Which of the following options could represent a possible set of interior angles of a triangle? 45°, 105°, and 120° O 60°, 150° and 150° 15. 35 and 40 35. 65, and 80​

Given:

The center of the circle is the origin and the radius is 5.

Required:

Find the equation of the circle.

Explanation:

The equation of the circle when the center is (a,b) and the radius is r is given as:

The center (a,b) = (0,0)

radius r = 5

So the equation of the circle is:

Final Answer:

Option C is the correct answer.

By definition, the x-coordinate of the terminal point is equal to cos t and the y-coordinate is equal to sin t. This allows us to easily find the values of sin t and cos t. To find tan t, we use the formula tan t = sin t / cos t, which we can substitute with our previously found values for sin t and cos t.

First need to understand what is meant by the terms "terminal point" and "unit circle". The unit circle is a circle with a radius of 1, centered at the origin of the coordinate plane. The terminal point is the point where the circle intersects with a line that starts at the origin and passes through an angle t measured in radians.
To find sin t and cos t, we need to look at the coordinates of the terminal point. Let's call the x-coordinate of the terminal point x' and the y-coordinate y'. By definition, x' = cos t and y' = sin t. Therefore, sin t = y' and cos t = x'.
To find tan t, we use the formula tan t = sin t / cos t. Substituting in our values for sin t and cos t, we get:
tan t = y' / x'
So, to summarize:
- sin t = y'
- cos t = x'
- tan t = y' / x'
In summary, we can use the unit circle to determine the values of sin t, cos t, and tan t for any angle t measured in radians. The terminal point on the unit circle is the point where the circle intersects with a line passing through the origin at angle t.

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Answer:

f(g(x)) = x² - 6x + 8

Step-by-step explanation:

to evaluate f(g(x)) , substitute x = g(x) into f(x)

f(x² - 6x + 13)

= x² - 6x + 13 - 5 ← collect like terms

= x² - 6x + 8

Hello!

The slope equation is y = mx + b

mx is the slope and b is the yintercept.

4. y= -3x + 5

See where I put the slope and y intercept above?

Those are where the numbers go in that equation.

5. 3x + y = 5

The standard for equation is: Ax + by = c

y = -3x + 5

we need to make the equation look like the standard form equation.

y = -3x + 5

lets add 3x to both sides

The answer is 3x + y = 5

6. m = \(\frac{3}{2}\)

We need to use this formula: \(m=\frac{y2-y1}{x2-x1} \\\\\\\)

The points said are: (2, 5) and (4, 8)

\(m=\frac{8-5}{4-2}\)

m = 3/2

M is the slope.

---------------

I hope this helps,

Have a great day!!

Answer:

1 2/5 = 1 1/2

7/9 = 1

4/9 = 1/2

3 5/7 = 4

Step-by-step explanation:

1. we must round 1 2/5

based on the answer choices we can determine that 1 1/2 is the most rational answer. This is because it is not only the only answer with the whole number, 1 but also 2/5 would round to 1/2.

2. We must round 7/9

This would round up to 1. This is because it is closest to the whole number, not 0 and not 1/2.

7 * 2 = 14

9 * 2 = 18

14/18 is only 4/18 away from being 1. This means that it would round up to 1.

3. we must round 4/9

This rounds to 1/2. If you multiply both side by 2:

4 * 2 = 8

9 * 2 = 18

8/18 for that to be 1/2 it would need 1/18. Thus this rounds up to 1/2.

4. We must round 3 5/7

5/7 would round up to a whole number.

3 + 1 = 4

Thus 3 5/7 = 4 when rounded to the nearest whole number.

The angle of elevation of the observer to the kite is around 30 degrees

The hypotenuse in the given question is 405 feet, while the height of the kite from the ground is 210 feet.

It is also stated that the kite's height from the ground does not change.

The tangent function may be used to calculate the angle of elevation.

tan(angle of elevation) = height of the kite / horizontal distance to the kite

Since the height of the kite is 210 feet and the horizontal distance (the length of the kite string) is 405 feet, we can calculate the angle of elevation:

Let Ф be the angle of elevation

tan(angle of elevation) = 210/405

Ф = tan-1(210/405)

Ф = tan-1(0.516)

Ф = roughly 30 degrees

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Answer

NO

step by step explanation:

The definition of outlier is observational data that appears with extreme values, either univariate or multivariate. What is meant by extreme values in observations are values that are far or completely different from most of the other values in the group

I hope this helps

Answer:

15 miles

Step-by-step explanation:

5 = price per mile   x= number of miles   1.5 = pick-up fee   76.5 = total  

5x + 1.5 = 76.5

5x = 76.5 - 1.5

5x = 75

x =75/ 5

x = 15

The function (g+h)(n-4) is the sum of the function g(n-4) and h(n-4) will be written as (g+h)(n-4) = n² - 7n + 9.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The functions are given below.

g(n) = n² + 4n

h(n) = - 3n - 3

The function (g+h)(n) is calculated as,

(g+h)(n) = g(n) + h(n)

(g+h)(n) = n² + 4n - 3n - 3

(g+h)(n) = n² + n - 3

Put n = n - 4, then we have

(g+h)(n-4) = (n - 4)² + (n - 4) - 3

(g+h)(n-4) = n² + 16 - 8n + n - 4 - 3

(g+h)(n-4) = n² - 7n + 9

The function (g+h)(n-4) will be (g+h)(n-4) = n² - 7n + 9.

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2.25 kilometers on the ground is represented by 9cm on the map

According to the question, the scale on the map is in the ratio 1 : 25000

That is the     length on the map = length of the ground

                               1cm = 25000 cm

                                1 cm = 25000/100000 km

                                1 cm = 0.25 km

Now we have to find the length of the ground in kilometres which is represented by 9cm on the map

That is we have to find the ratio,  9cm : x km

As from above, we know that,

                          1cm = 0.25 km

                           9 cm = 0.25*9 km

                                    = 2.25 km

Hence 2.25 km on the ground is represented by 9 cm on the map

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The number terms in the given expression is 3, they are 5xy, -3x and -82.

The given expression is 5xy-3x-82.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The terms involved in an expression in math are:

Constant: A constant is a fixed numerical value.

Variable: A variable is a symbol that doesn't have a fixed value.

In the given expression 5xy-3x-82, there are three terms, which are 5xy, -3x and -82.

Therefore, the number terms in the given expression is 3, they are 5xy, -3x and -82.

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Answer:

the answer is 40

Answer:

8 the answer is 8 if u need help just tell me cuz i just did this quiz and i got a 90 and i dont think urs is diffrent then mine

Step-by-step explanation:

Answer:

  C) The difference between the 75th and 25th percentiles is 12 inches.

Step-by-step explanation:

The interquartile range is the length of the "box" in a "box and whisker" plot. One end is the 25th percentile, and the other end is the 75th percentile. It is the difference between the maximum and minimum of the middle 50% of the data.

For the baker's loaf-length data set, the interquartile range being 12 inches means the loaves in the 75th percentile are 12 inches longer than the loaves in the 25th percentile. This could be described by choice C.

The solution to the given linear equation is x = 9

From the question, we are to solve the given linear equation

The given equation is

7x + 3x - 18 = 6(x + 3)

By the distributive property, we get

7x + 3x - 18 = 6x + 18

Combine like terms

7x + 3x - 6x = 18 + 18

Addition property of equality

10x - 6x = 36

Subtraction property of equality

4x = 36

Division property of equality

x = 36/4

x = 9

Hence, the solution to the given linear equation is x = 9

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Answer:

x = 9

Step-by-step explanation:

7x + 3x - 18 = 6 (x + 3) 

7x + 3x - 18 = 6 (x + 3) Use the distributive property, which gets us 7x + 3x - 18 = 6x + 18

Combine terms, first 18 + 18 = 36 

Then you use the addition property of equality 7x + 3x = 10x 

You now have 10x - 6x = 36 

Then you use the subtraction property of equality, which subtracts 10x and 6x 

You're left with 4x = 36 

Then you do the division property of equality, so 4x divided by 4 is one and 36 divided by 4 is 9

The answer is x = 9 

Added this after doing the problem myself :)

Answer:

10π

Step-by-step explanation:

The circumference of a circle is the distance of the outside of the circle. The formula for circumference is C=2πr.

In the question, you are given the diameter. Diameter is the radius times 2. So, to find the radius you can divide the diameter by 2. Since, 10cm/2 is 5 cm, 5cm is the radius.

Then, plug this information into the formula to solve for C.

This means that, in terms of pi, the circumference is 10π cm.

The complete factorization of the polynomial x³ + 2x² -x - 2 is equal to (x + 2)(x + 1)(x - 1)

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

A polynomial is an expression consisting of coefficients and variables forming an equation.

Given the polynomial:

x³ + 2x² -x - 2

Factorizing:

= (x + 2)(x² - 1)

= (x + 2)(x + 1)(x - 1)

The polynomial x³ + 2x² -x - 2 is equal to (x + 2)(x + 1)(x - 1)

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The conversion 336g to m³ is impossible because they measure different units

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

Convert 336g to m³

To convert a unit to another, the units must measure the same quantity

Take for instance:

Grams can be converted to kilograms because they both measure mass

Using the above as a guide, we have the following:

336g to m³  cannot be done because of the different quantities they represent

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Answer:

The percent increase is 12%

Step-by-step explanation:

Hope this helps

Answer:

12%

Step-by-step explanation:

Answer:

The ladder is 7 Meters up the wall.

Answer:

i think its a but im not sure and i dont know how to explain it

The formula to calculate the circumference of a circle is given by \(\displaystyle\sf C=2\pi r\), where \(\displaystyle\sf C\) represents the circumference and \(\displaystyle\sf r\) is the radius of the circle.

Given that the diameter of the above ground circular swimming pool is 30 ft, we can find the radius by dividing the diameter by 2. So, the radius \(\displaystyle\sf r\) would be \(\displaystyle\sf \frac{30}{2}=15\) ft.

Now, substituting the value of \(\displaystyle\sf r\) into the formula, we have:

\(\displaystyle\sf C=2\pi ( 15)\)

Using \(\displaystyle\sf \pi =3.14\), we can calculate the circumference:

\(\displaystyle\sf C=2( 3.14)( 15)\)

\(\displaystyle\sf C=2( 3.14)( 15)\)

\(\displaystyle\sf C=94.2\) ft

Therefore, the circumference of the pool is 94.2 ft.

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The percentage change in frequency is 0%.Hence, the natural frequency of torsional vibration of the custen is given by f = 25.7 / L₀^(1/2) and the percentage change in frequency is 0%.

We are given that:

Total moment of inertia of moving parts = I = 1 kgm²

Moment of inertia of air-screw = I = 18 kgm²

Outer diameter of hollow shaft = D₀ = 80 mm

Inner diameter of hollow shaft = Dᵢ = 35 mm

Length of hollow shaft = L = 0.30 m

Stiffness of the crank-throw = K = 2.5 × 10⁴ Nm/rad

Shear modulus of elasticity = G = 83000 N/mm²

We need to calculate the natural frequency of torsional vibration of the custen.

The formula for natural frequency of torsional vibration is: f = (1/2π) [(K/L) (J/GD)]^(1/2)

Where, J = Polar moment of inertia

J = (π/32) (D₀⁴ - Dᵢ⁴)

The formula for equivalent length of hollow shaft is given by:

q₁ = q₁₁ + q₁₂

Where, q₁₁ = (π/32) (D₀⁴ - Dᵢ⁴) / L₁q₁₂ = (π/64) (D₀⁴ - Dᵢ⁴) / L₂

L₁ = length of outer diameter

L₂ = length of inner diameter

For the given shaft, L₁ + L₂ = L

Let L₁ = L₀D₀ = D = 80 mm

Dᵢ = d = 35 mm

So, L₂ = L - L₁= 0.3 - L₀...(1)

For the given crank-throw, q₁ = (π/32) (D⁴ - d⁴) / L, where D = 80 mm and d = 80 mm

Hence, q₁ = (π/32) (80⁴ - 35⁴) / L

Therefore, q₁ = (π/32) (80⁴ - 35⁴) / L₀...(2)

From the formula for natural frequency of torsional vibration, f = (1/2π) [(K/L) (J/GD)]^(1/2)

Substituting the values of K, J, G, D and L from above, f = (1/2π) [(2.5 × 10⁴ Nm/rad) / (L₀) ((π/32) (80⁴ - 35⁴) / (83000 N/mm² (80 mm)³))]^(1/2)f = (1/2π) [(2.5 × 10⁴ Nm/rad) / (L₀) (18.12)]^(1/2)f = 25.7 / L₀^(1/2)...(3)

Now, if we assume that the air-screw mass is infinite, then the moment of inertia of the air-screw is infinite.

Therefore, the formula for natural frequency of torsional vibration in this case is:

f = (1/2π) [(K/L) (J/GD)]^(1/2)Substituting I = ∞ in the above formula, we get:

f = (1/2π) [(K/L) (J/GD + J/∞)]^(1/2)f = (1/2π) [(K/L) (J/GD)]^(1/2)f = 25.7 / L₀^(1/2)

So, in this case also the frequency is the same.

Therefore, the percentage change in frequency is 0%.Hence, the natural frequency of torsional vibration of the custen is given by f = 25.7 / L₀^(1/2) and the percentage change in frequency is 0%.

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Answer: -15 divided by 0.3 is the same as -15/3/10 but to solve we can do -15 times 10/3 witch is -150/3=-50

Step-by-step explanation:

Answer:

98=50+3t

Step-by-step explanation:

5*10

50

98-50

48

48/3

16

The linear equation is 98 = 50+3t and the no of tomatoes sold is 16.

Given that,

Based on the above information, the calculation is as follows:

98 = 50+3t

98 - 50 = 3t

48 = 3t

t = 16

Therefore we can conclude that The linear equation is 98 = 50+3t and the no of tomatoes sold is 16.

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It is confirmed that 9/10 divided by 3/4 is indeed equal to 36/30.To check 9/10 divided by 3/4 is equal to 36/30, we can follow these steps:1. Convert 9/10 to an equivalent fraction with a denominator of 30 by multiplying both the numerator and denominator by 3:9/10 × 3/3 = 27/30.2.

Convert 3/4 to an equivalent fraction with a denominator of 30 by multiplying both the numerator and denominator by 10:3/4 × 10/10 = 30/40 = 3/4.3. Now we can rewrite the division as multiplication, where we multiply the first fraction by the reciprocal of the second fraction:27/30 ÷ 3/4 = 27/30 × 4/3.4.

Simplify the fraction by canceling out the common factors between the numerator and denominator:27/30 × 4/3 = 9/10 × 4/1 = 36/10.5. Reduce the fraction by dividing the numerator and denominator by their greatest common factor (GCF) of 2:36/10 ÷ 2/2 = 18/5.6.

Check whether the simplified fraction 18/5 is equal to the given fraction 36/30. To do this, we can multiply both the numerator and denominator of 18/5 by 6 to get an equivalent fraction with a denominator of 30:18/5 × 6/6 = 108/30. We can see that 108/30 is equal to 36/10, so we have confirmed that 9/10 divided by 3/4 is indeed equal to 36/30.

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The correct answer is A. The selling price of a bond is affected by the coupon rate and the market interest rate.

If the coupon rate is less than the market interest rate, investors will not be interested in buying the bond because they can get a higher return elsewhere. This results in the selling price of the bond being less than its face value of $10,000.
The selling price of a $10,000 5-year bond will be less than $10,000 if the:
A. Coupon rate is less than the market interest rate

This is because when the coupon rate (the interest paid by the bond) is lower than the market interest rate, investors would prefer to invest in other options that offer a higher return. Therefore, to attract buyers, the bond's selling price would be discounted to compensate for the lower coupon rate.

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Answer:

B

Step-by-step explanation:

The independent variable is t (time) because no matter what happens the weeks will still pass. The dependent variable is b (balance) because it depends on the amount of time passed. You can see that after every week the balance decreases by 50. So when the independent variable increases by 1, the dependent variable decreases by 50.

Answer:

1) B. -2 hours per person

2) C. 3.60 per pound

Step-by-step explanation:

1)

We can make a slope triangle connecting the points (4, 12) and (10,0)

We get -12/6, or -2 as our slope & final answer

2)

You can do x/y to find the unit rate for this one, or in this case 18/5 = 3.6