Answer:
Equation of the circle
(x - 0.7)² + (y - 1.3)² = 12.58
Step-by-step explanation:
The formula for the equation of a circle is given as:
(x - a)² + (y - b)² = r²,
where(a, b) is the center of the circle and r = radius of the circle.
a) We are told in the question that the equation of the circle passes through point(2, -2)
Hence,
Substituting 2 for x and -2 for y in the equation of the circle.
(x - a)² + (y - b)² = r²
(2 - a)² +(-2 - b)² = r²
Expanding the bracket
(2 - a) (2 - a) + (-2 - b)(-2 - b) = r²
4 - 2a - 2a +a² +4 +2b +2b +b² = r²
4 - 4a + a² + 4 + 4b + b² = r²
a² + b² -4a + 4b + 4 + 4 = r²
a² + b² -4a + 4b + 8 = r²............Equation 1
We are also told that the equation of the circle also passes through point (3,4) also, where 3 = x and 4 = y
Hence,
Substituting 3 for x and 4 for y in the equation of the circle.
(x - a)² + (y - b)² = r²
(3 - a)² +(4 - b)² = r²
Expanding the bracket
(3 - a) (3 - a) + (4 - b)(4- b) = r²
9 - 3a - 3a +a² +16 -4b -4b +b² = r²
9 -6a + a² + 16 -8b + b² = r²
a² + b² -6a -8b + 9 + 16 = r²
a² + b² -6a -8b + 25 = r²..........Equation 2
The next step would be to subtract Equation 1 from Equation 2
a² + b² -4a + 4b + 8 - (a² + b² -6a -8b + 25) = r² - r²
a² + b² -4a + 4b + 8 - a² - b² +6a +8b - -25= r² - r²
Collecting like terms
a² - a² + b² - b² - 4a + 6a + 4b + 8b +8- 25 = 0
2a + 12b -17 = 0
2a + 12b = 17...........Equation 3
Step 2
We are going to have to find the values of a and b in other to get our equation of the circle.
Since the center of the circle(a, b) lies on x + y = 2
Therefore, we have
a + b = 2
a = 2 - b
2a + 12b = 17 ..........Equation 3
Substituting 2 - b for a in
2(2 - b) + 12b = 17
4 - 2b + 12b = 17
4 + 10b = 17
10b = 17 - 4
10b = 13
b = 13/10
b = 1.3
Substituting 1.3 for b in
a + b = 2
a + 1.3 = 2
a = 2 - 1.3
a = 0.7
hence, a = 0.7, b = 1.3
Step 3
We have to find the value of r using points (2, -2)
(x - a)² + (y - b)² = r²
Where x = 2 and y = -2
(-2 - 0.7)² + (-2 - 1.3)² = r²
(-2.7)² + (-3.3)² = r²
1.69 + 10.89 = r²
r² = 12.58
r = √12.58 = 3.55
Step 4
The formula for the equation of a circle is given as:
(x - a)² + (y - b)² = r²,
where(a, b) is the center of the circle and r = radius of the circle
a = 0.7
b = 1.3
r² = 12.58
Equation of the circle =
(x - 0.7)² + (y - 1.3)² = 12.58
Please help I’ll mark brainliest
Answer:
A is the correct answer
Hope this helps :)
Answer:
A is the answerStep-by-step explanation:
This is because you have to substitute numbers.
So,
f(x) = 4 * 2^x
f(1) = 4 * 2^1 = 8
f(2) = 4 * 2^2 = 16
f(3) = 4 * 2^3 = 32
This shows exponential growth. Hope this helped!
Hope this helps,
Kavitha
at the rate of 15 per 6 oz. bar of chocolate, how much would a pound
Answer:
40
Step-by-step explanation:
We know there are 16 oz in a pound
We can use ratios
15 x
----- = ----------
6 oz 16 oz
Using cross products
15 * 16 = 6x
240 = 6x
divide by 6
240/6 = 6x/6
40 =x
A polygon with 9 sides is shown. An exterior angle has a measure of x degrees. In the regular nonagon shown, what is the measure of angle x? 36° 40° 45° 60°
Answer:
40°Step-by-step explanation:
First we must know that the sum of all the exterior angle of all polygons is 360°.
Measure of each angle of a polygon = 360°/total sides of the polygon
Since a regular nonagon has 9 sides, the measure of each angle of a polygon is expressed as thus;
Measure of each angle of a polygon = 360°/9
Measure of each angle of a polygon = 40°
Hence the measure of an exterior angle x of a nonagon is 40°
Answer:
B in Edg
Step-by-step explanation:
Expand And Simplify
2(3a - 2b) + b
Answer:
the expansion is 6a-4b+b
the simplification is 6a-3b
Answer:Hey there...
Step-by-step explanation: 2(3a - 2b) + b
Apply Distributive property
(2*3a - 2*2b) + b
( 6a - 4b) + b
2b + b
= 3b
Hope this helps :)
Which describes how square S could be transformed to square S prime in two steps? Assume that the center of dilation is the origin. On a coordinate plane, square S has points (0, 0), (5, 0), (5, negative 5), (0, negative 5). Square S prime has points (0, 1), (0, 3), (2, 3), (2, 1). a dilation by a scale factor of Two-fifths and then a translation of 3 units up a dilation by a scale factor of Two-fifths and then a reflection across the x-axis a dilation by a scale factor of Five-halves and then a translation of 3 units up a dilation by a scale factor of Five-halves and then a reflection across the x-axis
Answer:
The correct option is;
A dilation by a scale factor of Two-fifths and then a translation of 3 units up
Step-by-step explanation:
Given that the coordinates of the vertices of square S are
(0, 0), (5, 0), (5, -5), (0, -5)
Given that the coordinates of the vertices of square S' are
(0, 1), (0, 3), (2, 3), (2, 1)
We have;
Length of side, s, for square S is s = √((y₂ - y₁)² + (x₂ - x₁)²)
Where;
(x₁, y₁) and (x₂, y₂) are the coordinates of two consecutive vertices
When (x₁, y₁) = (0, 0) and (x₂, y₂) = (5, 0), we have;
s = √((y₂ - y₁)² + (x₂ - x₁)²) = s₁ = √((0 - 0)² + (5 - 0)²) = √(5)² = 5
For square S', where (x₁, y₁) = (0, 1) and (x₂, y₂) = (0, 3)
Length of side, s₂, for square S' is s₂ = √((3 - 1)² + (0 - 0)²) = √(2)² = 2
Therefore;
The transformation of square S to S' involves a dilation of s₂/s₁ = 2/5
The after the dilation (about the origin), the coordinates of S becomes;
(0, 0) transformed to (remains at) (0, 0) ....center of dilation
(5, 0) transformed to (5×2/5, 0) = (2, 0)
(5, -5) transformed to (2, -2)
(0, -5) transformed to (0, -2)
Comparison of (0, 0), (2, 0), (2, -2), (0, -2) and (0, 1), (0, 3), (2, 3), (2, 1) shows that the orientation is the same;
For (0, 0), (2, 0), (2, -2), (0, -2) we have;
(0, 0), (2, 0) the same y-values, (∴parallel to the x-axis)
(2, -2), (0, -2) the same y-values, (∴parallel to the x-axis)
For (0, 1), (0, 3), (2, 3), (2, 1) we have;
(0, 3), (2, 3) the same y-values, (∴parallel to the x-axis)
(0, 1), (2, 1) the same y-values, (∴parallel to the x-axis)
Therefore, the lowermost point closest to the y-axis in (0, 0), (2, 0), (2, -2), (0, -2) which is (0, -2) is translated to the lowermost point closest to the y-axis in (0, 1), (0, 3), (2, 3), (2, 1) which is (0, 1)
That is (0, -2) is translated to (0, 1) which shows that the translation is T((0 - 0), (1 - (-2)) = T(0, 3) or 3 units up
The correct option is therefore a dilation by a scale factor of Two-fifths and then a translation of 3 units up.
Answer:
a
Step-by-step explanation:
How does the graph of y = a(x – h)2 + k change if the value of h is doubled? The vertex of the graph moves to a point twice as far from the x-axis. The vertex of the graph moves to a point twice as far from the y-axis. The vertex of the graph moves to a point half as far from the x-axis. The vertex of the graph moves to a point half as far from the y-axis.
Answer:
The vertex of the graph moves to a point twice as far from the y-axis.
Step-by-step explanation:
How does the graph of y = a(x – h)2 + k change if the value of h is doubled?
The vertex of the graph moves to a point twice as far from the x-axis.
The vertex of the graph moves to a point twice as far from the y-axis.because the role of h is to indicate the distance of the vertex from the y-axis.
The vertex of the graph moves to a point half as far from the x-axis.
The vertex of the graph moves to a point half as far from the y-axis.
Transformation involves changing the position of a function.
When h is doubled in [tex]\mathbf{y = a(x - h)^2 + k}[/tex], the vertex of the graph moves to a point twice as far from the y-axis.
The function is given as:
[tex]\mathbf{y = a(x - h)^2 + k}[/tex]
When the value of h is doubled, the new function becomes:
[tex]\mathbf{y' = a(x - 2h)^2 + k}[/tex]
Rewrite as:
[tex]\mathbf{y' = a(x - h- h)^2 + k}[/tex]
The above equation means that:
Function y will be translated to the right by h units
Assume the vertex is:
[tex]\mathbf{Vertex = (2,5)}[/tex]
The new vertex will be:
[tex]\mathbf{Vertex = (4,5)}[/tex]
Comparing the vertices, it means that:
The new function will have its vertex twice as far from the y-axis
Hence, option (b) is correct.
Read more about transformation at:
https://brainly.com/question/13801312
An oblique prism has trapezoidal bases and a vertical height of 10 units. An oblique trapezoidal prism is shown. The trapezoid has base lengths of x and 2 x, and a height of x. The distance between the 2 trapezoid bases is 20. The vertical height of the prism is 10. Which expression represents the volume of the prism? 10x3 cubic units 15x2 cubic units 20x3 cubic units 30x2 cubic units
Answer:
volume of trapezoidal prism = 15x^2 cubic units
Step-by-step explanation:
First, area of the trapezoidal bases.
Parallel sides measure x and 2x, for an average of 1.5x.
Height = x
Area of trapezoidal base = 1.5x*x = 1.5x^2
Volume of prism = area base * height
(length does not matter, height does)
= 1.5x^2 * 10 = 15x^2
The volume of the prism is 15x² cubic units if the oblique prism has trapezoidal bases and a vertical height of 10 units option (B) 15x² cubic units is correct.
What is a trapezoid?It is defined as the quadrilateral having four sides in which two sides are parallel to each other, it is a 2-dimensional geometry.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
It is given that:
An oblique prism has trapezoidal bases and a vertical height of 10 units.
As we know, the area of the trapezoidal bases:
From the figure:
Height = x
Area of trapezoidal base = (1.5x)(x) = 1.5x²
The volume of prism = area base×height
= 1.5x²×10 = 15x² cubic units
Thus, the volume of the prism is 15x² cubic units if the oblique prism has trapezoidal bases and a vertical height of 10 units option (B) 15x² cubic units is correct.
Learn more about the trapezoid here:
brainly.com/question/8643562
#SPJ6
ABCD is a square. Square A B C D is shown. A diagonal is drawn from point A to point C. The measure of angle B A C is question mark. What is the measure of angle BAC? 30° 45° 60° 90
Answer:
45°
Step-by-step explanation:
Since the diagonal cuts the square into two triangles, the angles b, a, and , c all add up to 180°. Because the shape is a square we know that one of the angles is right/90° meaning the two remaining angles are 45°. Angles a, and c had the diagonal drawn through so those two angles are each 45° and b is 90°, and since they are asking for bac we know that they want the middle angle, i.e angle A.
Since ABCD is a square, and AC is the diagonal of the square, therefore, the measure of angle BAC would be: B. 45°.
What is a Square?A square is a quadrilateral that has four interior angles of 90 degrees each, and also has four equal sides.The diagonal of a square bisects each vertex of the square into equal halves.Thus, since ABCD is a square, and AC is the diagonal of the square, therefore, the measure of angle BAC would be: B. 45°.
Learn more about a square on:
https://brainly.com/question/24579466
In a right triangle the lengths of the legs are a and b. Find the length of a
hypotenuse, if:
a =5, b =6.
PLEASE ANSWER ASAP
Answer:
7.8
Step-by-step explanation:
because if you square 5 and 6 you get 25 and 36. Add them together and you get 61. Square 61 to get 7.8102... which you can round to 7.8
The equation to find the hypotenuse of a right triangle is a^2+b^2=c^2
on the average 5 oranges will give 3 cupful of juice. if 2 cupfuls make a pint, how many oranges must be used to make 3 gallons of juice.
Answer:
90 oranges
Step-by-step explanation:
First, find out how many cupfuls are in 3 gallons of juice.
2 cups = 1 pint
2 pints = 1 quart
4 quarts = 1 gallon
16 cups = 1 gallon
48 cups = 3 gallons
For every 5 oranges, you get 3 cupfuls of juice. This gives you the ratio of 5/3. Multiply 48 cups, which is 3 gallons, by the ratio to find out how many oranges you will need.
48 × 5/3 = 90
You will need 90 oranges for 3 gallons of juice.
Answer:
80 oranges are used to make 3 gallons of juice
Step-by-step explanation:
1 gallon = 8 pint
3 gallons = 3 * 8 = 24 pint
1 pint = 2 cup full of juice
24 pint = 24 * 2 = 48 cups
Now, we have to find how many 3 cups are in 48. So, 48 ÷ 3 = 16
3 cup of juice is taken form 5 oranges.
Therefore, 16 groups of 3 cups of juice will be taken from 5 *16 = 80 oranges
Determine if the event shows uniform probability or not. You have a spinner with 8 equal spaces on it. Each space is numbered with a different integer between 1 and 8.
Answer:
it does show uniform probability.
Step-by-step explanation:
because the spaces are all equal, so there is an equal chance of every integer being picked.
Sarah’s room is in the shape of a rectangle that is 15 feet long and 11 feet wide. Which expression can she use to find the total amount of carpeting (in square feet) that she needs to cover the floor? A.15-11 B. 11x15 C.15+11 D. 2(15+11)
Answer:
The answer is choice B , 11 x 15
Step-by-step explanation:
To find area, you multiply one side by the adjacent side
11 and 15 are both adjacent, so you multiply to find the area of Sarah's room
Hope this helps !!!! Brainliest would be appreciated
Answer:
11x15
Step-by-step explanation:
it is the answer above because the dimensions of the room are 11 by 15 so written in an expression it is the answer above
a man buys a dozen cameras for $1800.He sells them at a profit of $36 each.Express his profit as a percentage of his selling price.
Step-by-step explanation:
The solution is the document i sent please check through.
Starting at sea level, a submarine descended at a constant rate to a depth of −5/6 mile relative to sea level in 4 minutes. What was the submarine's depth relative to sea level after the first minute? Answer with a fraction :3
Answer:
-5/24 miles
Step-by-step explanation:
The submarine descends at a rate of -5/6 miles every 4 minutes.
To find the depth of the submarine relative to sea level after the first minute, we have to multiply the rate of descent by he time spent (1 minute). That is:
[tex]\frac{\frac{-5}{6} }{4} * 1[/tex]
=> D = -5 / (6 * 4) = -5/24 miles
Therefore, the submarine's depth is -5/24 miles.
Answer:
-1 1/5
Step-by-step explanation:
I took the test and this was the correct answer :D
If f(x) = 4x - 20, what is f(4)?
O A. -4
оо
O B. -12
O c. 4
O D. 16
Answer:
A. - 4
Step-by-step explanation:
f(4) = 4(4) - 20 = 16 - 20 = - 4
2. The diagram shows a playground which is a combination
of three different shapes. TSVU is a square, SRQV is a
trapezium and PQVU is a parallelogram. Calculate the
total area of the playground.
Answer:
The diagram shows a playground which is a combination
of three different shapes. TSVU is a square, SRQV is a
trapezium and PQVU is a parallelogram. Calculate the
total area of the playground
Hi, I don't know how to do these, if you could help me answer them, that would be great
Answer:
137°Step-by-step explanation:
From the diagram, mAD lies on the line BDF. Sum of angle on a straight line is 180°. According to the line BDF; mAB + mAD = 180°
From the diagram, mAB = 43°. Substituting this value into the above equation;
mAB + mAD = 180°
43° + mAD = 180°
mAD = 180°-43°
mAD = 137°
Hence, the measure of angle mAD is 137°
what is 25 (10 + 50) - 25?
Answer:
1,475
Step-by-step explanation:
10 + 50
= 60
60 * 25
= 1,500
1,500 - 25
= 1,475
Answer:
Hey there!
25(10+50)-25
25(60)-25
1500-25
1475
Hope this helps :)
Suppose ACT Reading scores are normally distributed with a mean of 21 and a standard deviation of 6.2. A university plans to admit students whose scores are in the top 30%. What is the minimum score required for admission
Answer:
24.25
Step-by-step explanation:
The minimum admission score is at the 70th percentile of the normal distribution which, according to a z-score table, corresponds to a z-score of 0.524.
The z-score, for any given value X, is determined by:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
If the mean score is 21 and the standard distribution is 6.2, the minimum required score for admission is:
[tex]0.524=\frac{X-21}{6.2}\\X=24.25[/tex]
The minimum score required for admission is 24.25.
help me please I dont remember how to do this
Answer:
A
Step-by-step explanation:
Expand brackets.
-4y - 28 = -4y - 18 - 10
Both sides have -4y, the equation has no solutions.
-4y + 4y = - 18 - 10 + 28
0 = 0
There are no solutions.
Simplify the expression 11+2/3(15-21a)
Answer:
21-14a
Step-by-step explanation:
You have to distribute the (2/3) into the (15-21a) then add it to the 11. So after distributing the (2/3) into the (15-21a) is (10-14a). Then add that to the 11
Answer:
-14a + 21
Step-by-step explanation:
11 + 2/3(15 - 21a)
Expand brackets.
11 + 2/3(15) + 2/3(-21a)
11 + 30/3 + -42/3a
Evaluate.
11 + 10 + - 14a
21 + - 14a
What is the area of this triangle? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Greetings from Brasil...
We need to use the Cosine Law in Any Triangle, so we can use Heron's formula.
AC² = AB² + BC² - 2.AB.BC.COS B
AC² = 11² + 9² - 2.11.9.COS 63
AC ≈ 10,63
Heron's Formula:
Area = √[P.(P - AB).(P - BC).(P - AC)]
where P = (AB + BC + AC)/2
P = (11 + 9 + 10,63)/2 ⇒ P ≈ 15,31
Area = √[15,31.(15,31 - 11).(15,31 - 9).(15,31 - 10,63)]
Area ≈ 44,21 u.a.multiply: 4x ^3sqrt 4x^2 (2 ^3sqrt 32x^2 * x ^3sqrt 2x)
Answer:B on edge 2020 :)
Step-by-step explanation:
its b
Step-by-step explanation:
edge 2022
Given that ACAB - ACED, lind the value of y to 1 dermal place
Answer:
y = 15
Step-by-step explanation:
The triangles CAB and CED are similar (Using the case AA), so we can write the following relations:
[tex]\frac{12}{28} =\frac{15}{x}=\frac{y}{35}[/tex]
Using the first two fractions, we can find the value of x:
[tex]\frac{12}{28} =\frac{15}{x}[/tex]
[tex]12x = 28*15[/tex]
[tex]12x = 504[/tex]
[tex]x = 504/12 = 42[/tex]
Using the first and last fractions, we can find the value of y:
[tex]\frac{12}{28} =\frac{y}{35}[/tex]
[tex]28y = 12*35[/tex]
[tex]28y = 420[/tex]
[tex]y = 420/28 = 15[/tex]
Given that (1,-8) is on the graph of f(x), find the corresponding point for the function 1/2 f(x)
Answer: 1 (-4)
Step-by-step explanation: f(x) is a function of x giving you a y value. 1/2 f(x) means you're halving every y value that plugging in x gives you.
When a biased coin is tossed, heads is three times as likely to come up as tails. Rearrange the following procedure in the correct order to find the probability that should be assigned to the outcome of heads and tails?
1. p(T) = 1/4 and p(H) = 3/4
2. since heads and tails are the only two outcomes p(H) + p(T) = 1.
3. p(H) = 3p(T)
4. 3p(T) + p(T) = 1
5. 4p(T) = 1
Answer: 1
Step-by-step explanation:
If heads is 3 more likely to come up than tails, then there are 3 heads for every tails.
Hope it helps <3
What is the equation of a circle with center (0, 5) and radius 8
Answer:
See below.
Step-by-step explanation:
Recall that the equation for a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h,k) is the center and r is the radius.
We know the center is (0,5) and the radius is 8. Plug in the numbers:
[tex](x-(0))^2+(y-(5))^2=(8)^2[/tex]
We can remove the parentheses on the left. Therefore, the equation will be:
[tex]x^2+(y-5)^2=64[/tex]
Answer:
( x) ^2 + ( y-5) ^2 = 64
Step-by-step explanation:
The equation of a circle can be written as
( x-h) ^2 + ( y-k) ^2 = r^2 where ( h,k) is the center and r is the radius
( x-0) ^2 + ( y-5) ^2 = 8^2
( x) ^2 + ( y-5) ^2 = 64
40 points and brainliest!!!!
In Triangle XYZ, m
triangles?
O XYZ = TUV
O XYZ = VUT
O No congruency statement can be made because only two angles in each triangle are known.
O No congruency statement can be made because the side lengths are unknown.
Answer:
Option (4).
Step-by-step explanation:
In the figure attached,
Two right triangles ΔXYZ and ΔTUV have been given,
Given:
1). m∠Y = m∠U = 30°
2). m∠Z = m∠V = 60°
3). m∠X = m∠T = 90°
For congruence of two right triangles, measure of at least one side should be known along with the measure of angles (LA, HA, LL, HL properties of congruence).
Therefore, these triangles may be similar but not congruent.
Option (4) is the correct option.
Answer:
D.No congruency statement can be made because the side lengths are unknown.
Step-by-step explanation:
EDG
Ben and his three sisters are competing to see who gets home first from their grandmother's
house. There are four different routes from her house back to their home in Garland. Ben
chooses Route 1. What are the possible outcomes of the routes taken by the family if Ben
chooses first? Label that set S.
Answer: {Route2, Route3, Route4} (Total 3 outcomes)
Step-by-step explanation:
Given: There are 4 different routes from Ben's house back to their home in Garland.
Let Sample space for all outcomes: {Route1, Route2, Route3, Route4 }
Ben chooses Route 1.
The possible outcomes of the routes taken by the family if Ben chooses first:
{Route2, Route3, Route4}
Hence, the possible outcomes of the routes taken by the family if Ben chooses first: {Route2, Route3, Route4} (Total 3 choices)
Can somebody please help? i need to graph the piecewise function. i won't forget to give brainliest.
Answer: see graph (attached)
Step-by-step explanation:
Plot coordinates for each line. You MUST include the boundary points.
y = 3x - 5 x ≤ 1
Choose x = -2, then y = 3(-2) - 5 = -11
Must include x = -1, then y = 3(-1) - 5 = -8
Draw a line starting at (-1, -8) and passing through (-2, -11)
y = -2x + 3 -1 < x < 4
Must include x = -1, then y = -2(-1) + 3 = 5
Must include x = 4, then y = -2(4) + 3 = -5
Draw a line segment starting at (-1, 5) and ending at (4, -5).
Note that both are strictly less than so must have open dots.
y = 2 x ≥ 4
Must include x = 4, then y = 2
Choose x = 5, then y = 2
Draw a line starting at (4, 2) and passing through (5, 2)