Given the following diagram, find the missing measure 2 m_2 = 2x°, m _3 = 5x, m 1 = 0 2x + 5% 5x - 2x 180 - 5x 180 - 7x

Answer:

Step-by-step explanation:

Refer to attached

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The triangle DCF can be divided into DEC and DEF as per picture and the area of them is:

Area of ΔDEF

Area of ΔDEC

Since D and E are midpoints of AB and BC:

So the area of ΔDCF is:

Since the area of ABC is A = 1/2bh we have:

Solving for A:

Answer:

7 1/6

Step-by-step explanation:

3/6 + 4/6 = 7/6

4 + 2 = 6

6 7/6

*Simplify*

7 1/6

(Hope this helps!)

Yours Truely, TheAnimeCatUwU

The first physical coordinate y1 can be expressed as y1 = [1 0 0]Y, & The mass-normalised mode shapes can be  normalising the mode shape vectors f1, f2, and f3.

Part (a)

In Equation Q2, the spectral matrix, undamped natural frequencies, damping ratios, and fundamental frequency need to be calculated.

The mass matrix is given by [85.16400 083.3770 0046.999; 0.079400 00.7030 001.07 × 10; 0.013600 03.1390 005.124 × 10].

The stiffness matrix is given by [0.16400 00.3770 000.999; 0.079400 00.7030 001.07 × 10; 0.013600 03.1390 005.124 × 10].

The damping matrix is given by [0 0 0; 0 0 0; 0 0 0].The undamped natural frequencies, damping ratios, and fundamental frequency for the system in Equation Q2 can be calculated from the spectral matrix.

The characteristic equation can be written as det(K-mω^2M)=0.where K is the stiffness matrix, M is the mass matrix, ω is the angular frequency, and m is the mass-normalised mode shape.

The roots of this equation are the undamped natural frequencies, and the damping ratios can be calculated from the undamped natural frequencies and mode shapes.

The mass-normalised mode shapes can be calculated by normalising the mode shape vectors f1, f2, and f3.

Part (b)

The mass-normalised mode shapes can be calculated using the mode shape vectors f1, f2, and f3.Part (c)The response of the system for the first physical coordinate y1 can be calculated using the mode superposition method. The initial modal displacements and velocities are given in terms of the modal coordinates.

The response is then calculated using the equation y(t)= Σ ai φi(t), where ai are the modal amplitudes, and φi(t) are the modal shapes given by the mode shape vectors f1, f2, and f3.

The first physical coordinate y1 can be expressed as y1 = [1 0 0]Y, where Y is the vector of physical coordinates. The modal amplitudes can be calculated from the initial modal displacements and velocities.

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Answer:

there are 24 large dogs

Step-by-step explanation:

add the ratio 3 plus 4

for large dogs you have 3/7×56

Answer:

8

Step-by-step explanation:

the slope is 8 but in slope intercept the equation is y = 8x - 6

Answer;

22.88m

Explanation

The formula for finding the area of the trinagle is expressed as;

a and b arethe sides of the triangle

theta is the central angle between the sides

Given

a = 12m

b = 7m

theta = 33 degrees

Substitute the given values into the formula as shown;

Hence the area of the triangle to the nearest hundredth is 22.88m

Sample size and the confidence level width have an inverse relationship. As the sample size increases, the confidence level width decreases.

When determining a confidence interval for a population parameter, such as the mean or proportion, a larger sample size provides more information about the population. This increased information leads to a narrower confidence interval.

The confidence level width is influenced by two factors: the sample standard deviation (or the variability of the data) and the critical value associated with the desired confidence level. As the sample size increases, the sample standard deviation becomes a more accurate estimate of the population standard deviation. This reduces the variability and leads to a narrower confidence interval.

A larger sample size leads to a decrease in the confidence level width, providing a more precise estimate of the population parameter with a higher level of confidence.

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Explanation:

a) Line BD is an angle bisector. It divides the angle at B into equal halves.

BD is also a median of the triangle as the line starts from th vertex and divides the opposite side into two equal parts.

Angle bisector of ∠B

median of triangle ABC

b) HI is a perpendicular bisector of line FG. It makes angle 90 degrees with the base.

HI is also an altitude of triangle FGH

c) MN is not a median of triangle JKL as the line doesnot start from the vertex of the triangle

MN is a perpendicular bisector of line KL

Answer...

Ok done. Thank to me >:33

Answer:

0

Step-by-step explanation:

Answer:

5y=39

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

A= (4-1)^3

simplify A to be 3^3

Which gives us 27

B=(2*3)^2-9

simplify B

first multiply the 2 numbers in paranthesis which gives us 6. raise it to the power of 2 which is 39 and then subtract 9. Gives us 27.

C=15^3*4-12

Simplify the exponent first. 3*4 gives us 12 and 12-12 equals 0. Anything raised to the power of 0=1

If A-B^C is the equation we can write 27-27 raised to the power of 1 which is 0

Answer:

A.

Step-by-step explanation:

Convex polygon

A polygon is a figure that has no curved lines. A convex polygons has no "caves."

In this instance, answer choices B, C, and D all have curved lines which means that they aren't polygons. Additionally, as an example of a concave polygon, answer choice D creates a sort of "cave."

Therefore, answer choice A is a convex polygon.

Hope this helps!

The cross product of  three vectors is not associative in nature.

Considering three vectors such  as : A=(2,1,3), B=(1,0,2) and  C=(1,1,0)

we  know that the  associative law depicts that :

A x (B x C) = (A x B) x C ,while doing the operation for the  considered vectors :

A x (B x C) =(2,1,3)x ((1,0,2)x (1,1,0))

                  =(2,1,3)x (-2,2,1)

     =(-5,-8,6)

(A x B) x C=  ((2,1,3)x (1,0,2))x (1,1,0)

            = (2,-1,1) x (1,1,0)

  =(-1,1,3)

So  for this vector operation, A x (B x C)  is not  equal to  (A x B) x C, so you can sum up that cross product of three vectors can't be associative every possible time.

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The perimeter of television is = 100 inches

The study of measuring geometric shapes and their qualities such as length, volume, shape, surface area, lateral surface area, and so on is known as mensuration. Mensuration will be covered in fundamental mathematics.

let the length be 16x and width be 9x

area given = 576 sq. inches

16x * 9 x = 576

144 \(x^{2}\) = 576

x = 24/12

x = 2

length = 32

width = 18

perimeter = (32 + 18)*2  =100 inches

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The exact value of cos^-1( √3/2) = 30°

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

There are special angles in trigonometry, this angles have exact value and can be obtained without using calculator. Examples of this calculator are; 30°, 60°, 45°

sin30 = 1/2

cos 30 = √3/2

tan 30 = 1/√3

cos 60 = 1/2

sin 60 = √3/2

tan 60 = √3

Therefore, if cos^-1( √3/2) = x

cos x = √3/2

cos 30 = √3/2

cos x = cos 30

therefore x = 30

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Answer:

2,-3

Step-by-step explanation:

Using the properties of multiplication to compare the expressions 3 to the eighth power and 3 to the fifth power x 3 to the third power, it can be seens that that the two expressions are equal to each other.

The properties of multiplication state that when multiplying two expressions with the same base, we can add their exponents together. This means that 3 to the fifth power x 3 to the third power is equal to 3 to the eighth power.

In mathematical notation, this looks like:

3^8 = 3^5 x 3^3

Using the properties of multiplication, we can add the exponents together:

3^8 = 3^(5+3)

Simplifying the exponent:

3^8 = 3^8

This shows that the two expressions are equal to each other. Therefore, we can conclude that 3 to the eighth power and 3 to the fifth power x 3 to the third power are the same value.

Note: The question is incomplete. The complete question probably is: Use the properties of multiplication to compare the expressions 3 to the eighth power and 3 to the fifth power x 3 to the third power.

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Answer:

0.09

Step-by-step explanation:

Total = 35+5+10+5 = 55

P(string&brass) = 5/55

= 1/11 = 0.09090909

Answer:

Step-by-step explanation:

13b - 13

13( b - 1)

Answer:

546

Step-by-step explanation:

Surface Area = 2(lw + lh + wh)

plug in 21 10.5 and 2.5

Answer:

0.5+d=h

Step-by-step explanation:

If a plant is growing at a steady rate of 0.5 inches (h) in 1 day (d) then after one day your equation should look like: 0.5+1 which would give you the height of the plant in inches. If this is true, then you would keep the height per day the same (0.5) substitute the 1 for d (one day); then your equation would look like this: 0.5+d which would give you the height of the plant in inches (h).

0.5+d=h

The function that helps Yazmin to see how many days it takes is h = 1 + 0.5d.

Functions were originally the idealization of how a varying quantity depends on another quantity.

Now it is given that,

Height of sprout =  1 inch

Growth per day =  1/2 inch

Let h = height of the plant (inches), and let d = number of days (days)

∵ Growth per day =  1/2 inch

So, Growth of plant in d days = d * 1/2 = d/2 = 0.5d

Thus,  height of the plant, h = 1 + Growth of plant in d days

⇒ h = 1 + 0.5d

Thus, the function that helps Yazmin to see how many days it takes is h = 1 + 0.5d.

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Answer:

2a )  4/-13

2b)   6/5

The triangular table does not represent a right triangle.

b) The Pythagorean theorem asserts that the total of the square of both of the shorter sides of a right triangle equals the square of the side that is longest (the hypotenuse). The side lengths in this example are 4 feet, 3 feet, and 2 feet. To see if the Pythagorean theorem is true with these side lengths, we can apply it.

Taking each square of side lengths: 42 = 16 32 = 9 22 = 4

If the table were a right a triangle, the total of the squares of the two smaller sides (9 + 4 = 13) should equal the square of the side that is longest (16), according to the Pythagoras theorem. In this situation, however, 13 does not equal 16.

As a result, the triangular tables does not meet the Pythagorean theorem criteria, showing that it is not a triangle with a right angle.

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Mrs Gomez is buying a triangular table for the corner of her classroom. The side lengths of the table are 4 feet, 3 feet, and 2 feet. The triangular table is not a right triangle since the sum of the squares of the two shorter sides (9 + 4 = 13) does not equal the square on the longest side (16), proving that the triangle is not a right triangle. Thus Option B. is the correct answer.

In order to determine whether or not the triangular table is a right triangle, we must first see if the Pythagorean theorem holds true for the specified side lengths. According to the Pythagorean theorem, the square of the hypotenuse, the longest side of a right triangle, equals the sum of the squares of the lengths of the other two sides.

Let's compute the squares of the side lengths given:

2² = 4

3² = 9

4² = 16

Let's now evaluate the available options for answers:

OA. Yes, because 2² + 3² = 4².

4 + 9 = 16

This option is incorrect since the squares of the two shorter sides do not add up to the square of the longest side.

OB. No, because 2² + 3² > 4².

2² + 3² = 4 + 9

2² + 3² = 13

4² = 16

This option is correct since 13 does not equal 16. Hence, the triangular table is not a right triangle

OC. No, because 2² + 3² + 4².

This option seems to be incomplete because to decide whether it is a right triangle or not, there is no comparison or equation.

OD. Yes, because 2 + 3 + 4.

This option is incorrect because it just adds the side lengths without taking the Pythagorean theorem into account.

Therefore, Option B is the correct answer.

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Answer:

- 1

Step-by-step explanation:

y = mx + b ( "m" is slope and "b" is y-intercept )

The equation of a given line is

y = - 2x - 2

Coordinates of x-intercept are ( x, 0 ) ⇒ 0 = - 2x - 2 ⇒ x = - 1

The x-intercept of the line is ( - 1 )

The test statistic for this test is 3.09.

To calculate the test statistic for this test, we need to use the formula:

t = \((\bar x - \mu) / (s /\sqrt n)\)

where:

\(\bar x\) = the sample mean difference (after - before)

\(\mu\) = the population mean difference (assumed to be 0 if the test preparation course has no effect)

s = the standard deviation of the differences

n = the sample size (in this case, 30)

Plugging in the values given in the problem, we get:

t = \((6 - 0) / (10 / \sqrt 30)\) = 3.09

To determine whether a test preparation course improves scores on the ACT test, we can use a paired samples t-test.

This test compares the mean difference between two related groups (in this case, the pre- and post-test scores of the same students) to the expected difference under the null hypothesis that there is no change in scores.

The test statistic for a paired samples t-test is given by:

t = (mean difference - hypothesized difference) / (standard error of the difference)

The mean difference is the average difference between the two groups, the hypothesized difference is the expected difference under the null hypothesis (which is 0 in this case), and the standard error of the difference is the standard deviation of the differences divided by the square root of the sample size.

The mean difference is 6 points, the hypothesized difference is 0, and the standard deviation of the differences is 10 points.

Since there are 30 students in the sample, the standard error of the difference is:

SE =\(10 / \sqrt{(30)\)

= 1.83

Substituting these values into the formula for the test statistic, we get:

t = (6 - 0) / 1.83 = 3.28

The test statistic for this test is therefore 3.28.

To determine whether this test statistic is statistically significant, we would need to compare it to the critical value of t for 29 degrees of freedom (since there are 30 students in the sample and we are estimating one parameter, the mean difference).

The critical value for a two-tailed test at a significance level of 0.05 is approximately 2.045.

The test statistic (3.28) is greater than the critical value (2.045), we can conclude that the difference in scores between the pre- and post-test is statistically significant at a significance level of 0.05.

The test preparation course did indeed improve scores on the ACT test. It's important to note that this is just a single study and that further research would be needed to confirm these results.

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Answer:

115 lbs = 52.16 kilograms

Step-by-step explanation:

115 pounds is a little over 52kg

Answer:

110/5=2

2,5.5=15

2+15=17

Step-by-step explanation:

Based on the given informations, the angle between the ladder and the ground is decreasing at a rate of 0.009 radians/second when the ladder is 5.8 feet away from the house.

Let's call the distance between the base of the ladder and the house "x". The length of the ladder is 24 feet, so the height it reaches up the house is given by the Pythagorean theorem:

h² = 24² - x²

Differentiating both sides with respect to time:

2h dh/dt = -2x dx/dt

We want to find dh/dt when x = 5.8 feet and dx/dt = 0.25 feet/second. First, we need to solve for h:

h² = 24² - 5.8² = 557.84

h = 23.63 feet

Substituting x = 5.8 feet, h = 23.63 feet, and dx/dt = 0.25 feet/second:

2(23.63) dh/dt = -2(5.8)(0.25)

dh/dt = -0.06 feet/second

So the tip of the ladder is slipping down the side of the house at a rate of 0.06 feet/second.

To find the rate of change of the angle, we can use the formula:

tan(Θ) = h/x

Differentiating both sides with respect to time:

sec²(Θ) d(Θ)/dt = (1/x) dh/dt - (h/x²) dx/dt

We already know x = 5.8 feet, h = 23.63 feet, and dx/dt = 0.25 feet/second. We just calculated dh/dt to be -0.06 feet/second. To find sec(theta), we can use the fact that cos(Θ) = x/h:

cos(Θ) = x/h = 5.8/23.63 = 0.245

sec(Θ) = 1/cos(theta) = 4.0816

Substituting these values into the formula above:

(4.0816)² d(Θ)/dt = (1/5.8)(-0.06) - (23.63/5.8²)(0.25)

d(Θ)/dt = -0.009 radians/second (rounded to 3 decimal places)

Therefore, the angle between the ladder and the ground is decreasing at a rate of 0.009 radians/second when the ladder is 5.8 feet away from the house.

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