In ΔUVW, w = 5. 3 inches, v = 3. 6 inches and ∠V=32°. Find all possible values of ∠W, to the nearest 10th of a degree

(x + 2) is a factor of both the polynomials A(x) = x³ - 3x² - 10x and C(x) = x³ - 2x² - 13x - 10.

Hence options (A) and (C) are correct.

We know from the Factor Theorem that,

"If (x - a) be a factor of the polynomial f(x) then f(a) = 0."

Here (x + 2) should be factor the chosen polynomial.

Here, a = -2

Given functions are:

A(x) = x³ - 3x² - 10x

B(x) = x³ + 5x² + 4x

C(x) = x³ - 2x² - 13x - 10

D(x) = x³ - 6x² + 11x - 6

Now, substituting x = -2 we get,

A(-2) = (-2)³ - 3(-2)² - 10(-2) = -8 - 12 + 20 = 0

B(-2) = (-2)³ + 5(-2)² + 4(-2) = -8 + 20 - 8 = 4

C(-2) = (-2)³ - 2(-2)² - 13(-2) - 10 = -8 - 8 + 26 - 10 = 0

D(-2) = (-2)³ - 6(-2)² + 11(-2) - 6 = -8 - 24 - 22 - 6 = -60

Using Factor Theorem we can conclude that (x + 2) is a factor of both the polynomials A(x) and C(x).

Hence options (A) and (C) are correct.

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The given question is incomplete. The complete question will be -

Answer:

(-2,1)(-1,1)(0,1)(1,1) or y=2 x=[-2,1]

Step-by-step explanation:

Brainliest Please

Answer:

Volume of square pyramid=120,000 m³

Step-by-step explanation:

We are given: Base of square pyramid = 60 m

Height of square pyramid = 100 m

We need to find Volume of square pyramid.

The formula used is: \(Volume \ of \ square \ pyramid=\frac{1}{3}a^2h\)

Where a is base and h is height of square pyramid

Putting values in formula and finding volume of square pyramid

\(Volume \ of \ square \ pyramid=\frac{1}{3}a^2h\\Volume \ of \ square \ pyramid=\frac{1}{3}(60)^2(100)\\Volume \ of \ square \ pyramid=\frac{1}{3}(3600)(100)\\Volume \ of \ square \ pyramid=120,000\ m ^3\)

So, Volume of square pyramid=120,000 m³

If a bacterial growth rate is 3 cells every 2 minutes and there were initially 260, there will be 290 cells after 21 minutes which is found by using multiplication and addition.

what is Multiplication?

Multiplication is an arithmetic operation that combines two or more numbers to find their product. It is one of the fundamental operations in mathematics and is denoted by the "×" or "*" symbol.

The growth rate of the bacteria is 3 cells every 2 minutes. This means that in a span of 2 minutes, the number of cells increases by 3.

To find the total number of cells after 21 minutes, we need to calculate the number of 2-minute intervals in 21 minutes. Since there are 10 intervals of 2 minutes in 20 minutes (10 intervals * 2 minutes = 20 minutes), we know that the number of cells at the end of 20 minutes is 260 + (10 intervals * 3 cells) = 290 cells.

Now, for the remaining 1 minute, we can calculate the additional cells. In this case, the growth rate is still 3 cells every 2 minutes. Therefore, in 1 minute, the number of cells increases by (1/2) * 3 = 1.5 cells. Thus, the total number of cells after 21 minutes is 290 + 1.5 = 291.5 cells.

Since we cannot have a fraction of a cell, we round the result to the nearest whole number. Therefore, after 21 minutes, there will be 290 cells.

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Answer:

The magnitude is sqrt((-4)^2 + (-9)^2) = 9.85. The angle is atan(-9/-4) = 180 deg + 66 deg = 246 deg = -114 deg.

Step-by-step explanation:

hope it help

Answer:

9.85

Step-by-step explanation:

|v|= √9²+(-4)²

=√81+16

=√97

|v|= 9.85

Answer:

20

Step-by-step explanation:

because 4.6 + 5.4 = 10

then you need to multiply 2 to 10 so its 20

Answer:

the answer is 20 meters

Step-by-step explanation:

The perimeter is 20 meters

The hole will be of a radius of 7.63 inches when its perimeter is 48 inches.

The hole is in the form of a circle.

The perimeter of the circle = perimeter of the hole = 48 inches.

Let r be the radius of the vent,

The perimeter of the circle is known as the Circumference.

Circumference of the circle is given by \(2\pi r\)

So,

\(2\pi r = 48\\\\2*\frac{22}{7} *r =48\\\\r =\frac{48*7}{22*2} =7.63\)

The hole will be of a radius of 7.63 inches.

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Answer: x=5

1/5x= 4/3-1/3  

1/5x=1

x= 1:1/5

x=5

Answer:

X=5

Step-by-step explanation:

If we sample the function x(t) = cos(75t) at the Nyquist frequency, the resulting discrete frequency would be half of the Nyquist frequency, which is equal to half of the highest frequency component in the continuous signal.

In this case, the highest frequency component in x(t) is 75 Hz, as determined by the coefficient of t in the cosine function. According to the Nyquist-Shannon sampling theorem, to accurately represent a signal, the sampling frequency must be at least twice the highest frequency component. Therefore, the Nyquist frequency in this scenario would be 2 * 75 Hz = 150 Hz.

Since we are sampling at the Nyquist frequency, the resulting discrete frequency would be half of the Nyquist frequency, which is 150 Hz / 2 = 75 Hz. Hence, when sampling x(t) at the Nyquist frequency, the resulting discrete frequency would be 75 Hz.

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Answer:

Step-by-step explanation:

2x + y = -3

4x + 2y = -6

-4x - 2y = 6

 4x + 2y = -6

0 =0

infinitely many solutions

Answer:

Slop intercept form

Y=-2x - 3

Y= -2x -3

Or find the x and y intercept

X -intercept is (- 3/2, 0)

Y -intercept is (0, 3)

Step-by- step

Therefore, the slope of the line passing through the points (-8, 5) and (7,0) is -1/3.

The slope of the line passing through the points (-8, 5) and (7,0) can be found by using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

To find the slope (m), we can use the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

So, using the coordinates (-8, 5) and (7,0), we have:

m = (0 - 5) / (7 - (-8)) = -5 / 15 = -1/3

Therefore, the slope of the line passing through the points (-8, 5) and (7,0) is -1/3.

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The measure of each angle is equal to the measure of its supplementary angle.

Angle is a figure formed by two rays sharing a common endpoint. It is typically measured in degrees, with a full circle measuring 360°. Angles are used to describe the direction of lines and the relationships between them. Angles can also be used to describe the shape of objects and figures.

(1) Angles subtended by arc PT at the circumference are ∠POT and ∠PTQ.
(2) Angles subtended by arc TS at the circumference are ∠TSQ and ∠TSR.
(3) Angles subtended by arc SR at the circumference are ∠SRP and ∠SRQ.
(4) Angles subtended by arc RQ at the circumference are ∠RQP and ∠RQS.

The angles stated in question 2(a) above are all pairs of supplementary angles, which means that they add up to 180°. This means that the measure of each angle is equal to the measure of its supplementary angle.

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(a) (i) Angles subtended by arc PT at the circumference are ∠POT and ∠PTQ.
(ii) Angles subtended by arc TS at the circumference are ∠TSQ and ∠TSR.
(iii) Angles subtended by arc SR at the circumference are ∠SRP and ∠SRQ.
(iv) Angles subtended by arc RQ at the circumference are ∠RQP and ∠RQS.

(b) The angles stated in question 2(a) above are all pairs of supplementary angles, which means that they add up to 180°.

Angle is a figure formed by two rays sharing a common endpoint. It is typically measured in degrees, with a full circle measuring 360°. Angles are used to describe the direction of lines and the relationships between them. Angles can also be used to describe the shape of objects and figures.

The angles stated in question 2(a) above are all pairs of supplementary angles, which means that they add up to 180°. This means that the measure of each angle is equal to the measure of its supplementary angle.

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The given statement is false. A pooled model will produce biased coefficient estimates when factors in the error term are not correlated with the independent variable.

A pooled model is a method that entails the estimation of regression coefficients over different groups or periods by pooling the data from those groups or periods. When a pooled model is used, the dataset is combined from different groups and treated as one group, making it a more significant dataset. It is a statistical approach that includes data from two or more groups to examine variables in a wider context.

A pooled model is used when all groups have the same coefficient estimates and the same variance. It is a helpful technique for identifying variables that influence an outcome over time, as it examines changes that occur over different periods.

The assumptions of a pooled model are:

Hence, the given statement is false.

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A probability that can be deducted through logical reasoning before an experiment is performed is Theoretical probability.

Theoretical probability is based on what is expected to happen, or a theory, using reasoning. It is based on knowledge and mathematics. An experiment is not conducted to find theoretical probability.

The formula to calculate the theoretical probability of event A happening is:

P(A) = number of desired outcomes / total number of possible outcomes

For example, the theoretical probability that a dice lands on “2” after one roll can be calculated as:

P(land on 2) = (only one way the dice can land on 2) / (six possible sides the dice can land on) = 1/6

Thus, A probability that can be deducted through logical reasoning before an experiment is performed is Theoretical probability.

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The equivalent expression is  -1.9b + 7.8.

There is a concept known as an analogous expression, which is an expression that has the same value as another expression but has a different appearance.

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.

Combine similar phrases now:

The definition of like words is the terms that have the same variable raised to the same power. Only the numerical coefficients can change in algebra.

When we combine the term b's coefficient, we get

1.3b + 7.8–3.2b

= (1.3−3.2)⋅b + 7.8

By condensing the equation, we obtain

= (- 1.9) +b + 7.8

= −1.9b + 7.8

There is a condensed equivalent formula of -1.9b + 7.8.

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By using the formula for area of triangle using coordinates, the following results are obtained

13) Area of triangle = \(\frac{15}{2} \ sq. units\)

14) Area of triangle = \(\frac{49}{2} \ sq. units\)

What is area of triangle?

Area of a triangle is the total space taken by the triangle. If the coordinates of triangle are \((x_1, y_1), (x_2, _2) \ and \ (x_3, y_3)\), then area of triangle is calculated by the formula

Area of triangle = \(\frac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|\)

13) The given coordinates are E (3, 1), F(3, -2) and G(-2, 2)

Area of triangle =

\(\frac{1}{2}|3(-2-2) + 3(2-1) + (-2)(1 -(-2))|\\\\\frac{1}{2}|3(-4) + 3(1) -2(3)|\\\\\frac{1}{2}|-12 + 3 - 6|\\\\\frac{1}{2}|-15|\\\\\frac{15}{2} \ sq. units\)

14) The given coordinates are E (-3, 4), F(4, 4) and G(3, -3)

Area of triangle =

\(\frac{1}{2}|(-3)(4-(-3)) + 4(-3-4) + 3(4-4)|\\\\\frac{1}{2}|(-3)(7)+4(-7)+3(0)]\\\\\frac{1}{2}|-21-28+0|\\\\\frac{1}{2}|-49|\\\\\frac{49}{2} \ sq. units\)

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\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

Slope of the given line is ~

\( \boxed{3}\)

\( \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}\)

Let's find the slope of the shown line, using coordinates of points (0 , 2) and (2 , 8) through which the line passes ~

that is ~

The procedure which is deemed to be the type of sample in discuss is; representative sample are free of bias.

Representative sampling and random sampling are two techniques used to help ensure data is free of bias. A representative sample on the other hand is a group or set chosen from a larger statistical population according to specified characteristics. A random sample is a group or set chosen in a random manner from a larger population.

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Answer:

-79.54

Step-by-step explanation:

To answer this question we have to use BIDMAS (brackets, indices, division, multiplication, addition and subtraction).

1) This means that we first have to do the brackets! We have to be careful to do the division inside the brackets first.

This leaves us with -15 -1.87 × 32 - 4.7

2) We next have to do the multiplication!

Leaving us with -15 - 59.84 - 4.7

3) Now we can just do the subtraction!

Hope this helps, have a lovely day! :)

Answer:

-79.54

Step-by-step explanation:

= -15+(-3.7+9.15/5)*32-4.7

= -15+(-3.7+1.83)*32- 4.7

= -15(-1.87)*32- 4.7

= -15 - 59.84 - 4.7

= -79.54

Answer:

This sh't confusing but I think the answer is bank B

Step-by-step explanation:

The leaf representation is given as

              14 l

              15 l 1447

              16 l 56

              17 l 8

              18 l 366

The 10th means that after the decimal, So the foundation must be the 15.1. This will be the 15.4, 15.7, 16.5 16.6 17.8 18.3 18.6 and 18.6.

In order to help visualize the shape of a distribution, a stem-and-leaf display or stem-and-leaf plot is a tool for presenting quantitative data in a graphical manner, comparable to a histogram.

The adoption of monospaced (typewriter) typestyles during that period contributed to their appeal since they made it simple for then-current computer technology to create the images. The improved graphic capabilities of modern computers have reduced the employment of these techniques.

While a stemplot is another name for a stem-and-leaf plot, it frequently refers to a different kind of chart. The term "simple stem plot" may refer to the mapping of a matrix of y values to a common x axis, along with the identification of the common x value by a vertical line and the individual y values by symbols on the line.

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Answer:

The 3rd and the 5th

2(3+9i) , 6(1+3i)

Step-by-step explanation:

The series diverges with an integral of 1/ln(16) and the series converges with an integral of 1/4 and a sum of 1/2.

We can use the integral test to determine the convergence of the series ∑n=1∞ 1/6n. The integral of the function f(x) = 1/6x is:

\(∫f(x) dx = (1/6) ln(x) + C\)

Using the limits of integration from 1 to ∞, we get:

∫1∞ f(x) dx = (1/6) ln(∞) - (1/6) ln(1) = ∞

Since the integral diverges, the series also diverges.

We can use the integral test to determine the convergence of the series ∑n=1∞ \((n+4)/(n^2+8n+4\)). The integral of the function f(x) = \((x+4)/(x^2+8x+4)\) is:

∫f(x) dx = (1/2) ln(x^2 + 8x + 4) + 3 ln|x + 4| + C

Using the limits of integration from 1 to ∞, we get:

∫1∞ f(x) dx = (1/2) ln(∞) + 3 ln(∞ + 4) - (1/2) ln(13) - 3 ln(5) = ∞

Since the integral diverges, the series also diverges.

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Answer:

if it explaining it you will have to add the answer then add the x

Step-by-step explanation:with your answer whiches A

(a) An observer standing beside a one-lane road counted in 5 minutes 20 cars traveling at 30 mph, 30 cars traveling at 50 mph and 10 cars traveling at 60 mph. The time-mean speed of the observed cars is 900 mph.

(b) The average headway of the cars is 5.08 minutes (approximately).

(a) To calculate the space and time-mean speeds of the observed cars, we need to consider the total distance traveled and the total time taken by the cars.

Given data:

Number of cars traveling at 30 mph = 20

Number of cars traveling at 50 mph = 30

Number of cars traveling at 60 mph = 10

To find the space-mean speed, we calculate the weighted average of the speeds based on the number of cars at each speed:

Space-mean speed = [(20 cars * 30 mph) + (30 cars * 50 mph) + (10 cars * 60 mph)] / (20 + 30 + 10)

               = (600 + 1500 + 600) / 60

               = 2700 / 60

               = 45 mph

The space-mean speed of the observed cars is 45 mph.

To find the time-mean speed, we calculate the total distance traveled and divide it by the total time taken:

Total distance traveled = (20 cars * 30 mph * 5/60 hours) + (30 cars * 50 mph * 5/60 hours) + (10 cars * 60 mph * 5/60 hours)

                      = (25 miles + 41.67 miles + 8.33 miles)

                      = 75 miles

Total time taken = 5 minutes = 5/60 hours

Time-mean speed = Total distance traveled / Total time taken

               = 75 miles / (5/60) hours

               = 75 miles * (60/5)

               = 900 mph

(b) Average headway is the average time interval between successive cars passing a given point.

To find the average headway, we need to calculate the total time taken by all the cars and divide it by the total number of intervals:

Total time taken by all the cars = (20 cars + 30 cars + 10 cars) * 5 minutes

                              = 60 cars * 5 minutes

                              = 300 minutes

Total number of intervals = 60 cars - 1 (as there is no interval after the last car)

Average headway = Total time taken by all the cars / Total number of intervals

              = 300 minutes / 59 intervals

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Answer:

1. irrational

2. irrational

3. rational

4. rational

5. irrational

6. rational

Step-by-step explanation:

A rational number includes any whole number, fraction, or decimal that ends or repeats. An irrational number is any number that cannot be turned into a fraction.

1.) pi is a never ending number which means that, according to the definition above, it must be IRRATIONAL

2.) the line above the 46 means that it is repeating, making it IRRATIONAL

3.) the square root of 100 is 10, making it RATIONAL

4.) -16 is an integer (a whole number that can be positive, negative, or zero), making it RATIONAL

5.) the square root of 21 results in a long decimal that cannot be converted into a fraction, by the definition above, it is IRRATIONAL

6.) 10 is a whole number, making it RATIONAL

Answer:

No solution I believe

Step-by-step explanation:

The assembly code for the given expression is "SUB dm[5000], dm[5004]; MOV dm[5008], dm[5000]".

To convert the expression "z = (x - y) * 1" into assembly code, we need to break it down into individual assembly instructions.

1. Subtracting the values of x and y:

The assembly instruction for subtraction is "SUB destination, source". In this case, we subtract the value of y from the value of x and store the result in a temporary register. So, the instruction will be "SUB dm[5000], dm[5004]".

2. Multiplying the result by 1:

In assembly, multiplying a value by 1 is simply storing the value as it is. Since we have the result of the subtraction in a temporary register, we can directly move it to the location of z.

The assembly instruction for moving a value is "MOV destination, source". Here, we move the value from the temporary register to the memory location dm[5008]. So, the instruction will be "MOV dm[5008], dm[5000]".

After executing these two instructions, the value of z will be updated with the result of (x - y) * 1.

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