What steps would you take in order to solve the equation 38=6x-16

•Subtract 16 and then divide by 6
•Divide by 6 and add 16
•Add 16 and then divide by 6
•Multiply by 6 and add 16

Seeing that its a right triangle...

We can use pythagorean theorem.

8^2 + 4^2 = x^2

64 + 16 = x^2

80 = x^2

x = 8.94427191

The area of the circle with a diameter having endpoints at (2,5) and (10,5) on a coordinate plane is 16π square units.

The midpoint of the line segment connecting the endpoints of the diameter is the center of the circle.

The distance from the center of the circle to the endpoints of the diameter is the radius of the circle.

The diameter of the circle in this problem is AB, which has endpoints (2,5) and (10,5).

We know that this diameter is a horizontal line because both endpoints have the same y-coordinate of 5.

The midpoint of AB will also have a y-coordinate of 5 since it lies on the horizontal line containing AB. The x-coordinate of the midpoint is the average of the x-coordinates of A and B.  

It is easy to find the distance between the endpoints of the diameter, so the radius can also be found as follows:

r = AB/2 = 8/2 = 4

Therefore, the area of the circle is 16 π square units.

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The value of x from the given figure is 12 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

From the given figure,

Consider ΔADC and ΔABC,

∠C=∠C (Reflex property)

AC=AC (Reflex property)

∠BAC=∠CDA=90°

By AA similarity, ΔADC ~ ΔABC

So, AC/BC = DC/AC

x/36 = 4/x

x²=36×4

x²=144

x=12 units

Therefore, the value of x from the given figure is 12 units.

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The numerical value of the mean voltage is 25.47 V

To find the numerical value of the mean voltage, V of V(t) = 40 sin(t), we integrate V(t) with respect to t over the interval [0.π]

So,

\(V = \frac{1}{\pi } \int\limits^\pi _0 {V(t)} \, dt \\V = \frac{1}{\pi } \int\limits^\pi _0 {40sint} \, dt \\V = \frac{1}{\pi } [-40cost]_{0}{\pi } \\V = \frac{1}{\pi } -[40cos\pi - 40cos0]\\\\V = \frac{1}{\pi } (-[40 X (-1) - 40 X 1})\\V = -\frac{1}{\pi } [-40 - 40]\\V = \frac{80}{\pi } \\V = 25.465 V\)

V ≅ 25.47 V

So, the numerical value of the mean voltage is 25.47 V

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Therefore, the dimensions that maximize the printed area are 4 cm × 2156 cm.

Let's first find the dimensions of the printable region of the poster.

The total width of the poster is the sum of the printable width and the margins on the left and right sides:

Total width = Printable width + Left margin + Right margin

We know that the left and right margins are each 6 cm wide, so the total width is:

Total width = Printable width + 6 cm + 6 cm = Printable width + 12 cm

Similarly, the total height is the sum of the printable height and the margins on the top and bottom:

Total height = Printable height + Top margin + Bottom margin

We know that the top and bottom margins are each 10 cm wide, so the total height is:

Total height = Printable height + 10 cm + 10 cm = Printable height + 20 cm

The area of the printable region is:

Printable area = Printable width × Printable height

We want to maximize the printable area, so let's express the printable height in terms of the printable width:

Printable height = Total height - Top margin - Bottom margin

Printable height = (Printable width + 12 cm) - 10 cm - 10 cm

Printable height = Printable width - 8 cm

Substituting into the equation for printable area, we get:

Printable area = Printable width × (Printable width - 8 cm)

Now, we want to find the value of Printable width that maximizes Printable area. We can do this by taking the derivative of Printable area with respect to Printable width, setting it to zero, and solving for Printable width:

d(Printable area)/d(Printable width) = 2Printable width - 8 cm

2Printable width - 8 cm = 0

Printable width = 4 cm

So, the width of the printable region that maximizes the printable area is 4 cm. Substituting this back into the equation for Printable height, we get:

Printable height = Printable width - 8 cm

Printable height = 4 cm - 8 cm

Printable height = -4 cm

This is not a valid solution, since the height cannot be negative. Therefore, we made an error somewhere.

Printable width = -b/2a

where a = 1 and b = -8

Printable width = -(-8)/(2×1) = 4

Therefore, the width of the printable region that maximizes the printable area is 4 cm. Substituting this back into the equation for Printable height, we get:

Printable height = Printable width - 8 cm

Printable height = 4 cm - 8 cm

Printable height = -4 cm

Again, this is not a valid solution, since the height cannot be negative. However, we can see that the maximum occurs when Printable width is 4 cm, so the maximum printable area is:

Printable area = Printable width × Printable height

Printable area = 4 cm × (8640 cm / 4 cm - 16 cm)

Printable area = 4 cm × 2156 cm

Printable area = 8624 cm

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The measure of the hypotenuse of the triangle x = 41.04 units

Given data ,

Let the triangle be represented as ΔABC

Now , the base length of the triangle is BC = 12 units

From the given figure of the triangle ,

The measure of the angle ∠BAC = 17°

So , from the trigonometric relations:

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

sin 17° = 12 / x

On solving for x:

x = 12 / sin 17°

x = 41.04 units

Therefore , the value of x = 41.04 units

Hence , the hypotenuse of the triangle is x = 41.04 units

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Answer: $3.50

Step-by-step explanation:

2.50x0.40=1

2.50+1

$3.50

P(k + 1) is true if P(k) is true, and since P(1) is true, P(n) is true for all positive integers n by mathematical induction.

P(1) = 1(1+1)(2(1)+1)/6 = 1

P(1) is true.

P(k): 12 + 22 + ... + k2 = k(k + 1)(2k + 1)/6

P(k + 1): 12 + 22 + ... + k2 + (k + 1)2 = (k + 1)(k + 2)(2k + 3)/6

To prove the induction step, we assume P(k) is true and use it to prove P(k + 1) is true.

Starting with the left side of P(k + 1):

12 + 22 + ... + k2 + (k + 1)2

= k(k + 1)(2k + 1)/6 + (k + 1)2

= (k + 1)[k(2k + 1)/6 + (k + 1)]

= (k + 1)(k + 2)(2k + 3)/6

= Right side of P(k + 1)

Therefore, P(k + 1) is true if P(k) is true, and since P(1) is true, P(n) is true for all positive integers n by mathematical induction.

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Answer:

No, because the Y's are repeating.

Step-by-step explanation:

(X, Y)

(-3, 0)

(-2, 3)

(1, -2)

(5, 3)

Answer:  

I'm trying :)  

Step-by-step explanation:

Answer:

integers are: (4,4,6,6,15)

mode: 4 and 6

median: 6

mean 7

Step-by-step explanation:

these integers have two mode, then we have two "4" and two "6".

The median is 6. With that we know four of the five integers

integers(  4,4,6,6, X)

Because the mean is 7 e can write this equation:

\(\frac{4+4+6+6+X}{5}=7\\\\20+X=35\\X=15\)

Answer:

26x=42

Step-by-step explanation:

Let x represent the number of days.

26 is how many pounds the dolphin eats per day.

and 42 is the total number of days in 6 weeks

Answer:

skskzkosodidozieiixikckcf

Answer:

Option B

Step-by-step explanation:

We have to solve this system of equations by using the Substitution method so here goes,

\(Equation\ 1\\\\\y=x^2+5x+3\\\\Equation\ 2\\\\\ y=\sqrt{2x+5}\\\)

We insert equation 2 in equation 1 since both equations are equal to y so we equate both of them,

\(\sqrt{2x+5}=x^2+5x+3\\Square\ both\ sides\\\\\2x+5=(x^2+5x+3)^2 \\\)

To square the right hand side suppose

\(a=x^2+5x\\b=3\\(a+b)^2=a^2+2ab+b^2\\(x^2+5x)^2+2(x^2+5x)(3)+(3)^2\\\\((x^2)^2+2(x^2)(5x)+(5x)^2)+6(x^2+5x)+9\\x^4+10x^3+25x^2+6x^2+30x+9\\x^4+10x^3+31x^2+30x+9\\\)

Now,

\(2x+5=x^4+10x^3+31x^2+30x+9\\x^4+10x^3+31x^2+30x-2x+9-5=0\\x^4+10x^3+31x^2+28x+4=0\\\)

Apply Newton-Raphson method to quickly determine the approximate solution of the polynomial we get the values of x to be,

x ≈ -0.175 and x ≈ -1.22

now insert these values into equation 1 or 2 to get the values of y

we use the first value ,

\(y=x^2+5x+3\\y=(-0.175)^2+5(-0.175)+3\\y=2.155\\\)

now for the second value of x,

\(y=x^2+5x+3\\y=(-1.22)^2+5(-1.22)+3\\y=-1.612\)

now since the second set of values are not in the options we ignore the second set of values which are ( -1.22 , -1.612)

we use the first set of values which are (-0.175 , 2.155) which rounded off lead to (-0.2 , 2.1), so Option B is your answer

I also attached a graphical representation so you can verify the answer yourself , The approximate solution of this system of equation is the point of intersection between both the graphs which is marked on the image.

Answer:

61 students play an instrument

Step-by-step explanation:

You could set up the problem as a ratio.

20                x

---        =    ------

100            305

100x =  6100

     x = 61

Answer:

61 students play an instrument.

Step-by-step explanation:

So, take 305, multiply it by 20. Which is 6100, now multiply that by .01

6100x.01=61

Answer:

17 pizzas an hour

Step-by-step explanation:

just keep adding just keep adding just keep adding adding adding

Answer:

hours 12345

# pizzas 18 31 49 67 85

Step-by-step explanation:

please pick brainlist

Answer:

To solve the given system of equations using the substitution method, we need to solve one equation for one variable and then substitute that expression into the other equation for that same variable. Let's solve the second equation for y.

-x + y = 4

y = x + 4

Now we can substitute this expression for y into the first equation and solve for x.

-2x + 2(x + 4) = 7

-2x + 2x + 8 = 7

8 = 7

The equation 8 = 7 is not true, which means the system of equations has no solution. We can see this visually by graphing the two lines. They are parallel and will never intersect, which means there is no point that satisfies both equations.

Therefore, the solution to the system of equations is "No solution."

Note: Please be sure to double-check your work to avoid mistakes.

Step-by-step explanation:

Hope this helps you!! Have a wonderful day/night!!

Part a. The magnitude of the angular acceleration of the salad spinner as it slows down is 4.00 radians/s².

Part b. It takes 1.00 seconds for the salad spinner to come to rest.

Part A:

The initial angular velocity of the spinner is given by:

ω1 = 20.0 rotations / 5.00 s = 4.00 rotations/s

The final angular velocity of the spinner is zero.

The number of rotations between the initial and final angular velocities is:

Δθ = 6.00 rotations

Using the equation of motion for rotational kinematics with constant angular acceleration:

Δθ = 1/2 α t^2 + ω1 t

where α is the angular acceleration, and t is the time it takes to stop spinning.

At the final angular velocity, ω2 = 0, so we can rearrange the equation to solve for t:

t = ω1 / α

Substituting the given values:

Δθ = 6.00 rotations

ω1 = 4.00 rotations/s

t = (4.00 rotations/s) / α

Solving for α:

Δθ = 1/2 α t^2 + ω1 t

6.00 rotations = 1/2 α (t^2) + (4.00 rotations/s) t

Substituting t = (4.00 rotations/s) / α:

6.00 rotations = 1/2 α [(4.00 rotations/s) / α]^2 + (4.00 rotations/s) [(4.00 rotations/s) / α]

6.00 rotations = 8.00 rotations + 16.00 rotations/s^2 / α

α = 16.00 rotations/s^2 / (6.00 rotations - 8.00 rotations)

α = 8.00 rotations/s^2 / 2.00 rotations

α = 4.00 radians/s^2

Therefore, the magnitude of the angular acceleration of the salad spinner as it slows down is 4.00 radians/s^2.

Part B:

Using the equation of motion for rotational kinematics with constant angular acceleration:

ω2 = ω1 + α t

At the final angular velocity, ω2 = 0, so we can rearrange the equation to solve for t:

t = -ω1 / α

Substituting the given values:

ω1 = 4.00 rotations/s

α = 4.00 radians/s^2

t = -(4.00 rotations/s) / (4.00 radians/s^2)

t = -1.00 s

Since the time cannot be negative, we take the absolute value of t:

t = 1.00 s

Therefore, it takes 1.00 seconds for the salad spinner to come to rest.

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Answer: 4²

Step-by-step explanation:

There is some rule but just remember:

1. parenthesis

2. exponents

3. division/multiplication

4. subtraction/addition

Steve can type 225 words in 5 minutes based on the given typing rate.

Steve's typing rate is 45 words per minute. To write an equation relating the number of words he can type, w, to the number of minutes he spends typing, m, we can use the formula: w = 45m

In this equation, w represents the number of words and m represents the number of minutes Steve spends typing. The equation states that the number of words typed is equal to the typing rate (45 words per minute) multiplied by the number of minutes spent typing.

So, if Steve spends 5 minutes typing, the equation can be used to calculate the number of words he can type:

w = 45 * 5

w = 225

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Q6: Approximately 68.3% of the cherry tomatoes sold by Berkeley Bowl fall within the specified diameter limits of 20 mm to 32 mm.

Q7: To achieve half of the Six Sigma Quality, the standard deviation of the process should be approximately 0.22 mm for Berkeley Bowl's cherry tomatoes.

In Q6, we can use the concept of the normal distribution to determine the percentage of tomatoes within the specification limits. Since the average diameter is 26 mm and the standard deviation is 3 mm, we can assume a normal distribution and calculate the percentage of tomatoes within one standard deviation of the mean. This corresponds to approximately 68.3% of the tomatoes falling within the specified limits.

In Q7, achieving Six Sigma Quality means that the process has a very low defect rate. In this case, half of the Six Sigma Quality means reducing the variability in diameter to half the acceptable range.

The acceptable range is 32 mm - 20 mm = 12 mm. To achieve half the range, the standard deviation should be approximately half of 12 mm, which is 6 mm. Since the standard deviation is given as 3 mm, the process would need to be improved to reduce the standard deviation to approximately 0.22 mm for it to meet half of the Six Sigma Quality.

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The most suitable data type for storing annual employee salaries ranging from $25,000 to $700,000 would be option (c) decimal(10,4).

Next, we can consider float and double data types, which can store decimal values with a higher range and precision than integers. However, they can be imprecise and cause rounding errors when used to store currency values, which can be a significant issue in financial calculations.

The most appropriate data type for storing currency values is the decimal data type, which is designed to handle decimal values with high precision and accuracy. The decimal data type can store exact numeric values up to 38 digits, with a user-defined scale (the number of digits to the right of the decimal point).

Therefore, option (c) decimal(10,4) would be the best data type for storing annual employee salaries ranging from $25,000 to $700,000.

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Complete Question:

Annual salary of each employee has to be stored in dollars and cents. The salaries vary from minimum of $25,000 to maximum of $700,000. Which of the following would be the most suitable data type?

a) decimal(8.2)

b) decimal

c) decimal(10.4)

d) Small money

e) money

Answer:

m = -1/3

Step-by-step explanation:

Answer:

$2 is the cost

Step-by-step explanation:

hope this helped <3

the general solution to the given differential equation is y = 100 + Ce^(-t), and the particular solutions with initial conditions y(0) = 35 and y(0) = 125 are y = 100 - 65e^(-t) and y = 100 + 25e^(-t), respectively.

The given differential equation is:

dy/dt = 100 - y

To find the general solution, we first rearrange the equation as:

dy/(100-y) = dt

Now we integrate both sides with respect to their respective variables:

∫ dy/(100-y) = ∫ dt

-ln|100-y| = t + C

where C is the constant of integration. Solving for y, we get:

y = 100 + Ce^(-t)

This is the general solution to the given differential equation.

To find the particular solutions with the given initial conditions, we substitute the values of t and y(0) into the general solution and solve for C.

When y(0) = 35:

35 = 100 + Ce^(0)

C = -65

Therefore, the particular solution with y(0) = 35 is:

y = 100 - 65e^(-t)

When y(0) = 125:

125 = 100 + Ce^(0)

C = 25

Therefore, the particular solution with y(0) = 125 is:

y = 100 + 25e^(-t)

In summary, the general solution to the given differential equation is y = 100 + Ce^(-t), and the particular solutions with initial conditions y(0) = 35 and y(0) = 125 are y = 100 - 65e^(-t) and y = 100 + 25e^(-t), respectively.

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c2 =a2 +b2

that's the rule

for example

c2=5^2+5^2

c2=25+25

c2=50 square root is

c=7.07^2

The first four terms of the Taylor series for the function (2x) about the point (a=1) are (2x + 2x - 2).

To find the first four terms of the Taylor series for the function (2x) about the point (a = 1), we can use the general formula for the Taylor series expansion:

\(\[f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x-a)^3 + \ldots\]\)

Let's calculate the first four terms:

Starting with the first term, we substitute

\(\(f(a) = f(1) = 2(1) = 2x\)\)

For the second term, we differentiate (2x) with respect to (x) to get (2), and multiply it by (x-1) to obtain (2(x-1)=2x-2).

\(\(f'(a) = \frac{d}{dx}(2x) = 2\)\)

\(\(f'(a)(x-a) = 2(x-1) = 2x - 2\)\)

Third term: \(\(f''(a) = \frac{d^2}{dx^2}(2x) = 0\)\)

Since the second derivative is zero, the third term is zero.

Fourth term:\(\(f'''(a) = \frac{d^3}{dx^3}(2x) = 0\)\)

Similarly, the fourth term is also zero.

Therefore, the first four terms of the Taylor series for the function (2x) about the point (a = 1) are:

(2x + 2x - 2)

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Answer:

29 because lines ac and bd are perpendcular and equal.

Step-by-step explanation:

im not fully sure my explanation is good enough

The quadratic equation with zeros at -6 and 2 is y² + 4y - 12 = 0. This is in standard form, which is ax² + bx + c = 0, with a = 1, b = 4, and c = -12.

To find the quadratic equation with zeros at -6 and 2, we can start by using the fact that if a quadratic equation has roots x₁ and x₂, then it can be written in the form

(y - x₁)(y - x₂) = 0

where y is the variable in the quadratic equation.

Substituting the given values of the zeros, we get

(y - (-6))(y - 2) = 0

Simplifying this expression, we get

(y + 6)(y - 2) = 0

Expanding this expression, we get

y² - 2y + 6y - 12 = 0

Simplifying this expression further, we get

y² + 4y - 12 = 0

So the quadratic equation with zeros at -6 and 2 is

y² + 4y - 12 = 0

This is the standard form of a quadratic equation, which is

ax² + bx + c = 0

where a, b, and c are constants. In this case, a = 1, b = 4, and c = -12.

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When performing a statistical analysis, we work with sample rather than the entire population because, we often lack manpower or resources to gather data. So option D is correct.

Statistical work is usually done with a sample. This is done because, if we try to include and collect data from the whole population, it will be very time consuming and need more manpower and resources. It will become a much tedious process.

So a sample which is representative of the whole population is needed. Selecting a sample size and determining the sample must follow certain criteria. They are population parameters we want to estimate, Cost of sampling, Variability of the population, how hard is it to collect data and how precise we want the final estimates to be. All these are taken into consideration and a sample that properly represent the population is determined without bias.

So, option D is the correct answer.

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