The quotient of 12 times an unknown number and 13 is 6 what is the unknown number?

[tex]5\sqrt{3b}\qquad\boxed{YES}\\\\2\sqrt{21}\qquad\boxed{YES}\\\\x\sqrt8=x\sqrt{4\cdot2}=x\sqrt4\cdot\sqrt2=2x\sqrt2\qquad\boxed{NOT}\\\\2\sqrt{36}=2\cdot6=12\qquad\boxed{NOT}\\\\\sqrt5\qquad\boxed{YES}\\\\c\sqrt{12c^2}=c\sqrt{4\cdot3\cdot c^2}=c\sqrt4\cdot\sqrt3\cdot\sqrt{c^2}=c\cdot2\cdot\sqrt3\cdot|c|=2c|c|\sqrt3\qquad\boxed{NOT}[/tex]

Here, you are required to check if each expression can be simplified further

Expression 1, 2 and 5 are in the simplest form already

5√3b

Can not be simplified further

2√21 = 2√7 × 3

aCan not be simplified further

x√8

= x × √4 × 2

= x × √4 × √2

= x × 2 × √2

= 2x√2

Can be simplified further

2√36

= 2 × √36

= 2 × 6

= 12

Can be simplified further

√5

Can not be simplified further

c√12c²

= c × √4×3×c²

= c × √4 × √3 × √c²

= c × 2 × √3 × c

= 2c²√3

Can be simplified further

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The closing of the Albany bridge by Commodore Cornelius Vanderbilt was likely a strategic decision to protect and enhance his railroad enterprise, demonstrating the importance of controlling transportation infrastructure in the 19th century.

Commodore Cornelius Vanderbilt, known for his vast railroad empire, consolidated several smaller railroad lines to form the powerful New York Central Railroad Company. This consolidation allowed for more efficient connections from Midwestern suppliers to eastern markets, which was of great economic importance. The closing of the Albany bridge by Vanderbilt would have been one such strategic decision to enhance his railroad network and protect the interests of his enterprise.

The incident at Ebenezer Creek, where Union General Jefferson C. Davis ordered the cutting of the pontoon bridge to strand fleeing slaves and prevent them from crossing, shows the harsh decisions made during the Civil War. While this event does not directly relate to Vanderbilt closing the Albany bridge, it demonstrates the kind of pivotal and often harsh decisions made regarding bridges and the movement of people during that era for military or strategic reasons.

Answer:

Step-by-step explanation:

Given expression :

Step 1: = -4 3/7+(-3 4/7) + 7

Step 2: = -4 + (-3/7) + (-3) + (-4/7) + 7

Step 3: = -4 + (-3/7) + (-4/7) + (-3) + 7

Step 4: = -4 + (-1) + (-3) + 7

Step 5: = -8 + 7

Step 6: = -1

In 3rd step they just swap the positions of (-4/7) and (-3) to bring the like fractions with common denominator together.

Swapping the numbers is the Commutative Property of Addition.

[tex]Domain:\ x\geq0\ \wedge\ y\in\mathbb{R}[/tex]

[tex]\sqrt{8x^7y^8}=\sqrt8\cdot\sqrt{x^7}\cdot\sqrt{y^8}=\sqrt{4\cdot2}\cdot\sqrt{x^6\cdot x}\cdot\sqrt{y^{4\cdot2}}\\\\=\sqrt4\cdot\sqrt2\cdot\sqrt{x^6}\cdot\sqrt{x}\cdot\sqrt{(y^4)^2}=2\sqrt2\cdot\sqrt{x^{3\cdot2}}\cdot\sqrt{x}\cdot y^4\\\\=2y^4\sqrt2\cdot\sqrt{(x^3)^2}\cdot\sqrt{x}=2y^4\sqrt{2x}\cdot x^3\\\\=\boxed{2x^3y^4\sqrt{2x}}[/tex]

[tex]Used:\\\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\\sqrt{a^2}=a\ for\ a\geq0[/tex]

Answer:

c is correct

Step-by-step explanation:

edge 2020

Final answer:

The equivalent expressions for 102 - 42 are 60, -42, 60 - 42, and 102 - 42. The equivalent expressions for 33y - 11y are 22y, 22y - 11y, 33y - 11y, and 11y.

Explanation:

Equivalent expressions for 102 - 42:

Equivalent expressions for 33y - 11y:

Answer:

2

Step-by-step explanation:

3/2 + (-k) + (-2) =

= 3/2 + [-(-5/2)] - 2

= 3/2 + 5/2 - 2

= 8/2 - 2

= 4 - 2

= 2

Answer:

50√3 or  86.6

Step-by-step explanation:

Divide the hexagon into six equilateral triangles as in Figure 1 below.

Then draw a line from the midpoint of one side to the midpoint of the opposite side.

The height (h) of each triangle will be 5.

To find the area of the whole triangle, we first need to find the length of the base (see Figure 2).

If the base length (b) is 2s, we have the relation

5/s = tan60°

5/s = √3      Multiply each side by s

5 = s√3        Divide each side by √3

s = 5/√3       Rationalize

s = (5√3)/3

b = 2s

b = (10√3)/3

The area (A) of the triangle is

A = ½bh

A = ½ × (10√3)/3 × 5

A = (25√3)/3

There are six equilateral triangles in the hexagon, so

Total area = 6A

Total area = 6 × (25√3)/3

Total area = 50√3

Total area ≈ 86.6  

[tex]\bf \stackrel{x-intercept}{(\stackrel{x_1}{2}~,~\stackrel{y_1}{0})}\qquad \stackrel{y-intercept}{(\stackrel{x_2}{0}~,~\stackrel{y_2}{6})} \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{6-0}{0-2}\implies \cfrac{6}{-2}\implies -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=-3(x-2)\implies y=-3x+6[/tex]

Answer: 5

Step-by-step explanation: 5.07 rounds to 5

0.81 rounds to 1

so the best estimate for 5.07 x 0.81 = 5(1) = 5.......ANS

Answer:

4.05

Step-by-step explanation:

5 X 0.81 = 4.05 so I say C

Answer:

[tex]tan(\frac{5\pi}{3})=\sqrt{3}[/tex]

Step-by-step explanation:

we are given

[tex]tan(\frac{5\pi}{3})[/tex]

we know that

[tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]

so, we can write our expression as

[tex]tan(\frac{5\pi}{3})=\frac{sin(\frac{5\pi}{3})}{cos(\frac{5\pi}{3})}[/tex]

now, we can use unit circle

[tex]sin(\frac{5\pi}{3})=-\frac{\sqrt{3} }{2}[/tex]

[tex]cos(\frac{5\pi}{3})=-\frac{1}{2}[/tex]

now, we can plug values

[tex]tan(\frac{5\pi}{3})=\frac{-\frac{\sqrt{3} }{2}}{-\frac{1}{2}}[/tex]

[tex]tan(\frac{5\pi}{3})=\sqrt{3}[/tex]

Answer:

[tex] y = 300(0.78)^x [/tex]

Step-by-step explanation:

x is the number of years. y is the population after x years.

Each year, the population decreases by 22%, since 100% - 22% = 78%, and 78% = 0.78, each year, the population is 0.78 of the previous year's population.

year zero: y = 300

year 1: y = 300 * 0.78 = 300 * (0.78)^1

year 2: y = (300 * 0.78) * 0.78 = 300 * (0.78)^2

year 3: y = ((300 * 0.78) * 0.78) * 0.78 = 300 * (0.78)^3

year x: y = 300(0.78)^x

Answer:

Step-by-step explanation:

5/13.5 x 8/x (cross multiple) 108/5 (divide) = 21.6

Question

As an estimation we are told 5 miles is 8 km.  

Convert 13.5 miles to km

Answer:

Step-by-step explanation:

you can solve with an equation

5 : 8 = 13.5 : x

x = 8 * 13.5 : 5

x = 21.6

Answer:

19.49 per gallon

hope it helps

Step-by-step explanation:

total pay ÷ number of gallon = the cost of each gallon

97.45 / 5 = 19.49 per gallon

Answer:-47

Step-by-step explanation:

1# 11+4=15

2# 15+4=19

3# 19+4=23

4# 23+4=27

5# 27+4=31

6# 31+4=35

7# 35+4=39

8# 39+4=43

9# 43+4=47

REMEBER its negative not positive.

Answer:

12

Step-by-step explanation:

144/12 = 12

12 x 12 = 144

Answer:

12

Step-by-step explanation:

divide 12 by 144

Answer:

Most students chose math.

Step-by-step explanation:

art 4/25,

english 13%,

math .28,

other 7%,

science 21/100,

social studies .15

1. convert all values to the same unit (I used decimal)

Art: 4/25= 0.16

English 0.13

Math: 0.28

Other: 0.07

Science: 0.21

Social studies: 0.15

2. find the highest decimal point to determine most chosen subject.

Math is highest at 0.28

7. (x-7)(x-7)

8. (3x-5y)(3x-5y)

9. (x-15)(x+3)

10.(7m+6n)(7m+6n)

11. (2x+1)(2x+1)

12. (7x+2)(7x+2)

13. (p-18)(p+4)

Notice how 7,8,10,11, and 12 are all perfect squares. A good way to tell if a trinomial can be factored into a perfect square is if the square root of the coefficient of your variable multiplied by the square root of the constant (number with no variable) multiplied by 2 equals the middle term's coefficient.

For example, take 4x^2+16x+16. Taking the square root of 4 gives us 2. Taking the square root of 16 gives us 4. So, 2*2*4=16, which is our middle term, thus proving that this trinomial is indeed a perfect square.

Answer:

12 Meters Per Second

Step-by-step explanation:

Average Speed = Distance divided by time

Average Speed = 120 Meters / 10 Seconds

Average Speed = 12 Meters Per Second

if  sprinter can run 120 meters in 10 seconds then 12 meters per second is the average speed.

Speed is defined as the rate of change of position of an object in any direction

Given that A sprinter can run 120 meters in 10 seconds.

Average Speed = Distance divided by time

Speed = Distance/ Time

The distance is 120 meters and times is 10 seconds.

Speed=120/10

=12 meters per second

Hence, if  sprinter can run 120 meters in 10 seconds then 12 meters per second is the average speed.

To learn more on Speed click:

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Answer: The pilot traveling 400 mph rising at an angle 30 degrees is going to gain more altitude faster

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

Explanation:

Draw out the triangles as you see in the attached image below. We'll use the sine rule because we want to tie together the unknown height (h) which is the opposite side of the reference angle, to the known hypotenuse (the speed of the aircraft)

For the first plane,

sin(angle) = opposite/hypotenuse

sin(30) = h/400

h = 400*sin(30)

h = 200

so the first plane is gaining altitude at 200 mph (each hour, the plane is 200 miles higher up)

For the second plane

sin(angle) = opposite/hypotenuse

sin(40) = h/300

h = 300*sin(40)

h = 192.836282905961

h = 192.84

which is smaller than the previous result (200)

So we see that the first plane is rising faster

Answer:

a pilot traveling 400 mph and rising at an angle of 30 degrees

Step-by-step explanation:

[tex]\bf \begin{cases} 5x+7y=32\\ 8x+6y=46 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 5x+7y=32\implies 7y=32-5x\implies \boxed{y}=\cfrac{32-5x}{7} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting \underline{y} in the 2nd equation}}{8x+6\left(\boxed{ \cfrac{32-5x}{7}} \right)}=46\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{7}}{7\left( 8x+6\left( \cfrac{32-5x}{7} \right) \right)=7(46)} \\\\\\ 56x+6(32-5x)=322\implies 56x+192-30x=322[/tex]

[tex]\bf 26x+192=322\implies 26x=130\implies x=\cfrac{130}{26}\implies \blacktriangleright x=5 \blacktriangleleft \\\\\\ \stackrel{\textit{subsituting \underline{x} in the 1st equation}}{5(5)+7y=32}\implies 25+7y=32\implies 7y=7 \\\\\\ y=\cfrac{7}{7}\implies \blacktriangleright y=1 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (5,1)~\hfill[/tex]

Answer5,90,000

Step-by-step explanation:

780,000 subtract 190,000 = 590,000

after every 6 years

i'm not sure if its correct. please let me know

Answer:

The first three, (2, 8), (3, 9) and (4, 10).

Step-by-step explanation:

The unit rate, or rate of change, is another term for the slope.

The formula for slope is

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].

The slope in the table would be given by

m = (22-11)/(10-5) = 11/5 = 2.2.

For the slope of the line that goes through (2, 8) and (0, 0), we have

m = (8-0)/(2-0) = 8/2 = 4.  This is greater than 2.2.

For the slope of the line that goes through (3, 9) and (0, 0), we have

m = (9-0)/(3-0) = 9/3 = 3.  This is greater than 2.2.

For the slope of the line that goes through (4, 10) and (0, 0), we have

m = (10-0)/(4-0)/ = 10/4 = 2.5.  This is greater than 2.2.

For the slope of the line that goes through (5, 8) and (0, 0), we have

m = (8-0)/(5-0) = 8/5 = 1.6.  This is not greater than 2.2.

For the slope of the line that goes through (6, 7) and (0, 0), we have

m = (7-0)/(6-0) = 7/6 = 1.16.  this is not greater than 2.2.

For the slope of the line that goes through (7, 6) and (0, 0), we have

m = (6-0)/(7-0) = 6/7 = 0.86.  This is not greater than 2.2.

Answer:

y = 225

Step-by-step explanation:

since y and x are directly proportional the equation relating them is

y = kx ← k is the constant of proportionality

to find k use the given condition y = 288 when x = 32

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{288}{32}[/tex] = 9

y = 9x ← is the equation of proportionality

when x = 25, then

y = 9 × 25 = 225

Answer:

Step-by-step explanation:

Let x be the number of buses and y be the number of vans.

We know that there are 5 more buses than vans, therefore, we can set up:

[tex]x=y+5[/tex]

Since a bus transports 55 people and a van transports 12 people, therefore, we can set up:

[tex]55x+12y = 409\\[/tex]

Now lets solve the above two equations together by substitution

[tex]55(y+5)+12y = 409\\\\55y+275+12y=409\\\\67y+275=409\\\\67y=409-275\\\\67y=134\\\\y=2,x=2+5=7[/tex]

Total number of students and teachers who rode to the zoo in buses[tex]=55*7=385[/tex]

Total number of students and teachers who rode to the zoo in vans[tex]=12*2=24[/tex]

y-coordinate is 3 more than x-coordinate:  y = x + 3.

Substitute to the equation x + y = 21:

x + x + 3 = 21      subtract 3 from both sides

2x = 18      divide both sides by 2

x = 9

y = 9 + 3

y = 12

Final answer:

Kendra's original allowance was $10.

Explanation:

To find out how much Kendra's allowance was, we can use algebraic equations. Let 'x' represent Kendra's original allowance.

Kendra lost half of her allowance, which means she had x/2 left.

Then her mother gave her four more dollars, so now she has x/2 + 4.

Given that Kendra has $9, we can set up the equation x/2 + 4 = 9 and solve for x.

x/2 + 4 = 9

x/2 = 9 - 4

x/2 = 5

Multiplying both sides of the equation by 2, we get x = 10.

Therefore, Kendra's allowance was $10.

[tex]\sec x=\dfrac{1}{\cos x}\to \sec60^o=\dfrac{1}{\cos60^o}\\\\\text{Use the table of values of a trigonometric functions}\\\\\cos30^o=\dfrac{\sqrt3}{2}\\\\\sin\dfrac{\pi}{4}=\dfrac{\sqrt2}{2}\\\\\cos60^o=\dfrac{1}{2}\to\sec60^o=\dfrac{1}{\frac{1}{2}}=2\\\\\text{Substitute:}\\\\\cos30^o\sin\dfrac{\pi}{4}+\dfrac{\sec60^o}{3}=\dfrac{\sqrt3}{2}\cdot\dfrac{\sqrt2}{2}+\dfrac{2}{3}=\dfrac{\sqrt6}{4}+\dfrac{2}{3}\\\\=\dfrac{3\sqrt6}{3\cdot4}+\dfrac{4\cdot2}{4\cdot3}=\dfrac{3\sqrt6}{12}+\dfrac{8}{12}\\\\=\boxed{\dfrac{8+3\sqrt6}{12}}[/tex]

Answer:

No, every relation is not a function.  

Step-by-step explanation:

Every function is a relation because there are two points (x,y) somehow related to each other.

But every relation is not a function

The given ordered pairs are the function

Since, we are getting different value of y for ecah x.

The condition for function is we should get different value of y for each x.

Answer:

–6 or 6

Step-by-step explanation:

7|x| = 42

We need to isolate the absolute value, so we will divide each side by 7

7|x|/7 = 42/7

 |x| = 6

Now we remove the absolute values and set what is inside the absolute value equal to plus and minus what is on the right hand side

x = + 6 and x = -6

Answer:

Solve for x over the integers:

7 abs(x) = 42

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides by 7:

abs(x) = 6

Hint: | Eliminate the absolute value.

Split the equation into two possible cases:

Answer:  x = 6 or x = -6

Step-by-step explanation: