Answer:
radius = 5
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here r² = 25 ( take the square root of both sides )
r = [tex]\sqrt{25}[/tex] = 5
Find the length of side xx in simplest radical form with a rational denominator.
Answer:
[tex]\frac{\sqrt{10} }{2}[/tex]
Step-by-step explanation:
on a 45 - 45 - 90 triangle if the sides are x then the hypotenuse is x[tex]\sqrt{2}[/tex]
so,
[tex]\sqrt{5}[/tex] = x[tex]\sqrt{2}[/tex] (Divide by [tex]\sqrt{2}[/tex] )
[tex]\frac{\sqrt{5} }{\sqrt{2} }[/tex] = x (rationalize the denominator)
[tex]\frac{\sqrt{5} }{\sqrt{2} }[/tex] · [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex] = [tex]\frac{\sqrt{10} }{\sqrt{4} }[/tex] = [tex]\frac{\sqrt{10} }{2}[/tex]
The length of side is √10/2
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given triangle is a 45-90-45 so if the sides are x then the hypotenuse will be x√2
From the figure the hypotenuse of triangle is √5
SO equation it to x√2
We get √5=x√2
Divide both sides by √2
√5/√2=x
As the denominator should be a whole number we have to rationalize the denominator.
Multiply numerator and denominator with √2
√5/√2×√√2/√2
√10/2
Hence, the length of side is √10/2
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Solve for x. PLZ HELP ASAP!!!
X is a vertical angle to the angle marked as 100 degrees.
Vertical angles are the same so x = 100 degrees
Answer: 100 degrees
if C{1,2} and D={4,5,6}, find C×D by tabulation method. i need for exam
Answer:
Step-by-step explanation:
C * D = {(x,y): x is an element of C and y is an element of D.}
C * D = { (1,4), (1,5), (1,6), (2,4), (2,5), (2,6) }
Someone please help me with this algebra problem
Answer:
90
Step-by-step explanation:
Suppose that the natural rate of unemployment in a particular year is 4 percent and the actual unemployment rate is 13 percent. Instructions: Enter your answers as a whole number. a. Use Okun's law to determine the size of the GDP gap in percentage-point terms. percent b. If potential GDP is $500 billion in that year, how much output is forgone because of cyclical unemployment? $ billion
Answer:
a. 18 percent
b. $90 billion
Step-by-step explanation:
a. Calculation to use Okun's law to determine the size of the GDP gap in percentage-point terms.
First step is to find the difference between ACTUAL RATE of unemployment and NATURAL RATE of unemployment
Difference=13%-4%
Difference= 9%
Based on the information above calculation we can see that the ACTUAL RATE of unemployment EXCEEDS the NATURAL RATE of unemployment by 9%, which indicates a CYCLICAL UNEMPLOYMENT.
Thus, According to Okun's law, this translates into an 18 % GDP gap in percentage-point terms (= 2 × 9%).
Therefore the the size of the GDP gap in percentage-point terms is 18 percent
b. Calculation to determine how much output is forgone because of cyclical unemployment
Forgone Output :
By applying Okun’s law we known that the GDP gap is 18%, which means that we are 18% below the GDP amount which is given as $500 billion,
Hence,
Output forgone = (18/100) ×$500 billion
Output forgone=0.18×$500 billion
Output forgone=$90 billion
Therefore the Forgone Output is $90 billion
Please help me with this one
Answer:
240
Step-by-step explanation:
well do *
so 8x6x5 = 240 there's your answer
Answer:
[tex]S.A=1/2(8+8)(9^{2})+8\times 6+8\times 5[/tex]
[tex]=26\times2+48+40[/tex]
[tex]=140 ~cm^{2}[/tex]
-------------------------
HOPE IT HELPS
HAVE A GREAT DAY!!
A certain ferry moves up and down a river between Town A and
B. It takes the ferry two hours to travel to Town A and only an
hour and thirty minutes to return to Town B. If the current is 5mph
how far apart are the two cities?
Answer: 60 miles
Step-by-step explanation:
Given
It takes ferry 2 hours to travel to town A and only [tex]1.5\ hr[/tex] to travel back to town B.
Speed of current is [tex]u=5\ mph[/tex]
Suppose the speed of the ferry is [tex]v[/tex] mph
Distance traveled in both the cases is same, but it took more time traveling to city A that is, ferry is moving upstream and downstream for returning time.
[tex]\Rightarrow 2(v-5)=1.5(v+5)\\\Rightarrow 2v-10=1.5v+7.5\\\Rightarrow 0.5v=17.5\\\Rightarrow v=35\ mph[/tex]
Distance between the towns is [tex]2\times (35-5)=60\ \text{miles}[/tex]
Answer:
The distance between the two towns is 60 miles.
Step-by-step explanation:
Let the distance between A and B is d.
A to B , t = 2 hour
B to A , t' = 1.5 hour
Speed of current, u = 5 mph
Let the speed of ferry is v.
distance = speed x time
d = (v - 5) x 2 = (v + 5) x 1.5
2 v - 10 = 1.5 v + 7.5
0.5 v = 17.5
v = 35 mph
So, the distance is
d = (35 - 5) x 2 = 60 miles.
Ed buys a box of eggs costing £2.40, two packs of bacon for £2.60 each and two tins of baked beans.
He pays with a £10 note and gets 80p change.
How much does a tin of beans cost in pounds, £?
Answer:
£0.80
Step-by-step explanation:
1 box of eggs: £2.40
2 packs of bacon: 2 * £2.60
2 tins of baked beans: 2x
Change: 80p
Total = 2x + £2.40 + £5.20 + £0.80
Total = 2x + £8.40
2x + £8.40 = £10
2x = £1.60
x = £0.80
Answer: £0.80
Finding
What is |-1|?
Answer:
1.
Step-by-step explanation:
.
If US=52, ST=30, UT=40, VW=27, and XW=36, find the perimeter of ΔVWX. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.
Answer:
The perimeter is 109.8
Step-by-step explanation:
As we can see here, the angles of the triangles are congruent so we can say that both triangles are congruent
When two triangles are congruent, the ratio of their corresponding sides are equal
So we can get the scale factor here by looking at the sides facing each specific angle in both triangles
In the bigger triangle,
The side facing 34 degrees has a length of 30
In the smaller triangle,
The side facing 34 degree has a length of 27
So the scale factor to get the smaller from the bigger is 27/30 = 9/10 or 0.9
Likewise the side facing 51 degrees in the bigger is 40 while for the smaller, it is 36
So the ratio still stands at 36/40 = 9/10 or 0.9
In essence, the smaller triangle will have a perimeter that is 0.9 times that of the bigger
The perimeter of the bigger is simply the sum of the side lengths
We have this as;
(52 + 30 + 40) = 122
so that of the smaller would be;
122 * 0.9 = 109.8
In right triangle PQR, m∠Q = 90° and sin R=5/13
What is the value of cos R?
a) 5/13 b)5/12 c) 12/13 d) 12/5
Answer:
C
Step-by-step explanation:
Given
sinR = [tex]\frac{5}{13}[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]
This is a 5- 12- 13 triangle with legs PQ = 5, QR = 12, hypotenuse PR = 13
cosR = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{QR}{PR}[/tex] = [tex]\frac{12}{13}[/tex]
Jamal bought a diamond ring at a 20% discount. He paid $2640 for the ring. Naomi bought a similar ring but was given a discount of $924. What was the percentage discount given to Naomi?
Answer: 72%
Step-by-step explanation:
Set Jamal's original ring price = x
[tex]x - x(0.2) = 2640\\x(1-0.2)=2640\\x(0.8)=2640\\x=\frac{2640}{0.8}=3300[/tex]
Jamal's original ring price = $3300
Set Naomi's discount = y
[tex]3300-3300(y)=924\\=3300(1-y)=924\\1-y=\frac{924}{3300} \\-y=\frac{924}{3300} -1\\y=1-\frac{924}{3300}=1-0.28=0.72[/tex]
Naomi's discount is 0.72 = 72%
In a direct variation, the ratio of y -values to x -values is equal to a constant.
True or False?
HELP PLEASE
Answer:
True
Step-by-step explanation:
The equation of direct variation is
y = kx ← k is the constant of variation
To find k divide both sides by x
[tex]\frac{y}{x}[/tex] = k
That is the constant is the ratio of y- values to x- values
A quadratic equation is shown below:
6x2 + 17x + 9 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 4x2 − 4x + 1 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
(10 points)
Answer:
x = -0.70,-2.212.
Step-by-step explanation:
(a) The quadratic equation is :
[tex]6x^2 + 17x + 9 = 0[/tex]
Here,
a = 6, b = 17, c = 9
Put all the values in the quadratic formula.
[tex]x=\dfrac{-17+\sqrt{17^2-4\times 6\times 9}}{2(6)},\dfrac{-17-\sqrt{17^2-4\times 6\times 9}}{2(6)}\\\\x=-0.70,-2.12[/tex]
So, the solution of the given equation are -0.70,-2.212.
(b) Equation is : [tex]4x^2 -4x + 1 = 0[/tex].
Here, a = 4, b = -4 and c = 1
So,
[tex]x=\dfrac{-(-4)+\sqrt{(-4)^2-4\times 4\times 1}}{2(4)},\dfrac{-(-4)-\sqrt{(-4)^2-4\times 4\times 1}}{2(4)}\\\\x=0.5,0.5[/tex]
Hence, this is the required solution.
Which equation represents the graphed function?
O-3x + 2 = y
0 x+2=y
ox-3=y
O 2x - 3= y
Answer:
y = 3/2x -3
Step-by-step explanation:
The general equation of a straight line is;
y = mx + b
where m is slope and b is the y-intercept
Here, we can see that the graph intercepts the y-axis at the point y = -3
So b = -3
To get m, we can substitute any other point values on the plot
We can select (2,0)
So we have;
y = mx -3
0 = 2m -3
2m = 3
m = 3/2
so;
y = 3/2x -3
Find the smallest number by which 2250 should be multiplied ,so that the product is a perfect square.
Answer:
10
Step-by-step explanation:
[tex]2250[/tex] = 2x5x5x5x3x3
therefore,2and 5 don't have a pair so , 2x5=10 .
So, the smallest number by which 2250 is 10
Can some help with this problem
X,Y and Z from a business with capitals Rs 5000,Rs.4500 and Rs.6500 respectively,after 6 month,X doubles has capital and after next 3 months Y trebles his capital .If the profit at the end of the year amount to RS.8300,find the profit obtained by each X,Y and Z.
Answer:
Profit obtained by X = Rs. 2,976.64
Profit obtained by Y = Rs. 2,545.58
Profit obtained by Z = Rs. 2,777.78
Step-by-step explanation:
Total capital for the first 6 months = Rs 5000 + Rs.4500 + Rs.6500 = Rs. 16,000
Total capital for the next 3 months = Rs. 16,000+ Rs 5000 = Rs. 21,000
Total capital for the last 3 months of the year = Rs. 21,000 + (Rs 4500 * 2) = Rs. 30,000
Share of profit of each partner is the sum of all the ratios of his capital to total capital of the business at each point in time multiply by the ratio of the numbers of months covered by each capital to 12 months and then multiply by RS.8300.
Profit obtained by X = ((Rs 5000 / 16,000) * (6 / 12) * Rs. 8300) + ((Rs 10,000 / 21,000) * (3 / 12) * Rs. 8300) + ((Rs 10,000 / 30,000) * (3 / 12) * Rs. 8300) = Rs. 2,976.64
Profit obtained by Y = ((Rs 4500 / 16,000) * (6 / 12) * Rs. 8300) + ((Rs 4500 / 21,000) * (3 / 12) * Rs. 8300) + ((Rs 13,500 / 30,000) * (3 / 12) * Rs. 8300) = Rs. 2,545.58
Profit obtained by Z = ((Rs 6500 / 16,000) * (6 / 12) * Rs. 8300) + ((Rs 6500 / 21,000) * (3 / 12) * Rs. 8300) + ((Rs 6,500 / 30,000) * (3 / 12) * Rs. 8300) = Rs. 2,777.78
Confirmation of total profit shared = Rs. 2,976.64 + = Rs. 2,545.58 + Rs. 2,777.78 = Rs. 8,300
There are 35 times as many students at Wow University as teachers. When all the students and
teachers are seated in the 8544 seat auditorium, 12 seats are empty. How many students attend
Wow University?
Given:
There are 35 times as many students at Wow University as teachers.
When all the students and teachers are seated in the 8544 seat auditorium, 12 seats are empty.
To find:
The total number of students.
Solution:
Let x be the number of teachers at Wow University. So, the number of student is :
[tex]35\times x=35x[/tex]
When all the students and teachers are seated in the 8544 seat auditorium, 12 seats are empty.
[tex]x+35x=8544-12[/tex]
[tex]36x=8532[/tex]
[tex]x=\dfrac{8532}{36}[/tex]
[tex]x=237[/tex]
The number of total students is:
[tex]35x=35(237)[/tex]
[tex]35x=8295[/tex]
Therefore, the total number of students is 8295.
A bottling company marks a 0 for every bottle that comes out correct and a 1 for every defective bottle. Estimate the probability that the next bottle is defective
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]0 \to[/tex] Correct
[tex]1 \to[/tex] Defective
Required
The probability that the next is defective
The question is incomplete because the list of bottles that came out is not given.
However, the formula to use is:
[tex]Pr = Num ber\ o f\ d e f e c t i v e \div T o t a l\ b o t t l e s[/tex]
Take for instance, the following outcomes:
[tex]0\ 1\ 0\ 0\ 0\ 1\ 0\ 0\ 1\ 1\ 0\ 0\ 0\ 1[/tex]
We have:
[tex]Total = 14[/tex]
[tex]D e f e ctive = 9[/tex] --- i.e. the number of 0's
So, the probability is:
[tex]Pr = 9 \div 14[/tex]
[tex]Pr = 0.643[/tex]
Answer:
1/20
Step-by-step explanation:
000000000000100000
It is asking the probability of a defective bottle
there is one defective bottle out of 20
A group of friends wants to go to the amusement park. They have no more than $365 to spend on parking and admission. Parking is $16.25, and tickets cost $38.75 per person, including tax. Write and solve an inequality which can be used to determine pp, the number of people who can go to the amusement park.
Answer:
Inequality: [tex] 38.75p + 16.25 \le 365 [/tex]
Solution: [tex] p \le 9 [/tex]
Step-by-step explanation:
Let p = number of people.
Ticket for 1 person: $38.75
Tickets for n people: 38.75p
Parking: $16.25
[tex] 38.75p + 16.25 \le 365 [/tex]
[tex] 38.75p \le 348.75 [/tex]
[tex] p \le 9 [/tex]
Answer
380≥20.75p+15.5
Step-by-step explanation:
good luck
Which arc is a minor arc?
A)SQ
B)PSR
C)PS
D)SO
Answer:
Answer: The arc PS would be a minor arc · Step-by-step explanation: As a minor arc is one that is less that 180 degrees, it would be the only viable ...
Need help, please answer this
Answer:
In this exercise we need to solve the equation
3(x-2) = 2x + 6 - 2
We operate the parentheses and the right side
3(x-2) = 2x + 4
3x - 6 = 2x + 4
We add 6 to both sides
3x -6 + 6 = 2x + 4 + 6
3x = 2x + 10
We substract 2x
3x - 2x = 2x + 10 - 2x
x = 10
x = 10
Step-by-step explanation:
which eqation represents the line that passes through (-6, 7) and (-3, 6)
Answer:
The answer is y= - ⅓x + 5 in slope intercept form and y-7 = - ⅓ (x + 6) in point slope form.
true or false,the diagonal of a rectangle is longer than any of its sides. I want the answer with explanation If u don't I will report
Answer:
True
Step-by-step explanation:
Yes! The diagonal of a rectangle is longer than any of its sides.
Consider PQRS as a rectangle. It is known to us that each interior angle of a rectangle measures 90°. Now, after making the diagonal of the rectangle PQRS, the rectangle has been split into 2 right-angled triangles i.e, ∆PRS and ∆RPQ. In the right angled triangle, hypotenuse is always the longest side. Here, in ∆PRS and ∆RPQ, the bases are RS and QP ; perpendiculars are PS and QR and both triangles' hypotenuse is PR. As, hypotenuse is always the longest side, so PR will be longer than RS,QP,PS and QR. Clearly, the diagonal of a rectangle is longer than any of its sides.
Evaluate: 2(6+4) - 3(5)
70
1
5
85
Answer:
[tex]2(6 + 4) - 3(5) \\ 12 + 8 - 15 \\ = 5[/tex]
Answer:
1
Step-by-step explanation:
2*6+4-3*5
12+4-15
16-15
1
There are 36 pencils in 6 packs. Igor wants to know how many pencils are in 1 pack. Elsa wants to know how many pencils are in 3 packs. please help me I did not bring pencil and paper to Herman park
Answer:
18 pencils in 3 packs.
Step-by-step explanation:
Assuming that each pack will have the same amount of pencils. It is given that there are 36 pencils in all when one has 6 packs. Find the amount in each pack by dividing (total amount of pencils)/(amount of packs) = Amount of pencils per pack:
36/6 = 6
There are 6 pencils in each pack.
Now, Elsa wants to know how much pencils are in 3 packs. Multiply the amount of packs with the amount of pencils in each pack:
Total amount of pencils = amount of packs (3) x amount of pencils per pack (6)
= 3 x 6
= 18
There are 18 pencils in 3 packs.
~
Need help on this question asap pleasee
Answer:
I believe its the 1st answer.
someone please please help me!
Answer:
[tex]mDE=90[/tex]°
Step-by-step explanation:
In this problem, one is asked to find the measure of the arc in degrees. This problem provides one with a diagram since the center is unnamed, call the center point (O). One is given the information that angle (<DOE) has a measure of (90) degrees. One is asked to find the degree measure of the surrounding arc (DE).
The central angles theorem states that if an angle has its vertex on the center of a circle, the degree measure of the angle is equal to the degree measure of the surrounding arc. One can apply this here by stating the following:
[tex]m<DOE = mDE\\[/tex]
Substitute,
[tex]90=mDE[/tex]
A rectangle has an area of 18 cm2
The lengths of the sides are whole numbers.
How long could the sides of the rectangle be?
Give all the examples you can think of
Answer:
9 possible values of length and breadth.
Step-by-step explanation:
Given that the area of the rectangle is 18cm² . And the lengths of the sides are whole numbers. We need to tell the possible dimensions of the rectangle .
Let :-
[tex]\rm\implies Length = x [/tex]
[tex]\rm\implies Breadth = y [/tex]
We know that :-
[tex]\rm\implies Area = length \times breadth [/tex]
Put in the assumed variables[tex]\rm\implies Area = x y \\\\\rm\implies xy = 18cm^2 [/tex]
Now look out for the possible factors of 18 . That is , ( 1 × 18 ) , ( 2 × 9) , ( 3 × 6 ) , ( 6 × 3 ) , ( 9 × 2 ) , (18 × 1 ) . That is total 9 possible values .
