What is the greatest common factor (GCF) of 9 and 18

The vector and parametric equations are r(t) = [t/2, (4t/3 - 1), (1 - 3t/4)] and x = t/2, y = -1 + 4t/3, z = 1 - 3t/4.

We have P(0, -1, 1), Q(1/2, 1/3, 1/4)

We have to find a vector equation and parametric equations for the line segment that joins P to Q.

Vector equation of a line segment joining the points with position vectors r0 and r1 is given by

r =(1 - t)r0 + tr1

Where, t ∈ [0, 1]

Here, r0 = (0, -1, 1) and r1 = (1/2, 1/3, 1/4)

So, r(t) = (1 - t)(0, -1, 1) + t(1/2, 1/3, 1/4)

r(t) = [((1 - t)(0) -1(1 - t) + 1(1 - t)] + [t/2, t/3, t/4]

r(t) = [0, (t - 1), (1 - t)] + [t/2, t/3, t/4]

On simplification,

r(t) = [(t/2 + 0), (t + t/3 - 1), (1 - t + t/4)]

r(t) = [t/2, (4t/3 - 1), (1 - 3t/4)]

Where, t ∈ [0,1]

The parametric equations for the line segment are

x = t/2, y = -1 + 4t/3, z = 1 - 3t/4

Where, t ∈ [0, 1]

Therefore, the vector and parametric equations are r(t) = [t/2, (4t/3 - 1), (1 - 3t/4)] and x = t/2, y = -1 + 4t/3, z = 1 - 3t/4.

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The given question is incomplete, complete question is:

Find a vector equation and parametric equations for the line segment that joins P to Q. P(0, - 1, 1), Q(1/2, 1/3, 1/4).

Applying the properties of similar triangles, the other side lengths of ΔDEF are: B. 9 and 12

The ratio of the corresponding sides two triangles that are similar to each other are the same/equal.

here, we have,

Given that ΔABC and ΔDEF are similar triangles, therefore:

Let, a = 6, b = 8, and c = 12 be the sides of ΔABC.

Let, x, y, and z be the sides of ΔDEF.

Let z = 18

Thus:

a/x = b/y = c/z

Substitute

6/x = 8/y = 12/18

Find x using 6/x = 12/18:

6/x = 12/18

Cross multiply

x = 18*6/ 12

x = 9

Find x using 8/y = 12/18:

8/y = 12/18

Cross multiply

x = 18*8/12

x = 12

Therefore, applying the properties of similar triangles, the other side lengths of ΔDEF are: B. 9 and 12

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The gopher’s new elevation relative to the surface of the ground will be

13¹/₄ inches.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

Given that a gopher is in a hole that is 6¹/₄ in. below the surface of the ground. and, Then digs 7¹/₂ in. deeper.

The gopher’s new elevation relative to the surface of the ground will be calculated as;

⇒  6¹/₄ + 7¹/₂

⇒ 25/4 + 15/2

Make denominators the same as;

⇒ 25/4 + 30/4

⇒ (25 + 30) / 4

⇒ 55 / 4

⇒ 13¹/₄ inches.

Thus, the gopher’s new elevation relative to the surface of the ground will be 13¹/₄ inches.

The complete question is given below,

A gopher is in a hole that is 6 1/4 in. below the surface of the ground. It then digs 7 1/2 in. deeper. What is the gopher’s new elevation relative to the surface of the ground? Show your work.

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The expression (4a³b^4)³ when evaluated is 64a^9b^12

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

(4a³b^4)³

When expanded, we have

(4a³b^4)³ = 4³ * (a³)³ * (b^4)³

Evaluate the exponents

So, we have the following representation

(4a³b^4)³ = 64a^9b^12

Hence, the solution si 64a^9b^12

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By using the formula that connects the linear velocity to the angular velocity, we may convert metres per second (m/s) to radians per second (rad/s).

Using the formula that connects the linear velocity to the angular velocity, we may convert metres per second (m/s) to radians per second (rad/s).

The equation reads: Radius divided by linear velocity gives you the angular velocity (). (r) where R is in metres, V is in m/s, and is in rad/s.

Direct conversion from m/s to rad/s is not possible if the radius is omitted. The aforementioned formula can be used to determine the missing value and then convert m/s to rad/s if you know the radius or the angular velocity. You can use the formula to determine the angular velocity in rad/s, for instance, if you know the linear velocity v in m/s and the radius r in metres.

ω = v / r

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Answer:

Step-by-step explanation:

To find the surface area of the silo, we need to calculate the areas of the cylinder and hemisphere separately, and then add them together.

The formula for the surface area of a cylinder is:

A_cylinder = 2πrh + 2πr^2

where r is the radius of the base of the cylinder, and h is the height of the cylinder.

In this case, r = 15 feet and h = 30 feet, so we have:

A_cylinder = 2π(15)(30) + 2π(15)^2

A_cylinder = 900π + 450π

A_cylinder = 1350π

The formula for the surface area of a hemisphere is:

A_hemisphere = 2πr^2

where r is the radius of the hemisphere.

In this case, the radius of the hemisphere is also 15 feet, so we have:

A_hemisphere = 2π(15)^2

A_hemisphere = 450π

To find the total surface area of the silo, we add the surface areas of the cylinder and hemisphere:

A_total = A_cylinder + A_hemisphere

A_total = 1350π + 450π

A_total = 1800π

Using 3.14 for π, we can approximate the total surface area as:

A_total ≈ 5652 square feet

Therefore, the farmer will need to cover approximately 5652 square feet of surface area to paint the outside of the silo.

True (but a parallelogram is not always a square). This is because a parallelogram is a quadrilateral with 2 pairs of parallel sides, and a square fits the requirements.

The option representing the solution of the inequality is given as follows:

D) There are no solutions.

The inequality for this problem is defined as follows:

-6x + 14 < -28 and 3x + 28 < 25.

The and operation means that we must solve each inequality, and then obtain the intersection of the two solutions.

The solution to the first inequality is given as follows:

-6x + 14 < -28

6x - 14 > 28

6x > 42

x > 7.

The solution to the second inequality is given as follows:

3x + 28 < 25.

3x < -3

x < -1.

There is no intersection between x > 7 and x < -1, hence the system has no solutions.

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The inequality that represents the number of streamers x and balloons y the student council can buy is given as follows:

3.50x + 0.75y ≤ 100.

Each streamer costs $3.50, hence the total cost of purchasing x streamers is given as follows:

3.5x.

Each balloon costs $0.75, hence the total cost of purchasing y balloons is given as follows:

0.75y.

Then the total cost of purchasing x streamers and y balloons is given as follows:

3.50x + 0.75y.

The amount spent can be of at most $100, hence the inequality is given as follows:

3.50x + 0.75y ≤ 100.

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Answer:

21

Step-by-step explanation:

21

187/17 is 11, so x = 11. Substituting 11 in for x gives you 93 for the measure of angle Q and 87 for the measure of angle R.

Since, 01 kilogram is approximately equal to 2.2046226218 lbs.

Therefore, 65 Kilogram is 143.3 lbs.

Pound:

Pound is the name of a series of units of mass ranging from 300 to 600 grams. It refers to an avoirdupois pound (454 grams), most commonly divided by 16 avoirdupois ounces.

Kilogram:

The kilogram or kilogram (symbol: kg) is the basic unit of mass in the SI system. It is defined equal to the mass of the International Prototype in kilograms. It is the only SI base unit that uses prefixes and is still defined in terms of artifacts rather than basic physical properties. A kilogram is equivalent to £2.205 in the English system used in the United States.

According to the Question:

To find how many pounds are in kilograms, you can convert kg to pounds using this formula:

X(lb) = Y(kg) / 0.45359237

Now,

Converting 65 kg to lbs:

To convert 65 kg to pounds:

⇒ X(lbs) = 65(kg) / 0.45359237

⇒ 143.3005 lbs

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The coordinates of P are (-0.82, 3.56).

The coordinates of M are (-2.1, -2.2).

The midpoint of a line segment is written as,

x = (a + c)/2

y = (b + d) / 2

Where (x, y) are the coordinates of the midpoint and (a, b) and (c, d) are the two endpoints.

We have,

R = (4.3, 7.4)

T= (-8.5, -2.2)

S = (4.3, -2.2)

Segment RT is divided into 5 equal parts.

So,

TP : PR = 3 : 2 = m : n

The coordinates of P.

T= (-8.5, -2.2) = (a, b)

R = (4.3, 7.4) = (c, d)

x = [tex]\frac{mc + na}{m + n}[/tex]

x = [tex]\frac{3\times4.3 + 2\times-8.50}{5}[/tex]

x = [tex]\frac{12.9 - 17}{5}[/tex]

x = [tex]\frac{-4.1}{5}[/tex]

x = -0.82

And,

y = [tex]\frac{md + nb}{m + n}[/tex]

y = [tex]\frac{3\times7.4 + 2\times-2.2}{5}[/tex]

y = [tex]\frac{22.2 - 4.4}{5}[/tex]

y = 3.56

The coordinates of P are (-0.82, 3.56).

Now,

T= (-8.5, -2.2)

S = (4.3, -2.2)

M is the midpoint of TS.

So,

M = (x, y)

x = [tex]\frac{(4.3 - 8.5)}{2}[/tex] = [tex]\frac{x-4.2}{2}[/tex] = -2.1

y = [tex]\frac{-2.2 - 2.2}{2}[/tex] = [tex]\frac{-4.4}{2}[/tex] = -2.2

M = (x, y) = (-2.1, -2.2)

Thus,

The coordinates of P = (-0.82, 3.56).

The coordinates of M = (-2.1, -2.2).

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Answer:

The answer is (-3.38,1.64),(-0.82,-2.2)

Step-by-step explanation:

I just got it right on the test

The length of the shadow of the maple tree will be 15 meters.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

A shadow 30 meters long is cast by a fir tree that is 16 meters tall. If a nearby maple tree is 8 meters tall.

Let 'S' be the shadow of the maple tree. Then the equation is given as,

16 / 30 = 8 / S

0.533 = 8 / S

S = 8 / 0.533

S = 15 meters

The length of the shadow of the maple tree will be 15 meters.

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Answer: 125.4

llllljkjkjkjkkjkjkjkjkjkkjkjjkjkjkjkjkjkjjkjkjkjkjkkjkjkjjkjkjjkjkjkjkjkjkjkjkjkjkjkjkjkjjkjkjkjkjkjkjkjkjkjkkjjkkjkjkjkjkkjkjkjkjkjkjjkjkkjkjkjkjkjkjkjkjkjkjkjkkjkjkjkjkjkjkjkjkj

The length of the segment AC is 40 units

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

The quadrilateral ABCD is a rhombus

The diagonals of rhombus bisect each other

Using the above as a guide, we have the following:

AC = 2 * EC

Substitute the known values in the above equation, so, we have the following representation

AC = 2 * 20

Evaluate

AC = 40

Hence, the length is 40 uints

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The expression [tex](3 \times 5)^4[/tex] is equivalent to 10+5 to the fourth power.

Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.

To find equivalent expressions of some expressions, we can either make it look more complex or simple. Usually, we simplify it.

We need to find the expression into an equivalent form 10+5 to the fourth power

Therefore,

This expression 10+5 to the fourth power could also be given as;

10 + 5 = 15

That is [tex]15^4[/tex]

We can also write as;

[tex](3 \times 5)^4[/tex]

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Simplified form of the polynomial -4(2a+7)+3a+18 is -5a - 10. It is a binomial.

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Given expression,

-4(2a+7)+3a+18

using distributive property

-4(2a) -4(7) + 3a + 18

-8a - 28 + 3a + 18

Solving like terms

-5a - 10

The solved polynomial is a binomial, since it has two terms.

Hence, simplified form of the given polynomial is -5a - 10, it is a binomial

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The relative frequency is the proportion of the total numbers in a data set corresponds to a specific class interval and hence summing over all the relative frequencies must add up to 1, or 100%.

The frequency distribution table is made by building the class intervals of the raw data set, specifically when too many values are occurring many times; we group similar values in the same category, according to a pre-determined range of values. It is a two-column table in which the first column consists of class intervals and the second consists of the frequency corresponding to each interval.

The frequency distribution is made when the raw data is large and when the same number is repeated many times, that is where the concept of frequency comes into play.

Since, the frequency is the count of specific numbers in a data set, the sum of all frequencies corresponding to every class interval has to be the total number of values in the data set.

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The given question is incomplete, complete question is:

What is the sum of all frequencies in a frequency distribution? and why is the sum of all relative frequencies equal to 1?

Answer:

$1,489.88 (nearest cent)

Step-by-step explanation:

To calculate gross pay, multiply the number of hours worked by the pay per hour.

Warren worked 36.5 hours one week and 32 hours the week before.

Therefore, the total number of hours Warren worked was:

Multiply the total number of hours worked by Warren's rate of pay of $21.75 per hour:

Therefore, Warren's gross pay for the two weeks was $1,489.88 (nearest cent).

Answer:

$1489.875

Step-by-step explanation:

Warren's gross pay for 36.5 hours last week can be calculated as follows:

Gross pay for 36.5 hours = $21.75/hour * 36.5 hours = $793.875

Similarly, Warren's gross pay for 32 hours the week before can be calculated as follows:

Gross pay for 32 hours = $21.75/hour * 32 hours = $696

Adding the gross pay for the two weeks, we get:

Gross pay for 2 weeks = $793.875 + $696 = $1489.875

The overall profit of what Stuart sold is 52 dollars.

Stuart sold 8 couches and 11 armchairs at his furniture store yesterday and he made a 10 dollars loss on each couch and a 12 dollars profit on each armchair.

Therefore, the overall profit or loss can be calculated as follows:

Total loss on the couch = 8 × 10 = 80 dollars

Total profit on the armchairs = 11 × 12 = 132 dollars

Therefore,

Overall profits = 132 - 80

Overall profits = 52 dollars

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Answer:

Step-by-step explanation:1/9

Answer:

50%

12.5%

1%

10%

37.5%

87%

Answer:

27)50%

28)12.5%

29)1%

30)10%

31)38.4%

32)87%

The length of paper he used for wrapping paper is, 702 meters²

Surface area is the sum of the areas of all the faces (or surfaces) of a three-dimensional object. It is a measure of how much area the surfaces of an object take up in two dimensions. The surface area of a solid can be found by adding up the areas of its faces.

To calculate the amount of wrapping paper needed, we need to find the total surface area of the gift box. The surface area of a right rectangular prism is given by the formula:

surface area = 2(lw + wh + lh)

where l, w, and h are the length, width, and height of the prism, respectively.

In this case, the dimensions of the gift box are 9 meters, 9 meters, and 15 meters, so:

surface area = 2(9 x 9 + 9 x 15 + 15 x 9)

                     = 2(81 + 135 + 135)

                     = 2(351)

                     = 702 square meters

Therefore, Lavaughn used 702 square meters of wrapping paper for the gift box.

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Answer:

51,300 rupees

Step-by-step explanation:

Surface area of the 2 short walls = 2 x 30 x 2.5 = 150

Surface area of the 2 long walls = 2 x 50 x 2.5 = 250

Surface area of the floor = 50 x 30 = 1500

Total surface area = 150 + 250 + 1500 = 1900 m²

27 rupees/m² x 1900 m² = 51300 rupees

The reflex of angle A is 295 therefore, angle B is 295°

A reflex angle is an angle that is more than 180 degrees and less than 360 degrees. For example, 270 degrees is a reflex angle. In geometry, there are different types of angles such as acute, obtuse and right angles, which are under 180 degrees.

Given that angle B is the reflex angle of angle A, angle is measuring 65°

We need to find the measure of reflex Angle B

We know that,

To find the reflex angle of a given angle, we need to subtract the given measure from 360 degrees.

For example, the reflex angle of 110 degrees = 360 – 110 = 250.

Therefore,

Reflex Angle B = 360° - 65° = 295°

Hence, the reflex of angle A is 295 therefore, angle B is 295°

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The nurse should set the IV pump to deliver 125 mL/hr in order to administer the D5W 750 mL IV over 6 hr.

The nurse should set the IV pump to deliver 125 mL/hr in order to administer the D5W 750 mL IV over 6 hr. To calculate the infusion rate, you can use the formula:

Infusion rate (mL/hr) = Volume to be infused (mL) / Infusion time (hr)

In this case, the volume to be infused is 750 mL and the infusion time is 6 hr. Plugging these values into the formula, we get:

Infusion rate (mL/hr) = 750 mL / 6 hr = 125 mL/hr

Therefore, the nurse should set the IV pump to deliver 125 mL/hr in order to administer the D5W 750 mL IV over 6 hr.

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