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)
Answers
Part A: The total length of the two sides, 1 and 2, of the triangle is 10x² + 14x - 8
Part B: The length of the third side of the triangle is 10x³ -2x² - 16x + 2
Calculating the sides of a triangleFrom the given information,
The length of side 1 is
6x² - 4x - 2
and the length of side 2 is
18x + 4x² - 6
Part A
The total length of the two sides, 1 and 2, of the triangle will be
Length of side 1 + Length of side 2
That is,
6x² - 4x - 2 + 18x + 4x² - 6
This becomes,
6x² + 4x² + 18x - 4x - 2 - 6
10x² + 14x - 8
Therefore, the total length of the two sides, 1 and 2, of the triangle is 10x² + 14x - 8
Part B
The length of the third side will be
Perimeter of the triangle - the total length of sides 1 and 2
From the given information,
The perimeter of the triangle is 10x³ + 8x² - 2x - 6
Then,
Length of third side = 10x³ + 8x² - 2x - 6 - (10x² + 14x - 8)
Length of third side = 10x³ + 8x² - 2x - 6 - 10x² - 14x + 8
Length of third side = 10x³ + 8x² - 10x² - 2x - 14x - 6 + 8
Length of third side = 10x³ -2x² - 16x + 2
Hence, the length of the third side of the triangle is 10x³ -2x² - 16x + 2
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Related Questions
SOMEONE PLEASE HELP WILL MARK BRAINLIEST
Answers
Answer:
75.96°
Step-by-step explanation:
[tex] \angle A = \tan^{-1}\bigg(\frac{8}{2}\bigg)[/tex][tex] \angle A = \tan^{-1}(4)[/tex][tex] \angle A =75.963756532\degree[/tex][tex] \angle A \approx 75.96\degree[/tex]Julia has 42 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 180 square meters. List each set of possible dimensions (length and width) of the field.
Answers
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 a rectanglearea of rectangle = lw
where
l = lengthw = widthTherefore,
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
a = -1b = 21w = - 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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Respond
1. Describe a real-life situation that can be modeled by a function (a relation in which every input
value corresponds to only one output value). The situation must be different from the examples
provided in the reading and in the homework. Identify the input value and the output value of the function, and provide justification that your
relation does, in fact, represent a function.
2. Create a function in the form y = f(x) that models the relation described. You may choose variables in place of y or x that better represent the relation, as seen in the provided example.
3. Identify the domain and range of your function, using proper mathematical notation.
4. Cite any sources you may have used in
formulating your response.
Answers
A real-life situation that can be modeled by a function is that Bob has 20 pens and buys extra 5 pens weekly.
What is a function?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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if w=10, x=5, and y=6, what is the surface are of the figure?
Answers
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
how do i do this?? thanks in advance!
Answers
a) Fill in the gaps below to describe the transformations.
clockwise/anticlockwise about (-1,0) to give
triangle A'.
Triangle A' is then reflected in the line
to give triangle A".
b) What type of single transformation maps triangle A onto triangle A"?
A"
Triangle A is rotated
O
-4
A
Answers
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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NEED HELP ON THIS
If z=-1-i, find z^10 in rectangular form.
The polar form of this problem is 3cis90degrees, what’s the rectangular form?
Answers
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.
Select the reason that best supports statement 5 in the given proof. (See Image)
A distributive property
B substitution
C reflective property
D subtraction property of equality
Answers
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.
PLEASE HELP ME!!!!!!!
Answers
D. This is an experiment because it is applying a treatment
Step-by-step explanation: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.
Experiment - An experiment is when a scientist purposely applies a treatment and interferes with a person's life in order to gather information.Observational Study - This type of study attempts to study a person without interfering with their lives in any way.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.
[tex](sinx^{2} theta)\frac{x}{y}(1+costheata)[/tex]
Answers
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]
How to evaluate the expression?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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1.156÷106
Please help
Will give 20 points whoever gets this right
Thank you :)
Answers
Answer:
0.0109056604
that is the answer, I used a calculator
A pot of soup, currently 16°C above room temperature, is left out to cool. If that temperature
difference decreases by 6% per minute, then what will the difference be in 16 minutes?
If necessary, round your answer to the nearest tenth.
°C
Answers
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.
PLEASE HELP For what value of x is the parallelogram a rectangle. The arrows point to the entire diagonal, not just a segment.
Answers
Which is not a reason an athlete uses technology to assess performance?
A. To monitor development.
B. To tailor to their training program.
C. To send to college recruiters.
D. To analyze technique.
Answers
it’s C. To send to college recruiters
Reason:
You use technology to asses performance so you can better your technique, change up your training program to focus on the things you’re doing wrong and you can also see if you’ve made improvement.
A pizza shop has available toppings of bacon, sausage, pepperoni, onions, mushrooms, peppers and anchovies. How many different ways can a pizza be made with 3 toppings?
Answers
The number of ways a pizza with three different toppings out of 7 can be made is ⁷C₃(35).
What is Combination?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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Please help with this question.
Answers
Answer: 3
Step-by-step explanation:
Identify the zeros of the graphed function.
Question 8 options:
A)
x = –4, –2, 1
B)
x = –1, 0, 2, 4
C)
x = –4, –2, 0, 1
D)
x = –1, 2, 4
Answers
Answer:
A I think this is it
Step-by-step explanation:
Hope this helps :) :)
explanation
What is the approximate value of X?! Help ASAP please
Answers
Triangles are similar
x/5=12/1313x=60x=60/13x=4.615x=4.62Option 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
giving bralinest to correct answer.
Answers
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.
Hope this helps.
is -0.25 rattional or irrational
Answers
PLEASE HELP ME ANSWER THIS AAAA
Answers
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
L = 2 cmW = 2 cmH = d cmV = 20 cm³Substitute 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!
Select the correct answer.
The graph of function fis shown.
Which statement correctly compares the two functions?
OA. They have the same end behavior as x approaches -
B. They have the same end behavior as x approaches -
OC. They have different end behavior as x approaches -
Answers
They have the same x-intercept but different end behavior as x approaches ∞ :)
Rewrite the equation below so that it does not have fractions:
3/4x - 2 = 5/12
Do not use decimals in your answer.
Answers
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!!
The price of a tv was decreased by 20% to £1440. What was the price before the decrease?
Answers
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
A box contains 14 books & 7 pieces of dusters. Each piece of duster weighs 0.2 pounds each book weighs 1.1 pounds. The box & its contents together weigh 18.25 pounds. How much does the empty box weigh?
Answers
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
I need help with number 35
Answers
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
when A complete 1/3 part of any work B can complete 1/4 part of that same work. Similarly when B complete 1/5 part of that work C can complete 1/2 part of that same work. if A can complete that work in 20 hours, then in how many hours can C complete that work.
Answers
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
Solve this pls explain all steps for 22.5 = 1.5x
Answers
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
The rule for a pattern is subtract 4. The first number of the pattern is 41. Which choice is true about this pattern?
A.The numbers in the pattern are even.
B.The numbers in the pattern are odd.
C. The numbers alternate between even and odd.
Answers
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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Find the next two terms in this
sequence.
20, 32, 42, 50, 56, [?
Answers
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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