(c) Given a = [1,2,2], b = [2,6x − 3,4], and c = [−2,8y + 4,1], (i) find the value of x such that |a + b| = |a| + |b|; (ii) determine the value of y such that there exists a vector d satisfying a × d = c.

Answer:

x^2 + 10x + 20

Step-by-step explanation: When you multiply binomials, you are practically taking each term and multiplying it with others until you are out of combinations. However, when the product is represented in standard form, it requires the terms to be set within a specific order that prompts the term at the highest order/power placed on the furthest left side of the expression. The first term x^2 can be referred to as a term of the second power, 10x is seen as one to the first power (x^1 = 1st), and 20 as 0, since it is a constant.

The regular pentagon's perimeter is therefore sqrt(101) units when its adjacent edges are at A(-3, 5) and B(7, 6).

The perimeter of a two-dimensional object is the space surrounding it. It represents the total length of the shape's edges. Typically, the perimeter is calculated using measures like centimetres, metres, or feet.

given

We can use the calculation for the distance between the two provided vertices to determine the length of one side:

sqrt[(7 - (-3))2 Plus (6 - 5)2] yields AB. = sqrt[10^2 + 1^2] = sqrt(101) (101)

Since the five sides of a normal pentagon are all the same length, one side's length is:

sqrt(101) / 5

s = AB / 5

Now, utilising the method for the regular pentagon's perimeter, we have:

Circumference = 5s = 5 sqrt(101) / 5 = sqrt (101)

The regular pentagon's perimeter is therefore sqrt(101) units when its adjacent edges are at A(-3, 5) and B(7, 6).

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Answer:

y = 3x + 10

Step-by-step explanation:

y represents total he pays

x represents items he buys

total he pays = $3 for each item + $10 movie

y = 3x + 10

The vertex of the parabola is (5, 4). The solution has been obtained by using quadratic formula.

What is quadratic formula?

The quadratic formula is used to determine an equation's roots. This formula assists in evaluating the solutions of the quadratic equations instead of the factorization approach.

We are given equation as  y = -x² + 10x - 21.

Using quadratic formula, we know that x = -b/2a

So,

x = -10/-2

x = 5

On substituting this in the equation, we get

y = -5² + 10(5) - 21

y = -25 + 50 - 21

y = 4

Hence, the vertex of the parabola is (5, 4).

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Answer: 57.15[tex]\geq[/tex] 5.99x

Step-by-step explanation:

127.5-70.35[tex]\geq \\[/tex]x

57.15[tex]\geq[/tex] 5.99x

Answer:

(4[tex]x^{2}[/tex]+2)([tex]x^{2}[/tex]-3)

Step-by-step explanation:

 4x    +2

  x       -3

If a rectangular prism has dimensions of 1.5 feet by 3.5 feet by 2 feet, its volume, expressed in cubic feet, is 10.5 cubic feet.

The rectangular prism's measurements are —

3.5 feet in length

1.5 feet wide in Size

Height is two feet.

The volume of the rectangular prism is calculated by multiplying these dimensions collectively.

Volume equals length, width, and height, or 3.5 feet, 1.5 feet, and 2 feet.

= 10.5 cubic feet of volume

Hence, the rectangular prism has a volume of 10.5 cubic feet.

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About 5,000 more fans attended the third round finals than the third round time trials.

From the question, we are to find the approximate difference between the attendance of the third round finals and the third round time trials.

From the given data, we have:

Attendance Time             Trials                      Finals

1st round                           12,645                    17,352

2nd round                         16,234                    21,896

3rd round                          18,817                     23,773

Third round finals attendance = 23,773

Third round time trials attendance = 18,817

The difference between these two numbers is:

23,773 - 18,817 = 4,956

Rounding this to the nearest thousand gives:

4,956 ≈ 5,000

Hence, The number of fans that attended the third round finals than the third round time trials is about 5,000

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The order of the decimal number from least to greatest is

4.08< 4.7<4.76<4.9.

Decimals are a form of number in algebra that have a full integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the whole number from the fractional element of the number. A decimal number is, for instance, 34.5.

Here the given decimal numbers are,

=>  4.76, 4.9, 4.08,4.7

Now ordering the number from smallest to largest

=>4.08< 4.7<4.76<4.9.

Hence the order of the decimal number from least to greatest is 4.08< 4.7<4.76<4.9.

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Answer:

there is no chart or questions

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question is illustrated with the attached image.

Angle of elevation is the angle between a line of sight and the horizontal surface.

Let h be the height of the tower

First, calculate distance BC (x).

This is calculated using the following tan ratio,

tan52=h/x

h=xtan52

From the attached image:,

CD=47+x

tan31=h/x+47

h=(x+47)tan31

xtan52=(x+47)tan31,

solving for x we get, x=41.156m

h=xtan52=41.156 * tan52=53.2m

So, the value of the car after 2 years, rounded to the nearest dollar, is $8450.

To determine the value of the car after 2 years, we need to plug in x=2 into the exponential function y=20000*(13000/20000)^x.

y=20000*(13000/20000)^2

y=20000*(0.65)^2

y=20000*0.4225

y=8450

Therefore, the value of the car after 2 years is $8450.

To round to the nearest dollar, we can look at the decimal part of the number. Since the decimal part is less than 0.5, we can round down to the nearest whole number.

So, the value of the car after 2 years, rounded to the nearest dollar, is $8450.

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They will have to change the plugs, rotate the tyre, and replace the brake pads all at once for the first time​ after 30,000 km.

LCM is the abbreviated form for Least Common Multiple. LCM of two or more numbers is the lowest of all the common multiples of them.

Given,

Plugs are changed every 30,000 km

Rotate the tyres every 10,000 km

Replace the break pads blades every 15,000 km

All the three will be done together for the first time when all the multiples of the three distances intersect for the first time.

It is enough to find the LCM of 30000, 10000 and 15000 to find the least distance travelled when all the things are done together.

Multiples of 30,000 = 30000, 60000, 90000, ...........

Multiples of 10,000 = 10000, 20000, 30000, .......

Multiples of 15,000 = 15000, 30000, 45000, ........

The common multiple for the first time is 30,000.

Hence all the changes will be made to the car together for the first time after 30,000 km.

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The sum of number is 270, after adding 5 to each number , sum of numbers is 320 and mean is 32.

The mathematical average of a group of two or more numbers is arithmetic mean, add the numbers in a set together and divide by the total number of numbers in the set.

Here the mean of 10 number is 27. We know that ,

[tex]mean=\frac{sum of numbers}{total numbers}\\[/tex]

[tex]27= \frac{sum of numbers}{10}[/tex]

=sum of numbers = 27*10=270.

Now 5 added to each number, we need to add 5 in 10 times( because 10 total number), Then 5*10=50.

Sum of numbers after adding 5 to each number [tex]270+50=320[/tex]

Now, [tex]mean=\frac{320}{10}=32[/tex]

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[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{3.8\% of 25}}{\left( \cfrac{3.8}{100} \right)25}\implies \text{\LARGE 0.95}[/tex]

Answer:

To find 3.8% of 25, we can convert the percentage to a decimal and then multiply it by 25:

3.8% = 0.038 (converting percentage to decimal)

0.038 x 25 = 0.95

Therefore, 3.8% of 25 is 0.95.

Answer:

x= 27.4

Step-by-step explanation:

a triangle's angles always equal 180 so

34.6+118+x=180

add 34.6 and 118 to get

152.6+x=180

subtract both sides by 152.6 to get

x=27.4

Answer: Point B is (-2,0) and Point C is (0,3)

Step-by-step explanation:

We know x-intercept is when y=0 and y-intercept is when x=0

Let's first find the x-intercept by replacing y with 0.

6x-4(0)=-12

now let's solve for x

6x-0=-12

x=-2

so Point B is (-2,0)

Now let's find the y-intercept by replacing x with 0

6(0)-4y=-12

now solve for y

-4y=-12

y=3

So point C is (0,3)

Answer:

We can use trigonometry to solve this problem.

A is the taller platform, B is the shorter platform, and x is the length of the zipline cable that we want to find.

We can see that the angle between the horizontal and the zipline cable is 12 degrees, so we can use the tangent function to find x:

Therefore, the length of the zipline cable, rounded to the nearest foot, is 209 ft.

As a result, the floor's perimeter in the size illustration is 38,016 inches.

The perimeter of an object is the space surrounding its border. Find the perimeter of different forms by combining the lengths of their sides.

We can start by finding the scale factor that relates the length of the actual floor to the length of the scale drawing.

The length of the actual floor is 32 feet = 384 inches (since there are 12 inches in a foot).

The length of the scale drawing is given as 16 inches.

Therefore, the scale factor is:

384 inches / 16 inches = 24

This means that one inch on the scale drawing represents 24 inches in the actual floor.

To find the perimeter of the floor in the scale drawing, we need to multiply the perimeter of the actual floor by the scale factor.

The perimeter of the actual floor is:

2(32 feet) + 2(34 feet) = 64 feet + 68 feet = 132 feet

Converting to inches, we get:

132 feet x 12 inches/foot = 1584 inches

Multiplying by the scale factor of 24, we get:

1584 inches x 24 = 38,016 inches

Therefore, the perimeter of the floor in the scale drawing is 38,016 inches.

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To solve the equation -3(w-1)=-5w+1 for w, we will use the following steps:

Step 1: Distribute the -3 on the left side of the equation:
-3w + 3 = -5w + 1

Step 2: Combine like terms on both sides of the equation:
2w = -2

Step 3: Solve for w by dividing both sides of the equation by 2:
w = -1

Therefore, the solution for w is -1.

In HTML format, the answer would be:

<p>To solve the equation -3(w-1)=-5w+1 for w, we will use the following steps:</p>
<ol>
<li>Distribute the -3 on the left side of the equation:
-3w + 3 = -5w + 1</li>
<li>Combine like terms on both sides of the equation:
2w = -2</li>
<li>Solve for w by dividing both sides of the equation by 2:
w = -1</li>
</ol>
<p>Therefore, the solution for w is -1.</p>

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To make her prediction more accurate, Kathleen could modify her approach by using a larger and more representative sample size, or by conducting a more in-depth survey that accounts for regional and socioeconomic variations.

Kathleen's prediction is flawed because she assumed that the average number of pets per household would remain the same for all households in the state, which may not necessarily be true. The sample size of 200 households may not be representative of the entire population of households in the state, and there may be variations in the number of pets per household across different regions or socioeconomic groups.

To make her prediction more accurate, Kathleen could modify her approach by using a larger and more representative sample size, or by conducting a more in-depth survey that accounts for regional and socioeconomic variations. Alternatively, she could use data from existing sources, such as census data, to estimate the number of pets per household in different regions of the state and adjust her prediction accordingly. It's also worth noting that factors such as pet ownership trends, cultural attitudes towards pets, and population growth may also impact the accuracy of Kathleen's prediction and should be taken into account.

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The approximate area of the school is 22857 kilometer square.

The approximate area of the school can be found by multiplying the fraction of space covered by the STEM Innovation Academy building by the total area of the space.

In this case, the fraction of space covered is (4)/(7) and the total area of the space is 40,000 square kilometres.

To find the approximate area of the school, we can multiply these two values together:

(4)/(7) * 40,000 = 22,857.14

Therefore, the approximate area of the STEM Innovation Academy building is 22,857.14 square kilometres.

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The magnitude of the vector ū is approximately 5.10, and the angle is approximately 281.31°.

The magnitude of a vector is the length of the vector, and is calculated using the Pythagorean Theorem. The angle of a vector is the direction in which the vector points, measured counterclockwise from the positive x-axis.

To find the magnitude of the vector ū = (-1,5), we can use the formula:

magnitude = √(x^2 + y^2)

where x and y are the components of the vector.

Plugging in the values of x and y from the vector ū, we get:

magnitude = √((-1)^2 + (5)^2)

Simplifying the expression, we get:

magnitude = √(1 + 25)

magnitude = √(26)

magnitude ≈ 5.10

To find the angle of the vector, we can use the formula:

angle = tan^-1(y/x)

Plugging in the values of x and y from the vector ū, we get:

angle = tan^-1(5/-1)

angle = tan^-1(-5)

angle ≈ -78.69°

Since the angle is measured counterclockwise from the positive x-axis, we need to add 360° to get the angle in the correct quadrant:

angle = -78.69° + 360°

angle = 281.31°

Therefore, the magnitude of the vector ū is approximately 5.10, and the angle is approximately 281.31°.

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The overall chances of winning the games before playing were 52%, and after playing and winning once but losing twice, the overall chances of winning are 17.33%. This shows that the new information has changed your belief about the probability of winning, and you now suspect that your chances of winning are lower than before.

Before playing the games, the expected value of winning is calculated by multiplying the probability of winning with the corresponding probabilities and adding them together. This is shown below:

E(win) = (0)(0) + (0.1)(0.01) + (0.2)(0.02) + (0.3)(0.04) + (0.4)(0.1) + (0.5)(0.15) + (0.6)(0.2) + (0.7)(0.25) + (0.8)(0.16) + (0.9)(0.04) + (1)(0) = 0.52

After playing the games and winning once but losing twice, the expected value of winning is calculated by multiplying the probability of winning with the corresponding probabilities, and adding them together. However, the probabilities are adjusted based on the new information. The new probabilities are shown below:

P(win) = (0)(0) + (0.1)(0.01)(1/3) + (0.2)(0.02)(1/3) + (0.3)(0.04)(1/3) + (0.4)(0.1)(1/3) + (0.5)(0.15)(1/3) + (0.6)(0.2)(1/3) + (0.7)(0.25)(1/3) + (0.8)(0.16)(1/3) + (0.9)(0.04)(1/3) + (1)(0)(1/3) = 0.17333

Therefore, the overall chances of winning the games before playing were 52%, and after playing and winning once but losing twice, the overall chances of winning are 17.33%. This shows that the new information has changed your belief about the probability of winning, and you now suspect that your chances of winning are lower than before.

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(i) The unit vector d that is perpendicular to both a and b is d = (1/|d|) *

[tex][6x^2 - 12x + 9, 24x - 6, -2x - 8][/tex]
[tex]= [(6x^2 - 12x + 9)/|d|, (24x - 6)/|d|, (-2x - 8)/|d|][/tex]

2) Value of [tex]X[/tex]

[tex]Xd|d × c|/dx = (8032x^3 - 21384x^2 + 63976x - 22470)/√(2008x^4 - 7128x^3 + 31988x^2 - 22470x + 9848) = 0[/tex]

It can be found by taking the cross product of a and b, and then dividing by the magnitude of the resulting vector. The cross product of a and b is given by:

[tex]d = a × b = [(3)(3) - (6x)(2-x), (6x)(4) - (2)(3), (2)(2-x) - (3)(4)]= [9 - 12x + 6x^2, 24x - 6, 4 - 2x - 12]= [6x^2 - 12x + 9, 24x - 6, -2x - 8][/tex]

The magnitude of d is given by:

[tex]|d| = √((6x^2 - 12x + 9)^2 + (24x - 6)^2 + (-2x - 8)^2)= √(36x^4 - 144x^3 + 216x^2 - 144x + 81 + 576x^2 - 288x + 36 + 4x^2 + 32x + 64)= √(36x^4 - 144x^3 + 796x^2 - 400x + 181)[/tex]

The unit vector d is then given by:

[tex]d = (1/|d|) * [6x^2 - 12x + 9, 24x - 6, -2x - 8]= [(6x^2 - 12x + 9)/|d|, (24x - 6)/|d|, (-2x - 8)/|d|][/tex]

(ii) To find the value(s) of x such that d × c has the maximum length, we can take the cross product of d and c and find the magnitude of the resulting vector. The cross product of d and c is given by:

[tex]d × c = [((24x - 6)(-7) - (-2x - 8)(3)), ((-2x - 8)(-1) - (6x^2 - 12x + 9)(-7)), ((6x^2 - 12x + 9)(3) - (24x - 6)(-1))]= [-168x + 42 + 6x + 24, 2x + 8 + 42x^2 - 84x + 63, 18x^2 - 36x + 27 + 24x - 6]= [-162x + 66, 42x^2 - 82x + 71, 18x^2 - 12x + 21][/tex]

The magnitude of d × c is given by:

[tex]|d × c| = √((-162x + 66)^2 + (42x^2 - 82x + 71)^2 + (18x^2 - 12x + 21)^2)= √(26244x^2 - 21384x + 4356 + 1764x^4 - 6964x^3 + 5988x^2 - 5834x + 5041 + 324x^4 - 432x^3 + 756x^2 - 252x + 441)= √(2008x^4 - 7128x^3 + 31988x^2 - 22470x + 9848)[/tex]

To find the maximum length of d × c, we can take the derivative of |d × c| with respect to x and set it equal to 0:

[tex]d|d × c|/dx = (8032x^3 - 21384x^2 + 63976x - 22470)/√(2008x^4 - 7128x^3 + 31988x^2 - 22470x + 9848) = 0[/tex]

Solving for x gives the value(s) of x that maximize the length of d × c. This can be done using a numerical method or by finding the roots of the polynomial in the numerator.  

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Answer:

28cm

Step-by-step explanation:

[tex] \frac{44}{22} \times 14 = 28[/tex]

The value of x in the triangle given the midsegment points and sections is 1.35 units

The mid-segment of a triangle (also called a midline) is a segment joining the midpoints of two sides of a triangle.

The midsegments of triangle UWY are VR, VZ, ZR

To find the value of x, we use a theorem called the mid segment theorem which states that:

"The mid-segment of a triangle, which joins the midpoints of two sides of a triangle, is parallel to the third side of the triangle and half the length of that third side of the triangle."

The third side of triangle UWY is WY and it measures 2.7.

Therefore, x will be 2.7 divided by 2 2.7/2 which will give us the value 1.35 i.e. x = 1.35

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The answer is f(-x) = x^4 + 6x + 2 and the function is neither even nor odd.

To find f(-x), we simply substitute -x for x in the original function:

f(-x) = (-x)^4 - 6(-x) + 2 = x^4 + 6x + 2

Now, to determine if f is even, odd, or neither, we compare f(x) and f(-x). If f(x) = f(-x), then the function is even. If f(x) = -f(-x), then the function is odd. If neither of these conditions are met, then the function is neither even nor odd.

In this case, f(x) = x^4 - 6x + 2 and f(-x) = x^4 + 6x + 2. These are not equal, so the function is not even. However, if we multiply f(-x) by -1, we get:

-f(-x) = -x^4 - 6x - 2

This is also not equal to f(x), so the function is not odd either. Therefore, the function is neither even nor odd.

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