A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°

Answer:

81 square ft

Step-by-step explanation:

square B has a site lenght of 15ft

therefore square must have one of 3/5 of 15 which is 9

the area is 9x9=81

Answer:

27.5 miles per gallon

Step-by-step explanation:

38.5/1.4=27.5

Answer:

1 and 3

2 and 4

8 and 6

5 and 7

Step-by-step explanation:

:)

Using proportions, the width of the fountain in Luke's drawing is 4cm

To find the width of the fountain in Luke's drawing, you can use the proportion:

width(Luke's drawing) / width(fountain) = 2 cm / 5 m

We know that the height of the fountain in Isabella's drawing is 5 cm, and the scale of Isabella's drawing is 6 m to 3 cm, so we can use that information to find the width of the fountain:

width(fountain) = height(fountain) * (scale of Isabella's drawing) = 5 cm * (6 m / 3 cm) = 10 m

Now we can substitute that value into the proportion to find the width of the fountain in Luke's drawing:

width(Luke's drawing) = (width(fountain) * 2 cm) / 5 m = (10 m * 2 cm) / 5 m = 4 cm

So the width of the fountain in Luke's drawing is 4 cm.

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Answer:

152.7 cm/s

Step-by-step explanation:

The radius of DVD, r = 6 cm

The angular speed of DVD, \(\omega=243\ rev/min=25.45\ rad/s\)

We need to find the linear speed of the DVD.

The relation between linear speed and angular speed is given by :

\(v=r\omega\\\\v=0.06\times 25.45\\\\v=1.527\ m/s\)

or

v = 152.7 cm/s

So, the linear speed of the DVD is 152.7 cm/s.

Answer:

x < 5

Step-by-step explanation:

STEP

1

:

Pulling out like terms

1.1     Pull out like factors :

  30 - 6x  =   -6 • (x - 5)  

Equation at the end of step

1

:

STEP

2

:

2.1    Divide both sides by  -6  

Remember to flip the inequality sign:

Solve Basic Inequality :

2.2      Add  5  to both sides

            x < 5

Let h be the number of hats and s be the number of scarves that Alex can bring to the art fair. Then, the system of inequalities can be written as:

h ≤ 20 (since he can make at most 20 hats)

s ≤ 30 (since he can make at most 30 scarves)

h + s ≤ 40 (since he can make no more than 40 items altogether)

h + s ≥ 25 (since he wants to bring at least 25 items)

To graph this system of inequalities, we can plot the lines h = 20, s = 30, h + s = 40, and h + s = 25, and shade the region that satisfies all the inequalities. The resulting graph will be a quadrilateral with vertices at (20, 0), (0, 30), (10, 15), and (20, 5). The shaded region will be the area inside this quadrilateral that is above the line h + s = 25.

Answer:

$19.43

Step-by-step explanation:

when 5.5 pounds cost $14.74 then 1 pound costs $2.68

because 14.74 divided by 5.5 equals 2.68

To calculate the price of 7.25 you multiply the price for 1 pund by 7.25

7.25 * 2.68 = 19.43

Value of tan θ on the interval (270°, 360°) = -4/3

Pythagoras theorem states that in a right angled triangle, square of length of hypotenuse is equal to the sum of squares of lengths of other two sides, i.e. Perpendicular and base.

Given,

cosec θ = -5/4 on the interval (270°, 360°)

Given interval is on fourth quadrant.

Sine and cosecant are negative in fourth quadrant

cosec θ = -5/4

cosec θ = Hypotenuse/perpendicular

Comparing

Hypotenuse = 5

Perpendicular = 4

By Pythagoras theorem,

Base² = Hypotenuse² - Perpendicular²

Base² = (5)² - (4)²

Base² = 25 - 16

Base² = 9

Base = ±3

In fourth quadrant tangent is negative

tan θ = -4/3

Hence, -4/3 is the value of tan θ on the interval (270°, 360°).

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Answer:

  4 pairs

Step-by-step explanation:

You want the number of pairs of integers (m, n) such that m > n and m² -n² = 96.

The difference of squares is factored as ...

  m² -n² = (m -n)(m +n)

In order for the difference to be 96, these factors must be factors of 96.

The prime factorization of 96 is ...

  96 = 2^5 · 3

The number of divisors of 96 is the product of the exponents of these factors, each increased by 1:

  (5+1)(1+1) = 12

That is, there are 12/2 = 6 factor pairs ab such that a<b. They are ...

   96 = 1·96 = 2·48 = 3·32 = 4·24 = 6·16 = 8·12

The values of m and n relate to the values of 'a' and 'b' by ...

  m = (a+b)/2

  n = (b-a)/2

In order for m and n to be integers, the values of 'a' and 'b' must both have the same parity. That is, they must both be even, or both be odd. This eliminates the factor pairs 1·96 and 3·32, leaving 4 (a, b) pairs, hence 4 (m, n) pairs. Possible ordered pairs are ...

  (m, n) ∈ {(25, 23), (14, 10), (11, 5), (10, 2)} . . . . . 4 pairs

The pints of  water left in the aquarium is  2.5 pints

Using the conversion rule sho below:

1 cup  = 0.5 pint

If Sassan finds that 2 pints 1 cup of water have evaporated from the class aquarium, the total pint that evaporated is expressed as:

Total pint =  2  pints + 0.5 pint

Total pint =  2.5 pints

Hence the pints of  water left in the aquarium is  2.5 pints

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The given problem involves Bessel functions of half-integer order. In part (a), it is required to show that the substitution u = -1/2v converts Bessel's equation into + V = 0. In part (b), it needs to be demonstrated that the Bessel function of order 1/2 is equal to 2 times J1/2(x) TX, using the equation obtained in part (a) with s = 1/2. Finally, in part (c), Ja/2 and J-1/2 are to be found using J₁/2 from part (b) and the equation -sin z.

To begin, let's focus on part (a). By substituting u = -1/2v in Bessel's equation, which is equation (66) in the lecture notes, we obtain + V = 0. This substitution simplifies the equation and leads to a more manageable form.

Moving on to part (b), we can use the equation obtained in part (a) with s = 1/2. By applying this equation, we find that the Bessel function of order 1/2 is equal to 2 times J1/2(x) TX. This relationship provides a way to calculate the Bessel function of order 1/2 using the known Bessel function J1/2(x).

Finally, in part (c), we can utilize the result from part (b), J1/2(x) = 2 J1/2(x) TX, along with the equation -sin z. By substituting J1/2(x) with 2 J1/2(x) TX in the equation -sin z, we can find Ja/2 and J-1/2.

Overall, the problem involves demonstrating the conversion of Bessel's equation using a substitution, determining the Bessel function of order 1/2, and finding Ja/2 and J-1/2 using the obtained equation and -sin z.

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Answer: 0.01 = 10-2 .

Step-by-step explanation: have a good day!

Answer:

3

Step-by-step explanation:

|a| - |b| is the absolute value of a minus the absolute value of b

a = 8

b = -5

|8| - |-5|

8 - 5

3

The charge on the K+ ion is 1.6 × 10⁻¹⁹ C. This can be calculated using the force and electric field strength, which are related to the mass and acceleration of the ion.

The mass and acceleration of a K+ ion are given as 6.5 × 10⁻²³ kg and 1.7 × 10⁶ m/s², respectively.

To calculate the charge on the K+ ion, we need to use the formula:

F = ma

Where F is the force, m is the mass, and a is the acceleration.

We can rearrange the formula to solve for the force:

F = ma

F = (6.5 × 10⁻²³ kg) × (1.7 × 10⁶ m/s²)

F = 1.105 × 10⁻¹⁶ N

Next, we can use another formula to calculate the charge on the K+ ion:

F = qE

Where F is the force, q is the charge, and E is the electric field strength. We can rearrange the formula to solve for the charge:

q = F/E

We are given the acceleration of the K+ ion, which we can use to find the electric field strength:

E = a/q

We can substitute the value of acceleration a = 1.7 × 10⁶ m/s² and solve for the electric field strength:

E = a/q

q = a/E

Mass of K+ ion m = 6.5 × 10⁻²³ kg

Acceleration a = 1.7 × 10⁶ m/s²

Charge on K+ ion q = 1.6 × 10⁻¹⁹ C

The charge on the K+ ion is 1.6 × 10⁻¹⁹ C. This can be calculated using the force and electric field strength, which are related to the mass and acceleration of the ion.

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Answer:

Step-by-step explanation:

both  A and B are equivalent

The end behavior of the Polynomial f(x) = -4x⁶ + 6x² - 52 is;

B. f(x) is an even function so both ends of the graph go in the same

direction

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

Now, we are given the polynomial;

f(x) = -4x⁶ + 6x² - 52

Let us first test if the polynomial is even;

f(1) = -4(1)⁶ + 6(1)² - 52

f(1) = -50

Similarly;

f(-1) = -4(-1)⁶ + 6(-1)² - 52

f(-1) = -50

Since f(1) = f(-1), we can say that both ends of the graph go in opposite

directions.

Lastly, the leading coefficient is negative because it is -4 and as such it means that the left end goes down.

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Answer:

B

Step-by-step explanation:

(a+b)^2

using Pascal triangle

1 1

1 2 1

1 3 3 1

so the third term in the expansion of (a+b)^2

we use

1 2 1

a^2 + 2ab+b

hence the coefficient of third term is 1

option B is collect

The number of 15-year old students that took part in the survey is 300 students and 20 "15-year old" students spent between 35 and 45 minutes on social media.

A frequency polygon can be defined as a type of line graph that is used to plot a class frequency against the class midpoint.

For the 15-year old students, the total number of students would be calculated by adding all the data points at each frequency:

Total students = 30 + 30 + 50 + 60 + 40 + 50 + 40

Total students = 300 students.

In order to determine the number of 15-year old students than 11-year old that spent between 35 and 45 minutes on social media, we would calculate the average and then read it from the frequency polygon.

Average = (35 + 45)/2

Average = 80/2

Average = 40.

For the 11-year old, we have:

Frequency (40) = 40

For the 15-year old, we have:

Frequency (40) = 60

Now, we can calculate the difference as follows:

Difference = 60 - 20

Difference = 20 students.

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Answer:

Chelsea can buy 5 shirts.

Step-by-step explanation:

You can't split shirts when buying them, so Chelsea can buy 5 shirts.

Answer:

decay

Step-by-step explanation:

it is because 0.4 is less than 1 but greater than zero which signals exponential decay.

Answer:

decay

Step-by-step explanation:

it is because 0.4 is less than 1 but greater than zero which signals exponential decay.

The domain is the span of the x-values, and the range is the span of the y-values. In each, we are looking for the smallest and largest values.

Domain: x starts at -7, and goes to infinity (we cannot see an end)

(-7, infinity)

Range: y starts at negative infinity (we cannot see where it would start), and goes to 3

(negative infinity, 3)

Hope this helps!

Answer:

the domain starts at -7 ... only one answer has the domain starting at -7

domain(-7, infinity)

Step-by-step explanation:

the domain starts at -7 ... only one answer has the domain starting at -7

The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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Answer:

6

Step-by-step explanation:

15.50 x 6= 93 and 100-7=93 therefor its 6

Answer:

x = - 11

Step-by-step explanation:

3(x + 5) = x - 7

3x + 15 = x - 7

2x  = -7 - 15

2x = - 22

x = - 11

Hope this helps!

Answer:

Step-by-step explanation:

(3-7)/(-2+1)= -4/-1= 4

y - 7 = 4(x + 1)

y - 7 = 4x + 4

y = 4x + 11

Answer:

the length is 7 or 3 the width is 3 or 7

Step-by-step explanation:

7 x 3 = 21

Answer:

The crayon box is 9 centimeters long and 1.5 centimeters wide.

Step-by-step explanation:

L = 3 + 4w

p = 2L + 2w

21 = 2 (3 + 4w) + 2w

(show work)

w = 1.5

L = 3 + 4 * 1.5

(show work)

L = 9

pls mark brainliest :))