Laura is making a small sign in the shape of a triangle for her store. She wants the height of the triangle to be 4 inches. The area of the sign must be less than 14 square inches. (Laura doesn't want to buy more material.) Write an inequality that describes the possible base lengths (in inches) of the triangle.

Answer:

(0,-2)

Step-by-step explanation:

the answer is (0,-2) because -2 is where the line crosses over the y-axis. If we looked at a graph you would see that the line goes over 0 on the X-axis, which causes the line to touch the y-axis and intercept it at the -2 mark.

An easy way to find the answer for these sorts of questions is to draw out a graph and mark the coordinates on it and draw the line conecting them. Once you've done that you can easily see where the line intercepts on both the y and x axis.

Answer:

(0,-2)

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Answer: search it up

Step-by-step explanation:

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

Work Shown:

\(y = \frac{4x+30}{x+5}\\\\y = \frac{4x+20+10}{x+5}\\\\y = \frac{(4x+20)+10}{x+5}\\\\y = \frac{4(x+5)+10}{x+5}\\\\y = \frac{4(x+5)}{x+5}+\frac{10}{x+5}\\\\y = 4+\frac{10}{x+5}\\\\\)

Therefore, a = 10

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As an alternative approach, we could work in reverse like this:

\(y = 4+\frac{a}{x+5}\\\\y = 4*\frac{x+5}{x+5}+\frac{a}{x+5}\\\\y = \frac{4(x+5)}{x+5}+\frac{a}{x+5}\\\\y = \frac{4(x+5)+a}{x+5}\\\\y = \frac{4x+20+a}{x+5}\\\\\)

Then notice that the 20+a must be 30, so solving 20+a = 30 leads to a = 10

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As yet another alternative approach (well I suppose it's actually 2 extra approaches) we could use either polynomial long division or synthetic division. Either way, you should end up with a remainder of 10, which corresponds directly to a = 10

Answer:

x = -1

Step-by-step explanation:

The vertex is halfway between the focus and the directrix.

So here the directrix is  a vertical line  to the left of the vertex and passing through the point (2-3, 9) = (-1, 9)

It is x = -1.

The statements that are  true about this study are

This is further explained below.

Generally, a scientific technique is used to create a discovery, test a theory or show an established truth.

In conclusion, The following are accurate claims concerning this study:

Random sampling is used in this investigation. In this investigation, a control group is used. Repeated measurements are employed in this investigation.

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(a) The magnitude E is 1.04×10⁶ N/C.

(b) The direction of the electric field is radially inward since the net charge inside the shell is negative.

(c) The E direction is Q1 = 3.40×10⁻¹² C.

(d) The direction of the electric field is radially outward since the net charge inside the shell is positive.

(e) The interior surface of the shell is Q1 = 3.40×10⁻¹² C.

(f) The exterior surface of the shell is Q2 = 6.80×10⁻¹² C.

(a) The magnitude of the electric field at radial distance r from the axis of a thin-walled coaxial conducting cylindrical shell carrying a net charge Q is given by E = Q / (2πε₀r), where ε₀ is the permittivity of free space. For r = 2.00R₂, the net charge Q is Q₁ + Q₂ = (3.40×10⁻¹² C) - 2(3.40×10⁻¹² C) = -3.40×10⁻¹² C, and thus the electric field is E = |-3.40×10⁻¹² C / (2πε₀(2.00R₂))| = 1.04×10⁶ N/C.

(b) The direction of the electric field is radially inward since the net charge inside the shell is negative.

(c) For r = 5.00R₁, the net charge inside the shell is only Q1 = 3.40×10⁻¹²C, so the electric field is E = |3.40×10⁻¹² C / (2πε₀(5.00R₁))| = 1.23×10⁶ N/C.

(d) The direction of the electric field is gradually outward since the net charge inside the shell is positive.

(e) The charge on the interior facial of the shell is equal in magnitude and opposite in sign to the net charge inside the shell, which is Q1 = 3.40×10⁻¹² C.

(f) The charge on the exterior facial of the shell is equal in magnitude and opposite in sign to the net charge outside the shell, which is -Q2 = 2(3.40×10⁻¹² C) = 6.80×10⁻¹² C.

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Answer: * The third side of a triangle when we know two sides and angle between them.* The angles of a triangle when we know all three sides.It can be either of these forms;Given triangle ABC is right angle triangle.Law of cosines for this triangle is,since, ,  and .then,

Step-by-step explanation:

An approximate 95% confidence interval for the difference in the mean tooth damage is  (6.41 - 5.20) ± 2.26\(\sqrt{\frac{25}{10}+\frac{225}{15} }\)

For sweetened samples

The value of n = 10

The mean of the samples = 6.14

The standard deviation of the sample = 5.0

For unsweetened samples

The value of n = 15

The mean of  the sample = 5.20

The standard deviation of the sample = 15.0

We have to assume that necessary conditions for inference are met

The confidence interval = 95%

The equation will be

(6.41 - 5.20) ± 2.26\(\sqrt{\frac{25}{10}+\frac{225}{15} }\)

Therefore, the difference in the mean tooth damage is (6.41 - 5.20) ± 2.26\(\sqrt{\frac{25}{10}+\frac{225}{15} }\)

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Flight attendants for one carrier must be between 63 and 73 inches tall. The absolute value equations from the list below can be used to express these minimum and maximum heights is |x+68|<5.

Given that,

Flight attendants for one carrier must be between 63 and 73 inches tall.

We have to find what absolute value equations from the list below can be used to express these minimum and maximum heights.

In algebra, an absolute value function is a function where the variable is inside the bars denoting absolute values. The absolute value function is also known as the modulus function, and its most popular representation is function of x = |x|, where x is a real number. The absolute value function is typically written as function of x = a |x - h| + k, where a denotes the vertical stretch of the graph, h denotes the horizontal shift, and k denotes the vertical shift from the graph of function of x = |x|.

Therefore, The absolute value equations from the list below can be used to express these minimum and maximum heights is |x+68|<5.

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Answer:

I hope this helps you...

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To solve the given differential equation using Laplace transformation, we'll follow these steps:

Step 1: Apply the Laplace transformation to both sides of the equation.

Taking the Laplace transform of the equation, we have:

L{du(t)/dt} + 2L{dy(t)/dt} + 17L{y(t)} = -10L{dt/dt}

Using the properties of the Laplace transform, we get:

sU(s) - u(0) + 2sY(s) - y(0) + 17Y(s) = -10/s

Step 2: Apply the initial conditions.

Since we have the initial condition dy(0)/dt = 0, and y(0) = 0, we can substitute these values into the equation:

sU(s) - u(0) + 2sY(s) - 0 + 17Y(s) = -10/s

sU(s) + 2sY(s) + 17Y(s) = -10/s

Step 3: Solve for Y(s).

Rearranging the equation to isolate Y(s), we have:

Y(s)(2s + 17) = -10/s - sU(s)

Y(s) = (-10 - sU(s))/s(2s + 17)

Step 4: Take the inverse Laplace transform.

To find the solution y(t), we need to take the inverse Laplace transform of Y(s). However, the given u(t) = e is not in Laplace transform form. Please provide the correct Laplace transform expression for u(t) so that we can proceed with finding the inverse Laplace transform and the solution to the differential equation.

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There are 64 cups in 8 gallons.

To find the number of cups in 8 gallons, you can use the conversion rate of 8 cups per gallon. This means that the formula to find the number of cups in 8 gallons is:

Cups = 8 x Gallons

Thus, the calculation to find the number of cups in 8 gallons is:

Cups = 8 x 8

Cups = 64

Therefore, there are 64 cups in 8 gallons. This calculation shows that for every gallon, there are 8 cups. To find the number of cups in any number of gallons, you can multiply the number of gallons by 8. This calculation can be seen in the formula:

Cups = 8 x Gallons

By using this formula, you can easily find the number of cups in any number of gallons.

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Answer:

Step-by-step explanation:

25, i think

Step-by-step explanation:

If they are similar, then 10 is to 3      as  x is to 15

10/3 = x/15    multiply both sides by 15

 50 mm = x

Answer:

It takes 20/9 hours for both pumps to completely drain the pool.

Step-by-step explanation:

The rate of the first pump is emptying 1/4 of the pool in an hour.

The rate of the second pump is emptying 1/5 of the pool in an hour

The combined rate of these two per hour is

1/4 + 1/5 = 9/20

The time taken to completely drain the pool is 1 (the whole pool) divided by the combined rate. So:

9/20x = 1

x = 1/ ⁹⁄₂₀

x = 20/9

It takes 20/9 hours for both pumps to completely drain the pool.

Put this into the calculator to round to the nearest tenth.

Answer:

1=x

Step-by-step explanation

Add 14 to both side(because it is opposite)

-6=8x-14

+14       +14

8=8x

Divide both sides by 8

8/8=8x/8

1=1x(or just 1=x)

The answer will be X=1.

The angle measure from the ruler in this problem is given as follows:

63º.

The angle measure in the context of this problem is obtained using the ruler, which gives an angle measure between 0º and 180º, according to the arrow of the ruler.

The ruler is positioned between 60 and 70, three dots of the way, hence we apply the proportion to obtain the angle measure as follows:

60 + 3/10(70 - 60) = 63º.

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(a) The equation of a line perpendicular to the plane x - y + 2z = 3 can be written as x = x0 - t, y = y0 - 2t, and z = z0 - t, where (x0, y0, z0) is a point on the line and t is a parameter.

(b) The equation of a line parallel to the plane x - y + 2z = 3 can be expressed as x = x0 + 2t, y = y0 - 2t, and z = z0 + 4t, where (x0, y0, z0) is a point on the line and t is a parameter.

(a) To find a line perpendicular to the plane x−y+2z=3x−y+2z=3, we need to determine the normal vector of the plane. The coefficients of xx, yy, and zz in the plane equation represent the components of the normal vector. In this case, the normal vector is (1,−1,2)(1,−1,2).

A line perpendicular to the plane can be represented by a direction vector that is orthogonal (perpendicular) to the normal vector. We can choose any vector that is orthogonal to (1,−1,2)(1,−1,2), such as (−1,−2,−1)(−1,−2,−1).

To find the equation of the line, we also need a point on the line. Let's say the line passes through the point (x0,y0,z0)(x0​,y0​,z0​).

The equation of the line perpendicular to the plane x−y+2z=3x−y+2z=3 can be written as:

x=x0−tx=x0​−t

y=y0−2ty=y0​−2t

z=z0−tz=z0​−t

where tt is a parameter.

(b) To find a line parallel to the plane x−y+2z=3x−y+2z=3, we can use the same approach as in part (a) to find the normal vector of the plane, which is (1,−1,2)(1,−1,2).

A line parallel to the plane will have a direction vector that is also parallel to the normal vector. We can choose any vector that is parallel to (1,−1,2)(1,−1,2), such as (2,−2,4)(2,−2,4).

To write the equation of the line, we still need a point on the line. Let's assume the line passes through the point (x0,y0,z0)(x0​,y0​,z0​).

The equation of the line parallel to the plane x−y+2z=3x−y+2z=3 can be expressed as:

x=x0+2tx=x0​+2t

y=y0−2ty=y0​−2t

z=z0+4tz=z0​+4t

where tt is a parameter.

In both cases, the parameter tt allows us to generate different points on the line by varying its value.

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The perimeter of this rectangle with the given vertices is equal to 18 units.

The area of this rectangle with the given vertices is equal to 20 square units.

Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;

P = 2(L + W)

Where:

For the width, we would determine the distance between the vertices (-2, 2) and (3, 2)

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(3 - (-2))² + (2 - 2)²]

Distance = √[(5² + 0²]

Distance = √25

Distance = 5 units.

For the length, we have:

Length = 4 units.

Perimeter of this rectangle, P = 2(5 + 4)

Perimeter of this rectangle, P = 18 units.

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

A = 4 × 5

A = 20 square units.

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In general, higher confidence levels provide wider confidence intervals.

What is the concept of confidence level and confidence interval?

Confidence level:

The confidence level refers to the long term success rate of the method , that is , how often this type of interval will capture the parameter of interest.

Confidence interval:

A specific confidence interval gives a range of plausible values for the parameter of interest.

As the confidence level increases, the width of confidence interval also increases.

A larger confidence level increases the chance that the correct value will be found in the confidence interval. This means the interval is larger.

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Answer:

232.74

Step-by-step explanation:

We can do $215 times 1.0825 to find the cost. This gets us 232.74 rounded up.

Answer:

The answer is 2.6801 x 10^4

So the total cost of tying the lace around the tablecloth is $18.36.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

The length of the boundary of the square table cloth is 4 times its side length, so the length of the boundary is 4 * 54 cm = 216 cm.

To convert the length from centimeters to meters, we divide by 100:

216 cm / 100 = 2.16 meters

Finally, to find the cost of sticking the lace around the table cloth, we multiply the length of the lace by the cost per meter:

2.16 meters * ₹8.5 per meter = ₹18.36

So the cost of sticking the lace around the table cloth is ₹18.36.

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Answer:

41

Step-by-step explanation:

If x equals 3:

13x3 is 39

39+2 is 41

Answer: the answe is not at all close to the actual Nobel rate.

Step-by-step explanation:

The gallons of gas required by Ryan to travel 286 miles is 13.2 gallons.

As the stated question;

Total gallon of gas used to drive the 260 miles = 12 gallons

Let 'x' be the gallon of gas used to drive the 286 miles.

Then, bu using the proportion

12 / 260 = x / 286

Thus,

x = 286 x 12 / 260

x = 13.2 gallons

Thus, the amount of gas required by Ryan to travel 286 miles is 13.2 gallons.

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Answer:

Theres no question here so....yeah

Step-by-step explanation: