Let sin(2x) = cos(x), where 0° ≤ x < 180°. What are the possible values for x? 30° only 90° only 30° or 150° 30°, 90°, or 150°

The equation of each of the line are as follows;

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

Since the equation of this line is parallel to the line x + 2y = 4, the slope is given by;

Slope, m = -0.5

y - y₁ = m(x - x₁)

y + 3.5 = -0.5(x - 1)

y = -0.5x - 3

Since the equation of this line is perpendicular to the line 5x + 2y + 2 = 0, the slope is given by;

Slope, m = -5/2

m₁ × m₂ = -1

-5/2 × m₂ = -1

Slope, m₂ = 2/5

y - y₁ = m(x - x₁)

y - 2 = 2/5(x + 5)

y = 2x/5 + 4

Since the equation of this line passes through the origin (0, 0) and parallel to the line 4x - 5y = 10, the slope is given by;

Slope, m = 4/5

y - y₁ = m(x - x₁)

y - 0 = 4/5(x - 0)

y = 4x/5

Since the equation of this line is perpendicular to the line 3x - y = 4 and cuts the x-axis at -1, the slope is given by;

Slope, m = 3

m₁ × m₂ = -1

3 × m₂ = -1

Slope, m₂ = -1/3

y - y₁ = m(x - x₁)

y - 0 = -1/3(x + 1)

y = -1/3(x) - 1/3

Since the line is perpendicular to the y-axis and passes through the point (-3, 5), the equation is given by;

y = 5.

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The complete table for the time it takes to empty the barrel for the given rates is attached below. The value of constant k is 60.

To solve the problem, we can use the formula for inverse variation

time = k/leaking rate

where k is a constant of proportionality. We can find k by using the information given in the problem

30 = k/2

Solving for k, we get:

k = 60

Now we can use this value of k to fill in the table

Leaking rate (gallons per minute)                Time to empty (minutes)

      2                                                                           30

      1                                                                            60

      0.5                                                                        120

      0.25                                                                     240

      0.1                                                                        600

As the leaking rate decreases, the time to empty the barrel increases, because the liquid is leaking out more slowly.

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Hello!

For this you would just need to multiple straight across. Here's how you would set it up:

3/4 ·1/8

Then you would multiple 3 x 1 = 3

And 4 x 8 =32

Your answer should be 3/32, it cannot be simplified so that is the final answer :).

Answer: The slope of the ramp is defined as the rise over the run, where the rise is the height of the step (2 feet) and the run is the horizontal distance from the bottom of the ramp to the step (7.0 feet). However, since the ramp is not straight but inclined, we need to use the length of the ramp (7.3 feet) to calculate the actual horizontal distance it covers.

Therefore, the run of the ramp is the square root of the difference between the length of the ramp squared and the height of the step squared:

run = sqrt(7.3^2 - 2^2) = sqrt(52.29 - 4) = sqrt(48.29) ≈ 6.95 feet

Now we can calculate the slope of the ramp:

slope = rise / run = 2 / 6.95 = 0.2885 ≈ 2/7

Therefore, the slope of the ramp is approximately 2/7.

The equivalent logarithmic value of the given expression log 3  + log 6 is equal to logarithm of 18.

The expression is equal to,

log 3  + log 6

By using the law of multiplication we have,

Log A + Log B = Log ( A × B )

Using the properties of logarithms, we can simplify the expression and get the equivalent logarithm number ,

Substitute the value of A = 3 and value of B = 6 in the formula we have,

log 3 + log 6

= log (3 × 6)

= log 18

Therefore, the expression log 3 + log 6 is equivalent to the logarithm of 18.

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Answer:

We can solve this inequality for x as follows:

3 - 3x ≤ 4x + 7

Subtract 4x from both sides:

3 - 7x ≤ 7

Subtract 3 from both sides:

-7x ≤ 4

Divide both sides by -7, remembering to reverse the inequality since we are dividing by a negative number:

x ≥ -4/7

Therefore, the solution to the inequality is:

x ≥ -4/7

The surface area of the square pyramid using given dimensions is given by option a.  3,456m².

In the square pyramid,

Using Pythagoras theorem,

Height of the square pyramid is equal to,

In a right angled triangle,

Base = 18m

Hypotenuse = 30m

Height = √ Hypotenuse ² - base ²

Substitute the values we have,

⇒ height = √ 30² - 18²

⇒ height = √576

⇒ height =  24m

Dimensions of square pyramid are,

Base edge 'b' = 36m

height of the pyramid 'h' = 24m

Surface area of square Pyramid = b² + 2b√(b²/4) + h²

Substitute the values we have,

⇒Surface area of square Pyramid

= 36² + 2(36)√((36)²/4) + (24)²

= 1296 + 72√324 + 576

= 1296 + 2160

= 3,456m²

Therefore, the surface area of square Pyramid is equal to option a.  3,456m².

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The domain of the graph is -∝ < x < ∝ and the range of the graph is y > 0

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

The graph

On the graph, we can see that

The function is an exponential function

This means that the domain is the set of all real numbers

For the range

We can see that the y values are greater than 0

This means that the range is y > 0

Hence, the domain of the graph is -∝ < x < ∝ and the range is y > 0

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The media personality's argument is flawed because they are basing their conclusion on a single year's data and ignoring the overall trend of increasing global temperatures. To counter this argument, one can make the following points:

1. While it is true that the annual increase in temperature may be less than the margin of error, the trend of increasing temperatures over several decades cannot be ignored. The margin of error is a statistical concept that takes into account the uncertainty in the measurement, but it does not negate the overall trend.

2. Global temperature records show that the Earth's temperature has been steadily rising over the past century, with the 10 warmest years on record occurring since 2005. This trend cannot be explained by natural variability alone and is consistent with the effects of human-caused climate change.

3. The consequences of rising global temperatures, such as melting glaciers, rising sea levels, and more frequent extreme weather events, are already being felt around the world. Ignoring this trend could have devastating consequences for future generations.

In summary, the media personality's argument is based on a flawed understanding of statistics and ignores the overall trend of increasing global temperatures. The best counterargument is to highlight the overwhelming evidence of climate change and its potential consequences.

Answer: 5:9

Step-by-step explanation:

Hope this helps! :)

Answer:

$3.66.

Step-by-step explanation:

1 yard is equal to 3 feet. So, a 2-yard piece of brass wire is equivalent to 6 feet of brass wire. To find the price per foot, we need to divide the total cost by the total length. So, the price per foot is

Answer:

The size depends on their dimensions

Answer:

C. Their size depends on their dimensions

Locations in space or on a 2D flat surface are called points. Consider a house's address or even longitude and latitude coordinates. These places have no width, length, or height. A point has no dimensions. There are infinitely few points. They only seem to have a size because without it, the locations of the points wouldn't be visible.

This is why choices A B and D can be ruled out. Only choice C is true.

The solution of the differential equation is y + e²ˣ = Ceˣ, if Ceˣ > 0

or -y - e²ˣ = Ceˣ, if Ceˣ < 0.

The solution of the differential equation is calculated as follows;

dy/dx = e²ˣ + y

Apply the method of separating viables;

dy/dx = e²ˣ + y

dy/(y + e²ˣ) = dx

Integrate both sides;

∫ dy/(y + e²ˣ) = ∫ dx

ln|y + e²ˣ| = x + C

To solve for y, we need to exponentiate both sides;

|y + e²ˣ| = e^(x+C) = Ceˣ

The final solution becomes;

y + e²ˣ = Ceˣ, if Ceˣ > 0

or

-y - e²ˣ = Ceˣ, if Ceˣ < 0

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Answer:

254.3 ft^2

Step-by-step explanation:

First, let’s find the area of the entire circle. The area for a circle is 3.14 * radius^2

3.14*18^2 = 1017.36

Now, notice how the angle marked is 90 degrees, that means that this section of the circle is 90/360 (360 is the angle of a circle), or 1/4 of a whole circle. Now we can multiply 1/4 by the area to find 1/4 of the whole circle.

1017.36*1/4 = 254.34

Round to nearest tenth:

254.3 ft^2

you just need to replace

Answer:

In 8th grade math, it's essential to know the following words: variable, coefficient, expression, equation, absolute value, function, slope, y-intercept, x-intercept, exponent, rational number, irrational number, proportion, ratio, and statistic. It's also crucial to have a solid understanding of basic arithmetic operations, including addition, subtraction, multiplication, and division, as well as properties of fractions, decimals, and percentages. Understanding geometric principles such as area, perimeter, and volume is also vital. Mastery of these terms and concepts will help your nephew excel in 8th grade math.

Answer: variable, coefficient, expression, equation, absolute value, function, slope, y-intercept, x-intercept, exponent, rational number, irrational number, proportion, ratio, and statistic. It's also crucial to have a solid understanding of basic arithmetic operations, including addition, subtraction, multiplication, and division, as well as properties of fractions, decimals, and percentages

Im Proud of you Bryson :)

The volume of the prism in cubic inches is 4/9 cubic in if each cube in the prism measures 1/3 inch on one side.

Hence, the correct option is A.

If each cube in the prism measures 1/3 inch on one side, then the volume of one cube is (1/3)³ = 1/27 cubic inches.

To find the volume of the prism, we need to know how many cubes are in the prism. Let's assume the prism has dimensions of length L, width W, and height H, all measured in units of cubes. Then, the total number of cubes in the prism is L × W × H.

Therefore, the volume of the prism in cubic inches is

Volume = (L × W × H) × (1/27) cubic inches

From the given figure, we can find

L = 3 inch

W = 2 inch

H = 2 inch

Substitute the values in formula to find the volume

= (3 × 2 × 2) × (1/27) cubic inches

= 4/9 cubic inches

Hence, the correct option is A.

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The initial sum of the number of students in College P and College Q is 5040.

We have,

Let's assume that the number of students in college Q is represented by Q, and the number of students in college P is represented by P:

P = Q - 0.32Q = 0.68Q

We also know that if 960 more students enroll in college P, the two colleges will have the same number of students.

So, we can set up another equation:

P + 960 = Q

We can substitute the first equation into the second equation to eliminate P:

0.68Q + 960 = Q

Solving for Q, we get:

0.32Q = 960

Q = 3000

The initial number of students in college Q was 3000.

We can use this value to find the initial number of students in college P:

P = 0.68Q = 0.68(3000) = 2040

So, the initial sum of the number of students in College P and College Q is:

P + Q = 2040 + 3000 = 5040

Therefore,

The initial sum of the number of students in College P and College Q is 5040.

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The complete question.

College P has 32% less students then college Q if 960 more students college P , the two college will have the same number of student what is the sum of the number of student in college p and college Q initially?

1) 5880

2)5040

3)8400

4)6720​

Being Male and driving to work are independent events.

P(Drive | Male) = P(Drive)

Hence, Blank 1 is 'independent event' and Blank 2 is '='.

Probability of being male is,

P(Being male) = 0.54

Probability of driving to work is,

P(Driving to work) = 0.5

Probability of being male and driving to work is,

P(Being male and driving work) = 0.27

And P(Being Male)*P(Driving to work) = 0.54*0.5 = 0.27

Since, P(Being male and driving work) = P(Being male)*P(Driving to work)

Hence, Being Male and Driving to work are independent event.

P(Drive | Male) = P(Male and Drive)/P(Male) = 0.27/0.54 = 0.5

Since, P(Drive) = 0.5

Hence, P(Drive | Male) = P(Drive)

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Answer: this is hard

Step-by-step explanation:

Answer:

The measure of an inscribed angle in a circle equals half the measure of its intercepted arc.

3) 56 + 2x = (1/2)(112 + x)

x = 0, so the measure of arc BCD is

360° - 112° = 248°.

5) 3 + 20x = (1/2)(43x - 3)

6 + 40x = 43x - 3

3x = 9, so x = 3

The measure of arc MLK is

360° - (43(3) - 3)° = 360° - 126° = 234°.

Answer (Respuesta):

-4

Step-by-step explanation:

-2t + 5 = 13

-2t = 8

t = -4

f(-4) = 13

Respuesta: -4

5√2 is the value of x in the given triangle. Therefore, the correct option is option A among all the given options.

A polygon having three edges & three vertices is called a triangle. It can be considered one of the fundamental geometric shapes. A unique triangle and plane (i.e., the two-dimensional Euclidean space) are determined by any three non-collinear points in Euclidean geometry. In other words, every triangle has a location in a plane, and there is just one level that contains that triangle.

√2×√50 = √100 = 10.

1×√50 = √50 = 5√2

5√2 since √50 = √25×√2 = 5√2

Therefore, the correct option is option A among all the given options.

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Your question is incomplete but most probably your full question was,

The combinations of side lengths that would not form a triangle with vertices X, Y, and Z is A. XY = 15 mm, YZ = 10 mm, and XZ = 28 mm.

We shall us the triangle inequality theory for this problem.

According to this theory, the addition of the lengths of any two sides of a triangle must be greater than the length of the third side.

Therefore, for the sides XY, YZ, and XZ to form a triangle, we must have:

XY + YZ > XZ

YZ + XZ > XY

XZ + XY > YZ

We can check each option to see if it satisfies these conditions:

A. XY = 15 mm, YZ = 10 mm, XZ = 28 mm

15 + 10 > 28 (not satisfied)

10 + 28 > 15 (satisfied)

28 + 15 > 10 (satisfied)

Option A does not satisfy the condition XY + YZ > XZ, so it would not form a triangle.

B. XY = 18 mm, YZ = 10 mm, XZ = 25 mm

18 + 10 > 25 (satisfied)

10 + 25 > 18 (satisfied)

25 + 18 > 10 (satisfied)

Option B satisfies all the conditions, so it would form a triangle.

C. XY = 18 mm, YZ = 13 mm, XZ = 22 mm

18 + 13 > 22 (satisfied)

13 + 22 > 18 (satisfied)

22 + 18 > 13 (satisfied)

Option C satisfies all the conditions, so it would form a triangle.

D. XY = 15 mm, YZ = 10 mm, XZ = 22 mm

15 + 10 > 22 (satisfied)

10 + 22 > 15 (satisfied)

22 + 15 > 10 (satisfied)

Option D satisfies all the conditions, so it can form a triangle.

Therefore, the combinations that would not form a triangle is A, where XY = 15 mm, YZ = 10 mm, and XZ = 28 mm.

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Answer:

-12

Step-by-step explanation:

(-3)4

-3*4

-12

Elaborate ur question about - 34

75% of students of a class answered Question No. 1 correct and 55% answered Question No. 1 correct and 20% answered neither question correctly . 50 is the percentage of students who only answered one question

A percentage is a quantity or ratio that is expressed as a fraction of 100. It is symbolised by the '%' percentage sign. 'pct' or 'pc' are the acronyms used to indicate the percentage. In sense, the percentage is measured in terms of 100 and is defined as the amount of one quantity that is made up of another.

Students answer Q.1 or Q.2 or both correctly = ( 100 - 20) = 80%

x% students answered both correctly

( 75 - x) + ( 55 - x) + x = 80

130 - x = 80

x = 50

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Your question is incomplete but most probably your full question was,

75% of students of a class answered Question No. 1 correct and 55% answered Question No. 1 correct and 20% answered neither question correctly . What percent of students answered both question correctly ?

Expressing as single logarithm 3/2㏑4x⁶ - 2/5㏑2y²⁵ = ㏑(2x⁹/y¹⁰)

Since we have the logarithm expression

3/2㏑4x⁶ - 2/5㏑2y²⁵

To simplify, we proceed as follows

First, we use the power law of logarithm which states that

n㏑x = ㏑xⁿ

So, using this, we have that

3/2㏑4x⁶ - 2/5㏑2y²⁵ = ㏑4x⁶ - 2/5㏑2y²⁵

[tex]= ln4x^{6\times\frac{3}{2} } - ln2y^{25\times\frac{2}{5} } = ln4x^{3\times3} } - ln2y^{5\times2 }[/tex]

= ㏑4x⁹ - ln2y¹⁰

Using the subtraction law of logarithm, which states that

㏑a - ㏑b = ㏑(a/b), we have that

㏑4x⁹ - ln2y¹⁰ =  ㏑(4x⁹/2y¹⁰)

= ㏑(2x⁹/y¹⁰)

So, 3/2㏑4x⁶ - 2/5㏑2y²⁵ = ㏑(2x⁹/y¹⁰)

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Answer:

25%

Step-by-step explanation: Because a 25 % increase is calculated by multiplying by 1.25.

The values of a, h and k for the function include the following:

a = 2

h = 3

k = -2

In Mathematics and Geometry, the general form of a logarithm function is represented by the following mathematical equation:

f(x) = alog(±x + h) + k

Where:

Based on the given logarithm function f(x) = 2log₄(x + 3) - 2, we can reasonably infer and logically deduce that the scale factor (a) used is equal to 2.

This ultimately implies that, the values of a, h and k for the function are 2, 3, and -2 respectively.

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Answer:

the answer is true