The first circle has equation
(x - 2)² + (y + 1)² = 4²
and the second has equation
(x - 2)² + (y - 5)² = (√10)²
Solve for (x - 2)² :
(x - 2)² + (y + 1)² = 4² ==> (x - 2)² = 16 - (y + 1)²
(x - 2)² + (y - 5)² = (√10)² ==> (x - 2)² = 10 - (y - 5)²
Then
16 - (y + 1)² = 10 - (y - 5)²
16 - (y ² + 2y + 1) = 10 - (y ² - 10y + 25)
15 - 2y - y ² = -15 + 10y - y ²
30 - 12y = 0
12y = 30
y = 30/12 = 5/2
(this is the y coordinate of A and B)
Then solve for x :
(x - 2)² = 16 - (5/2 + 1)²
(x - 2)² = 15/4
x - 2 = ± √(15/4) = ±√15/2
x = 2 ± √15/2
(these are the x coordinates for either A or B)
The intersections are the points A = (2 - √15/2, 5/2) and B = (2 + √15/2, 5/2). We want to find the squared distance between them:
(AB)² = [(2 - √15/2) - (2 + √15/2)]² + (5/2 - 5/2)²
(AB)² = (-√15)² + 0²
(AB)² = 15
Solve EFD. Round the answers to the nearest hundredth.
A. m F ≈ 26, m D ≈ 64.01, FD = 7,921
B. m F ≈ 26, m D ≈ 64.01, FD = 89
C. m F ≈ 64.01, m D ≈ 26, FD = 89
D. m F ≈ 64.01, m D ≈ 26, FD = 7,921
Answer:
Option B
<F = 26°
<D = 64.01°
FD = 89
Answered by GAUTHMATH
For right triangle EFD, m ∠F ≈ 26°, m ∠D ≈ 64.01° and FD = 89
The correct answer is an option (B)
What is hypotenuse?It is the longest side of the right triangle.
What is Pythagoras theorem?For a right triangle,
[tex]a^{2}+ b^{2} = c^{2}[/tex], where c is hypotenuse and a, b area other two sides of the right triangle
For given example,
We have been given a right triangle EFD with hypotenuse FD.
Also, EF = 80, ED = 39
Using the Pythagoras theorem,
[tex]\Rightarrow FD^{2}= EF^{2} + ED^{2}\\\\ \Rightarrow FD^{2}= 80^{2} + 39^{2}\\\\ \Rightarrow FD^2 = 6400 + 1521\\\\ \Rightarrow FD^2 = 7921\\\\\Rightarrow FD = 89[/tex]
Consider, sin(F)
[tex]\Rightarrow sin(F)=\frac{ED}{FD} \\\\\Rightarrow sin(F)=\frac{39}{89}\\\\ \Rightarrow sin(F)=0.4382\\\\\Rightarrow \angle F=sin^{-1}(0.4382)\\\\\Rightarrow \angle F=25.98^{\circ}\\\\\Rightarrow \angle F\approx 26^{\circ}[/tex]
Now, consider sin(D)
[tex]\Rightarrow sin(D)=\frac{FE}{FD}\\\\ \Rightarrow sin(D)=\frac{80}{89}\\\\ \Rightarrow \angle D = sin^{-1}(0.8988)\\\\\Rightarrow \angle D = 64.009^{\circ}\\\\\Rightarrow \angle D \approx 64.01^{\circ}[/tex]
Therefore, for right triangle EFD, m ∠F ≈ 26°, m ∠D ≈ 64.01° and FD = 89
The correct answer is an option (B)
Learn more about Pythagoras theorem here:
https://brainly.com/question/343682
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help me out (geometry)
Answer:
⊥
Step-by-step explanation:
d and b meet at a 90 degree angle ( as shown by the box)
The lines are perpendicular (⊥)
Help Please Now!!!
Find the volume Of The Rectangle Prism
Answer:
180m cubed
Step-by-step explanation:
Multiply the length, width, and height together: 6×6×5=180
Answer:
Formula of a rectangular prism:
L x W x H
Now we place in the numbers and solve:
5 x 6 x 6 = 180 m3
Help and please explain I don't get khan academy
Answer:
same y intercept
Step-by-step explanation:
The y intercept is when r = 0
Function 1
p = -3/2 r - 5
Let r = 0
p = 0-5
p = -5
Function 2
When r = 0 p = -5
They both equal -5, so they both have the same y intercept
find two consecutive whole number such that five times the greater number makes 59 hint let the number be x and x + 1
Answer:
Step-by-step explanation:
Let the smaller number = x
Let the larger number = x + 1
5*(x + 1) = 59
You can do this. The problem says that when the larger number is multiplied by 5, you get 59. You are also told that the numbers are whole numbers. 59 divided by 5 leaves a remainder which is not a whole number.
Pls help with this question :)
Answer:
X=20
a< = 125
Step-by-step explanation:
I’m stuck on this one help anyone?
Answer:
just add a small amount to the 2.8 and square the result
Step-by-step explanation:
x x^2
2.8 7.84
2.81 7.8961
2.82 7.9524
2.83 8.0089
2.84 8.0656
2.85 8.1225
2.86 8.1796
2.87 8.2369
Page Section B 1 A={odd number between 6 andon and 8 § =) by B=&multiples of 5 less than too 100g e) G=& multiples of 5 greater than 100odd number between Shikshan
Answer:
write your question properly
Step-by-step explanation:
Si un proyectil asciende verticalmente, y después de 3 segundos alcanza su altura máxima, calcule la velocidad que lleva a la mitad de su trayectoria descendente
Answer:
The speed is 20.8 m/s
Step-by-step explanation:
If a projectile ascends vertically, and after 3 seconds it reaches its maximum height, calculate the velocity that it carries to the middle of its downward trajectory
Let the maximum height is h and initial velocity is u.
From first equation of motion
v = u + at
0 = u - g x 3
u = 3 g.....(1)
Use third equation of motion
[tex]v^2 = u^2 - 2 gh \\\\0 = 9 g^2 - 2 gh \\\\h = 4.5 g[/tex]
Let the speed at half the height is v'.
[tex]v^2 = u^2 + 2 gh \\\\v'^2 = 0 + 2 g\times 2.25 g\\\\v'^2 = 4.5\times 9.8\times9.8\\\\v' = 20.8 m/s[/tex]
In a company of 35 employees, four-sevenths work in sales. How many of the employees work in sales ?
Answer:
20
Step-by-step explanation:
Multiply 4/7 with 35, this will get you 140/7, which simplifies to 20 employees
Now use GeoGebra to measure the length of each side of quadrilateral ABCD, and use those lengths to calculate the perimeter of the quadrilateral. Do you get the same result that you obtained in part E? Take a screenshot of your work, and paste it below.
Answer:
Step-by-step explanation:
Choose the correct description of the graph of the inequality X - 3 greater than or equal to 25
A. Open circle on 8, shading to the left
B. Closed circle on 8, shading to the left.
C. Open circle on 8, shading to the right.
D. Closed circle on 8, shading to the right.
I’m pretty sure it’s D
Answer:
D. Closed circle on 8, shading to the right.
Someone help me please
===============================================
Explanation:
The table says that
5 students got an A10 students got a B15 students got a CThat's 5+10+15 = 30 students out of 35 total.
The probability is therefore 30/35 = 0.8571 approximately which rounds to 0.86
There's roughly an 86% chance of picking someone who got an A, B or C.
A photo printer is on sale for $195.50. The regular price is $230. What is the percent of the discount on the photo
printer?
The ratio of grapes in a fruit salad to people it will serve is 13/3. How many people will be served if Deb is using 30 grapes?
Answer:
6 + 12/13, or 90/13 people will be served
Step-by-step explanation:
Ratios stay the same, no matter the quantity.
Given this, we can say that (13 grapes / 3 people) = (30 grapes / x amount of people)
13/3 = 30 / x
multiply both sides by 3 to remove a denominator
13 = 30 * 3 /x
multiply both sides by x to remove the other denonimator
13 * x = 30 * 3
13 * x = 90
divide both sides by 13 to isolate the x
x = 90/13 = 6 + 12/13 ≈6.92 people
y=x+5 y=-2x-4 I need help with this problem will you help me?
Answer:
x = - 3, y = 2
Step-by-step explanation:
Given the 2 equations
y = x + 5 → (1)
y = - 2x - 4 → (2)
Substitute y = x + 5 into (2)
x + 5 = - 2x - 4 ( add 2x to both sides )
3x + 5 = - 4 ( subtract 5 from both sides )
3x = - 9 ( divide both sides by 3 )
x = - 3
Substitute x = - 3 into either of the 2 equations and evaluate for y
Substituting into (1)
y = - 3 + 5 = 2
Given g (n) = 3n + 2, f (n) = 2n^2 + 5
Find g (f (2))
a)8
b)41
c)133
d)21
Answer:
g(f(2)) = 41
b)41
Step-by-step explanation:
g(f(2)) = 41
f(2)= 2(2²) + 5 = 13
So g(f(2)) → g(n = 13)
g(n = 13)→ 3(13) + 2 = 41
plsssssssssss helppppppppp i want it right now pls
Answer:
hope this helps you
have a great day
SOMEONEEEE HELPPP MEEEEE PLEASEEEE!!!!
Answer:
[tex]{ \tt{ \tan(x) = \frac{opposite}{adjacent} }} \\ \\ { \tt{ \tan( \theta) = \frac{30}{16} }}[/tex]
Solve the equation 15x + 22 = 7x +62
Answer:
hope it helps you........
Answer:
x = 5
Step-by-step explanation:
1. Subtract 22 from both sides.
15x = 7x + 62 - 22
2. Simplify 7x + 62 - 22 to 7x + 40.
15x = 7x + 40
3. Subtract 7x from both sides.
15x - 7x = 40
4. Simplify 15x - 7x to 8x.
8x = 40
5. Divide both sides by 8.
x = [tex]\frac{40}{8}[/tex]
6. Simplify [tex]\frac{40}{8}[/tex] to 5.
x = 5
i need the answer for this question
A record club has found that the marginal profit,
Upper P prime (x ), in cents, is given by
Upper P prime (x )equals negative 0.0008 x cubed plus 0.20 x squared plus 46.8 x for x less than or equals 200,
where x is the number of members currently enrolled in the club. Approximate the total profit when 120 members are enrolled by computing the sum
Summation from i equals 1 to 6 Upper P prime (x Subscript i Baseline )Upper Delta x with Upper Delta x equals 20.
Solution :
Given :
[tex]$P'(x) = -0.0008x^3+0.20x^2+46.8x,$[/tex] for x ≤ 200
Total profit when 120 members are enrolled is :
[tex]$\sum_{i=1}^6P'(x_i) \Delta x$[/tex] with [tex]\Delta x = 20[/tex]
Using the left end points, we get,
The values of [tex]x_i[/tex] are : { 0, 20, 40, 60, 80, 100}
Therefore,
[tex]$P'(x_1) = P'(0)=-(0.0008)(0)^3+(0.20)(0)^2+(46.8)(0)$[/tex]
= 0
[tex]$P'(x_2) = P'(20)=-(0.0008)(20)^3+(0.20)(20)^2+(46.8)(20)$[/tex]
= 1009.6
[tex]$P'(x_3) = P'(40)=-(0.0008)(40)^3+(0.20)(40)^2+(46.8)(40)$[/tex]
= 2140.8
[tex]$P'(x_4) = P'(60)=-(0.0008)(60)^3+(0.20)(60)^2+(46.8)(60)$[/tex]
= 3355.2
[tex]$P'(x_5) = P'(80)=-(0.0008)(80)^3+(0.20)(80)^2+(46.8)(80)$[/tex]
= 4614.4
[tex]$P'(x_6) = P'(100)=-(0.0008)(100)^3+(0.20)(100)^2+(46.8)(100)$[/tex]
= 5880
[tex]$\sum_{i=1}^6P'(x_i) \Delta x = P'(x_1)\Delta x + P'(x_2)\Delta x + P'(x_3)\Delta x + P'(x_4)\Delta x + P'(x_5)\Delta x + P'(x_6)\Delta x $[/tex]
= (0)(20) + (1009.6)(20) + (2140.8)(20) + (3355.2)(20) + (4614.4)(20) + (5880)(20)
= (20)( 0 + 1009.6 + 2140.8 + 3355.2 + 4614.4 + 5880)
= (20)(17,000)
= 340,000 cents
[tex]$=\frac{340000}{100} \ \text{dollars}$[/tex]
= 3400 dollars
Hence, the required total profit is 3400 dollars.
What is the common difference of the arithmetic sequence-20,-16,-12,-18
Answer:
common difference = 4
Step-by-step explanation:
common difference is the difference between the successive term and its preceding term.
let's take the successive term of -20 that is - 16
common difference (d) = successive term - preceeding term
= -16 -(-20)
= -16 + 20
= 4
if we take the successive term of -16 that is -12
we'll get the same common difference.
d = -12 -(-16)
d = -12 + 16
d = 4
this means that the common difference for an AP remains constant.
Which graph shows the solution set of
Let j=+5 - 5+ |-5 x 1/5
What is the value of+J?
Answer:
j=|x|
Step-by-step explanation:
help me in this plz....
Answer:
70. 8x⁴
71. 3n - 10
72. a/5 + 12
Step-by-step explanation:
70. a number "x" raised to the fourth = x⁴
Product of 8 and x⁴ = 8 × x⁴
= 8x⁴
71. 3 times a number "n" = 3 × n = 3n
3n decreased by 10 = 3n - 10
72. Quotient of a number "a" and 5 = a/5
12 more than a/5 = a/5 + 12
Please hurry I will mark you brainliest
What is the equation in standard form for the line with slope 3 and y-intercept -4?
Answer: -3x+y=-4
Step-by-step explanation:
Standard form is Ax+By=C. In y=Mx+b form, it would be y=3x-4. To put it into standard form you subtract 3x from both sides. So then you have -3x+y=-4.
n(a)=60% n(o)=70% N(ano)=400 n(auo)complenment=10 find U and a only
n(A∪B)=n(A)+n(B)−n(A∪B)=50+60−40=70
n(AΔB)=n(A∪B)−n(A∩B)
⇒70−40=30.
Jessica ate 7 /10 of her orange before lunch and 1/10 of her orange after lunch. How much of her orange did she eat?
Answer:
8/10
Step-by-step explanation:
Which of the following equations would not have a solution that is the same as the solution to the system. shown below?
4x+y=7
-2x+5y=1
———————————————
1) 11y = 9
2) 2x + 6y = 8
3) -4x + 10y = 1
4) 12x + 3y = 21
please help asap and thank you in advance to anyone who answers this for me ! :)
Answer:
Step-by-step explanation: