Answers
Answer:
○ [tex]\displaystyle (x - 4)^2 + (y + 2)^2 = 25[/tex]
Explanation:
Accourding to one of the circle equations, [tex]\displaystyle (x - h)^2 + (y - k)^2 = r^2,[/tex]the centre of the circle is represented by [tex]\displaystyle (h, k).[/tex]Moreover, all negative symbols give you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must pay cloce attention to which term gets which symbol. Another thing you need to know is that the radius will ALWAYS be squared, so no matter how your equation comes about, make sure that the radius is squared. Now, in case you did not know how to define the radius, you can choose between either method:
Pythagorean Theorem
[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ 4^2 + 3^2 = r^2 \hookrightarrow 16 + 9 = r^2 \hookrightarrow \sqrt{25} = \sqrt{r^2} \\ \\ \boxed{5 = r}[/tex]
Sinse we are dealing with length, we only desire the NON-NEGATIVE root.
Distanse Equation
[tex] \displaystyle \sqrt{[-x_1 + x_2]^2 + [-y_1 + y_2]^2} = d \\ \\ \sqrt{[-7 + 4]^2 + [-2 - 2]^2} = r \hookrightarrow \sqrt{[-3]^2 + [-4]^2} = r \hookrightarrow \sqrt{9 + 16} = r; \sqrt{25} = r \\ \\ \boxed{5 = r}[/tex]
Sinse we are dealing with distanse, we only desire the NON-NEGATIVE root.
I am joyous to assist you at any time.
Related Questions
whats the answer.......
Answers
Answer:
up
Step-by-step explanation:
We should go 4 units up from the zero in the coordinate plane.
What is coordinate plane?A coordinate plane is a two-dimensional surface formed by two number lines. It is formed when a horizontal line (the X-axis) and a vertical line (the Y-axis) intersect at a point called the origin. The numbers on a coordinate grid are used to locate points.
Given that, in the ordered pair (3, 4), the value of y is 4.
Here, in the ordered pair (3, 4), 3 is x-coordinate and 4 is y-coordinate.
The perpendicular distance from the x-coordinate 3 and y-axis is 3 units, which is 3 units right to the y-axis.
The perpendicular distance from the y-coordinate 4 and x-axis is 4 units, which is 4 units up to the x-axis.
Hence, we should go 4 units up from the zero in the coordinate plane.
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Question 6 of 10
The graph of f(x) -13*-6 is shown below. g(x) is a transformation of f(x).
How would you write the equation for the function g(x)?
10+
9)
5
25-20-15-10
5 10 15 20 25
10-13-6-10-
-15+
O A 9-364-43
OB. 863)-23* +3
OC. 900---13--6
D. g(x) - 3* +2
Answers
The graph is attached.
Step-by-step explanation:
This will be an exponential function, which means it will be a smooth curve.
The y-intercept will be 35, since this is the starting population.
Since the population is increasing, the curve will increase as well.
Let R be the region in the first quadrant bounded above by the graph of y=1−x^2 and below by the graph of y=1−√x, as shown in the figure above. What is the area of the region?
Answers
1/3
have a good day/night
If R be the region in the first quadrant bounded above by the graph of y=1−x² and below by the graph of y=1−√x then area is 1/3.
To find the area of the region bounded by the graphs of y = 1 - x² and y = 1 - √x in the first quadrant.
we need to determine the points of intersection and integrate the difference between the two functions over that interval.
To find the points of intersection, we set the two functions equal to each other:
1 - x²= 1 - √x
x²= √x
Squaring both sides again, we have:
x⁴ = x
x(x³ - 1) = 0
This equation gives us two potential solutions: x = 0 and x = 1.
To determine the limits of integration, we need to find the x-value where the two curves intersect.
Since y = 1 - √x represents the upper curve, we can set the two functions equal to each other and solve for x:
1 - x² = 1 - √x
x² = √x
x⁴ = x
Since we are only interested in the first quadrant, the solution x = 0 is not relevant.
Therefore, the only point of intersection is x = 1.
Integrating the difference between the two functions over the interval [0, 1] will give us the area of the region R:
A = ∫[0, 1] (1 - x²) - (1 - √x) dx
Expanding and simplifying the integrand:
A = ∫[0, 1] 1 - x² - 1 + √x dx
A = ∫[0, 1] -x² + √x dx
Integrating each term separately:
A = [-x³/3 + (2/3)x^(3/2)]|[0, 1]
A = [-(1/3) + (2/3)] - [0]
A = 1/3
Therefore, the area of the region R is 1/3.
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Given: -7x<-21 choose the solution set
Answers
Answer:
x > 3
Step-by-step explanation:
The only thing you need to do is just divide both sides by -7
-7x/-7<-21/-7
x>3
I hope this helped!! Good luck (:
Re-write the quadratic function below in Standard Form
y=2(x+2)(x−4)
Answers
Answer:
Standard form:
y=2x^2-4x-16
A toy boat is bobbing on the water.
Its distance D(t)D(t)D, left parenthesis, t, right parenthesis (in \text{m}mstart text, m, end text) from the floor of the lake as a function of time ttt (in seconds) can be modeled by a sinusoidal expression of the form a\cdot\sin(b\cdot t)+da⋅sin(b⋅t)+da, dot, sine, left parenthesis, b, dot, t, right parenthesis, plus, d.
At t=0t=0t, equals, 0, when the boat is exactly in the middle of its oscillation, it is 1\text{ m}1 m1, start text, space, m, end text above the water's floor. The boat reaches its maximum height of 1.2\text{ m}1.2 m1, point, 2, start text, space, m, end text after \dfrac{\pi}{4}
4
π
start fraction, pi, divided by, 4, end fraction seconds.
Find D(t)D(t)D, left parenthesis, t, right parenthesis.
Answers
An equation for a toy boat is bobbing on the water is in the sinusoidal form which we can write as, D(t) = 0.2 sin2t +1
What is an Equation ?
An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, D(t) = acos2t +b
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given information,
Equation of bobbing, D(t) = a sinbt + d
By graph we can say that it is compressed two times,
So, value of b will be, 2
At t =0, height from the floor is 1 m
1 = a sin(2×0) + d
d = 0
At t =π/4, height from the floor is 1.2 m
1.2 = a sin(2×π/4) + 1
a = 0.2
By graph we can say that it is compressed two times,
So, value of b will be 2
Hence, An equation is D(t) = 0.2 sin2t +1
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3x+2=2x+7 solve for x pls it homework due for tomorrow
Answers
Answer:
× = 5
Step-by-step explanation:
3x + 2 = 2x + 7
x + 2 = 7
x = 5
Answer:
2.5[tex] \: [/tex]
Given Equation,
[tex] \\ {\longrightarrow{ \qquad{{ {\pmb{\rm { 3x+2=2x+7}}}}}}} \\ \\[/tex]
Subtracting 2 from both sides we get :
[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\rm { 4x+2 - 2=2x+7-2}}}}}}} \\ \\[/tex]
[tex]{\longrightarrow{ \qquad{{ {\pmb{\rm { 4x=2x+5}}}}}}} \\ \\[/tex]
Subtracting 2x from both sides we get :
[tex] \\ {\longrightarrow{ \qquad{{ {\pmb{\rm { 4x-2x=2x+5-2x}}}}}}} \\ \\ [/tex]
[tex]{\longrightarrow{ \qquad{{ {\pmb{\rm { 2x=5}}}}}}} \\ \\ [/tex]
Dividing 2 from both sides we get :
[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\rm { \frac{2x}{2} = \frac{5}{2} }}}}}}} \\ \\[/tex]
[tex]{\longrightarrow{ \qquad{{ {\pmb{\frak {x = 2.5 }}}}}}} \\ \\[/tex]
Therefore,
The value of x is 2.5solve for x and y please
Answers
Answer:
Step-by-step explanation:
The 2 triangles are similar so corresponding sides are in the same ratio.
3/x = 6/16
6x = 48
x = 8.
9/y = 6/16 = 3/8
3y = 72
y = 24.
Answer:
y = 24 mx = 8 musing proportional equation:
[tex]\rightarrow \sf \dfrac{AC}{CE} = \dfrac{DB}{DE}[/tex]
[tex]\hookrightarrow \sf \dfrac{9}{6} = \dfrac{y}{16}[/tex]
[tex]\hookrightarrow \sf 9(16)} = {6y}[/tex]
[tex]\hookrightarrow \sf y = 24[/tex]
====================
[tex]\rightarrow \sf \dfrac{AE}{CE} = \dfrac{EB}{DE}[/tex]
[tex]\hookrightarrow \sf \dfrac{3}{6} = \dfrac{x}{16}[/tex]
[tex]\hookrightarrow \sf 3(16)} = 6x[/tex]
[tex]\hookrightarrow \sf x = 8[/tex]
What is the slope of
the line?
Give your answer as
a fraction in simplest
form.
Answers
Answer:
3/5
Step-by-step explanation:
Rhis time we dont have another dot, so we just start from zero. We rise 3 and then run 5.
Hoped this helped!!
A triangle has angle measurements of 31°, 10°, and 139º. What kind of triangle is it?
Answers
Answer:
Its a Obtuse Angled Triangle
Step-by-step explanation:
This is due to one of the angles being over 90 Degrees
The measure of the arc from A to B that does not pass through C?
A-160
B-140
C-100
D-90
Answers
Answer: C
Step-by-step explanation:
In an invasion game such as Soccer, Football, or Handball, how can you tell which team is offense and which team is defense?
Answers
Answer:
The easiest way to determine whose offense or defense would be to check where the players are positioned at. Obviously, the main goals of Soccer or Football are in the back meaning people who are defending the goal are most likely to be behind the teammates who are offensive (common sense).
Step-by-step explanation:
PLEASEEE HELPPPP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answers
Answer:
98Step-by-step explanation:
the solution is in the picture
In the accompanying diagram, AB is a diameter of circle O, FECA and
FBG are secants, AD, DE, EB = 1:3:2 and BG = 40°. Find the measures of AD,
DE, EB, and AG.
Answers
Check the picture below.
so to split 180 in a 1 : 3 : 2 ratio, we'll simply divide 180 by (1 + 3 + 2) and distribute accordingly
[tex]\cfrac{180}{1+3+2}\implies 30\qquad \qquad \stackrel{1}{1(30)}~~:~~\stackrel{3}{3(30)}~~:~~\stackrel{2}{2(30)}\implies 30~:90~:60 \\\\[-0.35em] ~\dotfill\\\\ \widehat{AG}=180+40\implies \widehat{AG}=220[/tex]
What is the surface area for the following shape?
Answers
Answer:
The answer is : A 192 in cubic
Step-by-step explanation:
100 % correct
Answer:
208 in^2
Step-by-step explanation:
front: 6x4 = 24
back: 6x4 = 24
right: 6x8 = 48
left: 6x8 = 48
top: 4x8 = 32
bottom: 4x8 = 32
24+24+48+48+32+32 = 208
If 5,x,125 are in continued proportion, find valueee of xxxxx.....
Answers
Answer:
[tex] \pmb{SOLUTION:-}[/tex]
5,x,125 are in continued proportion,Then,
[tex] \displaystyle{ \frac{5}{x} = \frac{x}{125} }[/tex]
[tex]5 \times 125 = {x}^{2} [/tex]
[tex] {x}^{2} = 625[/tex]
[tex]x = \sqrt{625} [/tex]
[tex]x = 25[/tex]
Answer:
a₂ = ±25Step-by-step explanation:
5, x, and 125 are part of a geometric progressionWhat we know :
a (first term) = 5aₙ (final term) = 125n (number of terms) = 3Finding the common ratio (r)
aₙ = arⁿ⁻¹125 = (5)(r)³⁻¹25 = r²r = ± 5Finding x
x is the 2nd term of the progressiona₂ = ara₂ = 5(±5)a₂ = ±25Ann opened a savings account with an initial deposit of $250. Which combination will result in a zero balance in Ann's account?
A deposit $20 in the first week and withdraw $270 in the second week
B deposit $270 in the first week and withdraw $20 in the second week
C deposit $20 in the first week and withdraw $250 in the second week
D deposit $250 in the first week and withdraw $20 in the second week
Answers
Answer:
The answer is A 250+20 then 270-270=0
Peter earns each hour for the first 40 hours he works each week. For every hour, he works after 40 hours he earns $12 each hour last week, Peter earned $444. Which equation could be used to find the number of hours, h, during which Peter earned $12 last week?
Answers
Answer:
5
Step-by-step explanation:
I said so THATS WHY
How many quarts is 16000 gallons
Answers
64000quarts is 16000gallons
Answer:
64,000 quarts are in 16,000 gallons
Step-by-step explanation:
Formula - Divide the volume by 4
Hope this helps (:
explain how the model for 3/5 - 1/2 9s is different from the model for 3/5 - 3/10
Answers
The model is different because it has different denominator and numerator
For each statement, determine if the statement can be true or if the statement can never be true.
Select the correct choice in each row.
Answers
B.Yeah- vertical angles 90+90 equals 180
C.yeah-same as B
choose a random number between 1 and 20 . What is the probability that the number is greater than 5 and less than 15
Answers
Answer:
MY RANDOM ANSWER : my answer is 3
Step-by-step explanation:
The probablitiy of that is 9
How do you know when terms can be combined?
A. They are the same size
B. They have the same exponent
C. They have the same number
D. They have the same variable and exponent
Answers
Answer:
C. They have the same number
Help picture below 3 problems easy will give brainlest
Answers
Answer:
7. 64
22. 12.9
12. 22
Step-by-step explanation:
x = 154 154 - 90 = 64
15% of 86 is 12.9
A triangle's angles must all add up to 180.
90 + 68 = 158 180 - 158 = 22
What is the 15th term of the following sequence? 0.25, 0.5, 1, 2, 4…
Answers
4,096
Solution:In this case, we have a geometric sequence.In a geometric sequence, we use multiplication/division in order to get to the next term.In this case, we multiply each term by 2.So these are the terms:0.25, 0.5, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1,024, 2,048, 4,096Hope it helps.
Do comment if you have any query.
Help picture below problem 11
Answers
Answer:
B) angle B
Step-by-step explanation:
Since the question is telling you that both the triangles are essentially the same, you just have to look to see which letter of triangle ABC is in the same general place as triangle DEF.
In this case angle B is in the same general spot as angle E, so therefore B is your answer.
Hope this helps you :)
Find the surface area
Answers
=4 x π x 11^2
=4 x π x 121
=484π or 1520.530844cm^2
Two boys san around a track that is 400 meters long. Miguel ran around the track three
times in 240 seconds. Joseph ran around the track three times in 200 seconds. What was the
difference between the speeds of the two boys?
A.
1 meter per second
5 meters per second
B.
C.
6 meters per second
D.
11 meters per second
Answers
Using proportions, it is found that the difference between the speeds of the two boys was of:
A. 1 meter per second.
What is a proportion?A proportion is a fraction of a total amount. Following this concept, velocity is distance divided by time.
In this problem, Miguel ran 1 lap = 400 meters each 240/3 = 80 seconds, hence his speed is given by:
sM = 400/80 = 5 m/s.
Joseph ran 400 metters each 200/3 = 66.67 seconds, hence his speed is given by:
sJ = 400/66.67 = 6 m/s.
The difference is given by:
6 m/s - 5 m/s = 1m/s.
Hence, option A is correct.
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I WILL GIVE BRAINIEST!!!! Help!!!! 4. A stone nudged off the Royal Gorge Bridge near Cañon City, Colorado, falls 1053 feet before
hitting water. Because its speed increases as it falls, the distance it travels each second
increases. During the first second, it drops 16 feet. During the next second, it drops an
additional 48 feet. During the third second, it drops another 80 feet. The distances traveled
each second form an arithmetic sequence:
16, 48, 80, ...
Part I: How far does the stone fall during the 5th second? Find and use the explicit formula.
a. What is the first term of the sequence?
b. What is d, the common difference?
c. Write the explicit formula in function notation. Use f(n) = f(1) + (n - 1)d, where f(1)
Answers
Answer:
First term = a= 16.
Common difference, d, = 32.
Answer for the fifth second is = 144 feet.
Step-by-step explanation:
This question is simply an Arithmetic Progression, AP,.
so, the 1st second represents the first term and so on.
for the common difference, you just subtract the first from the second term and confirm by subtracting the second from the third term and i got 32.
6. Which describes a situation in which two
quantities must have a sum of 0?
A. a temperature above 0°F and another
temperature that is below 0°F
B. an elevator that is below the lobby
and then is above the lobby
C. an element that has the same number
of electrons as protons
D. a golfer who plays two rounds and has
one above par and one below
par.