find the component form of vector v

The triangle is isosceles as the two side AB = AC are equal in a triangle ABC has vertices A (0,0), B (3,3), and C (-3,3).

One of the fundamental shapes in geometry is represented by the symbol Δ and consists of three connected vertices.

Given:

ABC has vertices A (0,0), B (3,3), and C (-3,3),

Calculate the distance of the side as shown below,

[tex]AB = \sqrt{(3-0)^2 + (3 - 0)^2}[/tex]

AB = [tex]\sqrt{9 + 9}[/tex]

AB = √18

AB = 3√2

Similarly, calculate BC and AC,

AC = [tex]\sqrt{9 + 9}[/tex]

AC = √18

AC = 3√2

[tex]BC = \sqrt{(-3-3)^2 + (3 - 3)^2}[/tex]

[tex]BC = \sqrt{36 +0}[/tex]

BC = 6

Here, two sides AB = AC of a triangle are equal, so it is an isosceles triangle.

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The required value is evaluated as 110. The correct option is (B).

The percent value can be found by multiplying the given number with the percent divide by 100.

For example, 10% of 20 is 20 × 10/100 = 2.

The given expression for percentage is found as follows,

250% of 44

= 250/100 × 44

= 2.5 × 44

= 110

It can be written as 100 < 110 < 150.

Hence, the value of the given expression is 110 which is greater than 100 but less than 150 as 110 lies between the two numbers.

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Answer:

Priya:  S=20w+50

Vanessa:  S=25w+20

6 weeks

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Define the variables:

Given that Priya starts with $50 in her bank account, the y-intercept of the linear equation modelling her savings will be 50.

If she then deposits $20 each week for 12 weeks, the slope will be 20.

Therefore, the linear equation that models Priya's savings is:

Given that Vanessa starts with $20 in her bank account, the y-intercept of the linear equation modelling her savings will be 20.

If she then deposits $25 each week for 12 weeks, the slope will be 25.

Therefore, the linear equation that models Vanessa's savings is:

Create a table for each linear equation from part a.

Priya                       Vanessa

[tex]\begin{array}{|c|c|}\cline{1-2} w & S \\\cline{1-2} 1&70 \\\cline{1-2} 2& 90\\\cline{1-2} 3&110 \\\cline{1-2} 4&130 \\\cline{1-2} 5& 150\\\cline{1-2} 6&170 \\\cline{1-2} 7&190 \\\cline{1-2} 8&210 \\\cline{1-2} 9&230 \\\cline{1-2} 10&250 \\\cline{1-2} 11& 270\\\cline{1-2} 12& 290\\\cline{1-2} \end{aligned}[/tex]               [tex]\begin{array}{|c|c|}\cline{1-2} w & S \\\cline{1-2} 1&45 \\\cline{1-2} 2& 70\\\cline{1-2} 3& 95\\\cline{1-2} 4& 120\\\cline{1-2} 5& 145\\\cline{1-2} 6& 170\\\cline{1-2} 7& 195\\\cline{1-2} 8& 220\\\cline{1-2} 9& 245\\\cline{1-2} 10& 270\\\cline{1-2} 11& 295\\\cline{1-2} 12&320 \\\cline{1-2} \end{aligned}[/tex]

Create a graph for each linear equation (see attachment).

The week in which Priya and Vanessa will have the same amount of savings is the week where the S-values in the tables are the same, and the point of intersection of the graphed lines.

Therefore, from inspection of the tables and graphs from part b, Priya and Vanessa will have the same amount of savings in week 6.

The p-value is 0.15 which is greater than the significance value 0.10 so null hypothesis cannot be rejected at 10% significance level , we do not have enough evidences to state that no- show rate is less than 6%.

As given in the question,

Null hypothesis : No show rate for passengers booked on given flight is 6%

Alternative hypothesis: No show rate  for passengers booked on given flight  is less than the 6%

P = 6%

  = 0.06

1 -  P = 1 - 0.06

       = 0.94

random sample size 'n' = 380

no shows = 18

Sample proportion 'p' = 18/ 380

                                    = 0.047

Now , z test statistic value :

z = (p - P)/ √P (1- P)/n

 = (0.047 - 0.06)/√0.06( 0.94)/380

 = -0.013 /0.012

 = -1.083

p-value = 0.2788 ( using table)

0.2788 > 0.10

p-value is greater than significance value 0.10

Do not reject null hypothesis at 10% level of significance.

Therefore, as p-value is greater than significance value do not have enough evidences to state that no- show rate is less than 6%.

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The given equation has no solution. Option B is correct.

As mentioned, the solution of the equation 8.5m +8 = 8.5m is to be determined.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
Given expression,
8.5m + 8 = 8.5m
Now,
8.5m - 8.5m = 8
0 ≠ 8

Thus, the given equation has no solution. Option B is correct.

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y - 9 = -14(x + 2) is the point-slope form of the line with slope − 14 that passes through the point − 2 9 )

Given a line with slope -14 that passes through the point (-2, 9).

To determine the point-slope form of the line, we need to use the formula y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.

Substituting the values into the formula, we get:

y - 9 = -14(x + 2)

Therefore, the point-slope form of the line is y - 9 = -14(x + 2).

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Answer:

Step-by-step explanation:

Answer: He will need 49 tiles.

Step-by-step explanation:

Given: The patio will measure 13.5 feet by 43 feet.

Area of patio = 13.5 feet x 43 feet [Area = length x width]

= 580.5 sq. feet

Since area of each concrete tile = 12 sq. inch

Number of concrete tiles required to cover patio = (Area of patio) ÷ (area of each concrete tile)

= 580.5 ÷ 12

= 48.375 sq. inch ≈49

The side JE is equal to side IE because all the sides of the square are congruent.

It is a polygon with four sides. The total interior angle is 360 degrees. In a square, all the sides of the square are equal and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.

JH is opposite to JE and Hello is opposite to IE. Also, JH is congruent with HE.

Let 'm' be the side of the square.

HI = JE         (Congruent)

HJ = IE         (Congruent)

∠H = ∠J = ∠I = ∠E = 90°

Then the shape that is defined will be a square.

The side JE is equal to side IE because all the sides of the square are congruent.

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Answer:

x = 4.5

Step-by-step explanation:

Answer:

y = 300x + 100

Step-by-step explanation:

y = mx + c

the line intersects the y axis at 100, so c = 100

m = difference between y-coordinates / difference between x-coordinates

m = (400-100)/(1-0) = 300/1 = 300

y = 300x + 100

Rotation is the type of rigid transformation which is equivalent of two reflections across intersecting lines.

Define rigid transformation

A rigid  transformation is a transformation that persists the original size or shape of a given figure. Examples of rigid transformations are rotation, reflection etc;  

In mathematics a rigid transformation is also known as Euclidean Isometry or Euclidean transformation. Euclidean Isometry deals mainly with transformation of any figure. But, doesn't changes the length, shape or size of a given figure.

The concept of of two reflections across intersecting lines is equivalent to single rotation transformation of the original figure.  

Therefore the rigid transformation or Euclidean  isometry which is similar to two reflections across intersecting lines is rotation.  

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Answer:

No

Step-by-step explanation:

if you divide 8:3 you get 4:1.5 which is not equivalent. In order for them to be equivalent it would need to be 4:1 and 8:2

Answer: No

Step-by-step explanation:

Let's start with what we know. Ratios can also be written as fractions:

4/1 and 8/3

These fractions do not simplify to the same thing, therefore they are not equal.

The graph of the function f(x) = [x² if x ≤ 2] [x + 4 if x > 2]

From the question, we have the following parameters that can be used in our computation:

f(x) = [x² if x ≤ 2] [x + 4 if x > 2]

The above function is a piecewise function, and it can be split as follows:

f(x) = [x² if x ≤ 2]

f(x) = [x + 4 if x > 2]

The domain x ≤ 2 in f(x) = [x² if x ≤ 2]  means that:

The x values stop at 2 (i.e. 2 inclusive)

The domain x > 2 in f(x) = [x + 4 if x > 2] means that:

The x values starts at a value greater than 2 (i.e. 2 exclusive)

This is represented by the graph (d) with the open and closed circles

Hence, the graph is graph d

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AC bisects angle BAD and AC bisects angle BCD is proved using CPCT rule.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

Given that, ΔABC≅ΔADC.

We know that, corresponding parts of congruent triangle are equal.

So, ∠BAC=∠DAC (∵CPCT)

∠BCA=∠DCA (∵CPCT)

∠BAD=∠BAC+∠DAC

⇒ ∠BAD=2∠BAC

⇒ ∠BAC=∠BAD/2

So, AC bisects ∠BAD

∠BCD=∠BCA+∠DCA

⇒ ∠BCD=2∠BCA

⇒ ∠BCD/2=∠BCA

So, AC bisects ∠BCD

Hence, proved AC bisects ∠BAD and AC bisects ∠BCD.

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Answer:

sorry

Step-by-step explanation:

idrk

The height of the house is approximately 29.43 meters.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

We can use the tangent function to solve this problem.

The tangent of an angle is equal to the opposite side (the height of the house) divided by the adjacent side (the distance between the house and the building). In this case, the angle is 30 degrees and the opposite side is the height of the house, so we can write the following equation:

tan(30°) = height of house / 25√3

We can use a calculator or look up the value of tangent 30° to find that tangent 30 is approximately 0.577. Therefore, the equation becomes:

0.577 = height of house / 25√3

Multiplying both sides of the equation by 25√3 gives us:

height of house = 0.577 × 25√3

Plugging in the values and simplifying, we get:

height of house = 29.43 m

Therefore, the house's height is approximately 29.43 meters.

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Given that the hoop makes one complete oscillation in 2s, this implies that the period of oscillation is 2s

Then,

T = 2s

Let the Mass of the thin hoop be M

Let the Radius of the hoop be R

The moment of inertial of a hoop is

I = MR²

The period of a physical pendulum of small amplitude is given by

T = 2π √(I / Mgd)

Where,

T is the period in seconds

I is the moment of inertia in kgm²

M is the mass of the hoop

g is the acceleration due to gravity

g = 9.8m/s²

d is the distance from the rotational axis to the center of gravity

Therefore, d = R

Then, applying the formula

T = 2π √ (I / MgR)

So, we know that

I = MR²

Then,

T = 2π √( MR² / MgR)

T = 2π √(R/g)

Make R the subject of the formula

Square both sides

T² = 4π²(R/g)

T²g = 4π²R

Then, R = T²g / 4 π²

Since g = 9.8m/s² and T= 2s

R = 2² × 9.8 / 4π²

R = 0.993m

Then, the radius of the hoop is 0.993m

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Answer:

width = 6 cm

Step-by-step explanation:

Area = width x length

let x = length

width = x - 6

A = 72 cm² = x(x-6) =  x² - 2x

rewrite the equation:

x² - 2x - 72 = 0

solve for x by factoring or the quadratic equation:

(x-12)(x+6) = 0

x = 12, -6

therefore x = length = 12

Width = 12 - 6 = 6

The scalar equation of the plane that contains given points and lines can be written as: (-4)(x-1) + 4(y-2) + (-10)(z-3) = 0.

What is equation of plane?

A given point p(x, y, z) that is located on the plane and a normal vector n define the equation of a plane. A plane's vector and scalar components can be used to formulate the equation for the plane.

The parametric form of line equation,

[tex]p = p_0 + t. \vec v[/tex]

On comparing with the given equation in question, we can say that,

p = {x, y, z}, p₀ = {0, 6, 1,},  vec(v) = {3, -2, -2}

The scalar equation can be given by,

[tex][ \vec \omega, p - p_1] = 0[/tex]

Here, p₁ = {1, 2, 3} and ω is perpendicular to v and to the segment p₁ - p₀ So,

[tex]\vec \omega = \vec v \times (p_1 - p_0) = ( 3, -2, -2 ) \times (1, -4, -2)[/tex]

then,

[tex]\vec \omega = (-4, 4, -10)[/tex]

Therefore, the scalar equation can be written as:

(-4)(x-1) + 4(y-2) + (-10)(z-3) = 0

It can also be written as:

26 - 4x + 4y - 10z = 0

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Complete Question

Find a scalar equation of the plane that contains the point (1,2,3) and contains the line represented by the vector equation r(t) = [3t, 6 - 2t, 1 -2t] ?

Answer:

180 cups of hot chocolate and 95 cups of coffee

Step-by-step explanation:

multiply the cups by the price and add them together and it adds up to the total sales they got

Answer:

To calculate Nora's total annual interest on her $800 investment, we can use the following formula:

Interest = Principal x Rate x Time

In this case, the principal is $800, the rate is 6% per annum, and the time is 1 year. Plugging these values into the formula, we get:

Interest = $800 x 0.06 x 1

To convert the 6% rate to a decimal, we divide 6 by 100. This gives us 0.06. We then multiply the principal by the rate and the time to get the total annual interest. So the total annual interest on Nora's $800 investment is:

Interest = $800 x 0.06 x 1 = $48

Therefore, Nora will earn a total of $48 in interest on her $800 investment over the course of one year at a rate of 6% per annum.

Step-by-step explanation:

The height of the top section of the tower is 32 feet.

The radio station tower is built in two sections. The tower is 87 feet from the viewing point. The angle of elevation of the bottom section is 25 degrees. The angle of elevation from the top of tower (both sections) is 40 degrees. Let the height of the bottom section be y and height of the bottom and top section be z.

Considering a right-angled triangle, tangent formula states that:

Tan ɵ = opposite side/ adjacent side where ɵ is the angle of elevation.

Hence, when ɵ = 25, opposite side = y, and adjacent side = 87

Tan 25 = y/ 87

y = 40.57 feet

Hence, when ɵ = 40, opposite side = z, and adjacent side = 87

Tan 40 = z/87

y = 73 feet

Let the height of the top section of the tower be x.

Hence, x = 73 - 40.57 = 32.4 ≈ 32 feet

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The equation that best represents this scenario is x/(3x-4) =20/80. So, the correct option is B.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of bats be x.

The number of baseballs is four less than three times the number of bats.

The, the number of baseballs are 3x-4

The equipment is 80% baseballs. Then, the equipment is 20% bats.

So, the ratio from number of bats to number of baseballs is

x/(3x-4) =20%/80%

⇒ x/(3x-4) =20/80

Therefore, the option B is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

The sporting equipment has been sorted into baseballs and bats. The number of baseballs is four less than three times the number of bats. The equipment is 80% baseballs. Choose the equation that best represents this scenario

x/(3x-4) =80/20

x/(3x-4) =20/80

x/(3x-4) =80/100

x/(3x-4) =20/100

The equations that could be used to determine the number of small boxes sent and the number of large boxes sent is 85b = 440.

From the information, each small box can hold 20 books and each large box can hold 45 books.

There was also twice as many large boxes sent as small boxes, which altogether can hold 440 books.

This will be:

2(20b) + 45b = 440

where b = number of books

40b + 45b = 440

85b = 440

The equation is 85b = 440

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The action by X that develops the theme of the struggle between self-identity and perception by others is: He wears special clothing to show people that he has superpowers.

Self-identity: It defines the combining of the various roles individuals fulfill throughout their lives. It also tells about awareness and beliefs about the self as an object or being.

The second is people are viewed that the individual as internalized roles, also called role identity.

Today, our identities encompass memories, experiences, relationships, and values, these components, help to create our identities and the sense of ourselves.

There are some aspects that will contribute to the development of different types of identities. They are race/ethnicity, gender, age, and class.

Social identity can be represented in terms of three factors:

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Examining the table showing number of students gaining certificates for outstanding achievements the modal number is 4

The most frequent number, or the one that appears the most frequently.

In a frequency table the frequency shows the number of times a the data measured appears

Looking at the table the number that has most frequency is 4. This means that the people that collected 4 certificates are more than any other set of people.

The next is two which have a frequency of two while the least the people that collected 6 certificates. they have a frequency of 2 which means they are only tow people

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Answer:

To turn the given statement into an inequality, we can write it in the form "m - s >= 8", which means that the amount of money you have (m) minus the amount you spend on snacks (s) must be greater than or equal to 8. This inequality represents the constraint that your mom has placed on your spending, requiring you to spend at least $8 on the pizza. In mathematical notation, the inequality would be written as:

m - s >= 8

This inequality states that the amount of money you have, minus the amount you spend on snacks, must be greater than or equal to 8 in order for you to be able to buy the pizza.

Step-by-step explanation:

The 64th term of the arithmetic sequence -3, -14 -25, will be - 696.

An arithmetic sequence is the sequence of numbers where each consecutive numbers have same difference.

Given that;

The arithmetic sequence is,

⇒ -3, -14 -25.

Now,

Since, We know that;

⇒ nth term = a + (n - 1)d

Where, 'a' is first term, 'd' is common difference.

Here, The arithmetic sequence is,

⇒ -3, -14 -25.

First term (a) = - 3

Common difference (d) = - 14 - (-3)

                                    = - 14 + 3

                                    = - 11

So, We get;

⇒ 64th term = - 3 + (64 - 1) (-11)

                    = - 3 + 63 × - 11

                    = - 3 - 693

                    = - 696

Thus, 64th term = - 696

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The value of the numerical expression (6 + 3)² + [10 - (15/3)] will be 86.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ (6 + 3)² + [10 - (15/3)]

Simplify the expression, then we have

⇒ (6 + 3)² + [10 - (15/3)]

⇒ (9)² + [10 - 5]

⇒ 81 + 5

⇒ 86

The value of the numerical expression (6 + 3)² + [10 - (15/3)] will be 86.

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