Graph the function
Need help ASAP plz

Question:

1. Find the magnitude and the positive direction angle for u.

u = (-12, 5)

For theta degree, round to the nearest tenth as needed.

2. For the vector r = (-9, -10), find -9r.

Answer:

(1)

The magnitude of vector u is 13.

The positive direction of vector u is 157.4° (to the nearest tenth)

(2)

-9r = (81, 90)

Step-by-step explanation:

(1) For a given vector u = (a, b), the magnitude of u is given by;

\(|u| = \sqrt{a^2 + b^2}\)            --------------------(i)

The direction of such vector is given by;

θ = tan ⁻¹ (\(\frac{b}{a}\))                    -------------(ii)

Where;

a and b are the x and y components of the vector.

Now,

From the question,

u = (-12, 5)

(a) From equation (i), the magnitude of u is therefore;

\(|u| = \sqrt{(-12)^2 + (5)^2}\)

\(|u| = \sqrt{144 + 25}\)

\(|u| = \sqrt{169}\)

\(|u| = 14\)

Therefore, the magnitude of vector u is 13.

(b) From equation (ii) the direction of vector u is therefore;

θ = tan ⁻¹ (\(\frac{5}{-12}\))

θ = tan ⁻¹ (-0.41667)

θ = -22.62°

The direction here is negative, but we have been told to find the positive direction.

From the given x and y components of the vector, it can be deduced that the the vector lies in the negative x direction and the positive y direction.

Therefore, the vector lies in the second quadrant. This is shown in the diagram attached to this response.

To get the positive direction, m, we need to add 180° to the result of θ = -22.62° i.e

m = 180° + (-22.62)°

m = 157.38°

Therefore, the positive direction of vector u is 157.4° (to the nearest tenth)

(2) For the vector r = (-9, -10), we are asked to calculate -9r.

Since;

r = (-9, -10)

-9r = -9(-9, -10)    [Multiply by -9]

-9r = (81, 90)

Therefore, -9r = (81, 90)

Answer:

The Area of the trapezium is \(60cm^2\)

Step-by-step explanation:

Given,

Height (h)= 8cm

Sum of the parallel sides (a+b)= 15cm

Area of trapezium = \(1/2*h*(a+b)\)

                              =\(1/2*8*15\)

                              =\(4*15\)

Area of trapezium=60cm^2

Answer: Area = 60 cm²

Step-by-step explanation:

To find the area of a trapezium we use the formula

Area of trapezium = 1/2 (sum of parallel sides) × height

∴ Area = 1/2 ×15 cm × 8 cm

           = 60 cm²

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Answer:

$182.84

Step-by-step explanation:

169.30*0.08=13.54

13.54+169.30=

$182.84

Hope this helps!!

Answer:

Boiling B would probaly Have

a huge impact on the answer

Step-by-step explanation:

Answer:

C. (3 1/4 + 2 1/2 + 1) + (3 1/4 + 2 1/2+ 1)

Step-by-step explanation:

Since, this week you practice your instrument for 3 1/4 on Monday, 2 1/2 hours on Tuesday and 1 hour on Wednesday.

And, next week you practice for the same number of hours.

Same number = (3 1/4 + 2 1/2 + 1)

Thus, [C] (3 1/4 + 2 1/2 + 1) + (3 1/4 + 2 1/2+ 1) is correct.

~Lenvy~

Answer:

[C} \(\left(3\frac{1}{4}+2\frac{1}{2}+1\right)+\left(3\frac{1}{4}+2\frac{1}{2}+1\right)\)

Step-by-step explanation:

Given:

this week you practice your instrument for 3 1/4 on Monday, 2 1/2 hours on Tuesday and 1 hour on Wednesday.

Next week you practice for the same number of hours.

To Find:

What is the total number of hours you will have practiced over these six days?

Which expression correctly shows how to solve this problem

Solve:

Knowing that you practice for 3 1/4 on Monday, 2 1/2 hours on Tuesday and 1 hour on Wednesday. Next week you practice the same. Thus, we can know that [C} \(\left(3\frac{1}{4}+2\frac{1}{2}+1\right)+\left(3\frac{1}{4}+2\frac{1}{2}+1\right)\) is the correct answer.

Solution if needed.

\(\left(3\frac{1}{4}+2\frac{1}{2}+1\right)+\left(3\frac{1}{4}+2\frac{1}{2}+1\right)\)

\(=\left(\frac{13}{4}+\frac{5}{2}+1\right)+\left(3\frac{1}{4}+2\frac{1}{2}+1\right)\)

= \(\left(\frac{13}{4}+\frac{5}{2}+1\right)+\left(\frac{13}{4}+2\frac{1}{2}+1\right)\)

\(=\left(\frac{13}{4}+\frac{5}{2}+1\right)+\left(\frac{13}{4}+\frac{5}{2}+1\right)\)

\(\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\)

\(=\frac{27}{4}+\left(\frac{13}{4}+\frac{5}{2}+1\right)\)

\(=\frac{27}{4}+\frac{27}{4}\)

\(=\frac{27}{2}\)

\(=13\frac{1}{2}\)

Solution ⇒ \(=13\frac{1}{2}\)

[RevyBreeze]

Answer:

12 -20

30 - 5

Step-by-step explanation:

12 × 20 = 240

30 × 5 = 150

240 + 150 = 390

then 5 has 8 more than 20

5 × 8 = 40

30 +8 = 38

38 × 5 = 190

240 + 190 = 430

please mark as brainlist answer

The probability that precisely eight cell phone owners used their phones to guide their purchasing decisions is 31%.

Probability measures the ratio of the likelihood of an outcome happening out of possible outcomes.

Probability is depicted as fractions, decimals, or percentages because they show the chance that an expected event occurs in the face of many possible events.

This implies that probability can be zero or 1 but not less than zero or more than 1.

The probability that cell phone owners used their phones for guidance = 58%

The sample size of cell phone owners studied = 15

The probability of 8 phone owners out of 15 using their phones for guidance on purchase decisions = 53% (8/15)

The probability that of 8 from 15 of the 58% cell phone owners using their phones for purchase decisions = 31% (58% x 53%).

Thus, the probability that precisely eight cell phone owners used their phones to guide their purchasing decisions is 31%.

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Answer:

28,650

Step-by-step explanation:it says "how many more meaning your going to subtract.

59,466 - 30,816=

28,650

(Im 12 btw lol )

Answer:

-2x^4+10x^3-21x^2+19x-4

Step-by-step explanation:

Answer:

-2x^4+10x^3-21x^2+19x-4

Step-by-step explanation:

trust me bro

Answer:

D, g(x) = 1/4 x^2

Step-by-step explanation:

You can try plugging in the x and y values into each equation. The answer to this would be D, where if you plug in 2 as the x value, you get 1/4 * 4 which equals 1. This also makes sense because 2x would have a narrower curve while 1/2x would have a wider curve.

The angle  made by one of the tensions suspending particle P is 50⁰.

The angle θ made by one of the tensions is calculated by applying trig identities as follows;

the force opposite the angle = weight of the block = mg

W = 7.75 kg x 9.8 m/s²

W = 75.95 N

The angle θ made by one of the tensions is calculated as follows;

cos θ = (38 N ) / ( 59 N)

cos θ = 0.6441

θ = arc cos (0.6441)

θ = 50⁰

Thus, the angle θ made by one of the tensions is determined as 50 degrees.

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The missing part of the question is in the image attached.

The ordered pairs are (1,0), (2,6/5),(3,12/5)

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: The equation as y = 6x/5 - 6/5

putting (1,0) in the equation we get 6×1/5-6/5=0

Similarly we can find the ordered pair as y = 6/5x - 6/5

Hence, The ordered pairs are (1,0), (2,6/5),(3,12/5)

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Answer:

R ≈ 7.4

Step-by-step explanation:

Substitute I = 25000000 into the equation

log(25000000 ) = R , then

R ≈ 7.4 ( to 1 dec. place )

Answer:

The Richter scale measurements of an earthquake with intensity 25,000,000 is R ≈ 7.4

Step-by-step explanation:

Substitute I = 25000000 into the equation

R= log(25000000 ) , then by using calculator we get

R =7.3979

R≈7.4

Thus the Richter scale measurements of an earthquake with intensity 25,000,000 is R ≈ 7.4

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Answer: L is (-5, 2) M is (0,6) N is (2,4)

Step-by-step explanation:

Answer:

the correct answer is 290 / 605

Answer:

Step-by-step explanation:

One number is 2 more than another. The difference between their squares is 24. What are the numbers?

(x + 2)² - x² = 24

x² + 4x + 4 - x² = 24

4x + 4 = 24

4x = 20

x = 20 : 4

x = 5

----------------------

5 + 2 = 7

check

(5 + 2)² - 5² = 24

49 - 25 = 24

24 = 24

the answer is good

Answer:

Area ≈ 22 in²

Step-by-step explanation:

Finding ST (Base)

=> Tan 70 = \(\frac{opposite}{adjacent}\)

Where Opposite = ST and adjacent = 6

=> 1.22 * 6 = ST

=> ST = 7.33 in

Now, Finding the area:

=> Area = \(\frac{1}{2} (Base)(Height)\)

Where Base = 7.33, Height = 6

=> Area = 1/2 (7.33)(6)

=> Area = (7.33)(3)

=> Area ≈ 22 in²

The amount of Dividends of $3,000, $5,000, $34,500, and $71,000 were distributed to the 20,000 preferred and 25,000 common shareholders of Lightfoot Inc. over the first four years of operations.

To calculate the dividend per share of the preferred and common stock of Lightfoot Inc., the total amount of dividends paid out over the first four years must first be determined. This can be done by adding the given amounts of $3,000, $5,000, $34,500, and $71,000 to get a total of $113,500. To find the dividend per share for the preferred stock, the total dividend is divided by the number of shares (20,000) which gives a dividend per share of $5.68. To find the dividend per share for the common stock, the total dividend is divided by the number of shares (25,000) which gives a dividend per share of $4.54.

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Answer:

Simple interest = $600

Step-by-step explanation:

In this word problem, we will need to find the simple interest.

Formula:

I = prt or I = p x r x t

Simple interest: final answer

I = (2,000)(.02)(15) multiply.

I = 600

Simple interest: $600

Explanation:

Each equation asks for x . So let's solve it in a way so that at the end remains x = ,then the rest equation.

So first one,

1. a(x+b)=c

ax + ab = c

ax = c - ab

x = (c - ab ) / a

Now we can write that in two ways:

i. We already got the answer for the 2nd blank which is c - ab / a

ii. If we rearrange it so that there is a minus sign, it would be like: c/a  - b

Try solving the rest 3 by your self to make sure you understood them. Then scroll down to match the answers.

2. 8(x + a) = b

8x + 8a = b

8x = b - 8a

x = (b-8a)/ 8

First blank for 2nd equation: x = b/8  - a

Second blank: x = b - 8a  /  8

3. a(x - 9) = b

ax - 9a = b

ax = b + 9a

x = (b + 9a) / a

First blank for 3rd equation: x = b/a + 9

Second blank: x = b+9a  /  a

4. c(2 + x ) = 7

2c + cx = 7

cx = 7 - 2c

x = (7 - 2c) / c

First blank for 4th equation: x = 7/c  - 2

Second blank: x = 7 - 2c  / c

Do let me know if it's correct! <3

The area of triangle ABC is 23.5 square units and the perimeter is 20.4174 units.

To find the area and perimeter of the given triangle ABC, we need to apply the following formulas:Formula for Distance between two points:

The distance between two points (x1, y1) and (x2, y2) is given by:

AB = √(x2-x1)²+(y2-y1)²BC = √(x3-x2)²+(y3-y2)²AC = √(x3-x1)²+(y3-y1)²

Formula for Area of Triangle: If we know the length of the three sides of a triangle then,

using Heron's formula, we can calculate the area of the triangle as:

area = √s(s-a)(s-b)(s-c)where a, b, and c are the lengths of the sides of the triangle and s is the semi-perimeter of the triangle, which is given as s = (a+b+c)/2

Formula for Perimeter of Triangle: The perimeter of the triangle is the sum of the lengths of its sides.

That is: perimeter = AB + BC + ACArea of ΔABCAB

= √(1 - (-2))² + (5 - (-4))²AB

= √3²+9² = √90BC

= √(2 - 1)² + (2 - 5)²BC

= √1²+3² = √10AC

= √(2 - (-2))² + (2 - (-4))²AC

= √4²+6²

= √52Semi-Perimeter (s)

= (AB + BC + AC)/2

= (√90 + √10 + √52)/2

= 12.8572Area of ΔABC

= √s(s-a)(s-b)(s-c)

= √12.8572(12.8572-√90)(12.8572-√10)(12.8572-√52)

= 23.5

Perimeter of ΔABC = AB + BC + AC = √90 + √10 + √52 = 20.4174

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Answer:

a = 11 , b = 4

Step-by-step explanation:

to find a and b substitute the coordinates of the given points f(x) passes through into f(x)

f(x) = a\(b^{x}\)

substituting (0, 11 ) into f(x)

11 = a\(b^{0}\) [ \(b^{0}\) = 1 ] , then

11 = a

f(x) = 11\(b^{x}\)

substituting (2, 176 ) into f(x)

176 = 11b² ( divide both sides by 11 )

16 = b² ( take square root of both sides )

\(\sqrt{16}\) = b , that is

b = 4

thus a = 11 and b = 4 and

f(x) = 11 \((4)^{x}\)

Answer:

549 000

Step-by-step explanation:

4500×122 months=549 000

Answer:

\(6(6 - x)\)

Step-by-step explanation:

1) Expand.

\(6(x - 2x + 6)\)

2) Collect like terms.

\(6((x - 2x) + 6)\)

3) Simplify (x - 2x) + 6 to -x + 6.

\(6( - x + 6)\)

4) Regroup term.

\(6(6 - x)\)

Therefor, the answer is 6(6 - x).

As a result, the original discounted price is $1 while the weekly normal price is $9.

The fundamental formula for calculating a reduction is to increase the initial price by the provided percentage rate in decimal form. We must deduct the reduction from the initial price to determine the item's sale price.

From the given information, we have:

d + 6x = 55 (discounted price for 7 weeks)

d + 11x = 100 (discounted price for 12 weeks)

We can solve this system of equations by eliminating d. Subtracting the first equation from the second, we get:

5x = 45

Dividing both sides by 5, we get:

x = 9

Substituting x = 9 into one of the equations, we can solve for d. Using the first equation, we get:

d + 6(9) = 55

d + 54 = 55

d = 1

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Step-by-step explanation: Begin by studying the pattern.

Notice that if we divide the first term,

360, by 6, we get the second term, 60.

Similarly, if we divide the second term,

60, by 6, we get the third term, 10.

So each new term is equal to the previous term

divided by 2, so we use this idea to find any missing terms.

Answer:

the perimeter is "16" and the area is "15"

The set of all elements that are in either A or B is the union of A and B, which is 1, 2, 3, 4, 5, 6, 8, 9, 10. As a result, A u B = 1, 2, 3, 4, 5, 6, 8, 9, 10

Set operations are done on two or more sets to produce a combination of components based on the operation. There are three primary sorts of operations done on sets in a set theory, such as: Intersection of sets () Union of sets () Set difference (-).

¡) (A n B) u C:

The value of the intersection of A and B is 5, 8. As a result, (A n B) = 5, 8. The union of this set with C is thus 1, 2, 3, 4, 5, 6, 8. As a result, (A n B) u C = 5, 8 u 1, 2, 3, 4, 5, 6, 8 = 1, 2, 3, 4, 5, 6, 8.

¡¡) (A-B) u C:

A-B is the set of elements in A that are not in B, which is 3, 6. The union of this set with C is thus 1, 2, 3, 4, 5, 6, 8. As a result, (A-B) u C = 3, 6 u 1, 2, 3, 4, 5, 6, 8 = 1, 2, 3, 4, 5, 6, 8.

¡¡¡) (A u B):

The set of all elements that are in either A or B is the union of A and B, which is 1, 2, 3, 4, 5, 6, 8, 9, 10. As a result, A u B = 1, 2, 3, 4, 5, 6, 8, 9, 10.

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¡) (A ∩ B) ∪ C  = {1,2,3,4,5,6,8}.

¡¡) (A-B) ∪ C = {1,2,3,4,5,6,8,10}.

¡¡¡) (A ∪ B)' is the set of elements that are in U but not in {1,2,3,4,5,6,8,9,10}. This is simply the set {7}.

What is probability?

Probability is a measure of the likelihood of an event occurring.

Recall that:

A ∩ B denotes the intersection of sets A and B, i.e., the set of elements that are in both A and B.

A ∪ B denotes the union of sets A and B, i.e., the set of elements that are in either A or B or both.

A' denotes the complement of set A, i.e., the set of elements that are not in A.

Using these notations, we can solve each part of the question as follows:

¡) (A ∩ B) ∪ C

First, we need to find A ∩ B, which is the set of elements that are in both A and B. We can see that A={3,5,6,8,10} and B={1,2,4,5,8,9}. So, A ∩ B={5,8}.

Next, we take the union of (A ∩ B) and C. We have C={1,2,3,4,5,6,8}, so the final set is:

(A ∩ B) ∪ C = {5,8} ∪ {1,2,3,4,5,6,8} = {1,2,3,4,5,6,8}

Therefore, (A ∩ B) ∪ C = {1,2,3,4,5,6,8}.

¡¡) (A-B) ∪ C

First, we need to find A-B, which is the set of elements that are in A but not in B. We can see that A={3,5,6,8,10} and B={1,2,4,5,8,9}. So, A-B={3,6,10}.

Next, we take the union of (A-B) and C. We have C={1,2,3,4,5,6,8}, so the final set is:

(A-B) ∪ C = {3,6,10} ∪ {1,2,3,4,5,6,8} = {1,2,3,4,5,6,8,10}

Therefore, (A-B) ∪ C = {1,2,3,4,5,6,8,10}.

¡¡¡) (A ∪ B)'

Recall that A ∪ B denotes the union of sets A and B, i.e., the set of elements that are in either A or B or both. So, (A ∪ B)' denotes the complement of A ∪ B, i.e., the set of elements that are not in A or B.

We can see that A={3,5,6,8,10} and B={1,2,4,5,8,9}. So, A ∪ B={1,2,3,4,5,6,8,9,10}. Therefore, (A ∪ B)' is the set of elements that are not in {1,2,3,4,5,6,8,9,10}.

The universal set U={1,2,...,10}, so (A ∪ B)' is the set of elements that are in U but not in {1,2,3,4,5,6,8,9,10}. This is simply the set {7}.

Therefore, (A ∪ B)'={7}.

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The measure of the inscribed angle G in the circle is 85 degree.

An inscribed angle is simply an angle with its vertex on the circle and whose sides are chords.

The relationhip between an an inscribed angle and intercepted arc is expressed as:

Inscribed angle = 1/2 × intercepted arc.

Since the circle equals 360 degrees, we can determine the intercepted arc DF.

Hence:

Arc DF = 360 - ( 70 + 120 )

Arc DF = 360 - 190

Arc DF = 170°

Now, plug the value into the above formula:

Inscribed angle = 1/2 × intercepted arc.

Inscribed angle G = 1/2 × 170°

Inscribed angle G = 85°

Therefore, angle G has a measure of 85 degree.

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