Answer:
The equation of [tex]C_{1}[/tex] is: [tex]x^2+y^2=4[/tex]
and the equation of [tex]C_{2}[/tex] is: [tex]x^2+y^2-2\sqrt{2}x-2\sqrt{2}y+2=0[/tex]
Step-by-step explanation:
The standard form of circle equation: [tex](x-h)^2+(y-k)^2 = r^2[/tex] , where [tex](h,k)[/tex] is the center and [tex]r[/tex] is the radius of the circle.
The center of the circle [tex]C_{1}[/tex] is at origin or at (0, 0) and has radius of 2.
So, the equation of the circle [tex]C_{1}[/tex] will be........
[tex](x-0)^2+(y-0)^2=(2)^2\\ \\ x^2+y^2=4 ..........................................(1)[/tex]
Now, the center of [tex]C_{2}[/tex] is the point in the first quadrant, where the line [tex]y=x[/tex] intersects [tex]C_{1}[/tex]
Solving the equations [tex]x^2+y^2=4[/tex] and [tex]y=x[/tex] , we will get......
[tex]x^2+x^2= 4[/tex] (Substituting [tex]y[/tex] as [tex]x[/tex])
[tex]2x^2= 4\\ \\ x^2=2\\ \\ x=\pm \sqrt{2}[/tex]
So, [tex]y=x = \pm \sqrt{2}[/tex]
Thus, the center of the circle [tex]C_{2}[/tex] will be at [tex](\sqrt{2},\sqrt{2})[/tex] (Negative value is ignored as the point is in first quadrant)
Now, the distance between the center of [tex]C_{2}[/tex] and the x-axis is [tex]\sqrt{2}[/tex] and the circle touches the x-axis only at one point.
That means, the radius of the circle [tex]C_{2}[/tex] will be also [tex]\sqrt{2}[/tex]
So, the equation of the circle [tex]C_{2}[/tex] will be......
[tex](x-\sqrt{2})^2+(y-\sqrt{2})^2= (\sqrt{2})^2\\ \\ x^2-2\sqrt{2}x+2+y^2-2\sqrt{2}y+2=2\\ \\ x^2+y^2-2\sqrt{2}x-2\sqrt{2}y+2=0[/tex]
What is the solution of the equation when solved over the complex numbers?
x^2+27=0
Thanks!
Try this option:
x²+27=0;
[tex](x+\sqrt{-27})(x- \sqrt{-27})=0; \ => \ \left[\begin{array}{ccc}x=3 \sqrt{3}i\\x=-3 \sqrt{3}i \end{array}\right[/tex]
x = ± 3i√3
given x² + 27 = 0 (subtract 27 from both sides )
x² = - 27 ( take the square root of both sides )
x = ±[tex]\sqrt{-27}[/tex] = ± √(9 × 3 × -1 ) ← (i = √-1 )
= ± (√9 × √3 ×√-1 ) = ±3i√3
Please help need answers
see explanation below
(1) [tex]\frac{1}{5}[/tex] × [tex]\frac{2}{2}[/tex] = [tex]\frac{2}{10}[/tex] = 0.2
(2) [tex]\frac{6}{25}[/tex] × [tex]\frac{4}{4}[/tex] = [tex]\frac{24}{100}[/tex] = 0.24
(3) 2 [tex]\frac{3}{4}[/tex] = 2 +[tex]\frac{75}{100}[/tex] = 2.75
(4) 3 [tex]\frac{9}{10}[/tex] = 3 + 0.9 = 3.9
(5) 1.25 = 1 [tex]\frac{1}{4}[/tex] = [tex]\frac{5}{4}[/tex]
(6) 3.29 = 3 [tex]\frac{29}{100}[/tex] = [tex]\frac{329}{100}[/tex]
(7) 0.65 = [tex]\frac{65}{100}[/tex] = [tex]\frac{13}{20}[/tex] in simplest form
(8) 5.6 = 5 [tex]\frac{6}{10}[/tex] = 5 [tex]\frac{3}{5}[/tex] = [tex]\frac{28}{5}[/tex]
(9) he is incorrect
[tex]\frac{3}{5}[/tex] × [tex]\frac{20}{20}[/tex] = [tex]\frac{60}{100}[/tex] = 0.6 ≠ 3.5
If it snows tomorrow, then my dentist appointment will be canceled. If my dentist appointment is canceled, then I will clean under my bed. Therefore, if it snows tomorrow, then I will clean under my bed. Is this a Law of Detachment?
Yes this is a Law of Detachment.
What is the value of x?
Enter your answer in the box.
x =
PLEASEEE HELPP!!!!!!
Since the triangle is equilateral (you can tell by the tick on each side), all angles have the same measure as well.
The angles of a triangle sum up to 180 degress, so three equal angles must measure 60 degrees each.
So, in particular, we have
[tex] 7x+4 = 60 \iff 7x = 56 \iff x=8[/tex]
x = 8 and y = 6
ΔRST is an equilateral triangle
with all 3 sides equal in length and all 3 angles = 60°, hence
7x + 4 = 60 ( subtract 4 from both sides )
7x = 56 ( divide both sides by 7 )
x = 8
similarly
8y + 12 = 60 ( subtract 12 from both sides )
8y = 48 ( divide both sides by 8 )
y = 6
Write equivalent expressions for x^7×x^-2 and x^7/x^2. What do you notice? Explain how your results relate to the properties of integer exponents.
How many centimeters are in 7 meters 100cm/1m=?/7m
*EASY POINTS!*
How many times larger is 6 × 10^10 than 2 × 10^-3?
(Its an exponent question!)
If you need to, you can write and solve an equation for the factor you seek.
... 6×10^10 = factor × 2×10^-3
Divide by 2×10^-3 to find the value of the factor:
... (6×10^10)/(2×10^-3) = factor
... factor = (6/2)×10^(10-(-3))
... factor = 3×10^13
The first number is 3×10^13 times the second number.
_____
An exponent signifies repeated multiplication.
... 10×10×10 = 10³
Just as you cancel common factors when you do division, you can subtract exponents.
[tex]\dfrac{10\cdot 10\cdot 10}{10\cdot 10}=\dfrac{10}{1}=10\\\\\dfrac{10^3}{10^2}=10^{3-2}=10^1=10[/tex]
The same process works regardless of the signs of the exponents. When multiplying, we add exponents; when dividing we subtract the exponent of the denominator.
Slope -6/7; through (3,5) Write the equation using function notation. Please help me ASAP!!!!!!!! :(
f(x) = - [tex]\frac{6}{7}[/tex] x + [tex]\frac{53}{7}[/tex]
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
here m = - [tex]\frac{6}{7}[/tex]
partial equation is y = - [tex]\frac{6}{7}[/tex] x + c
to find c substitute (3, 5 ) into the partial equation
5 = - [tex]\frac{18}{7}[/tex] + c ⇒ c = [tex]\frac{53}{7}[/tex]
f(x) = - [tex]\frac{6}{7}[/tex] x + [tex]\frac{53}{7}[/tex]
Find the periodic rate that corresponds to the given compound rate, if the rate is compounded as follows.
(Round your answers to eight decimal places.)
Compound rate = 18%
(a) quarterly
Periodic rate = ?
(b) monthly
Periodic rate = ?
(c) daily
Periodic rate = ?
(d) biweekly (every two weeks)
Periodic rate = ?
(e) semimonthly (twice a month)
Periodic rate = ?
Answer:
a) 0.045b) 0.015c) 0.00049315d) 0.00692308e) 0.0075Step-by-step explanation:
Apparently, your periodic rate is that used to compute the interest accrued each period. It seems to be the compound (annual) rate divided by the number of periods in a year: quarterly, 4; monthly, 12; daily, 365; biweekly, 26; semimonthly, 24.
_____
If you want the effective annual rate to be 18% in each case, the numbers are different. For n periods per year, those are calculated as
[tex]\sqrt[n]{1.18}-1[/tex]
A periodic rate of 0.04224664 will give an effective annual rate of 18%.
Periodic rates for a 18% compound rate compounded quarterly, monthly, daily, biweekly, and semimonthly are calculated as follows :
Quarterly periodic rate: 0.18/4 = 0.045 or 4.5%Monthly periodic rate: 0.18/12 = 0.015 or 1.5%Daily periodic rate: 0.18/365 ≈ 0.000493 or 0.0493%Biweekly periodic rate: 0.18/26 ≈ 0.006923 or 0.6923%Semimonthly periodic rate: 0.18/24 ≈ 0.0075 or 0.75%Solve for z:
2 + 8 - z = -24
Show your work
A 12-foot ladder rests against a brick wall at angle of 60°. Which expression gives the value of x, the height on the brick wall where the ladder rests?
Using Pythagorean's Theorem we know that a^2 + b^2 = c^2
C is the length of the ladder, and we are given one of the sides, let's call that side b
_________
we have a^2 + b^2 = c^2, and a^2 = c^2 - b^2, so a = √ c^2 - b^2
_________ ______ ____
a = √12^2-3^2 = √ 144-9 = √ 135 = 11.61895
so the top of the ladder is 11.6 feet above the ground
here u go hope this helps
Answer:
12 sin60°
Remember SOHCAHTOA.
sinθ =
opposite
hypotenuse
sin60° =
x
12
x = 12 sin60°
What is the decimal equivalent of -11/9
Larry's Lemons is a street vendor business that sells lemonade and lemon bars. A cup of lemonade sells for $2 and a lemon bar sells for $1.50. When all related business expenses are included, a cup of lemonade costs $0.25 to prepare and a lemon bar costs $0.20 to prepare.
Last Monday, one of the vendors selling Larry's Lemons sold at least $500 worth of lemonade and lemon bars and its expenses were no more than $100. At least 150 cups of lemonade were sold.
Let x be the number of cups of lemonade sold last Monday and y be the number of lemon bars sold last Monday.
Which ordered pairs representing a combination of cups of lemonade and lemon bars could have been sold last Monday and make sense in the context of the situation?
Select each correct answer.
(160,110)(160,110)
(232.5,200)(232.5,200)
(155,305.5)(155,305.5)
(150,200)(150,200)
(180,100)
We can let x and y represent cups of lemonade and numbers of lemon bars, respectively. Then the constraints are ...
x ≥ 150y ≥ 02x +1.5y ≥ 5000.25x +0.20y ≤ 100A graph is shown in the attachment, with the ordered pairs plotted. It is not feasible to sell half cups of lemonade or half lemon bars, so the second and third choices must be excluded. The point (160, 110) falls outside the feasible region, so is not a correct choice.
The correct choices are ...
(150, 200)(180, 100)Final answer:
The only ordered pairs that meet the constraints of Larry's Lemons business situation are (150,200) and (180,100), as these combinations satisfy the conditions for revenue, expenses, and minimum amount of lemonade sold.
Explanation:
To find which ordered pairs (x, y) make sense in the context of Larry's Lemons' business situation, we need to consider the given conditions and set up inequalities to express the sales and expense constraints.
The conditions are:
A cup of lemonade sells for $2 and a lemon bar for $1.50.The cost to prepare a cup of lemonade is $0.25, and a lemon bar is $0.20.The vendor sold at least $500 worth of products.The vendor's expenses were no more than $100.At least 150 cups of lemonade were sold.Revenue Constraint:
For the revenue, we need to ensure that the seller made at least $500.
2x + 1.5y ≥ 500
Expense Constraint:
For the expenses, they should not exceed $100.
0.25x + 0.20y ≤ 100
Lemonade Sold Constraint:
Since at least 150 cups of lemonade were sold:
x ≥ 150
Now we check the given ordered pairs against these constraints:
(160,110): Given the constraints, this pair is feasible because the revenue is $2(160) + $1.50(110) = $470, which does not meet the revenue condition. Therefore, it is not a correct answer.(232.5,200): This pair does not represent whole units of lemonade and lemon bars, which doesn't make sense in this context as you can't sell half a cup of lemonade or half a lemon bar.(155,305.5): Similar to the above, this also includes half units and is thus not feasible.(150,200): Meets the revenue constraint, $2(150) + $1.50(200) = $500 in sales, and the expense constraint, $0.25(150) + $0.20(200) = $92.5 in expenses. It is a correct answer.(180,100): Also meets the constraints with revenue $2(180) + $1.50(100) = $510 and expenses $0.25(180) + $0.20(100) = $85. It is a correct answer.Only the ordered pairs (150,200) and (180,100) satisfy all the conditions of the problem.
PLS HELP 50 POINTS
write y=x-1 in function notation.
Answer:
f(x)=x-1
Step-by-step explanation:
replace y by f(x) to obtain functional notation
f(x) = x - 1
Create equations of two lines that are parallel to y=1/2x+5
Y = 1/2 + 5 , the slope of this equation is 1/2
The equations of the parallel lines must also have a slope of 1/2.
This is because parallel lines have the same value of slope.
Crispy clover, a popular vegetarian restaurant, introduced a new menu that had 20% more dishes than the previous menu. The previous menu had D dishes. Which of the following expressions could represent how many dishes crispy clovers new menu has? D+1/5D D+20 D+20D 20D 1.2D choose two answers.
The following expressions could represent how many dishes crispy clovers the new menu has [tex]\rm D+\dfrac{1}{5}D[/tex].
Given
Crispy clover, a popular vegetarian restaurant, introduced a new menu that had 20% more dishes than the previous menu.
The previous menu had D dishes.
How to represent the expression which models the given situation?If it has 20% more, it must mean that it is 1.2 of the previous menu (Because it is 100 percent, plus an extra 20).
Therefore,
The following expressions could represent how many dishes crispy clovers new menu has;
[tex]\rm= D (100 \ of \ the \ previous \ menu) }+ \dfrac{1}{5} \rm \times { 20 \ percent \ D \ of \ the \previous \ menu}\\\\=D+\dfrac{1}{5}D[/tex]
Hence, the following expressions could represent how many dishes crispy clovers the new menu has [tex]\rm D+\dfrac{1}{5}D[/tex].
To know more about Expression click the link given below.
https://brainly.com/question/962098
Dale is staining the wooden floor of a court. The court is in the shape of a rectangle. Its length is 46 feet and its width is 35 feet. Suppose each can of wood stain covers 115 square feet. How many cans will he need to cover the court?
You will need to find the area of the rectangular shaped wooden floor and divide that area by 115 square feet.
46 x 35 = 1610
1610 square feet/115 square feet
= 14 cans of wood stain
Answer:
It should be 14
Step-by-step explanation:
Suppose the supply function for product x is given by qxs = - 30 + 2px - 4pz.
a. how much of product x is produced when px = $600 and pz = $60?
Replace the variables with their values and do the arithmetic.
qxs = -30 +2(600) -4(60) = -30 +1200 -240
qxs = 930
930 of product x is produced.
Explanation of how to determine the quantity of product x produced when given specific prices, the quantity produced of product x is -150.
Supply Function: qxs = - 30 + 2px - 4pz
a. To determine the quantity produced when px = $600 and pz = $60, substitute these values into the supply function:
qxs = -30 + 2(600) - 4(60) = -30 + 120 - 240 = -150
Therefore, when px = $600 and pz = $60, the quantity produced of product x is -150.
Need some help on this PLEASE. I'm already almost failing. please help
Write an equation for the line parallel to the given line that contains C. C ( -1, 5); y = 2/5 x - 6
y = [tex]\frac{2}{5}[/tex] x + [tex]\frac{27}{5}[/tex]
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
y = [tex]\frac{2}{5}[/tex] x - 6 is in this form with slope m = [tex]\frac{2}{5}[/tex]
Parallel lines have equal slopes, thus
y = [tex]\frac{2}{5}[/tex] x + c is the partial equation of parallel line
to find c , substitute (- 1, 5 ) into the partial equation
5 = - [tex]\frac{2}{5}[/tex] + c ⇒ c = 5 + [tex]\frac{2}{5}[/tex] = [tex]\frac{27}{5}[/tex]
y = [tex]\frac{2}{5}[/tex] x + [tex]\frac{27}{5}[/tex] ← equation of parallel line
Based on the triangles, which statement is true?
The sum of interior angles of a triangle is 180°, and a linear pair is supplementary (adds to 180°). The appropriate choice is
... G. w = 105°, because ...
_____
In short, an exterior angle is equal to the sum of the opposite interior angles.
... w = 180 - (180 - (45 + 60)) = 180 -180 +45 +60
... w = 45 +60
I need help on 13-18 I don’t understand. Can you show me how to do the math??
The percent change is given by ...
... (percent change) = (new amount - old amount)/(old amount) × 100%
This can be rearranged to give a formula for the new amount. First, we'll rewrite it to a slightly different form.
... (percent change) = ((new amount)/(old amount) -1) × 100%
... (percent change)/100% = (new amount)/(old amount) -1 . . . . divide by 100%
... (percent change)/100% + 1 = (new amount)/(old amount) . . . add 1
... (old amount) × ((percent change)/100%) +1) = new amount . . . . multiply by old amount
We can now use this formula to find the new amount in each case.
13. 25 × (300%/100% +1) = 25 × 4 = 100 . . . . dollars
14. 160 × (-20%/100% +1) = 160 × 0.8 = 128 . . . . bananas
15. 56 × (-75%/100% +1) = 56 × .25 = 14 . . . . books
16. 52 × (25%/100% +1) = 52 × 1.25 = 65 . . . . companies
17. 12000 × (5%/100% +1) = 12000 × 1.05 = 12,600 . . . . miles
18. 710 × (-10%/100% +1) = 710 × 0.90 = 639 . . . . points
_____
Considering the above formula for percent change (or its "slightly different form"), you may want to reconsider your answers for problems 7–12.
What part of 35 is 56? *not a percent* help pls
Expressed as a fraction 56 is 56/35 of 35. That fraction can be reduced, and expressed several ways.
56/35 = 8/5 = 1 3/5 = 1.6
56 is 1 3/5 of 35
56 is 1.6 times 35
During the day, the temperature in Nome, Alaska rose 35 degrees. The low temperature for that day is -22 degrees. What was the high temperature for that day?
there are 14 girls on the volleyball team if this represents 25% of the girls who tried out how many girls tried out for the volleyball team show work mark braniest
The answer would be 56 because 14X4 = 56
There were 56 girls who tried out for the volleyball team, found by dividing the number of girls on the team (14) by the percentage that made the team (25%), which equals 14 divided by 0.25.
Explanation:The question asks us to find the total number of girls who tried out for the volleyball team if 14 girls (making up 25% of those who tried) made the team. To calculate the total number of girls who tried out, we can set up the equation based on the percentage:
25% of total girls = 14
We can rewrite 25% as 0.25 in decimal form:
0.25 × total girls = 14
To find the total number of girls, we divide both sides of the equation by 0.25:
total girls = 14 ÷ 0.25
total girls = 56
Therefore, 56 girls tried out for the volleyball team.
what is the equation in point-slope form of the line that passes through the point (1,-2) and has a slope of 3?
point slope form
y-y1 = m (x-x1)
y- (-2) = 3(x-1)
y+2 = 3(x-1)
y + 2 = 3(x - 1)
the equation of a line in point-slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
here m = 3 and (a, b) = (1, - 2), hence
y + 2 = 3(x- 1) ← in point-slope form
I need help with this problem please
Write a function with the following characteristics: 1.A vertical asymptote at x = 3 A horizontal asymptote at y = 2 An x-intercept at x=-5 2.A vertical asymptote at x=-1 An oblique asymptote at y = x + 2
1. The vertical asymptote requires the denominator have a zero at that location. The x-intercept requires the numerator have a zero at that location. The horizontal asymptote amounts to a multiplier of the function:
... y = 2(x +5)/(x -3)
2. The vertical asymptote requires the denominator have a zero at that location. The oblique asymptote is an add-on
... y = 1/(x +1) +(x +2)
... y = (x² +3x +3)/(x +1)
We can use rational functions to define functions with specific characteristics. A function with a vertical asymptote at x = 3, a horizontal asymptote at y = 2, and x-intercept at x = -5 could be written as f(x) = 2(x + 5) / (x - 3). A function with a vertical asymptote at x = -1 and an oblique asymptote at y = x + 2 can be written as f(x) = (x^2 + x - 2) / (x + 1).
Explanation:The subject here pertains to certain characteristics of functions, specifically regarding asymptotes and intercepts. In order to create a function with the required characteristics, you would typically use rational functions.
Vertical asymptotes occur when the denominator of a function is zero, horizontal asymptotes are connected to the degree of the polynomials in the function, and x-intercepts occur when the function itself equals zero.
Here's how we can write the function for each case:
A function with a vertical asymptote at x = 3, a horizontal asymptote at y = 2, and an x-intercept at x = -5 can be given as f(x) = 2(x + 5) / (x - 3). In this function, as x approaches 3, the function tends towards infinity, producing the vertical asymptote. As x approaches infinity, the function tends towards 2, leading to the horizontal asymptote. The function equals zero at x = -5, giving the x-intercept.A function with a vertical asymptote at x = -1 and an oblique (also termed a 'slant') asymptote at y = x + 2 can be given as f(x) = (x^2 + x - 2) / (x + 1). As x approaches -1, the function tends towards infinity, producing the vertical asymptote. The oblique asymptote y = x + 2 is found by performing polynomial long division on (x^2 + x - 2) by (x + 1).Learn more about Rational Functions here:https://brainly.com/question/27914791
#SPJ3
1.Factor
3x(y−4)−2(y−4)
2. Factor.
20xy−4y+35x−7
Please Help!!! I'm trying to get caught up as fast as i can but k12 has been giving me so much work I can't keep up!!
(1)
take out the common factor (y - 4 )
= (y - 4)(3x - 2)
(2)
factor by grouping (1/2 terms and 3/4 terms )
4y(5x - 1) + 7(5x - 1)
take out the common factor (5x - 1)
= (5x - 1)(4y + 7)
1. Factor out the (y-4)
(y-4) (3x-2)
2.Factor by grouping
20xy -4y +35x -7
4y(5x-1) +7(5x-1)
then factor out 5x-1
(5x-1)(4y+7)
PLEASE HELP!!! PERFORMANCE TASK FOR MATH. WILL MARK YOU BRAINLIEST
A) If grace and Claire’s parents each invested $7,600 into a college saving account when the girls were born, how much money will each girl have for college when she turns 18? Explain.
B) Do the functions show a positive or negative correlation between time and the amount of money saved? Explain.
A.) If Grace and Claire’s parents each invested $7,600 into a college savings account when the girls were born, how much money will each girl have for college when she turns 18? Explain.
Answer/Explanation:
For Grace, I plugged in 18 for x.
Work:
y= 1000(18) + 7600
y= 18000 = 7600
y= 25600
For Claire, I had to first find the slop by using rise over run.
11600-10000/3= 800
So the formula for Claire is y= 800x + 7600 and then you just plug in 18 for x.
Work:
y= 800(18) + 7600
y= 14,400 + 7600
y= 22,000
Therefore, Grace would have $25,600 at the end of 18 years old and Claire would have $22,000 when she turns 18 years old.
I hope that helped you or anyone else!! :)
The amount of money that Grace and Claire will have for college when they turn 18 will be $25600 and $22000 respectively.
Based on the information given, the amount that Grace will make will be:
= 1000x + 7600
= 1000(18) + 7600
= 18000 + 7600
= 25600.
The amount that Claire will make will be:
= 800x + 7600.
= 14400 + 7600
= 22000
The functions show a positive correlation between time and the amount of money saved.
Read related link on:
https://brainly.com/question/11216629
Given: △ABC, m∠A=60° , m∠C=45°, AB=8 Find: Perimeter of △ABC and the Area of △ABC
Try this solution (all the details are in the attached picture, answers are underlined with colour).
The perimeter of triangle of ABC is [tex]\boxed{28.73}[/tex] and the area of triangle ABC is [tex]\boxed{37.86}.[/tex]
Further explanation:
Given:
The measure of angle A is [tex]\angle A = {60^ \circ }.[/tex]
The measure of angle C is [tex]\angle C = {45^ \circ }.[/tex]
The length of side AB is [tex]AB = 8[/tex]
Calculation:
The sum of all angles of a triangle is [tex]{180^ \circ }.[/tex]
[tex]\begin{aligned}\angle A + \angle B + \angle C &= {180^ \circ }\\{60^ \circ } + \angle B + {45^ \circ } &= {180^ \circ }\\{105^ \circ } + \angle B &= {180^ \circ }\\\angle B&= {180^ \circ } - {105^ \circ }\\\angle B&= {75^ \circ }\\\end{aligned}[/tex]
The sine rule in triangle ABC can be expressed as,
[tex]\begin{aligned}\frac{{BC}}{{\sin {{60}^ \circ }}}&=\frac{8}{{\sin {{45}^ \circ }}}\\BC&=\frac{8}{{\frac{1}{{\sqrt2 }}}}\times\frac{{\sqrt 3 }}{2}\\BC&= 9.80\\\end{aligned}[/tex]
The length of AC can be calculated as follows,
[tex]\begin{aligned}\frac{{AB}}{{\sin {{45}^ \circ }}} &= \frac{{AC}}{{\sin {{75}^ \circ }}}\\\frac{8}{{\sin {{45}^ \circ }}} \times \sin {75^ \circ }&= AC\\10.93 &= AC\\\end{aligned}[/tex]
The perimeter of triangle ABC can be obtained as follows,
[tex]\begin{aligned}{\text{Perimeter}}&= AB + BC + AC\\&= 8 + 9.80 + 10.93\\&= 28.73\\\end{aligned}[/tex]
The area of triangle ABC can be obtained as follows,
[tex]\begin{aligned}{\text{Area}}&=\frac{1}{2} \times AB \times AC \times \sin \left( A \right)\\&= \frac{1}{2} \times 8 \times 10.93 \times \sin {60^ \circ }\\&= 4 \times 10.93 \times \frac{{\sqrt3 }}{2}\\&= 37.86\\\end{aligned}[/tex]
The perimeter of triangle of ABC is [tex]\boxed{28.73}[/tex] and the area of triangle ABC is [tex]\boxed{37.86}.[/tex]
Learn more:
1. Learn more about inverse of the function https://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Triangles
Keywords: angles, ABC, angle A=60 degree, perimeter, area of triangle, triangle ABC.