If PQ = 4i+3j+2k, find /PQ/​

9514 1404 393

Answer:

  (d)  100x^32

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)^c = a^(bc)

  √a = a^(1/2)

__

Then ...

  [tex]\displaystyle\sqrt{10000x^{64}}=(10^4\cdot x^{64})^{\frac{1}{2}}=10^{\frac{4}{2}}\cdot x^{\frac{64}{2}}=10^2\cdot x^{32}\\\\=\boxed{100x^{32}}[/tex]

Answer:

Step-by-step explanation:

5000x^8

Answer:

D

Step-by-step explanation:

Base perimeter = side x 5 = 4 x 5 = 20 in

LA = (base perimeter x slant height)/2 = (20 x 8)/2 = 80 in^2

SA = base area + LA = 27.5 + 80 = 107.5 in^2

Answer:

3 - (p*q) im not sure lol

Step-by-step explanation:

Answer:

2 Percent or %

Step-by-step explanation:

The decimal 0.02 would be equivalent to 2 percent, or 2 per hundred.

Answer:

0.02 is 2 percent as a percent

Answer:

-In(2x-15)=-3

ln(2x-15)=3

2x-15=e^3

2x-15=20

2x=35

x=17.5

Answer:

0,1,2,3

Step-by-step explanation:

9514 1404 393

Answer:

  46 units

Step-by-step explanation:

Each midline is half the length of the parallel side of ΔCAT. This tells us ...

  TO = AO = DG = 10

  AD = GO = 7

  GT = DO = 9

The perimeter of the trapezoid is ...

  TA +AD +DG +GT = (TO+OA) +AD +DG +GT

  = (10 +10) +7 +10 +9 = 46

The perimeter of the trapezoid is 46 units.

Answer:

WIDTH= 54yd, LENGTH= 216 yd

Step-by-step explanation:

​

Length can be denoted as L

Width can be denoted as W

From the question,

(L= 4W) ........... eqn(1)

But perimeter = [(2L + 2W)]........eqn(2)

Substitute eqn(1) into (2)

Perimeter= (8W + 2W) = 10W

From the question,

perimeter= 540 yd

540=10W

W=(540/10)= 54

W= 54 yd

Hence, WIDTH= 54yd

From equation (1) substitute W= 54 yd

(L= 4W)

L= (4×54)

L= 216 yd

Hence, LENGTH= 216 yd

The dimensions are WIDTH= 54yd, LENGTH= 216 yd

9514 1404 393

Answer:

 ∠1 = 40°

Step-by-step explanation:

Angles 1 and 2 are "alternate interior" angles, so are congruent.

  ∠1 = ∠2

  2x +20 = 3x +10

  10 = x . . . . . . . . . . .  subtract 2x+10 from both sides

The measure of ∠1 is ...

  ∠1 = 2x +10 = 2(10) +20 . . . . . degrees

  ∠1 = 40°

Answer:

4in

Step-by-step explanation:

The width of the rectangle is

36:9=4

Answer:

she is correct because there is not common factor of 3 and 8 so it cannot be factored

Step-by-step explanation:

Answer:

-10, -1

Step-by-step explanation:

See Image below:)

Answer:

A. He did not apply the distributive property correctly for 4(1+3i)

Step-by-step explanation:

Answer:

xoy = 40º

toy = 140º

zox = 110º

toz = 70º

zoy = 70º

Step-by-step explanation:

There are 18 spaces so each is 180 / 18 = 10º

xoy = 40º

toy = 140º

zox = 110º

toz = 70º

zoy = 70º

Answer:

xoy = 40 degree angle

toy = 140 degree angle

zox = 110 degree angle

toz = 70 degree angle

zoy = 70 degree angle

Step-by-step explanation:

Use protractor to measure. Each mark is equal to 10 degrees.

Step-by-step explanation:

by order pair we obtain:

[tex] \displaystyle \begin{cases} \displaystyle 3p = 2p - 1 \dots \dots i\\2q - p = 1 \dots \dots ii\end{cases}[/tex]

cancel 2p from the i equation to get a certain value of p:

[tex] \displaystyle \begin{cases} \displaystyle p = - 1 \\2q - p = 1 \end{cases}[/tex]

now substitute the value of p to the second equation:

[tex] \displaystyle \begin{cases} \displaystyle p = - 1 \\2q - ( - 1) = 1 \end{cases}[/tex]

simplify parentheses:

[tex] \displaystyle \begin{cases} \displaystyle p = - 1 \\2q + 1= 1 \end{cases}[/tex]

cancel 1 from both sides:

[tex] \displaystyle \begin{cases} \displaystyle p = - 1 \\2q = 0\end{cases}[/tex]

divide both sides by 2:

[tex] \displaystyle \begin{cases} \displaystyle p = - 1 \\q = 0\end{cases}[/tex]

by order pair we obtain:

[tex] \displaystyle \begin{cases} \displaystyle 2x - y= 3 \dots \dots i\\3y= x + y \dots \dots ii\end{cases}[/tex]

cancel out y from the second equation:

[tex] \displaystyle \begin{cases} \displaystyle 2x - y= 3 \dots \dots i\\ x = 2y \dots \dots ii\end{cases}[/tex]

substitute the value of x to the first equation:

[tex] \displaystyle \begin{cases} \displaystyle 2.2y-y= 3 \\ x = 2y \end{cases}[/tex]

simplify:

[tex] \displaystyle \begin{cases} \displaystyle 3y= 3 \\ x = 2y \end{cases}[/tex]

divide both sides by 3:

[tex] \displaystyle \begin{cases} \displaystyle y= 1 \\ x = 2y \end{cases}[/tex]

substitute the value of y to the second equation which yields:

[tex] \displaystyle \begin{cases} \displaystyle y= 1 \\ x = 2 \end{cases}[/tex]

by order pair we obtain;

[tex] \displaystyle \begin{cases} \displaystyle 2p + q = 2 \dots \dots i\\3q + 2p = 3 \dots \dots ii\end{cases}[/tex]

rearrange:

[tex] \displaystyle \begin{cases} \displaystyle 2p + q = 2 \\2p + 3q= 3 \end{cases}[/tex]

subtract and simplify

[tex] \displaystyle \begin{array}{ccc} \displaystyle 2p + q = 2 \\2p + 3q= 3 \\ \hline - 2q = - 1 \\ q = \dfrac{1}{2} \end{array}[/tex]

substitute the value of q to the first equation:

[tex] \displaystyle 2.p+ \frac{1}{2} = 2[/tex]

make q the subject of the equation:

[tex] \displaystyle p = \frac{3}{4} [/tex]

hence,

[tex] \displaystyle q = \frac{1}{2} \\ p = \frac{3}{4} [/tex]

Answer:

see above

............

Answer:

Function A is less than the y value of Function B

Step-by-step explanation:

The y intercept of Function A is c = 3 [y = -3m + 3]

It's gradient will be m = 3 [ y = -9 + 3] to [y = -6]

Function B

Answer:  Choice C

Perpendicular because the slopes are negative reciprocals of each other.

=======================================================

Explanation:

Use the slope formula to find the slope of line AB

m = (y2-y1)/(x2-x1)

m = (-1-(-2))/(4-8)

m = (-1+2)/(4-8)

m = 1/(-4)

m = -1/4

The slope of line AB is -1/4

Repeat those steps for line CD

m = (y2-y1)/(x2-x1)

m = (-9-11)/(-2-3)

m = (-20)/(-5)

m = 4

The slope of line CD is 4

---------

The slopes of AB and CD are -1/4 and 4 respectively.

We can see that the two slopes are negative reciprocals of each other. Meaning that one slope will have us flip the fraction and the sign to form the other slope, and vice versa. Therefore, the two lines are perpendicular.

One useful property is that perpendicular slopes like this multiply to -1

(-1/4)*(4) = -1

---------

Side note: If the slopes were equal, then the lines would be parallel (assuming the two lines have different y intercepts).

Answer:

perpendicular because the slopes are negative reciprocals of each other

Step-by-step explanation:

Vector AB (8-4, -2 - -1) = AB(4, -1)

Vector CD(3- -2, 11- -9) = CD(5, 20)

Dot product of AB.CD = (4,-1).(5,20) = 4*5+(-1)*20 = 20-20 = 0 => perpendicular

Answer:

[tex]z = -3[/tex]

Step-by-step explanation:

Given

[tex]z^2 +11z+9 = 5z[/tex] --- the correct equation

Required

Solve

Equate to 0

[tex]z^2 +11z-5z+9 = 0[/tex]

[tex]z^2 +6z+9 = 0[/tex]

Expand

[tex]z^2 +3z+3z+9 = 0[/tex]

Factorize

[tex]z(z +3)+3(z+3) = 0[/tex]

Factor out z + 3

[tex](z +3)(z+3) = 0[/tex]

Split

[tex]z + 3 =0[/tex] --- twice

[tex]z = -3[/tex]

Answer:

Input - Output

2 - $290

12 - $690

24 - $1170

Step-by-step explanation:

Cost after n months:

The cost after n months is given by the following function:

[tex]C(n) = 40n + 210[/tex]

After 2 months:

This is C(2). So

[tex]C(2) = 40(2) + 210 = 80 + 210 = 290[/tex]

After 12 months:

This is C(12). So

[tex]C(12) = 40(12) + 210 = 480 + 210 = 690[/tex]

After 24 months:

This is C(24). So

[tex]C(24) = 40(24) + 210 = 960 + 210 = 1170[/tex]

Table:

Input - Output

2 - $290

12 - $690

24 - $1170

Answer:

27.4 feet down deep

Step-by-step explanation:

28 feet down, swins up for 0.3 feet times 6 or 1.8 feet up

leaving a total of 26.2 under the sea and he swims back down at 0.3 feet times 4 or 1.2 feet down. and the new total is 26.2 + 1.2 which equals 27.4 feet down in the deep sea

Answer:

27.4 feet

Step-by-step explanation:

.3 ft per sec for 6 sec = 1.8 feet

.3 ft per sec for 4 sec = 1.2 feet

28 - 1.8 + 1.2 = 27.4

Answer:

d^5

Step-by-step explanation:

d^8 / d^3

We know that a^b / a^c = a^(b-c)

d^(8-3)

d^5

Answer:

1,884

Step-by-step explanation:

The formula for solving the area of a right cylinder like this one is:

=2πrh+2πr2

Note:

Pls notify me if my answer is incorrect for the other users that will see this response. Thank you.

-kiniwih426

Answer:

80 degrees

Step-by-step explanation:

Since a triangle is 180 degrees

you then add to 2 degrees given and subtract it from 180

65+35=100

180-100=80 degrees

Answer:

2.844

Step-by-step explanation:

2.8436 is 2.844 when rounded to the nearest thousandth because the ten thousandth digit is 6, which means you round up for 3. Hope this helps!

Answer:

2.84

Step-by-step explanation:

2.8436 is rounded to the nearest thousands we get 2.84

Answer:

When someone is deaf they can’t hear, but they still have the ability to see. I believe the main part of living is being able to see, because even if you can’t hear at least you can see and remember the special moments that have occurred in your life. Of course, there are occasions in which it is necessary to hear, but being able to see is something truly valuable for someone because they are able to discover new things with their ability to see. Or maybe you can’t hear your partner tell you that they love you, but at least they can demonstrate it to you and actions speak louder than words in everything.

Step-by-step explanation:

I hope this helped you out

[tex]{\huge{\underbrace{\bf{\pink{Answer}}}}}[/tex]

Length of missing leg = 12 km

Using Pythagoras theorem

a² = 15² - 9²

a = √ 225 - 49

a = √144

a = 12 km

HOPE IT HELPS..

(Hypotenuse)² = (Base)²+ (Perpendicular)²

Taking, Hypotenuse As H

Base As B

Perpendicular As P

_________________________

H²= B²+ P²

[tex]15 {}^{2} = 9 {}^{2} + p {}^{2} \\ \\ p {}^{2} = 15 {}^{2} + 9 {}^{2} \\ \\ p {}^{2} = 225 - 81 \\ \\p {}^{2} = 144 \\ \\ p = \sqrt{144} \\ \\ p = 12[/tex]