Which of the following correctly uses the absolute value to show the distance between −70 and 15? (5 points)

|−70 − 15| = |−85| = −85 units
|−70 + 15| = |−55| = 55 units
|−70 − 15| = |−85| = 85 units
|−70 + 15| = |−55| = −55 units

Answer:

Thx

Step-by-step explanation:

Yes

The Docx is not accessible, check if its the wrong one.

answer:15x

Step-by-step explanation:

because 2x +3 is 5x 5x+10 is 15x

Answer:

Step-by-step explanation:

Here we are given Length of the rectangle 17 and Width 12.75. To find length of the diagonal of the rectangle we will substitute the value of length and width in required formula:

We know that,

\( \\ \: \: \dashrightarrow \: \: { \underline{ \boxed{ \pink{ \pmb{\mathfrak {Diagonal = \sqrt {(Length)^2 + (Width)^2 }}}}}}} \\ \\ \)

Substituting the required values:

\( \\ \: \: \dashrightarrow\sf \: \: Diagonal = {\sqrt{(17)^2 + (12.75)^2}} \\ \\ \)

\(\: \: \dashrightarrow\sf \: \: Diagonal = \sqrt{289 + 162.5625} \\ \\ \)

\(\: \: \dashrightarrow\sf \: \: Diagonal = \sqrt{451.5625} \\ \\ \)

\(\: \: \dashrightarrow \: \: \pink {\underline{ \boxed{ \pmb{\frak {Diagonal = 21.25}}}}} \\ \\ \)

Hence,

Step-by-step explanation:

Given :-

To find :-

⇝ Diagonal of rectangle

Solution :-

Formula for finding length of rectangle =

\( \sqrt{(length) {}^{2} + (width) {}^{2} } \)

putting the known values ,

\( \sqrt{(17) {}^{2} + (12.75) {}^{2} } \)

\( \sqrt{289 + 162.5625} \)

\( \sqrt{451.5625} \)

\(21.25 \: unit\)

The required diameter of the moon is approximately 3458.7 km.

Diameter of the moon = (distance to the moon) x (angle subtended by diameter at observer's eyes)

In this case, the distance to the moon is given as 384300 km and the angle subtended by the diameter of the moon at the observer's eyes is 31 minutes.

However, we need to convert the angle to radians first, since the formula requires the angle to be in radians.

1 degree = 60 minutes

1 radian = 180/π degrees

Therefore, 1 minute = (1/60) degree, and

31 minutes = 31/60 degrees = 0.5167 degrees

Converting this to radians, we get:

0.5167 x π/180 = 0.009 radians (rounded to three decimal places)

Now we can plug in the values into the formula:

diameter of the moon = (384300 km) x (0.009) = 3458.7 km

Therefore, the diameter of the moon is approximately 3458.7 km.

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The number of baby camels at the zoo is 44.

Given: The number of adult camels is 6 and the number of baby camels is 5 for every 6 camels respectively.

To find :We have to find how many baby camels are at the zoo.

Explanation:

Step 1:The ratio of adult camels and baby camels is 6:5

Step 2:Let the number of adult camels = 6x .

Step 3:Let the number of baby camels = 5x

Step 4:It is given that the total number of adult camels and baby camels is 44 at the zoo. So According to the questions,

⇒6x+5x=44

⇒11x=44

⇒x=44/11

⇒x=4

∴The number of adult camels = 6×4

                                               = 24

And the number of baby camels at the zoo.

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Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

Answer:

1. 11

2. 20

3. 34

4. 12.6

5. 18

6. 105

Step-by-step explanation:

We are told that ---> t = 0, x = 1.5, y = 6, and z = 23

1. y + 5

= 6 + 5

= 11

2. z - 2x

= 23 - 2(1.5)

= 23 - 3

= 20

3. 2z - 2y

= 2(23) - 2(6)

= 46 - 12

= 34

4. 2.6y - 2x

= 2.6(6) - 2(1.5)

= 15.6 - 3

= 12.6

5. 4(y - x)

= 4(6 -  1.5)

= 24 - 6

= 18

6. 4(2 + z) + 5

= 4(2 + 23) + 5

= 8 + 92 + 5

= 105

To show that the general term of the quadratic number pattern is given by \(tn = n^2 + 4n - 12\) , we need to find a quadratic expression that fits the given pattern.

Let's examine the given sequence: -7, 0, 9, 20. We notice that each term is increasing by a certain amount.

First, let's find the differences between consecutive terms:
0 - (-7) = 7
9 - 0 = 9
20 - 9 = 11

We observe that the differences between consecutive terms are not constant, so this indicates that the sequence is not linear.

To determine if the sequence follows a quadratic pattern, let's find the second differences:
9 - 7 = 2
11 - 9 = 2

The second differences are constant, which suggests a quadratic pattern.

Now, let's find the quadratic expression. We know that the general term of a quadratic sequence can be written as \(tn = an^2 + bn + c\), where a, b, and c are constants to be determined.

Using the given terms, we can form three equations:

1.\(For n = 1: -7 = a(1)^2 + b(1) + c\)
2. \(For n = 2: 0 = a(2)^2 + b(2) + c\)
3.\(For n = 3: 9 = a(3)^2 + b(3) + c\)

Simplifying these equations, we get:
1. a + b + c = -7
2. 4a + 2b + c = 0
3. 9a + 3b + c = 9

Solving this system of equations, we find a = 1, b = 4, and c = -12.

Therefore, the general term of the quadratic number pattern is given by\(tn = n^2 + 4n - 12\).

The general term of the quadratic number pattern is \(tn = n^2 + 4n - 12\).

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The rate at which the distance between the two cars is increasing two hours later is 52 mi/h.

To determine the rate of change of the distance between the cars, we can use the concept of relative velocity. Since one car is moving south and the other is moving west, their velocities are perpendicular to each other. Thus, we can use the Pythagorean theorem to find the distance between them at any given time.

After two hours, the southbound car would have traveled 48 mi/h * 2 h = 96 miles, and the westbound car would have traveled 20 mi/h * 2 h = 40 miles. Therefore, the distance between the cars is the hypotenuse of a right triangle with sides 96 miles and 40 miles.

Using the Pythagorean theorem, the distance between the cars is √(96^2 + 40^2) = √(9216 + 1600) = √10816 = 104 miles.

Since two hours have passed, the rate at which the distance is increasing is 104 miles / 2 hours = 52 mi/h. Therefore, the distance between the cars is increasing at a rate of 52 mi/h.

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Answer:

You can solve 1.2 word problems per minutes

Step-by-step explanation:

If 6 word problems were solved in 5 minutes, you must put this into a fraction. We're looking for how many word problems could be solved per minute, so we divide 5 by itself to get 1 and whatever you do to the bottom, you must do to the top, so 6 divided by 5 is 1.2

Hope this helped ;)

It should be noted that z^4 will be -32 in rectangular form.

Based on the information, z = r(cos θ + i sin θ), and provided positive integer n, then it is implied that:

z^n = r^n (cos nθ + i sin nθ)

In this instance, we need to solve for z^4 in rectangular form when z = -2 - 2i. Firstly, we must calculate |z| and arg(z):

|z| = √((-2)^2 + (-2)^2) = 2√2

arg(z) = arctan(-2/-2) = π/4

Leveraging De Moivre's theorem, we can effectively deduce the value of z^4 as:

z^4 = (2√2)^4 (cos (4π/4) + i sin (4π/4))

= 32 (cos π + i sin π)

= -32

Concludedly, z^4  resolved in rectangular form is -32.

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We first graph the three points given.

The centre of the circle seems to be located at the point (3,-2) and therefore, the radius is 2.

Then the equation of the circle is

The graph of this equation exactly goes through these three points as shown in the figure below.

Sothe non-parametric equation of the plane with the given normal vector and passing through the point (5, -6, 0) is: -5x + 6y + 6z + 61 = 0

In order to find the non-parametric equation of the plane, we need the normal vector and a point on the plane. The normal vector is given as (-5, 6, 6), and a point on the plane is (5, -6, 0).

The non-parametric equation of a plane is given by:

Ax + By + Cz = D

where (A, B, C) is the normal vector and (x, y, z) is a point on the plane. We can substitute the values into the equation to find the values of A, B, C, and D.

(-5)(x - 5) + (6)(y + 6) + (6)(z - 0) = 0

Expanding this equation:

-5x + 25 + 6y + 36 + 6z = 0

-5x + 6y + 6z + 61 = 0

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To determine the probability that neither card shows an even number with replacement, we need to calculate the probability of drawing an odd number on each card and multiply the probabilities together.

Let's assume we have a standard deck of 52 playing cards, where half of them are even numbers (2, 4, 6, 8, 10) and the other half are odd numbers (1, 3, 5, 7, 9).

Since the cards are replaced after each draw, the probability of drawing an odd number on each card is 1/2. Therefore, the probability that neither card shows an even number is:

P(neither card shows an even number) = P(odd on card 1) * P(odd on card 2) = 1/2 * 1/2 = 1/4

So, the probability that neither card shows an even number, with replacement, is 1/4.

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Answer:C

Step-by-step explanation:

because......

The rate of change is meaning the slope. The slope of A is 8, therefore, the answer would be 7.

hope this helps :)

The two cars in relation to each other when they began travelling will be car B was 20 miles east of car A. Then the correct option is A.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

Car A is travelling east at a steady speed of 50 miles per hour.

Then the equation of car A is given as

y = 50x + C

where x be the number of miles and x be the number of hours.

Then we have

After 2 hours, it is 140 miles east of Johns town.

Then we have

y = 50x ..1

Car B is travelling east on the same road. its distance east of Johns town is represented by the graph.

Then the equation of car B will be

y = [(120 - 20) / (2 - 0)]x + 20

y = 50x + 20 ...2

Then the two cars in relation to each other when they began travelling will be car B was 20 miles east of car A.

Then the correct option is A.

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Answer:
Car A was 20 miles east of car B.

Step-by-step explanation:

Answer:

the answer is (s)

Step-by-step explanation:

(of lines, planes, surfaces, or objects) side by side and having the same distance continuously between them

The coordinates of A'B'C' are given as follows:

D. A'(4,4), B'(8,8), C'(-8,4).

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

The coordinates of the original triangle ABC are given as follows:

A(2,2), B(4,4), C(-4,2).

The scale factor for the dilation is given as follows:

k = 2.

Hence the coordinates of A'B'C' are obtained multiplying the coordinates of ABC by the scale factor of two, as follows:

A'(4,4), B'(8,8), C'(-8,4).

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Answer:

8(3v+3w-2)=(8×3v+8×3w-8×2)

Step-by-step explanation:

8×3v=24v.

8×3w=24w. [24v+24w-16]=(8×3v+8×3w-2×8)

8×(-2)=-16.

The required measurements for the given data set are:

1. Range = 10

2. Variance = 6.2875

3. Standard deviation = 2.5075

4. Lower Quartile = 5

5. Upper quartile = 8.5

6. Interquartile range = 3.5

7. Box plot is given below.

Given the data set is,

8, 7, 4, 5, 9, 13, 10, 8, 8, 7, 6, 5, 3, 11, 10, 8, 5, 4, 8, 6

Now arranging the data set in ascending order we get,

3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 8, 8, 9, 10, 10, 11, 13

Greatest observation = 13

Lowest observation = 3

So the range = Greatest Observation - Lowest Observation = 13 - 3 = 10.

Mean = (3 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 7 + 7 + 8 + 8 + 8 + 8 + 8 + 9 + 10 + 10 + 11 + 13)/20 = 7.25

Variance = (1/20) * [(3 - 7.25)² + (4 - 7.25)² + (4 - 7.25)² + (5 - 7.25)² + (5 - 7.25)² + (5 - 7.25)² + (6 - 7.25)² + (6 - 7.25)² + (7 - 7.25)² + (7 - 7.25)² + (8 - 7.25)² + (8 - 7.25)² + (8 - 7.25)² + (8 - 7.25)² + (8 - 7.25)² + (9 - 7.25)² + (10 - 7.25)² + (10 - 7.25)² + (11 - 7.25)² + (13 - 7.25)²] = (1/20) * (125.75) = 6.2875

Standard deviation is = √(6.2875) = 2.5075 [Rounding off to fourth decimal place]

Lower Quartile = Average of 5th and 6th observation from ascending arrangement = (1/2)*(5 + 5) = 5

Upper Quartile = Average of 15th and 16th observation from ascending arrangement = (1/2)*(8 + 9) = 8.5

Interquartile range = 8.5 - 5 = 3.5

Box plot of the given data set is as below,

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The probability that the sum of the numbers on the dice facing up add up to 3 is 1/18.

Probability is defined as the likeliness of an event to occur. The probability of any event to occur ranges from 0 to 1, and the sum of all the probabilities of all the events happening is 1.

probability = desired outcome / total outcomes

A 6-sided dice has numbers 1, 2, 3, 4, 5, 6 at each of the 6 sides.

The event of rolling two fair 6-sided dice, which the numbers on the dice facing up add up to 3, is by having (1, 2) or (2, 1).

probability = desired outcome / total outcomes

probability = 2 / (6 x 6)

probability = 2 / 36

probability = 1/18

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There are 230230 possible groups.

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.

Given that Total employees = 26

The Number of employees want to choose = 6

Tthe combination of m things taken k at a time is given by the following formula:

\(^mC_k = \dfrac{m!}{k! \times (m-k)!}\)

Putting m = 26 and k= 6, we obtain;

C = 230230

Therefore, we can conclude that there are 230230 possible groups.

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If two variables are correlated, a change in one must directly produce a change in the other. (False)

Correlation is a statistical measure that indicates the extent to which two or more variables fluctuate together. It is a value between -1 and 1 that represents the strength of the relationship between two variables.

False. If two variables are correlated, a change in one may or may not directly produce a change in the other. Correlation means that there is a relationship between two variables, but it does not necessarily mean that one causes the other. It's possible for two variables to be correlated without any causal relationship between them.

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The maximum rectangular area that can be fenced can be

2499 sq meters.

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

We know for a quadrilateral, A square has the maximum area.

We also know That the product of two numbers is maximum when the difference between them is minimum.

Given, A farmer has 2,000 meters of fencing and wants to use it to create a rectangular area for grazing.

So, 2(l + b) = 2000.

l + b = 1000.

For a square, it would be 500 and 500, But to be a rectangle it can be 49 and 51.

Therefore, The maximum area would be,

= (51×49) sq meters.

= 2499 sq meters.

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Jason's weight is 93 kg.

To calculate Jason's weight, we need to subtract the combined weight of the hand weights (2.5 kg + 2.5 kg = 5 kg) from the reading on the scale (98 kg).

Weight on the scale = Jason's weight + Weight of hand weights

98 kg = Jason's weight + 5 kg

Subtracting 5 kg from both sides of the equation:

Jason's weight = 98 kg - 5 kg

Jason's weight = 93 kg

Therefore, Jason's weight is 93 kg.

Based on the information provided, Jason's weight is calculated to be 93 kg.

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Answer:

since -5 and -5 are the same number, they are on the same y axis so the only distance we need to calculate is between the X coordinates

so when looking for distance you can not have a negative what |-3|+|9| is looking for is the distance from 0 on the X axis since distance can't be negative, (you go 3 miles away from your house in one direction, vs 3 miles in the opposite both ways is positive, even with opposite directions same with axis, it doesnt matter which way, only the number.) you need the absolute value of -3 to get the distance from the 0 on the x axis

short version: distance is positive and its adding the distances from the x axis to get distance from each other

Step-by-step explanation:

Answer:

give the person above me brainlest

Step-by-step explanation: