Solve x 2 =-6x-5 by completing the square

The point at which the given lines intersect is (6,0,2) and an equation of the plane that contains these lines is x+y=6.

(a) In the given question we have to find the point at which the given lines intersect.

r = [3,3,0] + t[3,-3,2]

r = [6,0,2] + s[-3,3,0]

The equations of the lines can be written as :

The points for first line is

L(1)⟹x=3+3t, y=3-3t, z=0+2t and

The points for second line is

L(2)⟹x=6-3s , y=0+3s , z=2+0s .

Set the z coordinates equal from the line one and two, and we get :

2t = 2

Divide by 2 we get

t=1 .

Substitute the value of t into the point of x of first line :

x=3+3(1)

x=3+3

x=6

Equating the value of x equal to the coordinate of x of line two

6=6-3s

Subtract 6 on both side, we get

-3s=0

s=0

Now substitute the value of t into the point of y of first line:

y=3-3(1)

y=3-3

y=0

Equating the value of y equal to the coordinate of y of line two

0=0+3s

s=0

Now substitute the value of t into the point of z of first line:

z=0+2(1)

z=2

Equating the value of z equal to the coordinate of z of line two

2=2+0(s=0)=2 .

We thus have the point of intersection is :

P=(x,y,z)

P=(6,0,2)

Hence, the point at which the given lines intersect is (6,0,2)

(b) The direction vector for the first line is

[tex]\vec{v_{1}}=3\hat{i}-3\hat{j}+2\hat{k}[/tex]

and the direction vector for the second line is

[tex]\vec{v_{2}}=-3\hat{i}+3\hat{j}+0\hat{k}[/tex]

We can find a normal vector to the line as :

[tex]\vec{N_{1}}=\vec{v_{1}}\times\vec{v_{2}}[/tex]

[tex]\vec{N_{1}}=\begin{vmatrix} \hat{i} &\hat{j} &\hat{k} \\-3 &3 &-2 \\ -3 &3 & 0 \end{vmatrix}[/tex]

[tex]\vec{N_{1}}=\hat{i}(0-(-6))-\hat{j}(0-6)+\hat{k}(-9-(-9))[/tex]

[tex]\vec{N_{1}}=6\hat{i}+6\hat{j}[/tex]

is a normal vector

But , we can also use

[tex]\vec{N}=\frac{\vec{N_{1}}}{6}[/tex]

[tex]\vec{N}=\hat i+\hat j[/tex]

as the normal vector to the plane .

We can thus use the point P=(6,0,2) and the normal vector [tex]\vec{N}=\hat i+\hat j[/tex] to write the equation of the plane :

1(x-6)+1(y-0)+0(z-2)=0

x-6+y+0=0

x+y=6

Hence, an equation of the plane that contains these lines is x+y=6.

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The right question is

(a) Find the point at which the given lines intersect.

r = [3,3,0] + t[3,-3,2] r = [6,0,2] + s[-3,3,0]

(x,y,z) = ( )

(b) Find an equation of the plane that contains these lines.

The equivalent expressions are 16a + b, 17b + 11a, and 17b.

A mathematical expression made up of variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division is called an algebraic expression.

In general, if anything is considered equal then the two of them are said to be equivalent. Similarly to this, if any two or more algebraic equations have identical solutions or roots then the equations are Equivalent expressions even they look different.        

Here we have

Expressions

3a +b +13a

20b +11a -3b

20b -5b +2b  

To simplify given expressions add or subtract like terms as given below

3a +b +13a => (3a+13a) +b = 16a + b

Therefore,

The equivalent expression of 3a +b +13a is 16a + b        

20b +11a -3b => (20b-3b) + 11a = 17b + 11a

Therefore

The equivalent expression of 20b +11a -3b is 17b + 11a  

20b-5b+2b => 20b+2b - 5b = 22b -5b = 17b

Therefore,

The equivalent expression of 20b-5b+2b is 17b

Therefore,

The equivalent expressions are 16a + b, 17b + 11a, and 17b.

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Answer:

Yes

Step-by-step explanation:

The value(s) of a where the tangent line to the graph of the function f(x) = -11x + is parallel to the line y = -19x - 18 is x=1,-1.

What is Slope of function?

Finding the rate at which the value of y (the dependent variable) changes in relation to x is what this method entails (independent variable). The slope itself identifies the line's slope and direction. Write the equation of the line in slope-intercept form to determine the slope from the equation. Utilize inverse procedures to find y, then write it as y=mx+b. Since the slope is the x variable's coefficient, or the number before x, you can thus readily observe the slope.

[tex]f(x)=-11 x+\frac{8}{x}$$[/tex]

Slope of function [tex]$\rightarrow f^{\prime}(x)=\frac{-21-8}{x^2}$[/tex]

Given line: y=-19 x-18

Slope [tex]$\rightarrow y^{\prime} \rightarrow-19$[/tex]

Since function and line both are parallel, hence slope of both will be equal.

[tex]$$\begin{aligned}-19 & =-11-\frac{8}{x^2} \\-8 & =\frac{-8}{x^2} \\x & =1,-1\end{aligned}$$[/tex]

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Answer:

The possible values of k are -0.56, -3.56, -2 and -1.

Step-by-step explanation:

We have the equation of the parabola, .

Substituting x=0, we get that  i.e. y = -1.5k

So, the y-intercept is (0,-1.5k).

Thus, the height of the triangle becomes |-1.5k| = 1.5k

Again, substituting y=0,  i.e.  i.e. x=3 and x=-k

So, the x-intercepts are (3,0) and (-k,0).

Thus, the base of the triangle is 3+k if k>-3 or -3-k if k<-3.

We see that 'k' cannot be 0 or -3 as if k=0, then height = 0, which is not possible. If k= -3, then the base = 0, which is also not possible.

As, area of a triangle = .

Substituting the values, we get,

1.5=

i.e.

i.e. k = -0.56 and k = -3.56

or

1.5=

i.e.

i.e. k = -2 and k = -1.

Thus, the possible values of k are -0.56, -3.56, -2 and -1.

The amount of sample after 25 years and the half life are given as 51.8 g and 12.83 years respectively.

An exponentially decaying function has a general form f(x) = (1 -r)ˣ, where r is called the decay rate. it can be found by having any two values of x for which f(x) is known.

The given function for the decay of an isotope is given as A(t) = 200[tex]e^-0.054t[/tex].

Now, the given problem can be solved as follows,

(a) The amount of sample after 25 years is given as,

A(25) = 200[tex]e^{-0.054 \times 25}[/tex]

         = 200[tex]e^{-1.35}[/tex]

         = 200 × 0.259                      

         = 51.8

(b) The half life can be calculated as,

100 =  200[tex]e^{-0.054t}[/tex]

=> [tex]e^{-0.054t}[/tex] = 1/2

=> t = 12.83        

Hence, the sample left after 25 years will be 51.8 g and it will take 12.83 years for the sample to decay to half of its amount.

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The number of One-person tubes and two-person tubes is 3 and 12 respectively.

It is the basic arithmetic operation, in which you are separating the number into some parts.

Given:

A group spends $277.50 to rent 15 tubes for a float down the Lchetucknee River. One-person tubes cost $12.50 and two-person tubes cost $20.

The equation can be written as,

12.5x + 20y = 277.5

Here, x is the number of One-person tubes and y is two-person tubes.

Also, x + y = 15

Solve the above equation by elimination method,

x = 3 and y = 15 - 3 = 12

Therefore, the number of One-person tubes and two-person tubes is 3 and 12 respectively.

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Answer:

x > 65/7

Step-by-step explanation:

First, we make the equation positive.

-7/5x < -13

We have to switch the sign when multiplying or dividing a negative number.

7/5x > 13

Now, we multiply by 5 and divide by 7.

7x > 65

x> 65/7

The solution to the inequality n - 4/7 ≥ -2/3 is (a) n ≥ -2/21

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

n minus four sevenths is greater than or equal to negative two thirds

By definition, inequalities are used to relate unequal values

Express the inequality properly

So, we have

n - 4/7 ≥ -2/3

Add 4/7 to both sides

So, we have

n ≥ -2/3 + 4/7

Evaluate the sum of the fractions

This gives

n ≥ -2/21

Hence, the solution is (a) n ≥ -2/21

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Answer:

x > 1

Step-by-step explanation:

I  am solving this equation, not including the "_" in the equation.

-3(x+2)<-9

Multiply both sides by -1 to reverse the inequality.

3(x+2)>9

Divide by 3

x+2>3

Subtract

x>1

Evan's error was that he subtracted  -2 1/2 from 4, and thus he got  6 1/2.  On adding he would be getting  1 1/2

A straight line of numbers is shown visually as a number line. This line is used to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals. On a horizontal number line, the numbers grow as we walk to the right and decrease as we move to the left.

It is given that Evan added -2 1/2 and 4 but got 6 1/2

The mistake that Evan did was instead of adding, he substracted -2 1/2 from 4, and thus he got 6 1/2. This is because

4 -  (-2 1/2)

= 4 + 2 1/2

=  6 1/2

This is wrong as he was asked to add -2 1/2 and 4 not to subtract.

Therefore, on adding -2 1/2 and 4, we get,

= 4 - 2 1/2

= 1 1/2

Evan's error was that he subtracted  -2 1/2 from 4, and thus he got 6 1/2         .  On Evan's error was that he subtracted  from 4, and thus he got          .  On adding he would be getting  1 1/2

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Answer:

Step-by-step explanation:

i believe the total would be 4

Answer: The set of integers greater than or equal to 2 is {2, 3, 4, 5, ...}. This set can be represented using set notation as:

{y: y is an integer and y ≥ 2}

This set includes all the integers that are greater than or equal to 2, including 2 itself. It does not include negative integers or fractions.

For example, the following are all elements of this set:

2, 3, 4, 5, 6, 7, 8, ...

The following are not elements of this set:

-1, 0, 1, 1.5, -3.14, ...

This set is infinite, because there are an infinite number of integers greater than or equal to 2.

The time taken for the population to reach 26.6 million is 2 years while the population in year 2000 is 18.5 million.

We can be able to  define population growth as the process by which the population of an area is increasing. We know that the increase or the decrease of population would have to be an exponential function.

Given that we have the function A =18.5e^0.1708t where A is the population after a given time from year 2000 and t is the number of years after year 2000. It then follows that 18.5 million refers to the population of the united states as at year 2000.

We now have;

26.6 =18.5e^0.1708t

26.6/18.5 = e^0.1708t

1.44 = e^0.1708t

ln(1.44) = 0.1708t

t = ln(1.44)/ 0.1708

t = 2 years

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Answer:

188 cents or $1.88

Step-by-step explanation:

We first want to find how many cents per one inch, and we do this by dividing 17 from 68 (68/17). This gets us 4 cents per inch. Now we need to multiply 4 by 47 (4 x 47). Now we get 188 cents. The equation for this would be y = 4x

Answer:

126 lineups

Step-by-step explanation:

This is a problem in combinatorics which asks in how many ways can a subset of 5 be formed from a larger set of 9

In general, if you were to see how many ways a subset of [tex]r[/tex] can be formed from a larger subset [tex]n[/tex] denoted by [tex]nC_r[/tex] we use the formula

[tex]nC_r = \dfrac{n!}{ r! (n - r)! }[/tex]

There are calculators that can compute this and I used a scientific calculator to do so.

[tex]9C_5 = 126[/tex]

The required solution (1, 4) of a linear system of the equation is determined by the elimination method.

Given the linear system of equations:

8x - 2y = 0 or 4x - y = 0 …(i)

-6x + 14y = 50 or -3x + 7y = 25 …(ii)

Equations (i) and (ii) constitute a system of two first-degree equations in the two variables x and y.

So, we have to find out the value of 'x’ and 'y’.

By multiplying 7 by equation (i) and adding both equations

28x - 7y -3x + 7y = 25

25x = 25

x = 25/25

x = 1

Substitute the value of x = 1 in the equation (i), and solve for y

4(1) - y = 0

y = 4

Hence, the required solutions are x = 1 and y = 4.

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The equation of the tangent to the given curve x = t⁴ + 3 , y = t³ + t at the corresponding point is y = x - 2   .

In the question ,

it is given that ,

the parametric equation is x = t⁴ + 3 , y = t³ + t ,

differentiating with respect to t ,

we get ,

dx/dt = 4t³  and   dy/dt = 3t² + 1

On dividing dx/dt by dy/dt to get the slope ,

we get

dy/dx = (3t² + 1)/ (4t³)

Substituting in t=1

dy/dx = (3 + 1)/4 = 1

Slope (m) = 1 ;

Substituting t = 1 , in the parametric equation ,

we have , x = 4 and y = 2 .

So , (y - 2) = 1(x - 4)

y - 2 = x - 4

y = x - 2

Therefore , the equation of the tangent is  y = x - 2  .

The given question is incomplete , the complete question is

Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x = t⁴ + 3 , y = t³ + 3 ; t = 4 ?

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Step-by-step explanation:

that is a college question ?

oh my ...

to clarify :

perpendicular means intersecting or touching at a right angle (90°).

bisector means it is a line that cuts the other line in half.

1.

because of the bisector this means DF = FC = DC/2.

so, since FC = 17, so is DF (=y) = 17.

2.

for the same reason

2x - 3 = x + 8

x - 3 = 8

x = 11

the angle must be 90°.

so,

5y = 90

y = 18

3.

for the same reason

10 = 4a

a = 10/4 = 2.5

4.

for the given reasons of 1-3, this figure is a kite. that means the left side is a mirror image of the right side. so, all the lengths on one side are equation to the lengths of the other side.

x - 11 = 19

x = 30

5.

for the same reasons

3y + 5 = 26

3y = 21

y = 7

6.

the perimeter of EDP is then

EP + DP + ED = 19 + 19 + (9 + 9) = 56

because ED = EC + CD

and for the above reasons EC = CD = 9

so, ED = 9 + 9 = 18

7.

the perimeter of EDQ is then

EQ + DQ + ED = 26 + 26 + 18 = 70

8.

for the same reasons as above

x = 90°

9.

remember, the sum of all angles in a triangle is always 180°.

180 = 90 + 55 + y

y = 180 - 90 - 55 = 35°

10.

180 = y + M + z = 35 + (55+71) + z = 161 + z

z = 180 - 161 = 19°

Answer:

5, -11. -3, 8. 10, 17. -15, 13.

Step-by-step explanation:

All you have to do is switch x and y

Answer:

Step-by-step explanation:

If a number is squared and then divided by 15, the resulting expression can be written as (x^2)/15, where x is the number. For example, if the number is 5, then the expression can be written as (5^2)/15 = 25/15. In general, the value of the expression (x^2)/15 will be the square of the number x divided by 15.

Answer:

70

Step-by-step explanation:

Substitute the value -3 into the expression and simplify:

10(4 - -3)

10(4 + 3)

10(7)

70

Write each power as repeated multiplication. Then evaluate and compare their values is the correct option to compare the value of each expression.

What is the relation between power and base?

Compare  7² and 2⁷.

7 ≠ 2

So, write the power as repeated multiplication of the given expression:

7²  = 7 * 7

2⁷ = 2*2*2*2*2*2*2

Evaluate:

7² = 49

2⁷ = 128

Compare the values:

128 > 49

2⁷ > 7²

Hence, Write each power as repeated multiplication. Then evaluate and compare their values is the correct option to compare the value of each expression.

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Answer:

no clue bro just help yourself

Step-by-step explanation:

add them

or multiply or divide or subtract and you'll get it

The size of each angle of triangle, starting with the largest 90°, 45° and 45°.

Polygon which has three sides and three vertices is called as triangle.

Sum of all the angles of the triangle is 180°.

Given that a right angled triangle has two equal sides.

And the largest triangle of right angled triangle is 90°.

Right angled triangle which has two equal sides can be called right angled isosceles triangle.

And if one angle of isosceles triangle have angle is 90°. Then the rest of the two angle will be 45°.

Therefore, The rest of these two angles of the right angled triangle are 45⁰.

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Answer:

Your answer is 48.16 grams.

Austin needs to pour 48.16 grams of salt.

Here the total amount of salt is 71.26 grams.

But he pours 23.1 grams.

So when we minus 71.26-23.1, it is equal to 48.16 grams.

Therefore, Austin needs to pour 48.16 grams of salt.

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Answer:

[tex]y = 5 - 3z[/tex]

Step-by-step explanation:

[tex]6z+2y=10[/tex]

divide by 2

[tex]3z + y = 5[/tex]

move the terms

[tex]y = 5 - 3z[/tex]

Answer: 4.5 years or 54 months

Step-by-step explanation: Divide $4,000 by $75 a month to get 53.33 then round to 54. 54 months = 4.5 years.

The perimeter of the quadrilateral is √2+√8+√5+√13

We can use the distance formula to find the length of the segments that make up the quadrilateral.

We must find the length of the segments between the points (0,2),(1,3)(1,3),(3,1)(3,1),(2,−1)(2,−1),(0,2)

Recall the distance formula d=√(x2−x1)2+(y2−y1)2Applying this formula to the four pairs of points gives the following.

d=√(1−0)2+(3−2)2=√1+1=√2d=√(3−1)2+(1−3)2=√4+4=√8d=√(2−3)2+(−1−1)2=√1+4=√5d=√(0−2)2+(2+1)2=√4+9=√13

So the perimeter of the quadrilateral is √2+√8+√5+√13

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The one-way communication time between the Jupiter and Earth increases.

Radio waves are a type of electromagnetic radiation with the longest wavelengths in the electromagnetic spectrum, typically with frequencies of 300 Ghz and below.

Given is that Jupiter and Earth travel along their respective orbits.

As the Jupiter and Earth travel along their respective orbits, they start to get apart from each other. This leads to an increase in one-way communication time.

Therefore, the one-way communication time increases as the Jupiter and Earth travel along their respective orbits.

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Answer:1285.7 meters per second.

Step-by-step explanation: divide 900,000 meters by 700 seconds

Answer:

A plane travels 360,000 meters in 900 seconds

Step-by-step explanation: