If f(x) = 6x
6x – 9 and g(x) = (x + 6,
which statement is true?

a) a as a column vector is [tex]\left(\begin{array}{c}1\\-2\end{array}\right)[/tex]

b) 2a -b as a column vector is [tex]\left(\begin{array}{c}1\\-7\end{array}\right)[/tex]

To write a vector as a column vector, the number at the top is the magnitude of the x component (horizontal component) of the vector and the number at the bottom is the magnitude of the y component (vertical component) of the vector

Magnitude of the vertical component = 1

Magnitude of the vertical component = -2

NOTE: Negative sign indicates that the direction of the vector is downwards

Thus, vector a as a column vector is

[tex]a = \left(\begin{array}{c}1\\-2\end{array}\right)[/tex]

Hence, a as a column vector is [tex]\left(\begin{array}{c}1\\-2\end{array}\right)[/tex]

Magnitude of the vertical component = 1

Magnitude of the vertical component = 3

[tex]b = \left(\begin{array}{c}1\\3\end{array}\right)[/tex]

Now, we are to work out 2a - b

That is,

[tex]2a -b = 2 \left(\begin{array}{c}1\\-2\end{array}\right)-\left(\begin{array}{c}1\\3\end{array}\right)[/tex]

[tex]2a -b = \left(\begin{array}{c}2\\-4\end{array}\right)-\left(\begin{array}{c}1\\3\end{array}\right)[/tex]

[tex]2a -b = \left(\begin{array}{c}2-1\\-4-3\end{array}\right)[/tex]

[tex]2a -b = \left(\begin{array}{c}1\\-7\end{array}\right)[/tex]

Hence, 2a -b as a column vector is [tex]\left(\begin{array}{c}1\\-7\end{array}\right)[/tex]

Learn more on Vectors here: https://brainly.com/question/21807172

#SPJ1

Answer:

n^2(n + 3)

Step-by-step explanation:

n^3 + 3n^2 factors as follows:  n^2(n + 3).  Note that this is an expression, not an equation.

Answer:

5

Step-by-step explanation:

LM + MN = LN

4+5x = 9x

Subtract 5x from each side

4+5x-5x = 9x-5x

4 = 4x

Divide by 4

4/4 = 4x/4

1 =x

We want MN

5x =5*1 = 5

MN =5

Answer:

the length of MN is 5(1), or 5

Step-by-step explanation:

Segments add up to 9x here:  4 + 5x = 9x, so 4 = 4x and x must therefore be 1.

Then the length of MN is 5(1), or 5, and the length of LN is 9(1) = 9.

Answer:

The statement is true

Step-by-step explanation:

We have been given an equation of hyperbola

In the given equation of hyperbola center is located at h at -1 and k at 2. so:

C:(h,k) = (-1,2)

Coordinated of the foci of the hyperbola are given as:

Foci: (h, k ± c)

Substitute the values of h and k into the coordinated of foci of hyperbola.

Foci: (-1, 2 ± c)

Where c can be found by using the given formula

c = √(a²+b²)

c = √(16+144)

c = 4√10

So the the coordinates of the foci are:

Foci: (-1, 2 - 4√10) and (-1, 2 + 4√10)

Thus, the statement given is true

Answer:

f=4

Step-by-step explanation:

6f = 24

÷6    ÷6

f=4

Answer:

f = 4

Step-by-step explanation:

6f = 24

f = 24/6

f = 4

Answer:

C. -n - 2

Step-by-step explanation:

Since there are no parenthesis for 3n + 2, you only distribute the 2 to (-2n - 1):

3n - 4n - 2

-n - 2

Answer:

C. -n - 2

Step-by-step explanation:

3n + 2(-2n - 1)

Expand the brackets.

3n + - 4n - 2

Add like terms.

- 1n - 2

-n - 2

Step-by-step explanation:

2x+3y=-14------equation i ×1

3x+y=-14--------equation ii ×3

2x+3y=-14

9x+3y=-42

-7x =- 28

x=4

Substitute for x in equation ii

3x+y= -14

3(4)+y=-14

12+y=-14

y=-14-12

y=- 26

Answer:

Step-by-step explanation:

To answer this question we should analyze both functions :

here we must solve both equations :

the first one is obvious x=0 the scond is more interesting :

x²+2=0⇔x²=-2 wich is impossible since x²≥0 unless we use complex numbers .

So we notice thatf has one intercept.

we added 2 to f to get g but no real intercepts

Answer:

1. A = 2184 yd. P = 212 yd.

Step-by-step explanation:

1. To find the perimeter of an object you need to do this formula: 2L * 2W which is 2 times the length times 2 times the width.

To find the Area you have to do this formula: H * W which means height times width.

2. They would need the area to fill the rectangle since you need to fill it and the area is the inside of the rectangle

3. She will need the perimeter since she is walking around the field and the perimeter is the outside (around) the shape.

Answer:

(-8, -2)

Step-by-step explanation:

Combine these equations:  You'll get 2y = -4, so that y = -2.

Substituting -2 for y in the second equation, you'll get -2 + x = -10, or x = -8

Thus the solution is (-8, -2)

Answer:

[tex]\frac{5}{2} ; -4[/tex]

Step-by-step explanation:

2x² + 3x - 20 = 0

a = 2 ; b = 3 ; c = -20

[ -b ± √(b² - 4ac) ] /2a = [-3±√(3²-4*2*-20]/2*2

                                 = [-3±√(9+160)]/4

                                = [-3±√169 ]/4

                                = [-3± 13]/4

                                = [tex]\frac{-3+13}{4} ;\frac{-3-13}{4}\\\\=\frac{10}{4} ; \frac{-16}{4}\\\\=\frac{5}{2} , -4[/tex]

2x² + 3x - 20 = 0

2x² + 8x - 5x - 20 = 0

2x(x+4) - 5(x+4) = 0

(x+4)(2x-5) = 0

x+4 = 0

x = -4

2x - 5 = 0

2x = 5

x = 5/2

Answer:

There you go.

Step-by-step explanation:

Please do tell me if it's wrong.

Answer:6z

Step-by-step explanation:

Question:

(4x - 5y + 3z) + (-4x +5y +3z)

First Step:

Remove parenthesis

4x - 5y + 3z + -4x +5y +3z

Second Step:

Add like terms

4x + -4x = 0

-5y + 5y = 0

3z + 3z = 6z

Final Answer

6z

<!> Brainliest is much Appreciated! <!>

Answer:

6z

Step-by-step explanation:

(4x - 5y + 3z) + (-4x +5y +3z)

Combine like terms

4x - 4x   -5y +5y  +3z+3z

0+0+6z

6z

Answer:

x = 1 1/4

Step-by-step explanation:

sqrt( 7x+2) = sqrt(3x+7)

Square each side

(sqrt( 7x+2))^2 = (sqrt(3x+7))^2

7x+2 = 3x+7

Subtract 3x from each side

7x-3x +2 = 3x+7-3x

4x+2 = 7

Subtract 2 from each side

4x+2-2 = 7-2

4x = 5

Divide by 4

4x/4 = 5/4

x = 1 1/4

Check for extraneous solution

sqrt( 7*5/4+2) = sqrt(3*5/4+7)

sqrt( 35/4 + 8/4) = sqrt(15/4+28/4)

sqrt( 43/4) = sqrt(43/4)

Solution is valid

Answer:

0.6 - 1/4

Convert the decimal to fraction

Thus

0.6 = 3/4

3/5 - 1/4

Find the LCM

the LCM is 20

We get

3/5 - 1/4 = (3(4) - 5)/ 20

= 12-5/20

= 7/20

2/5 + 0.75

0.75 = 3/4

Find the LCM

The LCM is 20

Thus

3/4 +2/5 = ( 3(5) + 2(4))/20

= 15 + 8 /20

= 23 / 20 or 1 3/20

1.75 - 1/6

Convert the decimal to fraction

1.75 = 7/4

Thus we get

7/4 - 1/6

Find the LCM

The LCM is 12

Thus

7/4 - 1/6 = ( 7(3) - 2)/12

= 21 - 2 / 12

= 19/ 12 or 1 7/12

3/10 + 2.125

Convert the decimal to fraction

2.125 = 17/8

Thus

3/10 + 17/8

Find the LCM

the LCM is 40

Thus

3/10 + 17/8 = ( 3(4) + 17(5))/40

= 12 + 85/40

= 97 /40 or 2 17/40

Hope this helps

Answer:

1.15

19/12

2.425

Step-by-step explanation:

2/5+0.75

2/5=4/10

4/10=0.4

0.75+0.4

1.15

1.75-1/6

1.75=7/4

7/4=14/8=21/12

21/12-2/12

19/12, or 1.5833...

3/10=0.3

0.3+2.125=2.425

Answer:

50 in.

Step-by-step explanation:

Real building:

height 300 ft

width 200 ft

Model building:

height 6 in.

width 50 in.

300/6=50

Hope this helps! :) :)

The scale model of building is 4 inches wide.

The height of a building is 300 feet
its width is 200 feet
A scale model of the building is 6 inches high

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

let scale model of the building is "x" inches wide.
= 300/6 = 200/x
x = 4

Thus, The scale model of building is 4 inches wide.

Learn more about Ratio here:
brainly.com/question/13419413

#SPJ2

Answer:

a = 34

b = 34

c = 36

Step-by-step explanation:

a ; b ; c = consecutive numbers =>

b = a + 1

c = a + 2

a + 2b + c - 7 = 133

a + 2(a + 1) + (a + 2) - 7 = 133

a + 2a + 2 + a + 2 - 7 = 133

4a = 133 + 7 - 4

4a = 136

a = 34

b = 34

c = 36

Answer:

70.257924 m^2

Step-by-step explanation:

Answer:

No.  She only estimated instead of hovering over the intersection to find the exact point.

Step-by-step explanation:

I used a graphing tool to graph the two lines. They pass at (6.25, -6.25). Since Keisha said the solution was (6, -6), which is not correct, she has most likely rounded the two values instead of finding the exact one.

Answer:

No. She used the wrong slopes when graphing the equations.

hope this helps i did it in Edge and got it right

mark me brainliest pls

Answer:

22 hours

Step-by-step explanation:

Ken saves 90% of his earnings.

So, he must earn

270/x =90/100

90x=270*100

90x=27,000

x=27000/90

=300

x=$300 to save $270

For starting 10hours, Ken earns $8 per hour so he earns total

$8*10 hours=$80

Now, Ken has to earn remaining

$220 at a rate of $10/hour, he must work for at least

$220/$10

=22hours

Answer:

a) 90°

b) 56°

Step-by-step explanation:

If we connect O with B to get two isosceles triangles: ΔAOB and ΔBOC

∠BOC= is central angle ans is twice as ∠BAC, so equals to 2*34°= 68°

Then ∠BCA= (180°- 68°)/2= 56°

∠ABC= ∠ABO+∠CBO= 34°+56°= 90°

Answer:

IT IS A..

Step-by-step explanation:

100 % sure

Answer:

( a ) 463 " human resource professionals " believe that the appearance of a job applicant is most important for a good first impression

( b )  Percent wise the confidence interval should be from about 86.6% to 93.4%

Step-by-step explanation:

I believe these first two parts here is sufficient enough to get you started!

" In a Harris poll of 514 human resource professionals, 90% said that the appearance of a job applicant is most important for a good first impression. Part A: Among the 514 human resource professionals who were surveyed, how many of them said that the appearance of a job applicant is most important for a good first impression?

Part B: Construct a 99% confidence interval estimate of the proportion of all human resource professionals believing that the appearance of a job applicant is most important for a good first impression. "

_____

( a ) We are given that n = 514, and p = 90%. The number of human resource professionals that said that the appearance of a job applicant is most important for a good first impression, should be the following -

514 x [tex]\frac{90}{100}[/tex]

= [tex]\frac{46260}{100}[/tex]

= 462.6

As the count of people can't be expressed as a fraction, the solution should be about 463 " human resource professionals. "

_____

( b ) Here the confidence level is 0.99 percent. Knowing that -

1 - ∝ = 0.99,

∝ = 1 - 0.99... = 0.01

Therefore, a 99% confidence interval estimate of the proportion of all human resource professionals believing that the appearance of a job applicant is most important for a good first impression should be calculated as directed in the attachment. By that the interval ranges as such -

0.8659 < p < 0.9341

And percent wise the confidence interval should be from about 86.6% to 93.4%

Answer:

2.5 gallons

Step-by-step explanation:

Quarts of juice Mary bought = 10 quarts

1 quart = 0.25 gallons

10 quarts = 0.25×10 = 2.5 gallons

Therefore she bought 2.5 gallons

Hope this helps : ) . Have a nice day !

Answer:

12 3/5

Step-by-step explanation:

Distributive property is when you take a number for example 3 and multiple all of the numbers inside the () in this case 4 1/5

1. multiple 3 by 4 =12

2 multiple3 by 1/5= 3/5

3 write your awnser 4 3/5

Hoped this helped

Answer:

A) tan(45°) help us to find the height of the tree because it relates our unknown with a known length (the length of the shadow)

B) tan(45°) = x/35.6

C) x = 35.6 ft

Step-by-step explanation:

B) From definition:

tan(45°) = opposite/adjacent

opposite to angle 45° is x ( the height of the tree), adjacent to angle 45° is the length of the shadow (35.6 ft). Replacing into the equation:

tan(45°) = x/35.6

C) tan(45°) = 1

Then:

1 = x/35.6

35.6 ft = x

#1

As here base is given

We need the height or perpendicular

so tangent is the easiest way to be used

#2(No problem given,may refering to part C)

#3

as sin45=cos45

Put value

Answer:

The average speed on this trip was 46.15 mph. The correct option is A.

Step-by-step explanation:

In order to calculate the average speed, we need to apply the following formula:

[tex]v_{avg} = \frac{\text{distance}}{\text{time}}[/tex]

We were given the distance between the two cities in miles, therefore we can directly apply it to the expression. Although the time was given in the hh:mm 12 h format and we need a diference in hours, so we will convert that as shown below:

[tex]\text{time departure} = 9 + \frac{50}{60} = 9.83 \text{ h}[/tex]

[tex]\text{time arrival} = 12 + 5 + \frac{30}{60} = 17.5[/tex]

The elapsed time of the trip is the difference between these:

[tex]\text{time} = 17.5 - 9.83 = 7.67 \text{ h}[/tex]

We can now apply it to the formula:

[tex]v_{avg} = \frac{354}{7.67} = 46.15 \text{ mph}[/tex]

The average speed on this trip was 46.15 mph. The correct option is A.

Answer:

A

Step-by-step explanation:

The quadrants are numbered from top right in a counter clockwise fashion. Since we know x is positive and y is negative, we can find that it is the fourth quadrant.

Answer:

True, this is a function

Step-by-step explanation:

There is a 1 to one correspondence between x and y

Each x goes to one y, so this is a function