Answer:
x=8 y=10
Step-by-step explanation:
x+y =18 x=(18-y)
3(18-y) +2y =44
54-3y+2y =44
54-y =44
-y=-10
y=10
x+10=18
x=8
The lengths of two sides of a triangle are shown.
Side 1: 3x^2 − 2x − 1
Side 2: 9x + 2x^2 − 3
The perimeter of the triangle is 5x^3 + 4x^2 − x − 3.
Part A: What is the total length of the two sides, 1 and 2, of the triangle? Show your work.(4 points)
Part B: What is the length of the third side of the triangle? Show your work. (4 points)
Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (2 points)
Answer:
See below ↓↓↓
Step-by-step explanation:
Part A
Total length = Side 1 + Side 2
3x² - 2x - 1 + 9x + 2x² - 33x² + 2x² + 9x - 2x - 1 - 35x² + 7x - 4Part B
Length of 3rd side = Perimeter - [Side 1 + Side 2]
L = 5x³ + 4x² - x - 3 - [5x² + 7x - 4]L = 5x³ + 4x² - x - 3 - 5x² - 7x + 4L = 5x³ - x² - 8x + 1Part C
Yes, as the resulting polynomial has a finite value we can conclude that polynomials are closed under addition and subtraction.
Part A: The total length of the two sides of the triangle is [tex]5x^2+7x-4[/tex]. This is obtained by adding the given two sides.
Part B: The length of the third side is [tex]5x^3-x^2-8x+1[/tex]. This is obtained by subtracting the sum of two sides from the perimeter of the triangle.
Part C: Yes, the Part A and Part B answers show that the polynomials are closed under addition and subtraction. This is because the expressions have like terms.
Polynomials:These are the expressions that are formed with constants, coefficients, and variables. based on the highest degree of the variable in the expressions, the polynomials are classified into many types.Calculation:Given that, a triangle has two sides of length [tex]3x^2-2x-1[/tex] and [tex]9x+2x^2-3[/tex]
The perimeter of the triangle is [tex]5x^3+4x^2-x-3[/tex]
Part A:
To find the total length of two sides, adding the two side
⇒ [tex](3x^2-2x-1)+9x+2x^2-3\\[/tex]
⇒ [tex]5x^2+7x-4[/tex]
(adding the like terms w.r.t their sign)
Part B:
To find the length of the third side, subtract the sum of two sides from the perimeter.
⇒ [tex](5x^3+4x^2-x-3)-(5x^2+7x-4)[/tex]
⇒ [tex]5x^3-x^2-8x+1[/tex]
Part C:
From Part A and Part B, it is proved that the polynomials undergo addition and subtraction. Hence, it is justified.
Therefore, Part A, Part B, and Part C were obtained.
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Find the distance between the two points rounding to the nearest tenth (if necessary). (-1,5) and (-7, -1)
Distance formula:
[tex]d = \sqrt{(x_{2}-x_1)^2 +(y_2-y_1)^2}[/tex]
Now replace the variables with the numbers (When you replace the numbers, it doesn't matter which is the first variable and second variable. Just do whatever is easiest).
[tex]d = \sqrt{(-1-(-7))^2+(5-(-1))^2}\\d = \sqrt{(-1+7)^2+(5+1)^2}\\d = \sqrt{6^2+6^2}\\d = \sqrt{36+36}\\d = \sqrt{72} \\d = 8.5[/tex]
Thus, the distance between the two points is 8.5
Which statement about the ordered pairs (2, -9) and (3,6) is true for the equation 5x - y/3 = 13?
A) (3, -6) is a solution to the equation.
B) Neither ordered pair is a solution.
C) (2, -9) is a solution to the equation.
D) Both ordered pairs are solutions.
Answer:
C) (2, -9) is a solution to the equation.
Step-by-step explanation:
To find if both or one point is the solution to the equation, substitute the x and y-values of both points into the equation to find which one makes a true and correct statement (the answer).
For (2, -9):
[tex]\sf5x - \frac{y}{3} = 13\\\\5(2) - \frac{-9}{3} = 13\\\\10-(-3)=13\\\\10+3=13\\\\ \boxed{13=13}\\\\\ \textsf{This is a true statement}\\\textsf{This means that (2, -9) is a solution to 5x - y/3 = 13}[/tex]
For (3, -6);
[tex]\sf5x - \frac{y}{3} = 13\\\\5(3) - \frac{-6}{3} = 13\\\\15-(-2)=13\\\\15+2=13\\\\ \boxed{17=13}\\\\\ \textsf{This is not a true statement}\\\textsf{This means that (3, -6) is not a solutions to 5x - y/3 = 13}[/tex]
Therefore, the correct answer is C
Hope this helps!
the price of 5 boxes of crackers at the store can be represented by the equation $17.75 divide 5 = k what would be the cost of 7 boxes of crackers
Answer:
24.85
Step-by-step explanation:
17.75/5 = 3.55
3.55 x 7 = 24.85 :)
Have an awesome day!
Please rate and mark brainliest!
Benjamin’s garden is shaped like a rhombus the area of the garden is 336 ft. The height of the rhombus that represents his garden is 16 feet what is the base of the rhombus
Answer: 21 ft
Step-by-step explanation:
What’s the area of the circle?
Answer:
153.86
Step-by-step explanation:
The area of a circle is π[tex]r^2[/tex].
Since the radius of that circle, and we are using 3.14 for π, we get:
[tex]3.14 * 7^2 = 153.86[/tex]
Answer:
Technically you should get :153.94
But for your answer choice its the 2nd one.
Step-by-step explanation:
area=πr^2
Which means that you would plug in 7 for r.
Which means it would look like this: area=π7^2
Next you would square 7 which comes out to 49
Lastly multiply 49 time π (3.14)
A gas tank holds exactly 14 gallons of gas. if the tank is 2/3 empty, how many gallons remain in the tank? (help!)
Answer:
4 and 2/3 is the answer
Step-by-step explanation:
14/3= 4 and 2/3
i do not know this answer
Answer:
15 miles
Use the Pythagoras theorem
Answer: 15
Step-by-step explanation:
Let's start by stating what we are given
The perimeter is 36
One side length is 12
And the other given side is 9
Finally we have an unknown side x
The value of all the sides added together is the perimeter.
So add all the sides
12+9+x=36
21+x=36
Subtract both sides by 21
21-21+x=36-21
x=15
if you answer this. i will forever love you. foreverrrrrrr
Answer:
Step-by-step explanation:
The Mean Value Theorem says that for continuous and differentiable function f(x) on the interval ( a, b ) there is number c ∈ ( a, b ) that
f'(c) = [tex]\frac{f(b)-f(a)}{b-a}[/tex] ....... (1)
~~~~~~~~~~~~~~~~
f(5) = 44
f(0) = - 1
5 - 0 = 5
f'(x) = 2x + 4 ⇒ f'(c) = 2c + 4
2c + 4 = [tex]\frac{44+1}{5}[/tex]
2c + 4 = 9 ⇒ c = [tex]\frac{5}{2}[/tex] (D).
A town population was 6000 people last year. The population this year is expected to increase by 4%. By how many people is the population expected to increase this year?
Can someone help me with this pls I would be so happy if I got help with this.
Step-by-step explanation:
Pam made a mistake when multiplied fractions.
Correct way of multiplication involves the multiplication of both numerator and denominator.
She should have written
[tex]\cfrac{3}{8}*\cfrac{17}{8} =\cfrac{51}{64}[/tex]
There are 85 students in a college mathematics class. Five students are
chosen to work on a project together. How many different groups of five
students are there in this class?
Answer:
17
Step-by-step explanation:
85/5=17
What is the measure of angle 8?
Answer:
32
Step-by-step explanation:
First, let's find angle 6 as we will need that to find angle 8.
angle 6 = 180 - 122 = 58(straight line angles equal to 180)
now sum of angles in a triangle = 180
so angle 8 = 180 - 90 - 58
= 32
Hope it helps:)
Answer:
32°
Step-by-step explanation:
We know that the exterior angle of the triangle is equal to the sum of the interior opposite angles.
Therefore,
< 1 + < 8 = 122°
Also, given that,
<1 = 90°
So,
< 1 + < 8 = 122°
90° + < 8 = 122
< 8 = 32°
Is FGH ~ JKL? If so, identify the similarity postulate or theorem that applies.
Answer: D
Step-by-step explanation:
There are two pairs of congruent angles.
The two triangles FGH and JKL are similar to each other by Angle-Angle property. Hence, option D is correct.
What is the similarity?If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
In the given figure we can see that the two triangles FGH and JKL have two angles equal that is ∠f =∠J = 30° and ∠L = ∠H =55°. Two angles are similar then the triangles are similar.
Hence, option D is correct.
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please help me with this Pythagorean Theorem
Answer:
[tex]\sqrt{22.25}[/tex]
Step-by-step explanation:
4 ^ 2 is 16
2.5 ^ 2 is 6.25
16 + 6.25 is 22.25
The square root of 22.25 is undefined so...
[tex]\sqrt{22.25}[/tex]
2,5,8,...
Find the 41st term.
Answer:
Step-by-step explanation:
hello :
this is the arithmetic -sequence because : 8-5=5-5=3 (comon dif)
An =A1+(n-1)r calculate......... (A1=2 and r=3 and n=41) continu...
Answer:
122
Step-by-step explanation:
What is the area of this rectangle?
16 sq m
18 m
14 sq m
9 m
What is an equation of the line that passes through the points (4, 7) and (-3, 7)?
Step-by-step explanation:
Slope= 7-7/-3-4
0/-7
0
y-7 = 0(x-4)
y-7= 0
y=7MARK ME AS BRAINLISTWhich graph shows the solution to 8y < 4x + 16? A. B. C. D.
Answer:
The answer is D.
Step-by-step explanation:
Find the boundary line, and then just shade the area.
y < 1/2x + 2
Answer:
d
Step-by-step explanation:
2023
Chase bought a pair of athletic shoes on sale for $38.85. The original price was $57.79. How much money did he save buying them on sale?
A.
$18.94
B.
$19.94
C.
$29.94
D.
$96.94
Answer:
A. 18.94
Step-by-step explanation:
57.79 (Original Price) - 38.85 (Sale Price) = 18.94 (Difference)
Three friends combine their
money to buy tickets for a hockey game. If they
share the change evenly, how much will each
friend receive? Write equations to represent the problem then solve.
Using proportions, considering that they spent $n to buy the ticket, each friend received an amount in dollars of [tex]\frac{n}{3}[/tex].
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, we consider that they spent $n to buy the ticket. Since there are 3 friends and the amounts were divided evenly, each friend received an amount in dollars of [tex]\frac{n}{3}[/tex].
More can be learned about proportions at https://brainly.com/question/24372153
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Question is in the pic below ;)))
Answer:
the first one
Step-by-step explanation:
1 x -4 = -4
3 x -4 = -12
and so on
If m/n = 5, then what is the value of m^2 - 25n^2?
=============================================
Work Shown:
m/n = 5
m = 5n
m^2 - 25n^2 = (m)^2 - (5n)^2
m^2 - 25n^2 = (m-5n)(m+5n)
m^2 - 25n^2 = (5n-5n)(5n+5n)
m^2 - 25n^2 = (0n)(10n)
m^2 - 25n^2 = (0)(10n)
m^2 - 25n^2 = 0
-----------------
Another approach:
m/n = 5
m = 5n
m^2 = (5n)^2
m^2 = 25n^2
m^2 - 25n^2 = 0
-----------------
Consider the example that m = 10 and n = 2.
We can see that m/n = 10/2 = 5
Furthermore,
m^2 - 25n^2 = 10^2 - 25*2^2 = 100 - 100 = 0
I'll let you try out other examples.
Can I help someone for brainiest?
(MATH ONLY)
answer this question with link to question
What is the area of the polygon? 30cm 21cm 14cm 46cm
Answer:
1,044
Step-by-step explanation:
14 x 46 = 644
16 x 25 = 400
644 + 400 = 1,044
Evaluate (2 minus 5 i) (p + q) (i) when p = 2 and q = 5 i.
29 i
29 i - 20
- 21 i
29
look at attachment hurry
Answer:
the top one on the right
Step-by-step explanation:
i used desmos graphing calculator
Which of the following are solutions to the inequality below? Select all that apply.
4 ≥
r
Answer:
r=1
Step-by-step explanation:
1 is lower than for. The sign also suggests that its could be 4 as well
If the mean absolute deviation is a really
large number, then what does that mean about
the data set?
Answer:
The data is more spread out so their is a greater variability in the data.
Step-by-step explanation:
The Mean absolute deviation is large, then the data is more spread out and there is greater variability in the data.
What is mean absolute deviation?Mean absolute deviation is "collected data set is the average of absolute deviations from the center point of the data set".
According to the question,
Formula for Mean absolute deviation = summation of ( absolute value of xₙ - x⁻ divided by number of data values), where ' xₙ' is the input data values and 'x⁻ ' is mean of the given data values .
When the mean absolute deviation is large number then the data spread out more and the variability is greater in data.
Hence, the Mean absolute deviation is large then there is greater variability in the data.
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A supervisor finds the mean number of miles that the employees in a department live from work. he finds x overbar = 29 and s = 3.6. which mileage is within a z-score of 1.5? 21 miles 24 miles 36 miles 41 miles
A supervisor finds the mean number of miles that the employees in a department live from work is 24. Then the correct option is B.
What is a z-score?The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
The z-score is given as
[tex]z = \dfrac{x-\mu }{s}\\[/tex]
x = 29
s = 3.6
z = 1.5
Then the mean will be
[tex]1.5 = \dfrac{29 - \mu }{3.6}\\\\\mu = 29 - 5.4\\\\\mu = 23.6 \approx 24[/tex]
More about the z-score link is given below.
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