Answer: The graph that represents a function is the parabola that opens to the left.
This can be determined by the following characteristics of the graph:
It is a parabola because it opens to the left and has a vertex on the y-axis.
It crosses the y-axis at (0, 3) and (0, negative 3), which means that it is symmetric about the y-axis, and also it crosses the x-axis at (9, 0) which means that it is a function.
A circle is not a function because, for any value of x, there are two different values of y that can be plotted on the graph (i.e. the point (5,0) and (-5,0) produce two different y values)
A straight line with a positive slope is not a function because, for any value of x, there is only one value of y that can be plotted on the graph.
So the parabola is the graph that represents a function.
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Gina Wilson Unit 10: Circles Homework 9: Standard Form of a Circle
The standard form (SF), center (C) and radius (R) are given as follow: (13) SF: (x + 4)² + (y - 3)² = 50, Center: (-4, 3), R: √50 (14) SF: (x - 2)² + (y - 6)² = 169, C: (2, 6), R: 13 (15) SF: (x + 7)² + (y + 5)² = 1, C: (-7, -5), R: 1 (16) SF: (x - 8)² + y² = 225, C: (8,0), R: 15 (17) SF: (x - 12)² + (y - 2)² = 63, C: (12, 2), R: √63 (18) SF: (x - 5)² + (y + 4)² = 100 , C: (5, -4), R: 10
Understanding Equation of CircleThe general form of a circle is given as:
(x - h)² + (y - k)² = r²
where:
(h, k) represents the center of the circle
r represents the radius.
Now we can use the above information to solve the following questions:
13. x² + y² + 8x - 6y - 25 = 0
Rearranging the equation:
x² + 8x + y² - 6y = 25
Completing the square for x terms:
(x² + 8x + 16) + y² - 6y = 25 + 16
Simplifying:
(x + 4)² + (y² - 6y) = 41
(x + 4)² + (y² - 6y + 9) = 41 + 9
(x + 4)² + (y - 3)² = 50
Center: (-4, 3)
Radius: √50
14. x² + y² - 4x - 12y - 129 = 0
Rearranging the equation:
x² - 4x + y² - 12y = 129
Completing the square for x terms:
(x² - 4x + 4) + y² - 12y = 129 + 4
Simplifying:
(x - 2)² + (y² - 12y) = 133
(x - 2)² + (y² - 12y + 36) = 133 + 36
(x - 2)² + (y - 6)² = 169
Center: (2, 6)
Radius: 13
15. x² + y² + 14x + 10y + 73 = 0
Rearranging the equation:
x² + 14x + y² + 10y = -73
Completing the square for x terms:
(x² + 14x + 49) + y² + 10y = -73 + 49
Simplifying:
(x + 7)² + (y² + 10y) = -24
(x + 7)² + (y² + 10y + 25) = -24 + 25
(x + 7)² + (y + 5)² = 1
Center: (-7, -5)
Radius: 1
16. x² + y² - 16x - 161 = 0
Rearranging the equation:
x² - 16x + y² = 161
Completing the square for x terms:
(x² - 16x + 64) + y² = 161 + 64
Simplifying:
(x - 8)² + y² = 225
Center: (8, 0)
Radius: 15
17. x² + y² = 24x + 4y - 85
Rearranging the equation:
x² - 24x + y² - 4y = -85
Completing the square for x and y terms:
(x² - 24x + 144) + (y² - 4y + 4) = -85 + 144 + 4
Simplifying:
(x - 12)² + (y - 2)² = 63
Center: (12, 2)
Radius: √63
18. x² + y² - 9x + 2y = x - 6y + 59
Rearranging the equation:
x² - 9x - x + y² + 2y + 6y = 59
Combining like terms:
x² - 10x + y² + 8y = 59
Completing the square for x and y terms:
(x² - 10x + 25) + (y² + 8y + 16) = 59 + 25 + 16
Simplifying:
(x - 5)² + (y + 4)² = 100
Center: (5, -4)
Radius: 10
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100 Points! Algebra question. Photo attached. Solve the equation. Please show as much work as possible. Thank you!
Answer:
[tex] \sin(x) + \sin(2x) = 0[/tex]
[tex] \sin(x) + 2 \sin(x) \cos(x) = 0[/tex]
[tex]( \sin(x) )(1 + 2 \cos(x) ) = 0[/tex]
sin(x) = 0 or 1 + 2cos(x) = 0
2cos(x) = -1
cos(x) = -1/2
x = kπ or x = 2π/3 + 2kπ or
x = 4π/3 + 2kπ
(k is an integer)
Linda is adding padding to all of the surfaces inside her attic for extra warmth in the winter.
We have that Linda's net and expression incorrect
With the Expression of the surface area of attic
45 (40 + 25 + 25) + 1/2 (40 x 15)
Hence, Surface area is,
X = 4050 + 600
X = 4650 feet²
Hence, The answer is No, Because Her expression for the triangles are incorrect;
1/2(40 x 15)
Instead of,
1/2 x 40 x 15
Hence, Linda's net and expression incorrect,
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Complete question is,Linda is adding padding to all of the surfaces inside her attic for extra warmth in the winter.
She needs to find the approximate surface area of the attic, including the walls, floor, and
ceiling. The attic is in the shape of a triangular prism. Linda draws the net and writes
the expression below to represent the surface area of the attic. Are Linda's net and
expression correct?
At the neighborhood block party, Joel served 1/6 of a gallon of hot chocolate and 1/12 of a
gallon of apple cider. How much more hot chocolate than apple cider did Joel serve?
Write your answer as a fraction or as a whole or mixed number.
gallons
Answer:
1/12 gallons
Step-by-step explanation:
We can determine how much more hot chocolate than apple cider die Joe serve by subtracting 1/12 from 1/6.
Step 1: Since 1/12 has the bigger denominator and 6 * 2 = 12, let's give 1/6 the same denominator as 1/12 by multiplying the entire fraction by 2/2
(1/6) * (2/2) = 2/12
Step 2: Now we can subtract 1/12 from 2/12:
2/12 - 1/12 = 1/12
Thus, Joel served 1/12 more gallons of hot chocolate than apple cider.
please fast if could
Answer:9/41
SOH = opposite over hypotenuse
Step-by-step explanation:
2 A car dealer, at a year-end clearance, reduces the price of last year's models by a certain amount. If a certain four-door model has been sold at a discounted price of Birr 51,000, with a discount of Birr 9,000, what is the percentage of discount?
For calculating the percentage of discount, we can use the formula:
Percentage of discount = (Discount amount / Original price) * 100
We have given that the discounted price is Birr 51,000 and the discount amount is Birr 9,000,we need to find the original price.
Original price = Discounted price + Discount amount
Original price = 51,000 + 9,000 = 60,000 Birr
Now, we can calculate the percentage of discount:
Percentage of discount = (9,000 / 60,000) * 100 = 15%
Hence, the percentage of discount for the four-door model is 15%.
An advertising executive thinks that the proportion of consumers who have seen his company advertisement in newspaper is around 0.65. The executive want to estimate the customer proportion to within ± 0.05 and have a 98% confidence in the estimate. How large a sample should be taken?
Answer:
To determine the sample size required to estimate the proportion of consumers who have seen the company's advertisement in the newspaper, we can use the formula for sample size calculation for proportions. The formula is as follows:
n = (Z^2 * p * q) / E^2
Where:
n = required sample size
Z = Z-score corresponding to the desired confidence level (in this case, 98% confidence corresponds to a Z-score of approximately 2.33)
p = estimated proportion (0.65)
q = 1 - p (the complement of the estimated proportion)
E = maximum error tolerance (+/- 0.05)
Let's plug in the values and calculate the sample size:
n = (2.33^2 * 0.65 * 0.35) / (0.05^2)
n = 339.28
Rounding up to the nearest whole number, the required sample size is 340.
Read instructions and do this on a separate piece of paper and draw all lines with a ruler or any straightedge. I will mark you brainliest.
The required angles (corresponding, vertical and alternate) in relation to the Parallel lines are attached accordingly.
What is a parallel line?Parallel lines are coplanar infinite straight lines that do not cross at any point in geometry. Parallel planes are planes that never intersect in the same three-dimensional space.
When two parallel lines cross by any other line (i.e. the transversal), corresponding angles are generated in matching corners or corresponding corners with the transversal.
When two parallel lines are sliced by a transversal, the resulting alternate exterior angles are congruent, according to the Alternate Exterior Angles Theorem.
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Here is a right-angled triangle.
8.2 cm
y cm
12.3 cm
Work out the value of y.
Give your answer correct to 1 decimal place.
The value of y from the given right angled triangle is 9.2 cm.
Given that, a right angled triangle has 8.2 cm, y cm and 12.3 cm.
Let, hypotenuse = 12.3 cm, perpendicular = 8.2 cm and base = y cm.
By using Pythagoras theorem, we get
8.2²+y²=12.3²
67.24+y²=151.29
y²=151.29-67.24
y²=84.05
y=9.2 cm
Therefore, the value of y from the given right angled triangle is 9.2 cm.
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factor the expression w^2(w+8)-5(w+8)
Answer:
Step-by-step explanation:
Let's factor the expression w^2(w+8)-5(w+8):
First, we can see that (w+8) is a common factor in both terms of the expression.
So, we can factor out (w+8) from both terms:
(w+8)(w^2 - 5)
Now, the expression is factored as (w+8)(w^2 - 5).
Which graph shows the solution of h (x) = 2x^2 - x - 1?
The solution to the function h(x) = 2x² - x - 1 is given by the graph attached which is a positive quadratic graph.
Understanding Quadratic GraphA quadratic graph represents a quadratic equation in the form:
y = ax² + bx + c,
where a, b, and c are constants.
The graph of a quadratic equation is a curve called a parabola.
The general shape of a quadratic graph depends on the value of the coefficient "a." If "a" is positive, the graph opens upward, and if "a" is negative, the graph opens downward.
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Suppose that a safety deposit box at your bank costs $45/month to rent. How much would
it cost for you to rent the box for 15 years?
It would cost [tex]$8,100[/tex] to rent the safety deposit box for 15 years at a rate of [tex]$45[/tex] per month.
The total cost of renting a safety deposit box for 15 years, we need to first determine the total number of months in 15 years.
Since there are 12 months in a year, the total number of months in 15 years is:
15 years x 12 months/year = 180 months
So, if the safety deposit box costs [tex]$45[/tex] per month to rent, then the total cost of renting the box for 15 years would be:
180 months x [tex]$45[/tex]/month = [tex]$8,100[/tex]
We must first ascertain the entire number of months in 15 years in order to compute the total cost of renting a safety deposit box for 15 years.
Since there are 12 months in a year, there are a total of 180 months in 15 years: 15 years multiplied by 12 months per year.
In this case, if the monthly rental fee for the safety deposit box is [tex]$45[/tex] and the rental period is 15 years, the total cost would be calculated
180 months x [tex]$45[/tex]/month = [tex]$8,100[/tex]
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Is 34.05 greater than 34.59
No, 34.05 is not greater than 34.59.
When comparing two numbers, we look at their digits from left to right.
In this case, both numbers start with 34, which means they have the same value in the tens place.
However, when we move to the decimal part, 0.05 is smaller than 0.59.
Therefore, 34.05 is smaller than 34.59.
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Please help with picture below
The complete statement should be If 3m = 7n, then m/n = 7/3. The proportion was obtained by solving for m, and then using the converse of the cross products property. Option B
What does the converse of the cross product property say?The converse of the cross products property states that if two ratios are equal, then the product of the means is equal to the product of the extremes.
To justify the answer, you solve for m/n in the original equation by dividing each side by 3n, which gives you m/n = 7/3.
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Mary is building a fence around her triangular garden. How much fencing, in feet, does she
need? Round to the nearest foot.
AC=13 ft
C=40°
B=49°
The length of fencing needed around her triangular garden is 41 feet.
What is a triangle?A given shape which has three sides and three measures of internal angles which add up to 180^o is said to be a triangle.
For Mary to build a fence around her triangular garden, the amount of fencing needed can be determined by adding the length of each side of the garden.
So that;
A + B + C = 180^o
A + 49 + 40 = 180
A = 180 - 89
= 91
A = 91^o
Applying the sine rule, we have;
a/Sin A = b/Sin B = c/Sin C
a/Sin A = b/Sin B
a/Sin 91 = 13/ Sin 49
aSin 49 = 13*Sin 91
= 12.998
a = 12.998/ 0.7547
= 17.22
a = 17 ft
Also,
b/Sin B = c/Sin C
13/Sin 49 = c/ Sin 40
cSin 49 = 13*Sin 40
= 8.3562
c = 8.3562/ 0.7547
= 11.0722
c = 11 feet
Thus the amount of fencing required = 13 + 17 + 11
= 41
The fencing required is 41 feet length.
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Gramma Gert's Granola is Noah's favorite brand of granola bars. They come in regular-size
bars or snack-size bars. Both sizes are shaped like rectangular prisms. The regular-size bar is
1 inches wide, of an inch tall, and has a volume of 4 cubic inches. The snack-size bar
has the same width and height, but it has a volume of 3 cubic inches.
How much longer is the regular-size granola bar than the snack-size granola bar?
Write your answer as a whole number, proper fraction, or mixed number.
inches
The regular-size granola bar is 1 1/3 inches longer than the snack-size granola bar.
The regular-size granola bar has a volume of 4 cubic inches, while the snack-size bar has a volume of 3 cubic inches.
Since both bars have the same width and height, we can use the formula for the volume of a rectangular prism to find the length of each bar:
Regular-size bar: V = lwh = 4 cubic inches, w = 1 inch, h = 3/4 inch
l = V/wh = 4/(1 × 3/4) = 16/3 inches
Snack-size bar: V = lwh = 3 cubic inches, w = 1 inch, h = 3/4 inch
l = V/wh = 3/(1 × 3/4) = 4 inches
Therefore, the regular-size granola bar is (16/3 - 4) = 4/3 inches longer than the snack-size granola bar.
This can also be written as the mixed number 1 1/3 inches.
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Help
please
please
please
Answer: x=25 degrees
Step-by-step explanation:
25 degrees (blue) and x degrees (orange) are vertical angles. Vertical angles always equal each other.
(80 degrees {green} is just there to throw you off)
The lengths of the legs of a 45°-45°-90° triangle can be described by the expressions 3x − 10 and x + 2. What is the length of the legs of the triangle?
Answer:
8
Step-by-step explanation:
3x - 10 = x + 2
2x = 12
x = 6
3x - 10 = 3(6) - 10 = 8
The length of each leg of the triangle is 8.
!! Help please and thank you !!
Find the measure of the arc or angle in circle O given that mCD = 86° and mBE - 95°.
14. The measure of angle ABC is 90⁰.
15. The measure of angle CED is 43⁰.
16. The measure of angle BDE is 47.5⁰.
17. The measure of angle CBD is 43⁰.
18. The measure of arc AD is 94⁰.
19. The measure of angle BCE is 47.5⁰.
20. The measure of angle ABD is 47⁰.
21. The measure of arc ABC is 180⁰.
What is the measure of the missing angles?The measure of the missing angles is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.
The measure of angle ABC is calculated as follows;
m∠ABC = 90⁰ (since line AC is the diameter)
The measure of angle CED is calculated as follows;
m∠CED = ¹/₂ (arc CD) (interior angle of intersecting secants)
m∠CED = ¹/₂ (86⁰) = 43⁰
The measure of angle BDE is calculated as follows;
m∠BDE= ¹/₂ (arc BE) (interior angle of intersecting secants)
m∠BDE = ¹/₂ (95⁰) = 47.5⁰
The measure of angle CBD is calculated as follows;
m∠CBD = ¹/₂ (arc CD) (interior angle of intersecting secants)
m∠CBD = ¹/₂ (86⁰) = 43⁰
The measure of arc AD is calculated as follows;
arc ABC = 180 (sum of angles in a semi circle)
arc ADC = 180 (sum of angles in a semi circle)
arc ADC = arc AD + arc CD
180 = AD + 86
AD = 94⁰
The measure of angle BCE is calculated as follows;
m∠BCE= ¹/₂ (arc BE) (interior angle of intersecting secants)
m∠BCE = ¹/₂ (95⁰) = 47.5⁰
The measure of angle ABD is calculated as follows;
m∠ABD = ¹/₂ (arc AD) (interior angle of intersecting secants)
m∠ABD = ¹/₂ (94⁰) = 47⁰
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In triangle ABC, find a if b = 2, c = 6,
and A = 35°
a. 20.3
b. 7.7
c. 5.5
d. 4.5
The value of a in the triangle, given that in the triangle ABC, b = 2, c = 6, and A = 35° is 7.7 (option A)
How do i determine the value of a?We can obtain the value of a in the triangle ABC as shown in the attached photo by using the cosine rule as illustrated below:
Side b = 2Side c = 6 Angle A = 35°Value of a =?Cosine rule states as follow:
a² = b² + c² + 2bc Cos A
Inputting the given parameters, we can obtain the value of a as follow:
a² = 2² + 6² + (2 × 2 × 6 × Cos 35)
Clear the bracket
a² = 4 + 36 + 19.66
a² = 59.66
Take the square root of both sides
a = √59.66
a = 7.7
Thus, we can conclude from the above calculation that the value of a is 7.7 (option A)
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Complete the equations. 95 × 1 0^3 =? 95 × 1 0^4=? 95×10^5 =?
Answer:
95 × 10^3 = 95000
95 × 10^4 = 950000
95 × 10^5 = 9500000
PLS HELP
The circle has center O . Its radius is 2 cm , and the central angle A measures 160 . What is the area of the shaded region? Given the exact answer in terms of pi , and be sure to include the correct unit in your answer.
The correct answer is [tex]\dfrac{16\pi }{9}[/tex]
What is Area of a shaded region?The area of a shaded region is [tex]\sf \dfrac{n\pi r^2}{360}[/tex]
How to calculate this problem?The Radius given is 2The central angle given is 160°We need to find the area of the shaded regionSo, applying the formula [tex]\sf \dfrac{n\pi r^2}{360}[/tex]
[tex]\sf =\dfrac{160\pi r^2}{360}=\dfrac{160\pi (2^2)}{360} =\dfrac{160\times\pi \times4}{360} =\dfrac{16\pi }{9}[/tex]
Hence the area of shaded region is [tex]\dfrac{16\pi }{9}[/tex]
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Find g(0), g(-1), g(2), and g(2/3)
for g(x) =x/ square root 1-x^2
Given statement solution is :- Outputs and values g(2/3) = 2/3.
To summarize:
g(0) = 0
g(-1) = undefined
g(2) = undefined
g(2/3) = 2/3
To find the values of g(x) for the given inputs, we substitute each input into the function g(x) = x / √([tex]1 - x^2[/tex]). Let's calculate the values:
g(0):
Substitute x = 0 into the function:
g(0) = 0 / √([tex]1 - 0^2[/tex])
= 0 / √(1 - 0)
= 0 / √1
= 0
Therefore, g(0) = 0.
g(-1):
Substitute x = -1 into the function:
g(-1) = (-1) / √(1 - [tex](-1)^2[/tex])
= (-1) / √(1 - 1)
= (-1) / √0
Since the square root of 0 is undefined, g(-1) is undefined.
g(2):
Substitute x = 2 into the function:
g(2) = 2 / √([tex]1 - 2^2[/tex])
= 2 / √(1 - 4)
= 2 / √(-3)
Since the square root of a negative number is undefined in the real number system, g(2) is undefined.
g(2/3):
Substitute x = 2/3 into the function:
g(2/3) = (2/3) / √(1 - [tex](2/3)^2[/tex])
= (2/3) / √(1 - 4/9)
= (2/3) / √(5/9)
= (2/3) / (√5/√9)
= (2/3) / (√5/3)
= (2/3) * (3/√5)
= 2√5 / 3√5
= 2/3
Therefore, outputs and values g(2/3) = 2/3.
To summarize:
g(0) = 0
g(-1) = undefined
g(2) = undefined
g(2/3) = 2/3
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UNIT ISCALING
SCALE DRAWING OF A SCHOOL BUS HAS A SCALE OF 1/2 INCH TO 5 FEET. IF THE
ENGTHS OF THE SCHOOL BUS IS 4 1/2 INCHES ON THE SCALE DRAWING, WHAT IS THE
ACTUAL LENGTH OF THE BUS? EXPLAIN OR SHOW YOUR REASONING
The actual length of the bus is given as follows:
45 feet.
How to obtain the actual length of the bus?The actual length of the bus is obtained applying the proportions in the context of the problem.
The scale drawing is of 0.5 inches to 5 feet, hence the length represented by each inch of drawing is given as follows:
5/0.5 = 10 feet.
The length of the drawing is given as follows:
4.5 inches.
Hence the actual length of the bus is given as follows:
4.5 x 10 = 45 feet.
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The table of values below represents a linear function and shows the amount of snow that has fallen since a snowstorm began. What is the rate of change?
Snowfall Amount
Length of Snowfall
(hours)
Amount of Snow on the Ground
(inches)
0
3.3
0.5
4.5
1.0
5.7
1.5
6.9
2.0
8.1
1.2 inches per hour
2.4 inches per hour
3.3 inches per hour
5.7 inches per hour
The average rate of change for this problem is given as follows:
2.4 inches per hour.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function.
The change in the output is given as follows:
8.1 - 3.3 = 4.8.
The change in the input is given as follows:
2 - 0 = 2.
Hence the average rate of change is given as follows:
4.8/2 = 2.4 inches per hour.
Missing InformationThe table is given by the image presented at the end of the answer.
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what is the equation that contains the point M(1,10,3), N(4,10,6) and P(7,10,9)?
The equation of the line is: x = 1 + 3t,, y = 10, z = 3 + 3t.
How to determine the equation of the lineTo determine the equation of the line passing through points M(1, 10, 3), N(4, 10, 6), and P(7, 10, 9), we need to find the direction vector of the line.
Let's denote the direction vector as D = (a, b, c). The line can be represented by the parametric equations:
x = 1 + at,
y = 10 + bt,
z = 3 + ct,
To find the direction vector, we can use two points on the line, for example, M and N. The direction vector can be obtained by subtracting the coordinates of M from the coordinates of N:
D = N - M = (4 - 1, 10 - 10, 6 - 3) = (3, 0, 3).
So, the equation of the line passing through M(1, 10, 3) and having the direction vector D = (3, 0, 3) is:
x = 1 + 3t,
y = 10 + 0t = 10,
z = 3 + 3t.
Therefore, the equation of the line is:
x = 1 + 3t,
y = 10,
z = 3 + 3t.
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In ΔJKL,
�
�
‾
JL
is extended through point L to point M,
m
∠
�
�
�
=
(
3
�
−
16
)
∘
m∠JKL=(3x−16)
∘
,
m
∠
�
�
�
=
(
2
�
+
15
)
∘
m∠LJK=(2x+15)
∘
, and
m
∠
�
�
�
=
(
8
�
−
19
)
∘
m∠KLM=(8x−19)
∘
. Find
m
∠
�
�
�
.
m∠LJK.
The angle measure of LJK is 27 degrees
How to determine the angleFollowing the triangle sum theorem, we have that the sum of the interior angles of a triangle is 180 degrees
Also, we need to know that the sum of angles on a straight line is 180, then, we have;
<JLK = 180 - <LKM = 180 - (8x - 19)
Then, substitute the value, we have that;
<JKL + < JLK + < KJL = 180
Then,
3x - 16 + (180 - (8x - 19)) + 2x + 15 = 180
expand the bracket, we have;
3x - 16 - 8x - 19 + 2x + 15 = 0
add the like terms
-3x + 18 = 0
collect the terms
-3x = -18
x = 6
Then, the angle LJK = 2x + 15 = 2(6) + 15 = 27 degrees
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A circle C has center at the origin and radius 5 . Another circle K has a diameter with one end at the origin and the other end at the point (0,15) . The circles C and K intersect in two points. Let P be the point of intersection of C and K which lies in the first quadrant. Let (r,θ) be the polar coordinates of P , chosen so that r is positive and 0≤θ≤2 . Find r and θ .
The value of R and θ is 6.18 and 53.13 degrees, under the condition that a circle C has center at the origin and radius 5 .
In order to evaluate the equation of the circle K. The diameter of K has endpoints at the origin and (0,15). Then, the center of K is at (0,7.5) and its radius is 7.5. Therefore, the evaluated equation of K is
x² + (y-7.5)² = 56.25.
The equation of circle C is x² + y² = 25.
The two circles intersect at two points. Now we have to evaluate the coordinates of these points.
Staging y = 5 - x² in the equation of K,
we get
x² + (5-x²-7.5)² = 56.25.
Applying simplification on this equation
x⁴ - 10x² + 31.25 = 0.
Calculating this quadratic equation gives us
x² = 5 ± √(10)/2.
If P lies in the first quadrant,
we choose x² = 5 + √(10)/2 and y = √(25-x²) to get P in Cartesian coordinates.
Converting P to polar coordinates gives us
r = √(x²+y²) and θ = arctan(y/x).
Staging x = √(5+√(10)/2) and y = √(25-x²) in these equations gives us
r ≈ 6.18 and θ ≈ 0.93 radians.
Using this formula to convert into degree
Rad × 180/π
= 0.93 × 180/π
≈ 53.13 degrees
Therefore, r ≈ 6.18 and θ ≈ 53.13 degrees.
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Hello I need help with homework
a) The rate of slower train is 110 km/hr
b) The speed of faster train is 112 km/hr
Given data ,
When two objects are moving towards each other, their combined rate is equal to the sum of their individual speeds.
So, the rate of the slower train as x km/hr. Since the faster train is traveling 12 km/hr faster, its rate will be ( x + 12 ) km/hr.
The combined rate of the two trains is x + (x + 12) = 2x + 12 km/hr.
We know that the trains travel a total distance of 696 km and meet in 3 hours. Using the formula distance = speed × time, we can set up the following equation:
(2x + 12) × 3 = 696
Simplifying the equation:
6x + 36 = 696
Subtracting 36 from both sides:
6x = 660
Dividing both sides by 6:
x = 110
Hence , the rate of the slower train is 110 km/hr, and the rate of the faster train is 110 + 12 = 122 km/hr.
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The scatter plot shows the number of apples Aniyah picked from her apple trees each year. The equation of the line of fit is:
y = 15.2x + 111
What is the predicted number of apples picked in year 5? Explain your answer.
Answer: 187 apples
Step-by-step explanation:
Substitute "year 5" into the equation. y = 15.2(5) +111.
y = 76 + 111
y = 187