HELP ME!!

The square of the sum of seven times a number and

seven

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:

18?

Step-by-step explanation:

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:

60 mph

Step-by-step explanation:

It takes two minutes to drive one mile at  30  mph. You are planning on covering two total miles. If your average speed is  60 mph, it would take two minutes to cover these two miles. So you have to go 60 mph.

Hope This Helps :)

The driver's speed is 30 miles per hour.

One mile is approximately 4 laps so 30 laps would be:

= 30 / 4

= 7.5 miles

The driver drove 7.5 miles in 15 minutes.

15 minutes in hours is:

= 15 / 60

= 0.25 hours

The speed of the driver is therefore:

= 7.5 miles / 0.25 hours

= 30 mph

The driver was therefore driving at a speed of 30 mph

Find out more at https://brainly.com/question/19940635.

Answer:

Step-by-step explanation:

Area of a rectangle is expressed as Length * Width

X = L*W where X is the area of the rectangle in fe²

If the triangle is eight times as long as it is wide, then L = 8W

Substitute L = 8W into the formula for calculating the area of a triangle, we will have;

X = L*W

X = (8W)*W

X = 8W²

The expression X in terms of W is therefore X = 8W²

Answer:

y=2x +3

Step-by-step explanation:

The slope hits the points (-1,2) and (0,2). If you count how many units are right and up, then that's your slope. In this case, the distance between those two points are 1 right and 2 up which is the same thing as 2. The y-intercept is 3 since the slope crosses the y-axis there.

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:

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:

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:

[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: true and stop deleting my answers im right im in collage

and I dont need to explain again when i already did so STOP and trust me

                                      A SNACK THAT SMILES BACK®

Answer:

12

Step-by-step explanation:

Answer:

2.4

Step-by-step explanation:

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:

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:

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:

[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:

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:

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:

  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:

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

Answer:

I'm just as confused as you lol

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:

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:

45 Feet

Step-by-step explanation:

4.5 divided by 0.5=9

9 times 5=45

Hoped this helped!

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