Determine if the given vector is in the range of t(x) = ax where a = 1 -2 0 3 2 1

Using sine law, the length of t is 11.34 units

A fundamental conclusion of trigonometry that connects a triangle's sides and angles is known as the law of sines. It claims that the following relationship holds for any triangle with sides a, b, and c and opposite angles a, b, and c:

a / sin A = b / sin B = c / sin C

In other words, each of the triangle's three sides has a length that is equal to the sine of the angle opposite it. Any triangle, correct or not, can be related to another triangle in this way.

When some of the information is available, it is common to utilize the Law of Sines to find the triangle's unknown side lengths or angle measurements. In addition to the Law of Cosines, it can also be employed alone.

Using sum of angle of triangle;

V + U + T = 180

v + 100 + 36 = 180

v + 136 = 180

v = 180 - 136

v = 44°

8 / sin 44 = t / sin 100

t = 8 sin100 / sin44

t = 11.34

The value of t is 11.34 units

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Yes , we can construct a triangle which has the side lengths as 11 cm 12 cm and 15 cm , because the given sides satisfies the criteria to form a triangle .

The Condition for the sides to form a triangle is that the Sum of the any two sides of the triangle must be greater than the third side of the triangle .

The sides of the triangle are given as ⇒ 11cm ,12cm and 15cm ;

On adding the two sides ,

we get ;

⇒ 11 + 12 = 23 > 15 ; True

⇒ 12 + 15 = 27 > 11 ; True

⇒ 11 + 15 = 26 > 12 ; True

So , we can see that all the three conditions are satisfied .

Therefore , the triangle can be constructed with the sides 11cm ,12cm and 15cm .

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Step-by-step explanation:

linear functions (or lines) have really only 2 attributes :

the slope (indicating the inclination of the line).

the y-intercept (the intersection with the y-axis) or the x-intercept. either way, they show the actual position of the line.

the lines intersect at one point, if they have different slopes.

they intersect at infinitely many points, if the slope and the y- or x-intercepts are equal (ultimately that means the lines are identical, so every point is an intersection point).

if they have the same slope but different y- or x-intercepts, it means they are parallel and will never intersect.

Answer:

James is 18 and Patrick is 38

Step-by-step explanation:

Let p = Patrick's age

Let j= James' age

p = j + 20

p + 2 = 2(j+2)        Substitute j + 20 for p

j + 20 + 2 = 2j + 4  Combine like terms.

j + 22 = 2j + 4  Subtract j from both sides

j -j + 22 = 2j - j + 4

22 = j + 4    Subtract 4 from both sides

22 - 4 = j + 4 - 4

18 = j

James is 18 years old.

Substitute 18 for j  in p = j + 20

p =  18 + 20

p = 38

Patrick is 38

Answer:

[tex]-11\sqrt{5}-11\sqrt{6}[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{11}{\sqrt{5}-\sqrt{6}}[/tex]

To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator.

The conjugate of a binomial is where we change the sign between the two terms of the binomial.  So the conjugate of (√5 - √6) is  (√5 + √6).

[tex]\implies \dfrac{11}{\sqrt{5}-\sqrt{6}} \cdot \dfrac{\sqrt{5}+\sqrt{6}}{\sqrt{5}+\sqrt{6}}[/tex]

[tex]\implies \dfrac{11(\sqrt{5}+\sqrt{6})}{(\sqrt{5}-\sqrt{6})(\sqrt{5}+\sqrt{6})}[/tex]

[tex]\implies \dfrac{11(\sqrt{5}+\sqrt{6})}{\sqrt{5}\sqrt{5}+\sqrt{5}\sqrt{6}-\sqrt{6}\sqrt{5}-\sqrt{6}\sqrt{6}}[/tex]

[tex]\implies \dfrac{11(\sqrt{5}+\sqrt{6})}{5-6}[/tex]

[tex]\implies \dfrac{11(\sqrt{5}+\sqrt{6})}{-1}[/tex]

[tex]\implies -11(\sqrt{5}+\sqrt{6})[/tex]

[tex]\implies -11\sqrt{5}-11\sqrt{6}[/tex]

Answer:

325 hamburgers were sold on Tuesday

Step-by-step explanation:

We can start solving the problem by using algebra. Let H be the number of hamburgers sold and C be the number of cheeseburgers sold. We know from the problem that:

H + C = 713 (total number of hamburgers and cheeseburgers sold)

C = H + 63 (there were 63 more cheeseburgers sold than hamburgers)

We can substitute the second equation into the first equation:

H + (H + 63) = 713

2H + 63 = 713

2H = 650

H = 325

Answer:

NO

Step-by-step explanation:

it is not possible for a cylinder to have a surface area greater than 100 cm² and a volume less than 100 cm³. The surface area of a cylinder is given by the formula 2πr² + 2πrh, where r is the radius of the base and h is the height of the cylinder. A cylinder with a surface area greater than 100 cm² would have to have a relatively large radius and/or height.

On the other hand, the volume of a cylinder is given by the formula πr²h. Even if the radius is small and the height is big, the product of both will be bigger than 100 cm³. Therefore, it is not possible for a cylinder to have a surface area greater than 100 cm² and a volume less than 100 cm³.

The sum of all possible values of n is 448.

Let n be a positive number.

We are given that 72!/n is a multiple of 2^n, but not a multiple of 2^(n-1).

We can start by finding all values of n that fit this criteria:

n = 1: 72!/1 = 479001600 is not a multiple of 2^1, but is a multiple of 2^0.

n = 2: 72!/2 = 1197500400 is not a multiple of 2^2, but is a multiple of 2^1.

n = 3: 72!/3 = 59875200 is a multiple of 2^3, but not a multiple of 2^2.

n = 4: 72!/4 = 29937600 is a multiple of 2^4, but not a multiple of 2^3.

n = 5: 72!/5 = 14968800 is a multiple of 2^5, but not a multiple of 2^4.

n = 6: 72!/6 = 7484400 is a multiple of 2^6, but not a multiple of 2^5.

n = 7: 72!/7 = 3742200 is a multiple of 2^7, but not a multiple of 2^6.

n = 8: 72!/8 = 1871100 is a multiple of 2^8, but not a multiple of 2^7.

n = 9: 72!/9 = 935550 is a multiple of 2^9, but not a multiple of 2^8.

n = 10: 72!/10 = 467775 is a multiple of 2^10, but not a multiple of 2^9.

Therefore, the sum of all possible values of n is 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 = 448.

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Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

When you roll a di, there is a  [tex]\frac{1}{2}[/tex] chance you will either get an even or an odd number. Since this needs to happen twice, we will square this fraction, giving us:

[tex](\frac{1}{2}) ^{2} = \frac{1}{4}[/tex]

So, the probability to roll an even number and then roll an odd number is [tex]\frac{1}{4}[/tex].

Hope this helped!

Answer:

U' (- 1, 3 )

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

U (- 1, - 3 ) → U' (- 1, 3 )

An expression that represents the height of a tree is 6.7 + 2.9.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Here, we have

Given

The initial height of the tree is 6.7 feet

The increase in height per year = 2.9 feet

Thus,

The expression will be = 6.7 + 2.9t,

Here t represents the number of years.

Hence, an expression that represents the height of a tree is 6.7 + 2.9.

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If the right hand side of the equation is non-negative real number, the equation will have two solution that include all real numbers.

An absolute value equation of the form |x| = k (where k is a constant) will have two solutions, one positive and one negative, that are the same distance from 0 on the number line.

To determine if the solutions of the equation include all real numbers, you can examine the value of k. If k is a non-negative real number, then the two solutions of the equation will include all real numbers, because any real number is either positive or negative and the same distance from 0 as k.

For example, if the equation is |x| = 5, the two solutions of the equation are x = 5 and x = -5, which include all real numbers.

On the other hand, if k is a negative real number or a complex number, the equation is not valid and there are no solutions.

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Agile methods of system development stresses intense team-based effort and reflects a set of community-based values.

Agile Method:

Agile software development is more than frameworks like Scrum, Extreme Programming, and Feature Driven Development (FDD).

Agile software development is more than practices such as pair programming, test-driven development, stand-ups, planning sessions, and sprints.

Agile software development is a collective term for a set of frameworks and practices based on the values ​​and principles stated in the Manifesto for Agile Software Development and the 12 principles behind them. In general, if you approach software development a certain way, it's good to live by those values ​​and principles and use them to find out what's right in your particular context.

One of the things that makes Agile different from other software development approaches is its focus on the people doing the work and how they work together. Solutions evolve through collaboration between cross-functional, self-organizing teams using contextually appropriate practices.

Collaboration and self-organizing teams are a big focus in the Agile software development community.

Alistair Cockburn suggested that a methodology is a set of rules that teams are willing to follow. This means that each team has its own methodology, which differs in many ways from that of every other team.

Agile methodologies are practices that teams follow to follow Agile values ​​and principles.

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Answer:

The slope of the line is -10/11

Step-by-step explanation:

To find the slope with points you would use the formula [tex]m = \frac{y2 - y1}{x2 - x1}[/tex]

Now since the line crosses the y-axis at 17, that would be where the y-intercept is, meaning there is a point at (0, 17).

With that, we can find the slope with (11, 7) and (0, 17) in the formula above

So, [tex]m = \frac{17 - 7}{0 - 11}[/tex]

which will simplified to, [tex]m = -\frac{10}{11}[/tex]

So the slope is - 10/11

The measure of the smaller angle between the hands of a 12-hour clock at 12:25 pm is 137.5 degrees.

The hour hand of a 12-hour clock completes one full rotation in 12 hours while the minute hand completes one full rotation in 60 minutes. To find the measure of the angle between the hands of a 12-hour clock at 12:25 pm, we need to calculate the relative position of the hands with respect to the 12 o'clock position.

At 12:25 pm, the minute hand is pointing to the 12.25 mark on the clock which is 25 minutes after 12 o'clock and the hour hand is pointing to the 12 o'clock mark.

The minute hand moves 360 degrees every 60 minutes, so in 25 minutes, it would have moved (360/60)*25 = 75 degrees.

The hour hand moves 360 degrees every 12 hours, so in 25 minutes, it would have moved (360/12*60)*25 = (30)*25 = 750/60 = 12.5 degrees.

The angle between the hands is the absolute difference between their positions.

the angle between the hands = |75-12.5| = 62.5 degrees

However, the clock has two hands and thus we have two angles between the hands.

Therefore, the measure of the smaller angle between the hands of a 12-hour clock at 12:25 pm is 180-62.5 = 137.5 degrees.

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Answer:

60mm

Step-by-step explanation:

240*1/4=60mm

Answer:

40 mm

Step-by-step explanation:

Given information:

To find the length of the children's shoes, multiply the length of the adult shoes by the scale factor:

[tex]\begin{aligned}\implies 240 \times \dfrac{1}{6}&=\dfrac{240 \times 1}{6}\\\\&=\dfrac{240}{6}\\\\&=\dfrac{40 \times 6}{6}\\\\&=40\; \sf mm\end{aligned}[/tex]

Therefore, the length of the children's shoes is 40 mm.

Answer: The volume of a sphere can be calculated using the formula V = 4/3 * pi * r^3, where V is the volume and r is the radius of the sphere. In this case, we can use the Pythagorean theorem to find the radius of the sphere. The hypotenuse of the right triangle is 16 cm and is also the diameter of the sphere, therefore the radius of the sphere is half of the hypotenuse or 8 cm.

Now we can use this value of radius to calculate the volume of the sphere.

V = 4/3 * pi * 8^3

V = 4/3 * pi * 512

V = 2197.333 cm^3 (rounded to the nearest hundredth)

So, the volume of the sphere is 2197.333 cm^3

Step-by-step explanation:

Answer:

I don't know ooo y the same time that I can come get you if you want to

Therefore , the solution of the given problem of linear equation comes out to be chris sold = g/8 -17.

A model of linear regression is one that follows the algebraic formula y=mx+b. The y-intercept is m, and the slope is B. Although both y and x are distinct parameters, the foregoing sentence is sometimes referred to as a "mathematical equation with two variables." Bivariate linear equations only have two variables. Application areas of linear equations result in zero in all cases. The equation for one linear equation is Y=mx+b where m is the slope and b is the y-intercept. Y=mx+b is the formula for an equation, where m stands for slopes and b for the y-intercept.

Here,

Given : there are 8 employees on the game .

chris sold 17 fewer games than what the team averaged per employee.

Thus,

g be the number of total employee selling games:

=> chris sold = g/8 -17

Therefore , the solution of the given problem of linear equation comes out to be chris sold = g/8 -17.

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Reason:

The ratio of white to green is 2:5.

The ratio of green to blue is 1:3, which can be scaled up to 5:15 after multiplying both parts by 5.

Write out the ratios 2:5 and 5:15 to notice that we have the inner '5's match up. This gives a triple ratio of 2:5:15 which is the ratio of white to green to blue in that exact order.

Ignoring the middle value gives the ratio of white to blue being 2:15

For every 2 white beads, there are 15 blue beads.

The potential energy of a 50kg boulder at the ledge of a cliff 250m high is 122500 J.

Potential energy is the energy carried by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.

The PE energy of a boulder 250 m from the ground is given by the formula

PE = h x m x g    where h is the height above the ground, m is the mass, and g is the acceleration of gravity.

Putting the given values in the equation

PE = 250m x 50 kg x 9.8 m/s²  =  122500 J

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Therefore , the solution of the given problem of differential equations comes out to be  y = cos x + c.

Sequences in which the difference between succeeding terms is constant are known as arithmetic progressions. For instance, an arithmetic progression with a tolerance of 2 is the sequence 5, 7, 9, 11, 13, and so on. An arithmetic progression (A.P.) is a progression where the tolerance between two succeeding numbers is always the same. Arithmetic progression can be of two types: There are a finite number of terms in a finite geometric progression. The series' early, late, tolerance, and number of terms can be determined.

Here,

Given :dy/dx = x+1

dy = (x+1)dx

=>y = 1/2x² + x +c

dy/dx = -sinx

dy = -sinx dx

=> y = cos x + c

Therefore , the solution of the given problem of differential equations comes out to be  y = cos x + c.

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As per the given distribution the consumer group claims that the difference in proportions has a mean of 0.05.

The term mean in math is defined as the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Here we have given that the consumer group is investigating two brands of popcorn, R and S.

And the population proportion of kernels that will pop for Brand R is 0.90 where as the population proportion of kernels that will pop for Brand S is 0.85.

Then the difference of the mean is calculated as,

=> 0.90 - 0.85

=> 0.05

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There are 10 possible 3-digit numbers which can be generated using numbers 1, 2, 3, 4, and 5 without repeating any digits.

There are 5 choices for the first digit, 4 choices for the second digit, and 3 choices for the third digit. This can be expressed using the combination formula:

nCr = n! / r!(n - r)!

So, the number of possible 3-digit numbers with no digit repeated can be calculated as 5C3 = 5!/(3!*2!) = 10.

Therefore, there are 10 possible 3-digit numbers which can be generated using numbers 1, 2, 3, 4, and 5 without repeating any digits. These numbers are 123, 124, 125, 134, 135, 145, 234, 235, 245, and 345.

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The function increasing on interval  [0, 3] and decreasing on the interval  [-6, 0] ∪ [3, 5].

What is increasing and decreasing function?

For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.

F is rising on the interval if f′(x) > 0 on an open interval.

F is decreasing on the interval if f′(x) < 0 on an open interval.

We have to find the intervals of increasing and decreasing function from the given graph.

From graph we can see that graph is increasing on the interval [0, 3].

And decreasing on the interval [-6, 0] ∪ [3, 5].

Hence, the function increasing on interval  [0, 3] and decreasing on the interval  [-6, 0] ∪ [3, 5].

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Answer: -4

Step-by-step explanation: Start where the y-intercept is and go from there to the next point.

You go down by 4 to go to the point and then to the left one.

-4/1 = rise/run

-4= rise/run

Answer: its A

Step-by-step explanation:

The solution set for the function f(x) ≤ 0 as required to be determined in the task content in interval notation is; ( infinity, 3 ].

It follows from the task content that the values of x for which f(x) ≤ 0 be determined considering the given graph.

As evident in the given graph; the portion of the graph which is below the x-axis (i.e below the line f (x) = 0 ) lies in the interval; ( infinity, 3 ] for variable x.

On this note, it can be inferred that the required solution set for f(x) ≤ 0 is; ( infinity, 3 ].

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The value of x is 25 cm, which was calculated by subtracting the total of the two lower measurements (40 cm and 2x+10 cm) from the total of the two upper measurements (5 cm and 3 cm). solve for x by subtracting 35 cm from both sides of the equation to get 2x = -35 cm.

x = 25 cm

We can calculate the value of x by subtracting the total of the two lower measurements (40 cm and 2x+10 cm) from the total of the two upper measurements (5 cm and 3 cm).

Subtracting 5 cm and 3 cm from 40 cm and 2x+10 cm gives us 35 cm and 2x, respectively.

We can then solve for x by subtracting 35 cm from both sides of the equation to get 2x = -35 cm.

Dividing both sides by 2 gives us x = -17.5 cm.

Since x must be a positive value, the correct answer is x = 25 cm.

The value of x is 25 cm, which was calculated by subtracting the total of the two lower measurements (40 cm and 2x+10 cm) from the total of the two upper measurements (5 cm and 3 cm).

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