Answers
Here we have some problems about circles, the solutions are:
a) 490.6 yd^2b) x = 15c) x = 27How to find the area of a circle?
We know that for a circle of diameter D, the area is given by:
A = pi*(D/2)^2
where pi = 3.14
In the image we can see that the diameter of the circle is 25 yd, replacing that in the area equation we get:
A = 3.14*(25yd/2)^2 = 490.6 yd^2
How to find the value of x?For the second image, each line creates two 180° angles. So, if we look at the tilted line, we can see that it is divided in two angles, one of 37° and the other that depends of x, so we can write:
180° = 37° + (9x + 8)°
180° - 37° - 8° = (9x)°
135°/9° = x = 15
So the value of x is 15.
For the last image:
Notice that we have a 90° angle denoted, then the other 3 sections must add up to 270°.
270° = 54° + (2x + 21)° + (5x + 6)°
Now we solve this for x:
270 - 54 - 21 - 6 = 2x + 5x
189 = 7x
189/7 = x = 27
x is equal to 27
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Related Questions
What is the product of (-a + 3)(a + 4)?
Answers
Answer:
-a^2-a+12
Step-by-step explanation:
thats the product of (-a + 3)(a + 4)
in a class of 40 students each student plays one indoor game such as ludu,card or oware. Ludu is played by 18, oware is played by 20, while card is played by 27, seven students play ludu and oware, twelve students play oware and card and four students play ludu, card and oware.
Determine how many students play.
(i) Ludu and card
(ii)Ludu and card but not oware.
Answers
Answer:
35 Learner's who plays ludu and cards
Which loan will cost its holder the most in interest?
A. $10,000 at 2 percent interest compounded for four years
B. $10,000 at 2 percent simple interest for four years
C. $5,000 at 4 percent simple interest for four years
D. $5,000 at 4 percent interest compounded for four years
Answers
Answer:
D. $5,000 at 4 percent interest compounded for four years
Hope this helps :)
The loan that will cost its holder the most in interest is option D. $5,000 at 4 percent interest compounded for four years.
To calculate the interest for each option, with the use of the relevant interest formulas.
For option A, compounded interest, by the use of the formula:
[tex]CI =A -P\\CI=A = P(1 + r/n)^{nt} - P[/tex],
where:
A is the final amount,CI is the compound interest P is the principal, r is the interest rate, n is the number of times interest is compounded per year t is the number of years.Plugging in the values, gives:
[tex]C.I= 10,000(1 + 0.02/1)^{(1\times4)} - 10,000[/tex]
By adding the value in the bracket gives:
[tex]C.I= 10,000(1 .02)^{4} - 10,000[/tex]
To evaluate [tex](1.02)^4[/tex], raise 1.02 to the power of 4 gives:
[tex](1.02)^4 \approx 1.082432[/tex]
Substituting this value back into the expression:
[tex]CI\approx10,000 \times 1.082432- 10,000[/tex]
On multiplication gives:
[tex]CI\approx10824.32- 10,000[/tex]
On subtraction gives:
[tex]CI\approx 824.32[/tex]
2. For option B, simple interest, by the use of the formula
[tex]SI = Prt[/tex]
where:
SI is the simple interest, P is the principal,r is the interest rate t is the number of years.Plugging in the values, we get:
[tex]SI = 10,000\times( 0.02\times4)[/tex]
By multiplying the value in the bracket gives:
[tex]SI = 10,000\times 0.08[/tex]
On multiplication gives:
[tex]SI = 800[/tex]
For option C, simple interest formula
[tex]SI = Prt[/tex]
where:
SI is the simple interest, P is the principal,r is the interest rate t is the number of years.Plugging in the values, we get:
[tex]SI = 5,000\times( 0.04\times4)[/tex]
By multiplying the value in the bracket gives:
[tex]SI = 5,000\times 0.16[/tex]
On multiplication gives:
[tex]SI = 800[/tex]
For option D, compounded interest, we get:
A = 5,000(1 + 0.04/1)^(1*4) - 5,000 ≈ $6,181.73
For option D, compounded interest, by the use of the formula:
[tex]CI =A -P\\CI=A = P(1 + r/n)^{nt} - P[/tex],
where:
A is the final amount,CI is the compound interest P is the principal, r is the interest rate, n is the number of times interest is compounded per year t is the number of years.Plugging in the values, gives:
[tex]C.I= 5,000(1 + 0.04/1)^{(1\times4)} - 5,000[/tex]
By adding the value in the bracket gives:
[tex]C.I= 5,000(1 .04)^{4} - 5,000[/tex]
To evaluate [tex](1.04)^4[/tex], raise 1.04 to the power of 4 gives:
[tex](1.04)^4 \approx 1.1699[/tex]
Substituting this value back into the expression:
[tex]CI\approx5,000 \times 1.1699- 5,000[/tex]
On multiplication gives:
[tex]CI\approx5,849.2928- 5,000[/tex]
On subtraction gives:
[tex]CI\approx849.2928[/tex]
Comparing the final loan interest, option D has the highest value, indicating that it will cost its holder the most in interest.
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On the grid, A(-3,1), B(1,-2), and C(4,2) are connected. Kaire claims triangle ABC is a right isosceles triangle.
Answers
Answer:
Yes its an isosceles triangle but not a right angle triangle.part A:
[tex]\sf AB^2 = (-2-1)^2 + (1+3)^2[/tex]
[tex]\sf AB^2 =25[/tex]
[tex]\sf AB =5[/tex]
[tex]\sf AC^2 = (2-1)^2 + (4+3)^2[/tex]
[tex]\sf AC^2 = 50[/tex]
[tex]\sf AC = 5\sqrt{2}[/tex]
[tex]\sf BC^2 = (2--2)^2 + (4-1)^2[/tex]
[tex]\sf BC^2 = 25[/tex]
[tex]\sf BC = 5[/tex]
Two sides are equal in the triangle of 5. Its an isosceles triangle.
part B:
if right angle triangle, then use the formula:
short side² + short side² = long side²
( 5√2 )² + 5² = ( 5√2 )²
75 = 50
Therefore, its not a right angle triangle.
Let U = {English, French, History, Math, Physics, Chemistry, Psychology, Drama}, A = {Math, History, Chemistry, English}, B = {Psychology, Drama, French, Chemistry, English}, and C = {Physics, History, French}. Find the following. n(B u C)
Answers
We are provided with ;
[tex]{\sf{U=\{English,\: French,\: History,\: Math,\: Physics,\: Chemistry,\: Psychology,\: Drama\}}}[/tex] [tex]{\sf{A=\{Math,\: History,\: Chemistry,\: English\}}}[/tex] [tex]{\sf{B=\{Psychology,\: Drama,\: French,\: Chemistry,\: English\}}}[/tex] [tex]{\sf{C=\{Physics,\: History,\: French\}}}[/tex]And we need no find [tex]{\bf n(B\cup C)}[/tex] . At first Let me tell you that here [tex]{\sf (B\cup C)}[/tex] represents the union of the set B and C.And [tex]{\sf n(B\cup C)}[/tex] represents the cardinal no. of the respective set or no. of elements present in the respective set.So let's find the set [tex]{\sf (B\cup C)}[/tex] first
[tex]{:\implies \quad \sf B\cup C=\{Physics,\: Drama,\: French,\: Chemistry,\: English,\: Psychology,\:History\}}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{n(B\cup C)=7}}}[/tex]
Alternative Method :-As we know that ;
[tex]{\boxed{\bf n(A\cup B)=n(A)+n(B)-n(A\cap B)}}[/tex]Where [tex]{\sf (A\cap B)}[/tex] is the Intersection of A and B or the set of common elements of A and B. So now by same concept , now finding the intersection of B and C :-
[tex]{:\implies \quad \sf B\cap C=\{French\}}[/tex]
So , [tex]{\sf n(B\cap C)=1}[/tex] . Now , putting the values in the formula;
[tex]{:\implies \quad \sf n(B\cup C)=n(B)+n(C)-n(B\cap C)}[/tex]
[tex]{:\implies \quad \sf n(B\cup C)=5+3-1}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{n(B\cup C)=7}}}[/tex]
A rectangular lot is 150 yards long and 100 yards wide. Give the length and width of another rectangular lot that has the same perimeter but a smaller area. width = yards Х 5 ? length = yards
Answers
Answer:A rectangular lot is 100 meters wide and 150 meters long.Give the length and width of another rectangular lot that has the same perimeter but a smaller area.
The rectangular lot is having length of 170 meters and width of 80 meters.
write an algebraic expression to answer each question do this on a sheet of paper
let z be father's age now
A.What will be his age after 10 years?
B.What was his age 2 years ago?
C.What was his age 7 years ago
Answers
Hello.
In 10 years, his age will be
[tex]\mathrm{z+10}[/tex]
The sum of his current age and 10 equals his age in 10 years.
2 years ago his age was
[tex]\mathrm{z-2}[/tex]
The difference of his current age and 2 equals his age 2 years ago.
7 years ago his age was
[tex]\mathrm{z-7}[/tex]
The difference of his current age and 7 equals his age 7 years ago.
Therefore, his age after 10 years will be [tex]\mathrm{z+10}[/tex], his age 2 years ago was [tex]\mathrm{z-2}[/tex], and his age 7 years ago was [tex]\mathrm{z-7}[/tex]
I hope it helps.
Have a nice day.
[tex]\boxed{imperturbability}[/tex]
Answer:
z+10
z-2
z-7
Step-by-step explanation:
hope it helps
determine a series of transformations that would map polygon ABCD onto polygon A’B’C’D’?
HELP QUICK!!!!
Answers
flip over y-axis, move down 3 units, then dilate by a factor of 1/2 with respect to A.
Use a conversion factor to solve.
1,000 mg
1g
mg
3.75 grams
Answers
Answer:
266.7
Step-by-step explanation:
Which of the following statements shows the distributive property?
A. 5(4-2) = 20 - 10
B. 5+ (4 - 2) = 20 - 10
C. 5(4-2) = 9 - 7
D. 5+(4 - 2) = 9+3
Answers
please hurry .The side of Mr. Miller’s barn has a length of 27 feet and an area of 656.1 square feet. How wide is the side of Mr. Miller’s barn?
Answers
Answer:
24.3
Step-by-step explanation:
area of a rectangle =length*width
if we know at least the 2 quantities already
total area = 656.1
and one of the sides = 27
we have to divide the are by one of the sides to get the remaining side
width = area/length
656.1 divided by 27 equals 24.3
Answer:
24.3 he was rii i got my answer frm here
Step-by-step explanation:
Solve the measurement conversion problem. 1 kg=1,000g
The ice cream shop was running low on sprinkles. The shop only had 200 grams of sprinkles . They ordered a 2.5-kilogram jar to restock. If they use 100 grams per week , how many weeks will it be until they run out of sprinkles ?
A) 270 weeks
B) 250 weeks
C) 27 weeks
D) 25 weeks
Answers
I have attached a picture that shows the equation used to solve.
Tom bought a soft drink for 4$ and 4candy bars. He spent a total of 12$ him Mitch did each candy bar cost
Answers
Answer:
$2 each
Step-by-step explanation:
Juan is 8 years older than his sister. In 3 years, he will be twice as old as she will be then. How old
are they now?
Answers
how do I solve this, pretty urgent please.
Answers
Answer:
1Step-by-step explanation:
Substitute:
[tex]x^{0.5} = y[/tex]Then the expression becomes:
[tex](\dfrac{1+y^3}{1-y+y^2}-y) \dfrac{1-y^2}{1-y} -y=\\[/tex][tex](\dfrac{(1+y)(1-y+y^2)}{1-y+y^2}-y) \dfrac{(1-y)(1+y)}{1-y} -y=[/tex][tex](1+y-y)(1+y)-y=[/tex][tex]1(1+y)-y=[/tex][tex]1+y-y=[/tex]1The result is 1 regardless the value of x other than 1.
Maria has 2 dollars, 3 dimes, and 4 pennies. Lisa has 1 dollar and 5 quarters. How much money do the
two girls have in all?
Answers
Answer:
The total will be 4.59. Since we have 2 dollars and then we have 3 dimes which a dime is equal to 10 cents, it is now 2 dollars and 30 cents. Now we have the 4 pennies, which a penny is 1 cent. So we have 2 dollars and 34 cents. Now we have a dollar and 5 quarters. A quarter is equal to 25 cents. So 4 quarters is equal to 1 dollar. So it will be 2 dollars and 25 cents for the other quarter that we have. Now we add 2.34 and 2.25 which we get 4.59 dollars(i tried my best ok).
Quick equation:2d+3(10)+4(1)=$2.34
2d+5(25)=$2.25
Why is this system no solution?
2y = 7 x -3
y = -2
Answers
Step-by-step explanation:
solved using substitution method
HbUhgghbjhgbijhnh(uhgbuygbuyg..
Answers
Answer:
5
Step-by-step explanation:
u gotta add the H's with The U's and then ye
A 6 miles
B 8 miles
C 4 miles
D 2 miles
Answers
Answer:
A 6 miles
Step-by-step explanation:
3m+6=24 3m=18 m=6 So mike traveled 6 miles by taxi
Find the value of x in a circle 3x, 7x+10
Answers
Answer:
you collect the like terms then your answer should be10x=10 consult a tutor because he or she may know better than me
Find the length of the side of a square with an area of 121 in
A. 484 in
B. 30.25 in
C. 11 in
D. 6.5 in
Answers
Answer:
C. 11
Step-by-step explanation:
Formulate
[tex]\sqrt{121}[/tex]
Calculate
[tex]121\frac{1}{2}[/tex]
Simplify using [tex]a^{\frac{n}{m} }=\sqrt[m]{a^{n} }[/tex]
[tex]\sqrt{121}[/tex]
Factor and rewrite the radicand in exponential form
[tex]\sqrt{11^{2} }[/tex]
Simplify the radical expression
[tex]11[/tex]
I hope this helps you
:)
Considering an arbitrary number system with the independent digits as 0,1 and x. What is the radix of the number system
Answers
Using it's concept, it is found that the radix of the arbitrary number system is of 3.
What is the radix of a number system?It is the number of different digits that the system has, for example:
The binary system has radix 2, as it has digits 0 and 1.The decimal digit has radix 10, as it has 10 digits from 0 to 9.In this problem, the digits are 0, 1 and x, hence the radix of the arbitrary number system is of 3.
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Which is a coefficient in this expression? 12−25(1−4)
Answers
Answer:
25
Step-by-step explanation:
A coefficient is a number multiplied by a variable and in this case the variable would be (1-4).
The number being multiplied by the variable is 25.
Help me please I know it’s not C please help me out !!!!!
Answers
Answer:
b
Step-by-step explanation:
The following radical phrase should be non-negative.
x - 3 ≥ 0
20. The sum of two consecutive odd numbers is 72. Find the numbers.
Answers
Answer:
35 and 37
35+37=72
Hope this helped.
Answer:
Step-by-step explanation:
either n=17
or The two odd numbers are 35 and 37
The curve above is the graph of a sinusoidal function. It goes through the points (-9,-4) and (5,-4) Find a sinusoidal function that matches the given graph. I’d needed, you can enter pi=3.1416.... as pi in your answer, otherwise use at least 3 decimal digits.
Answers
Which of the following set ordered pairs represents a function? Select all that apply.
Answers
keeping in mind that a function set doesn't have any X-repeats, or namely the x-coordinate of every pair doesn't repeat, let's check these sets.
Check the picture below.
Graph each of the functions to determine whether it passes the vertical line test.
Set #a is a function
Set #b is not a function
Set #c is a function
Set #d is a function
what is a function?A function is an equation with a single solution for y for each value of x. Each input of a particular type receives exactly one output when using a function.
given set of ordered pairs represents a function.
from the verticle line property of a function which states that It would be a function of all vertical lines intersecting it at minimum once. This is also called a vertical line test. A graph will be considered as a function if it has only one output y for each input x. Therefore, a vertical line cannot be a function.
In the given Sets Option b has two values at x = 1/2 hence it fails the verticle line test.
therefore, Option a, c, and d only satisfy the requirement of a function.
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A college student takes out a $7500 loan from a bank. Assuming the student has not started paying back the money, how much does the student owe after 1 year, if the bank charges 3.8% interest each year? after 1 year, if the bank charges 7.6% interest each year? after 2 years, if the bank charges 3.8% interest each year?
Answers
Answer:
Atter 1 year 28,500
After 2 years 57,00
Step-by-step explanation:
7500 x 3.8=28,500
7500 x 7.6=57,000
The square on the right is a scaled copy of the square on the left. Identify the scale factor. Express your answer in simplest form.
Answers
Answer:
x = 21/8
Step-by-step explanation:
So 8 is being multiplied by something to get to 21
So 8x = 21
Solve for x:
8x = 21x = 21/8-Chetan k
Are 5n + 9 + n and 3(2n + 9) equal expressions use substitution to take your answer
Answers
Answer: They are not equal expressions
Since this asks to solve by substitution, I will substitute with the number 2:
5n + 9 + n
5(2) + 9 + (2)
10 + 9 + (2)
21
-
3(2n + 9)
3(2(2) + 9)
3(4 + 9)
3(4 + 9)
39
The answer is no, because 21 ≠ 39
