Find the value of x so that the function has the given value.

Answer:

45+10x2------>65

45+10x3----->75

45+10x4------->85

Answer:

5/x+1=7/x-2

x=2/3

Decimal form: 0.6

Step-by-step explanation:

The complete question is

"Find the general solution of the given differential equation

y''-y=0, y1(t)=e^t , y2(t)=cosht

The function \(y(t)=e^t\)  is the solution of the given differential equation.

The function y(t)=cosht is the solution of given differential equation.

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

\(y_1(t) = e^t\)

Given differential equations are,

y''-y = 0

 So that,  

\(y' (t) = e^t, y'' (t) = e^t\)

Substitute values in the given differential equation.

\(e^t -e^t=0\)

Therefore, the function \(y(t)=e^t\)  is the solution of the given differential equation.

Another function;

\(y(t)=cosht\)  

So that,  

\(y"(t)=sinht\\\\y"(t)=cosht\)

Hence, function y(t)=cosht is solution of given differential equation.

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Therefore, the volume of the wedding cake is approximately 565.2 cubic inches.

The volume of a cylindrical wedding cake with a diameter of 12 inches and a height of 5 inches can be calculated using the formula for the volume of a cylinder, which is V = π * r^2 * h. In this case, the radius is half the diameter, so it is 6 inches. Substituting the values into the formula, we get V = 3.14 * 6^2 * 5, which equals 565.2 cubic inches when rounded to the nearest tenth. Therefore, the volume of the wedding cake is approximately 565.2 cubic inches. To find the volume of a cylindrical wedding cake, we can use the formula for the volume of a cylinder:

Volume = π * r^2 * h

Given:

Diameter = 12 inches

Radius = Diameter / 2 = 12 / 2 = 6 inches

Height = 5 inches

Pi (π) = 3.14

Substituting the values into the formula, we get:

Volume = 3.14 * 6^2 * 5

= 3.14 * 36 * 5

= 565.2 cubic inches (rounded to the nearest tenth

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If the area of a sector of a circle with a central angle of 240 degrees is 134 ft squared the radius of the circle is approximately 7.12 feet.

what is a circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center.

The formula for the area of a sector of a circle is:

A = (θ/360)πr²

where A is the area of the sector, θ is the central angle of the sector (in degrees), π is the mathematical constant pi (approximately 3.14159), and r is the radius of the circle.

We are given that the central angle of the sector is 240 degrees and the area of the sector is 134 ft². So we can plug these values into the formula and solve for r:

134 = (240/360)πr²

Simplifying the fraction inside the parentheses:

134 = (2/3)πr²

Multiplying both sides by 3/2:

201 = πr²

Dividing both sides by π and taking the square root:

r = √(201/π) ≈ 7.12 ft (rounded to two decimal places)

Therefore, the radius of the circle is approximately 7.12 feet.

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The percentage statement 28 is 35% of 80 is written in the form

a/b = p/100 as 28/80 = 35/100.

For the given question.

The statement defining the percentage is ;

28 is 35% of 80.

This can be written as;

35% of 80 = 28

Solve percentage.

35×80/100 = 28

35/100 = 28/80

Or,

28/80 = 35/100

This is the form

a/b = p/100

a = 28

b = 80

p = 35

Thus, the percentage statement 28 is 35% of 80 is written in the form

a/b = p/100 as 28/80 = 35/100.

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The proof that the Quadrilateral WXYZ is a rectangle is shown below

To prove that Quadrilateral WXYZ is a rectangle, we need to show that it has four right angles.

First, we can find the slopes of each pair of opposite sides to determine if they are perpendicular.

The slope of WX is:

m(WX) = (y2 - y1)/(x2 - x1) = (-2 - 1)/(2 - (-1)) = -1

The slope of YZ is:

m(YZ) = (y2 - y1)/(x2 - x1) = (6 - 3)/(4 - 7) = -1

Since the slopes of WX and YZ are equal , we know that they are opposite sides.

Now we can use the distance formula to check if the sides of the quadrilateral are congruent. The length of WX is:

√((2 - (-1))^2 + (-2 - 1)^2) = √18

The length of YZ is:

√((7 - 4)^2 + (3 - 6)^2) = √18

The length of WY is:

√((7 - (-1))^2 + (3 - 1)^2) = √68

The length of XZ is:

√((4 - 2)^2 + (6 - (-2))^2) = √68

We can see that opposite sides WX and YZ have the same length, as do opposite sides WY and XZ.

So, the quadrilateral is a rectangle

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Required base of the triangle is 6 ft.

What is the area of triangle?

The area of a triangle can be calculated using the formula:

Area = (base × height) / 2

where the base and height of the triangle are perpendicular to each other.

Alternatively, if you know the length of all three sides of the triangle, you can use Heron's formula to calculate the area:

Area = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle (i.e. half the perimeter) and a, b, and c are the lengths of the three sides.

To find the base of the given triangle when the area and height are given, we can use the formula:

Area = 1/2 x base x height

We are given that the area of the triangle is 24 ft² and the height is 8 ft². Substituting these values into the formula, we get:

24 = 1/2 x base x 8

Multiplying both sides by 2/8, we get:

base = 6

Therefore, the base of the triangle is 6 ft.

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Correct question is "The area of the triangle is 24 ft² and height of the triangle is 8 ft². Find base of the triangle?"

If a four digit personal identification number is selected, then the probability that there are no repeated digits is 0.504

Number of digits in the identification number = 4

0, 1, 2, 3, 4, 5, 6, 7, 8 and 9

There are 10 digits

The probability = Number of favorable outcomes / Total number of outcomes

Total number of outcomes = 10 × 10 × 10 × 10

= 10000

Number of outcomes that digits wont repeat = 10 × 9 × 8 × 7

= 5040

Substitute the values in the equation of probability

The probability = 5040 / 10000

= 0.504

Therefore, the probability there are no repeated digits is 0.504

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Answer:

The answer is M is -4

Step-by-step explanation:

You have to get the m by itself to figure out what equals m.

Hope this helps!

Answer:

a) The mass is released at t = 0 when h is minimum. Half a cycle later h reaches its maximum and another half a cycle it reaches its minimum again. Hence over one cycle, h varies with t as follows:

b) According to the graph obtained in part a), h(t) could be modeled by a cosine function shifted (translated) vertically up and horizontally to the right. Hence

Step-by-step explanation:

Answer:

To get 20 cups of purple paint, the table shows that we need 8 cups of blue paint and 12 cups of red paint. We can solve the problem using double (or triple) number lines.

Answer:

Look below.

Step-by-step explanation:

K(x)=x^2 isnt graphed but P(x)=x^2+n is. We could use this information to figure out what n is. In a quadratic function we always have the same points unless we are transforming it.

X   Y  

2   4

1    1

0   0

-1    1

-2   4

If we compare what the points were in the parent function to what is shown now we could see that the graph went down 6. From this information we can conclude that n must be -6.

Answer:

20

Step-by-step explanation:

Answer:

1) You divide x measure by a2 and y measure by b^2 to equal 1 whole.

2) Using the vertices 0,0 we look for the negative (x-h^2)/ a2   and (y-k)^2/b^2

Which means distance from center to a vertices is 'a ' and means (hk)

3) So the parabola is a conic section (a section of a cone). Equations. x-squared is a parabola. The simplest equation for a parabola is y = x2.   Most renowned is the given y = ax2 + bx + c

For graphs the difference from the given x2 equation is we keep double 'x' x2 to y and multiply h to 4p;  we see (x - h)2 = 4p (y - k) usually focusing upright g k and p. Note below this focus changes from y to x if rotated on transversal.

Real life objects ;

Ellipses, including orbits of planets, satellites, moons and comets, and shapes of boat keels, rudders, and some airplane wings. A medical device called a lithotripter uses elliptical reflectors to break up kidney stones by generating sound waves.

Hyperbola;

Satellites, lenses radios, monitors Graphing a hyperbola shows this immediately: when the x-value is small, the y-value is large, and vice versa. Many real-life situations can be described by the hyperbola, including the relationship between the pressure and volume of a gas.

Parabolas; Are also used in satellite dishes to help reflect signals that then go to a receiver.From the paths of thrown baseballs, to fountains, this geometric shape is prevalent, and even functions to help focus light and radio waves.

Using Parabolic Reflectors to Focus Light

Flat surfaces scattered light too much to be useful to mariners. Spherical reflectors increased brightness, but could not give a powerful beam. But using a parabola-shaped reflector helped focus light into a beam that could be seen for long distances.

The idea that a parabolic reflector could produce an image was already well known before the invention of the reflecting telescope.

The name "parabola" is due to Apollonius, who discovered many properties of conic sections. It means "application", referring to "application of areas" concept, that has a connection with this curve.

Where the focus–directrix property of the parabola and other conic sections is due to Pappus of Alexandria. (c. 340) an encyclopedist where 8 volumes survived.

Galileo showed that the path of a projectile follows a parabola, a consequence of uniform acceleration due to gravity.

Step-by-step explanation:

The standard equation for an ellipse, x 2 / a 2 + y2 / b 2 = 1, represents an ellipse centered at the origin and with axes lying along the coordinate axes. In general, an ellipse may be centered at any point, or have axes not parallel to the coordinate axes.

The standard for a parabola is (x - h)2 = 4p (y - k), where the focus is (h, k + p) and the directrix is y = k - p. If the parabola is rotated so that its vertex is (h,k) and its axis of symmetry is parallel to the x-axis, it has an equation of (y - k)2 = 4p (x - h), where the focus is (h + p, k) and the directrix is x = h - p.

Answer:

The answer is a parebola

Step-by-step explanation:

1) You divide x measure by a2 and y measure by b^2 to equal 1 whole.

2) Using the vertices 0,0 we look for the negative (x-h^2)/ a2   and (y-k)^2/b^2

Which means distance from center to a vertices is 'a ' and means (hk)

3) So the parabola is a conic section (a section of a cone). Equations. x-squared is a parabola. The simplest equation for a parabola is y = x2.   Most renowned is the given y = ax2 + bx + c

For graphs the difference from the given x2 equation is we keep double 'x' x2 to y and multiply h to 4p;  we see (x - h)2 = 4p (y - k) usually focusing upright g k and p. Note below this focus changes from y to x if rotated on transversal.

Real life objects ;

Ellipses, including orbits of planets, satellites, moons and comets, and shapes of boat keels, rudders, and some airplane wings. A medical device called a lithotripter uses elliptical reflectors to break up kidney stones by generating sound waves.

Hyperbola;

Satellites, lenses radios, monitors Graphing a hyperbola shows this immediately: when the x-value is small, the y-value is large, and vice versa. Many real-life situations can be described by the hyperbola, including the relationship between the pressure and volume of a gas.

Parabolas; Are also used in satellite dishes to help reflect signals that then go to a receiver.From the paths of thrown baseballs, to fountains, this geometric shape is prevalent, and even functions to help focus light and radio waves.

Using Parabolic Reflectors to Focus Light

Flat surfaces scattered light too much to be useful to mariners. Spherical reflectors increased brightness, but could not give a powerful beam. But using a parabola-shaped reflector helped focus light into a beam that could be seen for long distances.

The idea that a parabolic reflector could produce an image was already well known before the invention of the reflecting telescope.

The name "parabola" is due to Apollonius, who discovered many properties of conic sections. It means "application", referring to "application of areas" concept, that has a connection with this curve.

Where the focus–directrix property of the parabola and other conic sections is due to Pappus of Alexandria. (c. 340) an encyclopedist where 8 volumes survived.

Galileo showed that the path of a projectile follows a parabola, a consequence of uniform acceleration due to gravity.

Step-by-step explanation:

The standard equation for an ellipse, x 2 / a 2 + y2 / b 2 = 1, represents an ellipse centered at the origin and with axes lying along the coordinate axes. In general, an ellipse may be centered at any point, or have axes not parallel to the coordinate axes.

The standard for a parabola is (x - h)2 = 4p (y - k), where the focus is (h, k + p) and the directrix is y = k - p. If the parabola is rotated so that its vertex is (h,k) and its axis of symmetry is parallel to the x-axis, it has an equation of (y - k)2 = 4p (x - h), where the focus is (h + p, k) and the directrix is x = h - p.

The range of the function y = √(x +5)  is y ≥ 0

The domain of a function is the set of all possible values of x

The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.

we have

y = √(x +5)

Remember that the radicand of the function must be greater than or equal to zero

so (x +5) ≥ 0

solve for x

x ≥ -5

The domain is the interval ----> [-5,∞)

For x= -5

y = √(-5 +5) = 0

so

The range is the interval ----> [0,∞)

y ≥ 0

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Answer:

$0.60

Step-by-step explanation:

Well, to find the cost of one cookie, we have to divide 9 by 15.

9/15=.6

.6 as cents is 60 cents.

Each cookie costs 60 cents.

Hope this helped you!! Have a wonderful day ^^

Answer:

0.6 Cents per cookie

Step-by-step explanation:

If you divide the cost by 15 you'll get 0.6 Cents.

Hope this helps.

When using the graphical method in linear programming, the region that satisfies all of the constraints of the problem is called the feasible region.

The feasible region represents the set of all possible solutions that meet the given constraints of the linear programming problem. It is determined by graphing the constraints as inequalities on a coordinate plane and identifying the overlapping region where all the constraints are simultaneously satisfied. This region is bounded by the lines corresponding to the constraints and may take the form of a polygon, a line segment, or a single point, depending on the problem.

The feasible region is crucial in linear programming as the optimal solution, which maximizes or minimizes the objective function, must lie within this region. By analyzing the feasible region and evaluating the objective function at different points within it, the optimal solution can be determined.

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The simplified expression for √6x • √15x³ without a perfect square factor in the radicand is 3x√10x.

To simplify the expression √6x • √15x³ without a perfect square factor in the radicand, we can follow these steps:

Step 1: Use the product rule of square roots, which states that

√a • √b = √(a • b). Apply this rule to the given expression.

√6x • √15x³= √(6x • 15x³)

Step 2: Simplify the product inside the square root.

√(6x • 15x³) = √(90x⁴)

Step 3: Rewrite the radicand as the product of perfect square factors and a remaining factor.

√(90x⁴) = √(9 • 10 • x² • x²)

Step 4: Take the square root of the perfect square factors.

√(9 • 10 • x² • x^2) = 3x • √(10x²)

Step 5: Combine the simplified factors.

3x • √(10x²) = 3x√10x

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Answer:

4w+120.

Step-by-step explanation:

She downloads 4 songs for every week which is represented as 4w, and she started with 120 songs which is represented as +120.

Answer:

120 + 4w

Step-by-step explanation:

weeks = w

120 songs plus 4 in w weeks

120 + 4w

Answer:

Triangular prism;

Triangular base, 9 edges, 5 faces (2 triangular and 3 rectangular) and 6 vertices

Answer:

The answer is b

Step-by-step explanation:

the height of the rhombus is 12 inches

explanation: to find area you need to multiply langth times hight. 18×12=216

Answer:

h = 12 in.

Step-by-step explanation:

218 in.² ÷ 18 in.

12 in.

Answer:

Please can you repost the question the picture is not visible

Answer:

y=3x-13

Step-by-step explanation:

where do u get the 2?

Answer:

x=6 y=5

Step-by-step explanation:

use substitution because they y variable is already in the correct form for substitution

The required length of line segment JK would be 16 units.

The midpoint of a line segment is the point that divides the line segment into two equal parts. So, to find the length of the line segment JK, we can first find the coordinates of point J, which is the other endpoint of the line segment.

Let the coordinate of the point J would be (x, y)

Since the midpoint of the line segment is (2, -3), and point K is located at (-6, -3), we can use the midpoint formula to find the coordinates of point J:

2 = (x+(-6))/2 ; -3 = (y+(-3))/2

4 = x - 6 ; -6 = y -3

x = 10 ; y = -3

So the coordinate of the point J :(10, -3)

Now that we have the coordinates of both endpoints of the line segment, we can use the distance formula to find the length of the line segment:

length = √((10 - (-6))² + (-3 - (-3))²)

= √((10 + 6)² + (-3 + 3)²)

= √(16² + 0)

= √(256)

= 16

Therefore, the length of line segment JK is 16 units.

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The equation d=65t models the distance, d, that Malcolm's family travels after t hours. Malcolm's family travels 65 miles per hour faster than Theo's family.

The equation d=65t models the distance, d, that Malcolm's family travels after t hours. To calculate how much faster Malcolm's family travels than Theo's family, we must first know the speed of Theo's family. Let's say Theo's family travels at 25 miles per hour. To calculate the difference in speed between the two families, we must subtract 25 mph from 65 mph. The difference is then 40 mph, meaning Malcolm's family travels 40 mph faster than Theo's family.

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The energy diagrams of a mass in a spherical bowl can be analyzed to understand the potential energy distribution and the equilibrium points of the system.

In a spherical bowl, the gravitational potential energy is the dominant factor. As the mass moves within the bowl, its position relative to the center of the bowl determines its potential energy. The height of the mass above the bottom of the bowl corresponds to the potential energy at that point.

When analyzing the energy diagrams, several key points can be observed:

Lowest Point: The lowest point in the bowl represents the stable equilibrium position. At this point, the potential energy is at its minimum, and any slight displacement will cause the mass to move back towards the equilibrium position.

Highest Point: The highest point in the bowl represents the unstable equilibrium position. At this point, the potential energy is at its maximum, and any displacement will cause the mass to move away from the equilibrium position.

Potential Energy Curve: The energy diagram will have a curved shape, where the potential energy increases as the mass moves away from the equilibrium position. The shape of the curve will depend on the specific shape of the bowl.

Equilibrium Points: Apart from the lowest point, there may be other equilibrium points in the bowl where the potential energy is locally minimum. These points represent positions where the mass can temporarily rest without rolling down further, but they are not as stable as the lowest point.

Overall, analyzing the energy diagrams of a mass in a spherical bowl allows us to understand the equilibrium positions, potential energy distribution, and stability of the system. It provides insights into the behavior of the mass and how it will respond to external forces or disturbances.

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Answer:iqual like 12

Step-by-step explanation:xD i think :/

To determine if a high school's claim of having unusually high math SAT scores is justified, we can compare the sample mean with the population mean using a z-score.

The average math SAT score is given as 514 with a standard deviation of 113. A random sample of 60 students from the high school yielded a sample mean of 531. By calculating the z-score and comparing it to the range of usual events, we can assess the validity of the high school's claim. To determine if the high school's claim is justified, we calculate the z-score using the formula: z = (x - μ) / (σ / sqrt(n))

Where:
x is the sample mean (531),
μ is the population mean (514),
σ is the population standard deviation (113),
and n is the sample size (60).

Substituting the values into the formula: z = (531 - 514) / (113 / sqrt(60))
Calculating the z-score gives us a value. By comparing the z-score to the range of usual events, we can determine if the high school's claim is justified. The range of usual events is typically within ±2 standard deviations from the mean. If the z-score falls within this range, it suggests that the sample mean is not significantly different from the population mean, and the claim of unusually high scores may not be justified.

Please note that the provided explanation assumes a normal distribution and the use of a one-sample z-test.

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