What is the slope of the line?​

You have to graph the following function

This is a linear function with slope m=1, this means that each time x increases one unit, y also increases one unit.

To sketch this function you have to choose at least two values of x and determine the corresponding value of y.

Then plot the points and draw the line.

I will make a table with 5 points of the line:

Now what's left is to plot all points and link them with a line:

Step-by-step explanation:

The statements that describe the graph are,

The ball travels 24 cm in 1s.

It takes the ball 2s to complete a cycle

The midline is at f(x)=0

I hope it helped you

Answer:

42

Step-by-step explanation:

arrange the numbers either in ascending or descending order and find the one right in the middle

Answer:

48,236.7

Step-by-step explanation:

40,000 + 8,000 + 200 + 30 + 6 + 7/10

7/10 can also be written .7

The test results' standard deviation is around 33. Standard deviation is a measure of the spread or dispersion of a set of data. It measures how much the individual data points deviate from the mean of the data.

To find the standard deviation of this data, we first need to calculate the sample mean and variance:

Sample mean, = (290 + 805 + 708 + 606 + 504 + 401 + 302 + 05) / 31 = 56.45

Sample variance, \(s^2 = [(2-56.45)^290 + (80-56.45)^25 + (70-56.45)^28 + (60-56.45)^26 + (50-56.45)^24 + (40-56.45)^21 + (30-56.45)^22 + (0-56.45)^25] / (31-1) = 1080.56\)

To find the standard deviation, we take the square root of the variance:

Standard deviation, \(s = sqrt(s^2) = sqrt(1080.56) = 32.90\\\)

Rounding to the nearest unit, the standard deviation is approximately 33.

Therefore, the standard deviation of the test scores is approximately 33.

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Answer:

15 nautic miles, a simple proportion

19:342=x:270

Step-by-step explanation:

Your welcome :)

Answer:

Step-by-step explanation:

3/x = sin45

x = 3/sin45

x = 3 / ½(√2)

x = 3(2/√2)

x = 3((2√2)/2)

x = 3√2

The value of x from the give triangle is 3√2 units. Therefore, option D is the correct answer.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

From the given triangle, we have opposite = 3 units and hypotenuse = x units.

We know that, sinθ=Opposite/Hypotenuse

sin45°=3/x

1/√2 =3/x

x=3√2 units

Therefore, option D is the correct answer.

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A function is an algebraic expression that maps the transformation from one group of numbers to the other. The group of numbers which is used as an input is called the domain, while the group of number used as an ouput is called range of the function. The inverse of a function is the operation that does the oposite path, the domain and range are switched in such a way that the domain of the inverse is the range of the original and the range of the inverse is the domain of the original. With this in mind we can say that the correct answer is the first option.

Answer:

Option A is correct

Step-by-step explanation:

The domain of a function is the range of its inverse while the range of a function is the domain of the inverse

Answer: The answer should be B

Using the rates, it is found that it would take you 8.57 hours to design the website working alone.

The together rate is the sum of each separate rate.

In this problem:

Then:

\(\frac{1}{12} + \frac{1}{x} = \frac{1}{5}\)

\(\frac{x + 12}{12x} = \frac{1}{5}\)

\(12x = 5(x + 12)\)

\(12x = 5x + 60\)

\(7x = 60\)

\(x = \frac{60}{7}\)

\(x = 8.57\)

It would take you 8.57 hours to design the website working alone.

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Answer:

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

You simply add the coefficients together.
3 + 4 + 5 = 12

yes yes yes yes yes yes yes yes yes yes yes yes yes yes

Answer:

2(5) + 2√(3^2 + 7^2) = 10 + 2√58 = 25.2

B is the correct answer.

Answer: 20

Step-by-step explanation:

Let \(f(y)=x\)

\(x=\frac{1}{2}y+10\\\\x-10=\frac{1}{2}y\\\\y=h(x)=2x-\boxed{20}\)

Answer:

166

Step-by-step explanation:

:)

Answer:

1/4+1/3+1/8

=17/24

Step-by-step explanation:

1-17/24

=7/24

7/24×240

=70

Answers:

==========================================

Explanation:

Equation of the vertical line passing through point (-3, -5) is given by x = -3.

As given in the question,

Line passes through the point (-3, -5)

It represents the x- coordinate is equal to -3

And y- coordinate is equal to -5.

Condition for the line is given as vertical line.

Vertical line represent the value of x- coordinate remain constant.

It represent x-intercept

x = -3

x-intercept represents the equation of the vertical line.

Therefore, equation of the vertical line passing through point (-3, -5) is given by x = -3.

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Answer:(a) The rate of decay is 14.4% per day, which can be written as a decimal by dividing by 100: r = 0.144.

(b) The formula for continuous decay is given by:

A = A₀ * e^(-rt)

where A is the remaining amount of the substance after time t, A₀ is the initial amount, r is the rate of decay, and e is the mathematical constant approximately equal to 2.71828.

Plugging in the given values, we get:

A = 140 * e^(-0.144*15)

A = 140 * e^(-2.16)

A ≈ 47.23

Therefore, after 15 days, approximately 47.23 mg of the radioactive substance will be left, rounded to two decimal places.

Step-by-step explanation:

Using basic inference rules, we can establish the validity of the argument: p ⟹ ¬q, q V r, p V u, ¬r ├ u.

1. We are given the following premises:

  - p ⟹ ¬q (Premise 1)

  - q V r (Premise 2)

  - p V u (Premise 3)

  - ¬r (Premise 4)

2. To prove the conclusion, u, we need to use the premises and apply inference rules.

3. From Premise 4 (¬r) and the Disjunctive Syllogism rule, we can deduce ¬q: (¬r, q V r) ⟹ ¬q.

4. From Premise 1 (p ⟹ ¬q) and Modus Ponens, we can conclude ¬p: (p ⟹ ¬q, ¬q) ⟹ ¬p.

5. From Premise 3 (p V u) and Disjunctive Syllogism, we obtain ¬p V u.

6. Using Disjunctive Syllogism with ¬p V u and ¬p, we can derive u: (¬p V u, ¬p) ⟹ u.

7. From Premise 2 (q V r) and Disjunctive Syllogism, we have q.

8. Finally, using Modus Tollens with q and ¬q, we can deduce ¬p: (q, p ⟹ ¬q) ⟹ ¬p.

9. Therefore, combining ¬p and u, we can conclude the desired result: ¬p ∧ u.

10. Since ¬p ∧ u is logically equivalent to u, we have established the validity of the argument: p ⟹ ¬q, q V r, p V u, ¬r ├ u.

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If ∆ABC is congruent to ∆PQR, find the length of QR.

Given that If ∆ABC is congruent to ∆PQR:

The simplest way to prove that triangles are congruent is to prove that all three sides of the triangle are congruent.

When all the sides of two triangles are congruent, the angles of those triangles must also be congruent.

From the triangle ABC, the side BC = 4,

Hence the PQR, the side QR = 4 since they are congruent

The image you described features a number line that goes from 0 to 6.5 in increments of 0.5.

On this number line, there is an arrow that starts at 0 and extends to 2.5, and then continues from 2.5 to 5.

This image can be visualized as follows:

0        1        2        3        4        5        6        6.5

|--------|--------|--------|--------|--------|--------|--------|

        |------------------------|------------------------|

             0 to 2.5                 2.5 to 5

The vertical lines represent the increments of 0.5 on the number line, and the arrow indicates the segments from 0 to 2.5 and from 2.5 to 5.

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When x = 13, the equation that is true is option D) 5(x - 9) = 20.

To determine which equation is true when x = 13, we can substitute the value of x into each equation and see which equation holds true. Let's go through each option:

A) 3(18 - x) = 67

Substituting x = 13:

3(18 - 13) = 67

3(5) = 67

15 = 67

The equation is not true when x = 13. Therefore, option A is false.

B) 4(9x) = 23

Substituting x = 13:

4(9*13) = 23

4(117) = 23

468 = 23

Again, the equation is not true when x = 13. Therefore, option B is also false.

C) 2(x - 3) = 7

Substituting x = 13:

2(13 - 3) = 7

2(10) = 7

20 = 7

Once again, the equation is not true when x = 13. Therefore, option C is false as well.

D) 5(x - 9) = 20

Substituting x = 13:

5(13 - 9) = 20

5(4) = 20

20 = 20

Finally, the equation is true when x = 13. Therefore, option D is true.

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Note: the translated questions is

X = 13, which equation is true?

Step-by-step explanation:

40 :100        yellow to purple,  divide both sides by 20

2:5

Answer:

the ratio of yellow to purple is 40:100 that is 2:5 in the simplest form.

Step-by-step explanation:

Hope it helps.

The equation of the line that passes through the point (-4,2) and the parallel to the line y = 1/4x + 1 is y = (1/4)x+3

The equation of the line parallel to the line is

y = 1/4 x +1

The slope intercept form is

y = mx + b

Where m is the slope of the line and b is the y intercept

By comparing the given equation and slope intercept form of the line

The slope of the line is m = 1/4

Then the point slope form is

\((y-y_1)= m(x-x_1)\)

The line is passing through the point (-4,2)

Substitute the values in the equation

(y-2) = 1/4(x-(-4))

y-2 = 1/4(x+4)

y-2 = (1/4)x+1

y = (1/4)x+3

Hence, the equation of the line that passes through the point (-4,2) and the parallel to the line y = 1/4x + 1 is y = (1/4)x+3

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The sprinter will complete the race in approximately 17.07 seconds.

To calculate the time for the race, we need to consider two parts: the acceleration phase and the constant velocity phase.

Acceleration Phase:

The acceleration of the sprinter is 1.64 m/s², and the distance covered during this phase is 25 m. We can use the equation of motion to calculate the time taken during acceleration:

v = u + at

Here:

v = final velocity (which is the velocity at the end of the acceleration phase)

u = initial velocity (which is 0 since the sprinter starts from rest)

a = acceleration

t = time

Rearranging the equation, we have:

t = (v - u) / a

Since the sprinter starts from rest, the initial velocity (u) is 0. Therefore:

t = v / a

Plugging in the values, we get:

t = 25 m / 1.64 m/s²

Constant Velocity Phase:

Once the sprinter reaches the end of the acceleration phase, the velocity remains constant. The remaining distance to be covered is 100 m - 25 m = 75 m. We can calculate the time taken during this phase using the formula:

t = d / v

Here:

d = distance

v = velocity

Plugging in the values, we get:

t = 75 m / (v)

Since the velocity remains constant, we can use the final velocity from the acceleration phase.

Now, let's calculate the time for each phase and sum them up to get the total race time:

Acceleration Phase:

t1 = 25 m / 1.64 m/s²

Constant Velocity Phase:

t2 = 75 m / v

Total race time:

Total time = t1 + t2

Let's calculate the values:

t1 = 25 m / 1.64 m/s² = 15.24 s (rounded to two decimal places)

Now, we need to calculate the final velocity (v) at the end of the acceleration phase. We can use the formula:

v = u + at

Here:

u = initial velocity (0 m/s)

a = acceleration (1.64 m/s²)

t = time (25 m)

Plugging in the values, we get:

v = 0 m/s + (1.64 m/s²)(25 m) = 41 m/s

Now, let's calculate the time for the constant velocity phase:

t2 = 75 m / 41 m/s ≈ 1.83 s (rounded to two decimal places)

Finally, let's calculate the total race time:

Total time = t1 + t2 = 15.24 s + 1.83 s ≈ 17.07 s (rounded to two decimal places)

Therefore, the sprinter will complete the race in approximately 17.07 seconds.

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Answer:

a

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

I might be wrong but i'm pretty sure it's right

Answer:

\(\frac{1}{2-tan(y)} = \frac{3\sqrt{3}}{6\sqrt{3}-1}\)

After Rationalising:

\(\frac{1}{2-tan(y)} = \frac{54 +3\sqrt{3}}{107}\)

Step-by-step explanation:

tan(x) = 3√3

x + y = 90 (complimentary angles)

⇒ x = 90 - y

tan(\(\frac{\pi}{2}\) - θ) = cot(θ)

⇒ tan(90 - θ) = cot(θ)

⇒ tan(90 - y) = cot(y)

⇒ tan(x) = cot(y)

⇒ cot(y) = 3√3

⇒ \(\frac{1}{tan(y)}\) = 3√3

⇒ tan(y) = \(\frac{1}{3\sqrt{3}}\)

\(2-tan(y) = 2 - \frac{1}{3\sqrt{3}} \\\\= \frac{2*3\sqrt{3} -1}{3\sqrt{3} } \\\\= \frac{6\sqrt{3} -1}{3\sqrt{3} }\\\\\\\implies \frac{1}{2-tan(y)} \\\\= \frac{3\sqrt{3}}{6\sqrt{3}-1}\)

Multiply and divide by : 6(√3) + 1

\(\frac{3\sqrt{3}}{6\sqrt{3}-1}\frac{6\sqrt{3}+1}{6\sqrt{3}+1}\\ \\= \frac{(3*6*\sqrt{3}*\sqrt{3}) + 3\sqrt{3}}{6^2 * (\sqrt{3})^2 -1^2}\\\\= \frac{18*3 +3\sqrt{3}}{36*3 -1}\\\\= \frac{54 +3\sqrt{3}}{108-1}\\\\= \frac{54 +3\sqrt{3}}{107}\)