3(2x+3)-4(3x-6)=16 show and explain.

Answer:

Step-by-step explanation:

Given the line L1 as y = 2x perpendicular to an unknown line L2 passing through the point P = (1, 2), we are to find the equation of line L2. to find the equation of the line L2, we will use the point-slope equation of a line expressed as y-y₀ = m(x-x₀)

m is the slope of the unknown line

(x₀, y₀) is the given point.

First is to get the slope of the known line:

comparing the line L1: y = 2x with the standard equation of the line y = mx+c, it can be seen that m = 2

Then we will calculate the slope of the required line.

Since L1 is perpendicular to L2, the product of their slope will be -1 i.e

mm₁ = -1 where m₁ is the slope of the required line L2.

Given m =2

m₁ = -1/m

m₁ = -1/2

Finally we will calculate the equation of line L2 by substituting the slope of line L2 and the point in the point slope equation above;

y-y₀ = m(x-x₀)

Given (x₀, y₀) = (1,2) and m₁ = -1/2

y-2 = -1/2(x-1)

open the parenthesis

y-2 = -x/2+1/2

multiply through by 2:

2y-4 = -x+1

2y+x = 1+4

2y+x = 5

Hence the equation of the line L2 is 2y+x = 5

Answer:

18?

Step-by-step explanation:

Answer:

I think the answer is A. 49% of the respondents were women

Answer:

t=-6.3

Step-by-step explanation:

-1 (t + 8) = -1.7

-1*t+-1*8=-1.7

-1t-8=-1.7

   +8      +8

-1t=-1.7+8

-1t=6.3

-1t/-1=6.3/-1

t=-6.3

I hope this helped you.

Please mark Brainliest.

Have a great day!!!!!!!!

Answer: -6.3

Step-by-step explanation:

let me know if you have any questions

Answer:

7123

Step-by-step explanation:

The only requirement is to have 7 in the thousands place, which I've done, and the rest of the numbers can be any number you choose!

Answer:

1) The polynomials [tex]p_{1}(t) = 1 +t^{2}[/tex] and [tex]p_{2}(t) = 1-t^{2}[/tex] are linearly independient, 2) The polynomials [tex]p_{1}(t) = 2\cdot t +t^{2}[/tex] and [tex]p_{2}(t) = 1+t[/tex] are linearly independent, 3) The polynomials [tex]p_{1}(t) = 2\cdot t - 4\cdot t^{2}[/tex] and [tex]p_{2}(t) = 6\cdot t^{2}-3\cdot t[/tex] are linearly dependent.

Step-by-step explanation:

A set is linearly independent if and only if the sum of elements satisfy the following conditions:

[tex]\Sigma_{i=0}^{n} \alpha_{i} \cdot u_{i} = 0[/tex]

[tex]\alpha_{0} = \alpha_{1} =...=\alpha_{i} = 0[/tex]

1) The set of elements form the following sum:

[tex]\alpha_{1}\cdot p_{1}(t)+\alpha_{2}\cdot p_{2}(t) = 0[/tex]

[tex]\alpha_{1}\cdot (1+t^{2})+\alpha_{2}\cdot (1-t^{2}) = 0[/tex]

[tex](\alpha_{1}+\alpha_{2})\cdot (1) +(\alpha_{1}-\alpha_{2})\cdot t^{2} = 0[/tex]

From definition this system of equations must be satisfied:

[tex]\alpha_{1} + \alpha_{2} = 0[/tex] Eq. 1

[tex]\alpha_{1}-\alpha_{2} = 0[/tex] Eq. 2

From Eq. 2:

[tex]\alpha_{1} = \alpha_{2}[/tex]

In Eq. 1:

[tex]2\cdot \alpha_{1} =0[/tex]

[tex]\alpha_{1} = 0[/tex]

[tex]\alpha_{2} = 0[/tex]

The polynomials [tex]p_{1}(t) = 1 +t^{2}[/tex] and [tex]p_{2}(t) = 1-t^{2}[/tex] are linearly independient.

2) The set of elements form the following sum:

[tex]\alpha_{1}\cdot p_{1}(t)+\alpha_{2}\cdot p_{2}(t) = 0[/tex]

[tex]\alpha_{1}\cdot (2\cdot t+t^{2})+\alpha_{2}\cdot (1+t) = 0[/tex]

[tex]\alpha_{2}\cdot (1) +(2\cdot \alpha_{1}+\alpha_{2})\cdot t +\alpha_1 \cdot t^{2} = 0[/tex]

From definition this system of equations must be satisfied:

[tex]\alpha_{2} = 0[/tex]

[tex]2\cdot \alpha_{1}+\alpha_{2} = 0[/tex]

[tex]\alpha_{1} = 0[/tex]

The polynomials [tex]p_{1}(t) = 2\cdot t +t^{2}[/tex] and [tex]p_{2}(t) = 1+t[/tex] are linearly independent.

3) The set of elements form the following sum:

[tex]\alpha_{1}\cdot p_{1}(t)+\alpha_{2}\cdot p_{2}(t) = 0[/tex]

[tex]\alpha_{1}\cdot (2\cdot t-4\cdot t^{2})+\alpha_{2}\cdot (6\cdot t^{2}-3\cdot t) = 0[/tex]

[tex](2\cdot \alpha_{1}-3\cdot \alpha_{2})\cdot t + (-4\cdot \alpha_{1}+6\cdot \alpha_{2})\cdot t^{2} = 0[/tex]

From definition this system of equations must be satisfied:

[tex]2\cdot \alpha_{1}-3\cdot \alpha_{2} = 0[/tex] (Eq. 1)

[tex]-4\cdot \alpha_{1}+6\cdot \alpha_{2} =0[/tex] (Eq. 2)

It is easy to find that each coefficient is multiple of the other one, that is:

[tex]\alpha_{1} =\frac{3}{2}\cdot \alpha_{2}[/tex] (From Eq. 1)

[tex]\alpha_{1} = \frac{6}{4}\cdot \alpha_{2}[/tex] (From Eq. 2)

[tex]\alpha_{1} = \frac{3}{2}\cdot \alpha_{2}[/tex]

Which means that polynomials [tex]p_{1}(t) = 2\cdot t - 4\cdot t^{2}[/tex] and [tex]p_{2}(t) = 6\cdot t^{2}-3\cdot t[/tex] are linearly dependent.

Answer:

6 pencils cost $5.16.

Step-by-step explanation:

1. Find the cost of one pencil.

Divide: $7.74 ÷ 9 = $0.86 for one pencil

2. Multiply 0.86 by 6

$0.86 × 6 = $5.16

Answer:

2/3 multiply with 7.74

=5.16

Answer:

12

Step-by-step explanation:

Answer:

2.4

Step-by-step explanation:

Answer:

Volume is the measure of how big an object is in three dimensions, so the volume of a box measure how much room there is inside of the box. To find it, you need to make a few simple measurements of length, width, and height, and then multiply them.

Step-by-step explanation:

Answer:

7.12

Step-by-step explanation:

The formula for the effective annual yield is given as:

i = ( 1 + r/m)^m - 1

Where

i = Effective Annual yield

r = interest rate = 7% = 0.07

m= compounding frequency = semi annually = 2

i = ( 1 + 0.07/2)² - 1

i = (1 + 0.035)² - 1

= 1.035² - 1

= 1.071225 - 1

= 0.071225

Converting to percentage

0.071225 × 100

= 7.1225%

Approximately to 2 decimal places = 7.12

Therefore, the annual effective yield = 7.12

Answer:

[tex]c=5[/tex]

Step-by-step explanation:

[tex]4(6c+5)-2(3c-5)=120[/tex]

Use the distributive property to expand the equation:

[tex]4(6c)+4(5)-2(3c)-2(-5)=120\\\\24c+20-6c+10=120[/tex]

Combine like terms to simplify the equation:

[tex]24c-6c+20+10=120\\\\18c+30=120[/tex]

Subtract 30 from both sides:

[tex]18c+30-30=120-30\\\\18c=90[/tex]

Isolate the variable c. Divide both sides by 18:

[tex]\frac{18c}{18}=\frac{90}{18}\\\\ c=5[/tex]

So, c is equal to 5.

:Done

Answer:

I'm just as confused as you lol

Answer:

h(-8)=-15

Step-by-step explanation:

Substitute t=-8

h(-8) =-2(-8+5)^2+3

       =-2(-3)^2+3

       =-2(9)+3

       =-18+3

       =-15

h(-8) = - 15

h(t) = - 2(t + 5)² + 3

replace t with - 8

h(-8) = - 2(- 8 + 5)² + 3

h(-8) = - 2(-3)² + 3

h(-8) = -2×9 + 3

h(-8) = - 18 + 3

h(-8) = - 15

Answer:

14hours

Step-by-step explanation:

Since Andre and Morgan are both heading to the same location i.e Florida, they will have the same distance.

Distance = Speed × Time

For Morgan:

His speed = 55mi/hr

Let his time = x

Distance covered by Morgan = 55x

For Andre

His speed = 70mi/hr

Time = x-3 (since morgan leaves 3 hours earlier than Andre)

Distance covered = 70× (x-3) = 70(x-3)miles

Since they are driving towards the same location;

55x = 70(x-3)

55x = 70x-210

55x-70x = -210

-15x = -210

x = 210/15

x = 14

Hence Morgan will have been driving 14hours before Andre catch up

Answer:

18 square units

Step-by-step explanation:

Since the shape is a square lets find the distance between two close point then square the distance to find the answer.

Lets take the point (-7,-5), (-4,-2)

Distance= √((y2-y1)²+(x2-x1)²)

Distance= √((-2--5)²+(-4--7)²)

Distance= √((-2+5)²+(-4+7)²)

Distance= √((3)²+(3)²)

Distance= √(9+9)

Distance= √18 units

Area= distance ²

area= √18²

Area= 18 square unit

Answer:

Picture number 3 is the answer

Step-by-step explanation:

A function is a relation in which each element in the domain is paired with exactly one element in the range not 2.

Picture number one has a range left with no domain so it's not a function

Picture number 2 is showing an element in the domain which paired 2 elements in the range so it's not a function

Picture 3 is correct because each element in the domain macthes one element in the range.

Picture 4 is wrong because it's showing elements in the domain that matches 2 elements in the range. Hope it makes sense.

The required relationship that represents a function is given by 3rd image. Option C is correct.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

The first image has a range with no domain, hence it is not a function. In 2nd image depicts an element in the domain that paired two elements in the range, indicating that it is not a function. In 3rd image, it is valid because each element in the domain corresponds to one element in the range. In picture 4, it is incorrect since it depicts domain components that match two range elements.

Thus, the required relationship that represents a function is given by 3rd image. Option C is correct.

Learn more about function here:

brainly.com/question/21145944

#SPJ2

Answer:

Step-by-step explanation:

Consider the following planes.  x + y + z = 5, x + 3y + 3z = 5

the parametric equations for the line of intersection of the planes are determined as follows:

From the first plane, the normal of the first plane is [tex]n_1 = (1,1,1)[/tex]

from the second plane, the normal of the second plane is [tex]n_2 = (1,3,3)[/tex]

[tex]n_1 \times n_2 = \begin {vmatrix} \left \begin{array}{ccc}i&j&k\\1&1&1\\1&3&3 \end{array}\right \end {vmatrix}[/tex]

= i(3-3) -j(3-1)+k(3-1)

= i(0) - j(2) + k(2)

= -2j +2k

Suppose z = 0

x+y + 0 = 5  ---(1)

x+3y + 3(0) = 5 (2)

subtracting by elimination

-2y = 0

y = 0/-2

y = 0

The intersection on point of the plane is (5,0,0)

The  equation of plane is r (t) =(5, 0, 0) + t(0, -2, 2)

∴

(x(t), y (t), z(t) ) = (5, -2t, 2t)

B) Find the angle between the planes

The angle between the planes can be represented by the equation:

[tex]cos \theta = \dfrac{a_1a_2+b_1b_2 + c_1c_2}{\sqrt{a^2_1+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2}}[/tex]

[tex]cos \theta = \dfrac{1 \times 1+1\times 3 +1 \times 3}{\sqrt{1^2+1^2+1^2}\sqrt{1^2+3^2+3^2}}[/tex]

[tex]cos \theta = \dfrac{1+ 3 +3}{\sqrt{3}\sqrt{19}}[/tex]

[tex]cos \theta = \dfrac{7}{\sqrt{3}\sqrt{19}}[/tex]

[tex]\mathbf{\theta = cos ^{-1} (\dfrac{7}{\sqrt{57}})}[/tex]

Answer:

B

Step-by-step explanation:

The arrow is going left four units. Since it's going left, we know that we are adding a negative number and since it's going left 4 units, we know that we are adding -4 in our equation. This narrows it down to options B and D. However, the arrow usually represents the second number being added, hence, the answer is B.

Answer:

First Graph

Step-by-step explanation:

3y-5x<-6

3y<5x-6

y<5/3x-6/3

y<5/3x-2

plug in the coordinates (0,0)

0<0-2

0<-2

0 is not less than -2

therefore the graph would be shaded opposite of (0,0)

Answer:

Two angles are said to be supplementary when they add up to 180°.

Answer:

Angles are supplementary if the add up to 180 degrees

Step-by-step explanation:

So many different angles can be supplementary.

Examples:

Ajacent Angles

Corresponding Angles

Alternate Interior Angles

Alternate Exterior Angles

And a few other angles

Hope This Helps :)

Answer:

whatever 42 times 10 equals, it also equals what ten minus 4 times seventy is

Step-by-step explanation:

so both 42 × 10

and 10 – 4 × 70

EQUAL

420

(pffft 420....sorry its funny)

Answer:

Associative properties

Step-by-step explanation:

42 x 10 = 420

(10-4)=6

6 x 70 = 420

Answer:

[tex]a^{2} +b^{2} =c^{2}[/tex]

Step-by-step explanation:

C is the horisontal and a or b can be the height, plug in the numbers and you solve for length.

Answer:

(sqr) 30^2/100^2+3^2

Step-by-step explanation:

Answer:

The answer is "x = 0"

Step-by-step explanation:

Step-by-step explanation: Hope this answer is helpful...

Make me as brainliest...

Answer:

  32 ft

Step-by-step explanation:

The length of the larger rectangle is double that of the smaller one. If we assume the rectangles are similar, the perimeter will be double as well:

  2·(16 ft) = 32 feet . . . . perimeter of larger rectangle

__

The width of the larger one is 2·1.8 ft = 3.6 ft.

Answer:

C) 32 feet

Step-by-step explanation:

＼(ﾟｰﾟ＼)

Answer:

yes

Given a 2D line e.g. (3,10) -> (8.3,16.5), how can I find any point on that line that has has whole-number coordinates?

I can easily iteratively walk along one of the axis in integer steps, seeing if the value on the other axis is integer, but this is slow for very very long lines.

Answer:

22 comic books.

Step-by-step explanation:

(20 - 9) * 2 First subtract 9 from 20

11 * 2 Multiply 11 by 2

22 is the product

Answer:

45 Feet

Step-by-step explanation:

4.5 divided by 0.5=9

9 times 5=45

Hoped this helped!