Answers
The perimeter and area of the equilateral, isosceles and right angled triangle are 16.2mm 12.6mm², 15.2in and 9.61in², 21.47yds and 16.81yds² respectively.
What is the area of the equilateral, isosceles and right angle triangle?Note that:
The perimeter of an Equilateral triangle is expressed as P = 3a
The area of an Equilateral triangle is expressed as A = ((√3)/4)a²
Where a is the dimension of the side.
The perimeter of an Isosceles triangle is expressed as P = 2a + b
The area of an Isosceles triangle is expressed as A = (ah)/2
Where b is the slant height, a is the dimension of the base and h is the height.
The perimeter of a Right angled triangle is expressed as P = a + b + c
The area of a Right angled triangle is expressed as A = (ab)/2
Where a and b is the dimension of the two sides other than the hypotenuse and c is the hypotenuse.
For the Equilateral triangle.
Given that;
a = 5.4mmPerimeter P = ?Area A = ?Perimeter P = 3a
P = 3 × 5.4mm
P = 16.2mm
Area A = ((√3)/4)(5.4mm)²
A = ((√3)/4)( 29.16mm² )
A = 12.6mm²
The Perimeter and Area of the Equilateral triangle are 16.2mm 12.6mm² respectively.
For the Isosceles triangle.
Given that;
Base a = 3.4inSlant height b = 5.9inPerimeter P = ?height h = ?Area A = ?Perimeter P = 2a + b
P = 2(b) + a
P = 2(5.9in) + 3.4in
P = 11.8in + 3.4in
P = 15.2in
The height h is the imaginary line drawn upward from the center of a.
First, we calculate the height using Pythagorean theorem
x² = y² + z²
Where x = b = 5.9in, y = a/2 = 3.4in/2 = 1.7in, and z = h
(5.9in)² = (1.7in)² + h²
34.81in² = 2.89in² + h²
h² = 34.81in² - 2.89in²
h² = 31.92in²
h = √31.92in²
h = 5.65in
Now, the area will be;
A = (ah)/2
A = (3.4in × 5.65in )/2
A = 19.21in²/2
A = 9.61in²
The Perimeter and Area of the Isosceles triangle are 15.2in and 9.61in² respectively.
For the Right angled triangle.
Given that;
a = 8.2ydsb = 4.1ydsc = 9.17ydsPerimeter P = ?Area A = ?Perimeter P = a + b + c
P = 8.2yds + 4.1yds + 9.17yds
P = 21.47yds
Area A = (ab)/2
A = ( 8.2yds × 4.1yds)/2
A = ( 33.62yds²)/2
A = 16.81yds²
The Perimeter and Area of the Right angled triangle are 21.47yds and 16.81yds² respectively.
Therefore, the perimeter and area of the equilateral, isosceles and right angled triangle are 16.2mm 12.6mm², 15.2in and 9.61in², 21.47yds and 16.81yds² respectively.
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Related Questions
Solve the equation
3(2x + 2) = 3x - 15
A. X = -7
B. X = -17/3
C. X = 3
D. X = 7
Answers
When starting a problem, almost every single problem needs to be understood by the person answering so they can see what needs to be done. In this example, we are given an expression and told to solve the equation which means that we need to solve for the unknown, in this case x.
Now that we know what we must do, we can start to solve the problem. Looking at the problem we can see that the step that we must take is to distribute 3 into the parenthesis.
Distribute
[tex]3(2x + 2) = 3x - 15[/tex][tex](3*2x) +(3* 2) = 3x - 15[/tex][tex](6x) +(6) = 3x - 15[/tex][tex]6x+6 = 3x - 15[/tex]Now that we distributed the values inside of the parenthesis we can move onto the next step which is to help isolate x. What we should do is subtract 6 from both sides which will help leave x with its coefficient alone.
Subtract 6 from both sides
[tex]6x+(6 - 6 )= 3x +(- 15 - 6)[/tex][tex]6x= 3x +(- 15 - 6)[/tex][tex]6x= 3x - 21[/tex]The next step that we should take to help solve for the unknown is to subtract 3x from both sides.
Subtract 3x from both sides
[tex](6x - 3x)= (3x - 3x) - 21[/tex][tex](6x - 3x)= - 21[/tex][tex]3x = - 21[/tex]The final step that we must take to help isolate the unknown would be to divide both sides by 3. This would remove the coefficient from x and we would get -21 divided by 3.
Divide both sides by 3
[tex]\frac{3x}{3} = \frac{- 21}{3}[/tex][tex]x = \frac{- 21}{3}[/tex][tex]x = -7[/tex]Therefore, after simplifying the expression that was given to solve for the unknown we were able to determine that the option that would best match the solution is option A, x = -7.
Answer:
a) x = -7
Step-by-step explanation:
Given: 3(2x + 2) = 3x - 15
1. Distribute:
3(2x) + 3(2) = 3x - 15
⟹ 6x + 6 = 3x - 15
2. Subtract 3x from both sides:
6x - 3x + 6 = 3x - 3x - 15
⟹ 3x + 6 = -15
3. Subtract 6 from both sides:
3x + 6 - 6 = -15 - 6
⟹ 3x = -21
4. Divide both sides by 3:
3x ÷ 3 = -21 ÷ 3
⟹ x = -7
5. Check your work:
3(2x + 2) = 3x - 15
3(2(-7) + 2) = 3(-7) - 15
3(-14 + 2) = -21 - 15
3(-12) = -21 - 15
⟹ -36 = -36 ✔
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i need help with this pls
Answers
Answer:
The answer is the first bullet. (number 1)
For each of the examples below, identify
the bearing of D from C.
a)
b)
N
220°
140°
155°
D
C
205°
Not drawn accurately
Answers
Answer:
140°
205°
Step-by-step explanation:
For A
The bearing of D from C is the angle at the line joining D and C while coming from the north pole in a clockwise direction.
from the diagram, the answer is = 140°
For B
The bearing of D from C is obtained same as A
so the answer is = 205°
PLease help 5 stars + thanks
Answers
Answer:
B.80
Step-by-step explanation:
a straight line adds up to 180 degrees. you already have 100. 180-100=80
Solve system of equation using elimination by addition.
Will give brainliest!!
Answers
Answer:
x = 6
Step-by-step explanation:
Add the system of equations together:
2x - 3y = 12
4x + 3y = 24
you get
6x = 36
divide by the coefficient
6x/6 = 1
36/6 = 6
x = 6
Not sure if you need the y, but if so, let me know!
Hope this helps!
Which of these is a reason you might use a credit union instead of a bank? (flocabulary)
A
They often don’t have any fees associated with their accounts.
B
They often have higher interest rates on savings accounts.
C
They often have higher interest rates on loans.
D
They are out to make a profit on your money.
Answers
please help with this math problem i will give brainliest
Write the rational number as a decimal.
−38 =
Answers
Answer:
-0.38
Step-by-step explanation:
What is the sum of √-2 and √-18?
O 4√2
O 4√21
O 5√2
O 5√21
Answers
Answer:
[tex]4 \sqrt{2} \: i[/tex]
Step-by-step explanation:
[tex] \sqrt{ - 2} + \sqrt{ - 18} \\ ( \sqrt{2} \times \sqrt{ - 1} ) + ( \sqrt{18} \times \sqrt{ - 1} ) \\ ( \sqrt{2} \times \sqrt{ - 1} ) + (3 \sqrt{2} \times \sqrt{ - 1} ) \\ \sqrt{2} i + 3 \sqrt{2} i \\ = 4 \sqrt{2} i[/tex]
The sum of √-2 and √-18 is 4i√2.
What are Irrational Number?Any real number that cannot be written as the quotient of two integers, p/q, where p and q are both integers, is referred to as an irrational number.
We have √-2 and √-18.
To find the sum of √-2 and √-18 we need to perform addition as
= √-2 + √-18
= √2i + √18i
= √2i + 3i√2
= 4i√2
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ANYONE?? PLEASE HELP??!
Answers
Answer:
the answer is B:42.8
Step-by-step explanation:
because when u do this :24+58+30+42+87+11+ 12+55+91+18 = 428
the total numbers here is 10. so 428÷10 = 42.8
That is how u get ur final answer
u hope have helped you dear
Hi, I'm in 7th grade and I'm about to fail Mathematics. Please help me...
2x - 5x =
Answers
i beliebe 3×=0
ao the answer should be x/0
Answer:
-3x
Step-by-step explanation:
The order of where the terms are placed definitely matter for subtraction. 5x-2x is 3x, but because the smaller number is first, we've gone into the negatives. Think of it like this:
2x - 5x
-2x -2x
__ __
0 -3x
Because we still have the - in front of the 3, it is a negative 3.
Hope this helps!
Investment increase exponentially by about 26% every 3 years. if you start with $2,000 investment how much money would you have after 45 years
Answers
Using an exponential function, it is found that you would have an amount of $64,060 in 45 years.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem, considering the initial value of A(0) = 2000, with a growth rate of r = 0.26 each 3 years, the equation is given by:
[tex]A(t) = 2000(1.26)^{\frac{t}{3}}[/tex]
In 45 years, the amount will be given by:
[tex]A(45) = 2000(1.26)^{\frac{45}{3}} = 64060[/tex]
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A new car is purchased for $29, 000 and over time its value
depreciates by one half every 3.5 years. What is the value of the car 20
years after it was purchased, to the nearest hundred dollars?
Answers
Answer:
290 take away 2 zeros wuxbeucheuxuejx
simplify the radical expression -2√2p*2√22
Answers
Answer:
Simplest form = -4√44p
Step-by-step explanation:
● -2√2p × 2√22
⇒ (-2)(2)(√2p)(√22)
⇒ -4√44p ...Answer...
hope that helps...
please help! please do not copy and paste i have seen the other ones
Given the function f(x) = 2(3)x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.
Part A: Find the average rate of change of each section.
Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other.
Answers
Answer:
Given function:
[tex]f(x)=2(3)^x[/tex]
Part AThe average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
[tex]\begin{aligned}\textsf{Average rate of change - Section A} & =\dfrac{f(1)-f(0)}{1-0}\\\\& =\dfrac{2(3)^1-2(3)^0}{1-0}\\\\& =\dfrac{6-2}{1}\\\\& =4 \end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Average rate of change - Section B} & =\dfrac{f(3)-f(2)}{3-2}\\\\& =\dfrac{2(3)^3-2(3)^2}{3-2}\\\\& =\dfrac{54-18}{1}\\\\& =36 \end{aligned}[/tex]
Part B[tex]\dfrac{\textsf{Average rate of change of Section B}}{\textsf{Average rate of change of Section A}}=\dfrac{36}{4}=9[/tex]
Therefore, the average rate of change of Section B is 9 times greater than Section A.
The function is an exponential function (with 3 as the growth factor) so the rate of change increases over time.
What is the volume of a triangle with a radius of 5 and a height of 6
Answers
In the 3rd quarter of year 5, what
were the approximate total sales in
the coastal region?
Answers
In the 3rd quarter of year 5, the approximate total sales in the coastal region is; $7 million
How to find total sales?
The image of the graph showing the quarterly sales has been attached. From the graph, the red lines indicates the coastal region, the blue lines indicates the northern region, and the green lines indicates the southern region.
From the graph, in the third quarter, we can trace the total sales on the y-axis to be approximately $7 million dollars.
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This table displays the market share in percent of four companies.
Which of the following ranges would be appropriate to use in order to represent the numerical data on the vertical axis of a Bar Chart?
A. 0 to 40
B. 10 to 20
C. 0 to 20
D. 20 to 40
Answers
The right method to use in order to represent the numerical data on the vertical axis of a Bar Chart is 0 to 40.
How do you set the vertical axis of a Bar Chart?In setting the vertical axis of a Bar Chart, note that it is vital for the categories to be natural as possible.
That is, the vertical axis should always begin with the number zero (0) and the scale values for the x axis must range from the lowest value on the left hand side to highest on the right hand side.
Therefore, due to the explanation given, the right method to use in order to represent the numerical data on the vertical axis of a Bar Chart is 0 to 40 as it range from 0 to the highest value.
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Answer:
A
Step-by-step explanation:
i think i can be wrong
oam. The pit
p is the pit?
The gymnastics center where Alexander
works has a rectangular pit filled with
foam. The pit has a volume of 70
m³, and it has a length of 7 m and a width
of 5 m. How deep is the pit?
35 m
2m
14 m
10 m
Answers
Answer:
2 m.
Step-by-step explanation:
Volume = length * width * depth
70 = 7 * 5 * d where d = depth
d = 70 / (7*5)
= 70/35
= 2 m.
What is the intermediate step in the form (x + a)2 = b as a result of completing the square for the following equation? x² + 4x = 12
Answers
The equation in the form (x + a)² = b is (x + 2)² = 16
How to determine the intermediate step?The equation is given as:
x² + 4x = 12
Take the coefficient of x
k = 4
Divide by 2
k/2 = 2
Square both sides
(k/2)² = 4
Add this result to both sides of x² + 4x = 12
x² + 4x + 4 = 12 + 4
Evaluate the sum
x² + 4x + 4 = 16
Express as a perfect square
(x + 2)² = 16
Hence, the equation in the form (x + a)² = b is (x + 2)² = 16
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What is the percentage of 0,4(That is a decimal fraction)
Answers
Answer:
0.4= 4/10= 2/5
Step-by-step explanation:
The first decimal place after the point represent the place holder "tenth's"
0.4 = 4/10
This can simply to 2/5
Hope it will help:-)
2 over 5
Step-by-step explanation:
0.4=4 over 10 simplify=2over5
Determine the value of Y.
Answers
Answer:
y=10°
Step-by-step explanation:
Here,
→(3x+18)°=(5x-4)°
→18°+4°=5x-3x
→22°=2x
→x=11°
Also,
3(4y+3)°+5x-4°=180°[The sum of the linear pair is 180°]
12y+9°+5x-4°=180°
12y+5°+5×11°=180°
12y+5°+55°=180°
12y=180°-60°
12y=120°
y=120°/12
y=10°
Opposite angles are equal
3x+18=5x-422=2xx=11Now
linear pairs are supplementary
3x+18+3(4y+3)=1803(11)+18+12y+9=18033+18+12y+9=18012y+60=18012y=120y=10Suppose you invest $1850 at an annual interest rate of 5.2% compound annually. write a function to re[resent the total earnings e(t) as a function of time in years,t.
Answers
Answer:$1,942.50
Step-by-step explanation:
A = P(1 + rt)
Calculation:
First, converting R percent to r a decimal
r = R/100 = 2.5%/100 = 0.025 per year.
Solving our equation:
A = 1850(1 + (0.025 × 2)) = 1942.5
A = $1,942.50
The total amount accrued, principal plus interest, from simple interest on a principal of $1,850.00 at a rate of 2.5% per year for 2 years is $1,942.50.
prove that n^2 +(n+1)^2 is always an odd number
Answers
I assume [tex]n\in\mathbb{Z}[/tex] (or at least [tex]n\in\mathbb{N}[/tex]).
[tex]n^2+(n+1)^2=n^2+n^2+2n+1=2n^2+2n+1=2(n^2+n)+1[/tex]
The above is always odd, because one of the factors of [tex]2(n^2+n)[/tex] is even, which makes the product even as well, and 1 is odd, and the sum of an even number and an odd number is an odd number.
The point-slope form of the equation of the line equation of the line that passes through (-9,-2) and (1,3) is y-3=1/2(x-1)
Answers
Answer:slope is 1/2, intercept is 2.5
Step-by-step explanation:slope is coefficient of x. Intercept is sun of constants on right side when left side is y. Add 3 to both sides
Compare the equations represented in the table, equation, and graph over
the interval
[-5, 3]. Which function is increasing the fastest?
Answers
Answer:
Tabled Function
Step-by-step explanation:
To determine which function is increasing the fastest over the interval [-5, 3], we need to calculate and compare each function's average rate of change over the given interval.
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Given interval: -5 ≤ x ≤ 3
Therefore, a = -5 and b = 3
Tabled function[tex]f(3)=7[/tex]
[tex]f(-5)=-17[/tex]
[tex]\implies \textsf{Average rate of change}=\dfrac{f(3)-f(-5)}{3-(-5)}=\dfrac{7-(-17)}{3+5}=3[/tex]
Equation: y = x² - 2[tex]f(3)=(3)^2-2=7[/tex]
[tex]f(-5)=(-5)^2-2=23[/tex]
[tex]\implies \textsf{Average rate of change}=\dfrac{f(3)-f(-5)}{3-(-5)}=\dfrac{7-23}{3-(-5)}=-2[/tex]
Graphed functionFrom inspection of the graph:
[tex]f(3)\approx8[/tex]
[tex]f(-5) \approx 0[/tex]
[tex]\implies \textsf{Average rate of change}=\dfrac{f(3)-f(-5)}{3-(-5)} \approx \dfrac{8-0}{3-(-5)}=1[/tex]
Therefore, the Tabled Function has the greatest average rate of change in the interval [-5, 3] and so it is increasing the fastest.
What is the range of the given function?
{(-2, 0), (-4,-3), (2, -9), (0, 5), (-5, 7)}
O {x|x = -5, -4, -2, 0, 2}
Oyly=-9, -3, 0, 5, 7}
O {x|x = -9, -5, -4, -3, -2, 0, 2, 5, 7}
Oyly = -9,-5, -4, -3, -2, 0, 2, 5, 7}
Answers
Answer:
see the attachment photo!
What is the closest point on the line y = 2x - 5 to (4, 8)?
Answers
Answer: I think it is (6.5, 8).
Step-by-step explanation:
I don't know if you had any choices, but I graphed it on Desmos and that was the closest point. I hope this helps!! :)
Simplify the expression.
(x6y-6)
————
(x8y-8)
Answers
Marissa jogged 5 miles on the first day.
Marissa jogged 6 miles on the second day.
Marissa jogged 9 miles on the third day.
Marissa jogged 3 miles on the fourth day.
Marissa jogged 3 miles on the ninth day.vvvvvThe scatterplot shows how many miles Marissa jogged over 10 days. Which statements are true? Check all that apply.
Marissa jogged 5 miles on the first day.
Marissa jogged 6 miles on the second day.
Marissa jogged 9 miles on the third day.
Marissa jogged 3 miles on the fourth day.
Marissa jogged 3 miles on the ninth day.Answer:
Step-by-step explanation:
tthe
Algebra please help!!
Answers
The airplane reaches its maximum height of 95 feet after 10 seconds
How to calculate the maximum height of an object?The maximum height of an object the point where the velocity of the object is zero.
Given the function that represents the height of the airplane is expressed as h(t) = -(t-10)² + 95
The maximum height is the point where h'(t) = 0
h'(t) = -2(t-10)
0 = -2t + 10
2t = 10
t = 5secs
Substitute t =10 into the function
h(5) = -(10-10)² + 95
h(5) = -0 + 95
h(5) = 95feet
Hence the airplane reaches its maximum height of 95 feet after 10 seconds
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Is this a proportional relationship? Please help!
Answers
Answer:
No
Step-by-step explanation:
If you draw a line, it will not go through the origin and there isn't a constant rate of change.