The quotient of (x4 5x3 – 3x – 15) and (x3 – 3) is a polynomial. what is the quotient?

Answer:

  p = 6i -3j +9k

  q = 3i -6j -3k

  r = 2p +q

  r = 5i -4j +5k

  R(5, -4, 5)

Step-by-step explanation:

Given points P(6, -3, 9) and Q(3, -6, -3) and R that divides PQ in the ratio 1:2, you want ...

The vector from the origin to a point (x, y, z) will be ...

  xi +yj +zk

where i, j, k are unit vectors in the direction of the x, y, and z axes, respectively.

Using this pattern, we find the position vectors p and q to points P and Q to be ...

  p = 6i -3j +9k . . . . . . . . . . . . . position vector p

  q = 3i -6j -3k . . . . . . . . . . . . . position vector q

Point R divides PQ in the ratio 1:2, so its position vector will be the weighted sum of p and q:

  r = (2p +q)/3 . . . . . . . . . . . . . . . . r in terms of p and q

Using the values of p and q from above, we find r to be ...

  r = (2(6i -3j +9k) +(3i -6j -3k))/3 = ((2·6+3)i +(2(-3)-6)j +(2·9-3)k)/3

  r = 5i -4j +5k . . . . . . . . . . r in terms of i, j, k

The coordinates of R are the coordinates of the head of position vector r:

  R(5, -4, 5) . . . . . . . . . . . . . coordinates of R

Answer:

5√3

Step-by-step explanation:

An equilateral triangle is a triangle that has all same 3 measurements of 60°, and since all measurements are same, all sides are also equal too.

Hence, there'll be 3 sides that are 10 units. Since the base is divided into half, each will be 5 for base.

Then apply Pythagoras Theorem where states that:

[tex]\displaystyle{c=\sqrt{a^2+b^2}}[/tex]  or [tex]\displaystyle{c^2=a^2+b^2}[/tex]

where c is hypotenuse, a and b can be defined either adjacent or opposite.

We know that our adjacent is 5 units, opposite is h unit(s) and hypotenuse is 10 units. Apply the theorem:

[tex]\displaystyle{10^2=h^2+5^2}[/tex]

Solve the equation for h-term:

[tex]\displaystyle{100=h^2+25}\\\\\displaystyle{100-25=h^2}\\\\\displaystyle{75=h^2}\\\\\displaystyle{h=5\sqrt{3} }[/tex]

Therefore, the height or value of h is 5√3

The picture is attached for visual reference regarding sides of triangle. If you have any questions, please let me know in the comment!

Answer:

x = 1

Step-by-step explanation:

A line with undefined slope is a vertical line with equation

x = c

where c is the value of the x- coordinates the line passes through

the line passes through (1, 5 ) with x- coordinate 1 , then

x = 1 ← equation of line

The correct answer is option B which is we need ∠L ≅  ∠R to prove congruency.

The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.

According to the SAS theorem which means Side Angle Side, The angle which is included between the two sides must be congruent.

Here we are given that

KL = NR

JL = MR

Now in the figure, we can clearly see that the angle included between JL & KL is L & the angle included between NR & MR is R.

So for the triangles to be congruent by SAS, angle L must be congruent to angle R.

∠L=∠R

Therefore the correct answer is option B which is we need ∠L ≅ ∠R to prove congruency.

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Answer: option b

Step-by-step explanation:

Answer:

x=28.93(rounded) x=28.929(not rounded)

Step-by-step explanation:

Step-by-step explanation:

25/3÷x=7/3÷8.1

25/3×8.1=7/3×x

135/2=7/3×x

x=135/2×3/7

x=405/14=28.929

The student has to plug y=2x+4 into 3x+y=9 to solve for the system of equations

Answer:

Step-by-step explanation:

The friend solved

Answer:

B (It isn't in the shaded region)

The correct statements about the synthetic division are C, D, F.

It should be noted that 4x² - 17x - 15 will be:

= 4x² - 20x - 3x - 15

= (x - 5)(4x + 3)

The roots of the polynomial will be:

= f(x) = 0

(x - 5) = 0

x = 5

4x + 3 = 0

x = -3/4

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According to the information, it can be inferred that the correct inequality is Mallory > Eva (option D).

To identify who is closer to the surface of the water we must read the distance that each of the characters is.

In this case, the person closest to the surface is Eva, who is 5 feet from the surface.

Now we must identify which inequality corresponds to reality. In this case the inequality that is correct is:

This inequality is correct because Mallory is further from the surface than Eva.

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Answer:

This really needs more information to answer correctly.  What is bria's movement relative to the bus stop?  Is she moving towards it, away, or to the side?

Step-by-step explanation:

Lacking this information, I can only say that as Bria's distance increases as she moves away from the bus stop (an assumption of direction).  Let's say the bus stop is x yards distant in the other direction.   Bria's distance from the bus stop varies from x+80 yards to x+190 yards.  The signs would change if she were moving towards the bus stop.  And they'd be something entirely different if a different angle were involved.

The value of the unknown length is 24

Represent the unknown length with x.

So, we have the following equivalent ratio:

30 : 30 + x = 25 : 45

Express as fraction

30/30 + x = 25/45

Simplify the fraction

30/30 + x = 5/9

Cross multiply

150 + 5x = 270

Evaluate the like terms

5x = 120

Divide by 5

x = 24

Hence, the value of the unknown length is 24

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The probability of choosing either  a raspberry or a strawberry sweet is 17/60.

P(s) ∩ P(c) = P(s) x P(c) =  1/12

where;

1/12 = P(s) x P(c)

1/12 = 1/5 x P(c)

P(c) = 5/12

P(s) ∪ P(c) = 1/5 + 5/12 = 17/60

Thus, the probability of choosing either  a raspberry or a strawberry sweet is 17/60.

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The value of the voltage is 18 - j volts if the current in a circuit is 3 + j2 amps and the resistance is 4 - j3 ohms option (c) is correct.

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have:

The current in a circuit is 3 + j2 amps and the resistance is 4 - j3 ohms.

As we know,

V = IR

V = (3 + j2)(4 - j3)

[tex]\rm V=\left(3\cdot \:4-2\left(-3\right)\right)+\left(3\left(-3\right)+2\cdot \:4\right)j[/tex]

j² = -1 (complex part)

After simplification:

V = 18 - j  volts

Thus, the value of the voltage is 18 - j volts if the current in a circuit is 3 + j2 amps and the resistance is 4 - j3 ohms option (c) is correct.

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Answer:

First Option

Step-by-step explanation:

First, we will find the equation for the total cost of the tickets.

Given x = Cost of 1 adult ticket

y = Cost of 1 Child ticket

Total Cost of tickets at $40:

2x + 4y = 40

To find which graph represent the cost of the tickets,

we can substitute x = 0 to find y and vice-versa.

If x = 0 ,

[tex]2(0) + 4y = 40\\4y = 40\\y = \frac{40}{4} \\= 10[/tex]

So when x = 0 , y = 10 which gives the coordinates (0,10).

Now if y = 0,

[tex]2x+4(0) = 40\\2x = 40\\x = \frac{40}{2} \\= 20[/tex]

So when y = 0 , x = 20 which gives the coordinates (20,0)

This shows that this particular line passes through these 2 points and therefore the answer is the first option.

Answer: A i just took the test

Step-by-step explanation:

Answer:

120%

Step-by-step explanation:

10.14 is more than all of 8.45.

8.45 is 100% of 8.45.

So 10.14 will be more than 100%.

10.14 ÷ 8.45 = 1.2

This is the decimal value.

To change to %, multiply by 100.

1.2 × 100 = 120

10.14 is 120% of 8.45

The value of w is 38400 when the value of c is 6 as per the concept of a proportional relationship.

Given:

We have to find the value of w at c = 6.

If c = 6, then the value of a becomes a = 48 times (6 divided by 3)

Therefore, the value of a can be evaluated as,

a = 48 x 6/3

a = 48 x 3

a = 144

To find the value of w, rearrange the value of 'a' in the multiple of 9.

For that, divide 144 by 9.

144/9 = 16.

Now, multiply 16 by 2400.

The final value of w = 2400 x 16

w = 38400

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Answer:

[tex]2n^3-3n^2-7n+3[/tex]

Step-by-step explanation:

[tex](n^2 -3n +1)(2n + 3) =\\n^2(2n) - (3n)(2n) + (1)2n + (n^2)(3) + (-3n)(3) + (1)(3)=\\2n^3 - 6n^2 + 2n + 3n^2 -9n + 3 =\\[/tex]

Collecting like terms and simplifying yields

[tex]2n^3-3n^2-7n+3[/tex]

First statement shows sample ,second shows population, third shows sample, fourth shows population, fifth shows sample, sixth shows sample, seventh shows population, eight shows sample.

Given eight statements which shows the variables in research of alcholic consumption.

Population is anentire group about which we want to find the conclusions.

Sample is a part of population for which the conclusions are drawn. The size of sample may varry with the effectiveness and the confidence level needed.

First statement is a sample because it defines a number of people.

Second statement is a population as it shows all the people fro age 18 to 25.

Third statement is a sample as it defines a percentage of people.

Fourth statement is a population as it contains all the workers.

Fifth statement is a sample because it shows number of restaurant workers.

Sixth statement is a sample because it shows a definite number.

Seventh statement is a population as it includes all the milkweed plants.

Eight statement is a sample as it contains a definite percentage.

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The rocket will take 2 seconds for the rocket to hit the ground.

We have,

To find the time it takes for the rocket to hit the ground, we need to determine when the height, h, becomes zero (since the ground is at height zero).

Given the equation for the height of the rocket at time t:

h = -4.9t² + 9.1t + 1.4, we can set h to zero and solve for t:

0 = -4.9t² + 9.1t + 1.4

This is a quadratic equation in the form of at² + bt + c = 0,

where a = -4.9, b = 9.1, and c = 1.4.

To solve for t, we can use the quadratic formula:

t = (-b ± √(b² - 4ac)) / 2a

Substituting the values:

t = (-(9.1) ± √((9.1)² - 4(-4.9)(1.4))) / 2(-4.9)

t = (-9.1 ± √(82.81 + 27.44)) / (-9.8)

t = (-9.1 ± √110.25) / (-9.8)

Now, we have two possible solutions for t:

t₁ = (-9.1 + √110.25) / (-9.8)

t₂ = (-9.1 - √110.25) / (-9.8)

Calculating these values:

t₁ ≈ -0.143

t₂ ≈ 2

Since time cannot be negative, the only meaningful solution is t₂ ≈ 2 seconds.

Thus,

The rocket will take 2 seconds for the rocket to hit the ground.

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A statement which correctly compares the two functions on the given interval [-1, 2] is: C. Both functions are increasing, but function g increases at a faster average rate.

First of all, we would determine the values of function g(x) on the given interval [-1, 2] as follows:

g(x) = -18(⅓)^x + 2

At x = -1, we have:

g(-1) = -18(⅓)^(-1) + 2

g(-1) = -52.

At x = 0, we have:

g(0) = -18(⅓)^(0) + 2

g(0) = -16.

At x = 1, we have:

g(1) = -18(⅓)^(1) + 2

g(1) = -4.

At x = 2, we have:

g(2) = -18(⅓)^(0) + 2

g(2) = 0.

By critically observing the values of each functions, we can logically deduce that both functions are increasing but function g(x) increases at a faster average rate because it started with a lower value and ended with a higher value.

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Answer:

the answer is 9

Step-by-step explanation:

if you use distributive property you'll find your answer

x = 9

Step-by-step explanation:

3(x+5)-2(x+2)=20

3x +15 - 2x - 4 = 20

3x - 2x = 20 + 4 - 15

x = 24 - 15

x = 9

Answer:

Hence the expression. [tex](y-6)(y-2)=y^{2} -8x-12[/tex]

Step-by-step explanation:

[tex]$$\begin{array}{r}y-6 \\\times \quad \underline{y-2} \\-2 y-12 \\\underline{y^{2}-6 y} \\y^{2}-8 y-12\end{array}$$[/tex]

Leo's water is at a greater temperature. And Manoj's water is closer to freezing.

The temperature refers to the degree of hotness ant coldness of the substance.

Water freezes at 0 °C.

Manoj's water is 3 °C.

Leo's water is 7 °C.

Leo's water is at a greater temperature.

Manoj's water is closer to freezing.

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The system of equations have 2 solutions

The system of equations is given as:

-1/3x² = 5/6 + 1/3y²

5y² = 25/2 - 5x²

Next, we plot the graph of the system of equations.

From the attached graph, the equations intersect at two points

Hence, the system of equations have 2 solutions

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Answer-

-1/2, -4

Step-by-step explanation:

A, E

Did the math to find the solution earlier, got right xoxo :)

The compound inequality which represents the number of ounces of clay is c≤4.5 or c≥12.

Given ELISA uses no more than 4.5 ounces of clay and to make a large vase, she uses at least 12 ounces of clay.

Let c denote the wide variety of oz of clay that Elisa makes use of to make one vase of both length.

The words "no more than" implies "much less than or equals to".

So, for a small vase c must be less than or equal to 4.5 ounce, which gives

c≤4.5       ...(1)

And to make a huge vase, she makes use of as a minimum 12 oz of clay.

The word "at least" implies "extra than or equals to"

So, for a large vase c must be more than or equal to 12 ounce, which gives

c≥12         ...(2)

By combining equations (1) and (2), we get

c ≤ 4.5 or c ≥ 12

Hence, the compound inequality represents the number of ounces of clay, c, that ELISA uses to make one vase of either size is c≤4.5 or c≥12.

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Answer:

D. c ≤ 4.5 or  c ≥ 12

Step-by-step explanation:

Answer:

ABCD-DEFG
Mark as brainlist pls!

Mary should pour around 3.7 liters or 226.08 in³ volume of water in the vase.

Given Information and Formula Used

Radius of the cylindrical vase, r = 3 inches

Height of the cylindrical vase, h = 8 inches

The formula for the volume, V of a cylinder is given as,

V = πr²h

Here, r is the radius of the cylinder and h is the height of the cylinder.

Calculating the Volume

Substituting the given values of r and h in the formula for the volume of cylinder, we get

Volume, V = π(3)²(8)

Using π = 3.14, we have,

V = 3.14(9)(8)

V = 226.08 cubic inches

Volume in Liters

Since, 1 Liter = 61.0237 cubic inches,

1 cubic inch = 1/61.0237 liters

⇒ 226.08 cubic inches = 226.08/61.0237 liters

⇒ 226.08 cubic inches ≈ 3.07 liters

Thus, Mary needs to pour approximately 3.07 liters volume of water in the vase.

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The dust particle is seen to have 400 times more mass than the pollen particle

We will use the scientific notation.

For example, 0, 002 can be written as:

2 × 10³

Where;

3 is the number of times the comma (,) must be run to the right to convert the quantity 0, 002 to 2.

0, 002

0| 0 0 2

0 0| 02 -----------1

0 0 0|2------------2

0 0 0 2| ----------3

Thus, for the given expression:

Powder particle 0.000000778 g

It can be written as: 0.0000008 g = 8 × 10⁻⁷

b = -7

In the same way

Pollen grain of 0.00000000155 g

It can be written as:

0.000000002 g = 2 × 10⁻⁹

To know how big the mass of the dust particle is with respect to the pollen, we have;

(8 × 10⁻⁷)/(2 × 10⁻⁹) = 400

Complete question is;

The table below shows the approximate masses of a dust particle and a grain of pollen.

Dust Particle 0.000000778 g

Grain of Pollen 0.00000000155 g

The mass of a dust particle can be estimated and written in the form a × 10^b, where a = 8 and b =

The mass of a grain of pollen can be estimated and written in the form a × 10^b, where a = 2 and b =

Based on the estimates, the mass of a dust particle is approximately BLANK

times larger than the mass of a grain of pollen.

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