Yea imma need help asap. construct the triangle abc, with ab = 7cm, bc = 8cm, and ac = 6cm. measure and state the size of angle acb. i don't understand how you measure it.

The binary combination of the decimal 23 in a 6-bit one's complement system is 010000.

In a one's complement system, negative numbers are represented by taking the one's complement (flipping all the bits) of the corresponding positive number and adding a sign bit at the leftmost position. For example, in a 6-bit one's complement system, the positive number 23 would be represented as 010111 (since 23 in binary is 10111), and the negative number -23 would be represented as 101000 (which is the one's complement of 010111 with a sign bit of 1 at the leftmost position).

However, since we are asked to find the binary combination of the decimal 23 (which is a positive number), we can simply convert 23 to binary and pad it with zeros to get a 6-bit representation. The binary representation of 23 is 10111, so we can add two zeros at the left to get 010111. Therefore, the binary combination of the decimal 23 in a 6-bit one's complement system is 010000.

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can you add the question?

Add a picture of the question.

The given property “If AB=CD then CD=AB” is known as the symmetric property. Symmetric property is a type of equivalence relation in mathematics that states that if the relation between two elements is in the form of "if A is related to B, then B is related to A," then this type of relation is symmetric.

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Answer: $28-$33

Step-by-step explanation: Call the cost per pair x. She buys the first pair full price, so x, then 2 dollars off, so x-2, and 2 dollars off, so x-2, adding them up you get 3x-4= total money spent. Sinze this ranges from 80-95 solve equations and you get 28 and 33 respectively.

The graph starts at (1, 0), reaches its maximum value at (0, π/2), and then decreases towards (−1, π).

The function y = cos⁻¹(x) represents the inverse cosine function. Here's a rough sketch of the graph:

        ^

       |        /

       |       /

       |      /

       |    /

       |  /

--------|------------------>

       | /

       |/

So, the range of the inverse cosine function is limited to [0, π], and the domain is [-1, 1].

The graph starts at (1, 0), reaches its maximum value at (0, π/2), and then decreases towards (−1, π).

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Answer:

1/x = 1/4 + 1/3

Step-by-step explanation:

In 4 hours Bethany did the whole fraction 1 of the house.

In 1 hour he would do 1/4 of it.

In 3 hours Colin did the whole fraction 1 of the house.

In 1 hour he would do 1/3 of it.

In 1 hour they would both do (1/4 + 1/3)

If it takes both of them x hours to finish 1 whole fraction of the house.

In 1 hour they will both do 1/x

That means that:

1/x = 1/4 + 1/3

That is the equation. x can be solved for.

Answer:

Not directly proportional

Oh and can you give me brainliest

according to question the Laplace transform of f(t) is:

F(s) = 16/s^2 + 9/(s-1), defined for s > 1.

The Laplace transform of f(t) is defined by:

F(s) = L{f(t)} = ∫[0,∞) e^(-st) f(t) dt

Applying this definition to the given function:

F(s) = L{16t + 9e^t} = ∫[0,∞) e^(-st) (16t + 9e^t) dt

We can separate this integral into two parts and evaluate each part separately:

F(s) = ∫[0,∞) e^(-st) 16t dt + ∫[0,∞) e^(-st) 9e^t dt

To evaluate the first integral, we can use integration by parts:

u = 16t, dv/dt = e^(-st) -> du/dt = 16, v = -e^(-st)/s

∫[0,∞) e^(-st) 16t dt = [-16t e^(-st)/s] [0,∞) + ∫[0,∞) 16e^(-st)/s dt

= [16/s] ∫[0,∞) e^(-st) dt = [16/s] (1/s) = 16/s^2

To evaluate the second integral, we can use the fact that the Laplace transform of e^at is 1/(s - a):

∫[0,∞) e^(-st) 9e^t dt = 9 ∫[0,∞) e^(-(s-1)t) dt

= 9/(s-1)

Putting everything together, we have:

F(s) = 16/s^2 + 9/(s-1)

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Henry opens a savings account with an annual interest rate of 4.5 percent. After a year, he gets $75,000 in payment. He made a deposit into the savings account of $72,831.68.

Here are the steps on how to calculate the amount Henry invested:

Convert the annual interest rate to a monthly rate.

\(\begin{equation}4.5\% \div 12 = 0.375\%\end{equation}\)

Calculate the number of years.

\(\begin{equation}\frac{18 \text{ months}}{12 \text{ months/year}} = 1.5 \text{ years}\end{equation}\)

Use the compound interest formula to calculate the amount Henry invested.

\(\begin{equation}FV = PV * (1 + r)^t\end{equation}\)

where:

FV is the future value ($75,000)

PV is the present value (unknown)

r is the interest rate (0.375%)

t is the number of years (1.5 years)

\(\begin{equation}\$75,000 = PV \cdot (1 + 0.00375)^{1.5}\end{equation}\)

\$75,000 = PV * 1.0297

\(\begin{equation}PV = \frac{\$75,000}{1.0297}\end{equation}\)

PV = \$72,831.68

Therefore, Henry invested \$72,831.68 in the savings account.

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Answer:

A.

Step-by-step explanation:

Just find the lowest common multiple of 51 and 85.

51 = 3 * 17

85 = 5 * 17

3 * 5 * 17 = 255

The lowest common denominator for the fractions is 17.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

fraction = 8/51 and 19/ 85

Now, LCM of 51 and 85.

51 = 17 x 3

85= 17 x 5

So, the least common multiple is 17.

Hence, the lowest common denominator for the fractions is 17.

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The system has infinitely many solutions. The system is homogenous because all the equations have the same right-hand side of zero.

To solve a homogenous system, we can use the following steps:

1. Express the system in matrix form.

2. Find the determinant of the coefficient matrix.

3. If the determinant is zero, then the system has infinitely many solutions.

In this case, the coefficient matrix is:

[2 2 4]

[-4 -4 -8]

[0 -3 -3]

The determinant of this matrix is zero, so the system has infinitely many solutions.

To find one solution, we can set any of the variables to 1 and then solve for the other two variables. For example, if we set x = 1, then we get the following system of equations:

2y + 4z = 0

-4y - 8z = 0

-3y - 3z = 0

```

Solving for y and z, we get y = -2 and z = 1. Therefore, one solution to the system is (1, -2, 1).

Any other solution can be obtained by adding a multiple of this solution to the solution set.```

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The critical heat flux (CHF) is the maximum heat flux that can be transferred from a surface to a boiling liquid before the boiling process transitions from a stable regime to an unstable regime. The CHF is an important parameter in the design of heat transfer systems, as exceeding the CHF can lead to boiling crisis, which can cause severe damage to the system.

The CHF for a fluid depends on various factors such as fluid properties, surface properties, and flow conditions. One of the commonly used correlations for calculating CHF is the Kutateladze number (Ku) correlation, which is given by:

q_c = C (ρ_L^2 g Δh_f)^0.5 (σ/ρ_L)^0.1

where q_c is the critical heat flux, ρ_L is the liquid density, g is the acceleration due to gravity, Δh_f is the latent heat of vaporization, σ is the surface tension, and C is a constant that depends on the surface properties and flow conditions.

Using this correlation, we can calculate the CHF for the given fluids at 1 atm:

For mercury at 1 atm:

Density of mercury, ρ_L = 13,534 kg/m^3

Latent heat of vaporization of mercury, Δh_f = 2.66 x 10^5 J/kg

Surface tension of mercury, σ = 0.48 N/m

Acceleration due to gravity, g = 9.81 m/s^2

Using the Kutateladze number correlation with a constant value of C = 0.028, we get:

q_c = 0.028 * (13,534^2 * 9.81 * 2.66 x 10^5)^0.5 * (0.48/13,534)^0.1

q_c = 2.44 x 10^6 W/m^2

For ethanol at 1 atm:

Density of ethanol, ρ_L = 789 kg/m^3

Latent heat of vaporization of ethanol, Δh_f = 8.51 x 10^5 J/kg

Surface tension of ethanol, σ = 0.022 N/m

Acceleration due to gravity, g = 9.81 m/s^2

Using the Kutateladze number correlation with a constant value of C = 0.027, we get:

q_c = 0.027 * (789^2 * 9.81 * 8.51 x 10^5)^0.5 * (0.022/789)^0.1

q_c = 1.17 x 10^6 W/m^2

For refrigerant R-134a at 1 atm:

Density of R-134a, ρ_L = 1245 kg/m^3

Latent heat of vaporization of R-134a, Δh_f = 2.03 x 10^5 J/kg

Surface tension of R-134a, σ = 0.011 N/m

Acceleration due to gravity, g = 9.81 m/s^2

Using the Kutateladze number correlation with a constant value of C = 0.026, we get:

q_c = 0.026 * (1245^2 * 9.81 * 2.03 x 10^5)^0.5 * (0.011/1245)^0.1

q_c = 1.35 x 10^6 W/m^2

For water at 1 atm:

Density of water, ρ_L = 1000 kg/m^3

Latent heat of vaporization of water, Δh_f = 2

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The measures of x for the similar triangles are given as follows:7

11. x = 5.

12. x = 13.

13. x = 7.

14. x = 8.

For similar triangles, the equivalent side lengths are proportional, hence proportional equations are built to find the measures of x.

For item 11, the equation is given as follows:

44/55 = 48/(13x - 5)

4/5 = 48/(13x - 5)

Applying cross multiplication:

4(13x - 5) = 48 x 5

52x = 260

x = 260/52

x = 5.

For item 12, the equation is given as follows:

30/(5x - 11) = 65/117

65(5x - 11) = 30 x 117

325x = 4225

x = 4225/325

x = 13.

For item 13, the equation is given as follows:

65/169 = (7x + 1)/130

169(7x + 1) = 130 x 65

1183x = 8281

x = 8281/1183

x = 7.

For item 14, the equation is given as follows:

21/35 = (4x - 2)/50

3/5 = (4x - 2)/50

20x - 10 = 150

20x = 160

x = 160/20

x = 8.

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True. When computing a t statistic, it is necessary to use the sample variance (or standard deviation) to estimate the standard error for the sample mean.

The standard error represents the standard deviation of the sampling distribution of the sample mean. By using the sample variance (or standard deviation), we can estimate the variability of the sample mean from the population mean.

The formula to calculate the standard error of the sample mean is: standard deviation / √(sample size). The sample variance is used to estimate the population variance, and the sample standard deviation is the square root of the sample variance.

The t statistic is computed by dividing the difference between the sample mean and the population mean by the estimated standard error of the sample mean. This t statistic is used in hypothesis testing or constructing confidence intervals when the population parameters are unknown.

Therefore, the sample variance (or standard deviation) is crucial in calculating the estimated standard error, which in turn is necessary for computing the t statistic and making statistical inferences about the sample mean.

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Question 10

Draw a 30-60-90 triangle template. Refer to the diagram below.

We have 1 as the short leg, 2 as the hypotenuse and sqrt(3) as the long leg.

Place the angle theta as the reference angle such that it's opposite the sqrt(3) side.

That allows tan(theta) = sqrt(3)/1 = opposite/adjacent

In other words, tan(60) = sqrt(3)/1

So theta = 60 is one solution. We add on 180 to get the other solution. So the other solution is 60+180 = 240

So tan(60) = tan(240) = sqrt(3)

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

Question 11a

sin(theta) = -0.8

theta = arcsin(-0.8) or theta = 180-arcsin(-0.8)

theta = -53.1301  or theta = 180 - (-53.1301)

theta = -53.1301  or theta = 233.1301

Add 360 to the first angle to find a coterminal angle counterpart.

-53.1301 + 360 = 306.8699

So the two approximate solutions are

theta = 306.8699  or theta = 233.1301

and those round to 306.9 and 233.1 respectively.

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

Question 11b

cot(theta) = 1.8

tan(theta) = 1/(1.8)

theta = arctan( 1/(1.8) )  or theta = 180+arctan( 1/(1.8) )

theta =  29.0546 or theta = 180+29.0546

theta = 29.0546 or theta = 209.0546

theta = 29.1 or theta = 209.1

Answer:

x = 118.6°

Step-by-step explanation:

Law Of Cosines

In trigonometry, the law of cosines (also known as the cosine formula, cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles.

If a, b and c are three sides of a triangle and θ is the included angle of the sides a and b then the cosine rule states:

\(c^2 = a^2 + b^2 - 2ab\cos \theta\)

In this diagram we are asked to find angle x

The sides that include angle x are AB and BC

The third side is AC

We have

\(AB = 23\\BC = 20\\AC = 37\\\)

\(m\angle ABC = x^\circ\)

Therefore by the law of cosines,

AC² = AB² + BC² - 2(AB)(AC) cos(x)

⇒   37² = 23² + 20² - 2(23)(20) cos(x)

⇒   1369 = 529 + 400 - 920 cos(x)

Move -920cos(x) from right to left side(sign changes)
920cos(x) + 1369 = 929

Move 1369 to right side (sign changes)
920cos(x)  =  - 1369 + 929
                  = -440

Divide both sides by 920:

\(cos(x) = - \dfrac{440}{920} \\\\x = cos^{-1} \left(- \dfrac{440}{920}\right)\)

Using a calculator this works out to
x = 118.6° rounded to the nearest tenth

Phillip's net loss after adding 15 pencils to his collection and giving away 30 pencils is 15 pencils.

A term is composed of one mathematical expression. A single variable (a letter), a single integer (positive or negative), or a number of variables that have been multiplied but never added or subtracted are all examples of single variables. There is a number in front of certain words that are variables. A word or phrase is preceded by a coefficient.

To calculate Phillip's net gain or loss, we need to subtract the number of pencils he gave away from the number he added to his collection.

Let's use the variable "x" to represent the number of pencils Phillip had before he added 15 pencils to his collection.

Then the expression for the total number of pencils Phillip has after giving away 30 pencils would be:

x + 15 - 30

Simplifying this expression, we get:

x - 15

Therefore, x - 15 is the required expression.

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The polynomial function which has a leading coefficient 1 is (x-(7+i))(x-(5-i))(x-(7-i))(x-(5+i))

Given that a polynomial function has leading coefficient 1 and roots (7+i) and (5-i) with multiplicity 1.

We want to find the polynomial function.

As we know that the complex conjugate properties of the roots of a polynomial states that if a+bi is a root of a polynomial then their complex conjugate a-bi is also a root.

So, according to this property (7-i) and (5+i) with multiplicity 1 is also a root of polynomial.

Thus, all the roots are x=7+i, x=7-i, x=5+i and x=5-i

So, the polynomial is f(x)=(x-(7+i))(x-(5-i))(x-(7-i))(x-(5+i))

Hence, the polynomial function which has a leading coefficient 1 and roots (7+i) and (5-i) is (x-(7+i))(x-(5-i))(x-(7-i))(x-(5+i)).

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The number of ways 3 courses can be selected is 3654.

What are the Permutation and Combination?

Permutations and combinations are the various ways in which objects from a set can be selected to form subsets, generally without replacement. When the order of selection is a factor, this selection of subsets is called a permutation; when it is not, it is called a combination.

Total no. of courses available = 29

Courses needed to graduate = 3

No of ways these courses can be selected:

                    = ²⁹C₃

                    = 29!/ [(29-3)! - 3!]

                    = 29! / 26! 3!

                    = 29 * 28 * 27 * 26!/ 26! 3*2

                    = 29* 14* 9

                    = 3654

So, the number of ways 3 courses can be selected is 3654.

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Answer:

Axis is a vertical line at x = 2

Vertex is (2, -1)

y-intercept is (0, 3)

Solutions are x = 1 and x = 3

Step-by-step explanation:

To draw the graph of the quadratic equation you must find at least 5 points lie on the graph by choose values of x and find their values of y

Let us do that

Use x = -1, 0, 1, 2, 3, 4, 5

∵ y = x² - 4x + 3

∵ x = -1

∴ y = (-1)² - 4(-1) + 3 = 1 + 4 + 3 = 8

→ Plot point (-1, 8)

∵ x = 0

∴ y = (0)² - 4(0) + 3 = 0 + 0 + 3 = 3

→ Plot point (0, 3)

∵ x = 1

∴ y = (1)² - 4(1) + 3 = 1 - 4 + 3 = 0

→ Plot point (1, 0)

∵ x = 2

∴ y = (2)² - 4(2) + 3 = 4 - 8 + 3 = -1

→ Plot point (2, -1)

∵ x = 3

∴ y = (3)² - 4(3) + 3 = 9 - 12 + 3 = 0

→ Plot point (3, 0)

∵ x = 4

∴ y = (4)² - 4(4) + 3 = 16 - 16 + 3 = 3

→ Plot point (4, 3)

∵ x = 5

∴ y = (5)² - 4(5) + 3 = 25 - 20 + 3 = 8

→ Plot point (5, 8)

→ Join all the points to form the parabola

From the graph

∵ The axis of symmetry is the vertical line passes through the vertex point

∵ x-coordinate of the vertex point is 2

∴ Axis is a vertical line at x = 2

∵ The coordinates of the vertex point of the parabola are (2, -1)

∴ Vertex is (2, -1)

∵ The parabola intersects the y-axis at point (0, 3)

∴ y-intercept is (0, 3)

∵ x² - 4x + 3 = 0

∵ The solutions of the equation are the values of x at y = 0

→ That means the intersection points of the parabola and the x-axis

∵ The parabola intersects the x-axis at points (1, 0) and (3, 0)

∴ Solutions are x = 1 and x = 3

Answer:

Area = 6x² - 20x + 16

Step-by-step explanation:

The area of a rectangle is length x width.

Plug the values into that equation:

\(A = (2x-4)(3x-4)\)

Now you use the FOIL method to find the answer:

First: 2x × 3x = 6x²

Outer: 2x × (-4) = - 8x

Inner: (-4) × 3x = - 12x

Last: (-4) × (-4) = 16

Area = 6x² + (-8x) + (-12x) + 16

Area = 6x² - 20x + 16

The original price of the dishes is $80

The sale price is $72

10% was off from the original price to get the sale price

The original price can be calculated as follows

100-10

= 90%

Let y represent the original price

72 ÷ 90/100

= 72 ÷ 0.9

= 80

Hence the original price of the dishes before 10% was taken off is $80

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Answer:

\(\huge\boxed{\sf x = 51}\)

Step-by-step explanation:

4x + 9 - 3x - 15 = 45

4x - 3x + 9 - 15 = 45

x - 6 = 45

x = 45 + 6

\(\rule[225]{225}{2}\)

Answer:

\( \sf \: x = 51\)

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 4x + 9 - 3x - 15 = 45

Then the value of x will be,

→ 4x + 9 - 3x - 15 = 45

→ (4x - 3x) + (9 - 15) = 45

→ (x) + (-6) = 45

→ x - 6 = 45

→ x = 45 + 6

→ [ x = 51 ]

Hence, the value of x is 51.

If one in every 9 people in the town vote for party A, then the remaining 8 out of 9 people would vote for party B. Therefore, we can calculate the number of people who vote for party B by multiplying the total number of people in the town by 8/9.
So, in a town of 810 people, 720 people would vote for party B, while the remaining 90 people would vote for party A.
In a town of 810 people, one in every 9 people votes for party A, and all others vote for party B. To find the number of people voting for party B, first, calculate the number of people voting for party A: 810 / 9 = 90 people. Since the remaining people vote for party B, subtract the number of party A voters from the total population: 810 - 90 = 720 people. or 810 x (8/9) = 720. Therefore, 720 people in the town vote for Party B.

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Answer: 70.77 or 71 if rounded up

Step-by-step explanation:

Add all the scores then divide to 18.

The addition of the polynomial \(x^{3}+3xy-2xy^{2} +y^{3}\) with \(2x^{3}-5x^{2} y-3xy^{2}-2y^{3}\) is  \(3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}\).

What is a polynomial?

⇒ A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

⇒ In the addition of polynomials, the like terms are added while in subtraction, the like terms are subtracted.

Calculation;

We have been given two polynomial which we have to add   \(x^{3}+3xy-2xy^{2} +y^{3}\) and \(2x^{3}-5x^{2} y-3xy^{2}-2y^{3}\)

The sign after addition or subtraction will always be of the variable having more value.

\((x^{3}+3xy-2xy^{2} +y^{3} )+(2x^{3}-5x^{2} y-3xy^{2}-2y^{3})\)

On adding like terms with each other

⇒ \((x^{3} +2x^{3})+ 3xy-5x^{2} y-(2xy^{2}+3xy^{2})+(y^{3}-2x^{3})\)

⇒ \(3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}\)

Hence the addition of the polynomial\(x^{3}+3xy-2xy^{2} +y^{3}\) and \(2x^{3}-5x^{2} y-3xy^{2}-2y^{3}\) is \(3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}\).

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Answer:

y = 8/3(x) + 9

Step-by-step explanation:

The general equation of a straight line is slope intercept form is;

y = mx + b

where m is the slope and b is the y-intercept

To get the slope, we use the slope equation

we have this as:

m = (y2-y1)/(x2-x1)

(x1,y1) = (-6,-7)

(x2,y2) = (-3,1)

m = (1+7)/(-3 + 6) = 8/3

so we have the equation as;

y = 8/3(x) + b

to get the value of b, we make use of any of the two points

We substitute the coordinates of the two points into the equation

Let us use the point (-3,1)

Thus;

1 = 8/3(-3) + b

1 = -8 + b

b = 1 + 8

b = 9

So the full equation is;

y = 8/3(x) + 9

The rate of return you can expect if you invest your money at the riskless rate is approximately 3.44%.

To calculate the rate of return you can expect if you invest your money at the risk-free rate, you need to account for the effects of inflation. The rate of return adjusted for inflation is known as the real rate of return.

The real rate of return can be calculated using the following formula:

Real Rate of Return = (1 + Nominal Interest Rate) / (1 + Inflation Rate) - 1

Given the information provided:

Nominal Interest Rate = 6.8%

Expected Inflation Rate = 3.2%

Real Rate of Interest = 2.5%

Substituting these values into the formula, we can calculate the real rate of return:

Real Rate of Return = (1 + 0.068) / (1 + 0.032) - 1

Real Rate of Return = 1.068 / 1.032 - 1

Real Rate of Return ≈ 0.0344 or 3.44%

Therefore, if you invest your money at the risk-free rate, you can expect a real rate of return of approximately 3.44%. This means that after accounting for inflation, your investment will grow by 3.44% in terms of purchasing power.

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