The quotient of a number and 4​, minus 1​, equals 5/4. find the number

The measure of an interior angle of the regular polygon is 156 degrees and the polygon has 15 sides.

In a regular polygon, the measure of an exterior angle is equal to 360 degrees divided by the number of sides of the polygon. In this case, the measure of the exterior angle is given as 24 degrees. So we can set up the equation:

24 = 360 / n

Where n is the number of sides. Cross multiplying, we get:

n = 360 / 24 = 15

So the polygon has 15 sides. To find the measure of an interior angle, we can use the formula:

Interior Angle = 180 - Exterior Angle

Interior Angle = 180 - 24 = 156 degrees

The correct dependent variable in this experiment is the Length of wax after 10 minutes.

In the context of an experiment, the dependent variable is the variable that is being measured or tested in the experiment. It is the outcome that the experimenters are interested in observing to determine the effect of the independent variable.

 In this case, the students are investigating the thermal conductivity of copper and steel wires by observing how much wax melts over a fixed period of time when the wires are heated. The independent variable is the type of wire used (copper or steel), as this is what the students are changing to see its effect on the dependent variable.

The dependent variable is the length of wax remaining after 10 minutes because this measurement is expected to change based on the thermal conductivity of the wire. The better the thermal conductor, the more heat will be transferred along the wire, and the more wax will melt. Since the students are measuring how much wax has melted (by subtracting the length of wax after 10 minutes from the original length), this is the dependent variable.

The original length of wire and the original length of wax are control variables; they are kept constant to ensure that any differences in the dependent variable are due to the independent variable (the type of wire) and not due to other factors. The thermal conductivity of the wire is a property being indirectly measured through the observation of the dependent variable. It is not directly measured and thus is not the dependent variable.

Answer:

(C)

Step-by-step explanation:

It is given that a right triangle, ACB which is right angled at C has BC = 24 inches, and AB = 25 inches.

We know that m∠C=90°,

Using the trigonometry in ΔACB, we have

[tex]sinB=\frac{AC}{AB}[/tex]

Substituting the given values, we get

⇒[tex]sinB=\frac{24}{25}[/tex]

⇒[tex]B=sin^{-1}(0.96)[/tex]

⇒[tex]B=73.7^{\circ}[/tex]

Also, [tex]sinA=\frac{CB}{AB}[/tex]

Substituting the given values, we get

⇒[tex]sinA=\frac{7}{25}[/tex]

⇒[tex]A=sin^{-1}(0.28)[/tex]

⇒[tex]A=16.3^{\circ}[/tex]

Therefore, the measure of the angles in triangle ABC are  m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90°.

Thus, option C is correct.

The answer (APEX) is: "7 units."

The number will be greater than 54 such that a negative one-sixth of a number is less than -9.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

A mathematical phrase in which the sides are not equal is referred to as being unequal.

Inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

Let's suppose that number is x

Then,

negative one-sixth of x

-(1/6)x is less than -9

-(1/6)x < -9

-x < -54

Multiplying by - will change the sign of inequality

So,

x > 54

Hence "The number will be greater than 54 such that a negative one-sixth of a number is less than -9".

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The average rate of change of the function will be -93.75.

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

Given that the interval from x = 0 to x = 2 and the function is [tex]f(x)=250(0.5)^x[/tex].

Calculate the value of the function at x = 0 and x = 2

[tex]f(x)=250(0.5)^x[/tex].

[tex]f(0)=250(0.5)^0=250\\f(0)=250(0.5)^2=62.5[/tex].

The average rate of change will be calculated as,

Rate of change = ( 62.5 - 250 ) ( 2 - 0)

Rate of change = -93.75

Therefore, the average rate of change of the function will be -93.75.

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The equation that describes Emily's robot's movement is y = -mx + c where 'm' is the number of steps per second the robot climbs down, and 'c' is the initial number of steps. The equation would be negative because the number of steps decreases over time.

In the given context, Emily's robot is being tested for its ability to climb down steps. As it performs this task, the number of steps it needs to climb down decreases over time. This relationship could be described by a linear equation. If every second the robot climbs down a fixed number of steps, this would translate to a constant rate of change or slope in the graph. Therefore, the equation would be of the form y = mx + c, where 'm' is the slope (representing the number of steps per second the robot climbs down) and 'c' is the y-intercept (representing the initial number of steps).

For instance, if the robot climbs down 1 step per second, and we started with 10 steps, the equation would be y = -x + 10 (negative because the number of steps is decreasing).

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Okay, well we start out with the equation P=66, where P is perimeter. You should create equations using variables to explain each piece of information you are given. Follow the equations below and see if you can understand how to do another one like this. In this problem, l is length and w is width.

P = 66                               The perimeter is equal to 66

l = 3 + w                           The length of one side is 3 more than the width

2l + 2w = 66                      A rectangle's perimeter is calculated by adding the lengths and widths

2(3 + w) + 2w = 66           Use what you know about length from step 2 to replace the variable in step 3

6 + 2w + 2w = 66              Multiply

6 + 4w = 66                       Add like terms

4w = 60                            Subtract

w = 15                             Divide

l = 3 + w                         Remember step 2?

l = 3 + 15                       Replace the variable using your value for w

l = 18                             Add

And you're done! Always check your work. It helps to create a picture of a rectangle while you're doing these problems as well. As you get used to these problems more and more, you can show more or less work than I've shown, but try to stay true to what the teacher asks of you. Good luck!

Answer:

Answer B is correct

Answer:

P represents the population in year 0

Step-by-step explanation:

Assuming there are 4 walls

6/4 = 1.5 rolls per wall

Answer:

A

Step-by-step explanation:

Answer

39.8°

Explanation

To solve this we can use the trigonometric ratio tangent.

tan x = opposite / adjacent

           = 10/12

           = 0.8333...

x = tan⁻¹(0.8333..)

  = 39.8°

The best approximation for the measure of angle XYZ in the given triangle is 39.8 degrees.

To solve this we can use the trigonometric ratio tangent.

tan x = opposite side / adjacent side

We have given the,

Opposite side=10in

Adjacent side=12in

use this value in the gven formula

Therefore we get,

                tanx    = 10/12

                tanx  = 0.8333...

x = tan⁻¹(0.8333..)

x  = 39.8°

Therefore, The best approximation for the measure of angle XYZ is 39.8 degrees.

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Answer:

A. p=6.25h

because

6.25 (2) = p 12.50

6.25 (4) = p 25.00

6.25 (6) = p 37.50

6.25 (8) = p 50.00

Final answer:

The area of triangle ΔABC with m∠A = 120°, side b = 13 cm, and side c = 15 cm, when calculated using the formula for area ½ bc sin A, is approximately 84.2 cm² when rounded to the nearest tenth.

Explanation:

To find the area of triangle ΔABC with m∠A = 120°, side b = 13 cm, and side c = 15 cm, we will use the formula for the area of a triangle when two sides and the included angle are known:

Area = ½ bc sin A

First, we need to find the sine of angle A, which is sin(120°). Using a calculator, we find that sin(120°) ≈ 0.866. Now, we can plug in the values into the area formula:

Area = ½ × 13 cm × 15 cm × sin(120°)

Area = ½ × 13 cm × 15 cm × 0.866

Area ≈ ½ × 13 cm × 15 cm × 0.866 ≈ 84.225 cm²

Rounding to the nearest tenth, the area is approximately 84.2 cm².

Answer: positive

Step-by-step explanation:

The slope of a line is given by:-

[tex]m=\dfrac{\text{rise}}{\text{run}}[/tex]

From the given picture, it can be seen that the rise in the line l is positive since the change in the y coordinates increases as we from left to right.

Similarly we can see that  the run in the line l is positive since the change in the x coordinates increases as we from left to right.

By using above formula, the slope of line m is positive.

Final answer:

After solving the original equation 2/3(6x+12)=-24, we find x = -8. Comparing this solution with the provided equations, the ones that have the same value for x are 9x+18=-24, 18x+36/2=-24, and x=-8.

Explanation:

To find which equations have the same value for x as 2/3(6x+12)=-24, we must first solve the original equation to find the value of x it yields:

2/3(6x+12) = -24
Multiply both sides by 3/2 to eliminate the fraction:
6x + 12 = -24 * (3/2)
6x + 12 = -36
Subtract 12 from both sides:
6x = -48
Divide by 6:
x = -8

Now we will compare this solution with the other equations:

Therefore, the equations that have the same value of x as the original equation are 9x+18=-24, 18x+36/2=-24, and x=-8.

Final answer:

To measure 1 liter, one could fill a 500 mL cup twice, or fill a 300 mL cup once, a 500 mL cup once, and a 100 mL cup twice, summing to a total of 1,000 mL which equals 1 liter.

Explanation:

To measure exactly 1 liter using cups of 100 mL, 300 mL, and 500 mL, we can use two different methods. It's important to note that 1 liter (L) equals 1,000 milliliters (mL). Here are the steps for each method:

Method 1:

Fill the 500 mL cup twice and pour the contents into another container. (500 mL + 500 mL = 1,000 mL)

This gives you exactly 1 liter, since 1,000 milliliters is equivalent to 1 liter.

Method 2:

First, fill the 300 mL cup and pour it into an empty container.

Then, fill the 500 mL cup and add it to the same container. (300 mL + 500 mL = 800 mL)

Lastly, fill the 200 mL remaining by using the 100 mL cup twice. (100 mL + 100 mL = 200 mL)

Combining all the measurements gives you 1,000 mL, which is exactly 1 liter. (800 mL + 200 mL = 1,000 mL)

The equation relating the total cost with the number of hours will be c = 2.25h + 5.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have North parking garage where it costs $5 to bring your car into the garage plus $2.25 for every hour the car is parked.

Assume that [h] represents the number of hours the car was parked and [c] represents the total cost. Then, we can write the equation relating the total cost with the number of hours will be -

c = 2.25h + 5

Therefore, the equation relating the total cost with the number of hours will be c = 2.25h + 5.

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[The complete question is -

At the North parking garage it costs $5 to bring your car into the garage plus $2.25 for every hour the car is parked. If h, represents the number of hours the car was parked and c, represents the total cost, which equation would model this situation?]