which of the following equations can be used to find the misssing angle x in triangle 42

Answer:

a. 1.95 cm.

b. 3920 cm^2.

Step-by-step explanation:

(a) To find the length of the arc that subtends the central angle theta on a circle of diameter d, we can use the formula:

Arc Length = (theta / 360°) x (pi x d)

Substituting the given values, we get:

Arc Length = (1.6 / 360°) x (pi x 140 cm)

Arc Length ≈ 1.95 cm

Therefore, the length of the arc that subtends the central angle of 1.6 radians on a circle of diameter 140 cm is approximately 1.95 cm.

(b) To find the area of the sector determined by the central angle theta, we can use the formula:

Area of Sector = (theta / 2π) x pi x (r^2)

where r is the radius of the circle.

Since the diameter of the circle is given as 140 cm, the radius is half of that, which is 70 cm.

Substituting the given values, we get:

Area of Sector = (1.6 / (2 x pi)) x pi x (70 cm)^2

Area of Sector ≈ 3920 cm^2

Therefore, the area of the sector determined by the central angle of 1.6 radians on a circle of diameter 140 cm is approximately 3920 cm^2.

The missing step in the two column proof is

Statement              Reason

Δ DAC ≅ ΔBCA    ASA congruence theorem

The ASA theorem, also known as the angle side angle theorem, is a rule used in geometry to determine whether two triangles are congruent (meaning they have the same shape and size).

The angle side angle theorem states uses the side two parameters which includes:

The parameters are used for the theorem to say that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

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The percentage of the people that preferred cooking who where surveyed would be = 87.2%

The total number of people surveyed = 8

The total number of people that preferred cooking = 7

The percentage of people that preferred cooking;

= 7/8×100/1

= 700/8

= 87.2%

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Answer:

1st one is 6.9 X 10^6

2nd one is 2 x 10^5

Step-by-step explanation:

we should subtract (389/600) from (7/12) + (7/8) to obtain the multiplicative inverse of (4/3) - (2/9).

To find the multiplicative inverse of a fraction, we need to find another fraction that, when multiplied by the original fraction, results in a product of 1.

Let's start by finding the multiplicative inverse of the fraction (4/3) - (2/9):

(4/3) - (2/9) = (12/9) - (2/9) = (10/9)

The multiplicative inverse of (10/9) would be a fraction (a/b) such that:

(10/9) x (a/b) = 1

Multiplying both sides by (9/10) (the reciprocal of 10/9), we get:

(a/b) = (9/10) x (1/(10/9))

Simplifying the expression on the right-hand side, we get:

(a/b) = (9/10) x (9/10) = 81/100

So the multiplicative inverse of (4/3) - (2/9) is 81/100.

Next, we need to find what we should subtract from (7/12) + (7/8) to obtain 81/100.

We can first find a common denominator between (7/12) and (7/8), which is 24:

(7/12) = (7/12) x (2/2) = 14/24

(7/8) = (7/8) x (3/3) = 21/24

So, we can rewrite (7/12) + (7/8) as:

(14/24) + (21/24) = 35/24

To obtain the difference between 35/24 and 81/100, we subtract the smaller fraction from the larger one:

81/100 - 35/24 = (81/100) x (6/6) - (35/24) x (25/25)

= 486/600 - 875/600 = -389/600

Therefore, we should subtract (389/600) from (7/12) + (7/8) to obtain the multiplicative inverse of (4/3) - (2/9).

Final answer:

(7/12) + (7/8) - (389/600) = 1.0158 (rounded to four decimal places)

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Answer:

To find the lower and upper quartiles and the interquartile range, we first need to order the data from smallest to largest:

20, 22, 25, 28, 29, 30, 32, 33, 34

Next, we find the median (middle value) of the entire dataset:

Median = (29 + 30) / 2 = 29.5

This median value divides the data into two halves. We then find the median of the lower half of the data, which includes all values less than or equal to 29.5:

Lower half: 20, 22, 25, 28, 29

Median of lower half = (25 + 28) / 2 = 26.5

This value, 26.5, is the lower quartile (Q1).

Similarly, we find the median of the upper half of the data, which includes all values greater than or equal to 29.5:

Upper half: 30, 32, 33, 34

Median of upper half = (32 + 33) / 2 = 32.5

This value, 32.5, is the upper quartile (Q3).

Finally, we can calculate the interquartile range (IQR) as the difference between the upper and lower quartiles:

IQR = Q3 - Q1 = 32.5 - 26.5 = 6

Therefore, the lower quartile is 26.5, the upper quartile is 32.5, and the interquartile range is 6.

Answer: the answer is 4

Step-by-step explanation: good luck

Thus, the total surface area of the given right triangular prism is found as : 96 sq. in.

The bases of a prism, which can have up to n sides, are joined to one another by parallel lines that create planes. These bases plus planes would create right angles with one another in a right prism if they were perpendicular to one another.

surface area of right triangular prism S:

surface area of right triangular prism  = base area + 2*triangle area + 2* rectangle area

surface area of right triangular prism  = 4*8 + 2*(1/2*8*3) + 2*4*5

surface area of right triangular prism   = 32 + 24 + 40

surface area of right triangular prism  = 96

Thus, the total surface area of the given  right triangular prism is found as : 96 sq. in.

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The indicated value h(-1)  has a value of 0 when evaluated

From the question, we have the following parameters that can be used in our computation:

f(x) = - 2x ^ 2

g(x) = x - 3

h(x) = 2f(x) - g(x)

The indicated value of the function is

h(-1)

This means that

h(-1) = 2f(-1) - g(-1)

Calculate g(-1)

So, we have

g(-1) = -1 - 3

g(-1) = -4

Calculate f(-1)

So, we have

f(-1) = -2 * (-1)^2

f(-1) = -2

Recall that

h(-1) = 2f(-1) - g(-1)

Substitute the known values in the above equation, so, we have the following representation

h(-1) = 2 * -2 + 4

Evaluate

h(-1) = 0

Hence, the value is 0

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Answer:

The distance between (3, 4.1) and (3, 1.2) is approximately 2.9 units.

Step-by-step explanation:

You're welcome.

The rectangle with largest area has length 3 and width 3/2, with an area of 9/2.

What is a rectangle?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. As a result, it is sometimes referred to as an equiangular quadrilateral. Because the opposing sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

The equation for the area of a rectangle is length * width. For us here, it would be x * y. We can substitute the equation of the line for y and get

A = x * (6-x)/2

A = 3x - x2/2

To find the maximum of this equation, we first need to find a critical point. So we take the derivative and find the zeros:

A' = 3 - x = 0

x = 3

So we have a critical point at 3, which happens to be the maximum of the area equation. We plug this back into the line equation to get y:

y = (6 - 3)/2 = 3/2

So the rectangle with largest area has length 3 and width 3/2, with an area of 9/2.

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Answer:300

Step-by-step explanation:

We can find the answer the simple way.

There are 10 triangles in a regular pentagon

We used pythagorean theorm to find side b, 12

12*5*0.5 is 30

30*10 is 300

Yes, Jalen is correct because the rectangle has a perimeter of 20 inches with the smaller side measuring 3 inches and the longer side of the rectangle had to be 7 inches.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(3 + 7)

20 = 2(10)

20 = 20 (True).

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Answer:

Step-by-step explanation:

To find the result when the number 59 is decreased by 3.9%, we need to first calculate what 3.9% of 59 is.

To do this, we can multiply 59 by 3.9% (or 0.039), which gives us:

59 x 0.039 = 2.301

This tells us that 3.9% of 59 is 2.301.

Next, we need to subtract 2.301 from 59 to get the final result:

59 - 2.301 = 56.699

Therefore, the result when the number 59 is decreased by 3.9% is 56.699.  we could say that if you take 3.9% of 59 and subtract that amount from 59, the answer is 56.699.

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Answer:

The molar mass of a chemical compound is defined as the ratio between the mass and the amount of substance of any sample of said compound.

unit of measurement: g/mol.

A mole is the amount of substance that contains as many elementary entities as there are atoms in 12g of carbon-12.

Avogadro's number= 6.02*10^23 particles.

The mean of the data set is 82.77

If we want to find the mean, we would have to put it at the back of our minds that the mean is the same as the average. As such, we would have to take the sum of all the values that have been listed in the data set and divide by the total number of the data.

The first step is to arrange the data set orderly from smallest to largest;

70, 71,79, 82,88,85,87,91,92

We have nine values in the data set thus the mean is;

70+71+79+82+88+85+87+91+92/9= 745/9= 82.77

Hence the mean of the data set is 82.77

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On solving the provided question we can say that Manny would thus require 160 yards of fencing to surround the rectangular plot.

A boundary is a closed route that embraces, encircles, or delimits a two-dimensional form or length in one dimension. The perimeter of a circle or an ellipse is its outermost section. The perimeter calculation is used in a variety of real-world situations. The perimeter of a form is the radius of its edge. Discover how to calculate the perimeter by adding the lengths of the sides of various shapes. The perimeter of a shape may always be calculated by multiplying the lengths of its sides. The perimeter of a thing is the region that surrounds it. At your house, one example is an enclosed garden. The distance around anything is referred to as its perimeter. A 200-foot fence will be required for a 50-foot-by-50-foot yard.

P = 2(l + w), where l is the length and w is the width, gives the perimeter of a rectangle.

The length in this example is 35 yards, while the breadth is 45 yards. So,

[tex]P = 2(35 + 45)\\= 2(80)\\= 160 yards\\[/tex]

Manny would thus require 160 yards of fencing to surround the rectangular plot.

As a result, option (b) 160 yards is the right answer.

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The angles on the Unit Circle that make the equation -√3 csc(2θ) = 2 true are θ = π/6 + 2πn and θ = 5π/6 + 2πn, where n is an integer.

From the information, the following can be deduced:

-√3 csc(2θ) = 2

csc(2θ) = -2/√3

sin(2θ) = -√3/2

We know that sin(2θ) = 2sin(θ)cos(θ) by the double-angle identity for sine,

2sin(θ)cos(θ) = -√3/2

2sin(θ)cos(θ) = -√3/2

sin(θ)cos(θ) = -√3/4

sin(θ)cos(θ) = sin(π/3)sin(θ)

cos(θ) = sin(π/3)

θ = π/6 + 2πn, 5π/6 + 2πn

Therefore, the angles on the Unit Circle that make the equation -√3 csc(2θ) = 2 true are θ = π/6 + 2πn and θ = 5π/6 + 2πn, where n is an integer

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The range of 1 year performance is more than 1 Day performance.

We have,

1 year performance: -30%, -20%, -10% 0%, 10%, 20%, 30%

1 Day performance : -3%, -2%, -1%, 0, 10%, 20%, 30%

Now, the range of 1 year performance

= Highest - lowest

= 30 - (-30)

= 60

and, the range of 1 Day performance

= Highest - lowest

= 30 - (-3)

= 33

Thus, the range of 1 year performance is more than 1 Day performance.

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To find the ratio of edge lengths of two triangles given their area ratio, we need to take the square root of the area ratio.

To find the ratio of edge lengths of two figures given their volume ratio, you need to use the fact that volume is proportional to the cube of the edge length.

If we have two figures, Figure A and Figure B, with edge lengths a and b respectively, and their volumes are in the ratio of V(A) : V(B) = k, then we can set up the following equation:

(Volume of A) / (Volume of B) = (a^3) / (b^3) = k

We can then solve for the ratio of edge lengths:

a / b = (k)^(1/3)

Therefore, to find the ratio of edge lengths given the volume ratio, we need to take the cube root of the volume ratio.

This method works for any shape, as long as the volume formula for that shape involves the cube of the edge length. For example, this method works for cubes, rectangular prisms, cylinders, spheres, and so on.

For triangles, however, we cannot use this method directly because the volume of a triangle is not a function of its edge length. Instead, we can use similar triangles to find the ratio of their edge lengths.

If we have two similar triangles, with corresponding sides in the ratio of a : b, then their areas are in the ratio of (a^2) : (b^2). We can use this fact to find the ratio of their edge lengths:

a / b = sqrt(Area of first triangle / Area of second triangle)

So, to find the ratio of edge lengths of two triangles given their area ratio, we need to take the square root of the area ratio.

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The expressions that have the same value are: b) 3^4 = 81 and e) 9^2 = 81

To compare the expressions, we can simplify them using the rules of exponents:

a) 3^3 = 27

b) 3^4 = 81

c) 6^2 = 36

d) 6^3 = 216

e) 9^2 = 81

f) 9^3 = 729

Using the above as a guide, we have the following:

Therefore, the expressions that have the same value are: b) 3^4 = 81 and e) 9^2 = 81

So, options b and e have the same value.

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The calculated value of the perimeter of triangle ABD is 48 units.

Given that

A(1, 1), B(17, 1) and D(17, 13)

To find the perimeter of triangle ABD, we need to find the lengths of its three sides and add them up.

We can use the distance formula to find the lengths of the sides.

The distance between points A and B is:

AB = √((17 - 1)^2 + (1 - 1)^2) = √(256) = 16

The distance between points B and D is:

BD = √((17 - 17)^2 + (13 - 1)^2) = √(144) = 12

The distance between points D and A is:

DA = √((1 - 17)^2 + (1 - 13)^2) = √(256 + 144) = √(400) = 20

Therefore, the perimeter of triangle ABD is:

AB + BD + DA = 16 + 12 + 20 = 48

So, the perimeter of triangle ABD is 48 units.

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Therefore, the probability that the mean tariff rate of 600 randomly selected railroad-car shipments of ethanol will be within $90 of the mean tariff rate of all railroad-car shipments of ethanol is approximately 0.9732 or 97.32%.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability theory is widely used in many fields, including mathematics, statistics, physics, engineering, economics, and social sciences. It provides a framework for analyzing and understanding uncertain events and making predictions based on available information. Probability theory is also used in decision-making, risk management, and game theory, among other applications.

Here,

Let μ be the mean tariff rate of all railroad-car shipments of ethanol, and let x be the mean tariff rate of a random sample of 600 railroad-car shipments of ethanol. We want to find the probability that x will be within $90 of μ.

The standard error of the mean (SE) can be calculated as:

SE = σ / √(n)

where σ is the standard deviation of the population, n is the sample size.

Substituting the given values, we get:

SE = 1150 / √(600)

≈ 47.03

The probability that x will be within $90 of μ can be calculated by standardizing x using the standard error and the z-score formula:

z = (x - μ) / SE

z = ($90) / 47.03

≈ 1.915

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 1.915 is approximately 0.9732.

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The total cost of the bracelet after tax cost addition would be = $21.2

The initial cost of the bracelet = 20$

The percentage of tax = 6%

The cost of tax = 6/100 ×20/1 = $1.2

The total cost of the bracelet after the addition of tax would be = 20+1.2 = $21.2

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The power function that models the data is 0.117t^1.585.

In 1985, the average cost of natural gas was estimated to be $7.24 per 1000 ft³.

a. To model the data with a power function, use general form of a power function:

C = ktⁿ,

where C = average cost of natural gas, t = time in years, k = a constant, and n = power.

Take the logarithm of both sides to linearize the equation:

log(C) = log(k) + n × log(t)

Use a linear regression to find the slope and y-intercept of the line, which will give us the values of k and n:

n ≈ 1.585

log(k) ≈ -0.921

k ≈ 0.117

Therefore, the power function that models the data is:

C = 0.117t^1.585

b. To estimate the average cost of natural gas in 1985, we can substitute t = 11 (since 1985 is 11 years after 1974) into the power function:

C = 0.117(11)^1.585 ≈ 7.24

Therefore, estimate the average cost of natural gas in 1985 to be $7.24 per 1000 ft³.

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The function has vertical asymptotes at x = -3/2 and x = 1, a horizontal asymptote at y = 0, and a y-intercept at (0, -2/3).

In mathematics, a function is a relation between two sets that associates each element of the first set, called the domain, with a unique element of the second set, called the range. In other words, a function maps each input value to a unique output value.

The notation used to represent a function is f(x), where f is the name of the function and x is the input value. The output value is then given by the expression f(x).

Functions can be represented in various ways, such as tables, graphs, equations, and verbal descriptions. They are used to model real-world phenomena, analyze data, and solve problems in various fields, including science, engineering, economics, and finance.

To find the intercepts of the rational function, we set the numerator equal to zero and solve for x:

2/(2x² - x - 3) = 0

2 = 0 (there is no solution for x that makes the numerator zero)

Therefore, the rational function has no x-intercepts.

To find the y-intercept, we set x = 0:

f(0) = 2/(2(0)² - 0 - 3) = -2/3

Therefore, the y-intercept is (0, -2/3).

To find the vertical asymptotes, we set the denominator equal to zero and solve for x:

2x² - x - 3 = 0

Using the quadratic formula, we get:

x = (1 ± √(1 + 24))/4

x = (1 ± 5)/4

x = -3/2, 1

Therefore, the rational function has vertical asymptotes at x = -3/2 and x = 1.

To describe the behavior at the vertical asymptotes, we can use limits. Let's consider the vertical asymptote at x = -3/2:

lim x → -3/2+ f(x) = 2/(2(-3/2)² - (-3/2) - 3) = -∞

lim x → -3/2- f(x) = 2/(2(-3/2)² - (-3/2) - 3) = +∞

This means that as x approaches -3/2 from the right, the function approaches negative infinity, and as x approaches -3/2 from the left, the function approaches positive infinity. Therefore, the function has a vertical asymptote at x = -3/2 with a vertical (or infinite) discontinuity.

Let's now consider the vertical asymptote at x = 1:

lim x → 1+ f(x) = 2/(2(1)² - (1) - 3) = +∞

lim x → 1- f(x) = 2/(2(1)² - (1) - 3) = -∞

This means that as x approaches 1 from the right, the function approaches positive infinity, and as x approaches 1 from the left, the function approaches negative infinity. Therefore, the function has a vertical asymptote at x = 1 with a vertical (or infinite) discontinuity.

To analyze and draw the graph of the rational function, we can use the intercepts, asymptotes, and behavior at the vertical asymptotes that we found earlier. We can also find the horizontal asymptote by looking at the degree of the numerator and denominator:

Degree of numerator = 0

Degree of denominator = 2

Therefore, the horizontal asymptote is y =0

As we can see from the graph, the function has vertical asymptotes at x = -3/2 and x = 1, a horizontal asymptote at y = 0, and a y-intercept at (0, -2/3). The behavior at the vertical asymptotes is a vertical (or infinite) discontinuity.

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The complete question is:

The volume of the rectangular prism is 13.125 cubic yards.

To find the number of cubes that fit along the length, width, and height of the rectangular prism, we need to divide the length, width, and height by the edge length of each cube, which is 1/2yd.

Along the length: (2 1/2 yd) / (1/2 yd) = 5 cubes

Along the width: (3 1/2 yd) / (1/2 yd) = 7 cubes

Along the height: (1 1/2 yd) / (1/2 yd) = 3 cubes

Therefore, there are 5 cubes along the length, 7 cubes along the width, and 3 cubes along the height of the rectangular prism.

To find the volume of the rectangular prism, we can multiply the length, width, and height:

Volume = (2 1/2 yd) x (3 1/2 yd) x (1 1/2 yd)

Volume = (5/2 yd) x (7/2 yd) x (3/2 yd)

Volume = (13.125 yd^3)

Therefore, the volume of the rectangular prism is 13.125 cubic yards.

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