Rearrange the equation below to highlight the variable Y.

3x+1/2y=-4

Answer:

56. In the Vector Addition Lab, Anna starts at the classroom door and walks:

2.0 meters, West

12.0 meters, North,

31.0 meters, West,

8.0 meters, South

3.0 meters, East

Using either a scaled diagram or a calculator, determine the magnitude and direction of Anna's resulting displacement.

Answer: 30.3 meters, 172 degrees

To insure the most accurate solution, this problem is best solved using a calculator and trigonometric principles. The first step is to determine the sum of all the horizontal (east-west) displacements and the sum of all the vertical (north-south) displacements.

Horizontal: 2.0 meters, West + 31.0 meters, West + 3.0 meters, East = 30.0 meters, West

Vertical: 12.0 meters, North + 8.0 meters, South = 4.0 meters, North

The series of five displacements is equivalent to two displacements of 30 meters, West and 4 meters, North. The resultant of these two displacements can be found using the Pythagorean theorem (for the magnitude) and the tangent function (for the direction). A non-scaled sketch is useful for visualizing the situation.

Applying the Pythagorean theorem leads to the magnitude of the resultant (R).

R2 = (30.0 m)2 + (4.0 m)2 = 916 m2

R = Sqrt(916 m2)

R = 30.3 meters

The angle theta in the diagram above can be found using the tangent function.

tangent(theta) = opposite/adjacent = (4.0 m) / (30.0 m)

tangent(theta) = 0.1333

theta = invtan(0.1333)

theta = 7.59 degrees

This angle theta is the angle between west and the resultant. Directions of vectors are expressed as the counterclockwise angle of rotation relative to east. So the direction is 7.59 degrees short of 180 degrees. That is, the direction is ~172 degrees.

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57. In a grocery store, a shopper walks 36.7 feet down an aisle. She then turns left and walks 17.0 feet straight ahead. Finally, she turns right and walks 8.2 feet to a final destination. (a) Determine the magnitude of the overall displacement. (b) Determine the direction of the displacement vector relative to the original line of motion.

Answer: (a) 48.0 feet; (b) 21 degrees from the original line of motion

This problem is best approached using a diagram of the physical situation. The three displacements are shown in the diagram below on the left. Since the three displacements could be done in any order without effecting the resulting displacement, these three legs of the trip are conveniently rearranged in the diagram below on the right.

Now it is obvious from the diagram on the right that the three displacement vectors are equivalent to two perpendicular displacement vectors of 44.9 feet and 17 feet. These two vectors can be added together and the resultant can be drawn from the starting location to the final location. A sketch is shown below.

Since these displacement vectors are at right angles to each other, the magnitude of the resultant can be determined using the Pythagorean theorem. The work is shown below.

R2 = (44.9 ft)2 + (17.0 ft)2 = 2305 ft2

R = Sqrt(2305 ft2)

R = 48.0 feet

The angle theta in the diagram above can be found using the tangent function.

tangent(theta) = opposite/adjacent = (17.0 ft) / (44.9 ft)

tangent(theta) = 0.3786

theta = invtan(0.3786)

theta = 20.7 degrees

This is the angle which the resultant makes with the original line of motion (the 36.7 ft displacement vector).

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58. A hiker hikes 12.4 km, south. The hiker then makes a turn towards the southeast and finishes at the final destination. The overall displacement of the two-legged trip is 19.7 km at 309 degrees . Determine the magnitude and direction of the second leg of the trip.

Answer: 12.7 km, 347 degrees

Like the previous problem (and most other problems in physics), this problem is best approached using a diagram. The first displacement is due South and the resulting displacement (at 309 degrees) is somewhere in the fourth quadrant. (It is in the fourth quadrant because 309 degrees lies between 270 degrees or due South and 360 degrees or due East.) For communication sake, we will refer to the first displacement as A and the second displacement as B. Note that A + B = R. Since the magnitude and direction of the resultant is known, the x- and y-components can be determined using trigonometric functions. Since the angle of 309 degrees is expressed as a counterclockwise angle of rotation with due East, it can be used as the Theta in the equation.

Rx = R•cos(theta) = 19.7 km • cos(309 deg) = 12.398 km

Ry = R•sin(theta) = 19.7 km • sin(309 deg) = -15.310 km (the "-" means South)

Whatever the magnitude and direction of B is, it must add on to vector A in order to give a southward displacement of 15.310 km and a eastward displacement of 12.398 km. This could be expressed by mathematical equations as

Answer:

D

Step-by-step explanation:

When multiplying numbers with the same base but different exponents, add the exponents together.

Answer:

1,3,4

Step-by-step explanation:

ıf we rearrange formula we can obtain

p=nrt/v

t=pv/nr

v=nrt/p

r=pv/nt

Answer:

y = 5/4x + 6

Step-by-step explanation:

take the y coordinate in (-8,6) which is 6.

take the slope.

y = (put slope here)x + (put y coordinate here) !

thats it :) have a good day!

Solving them, it is found that the equivalent equations are given as follows: 2 + x = 5, x + 1 = 4, -5 + x = -2.

Equivalent equations are equations that have the same solution.

In this problem, the equations and their solutions are given as follows.

Hence the equivalent equations are: 2 + x = 5, x + 1 = 4, -5 + x = -2.

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The product of the expressions (3 – 5i) and (–2 + 4i) is 14 + 2i. Then the correct option is A.

It is also known as the product. If the object n is given to m times then we just simply multiply them.

The expressions are (3 – 5i) and (–2 + 4i).

Then the product of the expressions will be

(3 – 5i)(–2 + 4i)

–6 –10i + 12i –20i²

We know that i² = –1, then we have

–6 + 2i –20 (–1)

–6 + 2i + 20

14 + 2i

More about the multiplication link is given below.

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Answer: B- 14+22i

Step-by-step explanation: edge 2023

Considering the situation described, the appropriate null hypothesis is given by:

[tex]H_0: p = 0.09[/tex]

At the null hypothesis, it is tested if the proportion is the expected one, that is, of 9%, hence:

[tex]H_0: p = 0.09[/tex]

At the alternative hypothesis, it is tested if there is enough evidence to conclude that the proportion is above 9%, hence:

[tex]H_1: p > 0.1[/tex].

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The interval at which the average rate of change of f(x) is negative is from x = 0 to x = 2.5.

The average rate of change is a type of function that describes the average rate at which a quanity decreases or increases with respect to another quanity.

Generally, for a function with a negative average rate of change, the graph must face down and have a negative slope.

Based on the graph shown in the image attached below, we can deduce that the interval for which the average rate of change of f(x) is negative is from x = 0 to x = 2.5.

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Answer:

22 is the perimeter.

Step-by-step explanation:

You find the perimeter by adding up all of the sides of a shape. 9 + 9 = 18. 18 + 4 = 22.

Answer:

4/3 πr^3

= 4/3π (6)^3

therefore the answer is C

Answer:

874

rem = 4.

Step-by-step explanation:

4374/ 5

= 874 remainder 4

Answer:

see image.

Step-by-step explanation:

Since this is a subtraction problem remember to 'add the opposite' So change to addition between the two sets of parenthesis and change all the signs/operations in the second term.

Then combine like terms. This means the terms can only be added or subtracted if the have exactly the same variables and exponents. See image.

Answer: -7/9

Step-by-step explanation: Get the LCM of the denominator 3 and 9

Place both fractions using same LCM

You will have - 3/9 -4/9 = -7/9

Because they both have negative signs, you will add 3 and 4

Answer:

-x² + 16x - 60

Step-by-step explanation:

Given expression:

Step 1. Insert brackets to isolate the "-" from the (x - 8)².

           ⇒ -(x - 8)² + 4

           ⇒ -[(x - 8)²] + 4

Step 2. Use the formula (a - b)² = a² - 2ab + b²

          ⇒ -[(x - 8)²] + 4

          ⇒ -[x² - 2(x)(8) + 8²] + 4

Step 3. Open the parenthesis

          ⇒ -[x² - 2(x)(8) + 8²] + 4

          ⇒ -x² + 2(x)(8) - 8² + 4

Step 4. Simplify as needed

          ⇒ -x² + 16(x) - 64 + 4

          ⇒ -x² + 16x - 60

Answer:

[tex]\sqrt32} inches[/tex]

Step-by-step explanation:

The crossbar and two given lengths form a right triangle.  We know this because we see a right angle marked on the diagram in between the two given sides.

Answer:

14,200 pounds.

1. Convert the mixed fraction into improper fraction:

To convert a mixed fraction into an improper fraction, we must multiply the whole number with the denominator and add the numerator to the product. The denominator of the improper fraction will remain the same as the denominator in the mixed fraction.

[tex]\implies 7 \dfrac{1}{10} = \dfrac{(7 \times 10) + 1}{10} = \dfrac{71}{10}[/tex]

2. Determine the number of pounds in 71/10 tons

It should be noted that:

Now, let's use the unitary method to determine the amount of pounds in 71/10 tons. Multiply both sides by 71/10 to do so.

[tex]\implies \text{1 ton = 2000 pounds}[/tex]

[tex]\implies \text{1 ton} \times \dfrac{71}{10} = 2000 \times \dfrac{71}{10}[/tex]

[tex]\implies \dfrac{71}{10}\text{ ton} = 200 \times 71[/tex]

Simplify as needed:

[tex]\implies \dfrac{71}{10}\text{ ton} = 14,200 \ \text{pounds}[/tex]

Answer:

slope = 1/6

all steps in picture. :)

Slope:-

Answer:

a) Low: 45 Q1=80 Q2=89 Q3=94 High=100 b) Look at attached image

Step-by-step explanation:

Organized numbers: 45,70,72|,80,|82,85,88|,89,|90,92,92|,94,|98,100,100

mark medians

Graph created in Desmos

Answer:

B. 140

just do an elimination process to figure out 160 is more wider and 90 is just too small

so it was between 100 and 140

The 98 percent confidence interval for the mean hours spent on personal tasks for 25-44 years olds will be (3.97, 4.11).

From the complete information, it should be noted that the mean is 4.04, the standard deviation is 0.81 and the number is 708.

Since the sample size is large, so the z-critical will be used. In this case, the critical value is 2.33.

The 98% confidence interval will be:

= 4.04 + 2.33(0.81/✓768)

= 4.11

Also, 4.04 - 2.33(0.81/✓768)

= 3.97

Therefore, the 98% confidence interval is (3.97, 4.11).

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Answer:

No

Step-by-step explanation:

the mean is 16 (add 4+5+5+8, then divide answer by 4) and the mode is 5 (occurs most in data)

Answer:

7x+12y ≤ 600

7x+12y = 600

Step-by-step explanation:

Lets first call cars x and minivans y. Since they want to raise 600, you can do the sign ≤ and 600

≤ 600

Since it is $7 per car, we can do 7x.

Since it is $12 per minivan, we can do 12y.

Together, they have to add up to 600 or more.

7x+12y ≤ 600

If you provide some options, I might be able to give a better answer. Without options, I can't tell if they want an exact answer or not. So technically, the answer could also be:

7x+12y = 600

Answer:

Quotient: 6

Remainder: None

Step-by-step explanation:

24 divided by 4 is 6.

Answer:

The area is 78.5.

Step-by-step explanation:

The formula for the area of a circle is π r^2

In this case, r = 5.

Answer:

A 5(0.5)^x

B 3(2)^x

C 5(3)^x

D 8(1.25)^x

E 8(0.75)^x

F 10(0.5)^x

Step-by-step explanation:

A 5(0.5)^x

(-1,10) goes by 1/2

B 3(2)^x doubles

C 5(3)^x triples

D 8(1.25)^x * 1 1/4

E 8(0.75)^x by 3/4

F 10(0.5)^x x 1/2

Answer: 78

Step-by-step explanation:

Area=b x h
13 x 6 =78

Answer:

78 m

Step-by-step explanation:

The formula to find the area of a rectangle or square = length * Height

A = L * H

In this scenario, the length is 6 and the height is 13

So the area (A) = 6 * 13 = 78

And don't forget your units ;)

Using it's concept, it is found that there is a 0.45 = 45% experimental probability of the coin landing on tails.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For an experimental probability, these number of outcomes are taken from previous trials.

In this problem, 9 out of 20 trials resulted in tails, hence the experimental probability is given by:

p = 9/20 = 0.45 = 45%.

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Answer:

Hello,

To find amount of inches in 58 centimeters, you need to use the information given.

0.4 inches = 1 centimeter

??? inches = 58 centimeter

58 x 0.4

= 23.20

Hence your answer is 23.2 inches are in 58 centimeters

Hope this helps ^^

Answer:

13

Step-by-step explanation:

This angle is called a reflective angle so the angles equal eachother. So put them equal to eachother and solve.

91=7x

x= 91÷7

x=13