jasper is picking out his clothes for school he can wear a t shirt polo or sweat shirt as a top for pants khakis jeans sweat pants corduroys and short he can wear boots or tennis shoes or sandals jasper also need a jacket he has a ski and a rain coat and a wool coat how many combinations did jasper pick in total

Answers

Answer 1

Jasper has a total of 135 possible combinations for his outfit.

To calculate the total number of combinations that Jasper can pick for his outfit, we need to multiply the number of options for each category: tops, pants, shoes, and jackets.

For tops, Jasper has three options: t-shirt, polo, or sweatshirt.

For pants, he has five options: khakis, jeans, sweatpants, corduroys, or shorts.

For shoes, he has three options: boots, tennis shoes, or sandals.

For jackets, he has three options: ski coat, raincoat, or wool coat.

To calculate the total number of combinations, we multiply the number of options for each category:

3 (tops) × 5 (pants) × 3 (shoes) × 3 (jackets) = 135

Jasper has a total of 135 possible combinations for his outfit.

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Related Questions

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?

Answers

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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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.

Answers

Answer: 187 apples

Step-by-step explanation:

Substitute "year 5" into the equation. y = 15.2(5) +111.

y = 76 + 111

y = 187

Complete the equations. 95 × 1 0^3 =? 95 × 1 0^4=? 95×10^5 =?

Answers

Answer:

95 × 10^3 = 95000

95 × 10^4 = 950000

95 × 10^5 = 9500000

factor the expression w^2(w+8)-5(w+8)​

Answers

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).

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?

Answers

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.

Answers

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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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.

Answers

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 region

So, 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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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

Answers

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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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

Answers

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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Write the polynomial as a product of linear factors.
x^(4)-x^(3)-5^(2)-x-6

Answers

The factored form of the polynomial [tex]x^4 - x^3 - 5x^2 - x - 6[/tex] is:

[tex](x - 2)(x^3 + x^2 - 3x - 7)[/tex]

We have,

To factor the polynomial [tex]x^4 - x^3 - 5x^2 - x - 6,[/tex]

we can look for its roots and express it as a product of linear factors.

First, let's check if there are any rational roots using the rational root theorem.

The possible rational roots can be found by taking the factors of the constant term (-6) and dividing them by the factors of the leading coefficient (1).

The factors of -6 are: ±1, ±2, ±3, ±6

The factors of 1 are: ±1

The possible rational roots are: ±1, ±2, ±3, ±6

By testing these values, we find that x = 2 is a root of the polynomial.

Using synthetic division, we can divide the polynomial by (x - 2) to find the quotient.

The quotient is [tex]x^3 + x^2 - 3x - 7.[/tex]

Now, we can continue factoring the quotient.

The polynomial x³ + x² - 3x - 7 does not have any rational roots.

We can try factoring it by grouping or using other factoring methods, but in this case, it does not factor nicely into linear factors.

Therefore,

The factored form of the polynomial [tex]x^4 - x^3 - 5x^2 - x - 6[/tex] is:

[tex](x - 2)(x^3 + x^2 - 3x - 7)[/tex]

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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?​

Answers

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%.

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.

Answers

The angle measure of LJK is 27 degrees

How to determine the angle

Following 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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Linda is adding padding to all of the surfaces inside her attic for extra warmth in the winter.

Answers

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?

Help
please
please
please

Answers

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 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

Answers

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 Information

The table is given by the image presented at the end of the answer.

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Please help with picture below

Answers

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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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

Answers

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.

Gina Wilson Unit 10: Circles Homework 9: Standard Form of a Circle

Answers

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 Circle

The 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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please fast if could

Answers

Answer:9/41

SOH = opposite over hypotenuse

Step-by-step explanation:

Hello I need help with homework

Answers

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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Find g(0), g(-1), g(2), and g(2/3)
for g(x) =x/ square root 1-x^2

Answers

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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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?

Answers

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°.

Answers

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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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°

Answers

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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Is 34.05 greater than 34.59

Answers

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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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 .

Answers

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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what is the equation that contains the point M(1,10,3), N(4,10,6) and P(7,10,9)?

Answers

The equation of the line is: x = 1 + 3t,, y = 10, z = 3 + 3t.

How to determine the equation of the line

To 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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Which graph shows the solution of h (x) = 2x^2 - x - 1?

Answers

The solution to the function h(x) = 2x² - x - 1 is given by the graph attached which is a positive quadratic graph.

Understanding Quadratic Graph

A 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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100 Points! Algebra question. Photo attached. Solve the equation. Please show as much work as possible. Thank you!

Answers

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)

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.

Answers

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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