Answers
Answer:
Option A, (x + 2)² + (y - 1) = 9
Explanation:
The equation form of a circle is (x - h)² + (y - k)² = r², where the center is ordered pair (h, k) and r represents the radius.
From the given information, the center is point (-2, 1) and the radius (r) is 3 units. With this, we can plug the information in and simplify:
(x - (-2))² + (y - (1))² = (3)²
(x + 2)² + (y - 1)² = 9
The equation for the given circle is (x + 2)² + (y - 1)² = 9
Related Questions
Using the law of cosines, a=2.2
Use your answer above to find m<B, to the nearest degree. m<B=__
Answers
Explanation:
1) Law of cosines:
In a triangle with sides a, b, c whose opposite angles are, respectively, A, B and C, the law of cosines states:
b² = a² + c² - 2 (a)(c) cos (B)
2) In the triangle of the figure you have
b = 4.0
B = ?
a = 2.2
c = 3.7
⇒ (4.0)² = (2.2)² + (3.7)² - 2 (2.2) (3.7) cos(B)
⇒ 16 = 4.84 + 13.69 - 16.28cos(B)
⇒ 16.28 cos(B) = 4.84 + 13.69 - 16 = 2.53
⇒ cos(B) = 2.53 / 16.28
⇒ X = arccos(2.53 / 16.28 ) = 81.06° ≈ 81°
Answer:
81
Step-by-step explanation:
Graph 12x-9y=36 please???
Answers
Answer:
The graph for 12x-9y=36 is given below
Step-by-step explanation:
The graph for 12x-9y=36 is given below.
[tex]12x-9y=36\\\frac{12x}{36}+\frac{9y}{-36}=1\\\frac{x}{3}+\frac{y}{-4}=1[/tex]
So x intercept is 3 and y intercept is -4.
The required graph is shown below which represents the equation 12x - 9y = 36.
To graph the equation 12x-9y=36, we can rearrange it to slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept.
First, solve for y by subtracting 12x from both sides and then dividing by -9. This gives us y=-4/3x+4.
Now we can see that the slope is -4/3 and the y-intercept is 4.
To graph this line, we can start at the y-intercept of (0,4) and then use the slope to find another point.
Since the slope is negative, we can move down 4 units (which is the denominator of the slope) and then move to the right 3 units (which is the numerator of the slope) to get another point at (3,0).
We can then draw a straight line through these two points to graph the equation.
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ABCD and DECF are both squares. If AC = 28 millimeters, what is the perimeter of DECF?
Answers
we know that
in the square ABCD
diagonal AC is equal to diagonal BD
EC=AC/2--------> EC=28/2-----> 14 mm
EC is the length side of the square DECF
so
perimeter of the square DECF=4*EC------> 4*14-----> 56 mm
the answer is
56 mm
Monica is shopping for candy for her wedding and needs lollipops and gummy bears for a display she is making for the reception. Lollipops are $1 per pound and gummy bears are $0.75 per pound. She knows she wants to spend exactly $15 on candy. If she spent $9 on lollipops, which of the following is the number of pounds of gummy bears she purchased?
6 8 9 12
Answers
We have been given that she wants to spend exactly $15 on candy.
Also, she spent $9 on lollipops. It means she spent [tex]15-9= $6[/tex] on gummy bears.
Also, we have been given that the cost of gummy bears are $0.75 per pound.
Thus, in 1$ she can purchase [tex]\frac{0.75}{6}[/tex] pounds of gummy bears.
Hence, in $6, she can purchase
[tex]\frac{1}{0.75} \times 6\\ \\ =8[/tex]
Therefore, she purchased 8 pounds of gummy bears.
Kim spun the spinner 75 times and got a three 30 times. What is the experimental probability?
Answers
So 30 / 75 = 0.4 = 40%
Hope this helps.
19. # Q Find the missing side length
Answers
the missing is the hypotenuse = √(6² + 8² ) = √100 = 10
The correct answer is the second
Hope this Helped!
;D
Brainliest??
Charles owed $390 to his friend. On the first day Charles paid his friend $12. Each following week the amount Charles paid his friend increased by the same amount. After 10 payments, Charles had paid back the full amount. By how much did each payment increase?
Answers
Amount owe=$390
Payment=$10
Number of payments=10
thus using the formula:
A=P(1+r)^n
plugging the values we get:
390=10(1+r)^10
solving for r we get
39=(1+r)^10
r=0.4425
thus the amount increased by 44.25%
find any points of discontinuity for each rational function. Sketch a graph. Describe any verticals or horizontal asympyoyes and any holes
(X^2-4)/(X+2)(X^2-49)
Answers
y = (x^2 -4)/((x +2)(x^2 -49))
the numerator factors to (x -2)(x +2), so the factor of (x +2) will cancel with that in the denominator, leaving
y = (x -2)/(x^2 -49)
There are points of discontinuity at the hole, x=-2, and at each of the vertical asymptotes, at x=-7, +7.
The horizontal asymptote is y=0.
To find the points of discontinuity and sketch the graph of the rational function (x^2-4)/(x+2)(x^2-49), we need to determine the values of x that make the denominator equal to zero. We find that x = -2, x = 7, and x = -7 are the points of discontinuity. We can then sketch the graph by plotting the vertical asymptotes at x = -2, x = 7, and x = -7, and determining the behavior of the function on each side of those points.
Explanation:To find the points of discontinuity for the rational function (x^2-4)/(x+2)(x^2-49), we need to determine where the denominator is equal to zero. The denominator has two factors, (x+2) and (x^2-49). Setting each factor equal to zero, we find that x = -2, x = 7, and x = -7. These are the points where the function has vertical asymptotes or holes.
To sketch the graph, we can start by plotting the vertical asymptotes at x = -2, x = 7, and x = -7. Next, we can examine the sign of the function on each side of the vertical asymptotes to determine the behavior of the graph. Finally, we can plot any holes in the graph at the corresponding x-values.
Additionally, we should determine if there are any horizontal asymptotes. For rational functions, horizontal asymptotes occur when the degree of the numerator is less than or equal to the degree of the denominator. In this case, the degree of the numerator is 2 and the degree of the denominator is 3, so there is no horizontal asymptote.
Factor 4x^2-20x-144
Answers
In the diagram, the base of the tower is at point H, and the top of the tower is at point F. If the distance from the base of the tower to point G is 7x feet and the distance from the base of the tower to point E is 6x + 12 feet, find GE, the distance across the lake.
A. 84 feet
B.
94 feet
C. 168 feet
D. 186 feet
Answers
This problem can be solved using triangle similarities:
Consider the Pythagorean Theorem with the formula; c^2=a^2+b^2
let: a=height from base to point
b1=base of the first triangle formed
b2-base of the second triangle formed
c1=c2= hypotenuse of the two triangles,
note:
they have equal hypotenuse and share the same height, thus a1=a2
sqrt[(a^2+(7x)^2)]=sqrt[a^2+(6x+12)^2]
sqrt(49x^2) =sqrt[(6x+12)^2]
7x=6x+12
x=12
GE=7x+6x+12
GE=7(12)+6(12)+12
GE= 168 feet
Thus, the answer is:
C. 168 feet
ABC has coordinates of A(–5, –7), B(6, –3), and C(2, 7). Find the coordinates of its image after a dilation centered at the origin with a scale factor of 2.
Answers
A' = 2A = (-10, -14)
B' = 2B = (12, -6)
C' = 2C = (4, 14)
The coordinates of the image after dilation with a scale factor of 2 are A'(-10, -14), B'(12, -6), C'(4, 14).
Explanation:Your question involves geometry and specifically, dilation transformations. A dilation is a transformation that moves each point along the ray from the center of dilation to the point. The number given as the scale factor tells you how much to move. In this case, we are asked to dilate the given points with a scale factor of 2 centered at the origin (0,0).
So, each coordinate of the original triangle should be multiplied by 2. Let's find each coordinate after dilation:
A: -5*2, -7*2 = A'(-10, -14)B: 6*2, -3*2 = B'(12, -6)C: 2*2, 7*2 = C'(4, 14)So, the coordinates of the image after a dilation with a scale factor of 2 are A'(-10, -14), B'(12, -6), and C'(4, 14).
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Express this equation in word form:
5 + ( 2 x 6 )
Answers
The parenthesis equation is two times six. Then out of that is 5. So it's 5 plus 2 times six.
-DustinBR
Alice collected donations of $50, $125, $10, $210, $50, $24, and $175 for charity. What is the mean of her collections?
Answers
To find the mean you add all the values up and divide the sum by the amount of numbers added
50 + 125 + 10 + 210 + 50 + 24 + 175 = 644
Divide the sum by the amount of numbers added
644 / 7 = 92
The answer is $92
Hope this helps!
Answer:92
Step-by-step explanation:
92
Lupe can ride her bike at a rate of 20 mph when there is no wind. On one particular day, she rode 2 miles against the wind and noticed that it took her the same amount of time as it did to ride 3 miles with the wind. How fast was the wind blowing
Answers
40+2w=60-3w
5w=20
w=4mph
The speed of the wind is 4 mph.
Let, the speed of the wind is W mph.
When Lupe rides with the wind, her effective speed is 20 + W mph, and when she rides against the wind, her effective speed is 20 - W mph.
We are given two pieces of information:
Lupe rode 2 miles against the wind, and it took her the same amount of time as riding 3 miles with the wind.
The time taken to cover a distance is equal to the distance divided by the speed.
Using this information, we can set up two equations:
Time taken against the wind = Time taken with the wind
2 / (20 - W) = 3 / (20 + W)
Now, let's solve for W:
2(20 + W) = 3(20 - W)
40 + 2W = 60 - 3W
5W = 20
W = 20 / 5
W = 4 mph
The speed of the wind is 4 mph.
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Please answer this question I need it fast:
Together, Mary Sue and Betty have 603 necklaces. Mary Sue has 115 more necklaces than Betty. How many necklaces does Betty have?
Answers
M = necklaces owned by Mary Sue
B = necklaces owned by Betty
You know that:
M + B = 603
M - B = 115
Therefore, when you have the sum and the difference of two numbers, in order to find the biggest number you have to sum the sum and the difference and divide it by 2, and in order to find the smallest number you have to subtract the difference from the sum and divide it by 2:
M = [(M + B) + (M - B)] ÷ 2
= [603 + 115] ÷ 2
= 359
B = [(M + B) - (M - B)] ÷ 2
= [603 - 115] ÷ 2
= 244
Hence, Mary Sue has 359 necklaces and Betty has 244 necklaces.
Answer:
mary sue: 359, betty; 244
Step-by-step explanation:
⇔↓⊕㏒㏑∞
How many different ways are there to choose 10 donuts from 20 varieties if at most 4 chocolate donuts are chosen?
Answers
If instead exactly 3 donuts are chocolate, then you have [tex]19^{17}[/tex] ways of choosing the others.
Continuing the pattern, we see that the total number of ways to choose up to 4 chocolate donuts is given by
[tex]\displaystyle\sum_{c=0}^419^{20-c}=19^{20}\sum_{c=0}^419^{-c}[/tex]
which comes out to be
39 678 289 291 775 535 447 366 041
Blue cassests hold 45 min. Of music
Green cassets hold 55 min. Of music
If Niko has 16 cassets containing 830 min. Of music
How many are blue? And how many are green?
Answers
Thus the total number of cassets will be:
b+g=16
hence
g=16-b.......i
The total amount was:
45b+55g=830..ii
plugging i in ii we get:
45b+55(16-b)=830
45b+880-55b=830
simplifying
45b-55b=830-880
-10b=-50
thus
b=5
hence
g=16-5=11
number of blue cassets was 5 and that of green was 11
A person whose eye level is 1.5 meters above the ground is standing 75 meters from the base of the jin mao building in shanghai, china. the person estimates the angle of elevation to the top of the building is about 80º. what is the approximate height of the building
Answers
we know that
in the right triangle ABC
tan 80°=opposite side angle 80°/adjacent side angle 80°
tan 80°=BC/AC----->BC=AC*tan 80°-----> BC=75*tan 80°---> BC=425.35 m
the approximate height of the building=BC+eye level
the approximate height of the building=425.35+1.5----> 426.85 m
the answer is
the approximate height of the building is 426.85 m
The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The height of the building from the ground is 426.85 meters.
What is Tangent (Tanθ)?The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
As it is given that the angle of elevation from the person's view is 80°, while the distance between the person and the base of the building is 75 meters, therefore, using the trigonometric function the height of the building top from the person eye level is,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}\\\\\\Tan(80^o) = \dfrac{\text{Height of the building}}{75\ meters}\\\\\\\text{Height of the building} = 75 \times tan(80^o) = 425.35\ meters[/tex]
Now, we know the height of the building top from a person's eye level, and we also know the person's eye level as well, therefore, the height of the building can be written as,
[tex]\text{Height of the building} = 425.35 + 1.5 = 426.85\rm\ meters[/tex]
Hence, the height of the building from the ground is 426.85 meters.
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a(3x-8)=b-18x
what is a value?
what is b value?
Answers
a*(3x-8)=b-18x
3ax-8a=18x+b
The only way for this to happen (non-trivially) is if the coefficients of x are equal, and the constant terms are equal
so
3ax=18x-----> 3a=18--------> a=6
-8a=b---------> b=-8*6-------> b=-48
the answer is
a=6
b=-48
determine the domain of the function h(x)= 9x/x(x^2-36)
Answers
Final answer:
The domain of the function h(x)=9x/x(x²-36) is all real numbers except 0, 6, and -6, because the function is undefined at these points.
In conclusion, the domain of h(x) is x ∈ ℝ, x ≠ 0, x ≠ 6, x ≠ -6.
Explanation:
The question asks to determine the domain of the function h(x) = 9x / x(x² - 36).
The domain of a function consists of all the real numbers x for which the function is defined. In this case, the function will be undefined when the denominator is zero because division by zero is not defined in mathematics.
To find these values, we set the denominator equal to zero and solve the resulting equation:
x(x² - 36) = 0.This can be factored further as x(x - 6)(x + 6) = 0, which gives us the zero points of x = 0, x = 6, and x = -6.
Therefore, the domain of h(x) is all real numbers except 0, 6, and -6.
In conclusion, the domain of h(x) is x ∈ ℝ, x ≠ 0, x ≠ 6, x ≠ -6.
How many positive integers $N$ from 1 to 5000 satisfy both congruences, $N\equiv 5\pmod{12}$ and $N\equiv 11\pmod{13}$?
Answers
So, we found that [tex]N=5\cdot13+11\cdot12^2=1649[/tex], but the least positive solution is [tex]1649\equiv89\pmod{\underbrace{156}_{12\cdot 13}}[/tex], and in general we can have [tex]N=89+156k[/tex] for any integer [tex]k[/tex].
Now, since [tex]5000=32\cdot156+8[/tex], or [tex]4992=32\cdot156[/tex], we know that there are 32 possible integers [tex]N[/tex] that satisfy the congruences.
Kendrick travel 2/3 mile to his friend’s house.He cycles 3/4 of his distance and walks the rest of the way.What fraction of a mile did he cycle?
Answers
solve by substitution 3x+2y=-5, 2x-5y=-16
Answers
The solution to the system of equations is [tex]\(x = -3\)[/tex] and [tex]\(y = 2\).[/tex]
let's solve the system of equations using the substitution method.
Given:
1. [tex]\(3x + 2y = -5\)[/tex]
2.[tex]\(2x - 5y = -16\)[/tex]
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve equation 1 for [tex]\(x\):[/tex]
[tex]\[3x = -2y - 5\][/tex]
[tex]\[x = \frac{-2y - 5}{3}\][/tex]
Step 2: Substitute the expression for [tex]\(x\)[/tex]from step 1 into the other equation.
Substitute [tex]\(x = \frac{-2y - 5}{3}\)[/tex] into equation 2:
[tex]\[2\left(\frac{-2y - 5}{3}\right) - 5y = -16\][/tex]
Step 3: Solve for [tex]\(y\).[/tex]
[tex]\[ \frac{-4y - 10}{3} - 5y = -16 \][/tex]
[tex]\[ -4y - 10 - 15y = -48 \][/tex]
[tex]\[ -19y - 10 = -48 \][/tex]
[tex]\[ -19y = -38 \][/tex]
[tex]\[ y = 2 \][/tex]
Step 4: Substitute the value of [tex]\(y\)[/tex] into one of the original equations to solve for [tex]\(x\).[/tex]
Let's use equation 1:
[tex]\[3x + 2(2) = -5\][/tex]
[tex]\[3x + 4 = -5\][/tex]
[tex]\[3x = -9\][/tex]
[tex]\[x = -3\][/tex]
So, the solution to the system of equations is [tex]\(x = -3\)[/tex] and [tex]\(y = 2\).[/tex]
Complete question:
solve by substitution 3x+2y=-5, 2x-5y=-16
When the sum of 5 and three times a positive number is subtracted from the square of the number, 0 results. Find the number.
Answers
[tex]Use\ the\ quadratic\ formula:\\a^2x+bx+c=0\\\\\Delta=b^2-4ac\\\\if\ \Delta > 0\ then\ x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\if\ \Delta=0\ then\ x_0=\dfrac{-b}{2a}\\\\if\ \Delta < 0\ then\ no\ solution[/tex]
[tex]x^2-3x-5=0\\\\a=1;\ b=-3;\ c=-5\\\\\Delta=(-3)^2-4\cdot1\cdot(-5)+3+20=29 \ \textgreater \ 0\\\\\sqrt\Delta=\sqrt{29}\\\\x_1=\dfrac{3-\sqrt{29}}{2\cdot1}=\dfrac{3-\sqrt{29}}{2} \ \textless \ 0\\\\x_2=\dfrac{3+\sqrt{29}}{2\cdot1}=\dfrac{3+\sqrt{29}}{2} \ \textgreater \ 0[/tex]
[tex]Answer:\ \boxed{x=\dfrac{3+\sqrt{29}}{2}}[/tex]
To solve for the positive number when the sum of 5 and three times the number is subtracted from the square of the number to yield zero, set up and solve the quadratic equation x^2 - 3x - 5 = 0 using the quadratic formula.
Explanation:The student has asked for help in finding a positive number when the sum of 5 and three times the number is subtracted from the square of the number, and the result is 0. This involves setting up a quadratic equation and solving for the number.
Let's denote this positive number as 'x'. According to the problem statement, the equation can be written as:
x2 - (5 + 3x) = 0.
We can then expand and simplify this equation:
x2 - 5 - 3x = 0
And, rearrange it into standard quadratic form:
x2 - 3x - 5 = 0
Next, we can either factorize this equation, if possible, or use the quadratic formula to find the value of 'x' that satisfies the equation. Since this equation does not factor neatly, we use the quadratic formula:
x = ∛2 - 4ac) / 2a
In this case, a = 1, b = -3, and c = -5. Plugging these into the quadratic formula, we find the two possible solutions for x. Only the positive solution is relevant since the problem states that the number is positive.
Dan uses a compass to draw an arc from Q, as shown. He wants to construct a line segment through R that makes the same angle with line segment QR as line segment PQ.
first chart
Which figure shows the next step to construct a congruent angle at R?
Charts 2 3 4 & 5
Answers
Answer:
Chart 2.
Step-by-step explanation:
In the figure Dan has constructed an angle at point Q.He wants to cinstruct an angle ar point R which is congruent to angle made at point Q.To construct the angle at point R Dan needs to draw an arc at point R .He will put the compass on point R and draw an arc .This is shown in the figure 2.
The figure is added below.
which values of x are solutions of the equation x^3+ x^2-2x=0
Answers
Please help confused
Answers
add the numbers in the set and divide by the quantity of numbers:
9 + 15 + 22 + 45 + 50 +60 + 65 = 266
266 / 7 = 38
the mean = 38
the absolute deviation is subtracting the number from the mean: ( all numbers are positive)
38 - 9 = 29
38 - 15 = 23
38-22 = 16
45-38 = 7
50 -38 = 12
60-38 = 22
65-38 = 27
Which expression has a value closest to 1? (Use 3.14 as the value of .)
Answers
b) square root 75 - square root 74 = 8.660254038-8.602325267=0.058
c) square root 37 - square root 26 = 6.082762530-5.099019514=0.98
s) 3 square root 5 - square root 20 / square root 2 =
3(2.236067978) - 4.472135955/1.414213562=6.708203934-3.162277661=
3.546
Answer: Option c square root 37 - square root 26
Answer:
C)square 37 - square root 26
Step-by-step explanation:
Amy volunteers at an animal shelter. She worked 10 hours in March, 12 hours in April, 14 hours in May, and 16 hours in June. If the pattern continues, how many hours will she work in December?
Answers
By continuing the pattern of Amy increasing her volunteer hours by 2 each month, she will work for 30 hours in December.
Explanation:To find out how many hours Amy will work in December, we must first identify the number of terms between June and December.
Counting inclusively, we see that there are seven months between June and December (June, July, August, September, October, November, December), which means we should look for the 7th term after June to find the number of hours Amy will work in December.
Since we have established an increase of 2 hours each month, we can calculate this by adding 7 terms of an arithmetic progression to Amy's last known volunteering hours.
To do this, we use the explicit formula for an arithmetic sequence:
Tn = a + (n - 1) * d,
where Tn is the term we wish to find, a is the first term in the sequence, n is the position of the term in the sequence, and d is the common difference between terms. Amy's last known volunteering hours in June (the 4th term in the sequence) were 16, with a common difference of 2.
Adding 7 intervals of 2 hours each gives us 14 additional hours by December.
Therefore, we add this to the 16 hours she worked in June: 16 + 14 = 30 hours.
Amy is expected to volunteer for 30 hours in December.
Adam charges 20$ to mow his neighbor's lawn every 2 weeks for the 18 weeks of grass growing season. he wants to but a new
Answers
Since Adam's expenses exceed his earnings, he will have a negative net earnings. Therefore, Adam will not earn any money this season. In fact, he will have a net loss of $7.50.
To calculate how much Adam will earn this season, subtract his expenses from his total earnings.
Earnings per mowing session: $20
Number of mowing sessions in the grass-growing season: 18 weeks / 2 weeks = 9 sessions
Total earnings: $20 per session * 9 sessions = $180
Expenses:
Cost of the lawn mower: $165
Cost of gasoline per session: $2.50 per session * 9 sessions = $22.50
Total expenses: $165 + $22.50 = $187.50
To find Adam's net earnings, subtract his expenses from his total earnings:
Net earnings = Total earnings - Total expenses
Net earnings = $180 - $187.50
Net earnings = -$7.50
Since Adam's expenses exceed his earnings, he will have a negative net earnings. Therefore, Adam will not earn any money this season. In fact, he will have a net loss of $7.50.
Adam charges $20 to mow his neighbors lawn every 2 weeks for the 18 weeks of grass-growing season. He wants to buy a nice lawn mower for $165 and gasoline costs $2.50 every 2 weeks. How much will Adam earn this season?