The equation of the first circle is (x + 1)^2 + (y - 1)^2 = r^2 and the equation of the second circle is (x + 1)² + (y - 1)² = 16
The equation of the perpendicular bisectorThe points are given as:
P(3, 0) and Q(0, 5)
The midpoint of PQ is
Midpoint = 0.5(3 + 0, 0 + 5)
Midpoint = (1.5, 2.5)
Calculate the slope of PQ
m = (y2 - y1)/(x2 - x1)
m = (5 - 0)/(0 - 3)
m = -5/3
A line perpendicular to PQ would have a slope (n) of
n = -1/m
This gives
n = -1/(-5/3)
n = 0.6
The equation is then calculated as:
y = n(x - x1) + y1
Where
(x1, y1) = (1.5, 2.5)
So, we have:
y = 0.6(x - 1.5) + 2.5
y = 0.6x - 0.9 + 2.5
Evaluate the sum
y = 0.6x + 1.6
Hence, the equation of the perpendicular bisector of PQ is y = 0.6x + 1.6
The center of the circleWe have:
y = x + 2
Substitute y = x + 2 in y = 0.6x + 1.6
x + 2 = 0.6x + 1.6
Evaluate the like terms
0.4x = -0.4
Divide
x = -1
Substitute x = -1 in y = x + 2
y = -1 + 2
y = 1
Hence, the center of the circle is (-1, 1)
The circle equationWe have:
Center, (a, b) = (-1, 1)
Point, (x, y) = (0, 5) and (3, 0)
A circle equation is represented as:
(x - a)^2 + (y - b)^2 = r^2
Where r represents the radius.
Substitute (a, b) = (-1, 1) in (x - a)^2 + (y - b)^2 = r^2
(x + 1)^2 + (y - 1)^2 = r^2
Substitute (x, y) = (0, 5) in (x + 1)^2 + (y - 1)^2 = r^2
(0 + 1)^2 + (5 - 1)^2 = r^2
This gives
r^2 = 17
Substitute r^2 = 17 in (x + 1)^2 + (y - 1)^2 = r^2
(x + 1)^2 + (y - 1)^2 = r^2
Hence, the circle equation is (x + 1)^2 + (y - 1)^2 = r^2
The value of a and bThe equation of the second circle is
2x² + y² + ax + by - 14 = 0
Rewrite as:
2x² + ax + y² + by = 14
For x and y, we use the following assumptions
2x² + ax = 0 and y² + by = 0
Divide through by 2
x² + 0.5ax = 0 and y² + by = 0
Take the coefficients of x and y
k = 0.5a k = b
Divide by 2
k/2 = 0.25a k/2 = 0.5b
Square both sides
(k/2)² = 0.0625a² (k/2)² = 0.25b²
Add the above to both sides of the equations
x² + 0.5ax +0.0625a² = 0.0625a² and y² + by + 0.25b² = 0.25b²
Express as perfect squares
(x + 0.25a)² = 0.0625a² and (y + 0.5b)² = 0.25b²
Add both equations
(x + 0.25a)² + (y + 0.5b)² = 0.0625a² + 0.25b²
So, we have:
2x² + ax + y² + by = 14 becomes
(x + 0.25a)² + (y + 0.5b)² = 0.0625a² + 0.25b²+ 14
Comparing the above equation and (x + 1)^2 + (y - 1)^2 = r^2, we have:
0.25a = 1 and 0.5b = -1
Solve for a
a = 4 and b = -2
This means that the value of a is 4 and b is -2
Show that the second circle is in the firstWe have:
a = 4 and b = -2
Substitute these values in (x + 0.25a)² + (y + 0.5b)² = 0.0625a² + 0.25b²+ 14
This gives
(x + 0.25*4)² + (y - 0.5*2)² = 0.0625*4² + 0.25*(-2)²+ 14
(x + 1)² + (y - 1)² = 16
The equation of the first circle is
(x + 1)² + (y - 1)² = 17
The radii of the first and the second circles are
R = √17
r = √16
√17 is greater than √16
Since they have the same center, and the radius of the first circle exceeds the radius of the second circle, then the second circle lies inside the first circle.
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Which of the following functions has a vertical asymptote at x=2, a horizontal asymptote at f(x)=1, and a root at x=−1?
A. f(x)=3x+2+1
B. f(x)=−3x−2+1
C. f(x)=3x+2−1
D. f(x)=3x−2+1
What is the equation of the line through the origin and (-2,3)?
Step-by-step explanation:
[tex]algenbraic[/tex]
The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either from Rome, Italy or New York, New York:
Maximum Minimum Q1 Q3 IQR Median Mean σ
Rome 16 0 3 13 10 8.5 8 5.4
New York 20 1 4.5 6 1.5 5.5 7.25 5.4
Which of the choices below best describes how to measure the center of this data? (5 points)
Group of answer choices
Both centers are best described with the mean.
Both centers are best described with the median.
The Rome data center is best described by the mean. The New York data center is best described by the median.
The Rome data center is best described by the median. The New York data center is best described by the mean.
It's NOT C "The Rome data center is best described by the mean. The New York data center is best described by the median." already tried, its incorrect.
The best description on measurement of the center of this data is; C. The Rome data center is best described by the mean. The New York data center is best described by the median.
How to find the center of the data?If we make the box and whisker plot of the Rome and New York data, we will see that there will clearly be an outlier in the New York data.
Thus;
Due to the fact that the data set for New York has an outlier and the mean is skewed, it means that we would use the median.
Finally, we see that the Rome data set is symmetrical because it has no outlier, and as such we can use the mean.
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NEED HELP PLEASE!!!!!
What is c−1(x) given c(x)=x3−5?
A. c−1(x)= ∛x+5
B. c−1(x)= ∛x+x
C. c−1(x)= ∛x- ∛5
D. c−1(x)= ∛x-5
Answer: A
Step-by-step explanation:
Let c(y)=x.
[tex]\implies x=y^3 -5\\\\x+5=y^3\\\\y=\sqrt[3]{x+5}\\\\c^{-1}(x)=\sqrt[3]{x+5}[/tex]
Schwiesow corporation has provided the following information: cost per unit cost per period direct materials $ 7.40 direct labor $ 3.80 variable manufacturing overhead $ 1.80 fixed manufacturing overhead $ 16,000 sales commissions $ 1.00 variable administrative expense $ 0.50 fixed selling and administrative expense $ 5,600 if 7,500 units are produced, the total amount of manufacturing overhead cost is closest to:
The total amount of manufacturing overhead cost is closest to $ 29,500.
In business, overhead or overhead rate refers to an ongoing fee for working in a commercial enterprise. Overheads are the expenditure that can not be quite simply traced to or recognized with any unique revenue unit, not like running fees which include uncooked cloth and exertions.
Overhead fees, frequently referred to as overhead or working prices, confer with those expenses associated with running a commercial enterprise that cannot be connected to creating or producing a product or service. they're the prices the business incurs to live in the enterprise, irrespective of its success degree.
Examples of overhead encompass hire, administrative expenses, or worker salaries. Overhead fees may be observed on a business enterprise's income assertion, wherein they are subtracted from its profits to reach at the internet profits discern.
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Charmaine's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Charmaine $4.25 per pound, and type B coffee costs $5.40 per pound. This month's blend used twice as many pounds of type B coffee as type A, for a total cost of $451.50. How many pounds of type A coffee were used
30 pounds of coffee A and 60 pounds of coffee B used.
According to statement
Type A coffee costs Charmaine $4.25 per pound
Type B coffee costs $5.40 per pound.
Total cost of month on coffee is $451.50
AND
B=2A -(1)
Let's form the equation
4.25A + 5.40B = 451.50
Put equation 1 in it then
4.25A + 5.40*2A = 451.50
15.05A = 451.50
A = 30 pounds then
B = 60 pounds.
So, 30 pounds of coffee A and 60 pounds of coffee B used.
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Office procedure note this 39-year-old patient returns to the office today because of a defect on the nail of his left big toe. he was seen three times in the last four months for this problem. this defect is very suspicious, and i felt it best to biopsy a portion of the nail plate and bed. the sample was sent to pathology. i told the patient that he will be called with the results, and then i will decide how to proceed. cpt code(s):
The CPT code that is used here is CPT code 11755.
What is the CPT code 11755?This is the code that is used as the biopsy of the nail bed. The CPT code is used to report this procedure.
Then it would be determined if it is a case of melanoma or lesion that is causing the issues with the individuals nails.
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he correct code for biopsy of the nail bed or nail plate.
The sum of 225 consecutive positive integers only has digits 1 or 0. What is the smallest possible value of the sum?
Answer:
1 +10=11 (since 0 is neither negative or positive the first and second positive integerswith 1 or 0
Determine the value of x and y, show calculations
The value for x and y are 140° and 70° respectively.
How to solve Polygon QuestionThere are two ways to solve polygon question. Formula for the sum of interior angle and sum of the exterior angle of regular polygon.
Sum of the interior = (n - 2)180
Sum of the exterior = 360/n
Where n = number of sides of a polygon.
The regular polygon in which x is one of its angle is called decagon
Sum of the interior = (n - 2)180
n = 10
Substitute n into the formula
Sum of the interior angle = (10 - 2)180
Sum of the interior angle = (8)180
Sum of the interior angle = 1440
Each angle = 1400/10
x = 140°
For y, the three angles are similar.
sum of angle in a triangle = 180
Since the each triangle is an isoceles triangle, angle at each base will be y
40 + y + y = 180
2y = 180 - 40
2y = 140
y = 70°
Therefore, the value for x and y are 140° and 70° respectively.
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what the picture says
By applying the law of cosine, the length of side BM is equal to 7.05 cm..
What is a polygon?A polygon can be defined as a two-dimensional geometric shape that comprises straight line segments and a finite number of sides. Also, some examples of a polygon include the following:
TriangleQuadrilateralPentagonHexagonNonagonOctagonNote: The number of sides (n) of a pentagon is 5.
In Geometry, the interior angle of both a regular and irregular polygon is given by this formula:
Interior angle = 180 × (n - 2)/n
Interior angle = 180 × (5 - 2)/5
Interior angle = 180 × 3/2
Interior angle = 108°.
For the central angle, we have:
Central angle, O = 360/5
Central angle, O = 72°.
By applying the theorem of intersecting secants, angle OCB will be given by this formula:
<OCB = ½ × (180 - 72)
<OCB = ½ × 108
<OCB = 54°.
In order to determine the length of side BM, we would apply the law of cosine:
cos(θ) = Adj/Hyp
cos54 = BM/12
BM = 12 × cos54
BM = 12 × 0.5878
Side BM = 7.05 cm.
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d all the time and I like the time you
Answer:
Step-by-step explanation:
1a+1b(a+b-c)+1b+1c(b=c-a)+ 1a+1c(c+a-b)
1a+1b-c+1b +1c-a+1a+1c-b
1a+2b-c+a+1c-b
2a+1b+c this is the answer I think lol
Alice and Bob both go to a party which starts at $5:00$. Each of them arrives at a random time between $5:00$ and $6:00$. What is the probability that the number of minutes Alice is late for the party plus the number of minutes Bob is late for the party is less than $45$
The probability comes out to be 9/32.
Deducing Arrival Time Possibility
All the possible arrival times by Alice and Bob, in minutes after 5 PM, is constrained by the values of given values of x and y,
x = 0, y = 0, x = 60, y = 60.
Here, let the values of x represent how many minutes after 5 PM Alice arrives at the party.
Let the y values represent the time in minutes that Bob arrives at the party after 5 PM.
Calculating the Required Probability
The times that concern us, however, are obtained by the following probability function,
x + y ≤ 45.
And x = 0, y = 0, and x + y ≤ 45 define the constraints of this probability function. Thus the perimeter of such a graph will be given as,
(45² / 2) = 1012.5 square units
Since the total area of the various arrival times is 60 x 60, or 3600 square units, the probability that Alice and Bob will arrive together after 5 o'clock in the evening in less than 45 minutes is therefore = 1012.5 / 3600 = 9/32
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Which expression does this graph illustrate?
Answer:
D
Step-by-step explanation:
The red line starts with a filled in circle that mean that the number -12 is included. The graph is saying that x can be -12 or any number above -12. The line under the > is telling you that 12 is included.
PLEASE HELP QUICKLY️️️
Answer:
first option x = 7
Step-by-step explanation:
"x" is the cathetus opposite the angle of 30°
14 is the hypotenuse
use the sine function
[tex]sin30^{0} =\frac{x}{14}[/tex]
[tex]x=14sen30^{0} =14(0.5)=7[/tex]
Hope this helps
If WX= 82 cm, find the length of YZ. (OV = 9cm and OV is perpendicular to YZ)
The length of the measure of YZ is 80cm
Perpendicular linesPerpendicular lines are lines that are at angle 90 degrees to each other. From the given diagram;
WX = 82cm
Required
Length. of YZ
Using the pythagoras theorem
YV = VZ = √41²-9²
YV = VZ = √1600
YV = VZ = 40
Since YZ = YV + VZ
YZ = 40cm + 40cm
YZ= 80cm
Hence the length of the measure of YZ is 80cm
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How does the figure help verify the triangle inequality theorem?
The line is drawn from a length of 15, two lines constructing a triangle and intersecting the arc from a length of the lines 7, 4
A.
by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third side
B.
by showing that only one triangle can be formed when the sum of the lengths of two sides equals the length of the third
C.
by showing that only one triangle can be formed when the sum of the lengths of two sides is less than the length of the third
D.
by showing that a triangle cannot be formed when the sum of the lengths of two sides equals the length of the third
The figure description helps; Choice A; by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third side.
What is the triangle inequality theorem?The triangle inequalities theorem postulates that the sum of lengths of two sides of a triangle must be greater than the length of the third side.
On this note, it follows that the since the sum of sides given in the description 7 and 4 is less than 15, the segments cannot be used to form a triangle.
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x+2/3 - x+1/5 = x-3/4 - 1
Answer:
x = 157/60
Step-by-step explanation:
x + 2/3 - x + 1/5 = x - 3/4 - 1
x - x - x = -2/3 - 1/5 - 3/4 - 1
-60x/60 = -40/60 - 12/60 - 45/60 - 60/0
-60x = -40 - 12 - 45 - 60
-60x = -157
x = -157/-60
x = 157/60
157/60 + 2/3 - 157/60 + 1/5 = 157/60 - 3/4 - 1
2/3 + 1/5 = 157/60 - 3/4 - 1
40/60 + 12/60 = 157-60 - 45/60 - 60/60
40 + 12 = 157 - 45 - 60
52 = 157 - 105
which situation is most likley to show a constant rate of change
Option B. The situation that would be more likely to show a constant rate of change would be B. The distance traveled by a truck driving at a constant speed compared with time.
How to solve for the rate of changeThis is the factor that is used to determine if there is a decrease or an increase in a given factor.
A good way to d this is by the use of time and speed to compare the distance that is being traveled.
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Complete question
Which situation is most likely to show a constant rate of change?
A. The weight of a child compared with its age in months
B. The distance traveled by a truck driving at a constant speed compared with time
C. The cost of a new car compared with the number of tires it has
D. The outside temperature compared with the time of day
Write down the equation of the straight line which passes through (0, -3) and parallel to the straight line y = -2x+1
Answer:
y = -2x - 3
Step-by-step explanation:
Equation of line:Parallel lines have same slope.
y = -2x + 1
Compare with the equation of line in slope intercept form y = mx + b
Here m is the slope and b is the y -intercept
m = -2
m = -2 ; line passes through (0 , -3)
Equation of line in slope intercept form:
[tex]\sf \boxed{\bf y - y_1=m(x-x_1)}[/tex]
y - [-3] = -2(x - 0)
y +3 = -2x
y = -2x - 3
If the clock tower in "Back to the Future" had a big hand length of 3 feet, what would be the length of the arc, in feet, the tip travels from 6:00pm to 6:20pm. Round to the nearest foot.
The length of the arc made by the big hand if the tip travels from 6:00pm to 6:20pm is 0.52 feet
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The clock reads 12 hours (720). The angle if the tip travels from 6:00pm to 6:20pm (20 minutes) is:
Ф = (20/720) * 360 = 10°
The length of the arc is given as:
Length of arc = (Ф/360) * 2π * length of hand = (10/360) * 2π(3) = 0.52 feet
The length of the arc made by the big hand if the tip travels from 6:00pm to 6:20pm is 0.52 feet
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BRANIEST + 15 POINT QUESTION
Let the missing number x
So, ATQ
[tex] \frac{3}{14} \times x = 6[/tex]
[tex] \frac{14}{3} \times \frac{3}{14} x = 6 \times \frac{14}{3} [/tex]
[tex] \frac{1}{3} \times 3x = \frac{14}{3} \times 6[/tex]
[tex]x = \frac{14}{3} \times 6[/tex]
[tex]x = 14 \times 2[/tex]
[tex]x = 28[/tex]
Therefore, 3/14 of 28 is 6...
Answer:
28
Step-by-step explanation:
Let the number we are looking for = [tex]x[/tex]
∴ [tex]\frac{3}{14}[/tex] of [tex]x[/tex] is 6
⇒ [tex]\frac{3}{14}[/tex] × [tex]x = 6[/tex]
• Divide both sides of equation by [tex]\frac{3}{14}[/tex] :
⇒ [tex]x = 6 \div \frac{3}{14}[/tex]
⇒ [tex]x = 28[/tex]
∴ The missing part is 28.
URGENT!!!!!!
A researcher orders a broth of 8.8% glucose for her lab. However, she needs a stronger broth, one that is 13.8% glucose. Fortunately, she has 69.7 liters of 39.4% glucose broth in the stock room. How much 13.8% glucose broth can she make? Round your answer to the nearest tenth of a liter.
Answer:426.6
Step-by-step explanation:
.138 x =.088(x - 69.7) + .394(69.7)
.138 x - .088x = 69.7(.394 - .088)
.05x = 21.3282
/
x = 426.564
This rounds to x = 426.6
Give me brainliestGiven the graph of the function, f(x) , what is the value of f (-2)?
The value of f(-2) is 0
How to evaluate the function?The graph of the function is added as an attachment
The graph is given as:
y = f(x)
When x =-2. we have
y = f(-2)
From the graph, we have:
x = -2 and y = 0
So, we have
f(-2) = 0
Hence, the value of f(-2) is 0
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five more than the product of two and a number,
decreased by seven;
evaluate when a = 8
Key Words
five
more than
product
two
a number
decreased by
seven
Intro
Replace With
5
+
X
2
a
7
Write and evaluate the expression. Then, complete the
statements.
First, write the expression
Second,
Third,
The answer is
V
8 in for the variable, a
by using
Done
P
Answer:
It was difficult reading the question, as written. Check my assumptions.
Step-by-step explanation:
"five more than the product of two and a number,
decreased by seven"
---
Let the "number" be a.
We are told "five more than . ." means +5,
"the product of two and a number" means 2a,
"decreased by seven" mean -7
Put the statements together to obtain:
+5+2a-7
Simplify to 2a-2
Evaluate when a = 8:
2a-2
2(8)-2
16-2
= 14
What is the range of the function f(x) = |x – 3| + 4?
R: {f(x) ∈ ℝ | f(x) ≥ 4}
R: {f(x) ∈ ℝ | f(x) ≤ 4}
R: {f(x) ∈ ℝ | f(x) > 7}
R: {f(x) ∈ ℝ | f(x) < 7}
Answer: R: {f(x) ∈ ℝ | f(x) ≥ 4}
Step-by-step explanation:
[tex]|x-3| \geq 0[/tex] for all real x, so the range is [tex]f(x) \geq 4[/tex].
Use the box-and-whisker plots to determine which statements are true.
The true statements are :
the average monthly temperatures of New Orleans are not as varied as that of Indianapolis.
The median of the average monthly temperatures of New Orleans is equal to the upper quartile of the average monthly temperature of Indianapolis.
What are the true options?
A box plot is used to study the distribution and level of a set of scores. The box plot consists whiskers. The whiskers represents the minimum and maximum scores.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
Range for New Orleans = 85 - 50 = 35
Range for Indianapolis = 75 - 25 = 50
Median for New Orleans = 70
Upper quartile for Indianapolis = 70
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PLEASE HELP IM SERIOUSLY STUCK
Answer: -1
Step-by-step explanation:
Remember to use the slope formula.
[tex]\frac{y2-y1}{x2-x1}[/tex]
Then plug in your points:
[tex]m=\frac{-1-(4)}{2-(3)}[/tex]
Simplify
[tex]m=\frac{-5}{5}[/tex]
Divide -5 by 5 and your Answer is:
[tex]m=-1[/tex]
Hopes this helps!
Answer:
-1
Step-by-step explanation:
As given in the picture you provided, the slope is defined as: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] and the reason for this, is because in subtracting y_1 from y_2, you're finding how much the y-value changed, or in other words, the rise. When subtracting x_1 from x_2 you're finding how much the x-value changed, or in other words the run. Another way of expressing the slope that you may have seen is: [tex]\frac{rise}{run}[/tex] which is essentially what this slope formula is doing.
One thing to note is that what I assign to (x_1, y_1) and (x_2, y_1) doesn't matter, as long as they're two different points on the linear line.
So let's just say that: [tex](x_1, y_1) = (-3, 4)[/tex] and that: [tex](x_2, y_2) = (2, -1)[/tex]
Now plugging these values into the equation we get: [tex]\frac{-1-4}{2-(-3)} = \frac{-5}{5} = -1[/tex]
So the slope is -1
Someone help me please
Answer:
[tex]\sqrt{60}[/tex]
Step-by-step explanation:
Use the Pythagorean theorem a^2 + b^2 = c^2
In this case you are given a and c, so set the equation up like
2^2 + b^2 = 8^2
b^2 = 8^2 - 2^2
b =[tex]\sqrt{8^{2} -2^{2} }[/tex]
b =[tex]\sqrt{60}[/tex]
PLEASE HELP!!! the photo has the question and options please help
The equation which expresses the number of bacteria, P, present at any time, t is P(t) = 4(2)^t
EquationNumber of bacteria = PTime = tCheck all options
When t = 1
P(t) = 8(4)^t
= 8(4)¹
= 8(4)
P(t) = 32
Not true
P(t) = 4(2)^t
= 4(2)¹
= 4(2)
= 8
True
P(t) = (2)^t
= (2)¹
= 2
Not true
P(t) = 8(2)^t
= 8(2)¹
= 8(2)
= 16
Not true
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Determine S9 of the series where a=6 and r=2
Hi
arithmetic serie mean that to change from a rank to an other, you add "r"
So : if 6 is S1, and 2 is pace,
then you need 8 hops to go from S1 to S9.
so you 'r going to add the reason 8 times.
so : S9 = 6 + 8 * 2 = 6 + 16 = 22
conclusion : S9 = 22