here are points A and B Plot the points for each dilation described

The velocity of a particle = i + 2t j

The acceleration of a particle = 2 j

The speed of a particle = [tex]\sqrt{1 + 4t^{2} }[/tex]

Here,

The position function is, [tex]r (t ) = ti + t^{2} j +2k[/tex]

We have to find, the velocity, acceleration, and speed of a particle with the given position function.

What is Velocity of a particle with the given position function?

The instantaneous velocity v(t) of a particle is the derivative of the position with respect to time. That is, v(t)=dx/dt.

Now,

The position function is, [tex]r (t ) = ti + t^{2} j +2k[/tex]

The velocity of a particle = [tex]\frac{d r(t)}{dt}[/tex]

[tex]r (t ) = ti + t^{2} j +2k[/tex]

[tex]\frac{d r(t)}{dt} = i + 2t j[/tex]

The acceleration of a particle = [tex]\frac{d^{2} r(t)}{dt^{2} }[/tex]

[tex]r (t ) = ti + t^{2} j +2k[/tex]

[tex]\frac{d r(t)}{dt} = i + 2t j[/tex]

[tex]\frac{d^{2} r(t)}{dt^{2} }= 2j[/tex]

The speed of a particle = [tex]| \frac{d r(t)}{dt}| = |v(t)|[/tex]

[tex]\frac{d r(t)}{dt} = i + 2t j[/tex]

[tex]|v(t)|=\sqrt{1 + 4t^{2} }[/tex]

Hence, The velocity of a particle = [tex]i + 2t j[/tex]

The acceleration of a particle = [tex]2 j[/tex]

The speed of a particle = [tex]\sqrt{1 + 4t^{2} }[/tex]

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Answer:

No.

Step-by-step explanation:

The function would be a discrete function if the individual points in the function didn't share the same x-coordinates. Both the points (0,1) and (0,3) share the same x-coordinate, x=0, so the function doesn't pass the vertical line test.

Answer:

∠ B = 82°

Step-by-step explanation:

complementary angles sum to 90° , then

∠ A + ∠ B = 90 , that is

x - 19 + 3x + 1 = 90

4x - 18 = 90 ( add 18 to both sides )

4x = 108 ( divide both sides by 4 )

x = 27

Then

∠ B = 3x + 1 = 3(27) + 1 = 81 + 1 = 82°

Answer:

2019

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

10⁰=1

9⁰=1

7⁰=1

5⁰=1

3⁰=1

1¹⁰⁰=1

so,

10⁰+9⁰+7⁰+5⁰+3⁰+1¹⁰⁰=1+1+1+1+1+1=6

Answer:

6

Step-by-step explanation:

We are working with exponents

Any number to the power of 0 is 1

a^0 = 1

1 to a power is 1

10⁰+9⁰+7⁰+5⁰+3⁰+1¹⁰⁰​

1 + 1 + 1 + 1 + 1 + 1

6

The value of A(215) and its interpretation are captured thus:

A(215) = 5515; If the accountant takes 215 hours to prepare the taxes, the cost will be $5,515

What does the function represents?

The function given as A(x) = 140 + 25x, represents the total cost of using the services of the accountants for tax computation and preparation, bearing in mind that the 140 means $140 which is the fixed charged irrespective of the number of hours it takes to prepare the tax returns whereas the 25x means that $25 is charged as variable fee for  every hour the accountant works on the tax computation

A(x) = 140 + 25x

In this case, A(215) means that 215 hours were made use of by the accountants, hence, to determine the total fees, we simply substitute for x

A(215) = 140+(25*215)

A(215) = 140+5375

A(215)=$5,515

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The value of the expression |x-1| if x>1 without using absolute value notation is x-1.

The Absolute value of any number may be defined as the distance of the given number on a number line from the point of origin. The absolute value of any number x is given by |x|. The absolute value of any number will always give a positive value regardless of the sign of the number.

For example, the absolute value of |-2| is given by 2 and the absolute value of |2| is also given by 2. Here, in the question it is given that x>1.

=> x>1

=> x-1>0

Thus, if x-1>0 then the absolute value of the expression |x-1| is given by x-1 as x-1>0.

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The value of measure of ls is 126 degrees.

It is given in the question that the measure of two supplementary angles, ls and lt, are in the ratio of 7:3.

We have to find the value of measure of ls.

Let the measure of two supplementary angles ls and lt be 7x and 3x respectively.

We know that, the sum of measure of  two supplementary angles is 180 degrees.

Hence, according to the data given in the question, we can write,

7x + 3x = 180 degrees

10x = 180

x = 180/10

x = 18 degrees

Hence,

mls = 7x = 7*18 = 126 degrees.

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Answer:

65

Step-by-step explanation:

- 2 digits ✅

- Has 13 as a factor ✅

- Sum of digits is 11 ✅

Answer:

9

Step-by-step explanation:

6 / 2(1+2)

6 / 2 (3)

6 / 2 * 3

3 * 3

9

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Step-by-step explanation:

15,910 like what said of calculator

7+(-1) = -3

Steps of adding 7+(-10) using number line are as following:

1) Draw a number line by ranging from -10 to +10.

2) Point out 7 on the number line.

3) Because -10 is added to 7 on the number line, please move 10 numbers left to 7 on the number line. We always go left in addition of a negative number on the number line.

4) The number we reach -3 on left side would be our final sum.

5) From the number we can clearly see that moving 10 number on left to 7, we get -3.

Note: We are moving left because of negative sign in front of 10.

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Answer:

(b*.18)

Step-by-step explanation:

In terms of tips, 18% of $1.00 is $0.18. So for every dollar in the total (b) we can assume that it is going to be 18% of the overall total. 18% is 18/100 or .18, so we know the tip will be .18 of b (b*.18).

Answer:

7 major of system units defination and function

Using linear function concepts, it is found that:

a) They intersect at (0,20).

b) They intersect at (14,0).

c) They intersect at (0,3).

d) The equation is: y = -10/7x + 20.

A linear function is modeled by:

y = mx + b

In which:

The intersections are the points where they cross, hence:

Main Street goes through points (0,20) and (14,0), hence the intercept is of b = 20 and the slope is found as follows:

(0 - 20)/(14 - 0) = -10/7.

Hence the equation is:

y = -10/7x + 20.

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Answer:

f(h(2)) = 3.

Step-by-step explanation:

Replace the x in f(x) by h(2).

h(2) = 3(2) - 5

       = 1,

so, f(h2) = 2(1) + 1

             =   3.

Answer:

5th - 13

6th - 20

7th - 27

8th - 34

Step-by-step explanation:

You add seven

Answer:

i think  the first one is   C and second one is C

Step-by-step explanation:

   the second one is a whole number because the square root of 49 is 7 and 7 is a whole.      

Answer:

Using the horizontal line test, the one to one functions are those which do not intersect with the line more than one time

In the given graphs, the fourth graph represents the one - one fucntion.

Use the concept of graph of fucntion defined as:

Drawing the curve that represents a function on a coordinate plane is known as graphing a function. Every point on the curve will satisfy the function equation if the curve (or graph) reflects the function.

The graph of a one-to-one function is a representation that shows each input value (x) uniquely paired with a corresponding output value (y), with no repetition or overlap in the mapping.
It passes both the vertical line test and horizontal line test, ensuring each input has a distinct output and vice versa.

In the fourth graph:

Apply the vertical line test and we get,

Each input has a distinct output.

Hence,

The fourth graph represents the one-one fucntion.

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The calculation for calculating the number of days the youngsters ate the bars for lunch is 11 = 32 - 3x.

An equation is a mathematical expression that represents the equivalence of two or more mathematical expressions.

When someone asks you to solve an equation, they typically want to determine the unknown values for which the equation is true (the equality between expressions should hold true for those values).

An equation's solutions are the values of the variables involved in the equation for which the equation holds true.

Given that Ms Jordan purchases a box of 32 granola bars every day, each of her three children consumes one granola bar for lunch, there are only 11 bars remaining.

The algorithm for calculating the number of days the youngsters ate the bars for lunch;

11 = 32 - 3x

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Answer:

(0,-2)

Step-by-step explanation:

That point is the y intercept. (4/3,0) would be the x.

Answer: 1/5

Step-by-step explanation: 3/15 divided by 3= 1/5

The answer is 1/5.

First, You have to figure out if there are any numbers that go into both the numerator and denominator evenly.

This number, in this problem, would be three.

This is because 3/3=1 and 15/3=5.

Given that it asks for a fraction in the simplest form, we of course have order those numbers as numerator and denominator.

The three is the numerator, or, above the fifteen, or the denominator.

This must mean that the one is the numerator.

Because the 1 is the numerator, that must mean the 5 is the denominator, which brings us to the answer.... 1/5

The minimum and maximum distance from the earth to the sun are 91.4 and 94.5 million miles respectively.

Absolute values are the value of any digit without considering the sign.

So all negative values will be considered positive for absolute value.

For example, the absolute value of -2 will be 2 and the absolute value of -7 will be 7.

Given that,

The average distance from the earth to the sun is 92.95 million miles.

Actual is varies by 1.55 million miles.

Minimum value  = | 92.95 - 1.55 | = 91.4 million mile

Maximum value =  | 92.95 +1.55 | = 94.5 million mile

Hence "The minimum and maximum distance from the earth to the sun are 91.4 and 94.5 million miles respectively".

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True

the sum of interior angles is equal to exterior

A point that is Interior to an Angle is found on the Exterior of the Angle

The statement is false

How do we explain?

A point that is interior to an angle is located within the angle, not on the exterior. The interior of an angle refers to the region enclosed by the angle's sides.

A point that is interior to an angle is located within the angle, not on the exterior. When we refer to the interior of an angle, we are referring to the space enclosed by the angle's sides and vertex.

In geometric terms, an angle consists of two rays that share a common endpoint called the vertex. The interior of the angle is the region between these two rays while on the other hand, the exterior of an angle refers to the space outside the angle, beyond its sides.

In conclusion, a point that is interior to an angle is found within the angle itself, not on the exterior.

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The correct option is d)10.01 kg​;       y + x = 10.01 kg.

When converting units, you are generally given one measure but instead asked to convert it to another.

For the given values in the question;

x = 10 g  and y = 10 kg

As, both the values are of mass.

For adding both values, the unit must be same.

So, convert the value of x in kg from g.

1 kg = 1000 g

Thus, 1 g = 1/1000 kg

10 g = 10/1000 kg

10 g = 0.01 kg

Now add both;

x + y = 0.01 + 10

x + y = 10.01 kg

Thus, the value of x + y is found as 10.01 kg.

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The correct question is-

a)10.1 kg

b)100.1 g

c)10.1 kg

d)10.01 kg​

Answer:

C

Step-by-step explanation:

You are looking for the arithmetic sequence.  

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1)d

In this case the formula is written:

t(x) = 3 + 4(x-1)

The 3 is the first term.  The 4 is how much the sequence is increasing each time.  (x-1) stands for the term we are looking for.  If we were looking for the 15th term, we would have (15-1) in the parentheses.

The perimeter of the triangle is 40 units

From the question, we are to determine the perimeter of the given triangle

From the given diagram, we can observe that the triangle is a right triangle

The vertical length of the triangle is 15 units

and the horizontal length of the triangle is 8 units

Thus,

We can find the hypotenuse by using the Pythagorean theorem

Let the hypotenuse be h

Then,

h² = 15² + 8²

h² = 225 + 64

h² = 289

h = √289

h = 17 units

Now, for the perimeter of the triangle

The perimeter of a triangle is the sum of all its three sides

Thus,

The perimeter. P, of the triangle is

P = 15 + 8 + 17

P = 40 units

Hence, the perimeter of the triangle is 40 units

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There is no such number that has the result is the same number written in base 7 and base 10.

Decimal and Octal numbers:

Decimal system is most familiar number system to the general public. It is base 10 which has only 10 symbols − 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

Whereas octal system is one of the number systems to represent numbers. It is base 8 which has only 8 symbols − 0, 1, 2, 3, 4, 5, 6, and 7.

Given,

When a three-digit number written in base 10 has its final digit moved to the beginning, the result is the same number written in base 7.

Here we need to find all such numbers.

Let abc be the starting number, where the catenated letters represent digits, and not factors like in the product

=> a x b x c

And each of a,b, and c can be elements of the list,

=> {1,2,3,4,5,6,7,8,9,0}

Except a≠0.

Since abc is a base-10 numeral, we can also write it as

=> 10²a + 10¹b + 10⁰c

Which can be expanded as,

=> 100a + 10b + c ----------------------(1)

Moving the last digits to the first slot makes the new number,

=> 100c + 10a + b------------------------(2)

So, here the value c≠0.

We know that, the digits in the base-10 numeral cab are identical to those of the base-7 numeral that is written as cab₇.

In the equation form it is equal to,

=> 7²c + 7¹a + 7⁰b

=> 49c + 7a + b ---------------------(3)

but since we're working in base 7 now, the digits a,b, and c cannot exceed 6.

Now, we want to solve for a, b, and c such that

By equalizing the equations 2 and 3,

=> 100c + 10a + b = 49c + 7a + b

=> 100c + 10a + b - 49c - 7a - b

=> (100 - 49)c + (10 - 7)a

=> 51c + 3a

=> 3 (17c + a)

Both a and c must be positive, but this equation has solution,

=> a = -17c

So there are no positive integers solutions, and hence no such number.

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