7 Determine whether the equation below does or does
not represent a proportional relationship. Support your
answer with a table or a graph.
Equation: y = 3x + 2
pls help

Answer:

B

Step-by-step explanation:

44/77

=0.55

Answer:

\(\displaystyle s(t)=\frac{3}{4}t^3+10t^3+5t+3\)

Step-by-step explanation:

Integrate v(t) with respect to time

\(\displaystyle \int(3t^3+30t^2+5)\,dt\\\\=\frac{3}{4}t^4+10t^3+5t+C\)

Plug-in initial condition to get C

\(\displaystyle s(0)=\frac{3}{4}(0)^3+10(0)^3+5(0)+C\\\\3=C\)

Thus, the position function is \(\displaystyle s(t)=\frac{3}{4}t^3+10t^3+5t+3\) given the velocity function and initial condition.

Answer:

2, 3, 7 or 8

Step-by-step explanation:

Answer:

x = 73

Step-by-step explanation:

The sum of both angles is 158

85+x = 158

Subtract 85 from each side

85+x-85 = 158-85

x = 73

Answer:

65

Step-by-step explanation:

150 - 85=65

Triagonometric function tan(A+B)/cot(A−B) is tan²A-tan²B/1-tan²Atan²B

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given,

tan(A+B)/cot(A-B)

tan(A+B)/1/tan(A-B)

(tanA+tanB/1-tanAtanB)/1/(tanA-tanB/1+tanAtanB)

tanA+tanB/1-tanAtanB)×tanA-tanB/1+tanAtanB

We know algebraic identity

(a+b)(a-b)=a²-b²

(tanA+tanB/1-tanAtanB)×(tanA-tanB/1+tanAtanB)

tan²A-tan²B/1-tan²Atan²B

Hence, triagonometric function tan(A+B)/cot(A−B) is tan²A-tan²B/1-tan²Atan²B

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The derivative of f(x) = sech^(-1)(x^2) is f'(x) = 2x/sqrt(1 - x^4).

a) To find f'(x) for f(x) = x*sin(x), we can use the product rule and the derivative of the sine function.

Using the product rule, we have:

f'(x) = (xsin(x))' = xsin'(x) + sin(x)*x'

The derivative of sin(x) is cos(x), and the derivative of x with respect to x is 1. Therefore:

f'(x) = x*cos(x) + sin(x)

So, the derivative of f(x) = xsin(x) is f'(x) = xcos(x) + sin(x).

(b) To find f'(x) for f(x) = sech^(-1)(x^2), we can use the chain rule and the derivative of the inverse hyperbolic secant function.

Let u = x^2. Then, f(x) can be rewritten as f(u) = sech^(-1)(u).

Using the chain rule, we have:

f'(x) = f'(u) * u'

The derivative of sech^(-1)(u) can be found using the derivative of the inverse hyperbolic secant function:

(sech^(-1)(u))' = 1/sqrt(1 - u^2)

Since u = x^2, we have:

f'(x) = 1/sqrt(1 - (x^2)^2) * (x^2)'

Simplifying:

f'(x) = 1/sqrt(1 - x^4) * 2x

So, the derivative of f(x) = sech^(-1)(x^2) is f'(x) = 2x/sqrt(1 - x^4).

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The Rs. 10,000 Regan lent to Sandip and Saline and the Rs.2160 more interest Saline paid than Sandip after 3 years at an 18% simple interest rate, indicates by expressing the amounts using equations, that the amount Regan gives to Sandip and Saline is Rs. 3,000 and Rs. 7,000 respectively.

An equation is the presentation of a statement of the equivalence between quantities, or expressions, by joining the expressions with a '=' sign.

The amount Regan has = Rs. 10,000

Let x represent the amount Regan lent to Sandip, we get;

The amount Regan lent to Saline = 10,000 - x

The interest rate of the loan Regan lent to Sandip and Saline = 18% simple interest

The interest Saline paid to Regan after 3 years, using simple interest = Rs. 2160 + The interest Saline paid to Regan

The simple interest formula is; I = P·R·T/100

Where;

P = The principal amount loaned

R = The interest rate = 18%

T = The time or duration of the loan = 3 years

Therefore;

(10000- x) × 18/100 × 3 = 2160 + x × 18/100 × 3

5400 - 0.54·x = 2160 + 0.54·x

5400 - 2160 = 0.54·x + 0.54·x = 1.08·x

3240 = 1.08·x

x = 3240 ÷ 1.08 = 3000

The amount Regan lent to Sandip, x = Rs. 3000

The amount Regan lent to Saline = 10,000 - x

x = 3000

10,000 - x = 10,000 - 3000 = 7,000 (substitution property)

The amount Regan lent to Saline = Rs. 7,000

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Answer:

Step-by-step explanation:

30% mark represents:

So

The difference is:

Answer:

25 students

Step-by-step explanation:

Answer:

Step-by-step explanation:

g(x) = x^2 + 6

f(x^2 + 6) = 2(x^2 + 6) + 1 = 2x^2 + 12 + 1 = 2x^2 + 13

There are two distinct sets of all four quantum numbers with n = 4 and ml = -2:

(n = 4, l = 2, ml = -2, ms = +1/2)

(n = 4, l = 2, ml = -2, ms = -1/2)

To determine the number of distinct sets of all four quantum numbers (n, l, ml, and ms) with n = 4 and ml = -2, we need to consider the allowed values for each quantum number based on their respective rules.

The four quantum numbers are as follows:

Principal quantum number (n): Represents the energy level or shell of the electron. It must be a positive integer (n = 1, 2, 3, ...).

Azimuthal quantum number (l): Determines the shape of the orbital. It can take integer values from 0 to (n-1).

Magnetic quantum number (ml): Specifies the orientation of the orbital in space. It can take integer values from -l to +l.

Spin quantum number (ms): Describes the spin of the electron within the orbital. It can have two values: +1/2 (spin-up) or -1/2 (spin-down).

Given:

n = 4

ml = -2

For n = 4, l can take values from 0 to (n-1), which means l can be 0, 1, 2, or 3.

For ml = -2, the allowed values for l are 2 and -2.

Now, let's find all possible combinations of (n, l, ml, ms) that satisfy the given conditions:

n = 4, l = 2, ml = -2, ms can be +1/2 or -1/2

n = 4, l = 2, ml = 2, ms can be +1/2 or -1/2

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The average value of the function f(x) = \(9 - x^2\) over the interval [-3, 3] is 6.0000. The values of x in the interval for which the function equals its average value are x = -2.4495 and x = 2.4495.

To find the average value of a function over an interval, we need to calculate the definite integral of the function over the interval and divide it by the length of the interval. In this case, we have the function

f(x) = \(9 - x^2\) and the interval [-3, 3].

First, we calculate the definite integral of f(x) over the interval [-3, 3]:

\(\(\int_{-3}^{3} (9 - x^2) \, dx = \left[9x - \frac{x^3}{3}\right] \bigg|_{-3}^{3}\)\)

Evaluating the definite integral at the upper and lower limits gives us:

\(\((9(3) - \frac{{3^3}}{3}) - (9(-3) - \frac{{(-3)^3}}{3})\)\)

= (27 - 9) - (-27 + 9)

= 18 + 18

= 36

Next, we calculate the length of the interval:

Length = 3 - (-3) = 6

Finally, we divide the definite integral by the length of the interval to find the average value:

Average value = 36/6 = 6.0000

To find the values of x in the interval for which the function equals its average value, we set f(x) equal to the average value of 6 and solve for x:

\(9 - x^2 = 6\)

Rearranging the equation gives:

\(x^2 = 3\)

Taking the square root of both sides gives:

x = ±√3

Rounding to four decimal places, we get:

x ≈ -2.4495 and x ≈ 2.4495

Therefore, the values of x in the interval [-3, 3] for which the function equals its average value are approximately -2.4495 and 2.4495.

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The slope is the amount deducted per month.

The equation of that models b after m months is: b = -150m + 1800 or b = 1800 - 150m.

The slope of a function can be described as the rate of change or unit rate. The linear function can be modelled using the equation, y = nm + a, where n is the slope/unit rate and a is the initial value/y-intercept.

With the information given, we can create two set of ordered pairs below:

(0, 1,800) and (3, 1,350)

Using the two ordered pairs calculate the slope:

Slope (n) = change in y / change in x = (1,800 - 1,350)/(0 - 3)

Slope (n) = 450/-3

Slope (n) = -150

The slope signify the amount of money that is deducted per month.

The initial value/y-intercept = a = 1,800.

Substitute m = -150 and b = 1,800 into b = nm + a

b = -150m + 1800 or b = 1800 - 150m

Thus, the slope is the amount deducted per month.

The equation of that models b after m months is: b = -150m + 1800 or b = 1800 - 150m.

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Answer:

i THINK this is correct

Step-by-step explanation:

x = 13

Answer:

I think its 13

Step-by-step explanation:

because the line above it which is 18 looks like the same length. So I would subtract 5 from 18 to get 13. because 13+5 is 18. Good luck!!

Answer:

D. 64 (cos(pi)+isin(pi))

Step-by-step explanation:

Put 2+2i into trigonometric form, raise the r value to the power of 4, and multiply the angle value (theta) by 4 to get the equation of z^4. In this case, r was 2(sqrt2), which raised to the 4th power was 64. The angle value was pi/4, which multiplied by 4 was pi. That's how we get the answer:

64 (cos(pi)+isin(pi)). How this helps!

Following are the calculation to the given value:

Given:

\(\to Z= 2+2i\)

To find:

\(Z^4=?\)

Solution:

\(\to Z= 2+2i\)

\(\therefore\\\\i^2= -1\)

\((a+b)^2= a^2+b^2+2ab\)

Square the given value:

\(\to Z^2= (2+2i)^2\)

         \(= 2^2+(2i)^2+2 \times 2 \times 2i\\\\= 4+4i^2+8i\\\\= 4-4+8i\\\\=8i\)

When \(Z^2= 8i\) then again square the value

\(\to ( Z^2)^2= (8i)^2\\\\\to Z^4= 64i^2\\\\\to Z^4= -64\\\\\)

Therefore, the final answer is "-64".

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Subtract full rotations of 2π until the angle is greater than or equal to 0 and less than 2π

sec(π4) – trigonometry value

The exact value of trigonometry - sec(π4) is 2√2.

Multiply 2√2 by √2.

2⋅√2⋅2

Combine and simplify the denominator.

2√2

Cancel the common factor of 2.

√2

There are various ways to display the outcome.

Exact Form:

√2

Decimal Form:

1.41421356…

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Answer: 125 hearts and 375 stars

Step-by-step explanation:

25% of 100 is 25. Take 100 and x it by 5. 100 x 5 is 500 making 25 x 5 125. That being said 125 hearts and 375 stars

Answer:

125 hearts and 375 stars

Step-by-step explanation:

Answer:

sorry I wish I could help but I'm stupid

x=36

hope this helped ;)

The angle in question measures 60 degrees.

What are supplementary angles?

Supplementary angles are two angles that has sum of 180 degrees. In other words, if you have two angles that are next to each other, and when you add them together, they equal 180 degrees, then those angles are considered to be supplementary.

Let x be the measure of the angle in question.

The supplement of an angle is the angle that, when added to the given angle, results in a sum of 180 degrees. So, the supplement of x is 180 - x.

The problem tells us that the given angle (x) is 120 degrees less than its supplement (180 - x).

Therefore, we can set up the equation:

x = (180 - x) - 120

Simplifying this equation, we get:

x = 60

So, the angle in question measures 60 degrees.

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Answer:

x = - 3

Step-by-step explanation:

The axis of symmetry passes through the vertex ( turning point ) of the graph and is a vertical line with equation

x = c ( c is the value of the x- coordinate of the vertex )

The vertex is (- 3, - 1 ) with x- coordinate - 3 , then

equation of axis of symmetry is x = - 3

Answer 2 1/10

work is shown in the picture above. I hope this helps.

Answer: (17 + 9)x

Step-by-step explanation:

x = number of minutes

17 = programmer amount per minute

9 = apprentice amount per minute

17x + 19x

(17 + 9)x

I hope this helped!

Answer:

17x + 9x

Step-by-step explanation:

Variable x for number of minutes

Simply multiply the rate of each individual by the variable

Result: 17x + 9x

Answer:

\(C=32(3.14)=100.48\text{ meters}\)

Step-by-step explanation:

We know that the circle has a diameter of 32 meters.

And we want to find its circumference.

The circumference of a circle is given by the formula:

\(C=\pi d\)

Where d is the diameter.

So, we will substitute 32 for d and we will use 3.14 for π. Hence, our circumference will be:

\(C=32(3.14)=100.48\text{ meters}\)

Answer:

100.48 m

Step-by-step explanation:

C=2(3.14)r

C=2(3.14)(16)

C= 100.48 m

Answer:

43 ffhfhfhfhfhfhchchchchchc

Answer:

It will take 225 days for Evie's chicken to lay 45 eggs

Step-by-step explanation:

Answer:

B. Two-thirds x + 17

Step-by-step explanation:

Let

x = number of baseball cards his brother has

two-thirds of the number of cards in his brother's baseball card collection = 2/3x

Barry = 2/3x + 17

A. Two-thirds x minus 17

= 2/3x - 17

B. Two-thirds x + 17

= 2/3x + 17

C. 17 x minus two-thirds

= 17x - 2/3

D. 17 x + two-thirds

= 17x + 2/3

The correct answer is

B. Two-thirds x + 17

Answer:

It's B

Step-by-step explanation:

I got a 100 on my test

1. The volume of the box is given by:

Volume = length x width x height = 9 in. x 2 in. x 12 in. = 216 cubic inches

So, the answer is 216 cubic inches.

2. The surface area of the box is given by:

Surface Area = 2lw + 2lh + 2wh = 2(9)(12) + 2(9)(2) + 2(2)(12) = 216 + 36 + 48 = 300 square inches

So, the answer is 300 square inches.

3. The surface area of the cereal box is 300 sq. in.

If cardboard costs $0.01 per square inch, then the cost of manufacturing this cereal box would be:

300 sq. in. x $0.01/sq. in. = $3.00

Therefore, the correct answer is -3.00.

4. The volume of the rectangular prism is given by:

Volume = length x width x height = 9 in. x 2 in. x 12 in. = 216 cubic inches

To find the surface area of the sphere, use the formula:

A = 4πr²

Plugging in r = 3.7 in.:

A = 4π(3.7 in.)² ≈ 172.11 square inches

Rounding this to the nearest square inch gives us:

A ≈ 172 square inches

5. The rectangular prism with dimensions of 9 in. x 2 in. x 12 in. would cost less in packaging.

6. The volume of the cylinder is given by:

Volume = πr²h = 390 cubic inches

Solving for r:

r ≈ 4 inches

Therefore, the approximate radius of the cylinder should be 4 inches to hold the same volume of cereal as the rectangular prism.

7. The surface area of the travel-size cereal box is given by:

Surface Area = 2lw + 2lh + 2wh = 2(3)(1.5) + 2(3)(4.5) + 2(1.5)(4.5) = 9 + 27 + 13.5 = 49.5 square inches

To find the length of each side in the cube with the same surface area, we use the formula:

Surface Area of Cube = 6s²

49.5 = 6s²

s ≈ 2.2 inches

So, the length of each side in the cube would be approximately 2.2 inches.

8. The rectangular prism with dimensions of 3 in. x 1.5 in. x 4.5 in. holds more volume than the cube with a side length of approximately 2.2 inches.

9. Some factors that a cereal company may consider in creating their packaging include how well it stacks for shipping and storing on shelves, how easy it is to hold and pour, and how much advertising space there is on the front of the design.

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Answer: The length of the path along the longest side of the park would be 35 yds.

Step-by-step explanation: Area of triangle = (1/2) x base x height294 = (1/2) x 21 x heightMultiplying both sides by 2 and dividing by 21, we get:height = 28So the other leg of the triangle is 28 yds.Now we can use the Pythagorean theorem to find the length of the hypotenuse:hypotenuse² = shortest side² + other leg²hypotenuse² = 21² + 28²hypotenuse² = 441 + 784hypotenuse² = 1225Taking the square root of both sides, we get:hypotenuse = 35Therefore, the length of the path along the longest side of the park would be 35 yds.

We write 5.14*10^5 to convert from 5.14*10^5.

What is scientific notation?

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