The center of a circle is at (2, -5) and it's radius is 12. What is the equation of the circle?
A.) (x+2)^2 + (y-5)^2 =24
B.) (x-2)^2 + (y+5)^2 = 24
C.) (x+2)^2 + (y-2)^2 = 144
D.) (x-2)^2 + (y+5)^2 = 144
Answer:
The answer is D
Step-by-step explanation:
It is D
The diagram shows the locations of John and Mark in relationship to the top of a tall building labeled A.
A) Describe < 4 as it relates to the situation
B) Describe < 3 as it relates to the situation
In circle H, HJ¯¯¯¯¯ is a radius and JK¯¯¯¯¯ is a tangent segment. Which statement must be true?
A) HJ=JK
B) ∠HJK is an obtuse angle.
C) HJ=HK
D) ∠HJK is a right angle.
sabendo que x2 + y2=74 e que xy=35, calcule valor de (x - y2)2
Stan's cookie recipe makes 242424 cookies and calls for exactly 384384384 sprinkles. He is wondering how many sprinkles (p)(p)left parenthesis, p, right parenthesis he will need to make 606060 cookies. He assumes each cookie will have the same number of sprinkles. How many sprinkles does Stan need to make 606060 cookies?
To find the number of sprinkles needed for 60 cookies, determine the number of sprinkles per cookie by dividing 384 by 24, which is 16. Then multiply 16 by 60 to get 960 sprinkles.
The question asks us to calculate the number of sprinkles (p) needed for 60 cookies when a recipe for 24 cookies calls for 384 sprinkles.
To solve this, we start by finding the number of sprinkles per cookie:
Divide the total number of sprinkles (384) by the number of cookies in the recipe (24).Multiply the result by the number of cookies we want to make (60).Therefore:
384 sprinkles ÷ 24 cookies = 16 sprinkles per cookie 16 sprinkles per cookie × 60 cookies = 960 sprinkles for 60 cookiesStan would need 960 sprinkles to make 60 cookies.
Factor each polynomial. Check your answer by distributing. 2x^2+5x+2
The function f(x)=35+15x represents the amount of money, in dollars, mr. lewis earns for working x hours. how much money does mr. lewis earn for working 25 hours?
By substituting x with 25 in the equation f(x)=35+15x, we find out that Mr. Lewis would earn $410 for working 25 hours.
Explanation:The function provided is f(x)=35+15x, which represents the amount of money Mr. Lewis earns for working x hours. In the case of Mr. Lewis working for 25 hours, we substitute the value of x with 25 in the equation to calculate his earnings. Therefore, f(25)=35+15(25)=35+375=$410. Hence, Mr. Lewis would earn $410 for working 25 hours.
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Which box plot represents the data?
135, 149, 156, 112, 134, 141, 154, 116, 134, 156
The box plot that represents the data is option B.
What is a box plot?A box plot is known to be a method that is employed to demonstrate the locality and skewness of numerical data. This is carried out graphically and done through the quartiles of the given numerical data.
Rearranging the given data, we have:
112,116, 134, 134, 135, 141, 149, 154, 156, 156
The minimum value after rearranging = 112.
First Quartile, Q1 = 134.
Second Quartile, Q2 or Median = 135+141/2 = 276/2 = 138
Third Quartile, Q3 = 154
Largest figure = 156
The answer is the second figure.
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The height of a tree in feet over x years is modeled by the function f(x). f(x)=301+29e−0.5x which statements are true about the growth of the tree? select each correct answer. the tree's maximum height is limited to 30 ft. the tree is initially 2 ft tall. between the 5th and 7th years, the tree grows approximately 7 ft. after growing 15 ft, the tree's rate of growth decreases.
Final answer:
The tree's maximum height is not limited to 30 ft but approaches 301 ft. Initially, the tree is 30 ft tall, not 2 ft. To verify the growth between the 5th and 7th years, one must calculate f(5) and f(7). The rate of growth indeed decreases over time.
Explanation:
When analyzing the function f(x) = 301 + 29e^{-0.5x} to understand the growth pattern of a tree, it is apparent that some statements about the tree's growth can be identified as true or false.
The tree's maximum height is not limited to 30 ft; instead, the model suggests that the height approaches 301 ft as x increases indefinitely, because the exponential term decreases towards zero.The tree is initially 30 ft tall, not 2 ft tall, since f(0) = 301 + 29 × 1 = 330 ft.Between the 5th and 7th years, the growth can be calculated using f(5) and f(7) to determine if it grows approximately 7 ft during that period.After growing 15 ft, the rate of growth would decrease since the exponential function's growth rate decreases as x increases.If arc AXC = 235°, what is m∠ABC?
a. 117.5°
b. 60°
c. 55°
d. 125°
Answer:
The correct option is c.
Step-by-step explanation:
Given information: The measure of arc AXC is 235°. Let the center of the circle be O.
The sum of all disjoint arcs is 360°. So,
[tex]Arc(AXC)+Arc(AC)=360^{\circ}[/tex]
[tex]235^{\circ}+Arc(AC)=360^{\circ}[/tex]
[tex]Arc(AC)=360^{\circ}-235^{\circ}[/tex]
[tex]Arc(AC)=125^{\circ}[/tex]
[tex]\angle AOC=125^{\circ}[/tex]
The measure of arc AC is 125°.
Line BA and BC are tangent on the circle O from the same point, so the sum of opposite angles of the quadrilateral is 180°.
[tex]\angle AOC+\angle ABC=180^{\circ}[/tex]
[tex]125^{\circ}+\angle ABC=180^{\circ}[/tex]
[tex]\angle ABC=180^{\circ}-125^{\circ}[/tex]
[tex]\angle ABC=55^{\circ}[/tex]
The measure of angle ABC is 55°. Therefore the correct option is c.
On a rectangular soccer field, Sang is standing on the goal line 20 yards from the corner post. Jazmin is standing 99 yards from the same corner post on the nearest adjacent side of the field. What is the distance from Sang to Jazmin?
A.119 yards
B.101 yards
C.10,201 yards
D.1,980 yards
Stephanie rdes her bike 2 miles to the post office, and then another 50 yards to the train station. How many yards long was her trip?
Which number would it be if rounded to the nearest foot
7191.51
A. 7191 FT
OR
B. 7192 FT
Write a single algebraic rule for the series of transformations: a reflection about the x-axis, a rotation of 90 degrees clockwise, and a translation of 4 units right and 2 units down.
Let d(t) =6t^2 be the distance function, find the average velocity from (4, 4.1)
24 inches is 250% of what length
Find the value of the lesser root of x^2-6x+8=0
Answer:
The value of lesser root is:
x=2
Step-by-step explanation:
We are given a quadratic equation in terms of variable " x " as:
[tex]x^2-6x+8=0[/tex]
We know that for any quadratic equation of the type:
[tex]ax^2+bx+c=0[/tex]
The roots of x are calculated as:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Here we have:
a=1 , b=-6 and c=8
Hence, on solving for roots:
[tex]x=\dfrac{-(-6)\pm \sqrt{(-6)^2-4\times 1\times 8}}{2\times 1}\\\\\\x=\dfrac{6\pm \sqrt{36-32}}{2}\\\\\\x=\dfrac{6\pm \sqrt{4}}{2}\\\\\\x=\dfrac{6\pm 2}{2}[/tex]
Hence, we have:
[tex]x=\dfrac{6+2}{2}\ or\ x=\dfrac{6-2}{2}\\\\x=\dfrac{8}{2}\ or\ x=\dfrac{4}{2}\\\\\\x=4\ or\ x=2[/tex]
Hence, the value of lesser root is:
x=2
A card is drawn randomly from a standard deck of cards. you win $10 if the card is a spade or an ace. what is the probability that you will win the game?
Using the discriminant, how many real number solutions does this equation have? 3x^2 – 2 = 5x
i need help!!!!!!!!!!!!!!?!!!
Which transformation is a rotation?
Answer:
the answer is c.
Step-by-step explanation:
Rewrite 0.85 as a fraction in lowest terms.
Please help!!!
Use DeMoivre's theorem to evaluate the expression
[sqrt 3( cos 5pi/3 + i sin 5pi/3)]^4 ? write the answer in rectangular form
a. 9sqrt3/2 + 9/2 i
b. 9sqrt3/2 - 9/2 i
c. -9/2 - 9sqrt3/2 i
d. -9/2 + 9sqrt3/2 i
Answer:
Option d - [tex]\sqrt3(\cos (\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))^4=-\frac{9}{2}+\frac{9\sqrt3}{2}i[/tex]
Step-by-step explanation:
Given : [tex]\sqrt3(\cos (\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))^4[/tex]
To find : Use DeMoivre's theorem to evaluate the expression?
Solution :
DeMoivre's theorem state that, for complex number
If [tex]z = r(\cos\theta+ i\sin \theta)[/tex] then [tex]z^n = r^n(\cos n\theta+ i\sin n\theta)[/tex]
We have given,
[tex]\sqrt3(\cos (\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))^4[/tex]
On comparing [tex]r=\sqrt3[/tex] and n=4
Applying DeMoivre's theorem,
[tex]=(\sqrt3)^4(\cos 4(\frac{5\pi}{3})+i\sin4(\frac{5\pi}{3}))[/tex]
[tex]=9(\cos (\frac{20\pi}{3})+i\sin(\frac{20\pi}{3}))[/tex]
[tex]=9(\cos (6\pi+\frac{2\pi}{3})+i\sin(6\pi+\frac{2\pi}{3}))[/tex]
[tex]=9(\cos (\frac{2\pi}{3})+i\sin(\frac{2\pi}{3}))[/tex]
We know, the value of
[tex]\cos (\frac{2\pi}{3})=-\frac{1}{2},\sin (\frac{2\pi}{3})=\frac{\sqrt3}{2}[/tex]
[tex]=9(-\frac{1}{2}+i\frac{\sqrt3}{2})[/tex]
[tex]=-\frac{9}{2}+i\frac{9\sqrt3}{2}[/tex]
Therefore, Option d is correct.
[tex]\sqrt3(\cos (\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))^4=-\frac{9}{2}+\frac{9\sqrt3}{2}i[/tex]
whats the equation of the line that passes through (3,8) and (6,0)
To begin this problem, we need to use the two points that we are given to find the slope of the line. Slope is defined as the change in y values divided by the change in x values, or rise/run, and is represented by the variable m.
m = (y1-y2)/(x1-x2) = (8-0)/(3-6) = 8/(-3) = -8/3
Now, we can use the slope and one of the points from our given values to create an equation of the line in point-slope form.
y = m(x-h) + k, where a point on the line is (h,k)
y = -8/3(x - 3) + 8
Now, we can distribute our slope and simplify through addition.
y = -8/3x + 8 + 8
y = -8/3x + 16
Therefore, your answer is y = -8/3x + 16.
Hope this helps!
What is the equation of the circle whose center and radius are given.
center ( 7, -3), radius = 7
Can someone help me please?
Write the equation for finding the nth term of the sequence. 18, 14, 10
A residual plot is shown. Which statements are true about the residual plot and the equation for the line of best fit for the data? Check all that apply.
The equation for the line of best fit is not a good approximation for the data because the points have a curved pattern.
The equation for the line of best fit is a good approximation for the data because the points are random, having no pattern.
The residual plot has a linear pattern.
The points of the residual plot are spread evenly above and below the x-axis.
The residual plot has the pattern of a curve.
The equation for the line of best fit is not a good approximation for the data because the points have a linear pattern
Only right answers, please. This is important for my grade.
Answer:
answer is 1 & 3 on edg
Step-by-step explanation:
What is the solution set of (x - 2)(x - 3) = 2?
a. {1, 4}
b. {2, 3}
c. {4, 5}
Factor this trinomial completely.
10x2 + 7x – 12
A. (2x + 3)(5x – 4)
B. (x + 4)(10x – 3)
C. (x + 3)(10x – 4)
D. (2x + 4)(5x – 3)
The trinomial "10[tex]x^2[/tex] + 7x - 12" is factored by finding two numbers that multiply to -120 and add up to 7, which are 15 and -8. Split the middle term, group, and factor by grouping to get (2x + 3)(5x - 4), which is option A.
Explanation:To factor the trinomial "10x2 + 7x − 12" completely, you want to find two binomials that, when multiplied together, will give you the original trinomial. To do this, you will need two numbers that multiply to give you the product of the coefficient of the x2 term (which is 10) and the constant term (which is −12), which equals −120, and also add up to the coefficient of the x term (which is 7).
The two numbers that meet these criteria are 15 and −8, since (15)(−8) = −120 and 15 + (−8) = 7. Next, split the middle term of the trinomial using these two numbers:
10x2 + 15x − 8x − 12
Now, group the terms:
(10x2 + 15x) − (8x + 12)
Factor out the greatest common factor from each group:
5x(2x + 3) − 4(2x + 3)
Finally, factor out the common binomial factor:
(2x + 3)(5x − 4)
Therefore, the correct factorization of the trinomial 10x2 + 7x − 12 is (2x + 3)(5x − 4), which corresponds to option A.
Cam rode her bike 5 times as far as Dante did. Dante rode 187 meters farther than Michael did. Cam rode 15.25 Kilometers. How many meters did Michael ride? Explain how you know you got your answer
It was found that Michael rode 2863 meters.
To find out how many meters Michael rode, we first need to establish the relationship between the distances Cam, Dante, and Michael rode. According to the problem, Cam rode 5 times as far as Dante did. If Cam rode 15.25 kilometers, we first convert this to meters by multiplying by 1000 (since there are 1000 meters in a kilometer):
15.25 km × 1000 = 15250 meters.
Now that we know Cam rode 15250 meters and that this is 5 times the distance Dante rode, we can find Dante’s distance:
15250 meters / 5 = 3050 meters.
Dante rode 3050 meters, which is 187 meters farther than Michael did. To find the distance Michael rode, we subtract 187 meters from Dante’s distance:
3050 meters - 187 meters = 2863 meters.
Therefore, Michael rode 2863 meters.