Suppose the longest side in a right triangle has the measure 4,6. If the acute angles have the measure of 30° and 60°, which is the exact measure of the longer leg?​

The linear system X₁ + 2X₂ = 3.21 and 4.02X₁ + IL || -1 = -1 using Cramer's rule, we need to find the values of X₁ and X₂.

To apply Cramer's rule, we first need to calculate the determinant of the coefficient matrix and the determinants of the matrices obtained by replacing each column of the coefficient matrix with the constant terms.

The coefficient matrix is:

| 1   2 |

| 4.02  IL || |

The determinant of the coefficient matrix, denoted as D, is given by:

D = (1 * IL ||) - (2 * 4.02)

  = IL || - 8.04

The matrix obtained by replacing the first column with the constant terms is:

| 3.21   2 |

| -1     IL || |

The determinant of this matrix, denoted as D₁, is given by:

D₁ = (3.21 * IL ||) - (-1 * 2)

   = 3.21IL || + 2

The matrix obtained by replacing the second column with the constant terms is:

| 1   3.21 |

| 4.02  -1 |

The determinant of this matrix, denoted as D₂, is given by:

D₂ = (1 * -1) - (4.02 * 3.21)

   = -1 - 12.9042

   = -13.9042

Now, we can find the values of X₁ and X₂ using the formulas:

X₁ = D₁ / D

X₂ = D₂ / D

Substituting the values we calculated earlier, we have:

X₁ = (3.21IL || + 2) / (IL || - 8.04)

X₂ = (-13.9042) / (IL || - 8.04)

This gives us the solution to the linear system.

Solve the linear system X 1 X1 + 2x2 3.21 + 4.02 IL || -1 -1 = via Cramer's rule if possible.

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Answer:

852 inches square

Step-by-step explanation:

2×(16×15 + 16×6 + 15×6)

Answer:

652 in²

Step-by-step explanation:

The formula is 2(wl+hl+hw)

h is height

w is width

l is length

Use PEMDAS/BIDMAS/BODMAS (do the parentheses then multiply it)

326*2 = 652

add your units

652 in^2

The total money made by each court would be as follows:

Centre Court: £838,824, No 1 Court: £514,305

No 2 Court: £164,000, No 3 Court: £82,000

To calculate the amount of money made by each court if all seats were sold, we need to multiply the number of seats by the corresponding ticket price for each court. Here are the calculations for each court:

Centre Court:

Number of seats: 14,979

Ticket price: £56

Total money made: 14,979 seats ×£56/seat = £838,824

No 1 Court:

Number of seats: 11,429

Ticket price: £45

Total money made: 11,429 seats ×£45/seat = £514,305

No 2 Court:

Number of seats: 4,000

Ticket price: £41

Total money made: 4,000 seats ×£41/seat = £164,000

No 3 Court:

Number of seats: 2,000

Ticket price: £41

Total money made: 2,000 seats × £41/seat = £82,000

Therefore, if all seats were sold, the total money made by each court would be as follows:

Centre Court: £838,824

No 1 Court: £514,305

No 2 Court: £164,000

No 3 Court: £82,000

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Answer:

[tex]-4a + 12[/tex]

Step-by-step explanation:

Answer:

y=6x-2

Step-by-step explanation:

slope=6

y-intercept=-2

y=6x-2

A. The volume of the solid formed by rotating the region bounded above by the parabola y = 3x-x² and y = 0 around the vertical line x = -1 is approximately 9.74 cubic units and B. The inverse function is found to be ln(x/(1 - x)).

To find the volume of the solid, we can use the method of cylindrical shells. The integral for the volume is given by V = ∫[a,b] 2πxf(x) dx, where f(x) represents the height of the shell at each x-coordinate.

First, we need to find the bounds of integration. The parabola y = 3x - x² intersects the x-axis at x = 0 and x = 3. Therefore, the bounds of integration are [0, 3].

Next, we need to express the height of the shell, f(x), in terms of x.

Evaluating the integral, we get V = ∫[0,3] 2π(x + 1)(3x - x²) dx. After integrating and simplifying, the volume is approximately 9.74 cubic units.

(B) To find the inverse of the function f(x), we swap the roles of x and y and solve for y. So, we start with y = eˣ/(1 - eˣ).

Step 1: Swap x and y: x = eʸ/(1 - eʸ).

Step 2: Solve for y: x(1 - eʸ) = eʸ.

Step 3: Expand and isolate eʸ: x - xeʸ = eʸ.

Step 4: Factor out eʸ: eʸ(x - 1) = x.

Step 5: Divide both sides by (x - 1): eʸ = x/(x - 1).

Step 6: Take the natural logarithm of both sides: y = ln(x/(x - 1)). Thus, the inverse function is g(x) = ln(x/(x - 1)), where x ∈ (0, 1).

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Complete question - A. The region bounded above by the parabola y = 3x-x2² and y = 0 is rotated around a vertical line x=-1 forming a solid, find its volume.

B. Given the following function which is one to one f(x) = eˣ/1-eˣ Find its inverse.

Answer: C

Step-by-step explanation:

Answer:

The population of Bear in 2050 is 4750000

Step-by-step explanation:

A) The exponential growth equation for bear is as follows -

dN/dT = rmax * N

Where dN/dT = change in population

rmax is the maximum rate of change

N = Base population

B) Here the per capita rate of increase (r) will always be a positive value irrespective of the and hence we will assume this population to be growing exponentially.

C) dN/dT = rmax * N

D) dN / 5 = 2.5 * 380,000

dN = 5*2.5 * 380000

= 4750000

Answer:

A is true and f is true

Step-by-step explanation:

Answer:

a, d, e, and g

Step-by-step explanation:

if you multiply two negatives, you get a positive

Let's start solving the given problem. Suppose that an urn contains 3 different types of balls: red, green, and blue. Let pi denote the proportion of red balls, p2 denote the proportion of green balls, and p3 denote the proportion of blue balls.

Here Pi = 1.

Suppose also that 100 balls are selected with replacement, and there are exactly 38 red, 29 green and 33 blue.

We need to find the M.L.E. p; of p1, i = 1, 2, 3.

The probability of obtaining red ball from the urn = pi. The probability of obtaining green ball from the urn = p2. The probability of obtaining blue ball from the urn = p3

Given that, 100 balls are selected with replacement.

Let's calculate the probability of getting 38 red, 29 green, and 33 blue balls from the urn,

P(38 Red and 29 Green and 33 Blue) = P(Red)38 x P(Green)29 x P(Blue)33 = p₁³⁸ x p₂²⁹ x p₃³³

Therefore, the likelihood of obtaining the 38 red, 29 green, and 33 blue balls is L(p1,p2,p3) = p₁³⁸ x p₂²⁹ x p₃³³

Since, L(p1,p2,p3) is a continuous function, so we have to find the critical points of the function to obtain the minimum value of p₁. Let's take natural logarithm on both sides of the function, we get ln

L(p1,p2,p3) = 38 ln p₁ + 29 ln p₂ + 33 ln p₃.

So, taking partial differentiation with respect to p1, p2 and p3 and equating them to 0. We get the following equations,∂ ln L / ∂p1 = 38/p1 = 0∂ ln L / ∂p2 = 29/p2 = 0∂ ln L / ∂p3 = 33/p3 = 0On

solving the above three equations, we get p1 = 38/100 = 0.38p2 = 29/100 = 0.29p3 = 33/100 = 0.33

Therefore, P₁= 0.38, S= 0.29, P3 = 0.33. Hence, the required solution is P₁= 0.38, S= 0.29, P3 = 0.33.

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Answer:

75.39 in^2 (round to the nearest hundreds)

Step-by-step explanation:

I think that we have to find the lateral area

circumference = 2 x radius x pi = 2 x 4 x pi = 25,13 in^2 (round to the nearest hundreds)

lateral surface = (circumference x slant height)/2 = (25,13 x 6)/2 = 75,39 in^2 (round to the nearest hundreds)

Answer:

-x² + 6x - 17

Step-by-step explanation:

First, expand (x-3)² using FOIL

(x - 3)(x - 3)

= x² - 6x + 9

Distribute the negative sign to the expression:

-(x² - 6x + 9)

-x² + 6x - 9

Now, subtract 8 from this

-x² + 6x - 9

= -x² + 6x - 17

So, the equation in standard form is -x² + 6x - 17

The answer is.. x^2+6x-17

Answer:

216 ft³

Step-by-step explanation:

h*w*l=v

[tex]12 \times 6 \times 3 = 216[/tex]

Answer:

y=45

Step-by-step explanation:

Let's solve your equation step-by-step.

10 y = 2 /9

Step 1: Cross-multiply.

10 y = 2 /9

(10)*(9)=2*y

90=2y

Step 2: Flip the equation.

2y=90

Step 3: Divide both sides by 2.

2y /2 = 90 /2

y=45

brainliest please?

Answer:

y = 45

Step-by-step explanation:

10/y=2/9

10 = y * 2/9  

10 = 2/9y

10 * 9 = 2/9y * 9

90 = 2y

90/2 = 2y/2

y = 45

ps: * means multiply

Im new here :) but hey you got these qs try your best okie

I hope and im glad to help

Answer:

2/5 is the simplest form.

Step-by-step explanation:

9/10 - 5/10 = 4/10 (9 - 5 = 4) 4/10 simplified is 2/5 (divide both 4 and 10 by 2 and you get 2/5).

Hope that helps!

The value of x =-3 and y=1 in the system of linear equation.

Given equations

-2x+3y+z=7

-4x-y-2z=15

x+2y+3z=-7

Using cramer's rule to find x and y

First we make matrix of coefficient of x,y and z and then find the determinant

[tex]A = \left[\begin{array}{ccc}-2&3&1\\-4&-1&-2\\1&2&3\end{array}\right][/tex]

Now we find determinant of A

|A|=-2(-3+4)-3(-12+2)+1(-8+1)

|A|=21

[tex]A_x=\left[\begin{array}{ccc}7&15&-7\\-4&-1&-2\\1&2&3\end{array}\right][/tex]

Determinant of Ax

|Ax|=7(-3+4)-3(45-14)+1(30-7)

|Ax|=-63

[tex]A_y=\left[\begin{array}{ccc}7&15&-7\\-4&-1&-2\\1&2&3\end{array}\right][/tex]

Determinant of Ay

|Ay|=-2(45-14)-7(-12+2)+1(28-15)

|Ay|=21

[tex]A_z=\left[\begin{array}{ccc}-2&3&1\\-4&-1&-2\\7&15&-7\end{array}\right][/tex]

Determinant of Az

|Az|=-2(7-30)-3(28-15)+7(-8+1)

|Az|=-42

Now we find for x, y and z

[tex]x=\frac{|A_x|}{|A|}[/tex]

= -63/21 = -3

[tex]y = \frac{|A_y|}{|A|}[/tex]

= 21/21 = 1

[tex]z = \frac{|A_z|}{|A|}[/tex]

= -42/21

= 2

Thus, the value of x =-3 and y=1 in the system of linear equation.

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Given question is incomplete, the complete question is below

using cramer’s rule, what are the values of x and y in the solution to the system of linear equations below?

Answer:

dogs - 13

cats - 39

Step-by-step explanation:

Let the number of dogs Ma Bernier have be represented with d

She has 3 times as many cats as dogs, the number of cats she has :

cats = 3d

The sum of the cats and dogs is 52

d + 3d = 52

4d = 52

divide both sides of the equation by 4

d = 13

She has 13 dogs

Cats = 3d

= 3 x 13 = 39

Answer:

BXC=70 degrees

Step-by-step explanation:

XBC = 55

corresponding angles are equal

XCB=55

isosceles base angles are equal

BXC=70

angles in a triangle add up to 180 degrees

Answer:

[tex]\frac{80-19.25}{6.75} = x[/tex]

Step-by-step explanation:

Subtract $19.25 from the Amount Used for Payment ($80) to get the amount spent, then divide the amount of each sandwich to get the amount of sandwiches bought.

circumference is around the circle the border of the circle the area of the circle is the space in the circle

Answer:

30 times

Step-by-step explanation:

1. find the possibility of the spinner landing on each section

1 / 5 = 0.2

2. multiply # of spins by the possibility

150 * 0.2 = 30 times

Y Let f:R → R be defined by f(3) = Then x2 +1' a is (b) f is not a measurable function.

To determine if f is a measurable function, we need to check if the preimage of any measurable set in the codomain (R) is a measurable set in the domain (R).

In this case, the function f(3) = x^2 + 1 is defined only at x = 3. Since the domain R is continuous and f is only defined at a single point, the preimage of any set in the codomain will either be an empty set or a singleton set containing only the point x = 3.

For example, consider the set [f > 3] in the codomain R. The preimage of [f > 3] under f would be the set of all x in the domain R such that f(x) > 3. However, since f is only defined at x = 3, the preimage would be the singleton set {3}.  Since {3} is not a measurable set in the domain R, f is not a measurable function.

Therefore , the correct option is (B) f is not a measurable function.

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Answer:

D

Step-by-step explanation:

A possible set of scores for the students is: 4, 4, 6, 6, 6

We are given that five students took the quiz. If the lowest score is 4 and the highest score is 6, we can say that the set of values ​​can be expressed as:

4, x, y, z, 6

Here we can see that the mode is 6 and the mean is 5.2. Therefore, at least one other student of hers has scored her 6, which could result in:

4, x, y, 6, 6

Therefore:

(4 + x + y + 6 + 6)/5 = 5.2

16+x+y=26

x + y = 10

So the other two numbers are probably 6 and 4, because 6 is the mode, so they can't both be 5.

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i) The cost function is x = 100,000 + 7n while the revenue function is y = 15n.

ii) The minimum number of customers for the business to break even is 12,500.

iii) The amount that Bob owes the bank after 3 years at 3% p.a. interest payable monthly, but without any repayment, is $109,272.70.

A function is a mathematical equation showing the equality of two or more algebraic expressions.

a) Renovation and appliances costs = $100,000

Average running cost per customer = $7

Selling price per customer = $15

i) Let the number of customers = n

Cost function, x = 100,000 + 7n

Revenue function, y = 15n

ii) For the business to break even, y must be equal to x:

15n = 100,000 + 7n

8n = 100,000

n = 12,500

iii) Bank loan = $100,000

Interest rate = 3% p.a.

Interest payment = monthly

Amount after 3 years without any repayment = $100,000 x 1.03^3

= $109,272.70 ($100,000 x 1.092727)

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Answer:

Factors of 22: 1, 2, 11, and 22.

Prime Factorization of 22: 22 = 2 × 11.Step-by-step explanation:

Answer:

55 grams

Step-by-step explanation:

11×5=55 grams

if its the same amount everyday then 55

(it made me type more)

Answer:55

Step-by-step explanation: 11x5

Answer:

A pyramid

Step-by-step explanation: