Rewrite 1/x^-3/6 in simplest radical form. show each step of your process

Answer:

Option D is correct.

The measure of [tex]\angleWYX = 150^{\circ}[/tex]

Step-by-step explanation:

[tex]\triangle WXY[/tex] is isosceles  and [tex]\angle YWX[/tex] and [tex]\angle YXW[/tex] are base angles.

Isosceles Triangle:

A triangle with two equal sides, and two congruent base angles that means the angles are equal

By the definition, the base angles are equal i.e, [tex]m\angle YWX=m\angle YXW[/tex]

Since, YZ bisects [tex]m\angle WYX[/tex]

Angle Bisector theorem: An angle bisector is a line or ray that divides an angle into two equal angles

then, [tex]\angle WYX =2\angle XYZ[/tex] or

Substitute the value of [tex]\angle XYZ=(15x)^{\circ}[/tex] ;

[tex]\angle WYX =2(15x)^{\circ} = (30x)^{\circ}[/tex]

The sum of measures of these three angles of  triangle WXY is equal to the 180 degree.

In triangle WXY we have;

[tex]\angle YXW+\angle WYX+\angle YWX=180^{\circ}[/tex]

Substitute the value of [tex]m\angle YWX=m\angle YXW=(2x+5)^{\circ}[/tex] and [tex]\angle WYX=(30x)^{\circ}[/tex] in above formula:

[tex]2\angle YXW+30x=180^{\circ}[/tex] or

[tex]2\cdot(2x+5)+30x=180^{\circ}[/tex]

Simplify:

[tex]4x+10+30x=180^{\circ}[/tex]

Combine like terms ;

[tex]34x+10^{\circ}=180^{\circ}[/tex] or

[tex]34x=170^{\circ}[/tex]

Simplify;

[tex]x= \frac{170}{34} =5^{\circ}[/tex]

Substitute the value of x in  [tex]\angle WYX [/tex];

[tex]\angleWYX = (30x)^{\circ} = 30 \cdot 5 = 150^{\circ}[/tex]

Therefore, the measure of [tex]\angleWYX = 150^{\circ}[/tex]

Answer:

150 D

Step-by-step explanation:

The distance between the points R (-1,1) and S (-4,-5) is [tex]3\sqrt{5}[/tex] units.

To find the distance between points R(-1, 1) and S(-4, -5), we can use the distance formula in a coordinate plane.

The distance formula is given by:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Using the given coordinates:

[tex]x_1 = -1, y_1 = 1[/tex](coordinates of point R)

[tex]x_2 = -4, y_2 = -5[/tex] (coordinates of point S)

[tex]d = \sqrt{(-4 +1 )^2 + (-5 - 1)^2}[/tex]

[tex]d = \sqrt{9 +36}[/tex]

[tex]d = \sqrt{45}[/tex]

[tex]d = \sqrt{9 \times 5}[/tex]

[tex]d = 3\sqrt{5}[/tex]

Hence, the distance between the points R (-1,1) and S (-4,-5) is [tex]d = 3\sqrt{5}[/tex] units.

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Answer: D.24 - 2d

Step-by-step explanation: I took the test Hope you have a good day. PEACE

Answer:

The average rate of change of a function f(x) in the first two seconds is 25.

Step-by-step explanation:

Given : Graph , X represent the time , function f(x).

To find : the average rate of change of a function f(x) in the first two seconds is____.

Solution : The rate of change of f(x) with respect to x is the slope of the line.

slope : [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].

In first two second  ( 0, 50 ) , ( 2, 100).

slope : [tex]\frac{100-50}{2-0}[/tex].

slope : [tex]\frac{50}{2 }[/tex].

the average rate of change of a function f(x) in the first two seconds is 25.

Therefore,The average rate of change of a function f(x) in the first two seconds is 25.

Answer:

ASA  and AAS

Step-by-step explanation:

We do not know if these are right triangles; therefore we cannot use HL to prove congruence.

We do not have 2 or 3 sides marked congruent; therefore we cannot use SSS or SAS to prove congruence.

We are given that EF is parallel to HJ.  This makes EJ a transversal.  This also means that ∠HJG and ∠GEF are alternate interior angles and are therefore congruent.  We also know that ∠EGF and ∠HGJ are vertical angles and are congruent.  This gives us two angles and a non-included side, which is the AAS congruence theorem.

Since EF and HJ are parallel and EJ is a transversal, ∠JHG and ∠EFG are alternate interior angles and are congruent.  Again we have that ∠EGF and ∠HGJ are vertical angles and are congruent; this gives us two angles and an included side, which is the ASA congruence theorem.

Answer: ASA  and AAS

Step-by-step explanation:

A fair coin is flipped six times. Then 1/22  is the probability that heads occurs exactly 4 times if it is known that heads occurs at least four times

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

The probability that heads occurs exactly 6 times if it is known that heads occurs at least four times is

P{H=6|H≥4}

= P{(H=6)∩(H≥4)}/P{H≥4}

= P{H=6}/P{H≥4}      

We need to calculate P{H=6}

P{H=6} = C(6,6)(½)6

= (½)6

P{H≥4} = P{H=4} + P{H=5} + P{H=6}

= C(6,4)(½)4(½)2 + C(6,5)(½)5(½) + C(6,6)(½)6

= (½)6[C(6,4) + C(6,5) + C(6,6)]

= (½)6[15 + 6 + 1]

= (½)6(22)

Therefore,

P{H=6|H≥4} = 1/22

1/22  is the probability that heads occurs exactly 4 times if it is known that heads occurs at least four times

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To solve this problem, we simply have to use ratio and proportion.

We know that 15 gallons is consumed in 10 minutes therefore the conversion factor is:

15 gallons / 10 minutes

Therefore in 77 minutes:

water consumed = (15 gallons / 10 minutes) * 77 minutes

water consumed = 115.5 gallons

Jim answered 30 out of 35 questions correctly, which is 85.7% correct when calculated using the percentage formula.

Jim got 30 questions correct out of a total of 35. To find the percentage of questions he got correct, you can use the formula for calculating percentages: Percentage = (Number of correct answers ÷ Total number of questions) × 100%. Applying this formula to Jim's case: Percentage = (30 ÷ 35) × 100% = 0.857 × 100% = 85.7%. Therefore, Jim got 85.7% of the questions correct.

To graph the solution set of the inequality 15x + 10y ≥ 1100, find the intercepts of the graph and draw a line passing through them. Then, test a point not on the line to determine which side represents the solution set. The solution set of the inequality is the region below the line on the graph.

To graph the solution set of the inequality 15x + 10y ≥ 1100, we can start by identifying the intercepts of the graph. An intercept is a point where the graph intersects either the x-axis or the y-axis. To find the x-intercept, we set y = 0 in the inequality: 15x + 10(0) ≥ 1100. Simplifying this equation, we have 15x ≥ 1100. Dividing both sides by 15, we get x ≥ 73.33. Therefore, the x-intercept is (73.33, 0).

To find the y-intercept, we set x = 0 in the inequality: 15(0) + 10y ≥ 1100. Simplifying this equation, we have 10y ≥ 1100. Dividing both sides by 10, we get y ≥ 110. Therefore, the y-intercept is (0, 110).

After finding the intercepts, we can draw a line passing through these two points. Since the inequality is ≥, the line will be solid (including the points on the line). Finally, we determine which side of the line represents the solution set. We can choose a test point not on the line, such as (0, 0), and substitute its coordinates into the inequality. If the inequality is true, the shaded region representing the solution set should be below the line.

If the inequality is false, the shaded region should be above the line. In this case, substituting (0, 0) into the inequality gives 15(0) + 10(0) = 0, which is less than 1100. Therefore, the shaded region should be below the line. The solution set of the inequality 15x + 10y ≥ 1100 is the region below the line on the graph.

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Answer:

Combine like terms

Subtraction property of inequality

Division property of inequality

Step-by-step explanation:

We are given tnat

[tex]75x+35\geq 7(11x+9)+4[/tex]

We have to find the missing justification in given solution

[tex]75x+35\geq 7(11x+9)+4[/tex]

Reason:Given

[tex]75x+35\geq 77x+73+4[/tex]

Reason:Distributive property

[tex]75x+35\geq 77x+67[/tex]

Reason:combine ike terms

[tex]-2x+35\geq 67[/tex]

Reason:Subtraction property of order

[tex]-2x\geq 32[/tex]

Reason:Subtraction property of inequality

[tex]x\leq -16[/tex]

Reason:Division property of inequality

Answer:

The answer is C, 40

Answer:

The correct option is A= 1/8 B= 5/16 C= 7/12 D= 5/6

Step-by-step explanation:

Consider the provided fractions.

First convert each fraction into decimal form as shown:

5/6 = 0.833..

7/12 = 0.5833..

1/8 = 0.125

5/16 = 0.3125

The largest number among them is 0.833.. i.e 5/6 and the smallest number among them is 0.125 i.e 1/8

Arrange them in increasing order as shown:

0.125, 0.3125, 0.5833.., 0.833.. or 1/8, 5/16, 7/12, 5/6

Now consider the provided figure. The alphabets are showing the number are in increasing order

Thus, the correct option is A= 1/8 B= 5/16 C= 7/12 D= 5/6

the average value of f(x) = 1/x over the interval [e, 2e] is, ln(2)/e.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

f(x) = 1/x over the interval [e, 2e].

i.e. we get,

[tex]\frac{1}{2e-e}[/tex] × [tex]\int\limits^{2e}_e {1/x} \, dx[/tex] =1/e. ln (x)[2e, e]

                        =ln(2e)/e - ln(e)/e

                        =[ln2+lne/e] - 1/e

                        =ln2/e +1/e -1/e

                        =ln(2)/e

hence,  the average value of f(x) = 1/x over the interval [e, 2e] is, ln(2)/e.

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The height of the rain barrel is required.

The height of the barrel is 2.39 feet.

r = Radius of barrel = 2 feet

V = Volume of barrel = 30 cubic feet

h = Height of barrel

Since, the barrel is cylindrical the volume of the barrel is

[tex]V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{30}{3.14\times 2^2}\\\Rightarrow h=2.3885\approx 2.39\ \text{feet}[/tex]

The height of the barrel is 2.39 feet.

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Answer:

the correct answer is B.-2/3

The ages of James, Paul and Dan is required.

James is 30 years old, Paul is 80 years old and Dan is 10 years old.

Let the ages of James be [tex]j[/tex], Paul be [tex]p[/tex] and Dan be [tex]j[/tex].

James is three times the age of Dan

[tex]j=3d[/tex]

Paul is two times the sum of the ages of James and Dan

[tex]p=2(j+d)\\\Rightarrow p=2(3d+d)\\\Rightarrow p=2(4d)=8d[/tex]

The combined ages of the people is 120

[tex]j+p+d=3d+8d+d\\\Rightarrow 120=12d\\\Rightarrow d=\dfrac{120}{12}\\\Rightarrow d=10[/tex]

[tex]j=3d=3\times 10\\\Rightarrow j=30[/tex]

[tex]p=8d=8\times 10\\\Rightarrow p=80[/tex]

So, James is 30 years old, Paul is 80 years old and Dan is 10 years old.

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Answer:

226.08

Step-by-step explanation: