A rectangular room must have a perimeter of 70 feet and an area of at least 200 square feet. Describe the possible widths of the room. Round your answers to the nearest tenth of a foot.

The approximate width of the room is at least
feet and at most
feet.

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.

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: 169.7

Step-by-step explanation:

Answer:

There are 1,014 kilograms of rice in 6 stacks of rice. 5 kilograms of rice remain.

Step-by-step explanation:

7 ÷ 1188 = 169

169 × 6 = 1,014

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.

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.

Answer:

Step-by-step explanation:

In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. For example, the complex conjugate of 3 + 4i is 3 − 4i. In polar form, the conjugate of is.

A complex conjugate is the element of a complex number that has the same real part but an opposite-sign imaginary part, and multiplying a complex number by its conjugate yields a real number.

A complex conjugate in mathematics is a paired element of a complex number that has the same real part but an opposite-sign imaginary part. When you have a complex number, let's call it A, which can be expressed in the form (a + ib) where 'a' is the real part and 'b' is the imaginary part, the complex conjugate of A, denoted as A*, would be (a - ib). One important property of complex conjugates is that when you multiply a complex number by its conjugate, you get a real number. This is because the product A* A = (a + ib) (a - ib) = a² + b².

For example, if a complex number is a = 3 + 4i, its complex conjugate would be a* = 3 - 4i. Multiplying a by its conjugate, we get a* a = (3 + 4i) (3 - 4i) = 9 + 16 = 25, which is a real number. This property is very useful, especially in fields such as quantum mechanics, where physical measurements must yield real numbers.

Answer:

x = 9 and x = −15

Step-by-step explanation:

|2x + 6| − 4 = 20

Add 4 to each side

|2x + 6| − 4+4 = 20+4

|2x + 6|  = 24

Now we have an absolute value equation that has the absolute value isolated.  We can separate them, have two equations, one positive and one negative.

2x+6 =24   and 2x+6=-24

Subtract 6 from each side

2x+6-6=24 -6    2x+6-6 = -24-6

2x = 18                   2x =-30

Divide by 2

2x/2 = 18/2          2x/2 = -30/2

x =9                        x=-15

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 \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:

Any graph which passes through the origin(0,0)

Step-by-step explanation:

To check a graph if it  represents direct variation or not, one needs to check whether it passes through the origin or not .

So any graph which passes through the origin is of direct variation.

And in equation form : [tex]y=kx\\ y=mx +b\\[/tex]

                                      ⇒b=0 , m=k

So it is of direct variation if it passes through the origin (0,0)

Answer: its c

Step-by-step explanation: i just got it right

Answer: D) 4/5

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

Explanation:

There are a few ways to see how this is the answer.

----------------

The first is to notice how 16/20 = 0.80 when using long division or a calculator. At the same time, 4/5 = 0.80 as well. So that means 16/20 = 4/5.

---------------

Another way to see how this works is to multiply top and bottom of 4/5 by 4. So we have 4*4 = 16 as the new numerator and 5*4 = 20 as the new denominator. Going in reverse, you can divide each piece of 16/20 by the GCF 4 to reduce this fraction into 4/5.

---------------

Finally, we can equate the two fractions and cross multiply

16/20 = 4/5

16*5 = 20*4

80 = 80

Both sides are the same value, so that confirms the original equation is true as well.

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:

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:

{-3, 1, 6 }

Step-by-step explanation:

the domain is the values of x ( input) from the relation in ascending order.

Values are not repeated.

domain {- 3, 1, 6 }

Answer:

{- 3, 1, 6 }

Step-by-step explanation:

The domain is the values of x inputs from the relation in ascending order.  Values cannot be repeated.

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

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

[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]

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:

[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:

12

Step-by-step explanation:

144/12 = 12

12 x 12 = 144

Answer:

12

Step-by-step explanation:

divide 12 by 144

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:

[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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Answer:

Rounding to the whole number or an estimation.

Step-by-step explanation: Pretty sure there isn't really a name for this

Rounding a number to its first digit is known as rounding to the nearest whole number. This method simplifies calculations while maintaining a number's approximate value.

The process of rounding a number to its first digit is often referred to as rounding to the nearest whole number. For example, if you have a number like 4.58, rounded to the nearest whole number it's 5, because the number next to 4 is 5 which is equal or higher than 5. But if the number was 4.42, rounded to the nearest whole number it's 4, because the number next to 4 is 2 which is less than 5. This rounding method applies when you want to make calculations simpler, while still keeping the number's value close to what it was.

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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

The answer is:

The probability that both John and Ted will be on time is 48%.

Since we are dealing with percentages, in order to make it easy to understand, let's remember that percentages are used to simplify the way we refer to something, talking in numeric terms. For example, meaning 100% it's equal to say that somethinh is complete, or absolute. Also, we can see the percentage as a ratio that is expressed as a fraction of the number 100 or [tex]\frac{1}{100}[/tex]

From the statement the know that John is late 20% of the time, making it easy to understand, it's equal to say that from 100 times, John is late 20 times.

So, calculating we have:

For John:

[tex]Probability=TotalTimes(percent)-LateTimes(Percent)\\\\Probability=100-20=80[/tex]

So, we have that the probability that John will be on time is 80%.

For Ted:

[tex]Probability=TotalTimes(percent)-LateTimes(Percent)\\\\Probability=100-40=60[/tex]

So, we have that the probability that Ted will be on time is 60%.

Now, to calculate the probability that both John and Ted will be on time, we need to calculate the combined probability. It can be calculated using the following equation:

[tex]CombinedProbability=Probability_{1}*Probability_{2}[/tex]

Let be:

[tex]Probability_{1}=80(percent)=\frac{80}{100}=0.8\\\\Probability_{2}=60(percent)=\frac{60}{100}=0.6[/tex]

So, substituting and calculating we have:

[tex]CombinedProbability=Probability_{1}*Probability_{2}[/tex]

[tex]CombinedProbability=0.8*0.6=0.48=48(percent)[/tex]

Hence, we have that the probability that both John and Ted will be on time is 48%.

Have a nice day!

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.

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[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