Give the coordinates for all three possible
locations of the fourth vertex.
Y
9
8
7
6
5
4
3
2
1
0
X
1 2 3 4 5 6 7 8 9

Answer:

Step-by-step explanation:

Ronald's walking speed is 3 miles per hour, and he walks for 2 hours, so he covers 3 * 2 = 6 miles. In the next hour, he runs at a speed of 6 miles per hour, covering an additional 6 miles. Therefore, Ronald traveled a total of 6 + 6 = 12 miles.

Answer:

The greatest area enclosed by the fence will be a square. If the farmer has 60 metres of perimeter fencing, he can use 15 meters of fencing for each side of the square. This would give him an area of 15² = 225 m². Since he can keep one chicken for every square meter, he can keep 225 chickens. Therefore, the farmer should arrange his fence in the shape of a square to get the greatest area.

Answer:

larger angle = 63°

Step-by-step explanation:

complementary angles sum to 90°

let x be the smaller angle then larger angle is x + 36 , then

x + x + 36 = 90

2x + 36 = 90 ( subtract 36 from both sides )

2x = 54 ( divide both sides by 2 )

x = 27

Then

larger angle = x + 36 = 27 + 36 = 63°

The equivalent equation of  r sinθ = 10 in rectangular coordinates is y²  +   y⁴/x² - 100 = 0.

The rectangular coordinates is calculated from the polar equation as follows;

r sinθ = 10

the conversion from polar to rectangular coordinates;

r² = x² + y²

r = √(x² + y²) ----- (1)

y/x = tanθ  ------ (2)

r sinθ = 10

√(x² + y²)(y/x) = 10

(x² + y²)(y²/x²) = 100

y²  +   y⁴/x² = 100

y²  +   y⁴/x² - 100 = 0

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The correct terms in the expression are,

⇒ 3x and 5x

We have to given that;

The quadratic equation is,

⇒ 15x² + x - 2 = (? - 1) (? + 2)

Now, We can simplify as;

⇒ 15x² + x - 2

⇒ 15x² + 6x - 5x - 2

⇒ 3x (5x + 2) - 1 (5x + 2)

⇒ (3x - 1) (5x + 2)

Thus, The correct terms in the expression are,

⇒ 3x and 5x

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Using Laws of Exponents, the solution to the given algebraic expression is: m⁹n¹⁵

Some of the Laws of Exponents are:

1) When multiplying the like bases, ensure you keep the base the same and then add the exponents.

2) When raising a base that has a power to another power, ensure you keep the base the same and then multiply the exponents.

3) When dividing like bases, ensure you keep the base the same and then subtract the denominator exponent from the given numerator exponent.

We are given the expression:

(m⁻³n⁻⁵)⁻³

Using the second law of exponents above, we have:

m⁻³*⁻³ x n⁻⁵*⁻³

= m⁹n¹⁵

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The verification of given segments in a triangle are parallel is as follow,

In triangle ABE, AC/ CE = BD/DE  are in proportion ⇒ CD || AB.

In triangle RVS, VT/TR = VU/US  are in proportion ⇒ UT || SR.

In the triangle ABE,

CD is the line segment divides AE and BE into equal parts.

AC = 1.5

CE = 1.5

BD = 1.5

DE = 1.5

AC/ CE = BD/DE

Line divides the two adjacent sides of a triangle are in proportion.

This implies ,

CD is parallel to AB.

In triangle RVS,

VT /TR = 90 /72

⇒VT /TR = 1.25

VU/US = 67.5/54

⇒VU/US = 1.25

This implies ,

VT/TR = VU/US are in proportion.

Hence , triangle proportionality theorem UT is parallel to RS.

Therefore, using triangle proportionality theorem in both the triangle that is,,

In triangle ABE , CD is parallel to  AB and in triangle RVS , UT || RS.

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Answer:

x = 99

Step-by-step explanation:

Since x is on a straight line the adjacent angle and x must equal 180. We will call this adjacent angle B. The angle to the right of B also is on a straight line.

So,

180 - 123 = the inside angle             Simplify

57

The addition of a triangles interior angles equals 180

180 = 42 + 57 + B                              Move variables to one side

180 - (42 + 57) = B                             Simplify

81 = B

Now we can solve for X

180 - 81 = x                                        Simplify

99

Answer:

49

Step-by-step explanation:

[tex]\int\limits^{12}_0 {-0.002t^{2} +0.7t} \, dt \\=(-0.002\frac{{12}^{3} }{3} )+(0.7\frac{{12}^{2} }{2} )\\-(-0.002\frac{{0}^{3} }{3} )-(0.7\frac{{0}^{2} }{2} )\\\\=(-0.002\frac{{12}^{3} }{3} )+(0.7\frac{{12}^{2} }{2} )-0-0\\\\=49.248\\[/tex]

The surface area of the prism for the given dimensions is equal to option B. 180 square centimeters.

Surface area of the prism

= Area of two right triangles + Area of rectangle 1 + Area of rectangle 2 + Area of the rectangle3

In a Triangle ,

Base = 12cm

height = 5cm

Area of the triangle = ( 1/2 ) × base × height

                                 = (1/2)× 12 × 5

                                 = 30 cm²

Length of rectangle 1 = 12cm

Width of rectangle 1 = 4cm

Area of rectangle 1 = 12 × 4

                                = 48 cm²

Length of rectangle2= 13cm

Width of rectangle 2 = 4cm

Area of rectangle 2= 13 × 4

                                = 52 cm²

Length of rectangle 3 = 5cm

Width of rectangle 3 = 4cm

Area of rectangle 3 = 5 × 4

                                = 20 cm²

Surface area of the prism

= Area of two right triangles + Area of rectangle 1 + Area of rectangle 2 + Area of the rectangle3

Substitute the values of the area we have,

⇒ Surface area of the prism  = 2(30 ) + 48 + 52 + 20

⇒ Surface area of the prism  =  180 square centimeters

Therefore, the surface area of the prism is equal to option B. 180 square centimeters.

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Answer:She is not correct The graph of g grows at a faster rate

than the graph of because 8 greater than 2

Step-by-step explanation:

Using PEMDAS, the exponents are done first.

8^3 = 512

4*2^3 = 32

This works for every number that X can be, 3 was just an example.

The missing side lengths for triangle ABC are 4, 4√3, and 8.

Based on the given information, it seems that the triangle is a right-angled triangle with angles of 30°, 60°, and 90°. Let's find the missing side lengths for triangle ABC using the given lengths and angles.
Identify the triangle type.
Since we have angles of 30°, 60°, and 90°, we are working with a 30-60-90 right-angled triangle.
Determine the ratio of side lengths.
In a 30-60-90 triangle, the ratio of the sides is 1:√3:2.
Find the corresponding side lengths.
Using the given lengths and the 1:√3:2 ratio, we can determine the side lengths for triangle ABC:
- If the shortest side (opposite the 30° angle) is 4, then the other sides would be 4√3 (opposite the 60° angle) and 8 (hypotenuse, opposite the 90° angle).

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Answer:

He rented the bike for 3 hours

Step-by-step explanation:

they charge $10 for just the bike and an adittional of $8 per hour and Willie payed $34 so u subtract 10 from 34 it leaves u with 24 and u then divide by 8 and u get 3 which means that he rented the bike for 3 hours :)

If the Raj’s bathtub is draining at rate of 1.5 gallons of water per-minute, then the range will be (c) all real numbers such that 0 ≤ y ≤ 40.

The "Range" of function is defined as the set of all possible "output-values'.

The amount of water remaining in the bathtub is decreasing as it drains, so the range of the function is bounded below by 0 (because we cannot have negative water in the bathtub) and above by 40 (the initial amount of water in the bathtub).

Looking at the given values of y, we can see that the value of "y" lies between 0 and 40.

Therefore, the correct option is (c).

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The given question is incomplete, the complete question is

Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, y, is a function of the time in minutes, x, that it has been draining.

   x          y

   0         40

  0.5     39.25

    1        38.5  

   1.5       37.75

What is the range of this function?

(a) all real numbers such that y ≤ 40

(b) all real numbers such that y ≥ 0

(c) all real numbers such that 0 ≤ y ≤ 40

(d) all real numbers such that 37.75 ≤ y ≤ 40.

The total length of the nylon rope that Jamie will use would be 15.3 feet of nylon rope.

Within this scenario specifically, one side of the right-angled triangle comprises the height of the tent (standing at 6.5-feet), and the other forms as the measure from the center of the tent to where Jaime stakes the ropes stretching outwards in another direction (with a calculated measure of 4-feet). Subsequently, we will refer to the extent of the nylon rope as R.

The Pythagorean theorem formula is:

R ² = 6.5 ² + 4 ²

R ² = 42. ²25 + 16

R ² = 58.25

R = 7. 63 ft

There are two ropes so the length would be :

= 7. 63 + 7. 63

= 15. 3 ft

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Answer:

Step-by-step explanation:

-11°

Answer:

CD = 4 , AD = 6

Step-by-step explanation:

AC is an angle bisector of ∠ BAD and divides the opposite side from the angle into segments that are proportional to the other two sides, that is

[tex]\frac{BC}{CD}[/tex] = [tex]\frac{AB}{AD}[/tex] ( substitute values )

[tex]\frac{6}{y-1}[/tex] = [tex]\frac{9}{2y-4}[/tex] ( cross- multiply )

6(2y - 4) = 9(y - 1) ← distribute parenthesis

12y - 24 = 9y - 9 ( subtract 9y from both sides )

3y - 24 = - 9 ( add 24 to both sides )

3y = 15 ( divide both sides by 3 )

y = 5

Then

CD = y - 1 = 5 - 1 = 4

AD = 2y - 4 = 2(5) - 4 = 10 - 4 = 6

Answer:

No

Step-by-step explanation:

No, y = 2x^3 + 5 is not a linear function. A linear function is a function that can be written in the form y = mx + b, where m and b are constants and x is the independent variable.

In the function y = 2x^3 + 5, we have a cubic term (x^3), which means that the function is not linear. The graph of a cubic function will have a curved shape, unlike a linear function, which will always be a straight line.

The simplification of the fractions given above through multiplication would be;

1.) 9 11/12

2.) 11 19/40

For question 1.)

2 5/6 × 3 2/4

Change the mixed fraction to single fraction;

= 17/6 × 14/4

= 17/6 × 7/2

= 119/12

= 9 11/12

For question 2.)

5 2/5 × 2 1/8

= 27/5 × 17/8

= 459/40

= 11 19/40

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Expressing each as a function of 15°, we have 6. tan165° = tan(150 + 15)° and 7. sin285° = sin(270 + 15)°

From the question, we have the following trigonometry function that can be used in our computation:

6. tan165°

7. sin285°

The above expressions are tangent and sine functions of 165 and 285 degrees

By mathematical expression, we have

165° = 150 + 15

285° = 270 + 15

This means that we can replace the expressions with 150 + 15 and 270 + 15

So in terms of 15 degrees, we have

6. tan165° = tan(150 + 15)° and 7. sin285° = sin(270 + 15)°

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Answer:

$8.92 each

Step-by-step explanation:

The graph of this function will behave as (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.

The demand function is given by d = 100 - 10p. This means that the quantity demanded (d) decreases as the price (p) increases.

The slope of the demand function is the rate of change of the quantity demanded with respect to the price. In this case, the slope is -10, which is negative. This indicates that as the price increases, the quantity demanded decreases.

The initial value of the demand function is 100, which represents the quantity demanded when the price is zero. This means that the demand function intersects the y-axis at (0, 100).

Therefore, the correct answer is (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.

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The value of distance between two points on graph is,

⇒ d = √32 units

We have to given that;

The coordinates of two points are,

⇒ (9, - 4) and (5, -8)

We know that;

The distance between two points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

Hence, The value of distance between two points on graph is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

⇒ d = √ (5 - 9)² + (- 8 - (-4))²

⇒ d = √ 16 + 16

⇒ d = √32

Thus, The value of distance between two points on graph is,

⇒ d = √32 units

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Answer:

The volume of the display case in cubic inches is 10,328 1/16 in.

The Taylor series for f(x) = e^2x at x = 1 is option D. Σ2ⁿ e²ˣ/n! (x - 1)ⁿ

The Taylor series for a function f(x) centered at x = a is given by:

f(x) = f(a) + f'(a)(x-a)/1! + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...

f'(a), f''(a), f'''(a), ... depict the first, second, third, and higher derivatives of f(x) evaluated at x = a.

In this case:

f(x) = e^(2x)

The first derivative is:

f'(x) = 2e^(2x)

The second derivative is:

f''(x) = 4e^(2x)

The third derivative is:

f'''(x) = 8e^(2x) etc.

Finding the Taylor series for f(x) = e^(2x) at x = 1, evaluate each derivative at x = 1:

f(1) = e^(2)

f'(1) = 2e^(2)

f''(1) = 4e^(2)

f'''(1) = 8e^(2) etc.

Plug these values into the Taylor series formula:

f(x) = f(1) + f'(1)(x-1)/1! + f''(1)(x-1)^2/2! + f'''(1)(x-1)^3/3! + ...

f(x) = e^(2) + 2e^(2)(x-1)/1! + 4e^(2)(x-1)^2/2! + 8e^(2)(x-1)^3/3! + ...

Simplify:

f(x) = e^(2) + 2e^(2)(x-1) + 2e^(2)(x-1)^2 + 4e^(2)(x-1)^3/3 + ...

Therefore, the Taylor series for f(x) = e^(2x) at x = 1 is: Σ2ⁿ e²ˣ/n! (x - 1)ⁿ which is option D.

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The country that had the greatest percentage of its students report being right-hand dominant with approximately 87% is UK

For Australia, 79 out of 120 students reported being right-hand dominant. So, the percentage of right-hand dominant students in Australia is:

(79/120) x 100 = 65.8%

For Canada, 68 out of 80 students reported being right-hand dominant. So, the percentage of right-hand dominant students in Canada is:

(68/80) x 100 = 85%

For the United Kingdom, 139 out of 160 students reported being right-hand dominant. So, the percentage of right-hand dominant students in the UK is

(139/160) x 100 = 86.9%

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The estimated number of the 160 ducks that have blue marks would be 5 ducks.

Assuming none of the 50 people have received a considerable reward, it is probable that winning a small prize bears higher odds than claiming a more substantial one. Estimating, the probability of achieving a large prize may be considered half as likely to succeed as obtaining a smaller sum:

P ( large prize ) :

= 0.5 x P(small prize)

= 0.5 x 0.06 = 0.03

Number of ducks with blue marks (large prize):

= ( total number of ducks ) x P( large prize )

= 160 x 0.03

= 4.8

= 5 ducks

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Let's call the two numbers we're trying to find x and y. We know that x + y = 12 and xy = 23. From the first equation, we can solve for one of the variables in terms of the other. So if we subtract x from both sides, we get y = 12 - x. Now we can substitute this expression for y into the second equation to get x(12 - x) = 23. Expanding this out, we get 12x - x^2 = 23. Rearranging, we get x^2 - 12x + 23 = 0. This quadratic equation can be factored as (x - 2)(x - 10) = 0. So either x = 2 and y = 10, or x = 10 and y = 2.

Answer:

The two numbers are 2 and 10.

Assuming that a fair coin was tossed twice, the probability that exactly one of the tosses is a head and the other toss is a tail is 1/2.

The probability of a certain event happening is the number of ways that event can occur, divided by the total number of possible outcomes. In this case, we are interested in finding the probability that exactly one of the two coin tosses results in a head and the other results in a tail.

There are two possible outcomes that satisfy this condition: HT and TH. Since the coin is fair, each of these outcomes has a probability of 1/4. Therefore, the total probability of getting exactly one head and one tail is:

P(HT or TH) = P(HT) + P(TH) = 1/4 + 1/4 = 1/2

In other words, there is a 50-50 chance of getting exactly one head and one tail when a fair coin is tossed twice.

To see why this is the case, we can think of each toss as an independent event with two possible outcomes (head or tail). There are four possible outcomes when we toss a coin twice, and two of these outcomes satisfy the condition of exactly one head and one tail. Therefore, the probability of getting exactly one head and one tail is 2/4, which simplifies to 1/2.

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