3x - 5 = 2x + 10
What’s the value of x

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

for more search question point  

https://brainly.com/question/28162977

#SPJ8

The cheapest price Sam would pay for 10kg of cake for the party is $5000 from Mega Mart.

To find the cheapest price Sam would pay for 10kg of cake for the party, we need to compare the prices of the available cakes and determine the most cost-effective option.

At Mega Mart, a 5kg cake costs $2500.

Therefore, the price per kilogram for this cake is:

Price per kilogram at Mega Mart = $2500 / 5kg = $500/kg.

At the same time, a 2kg chocolate cake costs $1200.

So, the price per kilogram for this cake is:

Price per kilogram for the chocolate cake = $1200 / 2kg = $600/kg.

Now, let's calculate the total price for 10kg of cake from each option:

Total price at Mega Mart for 10kg = $500/kg \(\times\) 10kg = $5000.

Total price for 10kg of chocolate cake = $600/kg \(\times\) 10kg = $6000.

Comparing the two options, we see that the Mega Mart cake is the more cost-effective choice.

Sam would pay a total of $5000 for 10kg of cake from Mega Mart, whereas the chocolate cake would cost $6000 for the same quantity.

Therefore, the cheapest price Sam would pay for 10kg of cake for the party is $5000 from Mega Mart.

In summary, Sam would pay the cheapest price of $5000 to purchase 10kg of cake for the party from Mega Mart.

For similar question on cheapest price.

https://brainly.com/question/1153322  

#SPJ8

We have a line with slope -1 and y-intercept of 8.

We can write the equation of this line as:

Then, we can test the values for each x-coordinate and see if it matches the y-coordinate indicated by the point:

Point (3,5)

Point (2,10)

Answer: the point (2,10) is not on the line.

Answer: 3

Step-by-step explanation:

N=7

Answer:

24,576

Step-by-step explanation:

24*4^(5)

Answer:

d

Step-by-step explanation:

Answer:

It would be d since its 1/2 and there asking for the whole cake

Answer:

5(k+2) = (5 · k) + (5 · 2)

= 5k + 10

Answer:

5(k+2) = (5+ k+2 ) + (5 __k_ )

= _k_ + _2__ I may be wrong sorry

Answer:

f(-3) = -21

Step-by-step explanation:

To find f(-3), we just need to plug x = -3 into f(x) so:

f(-3) = -4 * (-3)² + 15

= -4 * 9 + 15 = -36 + 15 = -21

Answer:

\(\Huge \boxed{-21}\)

Step-by-step explanation:

\(f(x) = -4x^{2} + 15\)

f(-3), the input is -3 for the function f(x).

The value of x  =  -3

\(f(-3) = -4(-3)^{2} + 15\)

Evaluate the expression.

\(f(-3) = -4(9)+ 15\)

\(f(-3) = -36+ 15\)

\(f(-3)=-21\)

The value of f(-3) is -21.

Given :

A function , x = 2cos t -3sin t               .....equation 1.

A differential equation , x'' + x = 0      .....equation 2.

To Find :

Whether the given function is a solution to the given differential equation.

Solution :

First derivative of x :

\(x'=\dfrac{d(2cos t - 3sin t)}{dt}\\\\x'=\dfrac{d(2cost)}{dt}-\dfrac{(3sint)}{dt}\\\\x'=-2sint-3cost\)

Now , second derivative :

\(x''=\dfrac{d(-2sint-3cost)}{dt}\\\\x''=-\dfrac{d(2sint)}{dt}-\dfrac{d(3cost)}{dt}\\\\x''=-2cost+3sint\)

( Note : derivative of sin t is cos t and cos t is -sin t )

Putting value of x'' and x in equation 2 , we get :

=(-2cos t + 3sin t ) + ( 2cos t -3sin t )

= 0

So , x'' and x satisfy equation 2.

Therefore , x function is a solution of given differential equation .

Hence , this is the required solution .

Answer:

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Since C is the largest half, then C is part of the largest whole.

Answer: C

Maximum: 1, Minimum: -3, Midline y = -1, Amplitude = 4, Period = π, Frequency = 1/π,  equation -4cos(2x) + 1:

Sinusoidal Functions

It refers to the oscillating functions like the sine or cosine which range from a minimum and maximum value periodically.

The graph shown can give us all the information we need to answer these questions:

Maximum: 1

Minimum: -3

The midline goes through the center value (mean) of the max and min values, i.e.

Equation of the midline:

y = (1-3)/2

y = -1

Amplitude is the difference between the maximum and minimum values

A =4

The period is the time it takes to complete a cycle. We can see the minimum value is first reached at x=0 and next at  x = π

Thus the period is

T = π

The frequency is the reciprocal of the period:

f = 1/T = 1/π

The angular frequency is

ω = 2πf

ω = 2

The equation of the function is a negative cosine (since it starts at the minimum) or a shifted sine or cosine. We'll choose the negative cosine, knowing all the parameters:

f(x) = -4cos(2x) + 1

Learn more about sinusoidal function at:
https://brainly.com/question/21008165

#SPJ1

Answer:

I won't solve it, because you asked me to.

Step-by-step explanation:

The first question we should ask ourselves is "what are we looking to solve?"

We are looking for some sort of value that satisfies that equation. We'll call it x

Reading from left to right:

The sum of twice a number and 13 is 75

         +            2              x              13 = 75

2x + 13 = 75

Answer:

Pro Painters are cheaper.

Explanation:

The given problem can be solved by using a Linear equation in 2 variables.

Pro Painters charged $200/hour +$6000

Let the Paint job takes 'x' hours and the total cost is 'y'.

Total cost:

y= \(200*x +6000\)    (This is a linear equation )

total cost for 35 hours job

y= 200 *35 +6000 dollars

y=7000+6000 dollars

y=13000 dollars

Illusion Ltd charges $150/hour +$ 8000.

Let the Paint job takes 'x' hours and the total cost is 'y'.

Total cost

y =\(150*x + 8000\)

for 35 hours total cost

y= 150*35+8000

y=5250+8000

y=13250 dollars

now, As $13250>$13000

Hence Pro painters are cheaper.

To know more about Linear Equations go to:

https://brainly.com/question/19954463

//SPJ2

Answer:

13.

Step-by-step explanation:

1) if the required number of years is 'x', then it is possbile to make up the equation:

43+x=2(15+x);

2) finally, x=13 [years].

Answer:

A

Step-by-step explanation:

Using the arc length formula,

\(S=9\left(\frac{3\pi}{4} \right) \approx \boxed{21.2}\)

The value of the angles are;

<1 = 45 degrees

<2 = 45 degrees

It is important to note the following properties of a rectangle;

We can see that;

< 1 = 90/2

Divide the values

< 1 = 45 degrees

Note that alternate angles are equal

< 1 = < 2

Then, the value is 45 degrees

Learn about rectangles at: https://brainly.com/question/25292087

#SPJ1

\(\huge\bold{ANSWER:}\)

\(\huge\bold{1,400} ~and~\huge\bold{361,000}\)

\(\huge\bold{SOLUTION:}\)

\(\huge\mathrm{100*14}\)

Multiply:

\(\huge\mathrm{1,400}\) (Answer)

\(\huge\mathrm{361*1,000}\)

Multiply:

\(\huge\mathrm{361,000}\)

_______________________________________

Additional Note:

\(\bigstar\) If we multiply by 100, we add 2 zeros.

Example: \(\bold{\underline{14*100=1,400}}\)

\(\bigstar\) If we multiply by 1,000, we add 3 zeros.

Example: \(\bold{\underline{361*1,000=361,000}}\)

______________________________________

Hope you find it helpful.

Feel free to ask if you have any doubts.

\(\bold{-MistySparkles^**^*}\)

Answer:

diameter = 2(radius)

Step-by-step explanation:

not sure what your question is but the diameter of a circle is equal to 2 times the length of its radius

Answer:

10^4

Step-by-step explanation:

4 0's so 10^4

Answer: If you mean to multiply, the answer is 8/15.

Step-by-step explanation:

Multiply numerator by numerator and denominator by denominator.

2 x 4 = 8

3 x 5 = 15

ANSWER: 8/15

Answer:

\(H)39.6\)

Step-by-step explanation:

To get the mean, you have to add all the numbers, then divide the sum by the amount of individual numbers there are.

In this problem, we see that there are 5 different numbers. If we add all those numbers together, they will equal 198.

\(198\) ÷ \(5 = 39.6\)

The linear relationship illustrated in the provided table can be effectively described by the equation Y = -4x + 2. Option D.

To determine the equation that represents the given table with the values of x and y, we can observe the pattern and find the equation of the line that fits these points.

Given the table:

X: 2 0 4

Y: -4 3 1

We can plot these points on a graph and see that they form a straight line.

Plotting the points (2, -4), (0, 3), and (4, 1), we can see that they lie on a line that has a negative slope.

Based on the given options, we can now evaluate each equation to see which one represents the line:

Y = 1/2x + 5

When we substitute the x-values from the table into this equation, we get the following corresponding y-values: -3, 5, and 6. These values do not match the given table, so this equation does not represent the table.

Y = -1/2x + 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: 4, 3, and 2. These values also do not match the given table, so this equation does not represent the table.

Y = 2x - 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -4, -3, and 5. These values do not match the given table, so this equation does not represent the table.

Y = -4x + 2

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -6, 2, and -14. Interestingly, these values match the y-values in the given table. Therefore, the equation Y = -4x + 2 represents the table.

In conclusion, the equation Y = -4x + 2 represents the linear relationship described by the given table. So Option D is correct.

For more question on equation visit:

https://brainly.com/question/29174899

#SPJ8

Answer: 20 log (2)

Step-by-step explanation:

Answer: Logarithms are mathematical functions that are used to represent the relationship between two quantities that are related by a power law. For example, if we have an exponential equation like 2^x = 8, we can use logarithms to solve for x: log2 8 = x.

In general, logarithms are written in the form logb a, where b is the base of the logarithm and a is the number we want to take the logarithm of. There are several different bases in that logarithms can be written in, including the common logarithm (base 10) and the natural logarithm (base e).

To evaluate a logarithm, we need to use the logarithmic properties and the change of base formula. One important property of logarithms is that logb (xy) = logb x + logb y. Another property is that logb (x/y) = logb x - logb y.

The change of base formula is used when we need to evaluate a logarithm in a different base than the one given. The formula is:

logb a = logc a / logc b

where c is any base other than b or a. By using this formula, we can convert a logarithm from one base to another in order to evaluate it using a calculator.

In the case of log4 25, we can use the common logarithm (base 10) or the natural logarithm (base e) to evaluate the logarithm. Using the change of base formula with the common logarithm, we have:

log4 25 = log(25) / log(4)

Using a calculator, we find that log(25) ≈ 1.39794 and log(4) ≈ 0.60206, so:

log4 25 ≈ 1.39794 / 0.60206

Simplifying this expression, we get:

log4 25 ≈ 2.32193

Rounding to the nearest thousandth, we get:

log4 25 ≈ 2.322

So, the value of log4 25 to the nearest thousandth is 2.322.

Step-by-step explanation:

Answer

\(\pink\sf{y=-1}\)

Step-by-step explanation

I'm assuming that this exercise is asking us to simplify the equation \(\sf{y=0.5(6)-4}\).

We know that 0.5 (6) means 0.5 multiplied by 6. That is the same as 6 divided by 2, which is 3:

\(\sf{y=3-4}\)

And now we just simplify the last part:

\(\sf{y=-1}\)

∴ answer: y = -1

The equation of a line parallel to the given line and passing through the point (0, 8) is 5y - 3x = 40

The equation of a line in point-slope form is expressed as;

y - y0 = m(x -x0)

where

m is the slope

(x0, y0) is the point on the line

Given the following parameters

Point (0,8)

Slope from the equation = 3/5

Substitute

y - 8 = 3/5(x - 0)
5(y -8) =3x

5y - 40 = 3x

5y - 3x = 40

Hence the equation of a line parallel to the given line and passing through the point (0, 8) is 5y - 3x = 40

Learn more on equation of a line here: https://brainly.com/question/13763238

#SPJ1

Answer:

slope = - \(\frac{3}{11}\)

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 14, 3 ) and (x₂, y₂ ) = (- 3, 0 )

m = \(\frac{0-3}{-3-(-14)}\) = \(\frac{-3}{-3+14}\) = - \(\frac{3}{11}\)

Answer:

The slope is M= -3/11  (M= Negetive three over eleven)

Step-by-step explanation: