Awnser for me quickly pleaseee

Solving for a, b, and c, we find that a = 2, b = -1, and c = 0. Therefore, the direction vector for the line is d = <2, -1, 0>, which is not the zero vector, so the line does not pass through the origin.

To see this, note that the curve is in vector form, which has the form r(t) = <x(t), y(t), z(t)>. The curve is a line if and only if there exists a direction vector d = <a, b, c> such that the position vector r(t) satisfies r(t) = r(0) + td for all t, where r(0) is the initial position vector.

In this case, we can see that the initial position vector is r(0) = <2(0), 3-0, 0> = <0, 3, 0>.

Now let d = <a, b, c>. Then the equation r(t) = r(0) + td becomes:

<2t, 3-t, 0> = <0, 3, 0> + t<a, b, c>

Simplifying this equation gives us the following system of equations:

2t = ta

3 - t = 3 + tb

0 = tc

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Answer:

X is 3

Step-by-step explanation:

15-x=12

X=15-12

X=3

Answer: 71 percent

Step-by-step explanation:

64-21=43

43/64=.71  

The area of the equilateral triangle with a side length of 8 cm is 16√(3) cm².

To find the altitude of an equilateral triangle with a side length of 8 cm, we can use the Pythagorean theorem.

The Pythagorean theorem is states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In these triangles, the side opposite the 60-degree angle is half the length of the hypotenuse, which is 8 cm. Using the Pythagorean theorem, we can find that the length of the altitude is:

Altitude = √(8² - (4²)) = √(48) = 4√(3)

Now that we know the altitude, we can plug it into the formula for the area of a triangle:

Area = (base x height) / 2 = (8 x 4√(3)) / 2 = 16√(3) cm²

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Answer:

26

8 2/3

Step-by-step explanation:

4 1/3 ×6

13/3×6

13/1×2=26

2 3/5 × 3 1/3

13/5 × 10/3

13/1 × 2/3

26/3=8 2/3

Answer:

819

Step-by-step explanation:

Answer:

b=13/12

Step-by-step explanation:

Good luck :)

Answer:

Choice D

Step-by-step explanation:

Choices A and B does not imply Dilation but Translation. Though Choice C implies Dilation, but it implies that \(\triangle J'K'L'\) is half the size of \(\triangle JKL\) but we can see that \(\triangle J'K'L'\) is larger than \(\triangle JKL\) so Choice D.

Answer:

Y = 68

Step-by-step explanation:

Here's an if-then statement to simplify the values:

-------------------------------------------------------------------------------------------------

If X=5 then Y=1, this is now the rule for this problem.

X is multiplied by 68 (5 x 68 = 340) so now Y is treated the same (1 x 68 = 68)

-------------------------------------------------------------------------------------------------

Therefore, Y should equal 68.

I hope this helped :)

*Notify me via comments if this post is incorrect*

Answer: 41666666669 / 50000000003

Step-by-step explanation:

Answer:

(0.7, -1)

Step-by-step explanation:

To find the coordinates for the midpoint you add each coordinate together and divide by 2.

M = (\(\frac{1.8 - 0.4}{2}, \frac{-3.4 + 1.4}{2}\))

M = \((\frac{1.4}{2}, \frac{-2}{2})\)

M = (0.7, -1)

the system of inequalities that represents the possible length in meters, l, and the possible width in meters, w, of the pool is given as w ≤ l - 10 and 2 l + 2 w > 62.

Let the length of the pool be x.

So, ATQ, the width will be represented by the inequality:

x - 10 ≥ width

w ≤ x - 10

w ≤ l - 10

Also, it is given that, the perimeter of the pool is more than 62 m
So, we get that:

P > 62

Also, we know that:

P = 2 l + 2 w

So, we get that:

2 l + 2 w > 62.

Therefore, the system of inequalities that represents the possible length in meters, l, and the possible width in meters, w, of the pool is given as w ≤ l - 10 and 2 l + 2 w > 62.

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Answer:

D

Step-by-step explanation:

i’m pretty sure

Using trigonometric functions, we can  find a side length of a right triangle with an angle and a side.

Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.

Trigonometric ratios can be computed either using the provided acute angle or by calculating the ratios of the right-angled triangle's sides.

You can determine the hypotenuse by dividing the length of the side by sin(θ) if you have an angle and the side opposite to it. Alternatively, to find the length of the side next to the angle, divide the length by tan(θ).

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Answer:

4

Step-by-step explanation:

Answer:

4, lol

Step-by-step explanation:

Answer:

5 : 7

Step-by-step explanation:

groom's side: 40

bride's side: 56

ratio groom to bride = 40/56 = 20/28 = 10/14 = 5/7

Answer: 5 : 7

question 9

a) 2 x 3 = 6m^2

b) diameter = 2m and radius = 1m

c) πr^2 is the equation, so 3.14 x 1^2 = 3.14m^2

and the semi circle is half of that, 1.57m^2

d) 6 + 1.57 = 7.57m^7

question 10

30 x 70 = 2,100m^2

πr^2 so 3.14 x 15^2 = 706.5m^2

2,100 + 706.5 = 2,806.5m^2

i hope this is correct :D

Answer:

4

Step-by-step explanation:

because i know

Answer:

bro just look on a caculater

Step-by-step explanation:

1087658.22

The possible collision points of the two paths are given as follows:

Each path is modeled by the equations presented as follows:

When the two paths collide, they are at the same position, hence the points are the values of θ that respect the condition given by:

\(r_1(\theta) = r_2(\theta)\)

Hence the equation to be solved is:

\(\sqrt{3} + 2\cos{\theta} = 4\cos{\theta}\)

Isolating the cosine variable, we have that:

\(2\cos{\theta} = \sqrt{3}\)

\(\cos{\theta} = \frac{\sqrt{3}}{2}\)

Applying the inverse cosine function, the angles are obtained as follows:

\(\theta = \cos^{-1}{\left(\frac{\sqrt{3}}{2}\right)}\)

Which has two solutions:

Hence the correct options are given by the first option and the last option.

The complete problem is given by the image shown at the end of the answer.

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Answer:

A and E.

Step-by-step explanation:

Answer:

the answer is one cup of oil for each cup of water. hope this helps!

The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.

To convert the given equation from standard form to vertex form, we need to complete the square.

The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.

Given equation: y = x² - 6x + 14

Move the constant term to the right side:

y - 14 = x² - 6x

Complete the square by adding and subtracting the square of half the coefficient of x:

y - 14 + 9 = x² - 6x + 9 - 9

Group the terms and factor the quadratic:

(y - 5) = (x² - 6x + 9) - 9

Rewrite the quadratic as a perfect square:

(y - 5) = (x - 3)² - 9

Simplify the equation:

y - 5 = (x - 3)² - 9

Move the constant term to the right side:

y = (x - 3)² - 9 + 5

Combine the constants:

y = (x - 3)² - 4

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Step-by-step explanation:

3×5 = 15

so, the first number n×3 = 24, n = 8

an and then we have

8 : 5 : 6 : 7 = 24 : 15 : 18 : 21

Answer:

b = 11.31

a = 12

Step-by-step explanation:

a.

64 + 64 = c^2

c^2 = 128

c = 11.31

answer b = 11.31

b.

soh cah toa

cos = adj/hyp

cos 60 = 6/hyp

hyp = 6/cos 60

hyp = 6/.50

hyp = 12

Answer:

See image below

Step-by-step explanation:

The expression for volume is (28-2x)(22-2x)x and when x=6, the volume is 840 inch^3.

A 3D object's volume is the amount of actual space it occupies. It is a 2D shape's 3D equivalent of area. It is quantified in cubic units like cm3. It means that the amount of space a closed form can occupy in three dimensions depends on its volume. Volume is a gauge of a thing's potential. For instance, a cup is said to have a 100 ml capacity if the brim can hold 100 ml of water. Another way to measure volume is the amount of space a three-dimensional item takes up.

According to question,

Let x be the height of the cubic box

Length = (28-2x)

Breadth = (22-2x)

Volume = x(28-x)(22-x)

When x =6

Volume = 6(28-6×2)(22-6×2)

=6(10)(14)

=840 inch^3

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Coordinate of circumcenter of the given triangle = (3, 2)

What is circumcenter of a triangle?

Circumcenter of a triangle is the point of intersection of the perpendicular bisectors of every sides of the triangle.

Let the coordinate of circumcenter be (x , y)

Distance of Circumcenter from (4,2) =

\(\sqrt{(x - 4)^2 + (y-2)^2\)

Distance of Circumcenter from (3, 3) =

\(\sqrt{(x - 3)^2 + (y-3)^2\)

Distance of Circumcenter from (2,2) =

\(\sqrt{(x - 2)^2 + (y-2)^2\)

By the problem,

\(\sqrt{(x - 2)^2 + (y-2)^2} = \sqrt{(x - 3)^2 + (y-3)^2}\\(x - 2)^2 + (y-2)^2} = (x - 3)^2 + (y-3)^2}\\x^2 - 4x + 4 + y^2 -4y + 4 = x^2 -6x + 9 + y^2-6y + 9\\6x - 4x +6y -4y = 18-8\\2x +2y = 10\\x+ y = 5\\\)..... (1)

Again,

\(\sqrt{(x - 4)^2 + (y-2)^2} = \sqrt{(x - 3)^2 + (y-3)^2}\\(x - 4)^2 + (y-2)^2} = (x - 3)^2 + (y-3)^2}\\x^2 - 8x + 16 + y^2 -4y + 4 = x^2 -6x + 9 + y^2-6y + 9\\8x - 6x +4y -6y = 20-18\\2x -2y = 2\\x- y = 1\\\)...... (2)

Adding (1) and (2)

\(2x = 6\\x = \frac{6}{2}\\x = 3\)

Putting the value of x in (1),

3 + y = 5

y = 5 - 3

y  = 2

Coordinate of circumcenter = (3, 2)

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3b + 0.5a

the variables b and a are unknown values that represent the number of bananas and apples to be bought. These are next to each of its prices for it to be multiplied once we know the variable.

The costs of the fruits are to be added and you will end up with the total cost of fruits.

Answer:

\(p\left(\dfrac{2}{3}\right)=-\dfrac{1280}{27}\)

\(p \left(-1 \right)=3\)

Step-by-step explanation:

Remainder Theorem

When we divide a polynomial p(x) by (x − a) the remainder is p(a).

Given:

\(\begin{cases}p(x)=6x^4+19x^3-2x^2-44x-24\\\\ a=\dfrac{2}{3}\end{cases}\)

To find p(a), set up the synthetic division problem with the coefficients of the polynomial p(x) as the dividend and "a" as the divisor.

\(\begin{array}{c|ccccc}\frac{2}{3} &6&19&-2&-44&-24\\\cline{1-1}\end{array}\)

Bring the leading coefficient straight down:

\(\begin{array}{c|ccccc}\frac{2}{3} & 6 & 19 & -2 & -44& -24\\\cline{1-1}& \downarrow & & & & \\\cline{2-6}& 6\end{array}\)

Multiply the number you brought down with the number in the division box and put the result in the next column (under the 19):

\(\begin{array}{c|ccccc}\frac{2}{3} & 6 & 19 & -2 & -44& -24\\\cline{1-1}& \downarrow &4 & & & \\\cline{2-6}& 6\end{array}\)

Add the two numbers together and put the result in the bottom row:

\(\begin{array}{c|crrrr}\frac{2}{3} & 6 & 19 & -2 & -44& -24\\\cline{1-1}& \downarrow &4 & & & \\\cline{2-6}& 6&23\end{array}\)

Repeat:

\(\begin{array}{c|crrrr}\frac{2}{3} & 6 & 19 & -2 & -44& -24\\\cline{1-1}& \vphantom{\dfrac12}\downarrow &4 &\frac{46}{3} & & \\\cline{2-6} \vphantom{\dfrac12}& 6&23&\frac{40}{3}\end{array}\)

\(\begin{array}{c|crrrr}\frac{2}{3} & 6 & 19 & -2 & -44& -24\\\cline{1-1}& \vphantom{\dfrac12}\downarrow &4 &\frac{46}{3} & \frac{80}{9}& \\\cline{2-6}& \vphantom{\dfrac12}6&23&\frac{40}{3}&-\frac{316}{9}\end{array}\)

\(\begin{array}{c|crrrr}\frac{2}{3} & 6 & 19 & -2 & -44& -24\\\cline{1-1}&\vphantom{\dfrac12} \downarrow &4 &\frac{46}{3} & \frac{80}{9}&-\frac{632}{27} \\\cline{2-6}& \vphantom{\dfrac12}6&23&\frac{40}{3}&-\frac{316}{9}&-\frac{1280}{27}\end{array}\)

The last number (remainder) is

\(-\dfrac{1280}{27}\)

Therefore, according to the remainder theorem:

\(p\left(\dfrac{2}{3}\right)=-\dfrac{1280}{27}\)

Check by substituting a = 2/3 into p(x):

\(\implies p\left(\dfrac{2}{3}\right)=6\left(\dfrac{2}{3}\right)^4+19\left(\dfrac{2}{3}\right)^3-2\left(\dfrac{2}{3}\right)^2-44\left(\dfrac{2}{3}\right)-24\)

\(\implies p\left(\dfrac{2}{3}\right)=\dfrac{32}{27}+\dfrac{152}{27}-\dfrac{8}{9}-\dfrac{88}{3}-24\)

\(\implies p\left(\dfrac{2}{3}\right)=-\dfrac{1280}{27}\)

-------------------------------------------------------------------------------------------------

Given:

\(\begin{cases}p(x)=x^3+3x^2-5x-4\\ a=-1\end{cases}\)

To find p(a), set up the synthetic division problem with the coefficients of the polynomial p(x) as the dividend and "a" as the divisor.

\(\begin{array}{c|crrr}-1 &1&3&-5&-4\\\cline{1-1}\end{array}\)

Bring the leading coefficient straight down:

\(\begin{array}{c|crrr} -1 & 1&3&-5&-4\\\cline{1-1}& \downarrow & & & \\\cline{2-5}& 1\end{array}\)

Multiply the number you brought down with the number in the division box and put the result in the next column (under the 3):

\(\begin{array}{c|crrr} -1 & 1&3&-5&-4\\\cline{1-1}& \downarrow & -1& & \\\cline{2-5}& 1\end{array}\)

Add the two numbers together and put the result in the bottom row:

\(\begin{array}{c|crrr} -1 & 1&3&-5&-4\\\cline{1-1}& \downarrow & -1& & \\\cline{2-5}& 1&2\end{array}\)

Repeat:

\(\begin{array}{c|crrr} -1 & 1&3&-5&-4\\\cline{1-1}& \downarrow & -1& -2& \\\cline{2-5}& 1&2&-7\end{array}\)

\(\begin{array}{c|crrr} -1 & 1&3&-5&-4\\\cline{1-1}& \downarrow & -1& -2& 7\\\cline{2-5}& 1&2&-7&3\end{array}\)

The last number (remainder) is 3.

Therefore, according to the remainder theorem:

\(p \left(-1 \right)=3\)

Check by substituting a = -1 into p(x):

\(\implies p(-1)=(-1)^3+3(-1)^2-5(-1)-4\)

\(\implies p(-1)=-1+3+5-4\)

\(\implies p(-1)=3\)

Answer:

Concept: Basic Multiplication