) Rotation

Given,

Triangles A , A' , A'' .

Here,

The triangles are rotated and reflected to get different triangles .

Firstly ,

Triangle A is made to be rotated by 90° in anticlockwise direction at point (-1 , 0) .

To get A'' triangle A' is reflected from horizontal axis.

Triangle A maps into triangle A'' by rotation .

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Answer:

A, 3

Step-by-step explanation:

Just look at x axis, find 6, and then start going up until you hit the line. Then record the point you hit.

Answer:

0.0109056604

that is the answer, I used a calculator

Answer:

5.9 C

Step-by-step explanation:

Plug in 16°C for the initial amount, 0.06 for the rate of decrease, and 16 minutes for the time elapsed.

y= a(1–r)t

y= 16(1–0.06)16 Plug in values

y= 16(0.94)16 Subtract

y= 16(0.37157…) Simplify

y= 5.94518… Multiply

Round to the nearest tenth.

5.94518… → 5.9

To the nearest tenth, the difference in temperature will be 5.9°C.

Answer:

144

Explanation:

In a regular polygon all angles and sides are equal. to find out to what all the angles add up to you take the number of sides subtract 1 and multiply by 180.

(10-2)*180=1440

1440/10=144

Answer:

Substitution

Step-by-step explanation:

In your premises, the state AB = BC is given to be true. In math, substitution is taking one value in an equation and "subbing it out for" one that we know has the same value. This means anywhere we see AB, we can substitute BC and the equation will still be true, because AB = BC.

In the example given, that changes AB + BC = AC to AB + AB = AC.

We substituted the AB with BC, because we know that they are of the same value.

Answer:

so the next 2 sequences would be 60 and 62

Step-by-step explanation:

The next two terms in the given arithmetic sequence are 60 and 62.

The arithmetic sequence is given as follows:

20, 32, 42, 50, 56, ?

To find the next two terms in the sequence, let's analyze the pattern:

The sequence increases by the following increments:

12, 10, 8, 6

We can observe that the increments are decreasing by 2 each time.

To find the next two terms, we can continue this pattern:

Increment: 4 (6 - 2)

Increment: 2 (4 - 2)

Adding the increments to the previous terms:

56 + 4 = 60

60 + 2 = 62

Therefore, the next two terms in the arithmetic sequence are 60 and 62.

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Answer: 3

Step-by-step explanation:

Triangles are similar

Option E

Answer:

Both of the triangles are similar but they look like they have been rotated a bit.  Sides x is similar to 12 and side 5 (the hypotenuse) is similar to 13.  Therefore we can just set up an equation and cross-multiply.

[tex]\frac{x}{5} = \frac{12}{13}[/tex]

[tex](x * 13) = (5 * 12)[/tex]

[tex]13x = 60[/tex]

Divide 12 from both sides

[tex]13x/13 = 60/13[/tex]

[tex]x=4.615[/tex]

Best option would be Option E, 4.62

The list of the set of dimension for fencing the building around a rectangular plot of land is 10.5 meters and 21 meters.

area of rectangle = lw

where

Therefore,

perimeter = 2w+ l

42 = 2w + l

l = 42  - 2w

Hence,

area = w(42 - 2w)

180 = 42w - 2w²

-2w² + 42w - 180 = 0

-w² + 21w - 90 = 0

The dimension w can be found as follows;

w = - b / 2a

where

w = - 21 / 2 ×  -1

w = 10.5 meters

Then,

l = 42  - 2w

l = 42 - 2(10.5)

l = 21 meters

Therefore, the dimensions are 10.5 meters and 21 meters.

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Answer:

10.672hrs ( maybe)

Step-by-step explanation:

A can complete the work in 20 hrs then 1/3 part can be completed in 20*1/3=6.67hrs

B can complete the 1/4 part of the work in same time then B can complete hole work in 6.67*4=26.68 hrs

B can complete the 1/5 part of work in 26.67/5=5.336hrs

according to question C can complete 1/2part of work in same time then the whole work can complete in

2*5.336=10.672hrs

Answer:

hello!!!!

the answer is 280

im not really sure... read the description.... since i dont see a picture attached i dont know the figure shape which makes it difficult to guarantee the correct answer for you....

please read the explanation.. it always helps...

Step-by-step explanation:

okay im going to guess that the figure is a rectangular prism... if not please correct me

if so.... then...

2(10*5 + 10*6 + 5*6)= 280

22.5 = 1.5x

x = 22.5/1.5

x = 15

hope it helps...!!!

Answer:

x = 15

Step-by-step explanation:

1.5x = 22.5

x = 22.5/1.5

assuming your finding x

Answer:

1.45

Step-by-step explanation:

weight of all books= 14×1.1= 15.4

weight of all duster=7×0.2= 1.4

weight of books and duster= 15.4+1.4=16.8

weight of the empty box = 18.25-16.8=1.45

Answer:A

Step-by-step explanation:

the correct choice is: B. The numbers in the pattern are odd.

To determine if the numbers in the pattern are even, odd, or alternate between even and odd, let's examine the first few numbers in the pattern:

First number: 41

Second number: 41 - 4 = 37

Third number: 37 - 4 = 33

Fourth number: 33 - 4 = 29

As we can see, the numbers in the pattern are decreasing by 4 in each step. The first number (41) is odd, and subsequently, each number is decreasing by an even value (4). Therefore, all the numbers in the pattern will be odd.

So, the correct choice is:

B. The numbers in the pattern are odd.

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Answer:

A I think this is it

Step-by-step explanation:

Hope this helps :) :)

Volume of a Rectangular Prism = length x width x height

Volume = 20

Length = 2

Width = 2

Height = d

20 = 2 x 2 x d

20 = 4 x d

d = 5

Answer: d = 5 centimeters

Hope this helps!

Answer:

d = 5 cm

Step-by-step explanation:

Volume of a rectangular prism: L*W*H

Substitute the values above into the formula:

V = L*W*H

20 = 2*2*d

20 = 4d

/4    /4

5 = d

Therefore, the value of d is 5 cm.

Hope this helps!

Answer:

75.96°

Step-by-step explanation:

Answer:

Equation = [tex]\frac{3}{4}[/tex] x - 2 = [tex]\frac{5}{12}[/tex]

First: [tex]\frac{3}{4}[/tex] x = [tex]\frac{5}{12}[/tex] + 2

Then: [tex]\frac{3}{4}[/tex] x = [tex]\frac{29}{12}[/tex]

Answer: x = [tex]\frac{29}{9}[/tex] —> 9x = 29

—-

Have a nice day!!

A real-life situation that can be modeled by a function is that Bob has 20 pens and buys extra 5 pens weekly.

It should be noted that a function simply means an expression that shows the relationship between the variables.

In this case, a real-life situation that can be modeled by a function is that Bob has 20 pens and buys extra 5 pens weekly.

The function will be:

= 20 + 5w

where w represents the number of weeks.

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The number of ways a pizza with three different toppings out of 7 can be made is ⁷C₃(35).

The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.

^nC_r = \dfrac{n!}{(n-r)!r!}\ , \ \ ^nP_r = \dfrac{n!}{(n-r)!}

where,

n is the number of choices available,

r is the choices to be made.

The number of ways a pizza with three different toppings out of 7 can be made is ⁷C₃(35).

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Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

Let [tex]z=r(\cos\theta+i\sin\theta)[/tex] be a complex number, where [tex]n[/tex] is an integer and [tex]n\geq 1[/tex]. By DeMoivre's Theorem, if [tex]z^n=r^n(\cos\theta+i\sin\theta)^n[/tex], then [tex]z^n=r^n(\cos n\theta+i\sin n\theta)[/tex].

Hence, we must first convert from rectangular to polar form:

[tex]z=-1-i\\\\r=\sqrt{a^2+b^2}\\\\r=\sqrt{(-1)^2+(-1)^2}\\\\r=\sqrt{1+1}\\\\r=\sqrt{2}[/tex]

[tex]\displaystyle \theta=\tan^{-1}\biggr(\frac{y}{x}\biggr)\\\\\theta=\tan^{-1}\biggr(\frac{-1}{-1}\biggr)\\ \\\theta=\tan^{-1}(1)\\\\\theta=45^\circ[/tex]

Therefore, the rectangular form for the complex number is [tex]z=\sqrt{2}(\cos45^\circ+i\sin45^\circ)[/tex], and now we can apply DeMoivre's Theorem to raise the complex number to the 10th power:

[tex]z=\sqrt{2}(\cos45^\circ+i\sin45^\circ)\\\\z^{10}=\sqrt{2}^{10}(\cos45^\circ+i\sin45^\circ)^{10}\\\\z^{10}=2^5(\cos10\cdot45^\circ+i\sin10\cdot45^\circ)\\\\z^{10}=32(\cos450^\circ+i\sin450^\circ)\\\\z^{10}=32(0+i)\\\\z^{10}=32i[/tex]

Therefore, [tex]z^{10}=32i[/tex] in rectangular form.

Problem 2

[tex]3\:\text{cis}\:90^\circ=3(\cos90^\circ+i\sin90^\circ)=3(0+i)=3i[/tex]

Therefore, [tex]3\:\text{cis}\:90^\circ=3i[/tex] in rectangular form.

Answer:

€ 1800

Step-by-step explanation:

x - 20% of x = 1440

x - 20x/100 = 1440

x - x/5 = 1440

(5x - x)/5 = 1440

4x/5 = 1440

therefore x = 1440 × 5/4 [ transpose 4/5 to right hand side ]

x = 360 × 5

= € 1800