How do you find the area of a rectangle? the rectangle is on a graph and it is slanted. It gives the coordinates to every corner.

In question 8, we have defined a checkerboard matrix, and we need to answer three parts. In 8.1, we will write out the 4x4 checkerboard matrix. In 8.2, we will find the basis for the null space of the matrix and determine the nullity and rank of the matrix. In 8.3, we will discuss the rank and nullity of a 17x17 checkerboard matrix.

8.1) The 4x4 checkerboard matrix will have alternating 1s and 0s based on the pattern defined by the sum of the row and column indices. The matrix will look as follows:

A =   [1, 0, 1, 0],

       [0, 1, 0, 1],

       [1, 0, 1, 0],

       [0, 1, 0, 1]]

8.2) To find the basis for the null space of matrix A, we need to find the vectors that satisfy the equation Ax = 0, where x is a vector. The nullspace is the set of all solutions to this equation. In this case, we can observe that any vector of the form [x, -x, x, -x] will be in the null space. Therefore, the basis for the null space will be a single vector, such as [1, -1, 1, -1]. The nullity of A, which is the dimension of the null space, will be 1. The rank of A can be determined by subtracting the nullity from the number of columns, so the rank will be 4 - 1 = 3.

8.3) The rank and nullity of the 17x17 checkerboard matrix will follow a similar pattern. The matrix will have alternating 1s and 0s based on the pattern defined by the sum of the row and column indices. Since the matrix is square, we can expect that the rank and nullity will have the same value. In this case, the rank and nullity of the 17x17 checkerboard matrix will both be 17/2 = 8.5. However, since rank and nullity must be integers, the rank, and nullity will be 8, with an equal number of linearly independent rows and zero rows.

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The portfolio beta of the share in which $900 is invested is 1.4

Given: Amount invested in share with a portfolio beta of 1.4 = $900.

Amount invested in share with a portfolio beta of 1.4 = $2100Total amount invested = $900 + $2100 = $3000We know that,Weighted average of portfolio beta = ∑wᵢβᵢ / ∑wᵢwhere, w = weight or amount invested and β = portfolio beta.,

Putting the values, we get,1.4 = 900/3000 * x + 2100/3000 * 1.4where x is the portfolio beta of the $900 invested share.Simplifying the equation, we get,1.4 = 0.3x + 0.98.

Multiplying by 10 on both sides, we get,14 = 3x + 9.8Solving for x, we get,x = (14 - 9.8)/3= 1.4.

Therefore, the portfolio beta of the share in which $900 is invested is 1.4. To get this result, we have calculated the weighted average of the portfolio beta using the formula:

Weighted average of portfolio beta = ∑wᵢβᵢ / ∑wᵢwhere, w = weight or amount invested and β = portfolio beta. We have also shown the steps of simplifying the equation and solving for x.

Thus, the portfolio beta of the share in which $900 is invested is 1.4.

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Option D is the correct answer

y = 3.5 sine (2 pi x) + 19)

The correct answer to the problem is y = 3.5 sin ( ( 2 pi x ) + 19 ).

We can quickly determine from the table that the mean position is at 19 cm from the ceiling as it is at 19 cm from the ceiling when the time is 0 sec, and the Amplitude is 3.5 as it is the maximum displacement from the mean position after T/4 second is 3.5 cm.

Now, we have Amplitude as 3.5 and the initial position at 19.

Now, we know that ω = 2π / T

But T is 1 sec in our case as the particle is taking 1 second to complete 1 oscillation,

So ω will become 2π.

so our equation will become after putting the values of Amplitude and initial position and ω as 2π ,

x = 3.5 sin ( 2π t + 19 )

but in question, they have denoted displacement as ' y ' and time as ' x '

So our final equation will become

y = 3.5 sin ( 2π x + 19 )

Hence, our final solution to the question is that the particle will perform Simple Harmonic Motion, and the equation of that will be

y = 3.5 sin ( 2 pi x + 19 )

where y is denoted as displacement and x is denoted as time.

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Step-by-step explanation:

To solve this problem, we need to find the scale factor that will allow us to enlarge the 12" x 9" painting to fit the 24' x 16' wall.

First, we need to convert all the units to the same system. Let's convert the painting size to feet:

12 inches = 1 foot (since there are 12 inches in a foot)

9 inches = 0.75 feet (since 9/12 = 0.75)

So the size of the painting in feet is 1 foot by 0.75 feet.

Next, we can find the scale factor by dividing the size of the wall by the size of the painting:

Scale factor = (24 feet) / (1 foot) = 24

Scale factor = (16 feet) / (0.75 feet) = 21.33 (rounded to two decimal places)

We use the smaller of the two scale factors, which is 21.33, to ensure that the painting will fit within the dimensions of the wall.

Finally, we can find the size of the enlarged painting by multiplying the original size by the scale factor:

Width of enlarged painting = 1 foot x 21.33 = 21.33 feet

Height of enlarged painting = 0.75 feet x 21.33 = 15.99 feet

Therefore, the largest possible complete design that can be painted on the 24' x 16' wall is approximately 21.33 feet by 15.99 feet, using a scale factor of 21.33.

Answer:

the largest possible complete design that can be painted on the 24' x 16' wall is 21' x 15.75'

Step-by-step explanation:

Here, the double prime (double commas) ('') mean inches and the single prime(single comma) (') means foot.

So, the painting is (12" )(9") so it is 12 inches by 9 inches.

While the wall is (24')(16') so it is 24 feet by 16 feet.

We have to find the largest possible complete design that can be painted on the wall

Now, since 12 inches = 1 foot

And for the design to be complete, the design must fit on the wall

now, for every 12 inches we add to the height (the first part i.e 24)

We add 9 inches to the width (the 2nd part i.e. 16)

starting from one side,

we have,

(12 inch)(9 inch) = (1 feet)(9/12 feet)

(12 inch)x(9 inch) = (1 feet)x(3/4 feet)  (i)

where we get the 2nd term, 9/12 as follows,

Since,

[tex]12 \ inches = 1 foot\\so, \\1 \ inch = (1/12) feet\\and,\\9 \ inches = 9/12 \ feet[/tex]

Now, 9/12 = 3/4

so, 9 inches = 3/4 feet

We have obtained the required ratio, we just now check how far this ratio can go until we exceed the limit of the wall, 24 feet by 16 feet,

so, for example,

Now, this means that when we increase the height by 12 inches = 1 foot,

we also have to increase the width by 3/4 feet = 9 inches

so, if we muliiply the height by 2, we also multiply the width by 2 to get,

(24 inch)x(18 inch) = (2 ft) x (3/2 ft)

now, (2 ft) x (3/2 ft) is smaller than (24 ft) x (16 ft),

Similarly, If we multiply the height by 24, we also have to multiply the width by 24, in which case we get,

24 ft by 24(3/4)ft

(24 ft) x (18 ft) which is greater than the allowed, (24 ft) x (16 ft) (i.e. 18 > 16)so this design cannot fit on the wall

(24 ft) x (18 ft) cannot be painted on the wall since the wall is smaller,

Trying 23, we get,

(23 ft) x (23(3/4) ft) = (23 ft) x (17.25 ft) which is still greater

so we try 22,

(22 ft) x (22(3/4) ft) = (22 ft) x (16.5 ft) which is Still greater

We try 21 to get,

(21 ft) x (21(3/4) ft) = (22 ft) x (15.75 ft) Which is smaller than the wall

So, the largest possible complete design that can be painted on a 24' x 16' wall is 22' x 15.75'

Doing this in another way,

1 inch = 1/12 feet

9 inches = 3/4 feet

We have to find the greatest possible ratio between the height and width of the painting that can be fitted on the wall,

the ratio is height/width = 12 inches/9 inches = 1 ft/(3/4 ft)

and this has to be the greatest ratio less than 24 ft/(16 ft)

If we multiply and divide the ratio by 21, we get,

[tex]21 \ ft/((21)(3/4\ ft))[/tex]

which gives,

21 ft/ 15.75 ft

or in the other form, the painting is 21' x 15.75' < 24' x 16' (both 21' < 24' and 15,75' < 16')

But if we multiply by 22,

we get

22 ft /(22)(3/4) ft  

in the other form, the ratio is 22' x 16.5'

but since 16.5' is greater than 16',

the 22' x 16.5' design cannot be painted on the wall ( the wall has too little width 16' instead of 16.5')

So, the largest possible complete design that can be painted on the 24' x 16' wall is 21' x 15.75'

Answer:

ok

Step-by-step explanation:

Answer:

its the second one -1/2

======================================================

Explanation:

There are 3 colors of sweaters {red, green, purple} and 2 colors of skirts {tan, black}

So far there are 3*2 = 6 different outfit combinations. Imagine a table with 3 rows representing the sweater colors and 2 columns representing the skirt colors. There would be 6 cells in the table representing each possible combination. One cell would have (red sweater, tan skirt) for instance.

For each of those 6 combinations, we also have 2 shoe colors. So overall we have 6*2 = 12 outfit combinations

The tree diagram is shown below. Note how there are 3*2*2 = 12 different paths to follow.

Answer:

The answer is

Step-by-step explanation:

The midpoint M of two endpoints of a line segment can be found by using the formula

[tex]M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )\\[/tex]

From the question the points are

A(-2, 3), B(5,-1)

The midpoint is

[tex]M = ( \frac{ - 2 + 5}{2} \: , \: \frac{3 - 1}{2} ) \\ = ( \frac{3}{2} \: , \: \frac{2}{2} )[/tex]

We have the final answer as

[tex]( \frac{3}{2} \: , \: 1) \\ [/tex]

Hope this helps you

Tiffany needs to score at least 92 on the last quiz to achieve an average of at least 85.The correct answer is option 3: x ≥ 92.

To find the scores on the last quiz that will allow Tiffany to get an average of at least 85, we need to determine the minimum score she must achieve on the last quiz.

Let's calculate Tiffany's average after the first four quizzes:

(72 + 87 + 83 + 91) / 4 = 333 / 4 = 83.25

To obtain an average of at least 85, Tiffany needs the sum of her scores on all five quizzes to be at least (85 * 5) = 425.

Let's assign the variable "x" to the score on the last quiz.

Therefore, the inequality to represent the minimum score Tiffany needs on the last quiz is:

x + 72 + 87 + 83 + 91 ≥ 425

Simplifying the inequality:

x + 333 ≥ 425

Subtracting 333 from both sides:

x ≥ 425 - 333

x ≥ 92

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Given parameters:

Distance takes into consideration the path covered by a body in motion.

Here we need to carefully analyse the problem sentence by sentence to arrive at the solution, the total height of jump.

This is the reference plane and it is the water surface. Area below the reference have a negative sign to show that they are below the surface. Those above are positive.

On jumping to the surface, Ralph covered 35ft

jumping out it gained 27ft, total height is 35ft + 27ft = 62ft

   Now, returning to the water, it covred another 27ft;

    Distance covered now is 62ft + 27ft  = 89ft

Distance of dive = 18ft,

  Total distance now is (89 + 18)ft  = 107ft

The total vertical distance the Ralph traveled is 107ft.

Answer:

  56 cm

Step-by-step explanation:

Here's what the question is asking for.

  150 ≤ 1.25h ≤ 220

  120 ≤ h ≤ 176 . . . . the range of heights that can use the skis

  176 -120 = 56 cm . . . . the difference in heights

__

Here's an easier way to calculate it.

  220/1.25 -150/1.25 = (220 -150)/1.25 = 70/1.25 = 56

  The height difference is 56 cm.

_____

We judge one subtraction and one division to be easier and less error-prone than two divisions and a subtraction.

Answer:

x = 4/3 + 2y/3

Step-by-step explanation:

Step 1: Write equation

6x - 4y = 8

Step 2: Solve for x

Roxanne could save only $1 per Month by switching to Jasmine Bank.

The given table shows the checking account features and fees for Jasmine Bank and East Medina Bank. Here are the features and fees for both banks:

Jasmine Bank East Medina Bank Checking account services $10 per month $6 per month transactions (bank ATM) No ATM fees $1 per transaction ATM transactions (nonbank ATM) No ATM fees $3 per transaction online banking $4 per month Free online banking with a linked savings account

Otherwise, $5 per month Roxanne has a checking account at East Medina Bank. She uses online banking to pay bills and send birthday money to her nieces and nephews.

Roxanne uses a bank ATM once a month and a nonbank ATM near her apartment 2 times each month .

Roxanne's monthly fees at East Medina Bank :

East Medina Bank checking account service: $6 per month Nonbank ATM transaction fees:

$3 x 2 = $6 per month Online banking fee: Free Bank ATM transaction fee: $1 x 1 = $1 per month total monthly fees: $13 per month Roxanne's monthly fees at Jasmine Bank:

Jasmine Bank checking account service:

$10 per month on bank ATM transaction fees:

$0Online banking fee: $4 per monthBank ATM transaction fee:

$0Total monthly fees: $14 per monthRoxanne would save $1 per month by switching to East Medina Bank.

This is because she would be paying $14 per month at Jasmine Bank and $13 per month at East Medina Bank. Therefore, Roxanne could save only $1 per month by switching to Jasmine Bank.

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We have to find the time required for an object to cool from 300°F to 260°F by evaluating the following where t is time in minutes:t = 10/ln 2 ∫260300 (1/T - 100) dT.

To find the time t, let's first evaluate the integral using integration by substitution: Let u = T, then du/dT = 1 dT= du

Now we have,[tex]t = 10/ln 2 ∫260300 (1/T - 100) dT= 10/ln 2 ∫260300 (1/u - 100) du= 10/ln 2 ln|u| - 100u |_260^300= 10/ln 2 [ ln|300| - ln|260| - 100(300) + 100(260) ]= 10/ln 2 [ 5.7038 -  3000 + 2600 ]= 10/ln 2 ( - 94.6913 ) ≈ 133.4775[/tex]

minutes.

Therefore, the time required for the object to cool from 300°F to 260°F is approximately 133.4775 minutes.

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Answer:

start at positive 3 and the go left one then up two

Step-by-step explanation:

I don't have a picture of the graph, sorry

Answer:

your right it's d

Step-by-step explanation:

it's d it's d it's d it's d

Answer:

the domain is real number

Answer:

=42+115x

10x

Step-by-step explanation:

3(7/5x+ 4) – 2( 3/2- 5/4)

=21/5x+12-2(6/4-5/4)

=21/5x+12-2×1/4

=21/5x+12-1/2

=21/5x+24/2-1/2

=21/5x+23/2

=42/10x+115x/10x

=42+115x

10x

Answer:

1 to 5

Step-by-step explanation:

Answer:

I think it's 3

Step-by-step explanation:

-36+24+15=3

Answer:

0.1

Step-by-step explanation:

Answer:

1/5 divided by 2 = z

=> (1/5)/2 = z

=> 0.2 / 2 =z

=> 0.1 = z

If my answer helped, kindly mark me as the brainliest!!

Thank You!!

Answer:

3/8

I just yeeted it into my calculator

The value of ∫ f(x) dx over the interval [3, 5] is 7. none of the option is correct.

To find the value of ∫ f(x) dx, we need to evaluate the integral of the function f(x) over a given interval. In this case, the function f(x) is defined piecewise:

f(x) = 2 for x < 3

f(x) = x - 1 for x ≥ 3

Let's find the integral of f(x) over a specific interval. We'll consider the interval [3, 5] for this example.

∫ f(x) dx = ∫ [2 for x < 3] + ∫ [x - 1 for x ≥ 3]

Since the lower limit of integration is 3, we'll consider the second part of the piecewise function for the interval [3, 5]:

∫ [x - 1 for x ≥ 3] = ∫ (x - 1) dx from 3 to 5

Now, let's evaluate this integral:

∫ (x - 1) dx = ([tex]1/2)x^2 - x[/tex] evaluated from 3 to 5

= [[tex](1/2)(5)^2 - 5] - [(1/2)(3)^2 - 3[/tex]]

= (1/2)(25 - 5) - (1/2)(9 - 3)

= (1/2)(20) - (1/2)(6)

= 10 - 3

= 7

Therefore, the value of ∫ f(x) dx over the interval [3, 5] is 7.

Since the given options for the answer are not specific to any interval, we cannot determine the exact value of the integral without knowing the interval. If there is a specific interval provided, we can evaluate the integral accordingly.

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Answer:

Rotation of 90 degrees counterclockwise about the origin

Step-by-step explanation:

well counterclockwise means you rotate the figure to the left and this figure is rotated to the left

Answer:

y=2/3x-2

Step-by-step explanation:

Slope intercept is y=m(x)+b

m is the slope, so substitute

b is the y intercept so also substitute

Hope this helps :-)

Answer:

< 6 cm to > 26 cm i believe

Step-by-step explanation:

Since we have the equation that models the movement of the ball, we simply need to replace the corresponding values in the equation.

Althought there seems to be an X missing, so it should be

y=-0.03*x^2+1.6x  

like this, the graph should be as the picture shows.

We can immediately see in the picture that the football does go over the goal post, let's see how much, by replacing the values:

y=-0.03*40^2+1.6*40=-0.03*1600+64=16

since the pole is 10 ft high, the ball is 6 above the post

Answer:

y=4x

Step-by-step explanation:

Plug the numbers in:

4*0=0--> (0,0)

4*1=4-->(1,4)

4*2=8-->(2,8)

4*3=12-->(3,12)