I’m stuck on these 3 questions help

Answer:

  ∠2 = 60°

Step-by-step explanation:

You want the measure of angle 2, where angles 1 and 2 form a linear pair and are marked ∠1 = 5x-5, and ∠2 = 2x+10. You are shown that x=25 and angle 1 is 120°.

There are two ways you can find the measure of angle 2.

1. Use the fact that angle 2 is supplementary to angle 1, which is given as 120°.

  ∠2 = 180° -∠1 = 180° -120°

  ∠2 = 60°

2. Use the expression in x to find angle 2, since you know the value of x.

  ∠2 = 2x +10 = 2(25) +10 = 50 +10

  ∠2 = 60°

__

Additional comment

It looks like you have figured out how to find x. You use the fact that the total of the two angle measures of a linear pair of angles is 180°.

  (5x -5) +(2x +10) = 180

  7x = 175 . . . . . . subtract 5

  x = 25 . . . . . . . divide by 7

The shaded area of the diagram is 23 square inches when side of large square is 6 inches.

What is square ?

A square is a geometrical shape that has four sides of equal length and four angles of 90 degrees each. It is a two-dimensional polygon with four vertices or corners. The area of a square can be calculated by multiplying the length of one of its sides by itself (i.e., squaring it) using the formula

[tex]A = s^2[/tex] , where A is the area and s is the length of one side of the square.

To calculate the shaded area, we need to subtract the area of the two small squares from the area of the large square and then subtract the area of the unshaded region (which is the area of the two overlapping squares).

The area of the large square is:

[tex]$(6\text{ in})^2 = 36\text{ in}^2$[/tex]

The area of the two small squares is:

[tex]$(2\text{ in})^2 + (3\text{ in})^2 = 4\text{ in}^2 + 9\text{ in}^2 = 13\text{ in}^2$[/tex]

Therefore, the expression for the shaded area is:

[tex]$36\text{ in}^2 - 13\text{ in}^2[/tex]

Simplifying this expression, we get:

[tex]$23\text{ in}^2$[/tex]

Therefore, the shaded area of the diagram is 23 square inches.

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The interest earned and the balance of the account are given as follows:

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which the parameters are listed as follows:

Considering that she uses Financial Life Inc., the parameters are given as follows:

A = 850, r = 0.029, n = 12, t = 5.

Hence the balance of the account is given as follows:

A(5) = 850 x (1 + 0.029/12)^60

A(5) = $982.46.

The interest earned is given as follows:

982.46 - 850 = $132.46.

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The simplest form of 4/81x^85 is 3x^2(√1)/75.

Option A is correct.

How do we write an expression on its simplest form?

In order to reduce an algebraic expression to its simplest form, we need to reduce or simplify an expression as much as feasible by carrying out any suggested processes in order to write it in its simplest form.

During the process, we should factor, combine like words, eliminate common factors, and simplify any fractions or radicals.

In conclusion, the simplest form of the expression 4/81x^85 is  written as 3x^2(√1)/75.

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Answer:

Step-by-step explanation:

Using the Pythagorean Theorem, we can find the length of the hypotenuse.

a² + b² = c²

6² + 8² = c²

36 + 64 = c²

100 = c²

√100 = c

10 = c

Answer: 10 units

Step-by-step explanation:

To find the hypotenuse of a triangle, use the Pythagorean Theorem (A² + B² = C²).

In this equation, A is 6, B is 8, and C is x, or the hypotenuse.

1. 6² + 8² = x²

2. 36 + 64 = x²

3. 100 = x²

4. √100 = √x²

(Taking the square root of both sides, cancelling out x²)

5. 10 = x

Answer:

204 inches

Step-by-step explanation:

17ft * 12inches/ft = 204inches

Answer:204

Step-by-step explanation:

17ft = to 204 inches

Answer:

The margin of error in a confidence interval depends on the sample size, the standard deviation of the population (which is not given in the problem), and the level of confidence. Since the standard deviation is not given, we cannot calculate the margin of error exactly. However, we can estimate the margin of error using a standard deviation of 1 (which is a common assumption) and a level of confidence of 95%, which corresponds to a z-score of 1.96.

The formula for the margin of error for a 95% confidence interval is:

Margin of error = z * (standard deviation / sqrt(sample size))

Assuming a standard deviation of 1 and a sample size of 1 (since we are talking about the average time of a single child), we get:

Margin of error = 1.96 * (1 / sqrt(1)) ≈ 1.96

Therefore, we can estimate the margin of error in the report to be around 1.96 minutes. This means that the true average time a 10-year-old American child spends playing outdoors per day is likely to be within 1.96 minutes of the reported average, with a 95% level of confidence.

Step-by-step explanation:

The change in price can be expressed using any of 6/5, 1.2 and 120%

Given that

12.5x = 15

This means that the increment factor in the price is x

We have

12.5x = 15

The value of x is

x = 15/12.5

Evaluate

x = 1.2 as decimal

As fraction, we have

x = 6/5

As percentage, we have

x = 120%

See attachment for the description of the figure

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The height of the ladder is given as follows:

h = 13.7 ft.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

We have that the height of the ladder is the hypotenuse, while a side length of 13 is opposite to an angle of 72º, hence the sine is applied to find the height as follows:

sin(72º) = 13/h

h = 13/sine of 72 degrees

h = 13.7 ft.

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Note that the graph of the solution presented by Randy and Angela  will be given as a straight line graph as attached. The solution is x ≥ 6.

Let's take a step by step approach.

-3x + 18 ≤ 0

Subtracting 18 from both sides, we have:

-3x + 18 -18 ≤ 0 -18

-3x ≤ -18

To find x , we must divide both sides by -3

x ≤ 6

Hence, the solution of the inequality by Randy and Angela is x ≤ 6. See this in the attached Line Graph.

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The value of dy/dx is -2 at the given points.

We need to find dy/dx at the point (1/2,2) for the equation [tex]ln(xy) + y^2 = 4[/tex].

First, we can take the partial derivative of both sides of the equation with respect to x, treating y as a constant:

[tex]d/dx [ln(xy) + y^2] = d/dx [4][/tex]

Using the chain rule on the first term, we get:

[tex](1/xy) * y * dy/dx + 2y * dy/dx = 0[/tex]

Simplifying the expression:

[tex]dy/dx = -(2y)/(y + x(ln(xy)))[/tex]

Now we can plug in the values x = 1/2 and y = 2:

dy/dx = -(2(2))/(2 + 1/2(ln(1/2*2)))

dy/dx = -(4)/(2 + ln(1))

dy/dx = -4/2

dy/dx = -2

Therefore, the value of dy/dx at the point (1/2,2) is -2.

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Step-by-step explanation:

150 ml   /   ( 2 hr) = 75 ml/hr

Approximately 32.3% of the students in the School of Rock play bass.

We must determine both the total number of students enrolled in the school and the number of students who play bass in order to determine the percentage of students who play the instrument.

We can see that there are 13 students in the sixth grade, seven students in the seventh grade, and eleven students in the eighth grade from the table. As a result, the School of Rock currently has a total of:

13 + 7 + 11 = 31

To find the number of students who play bass, we look at the second column of the table and see that there are 10 students who play bass.

So the percentage of students who play bass is:

(10/31) x 100% ≈ 32.3%

Rounding to the nearest tenth of a percent gives us:

32.3% ≈ 32.3%

Therefore, approximately 32.3% of the students in the School of Rock play bass.

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I think

Step-by-step explanation:

in order to find x and y we use pythagorus theorem ok

Answer:

Step-by-step explanation:

This is a 30-60-90

Short leg is x because that is across 30 which is x

long leg is y which is x√3

and hypotenuse is 2x

S to find x

2x=[tex]\frac{4\sqrt{3} }{3}[/tex]

x = [tex]\frac{2\sqrt{3} }{3}[/tex]

y=[tex]\frac{2\sqrt{3} }{3}[/tex] *[tex]\sqrt{3}[/tex]

y=2*3/3

y=2

you can also use pythagorean if you don't remember the rules for 30-60-90.  I can show you how and edit this if you want more, mention in comments

The unknown angles of the similar triangle are as follows:

m∠W =  55°

m∠X = 90°

m∠Y = 35°

Similar triangles are triangles that have the same shape, but their sizes may vary.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Therefore, the corresponding angles of the triangles are congruent.

Hence, the triangle is assume to be drawn accurately.

Therefore,

m∠W = m∠D

m∠X = m∠E

m∠Y = m∠C  

Therefore,

m∠W = 180 - 90 - 35 = 55 degrees

m∠X = 90 degrees

m∠Y = 35 degrees

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Answer:

48 = 1/2 * b * (b - 4)

b

Step-by-step explanation:

According to the problem, the height of the triangle is 4m less than the base. We can express this mathematically as:

height = b - 4

The area of a triangle is given by the formula:

area = 1/2 * base * height

Substituting the given values, we get:

48 = 1/2 * b * (b - 4)

Simplifying the equation:

96 = b^2 - 4b

Rearranging and setting the equation equal to zero:

b^2 - 4b - 96 = 0

We can solve for b using the quadratic formula:

b = (-(-4) ± sqrt((-4)^2 - 4(1)(-96))) / (2(1))

b = (4 ± sqrt(16 + 384)) / 2

b = (4 ± 20) / 2

We take the positive root since the base of a triangle cannot be negative:

b = (4 + 20) / 2

b = 12

Therefore, the length of the base is 12 meters.

but in the question above is b

Answer:

Step-by-step explanation:

To show that the points A(-1,-3), B(6, 1), and C(2,-5) form the vertices of a right angle triangle, we need to show that one of the angles of the triangle is a right angle, i.e., it measures 90 degrees.

We can use the Pythagorean theorem to check if the triangle is a right triangle. According to the Pythagorean theorem, the square of the length of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the lengths of the other two sides.

First, let's calculate the lengths of the sides of the triangle:

AB = sqrt((6 - (-1))^2 + (1 - (-3))^2) = sqrt(49 + 16) = sqrt(65)

BC = sqrt((2 - 6)^2 + (-5 - 1)^2) = sqrt(16 + 36) = sqrt(52)

AC = sqrt((2 - (-1))^2 + (-5 - (-3))^2) = sqrt(9 + 4) = sqrt(13)

Next, let's check if the Pythagorean theorem holds true for this triangle:

If AB is the hypotenuse:

AB^2 = 65

BC^2 + AC^2 = 52 + 13 = 65

Since AB^2 = BC^2 + AC^2, we can conclude that angle BAC is a right angle.

Therefore, the points A(-1,-3), B(6, 1), and C(2,-5) form the vertices of a right angle triangle, with angle BAC measuring 90 degrees.

Answer: no

Step-by-step explanation:

no it cannot be simplified

3 cannot be divided into both 5's and the √3 is already simplifed

The total volume of the party hat shaped cone is V = 39.3 inches³

Given data ,

Let the diameter of the party shaped cone be d = 5 inches

So , the radius of the cone r = 2.5 inches

Now , the height of the hat = 6 inches

And , Volume of Cone = ( 1/3 ) πr²h

V = ( 1/3 ) ( 3.14 ) ( 2.5 )² ( 6 )

V = ( 1/3 ) ( 117.75 )

V = 39.3 inches³

Hence , the volume of cone is V = 39.3 inches³

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Answer:

Step-by-step explanation:

P=10.1

A=3.08

P=4.7+3.2+2.2 =10.1

A=1/2 b h = 1/2 (2.2)(2.8)

The graph C represents the image of the triangle PQR, after a translation of 2 units right and a reflection across the line x = 1

A translation in math moves a shape left or right or up or down.

The graph C represents the image of the triangle PQR

After a translation of 2 units right and a reflection across the line x = 1

Because if you move the triangle two to the right then X=1

X=1 means the line is up and down going thought x=1

and if that line you make you reflect across it would be C

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Answer:
x = 4.2071

​x = 3.1464

Step-by-step explanation:

(x-7/2)^2+(x-7/2)^2=1

x^2 - 7x + 49/4 + x^2 - 7x + 49/4 = 1

2x^2 - 14x + 49/2 = 0

x = −(−14) ± (√(−14) − (4×2×(47/2)) / 2 x 2

x = 14 ± 2.8284 / 4

x = 14 + 2.8284 / 4

x = 4.2071

x = 14 - 2.8284 / 4

​x = 3.1464

The simplified algebraic expression is given as follows:

[tex]5\frac{(-1 + \sqrt{3})}{3}[/tex]

The algebraic expression in the context of this problem is defined as follows:

[tex]\frac{-5 + 5\sqrt{3}}{3}[/tex]

To simplify, we must obtain the common factor of the numerator, which is of 5, as both terms are divisible by 5, as follows:

Hence the simplified algebraic expression is given as follows:

[tex]5\frac{(-1 + \sqrt{3})}{3}[/tex]

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Answer: 225

Step-by-step explanation:

Create a ratio part/whole for radians = part/whole for degrees

[tex]\frac{\frac{5\pi }{4} }{2\pi } = \frac{x}{360}[/tex]      Keep change flip because you are dividing fractions for left side

[tex]\frac{5\pi }{4} (\frac{1}{2\pi }[/tex]) = [tex]\frac{x}{360}[/tex]

[tex]\frac{5}{8} (\frac{360}{1} ) =x[/tex]

x = 225

20 degrees is the value of the variable x.

Angle ABD is 90 degrees, angle ABC is X degrees, and the measure of angle DBC (3x+10)

x + 3x +10=90

4x +10 =90

4x= 90-10

4x =80

x= 80÷4

x=20

Therefore, the value of the variable x is 20 degrees

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Answer:

Step-by-step explanation:

The correct statement regarding p-values and decision of the hypothesis is given by:

c.) With a p-value of 0.04 and a significance level of 3%, you failed to reject the null hypothesis.​

Given that;

To find the correct statement regarding p-values and decision of the hypothesis

Since, Depends on if the p-value is less or more than the significance level:

If it is more, the null hypothesis is not rejected.

If it is less, it is rejected.

Hence the correct statement for this problem is given by:

c.) With a p-value of 0.04 and a significance level of 3%, you failed to reject the null hypothesis.​

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Answer:

rate of change is 3/4 or 3/4x

Step-by-step explanation: