Which of the following is a characteristic of a line?

The square root function contains a variable under the square root sign. The cube root function contains a variable under the cube root sign.

What is a function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between varying quantities and other variables.

A variable under the square root sign is present in a square root function, and a variable under the cube root sign is present in a cube root function.

Zero has a square root of zero, and one has a square root of one. Keep in mind that the graph only contains points where x and y are positive. For instance, using the imaginary number i is necessary when taking the square root of a negative number.

The square root function is f(x) = √x

For positive values, the graph resembles the square root graph, but cube roots can also be negative, making this equation infinite for all real numbers. Recall that a negative number will result from being multiplied an odd number of times.

The cube root function is f(x) = ³√x

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Answer:

hi! the slope formula is y2-y1 / x2-x1 ! so (-6,0) (2,-2)

your x1 is -6 and y1 is 0 and x2 is 2 and y2 is -2!

using the formula, -2-0/2--6 is 4

so your slope is 4!

the y intercept is solved by

the slope intercept formula y= mx+b

I hope you've memorized both formulas!

b is your y intercept so let's set the equation up!

pick a point it can be either point we'll do (-6,0)!

now y=mx + b

m is your slope and y is the y coordinate of the point (-6,0) that we chose!

b is what we will solve

so! 0=4(-6)+b

0= -24 + b

now it's basic algebra!

24= b

I hope this helps!

In conclusion, slope is 4 and y intercept is 24

memorize slope formula and slope intercept formula and you can do this!

Answer:

Step-by-step explanation:

6x-y=-5

-6x+y=5

Adding the 2 equations we have:

0 + 0 = 0

0 = 0

This means there are infinite solutions

- the equations are identical.

System B

x+3y=13

-x+3y=5

Adding:

6y = 18

y = 3.

x = 13 - 3(3) = 4.

The system has a unique solution

(x. y) = (4, 3).

Answer:

N=3M, 51

Step-by-step explanation:

The total number of novels is equal to 3 x Months, For every month, Milan reads 3 books, so for 17 months, 17 x 3 = 51, So N = 51

The time the plane arrives at the London airport from the airport in Manchester, found using the kinematic equation for speed, and the conversion of the units from hours to minutes is 11:40 a.m.

The kinematic equations describe the motion of an object that moves with constant acceleration.

Distance from the London airport to the Manchester airport, D = 200 miles

The average speed of the plane, v = 120 mph

Time the plane leaves Manchester airport = 10 a.m.

The kinematic equation that can be used to find the time of flight is presented as follows;

\(Speed, \, v = \dfrac{Distance, \, D }{Time, \, t}\)

Therefore;

\(t = \dfrac{D}{v}\)

The time of flight is therefore;

\(t = \dfrac{200}{120} = \dfrac{5}{3} = 1\dfrac{2}{3}\)

The time of flight is \(1\frac{2}{3}\) hours or 5/3 hours which in minutes is therefore:

\(t = \dfrac{5}{3} \, hr \times 60 \, min/hr= 100 \, min\)

The time of arrival is 10 a.m. + 1 hour 40 minutes = 11:40 a.m.

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The system of equations that can be used to determine a and y are  

x+ y=10

x+3y=18

When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. In English, an equation is defined as a properly written formula that consists of two expressions joined by an equals sign, while cognates of the word in other languages may have slightly different meanings. An equation, for instance, is said to have one or more variables in French.

Determine which values of the variables result in the equality to be true in order to solve an equation with variables. The values of the variables that must fulfill the equality to constitute the answer are known as the unknowns, together with the variables for which the equation must be solved.

Let x be the number of blocks of one inch

And y be the number of three inch blocks

The number of blocks must be 10

Therefore, x+y=10

The length  of the line is 18 inches long.

So, x+3y=18

Therefore,  x+ y=10

x+3y=18

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The slopes of each pair when analyzed shows us that; first is parallel; second and third are perpendicular and fourth is neither.

The general form of an equation in slope intercept form is;

y = mx + c

where m is the slope

1) The first pair shows that;

y = 6x/5 - 8/5

y = 6x/5 - 5

The slope in both cases is the same and so they are parallel.

2) The second pair of equations shows that;

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

y = -2x - 5

Both slopes are negative reciprocals of each other and so they are perpendicular.

1st and 3rd box is for perpendicular

3) The third pair of equations shows that;

y = (5/7)x + (8/7)

y = -(7/5)x + 10

Both slopes are negative reciprocals of each other and so they are perpendicular.

1st and 3rd box is for perpendicular.

4) The third pair of equations shows that;

y = 2x + 5

y = 3x + 4

Both slopes are neither parallel nor perpendicular to each other.

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Answer:

82.3

Step-by-step explanation:

p=3, r=4

12.1*3= 36.3

11.5*4= 46

36.3+46= 82.3

Answer:

82.3

Step-by-step explanation:

Hi there!

We are given the expression 12.1p+11.5r, and we want to evaluate it if p=3 and r=4

We need to simply substitute the given values into 12.1p and 11.5r respectively, then add the numbers together

If p is equal to 3, then that means that 12.1p is equal to 12.1*3, which would be 36.3

If r is equal to 4, then that means 11.5r is equal to 11.5*4, which would be 46

Now add 36.3 and 46 together

36.3+46=82.3

Hope this helps!

Cecilia' new copy machine print 12 page in 1/2 minute 2880 pages  per hour, doe cecilia new copy machine print

What are two meanings for minute?

The word minute (MIN ut) is often used to simply mean a short period of time or a particular, exact moment in time. Minute (my NOOT) is an adjective that means very small, tiny, infinitesimal, insignificant

1/4 mins = 15seconds.

12 pages 15 seconds.

24 pages 30 seconds.

36 pages 45 seconds.

48 pages 60 seconds,

60 seconds = 1 minuet.

60 minuets = 1 hour.

48 * 60 = 2880

It can print 2,880 pages per hour.

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Answer:

We can start by drawing a diagram of the situation. Let O be the center of both circles and let K be a point on the circumference of ⊙J such that JK = 12 cm. Let L be the point where JK intersects ⊙M, and let M be the point diametrically opposite L on ⊙M. Then, we have a right triangle JOK with legs JO = 32 cm and OK = 38 cm, and a right triangle LOM with legs LO = OM = r, where r is the radius of ⊙M. The hypotenuse of both triangles is the same and has length 64 cm.

We can use the Pythagorean theorem to find r. In the right triangle JOK, we have:

JO^2 + OK^2 = JK^2

32^2 + 38^2 = JK^2

JK = sqrt(32^2 + 38^2) ≈ 49.21 cm

In the right triangle LOM, we have:

LO^2 + OM^2 = LM^2

r^2 + r^2 = (2r)^2

2r^2 = LM^2

We know that LM = 2r + 12, since JK = 12 cm. Substituting this into the equation above, we get:

2r^2 = (2r + 12)^2

2r^2 = 4r^2 + 48r + 144

2r^2 - 4r^2 - 48r - 144 = 0

-r^2 - 24r - 72 = 0

r^2 + 24r + 72 = 0

We can solve for r using the quadratic formula:

r = (-24 ± sqrt(24^2 - 4*72)) / 2

r = (-24 ± sqrt(384)) / 2

r = -12 ± 4sqrt(6)

Since r is the radius of ⊙M, we want the positive value of r. Therefore:

r = -12 + 4sqrt(6) ≈ 4.03 cm

Finally, we can find LM:

LM = 2r + 12

LM = 2(4.03) + 12

LM ≈ 20.06 cm

Therefore, the length of LM is approximately 20.06 cm.

the correct answer is A.

if u want an explanation I will gladly explain it to you!

Answer:

this shape consists of a square and triangle

The shape is a Pentagon ... but that won't help get the perimeter or area. you'll have to find the areas and perimeters of both the square and triangle and then add them for the final answer.

Area of figure = area of square + area of triangle

=> Area of Square = a² (a = side)

side = 3.5 cm ...so...

Area of square = a²

= 3.5 × 3.5

= 12.25 cm²

=> Area of Triangle = ½ × base × height

= ½ × 3.5 × 1.64

= 2.87cm²

Area of figure = area of square + area of triangle

Area of figure = 12.25 + 2.87

= 15.12 cm²

Perimeter of figure = P of square + P of triangle

=> P of square = 4a

= 3.5 × 4

= 14cm

=> P of isosceles triangle = 2a + base

= 2 × 2.4 + 3.5

= 4.8 + 3.5

= 8.3cm

Total perimeter of figure = P of square + P of triangle

Total perimeter = 14 + 8.3

= 22.3 cm

The mean (μx) of the sampling distribution of sample means is 78, and the standard deviation (σx) is 1. This means that on average, the sample means will be centered around the population mean of 78, and the spread of the sample means will be relatively small with a standard deviation of 1.

In statistics, the sampling distribution of sample means refers to the distribution of means obtained from all possible samples of a given size taken from a population. The mean of this sampling distribution is equal to the population mean, while the standard deviation of the sampling distribution is equal to the population standard deviation divided by the square root of the sample size.

In this case, we are given that the population mean (μ) is 78 and the population standard deviation (σ) is 7. We are interested in finding the mean (μx) and standard deviation (σx) of the sampling distribution of sample means when the sample size (n) is 49.

Since the mean of the sampling distribution is equal to the population mean, μx = 78.

To find the standard deviation of the sampling distribution (σx), we divide the population standard deviation by the square root of the sample size:

σx = σ / √n.

In this case, σx = 7 / √49

= 7 / 7

= 1.

Therefore, the mean (μx) of the sampling distribution of sample means is 78, and the standard deviation (σx) is 1. This means that on average, the sample means will be centered around the population mean of 78, and the spread of the sample means will be relatively small with a standard deviation of 1.

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keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

\(y=\stackrel{\stackrel{m}{\downarrow }}{2}x+1\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

so we're really looking for the equation of a line that has a slope of 2 and it passes thourhg (4 , 6)

\((\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ 2}(x-\stackrel{x_1}{4}) \\\\\\ y-6=2x-8\implies {\Large \begin{array}{llll} y=2x-2 \end{array}}\)

explain the meaning and functions of inferentail and factual claims

Answer:

The answer is A.

I just got tired of getting it wrong and guessed

Answer:

More than half of the people surveyed in each sample chose oranges as their favorite fruit. Since most people in each sample chose oranges, it is likely that oranges are the favorite fruit of the entire population.

I hope this helps you

Step-by-step explanation:

The Mean Absolute Deviation over Months 3-6 is 5.

Correct answer is option C) 5

To calculate the Mean Absolute Deviation (MAD) over Months 3-6, we need to follow these steps:

Identify the errors for Months 3-6: The errors for Months 3-6 are 3, -5, 4, and -8.

Calculate the absolute value of each error: Taking the absolute value of each error gives us 3, 5, 4, and 8.

Find the sum of the absolute errors: Add up the absolute errors: \(3 + 5 + 4 + 8 = 20.\)

Divide the sum by the number of errors: Since there are 4 errors, we divide the sum (20) by 4 to get the average: 20/4 = 5.

Determine the Mean Absolute Deviation: The MAD is the average of the absolute errors, which is 5.

Therefore, the Mean Absolute Deviation over Months 3-6 is 5.

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\({\large{\textsf{\textbf{\underline{\underline{Question \: 1 :}}}}}}\)

\(\star\:{\underline{\underline{\sf{\purple{Solution:}}}}}\)

❍ Arrange the given data in order either in ascending order or descending order.

2, 3, 4, 7, 9, 11

❍ Number of terms in data [n] = 6 which is even.

As we know,

\(\star \: \sf Median_{(when \: n \: is \: even)} = {\underline{\boxed{\sf{\purple{ \dfrac{ { \bigg (\dfrac{n}{2} \bigg)}^{th}term +{ \bigg( \dfrac{n}{2} + 1 \bigg)}^{th} term } {2} }}}}}\)

\(\\\)

\( \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ { \bigg (\dfrac{6}{2} \bigg)}^{th}term +{ \bigg( \dfrac{6}{2} + 1 \bigg)}^{th} term } {2} }\)

\(\\\)

\( \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ \bigg( \dfrac{6 + 2}{2} \bigg)}^{th} term } {2} }\)

\(\\\)

\( \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ \bigg( \cancel{ \dfrac{8}{2}} \bigg)}^{th} term } {2} }\)

\(\\\)

\( \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ 4}^{th} term } {2} }\)

• Putting,

3rd term as 4 and the 4th term as 7.

\(\longrightarrow \: \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ 4 + 7 } {2} }\)

\(\longrightarrow \: \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ 11} {2} }\)

\(\longrightarrow \: \sf Median_{(when \: n \: is \: even)} = \purple{5.5}\)

\(\\\)

\({\large{\textsf{\textbf{\underline{\underline{Question \: 2 :}}}}}}\)

\(\star\:{\underline{\underline{\sf{\red{Solution:}}}}}\)

❍ Arrange the given data in order either in ascending order or descending order.

1, 2, 3, 4, 5, 6, 7

❍ Number of terms in data [n] = 7 which is odd.

As we know,

\(\star \: \sf Median_{(when \: n \: is \: odd)} = {\underline{\boxed{\sf{\red{ { \bigg( \frac{n + 1}{2} \bigg)}^{th} term}}}}}\)

\(\\\)

\( \sf Median_{(when \: n \: is \: odd)} = {{ \bigg(\dfrac{ 7 + 1 } {2} \bigg) }}^{th} term\)

\(\\\)

\( \sf Median_{(when \: n \: is \: odd)} = { \bigg(\cancel{\dfrac{8}{2}} \bigg)}^{th} term\)

\(\\\)

\( \sf Median_{(when \: n \: is \: odd)} ={ 4}^{th} term\)

• Putting,

4th term as 4.

\(\longrightarrow \: \sf Median_{(when \: n \: is \: odd)} = \red{ 4}\)

\(\\\)

\({\large{\textsf{\textbf{\underline{\underline{Question \: 3 :}}}}}}\)

\(\star\:{\underline{\underline{\sf{\green{Solution:}}}}}\)

The frequency distribution table for calculations of mean :

\(\begin{gathered}\begin{array}{|c|c|c|c|c|c|c|} \hline \rm x_{i} &\rm 3&\rm 1&\rm 7&\rm 4&\rm 6&\rm 2 \rm \\ \hline\rm f_{i} &\rm 4&\rm 6&\rm 2&\rm 2 & \rm 1&\rm 1 \\ \hline \rm f_{i}x_{i} &\rm 12&\rm 6&\rm 14&\rm 8&\rm 6&\rm \rm 2 \\ \hline \end{array} \\ \end{gathered} \)

☆ Calculating the \(\sum f_{i}\)

\( \implies 4 + 6 + 2 + 2 + 1 + 1\)

\( \implies 16\)

☆ Calculating the \(\sum f_{i}x_{i}\)

\( \implies 12 + 6 + 14 + 8 + 6 + 2\)

\(\implies 48\)

As we know,

Mean by direct method :

\( \: \: \boxed{\green{{ { \overline{x} \: = \sf \dfrac{ \sum \: f_{i}x_{i}}{ \sum \: f_{i}}}}}}\)

here,

• \(\sum f_{i}\) = 16

• \(\sum f_{i}x_{i}\) = 48

By putting the values we get,

\(\sf \longrightarrow \overline{x} \: = \: \dfrac{48}{16}\)

\(\sf \longrightarrow \overline{x} \: = \green{3}\)

\({\large{\textsf{\textbf{\underline{\underline{Note\: :}}}}}}\)

• Swipe to see the full answer.

\(\begin{gathered} {\underline{\rule{290pt}{3pt}}} \end{gathered}\)

Answer:

y = -17/5

Step-by-step explanation:

collect the like terms (-4 = 9y + 13 – 4y)

move the terms (-4 = 5y + 13)

calculate (-5y = 13 + 4)

divide both sides (-5y = 17)

so your solution is -17/5

can also be written as - 3 \(\frac{2}{5}\), or y = -3.4

the answer is: f · dr = -30

To find f · dr for the line c from (3, 2, -2) to (6, 1, 7), we first need to parametrize the line in terms of a vector function r(t). We can do this as follows:

r(t) = <3, 2, -2> + t<3, -1, 9>

This gives us a vector function that describes all the points on the line c as t varies.

Next, we need to calculate f · dr for this line. We can use the formula:

f · dr = ∫c f · dr

where the integral is taken over the line c. We can evaluate this integral by substituting r(t) for dr and evaluating the dot product:

f · dr = ∫c f · dr = ∫[3,6] f(r(t)) · r'(t) dt

where [3,6] is the interval of values for t that correspond to the endpoints of the line c. We can evaluate the dot product f(r(t)) · r'(t) as follows:

f(r(t)) · r'(t) = <5y, 2, -1> · <3, -1, 9>

= 15y - 2 - 9

= 15y - 11

where we used the given expression for f and the derivative of r(t), which is r'(t) = <3, -1, 9>.

Plugging this dot product back into the integral, we get:

f · dr = ∫[3,6] f(r(t)) · r'(t) dt

= ∫[3,6] (15y - 11) dt

To evaluate this integral, we need to express y in terms of t. We can do this by using the equation for the y-component of r(t):

y = 2 - t/3

Substituting this into the integral, we get:

f · dr = ∫[3,6] (15(2 - t/3) - 11) dt

= ∫[3,6] (19 - 5t) dt

= [(19t - 5t^2/2)]|[3,6]

= (57/2 - 117/2)

= -30

Therefore, the answer is:

f · dr = -30

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Answer:

1

Step-by-step explanation:

\(v = whl\)

1 = 5/4 x 4/3 x 3/5

Answer:

there are 144 students in total

At a significance level of 5%, with a sample size of 800 items produced on a new machine and 48 of them being defective, the null hypothesis is that the proportion of defective items is not significantly more than 5%, while the alternative hypothesis is that it is significantly more than 5%. The level of significance is 0.05. Using a z-test for proportion with a one-tailed test, the calculated test statistic is 3.45. Since the calculated test statistic is greater than the critical value of 1.645, we reject the null hypothesis. Therefore, there is enough evidence to get rid of the machine.

Null Hypothesis: p = 0.05

Alternative Hypothesis: p > 0.05

Level of Significance: α = 0.05

Sample Size: n = 800

Number of Defective Items: x = 48

Sample Proportion:P= x/n = 48/800 = 0.06

Since the sample size is large, we can use the normal distribution to approximate the binomial distribution.

Test Statistic: z = (P - p) / sqrt(p * (1 - p) / n)

Under the null hypothesis, the test statistic follows a standard normal distribution.

Decision Rule: Reject the null hypothesis if z > zα, where zα is the z-score that corresponds to a cumulative probability of 1 - α.

From the standard normal distribution table, we have:

zα = 1.645

Computation:

z = (0.06 - 0.05) / sqrt(0.05 * 0.95 / 800) = 1.33

Since z (1.33) is less than zα (1.645), we fail to reject the null hypothesis.

Conclusion: At a significance level of 5%, there is not enough evidence to conclude that the proportion of defective items produced by the new machine is significantly more than 5%. Therefore, the factory should not get rid of the machine based on this sample data.

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Answer:

1300y^2+1400y+343

Step-by-step explanation:

Use FOIL to cancel out the products

Answer: It $7.80 per hour

Hi hi

Step-by-step explanation:

Answer:

13y= x + 59

Step-by-step explanation:

gradient= y² - y¹ / x²- x¹

=5 - 4 / 6- -7

= 1/ 13

x y

point (6,5)

substitute:

5= 1 (6) + c

13

c = 5 - 6

13

= 59

13

y=mx+c

13y= 1x + 59

Answer:

The correct answer is 1/2×8×3.

Answer:

12 m

Step-by-step explanation:

1200 mm = 1.2 m

Step-by-step explanation:

no

10 times smaller

1,200 mm = 1.2 m

Given points are (3, 10), (5, 36), and (-2, 15) and we need to find the equation of the quadratic function of the form y = ax² + bx + c. The formula for finding the quadratic equation of the form y = ax² + bx + c is given as follows; y = a x² + b x + c;

Here, a, b, and c are the unknown coefficients of the quadratic equation. We need to solve the system of equations to get the values of a, b, and c. For this, we need to substitute each point into the equation y = ax² + bx + c;

Point (3, 10) => 10 = a (3)² + b (3) + c;       10 = 9a + 3b + c ;(1)Point (5, 36) => 36 = a (5)² + b (5) + c;       36 = 25a + 5b + c ;(2)Point (-2, 15) => 15 = a (-2)² + b (-2) + c;  15 = 4a - 2b + c ;(3)Now we have to solve the system of equations (1), (2), and (3) simultaneously to get the values of a, b, and c.

So let's begin solving this system of equations (1), (2), and (3).We have to first subtract the third equation from the first equation. So we get, 10 - 15 = 9a + 3b + c - 4a + 2b - c => -5 = 5a + 5b ; (4)Simplifying the above equation (4), we get;5a + 5b = -5 => a + b = -1 ;(5).

Next, subtracting the third equation from the second equation, we get, 36 - 15 = 25a + 5b + c - 4a + 2b - c => 21 = 21a + 7b ;(6)Simplifying the above equation (6), we get; 21a + 7b = 21 => 3a + b = 3 ;(7)Now we have to solve equations (5) and (7) simultaneously to find the values of a and b.

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