Which system of equations has only one solution?

Step-by-step explanation:

[tex]1a.\\ 8-y=2\qquad\text{subtract 8 from both sides}\\-y=-6\qquad\text{change the signs}\\\boxed{y=6}\\\\1b.\\11-9=2-b\\2=2-b\qquad\text{subtract 2 from both sides}\\0=-b\to \boxed{b=0}\\\\2a.\\5=\dfrac{c}{3}\qquad\text{multiply both sides by 3}\\15=c\to \boxed{c=15}\\\\2b.\\2=5-t\qquad\text{subtract 5 from both sides}\\-3=-t\qquad\text{change the signs}\\3=t\to\boxed{t=3}\\\\3a.\\5n=10\qquad\text{divide both sides by 5}\\\boxed{n=2}\\\\3b.\\a+6=12\qquad\text{subtract 6 from both sides}\\\boxed{a=6}[/tex]

[tex]4a.\\v-10=7\qquad\text{add 10 to both sides}\\\boxed{v=17}\\\\4b.\\7=7n+7n\\7=14n\qquad\text{divide both sides by 14}\\\dfrac{7}{14}=n\\\boxed{n=\dfrac{1}{2}}\\\\5a.\\m+11=12\cdot4\\m+11=48\qquad\text{subtract 11 from both sides}\\\boxed{m=37}\\\\5b.\\6y=7+5\\6y=12\qquad\text{divide both sides by 6}\\\boxed{y=2}\\\\6a.\\b-8=3\qquad\text{add 8 to both sides}\\\boxed{b=11}\\\\6b.\\1+c=8\qquad\text{subtract 1 from both sides}\\\boxed{c=7}[/tex]

Answer:

B.612 units2

Step-by-step explanation:

To solve surface area you multiply the area of each of the faces then you add the areas together. So the equation you need to solve is 13×6+13×6+12×13+12×13+12×6+12×6

After you solve that equation the answer you should get is 612.

Answer:

612

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

2/10=3/x-9

2(x-9)=30

2x-18=30

2x=30+18

2x=48

x=24

Answer:

The value of x in the given phrase is 24.

Step-by-step explanation:

Given phrase,

2 over 10 equals 3 over quantity x minus 9

[tex]\frac{2}{10}=\frac{3}{x-9}[/tex]

By cross multiplication,

[tex]2x-18=30[/tex]

Adding 18 on both sides,

[tex]2x=48[/tex]

Divide both sides by 2,

[tex]x=24[/tex]

Hence, the value of x is 24.

Final answer:

In converting 7.5 pounds to ounces, the unit placed in the denominator of the ratio is pounds. To do the conversion, multiply the number of pounds by 16, since there are 16 ounces in one pound. Therefore, 7.5 pounds is equal to 120 ounces.

Explanation:

When converting 7.5 pounds to ounces, we start by identifying the conversion factor between these two units of weight. The unit you would place in the denominator of your ratio is pounds, since the relationship is that 1 pound is equivalent to 16 ounces. So, the conversion from pounds to ounces requires multiplying the number of pounds by 16.

Here's how you would set up your conversion:

First, write down the amount of pounds you want to convert (7.5 pounds).

Multiply this amount by 16, the number of ounces in one pound (7.5 x 16).

The product will give you the amount in ounces (7.5 x 16 = 120 ounces).

The unit in the denominator for the ratio used in this conversion is pounds, as you are starting with pounds and converting to ounces.

Answer:

See below.

Step-by-step explanation:

a. That would be a cylinder.

b.The height of the cylinder will be n * thickness of one circle where  n is the number of circles.  The volume of the cylinder is π r^2 h where h is the height of the stack.

c.  That would be a cone

d. The height of the cone will be n * thickness of one circle where n is the number of similar circles.

Volume of the cone = 1/3 * π r^2  h    where h is the height of the stack of circles.

Answer:

a) 16.7

b) 13.5

Step-by-step explanation:

AC and DE are parallel, so ∠CAB and ∠EDB are corresponding angles, and ∠ACB and ∠DEB are corresponding angles.

Therefore, ΔABC and ΔDBE are similar triangles.  We can use this to write a proportion.

a)

(25 + x) / (18 + 12) = x / 12

12 (25 + x) = x (18 + 12)

300 + 12x = 30x

300 = 18x

x = 16.7

b)

x / (7 + 2) = 3 / 2

x = 13.5

Answer:

Amplitude = 1 foot; period = 12 hours; midline: y = 5

Step-by-step explanation:

The Chesapeake Bay tides vary between 4 feet and 6 feet.

This means the range is

[tex]4 \leqslant f(t) \leqslant 6[/tex]

The period is the length of the interval on which the function completes one full cycle.The tide is at its lowest point when time (t) is 0 and completes a full cycle in 12 hours.

The interval is [0,12] and its length is 12, hence the period is 12.

The midline

[tex]y = \frac{min + max}{2} [/tex]

[tex]y = \frac{4 + 6}{2} = 5[/tex]

The amplitude is the distance from the midline to the peak.

The amplitude is |5-4|=|5-6|=1

The first choice is correct.

The amplitude of the function modeling the Chesapeake Bay tides is 1 foot, the period is 12 hours, and the midline is at y = 5 feet.

The amplitude of a function that models a periodic phenomenon, like the tides in this case, is half of the total variation in height. Since the tides vary between 4 feet and 6 feet, the total variation is 2 feet (6 feet - 4 feet), and thus, the amplitude is 1 foot (2 feet / 2).

The period of the function is the time it takes for the tidal cycle to repeat itself. Given that the tide completes a full cycle in 12 hours, the period of the function is 12 hours.

The midline represents the average value around which the tide oscillates. It can be found by averaging the maximum and minimum tide levels. Therefore, the midline is (4 feet + 6 feet) / 2 = 5 feet.

Considering these calculations, the correct amplitude is 1 foot, the period is 12 hours, and the midline is y = 5 feet for the function that would model the periodic phenomenon of the Chesapeake Bay tides.

Let the balance = Y and the number of weeks = x

She takes out 15 per week, so multiply 15 by x ( the number of weeks) to get 15x.

You would then want to subtract that from the amount she started with in her account.

The equation becomes: Y = 150 - 15x

recall your d = rt, distance = rate * time.

w = speed of the wind.

14 = speed of the bicycle without wind.

now, against the wind, the bicycle is not really going 14 mph fast, is really going "14 - w", since the wind is eroding speed from it, likewise, when the bicycle is going with the wind is not going 14 mph fast either, is really going "14 + w" due to the wind adding speed, let's say it took "t" hours against and also "t" hours with it.

[tex]\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{against the wind}&10&14-w&t\\ \textit{with the wind}&20&14+w&t \end{array}~\hfill \begin{cases} 10=(14-w)t\\ \frac{10}{14-w}=\boxed{t}\\ \cline{1-1} 20=(14+w)t \end{cases}[/tex]

[tex]\bf 20=(14+w)t\implies \cfrac{20}{14+w}=t\implies \stackrel{\textit{substituting in the 2nd equation}}{\cfrac{20}{14+w}=\boxed{\cfrac{10}{14-w}}} \\\\\\ 280-20w=140+10w\implies 280=140+30w\implies 140=30w \\\\\\ \cfrac{140}{30}=w\implies \cfrac{14}{3}=w\implies 4\frac{2}{3}=w[/tex]

Answer: C.

Step-by-step explanation: A cube’s volume is Length x Width x Height. Since a cube has all equal sides, a perfect cube would have 3 of the same numbers being multiplied, 8 x 8 x 8.

Option c is correct, 512 is a perfect cube because 512=8×8×8 is a correct statement about perfect cube.

A number system is defined as a system of writing to express numbers.

A perfect cube of a number is a number that is equal to the number, multiplied by itself, three times.

25 is not a perfect cube but it is a perfect square

30 is not a perfect cube

512 is a perfect cube because 8³=512

512=8×8×8

1875 is not a perfect cube.

Hence, 512 is a perfect cube because 512=8×8×8 id a correct statement about perfect cube.

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Answer:

The houses surveyed had between 1 and 10 rooms ..

Step-by-step explanation:

We can see from the histogram that the minimum number of rooms any house had was 1 and the maximum number of rooms were 10.

Range is the difference between highest and lowest value of a data set.

Hence, the range from the given histogram can be determined as:

The houses surveyed had between 1 and 10 rooms ..

Answer:  The houses surveyed had between 1 and 10 rooms.

Step-by-step explanation:

From the histogram, the minimum number of rooms = 1

The maximum number of rooms = 10

Hence, the range of rooms in Henry's histogram is between 1 and 10 rooms.

Answer:

The equation is 10x - 960y = 96

A = 10 , B = -960 , C = 96

Step-by-step explanation:

* Lets explain the standard form of the linear equation

- The standard form of the linear equation is :

 AX + BY = C , where A , B , C are constant

- A is a positive integer, and B, and C are integers

- The slope of the line is -A/B

- The y-intercept is C/A

- Lets solve the problem

∵ The equation of the line is 8y = 1/12 x - 0.8

- At first multiply the equation by 12 to make the coefficient of x integer

∴ (8 × 12) y = (1/12 × 12) x - (0.8 × 12)

∴ 96y = x - 9.6

- Multiply the two sides of the equation by 10 to make 9.6 integer

∴ (96 × 10) y = (1 × 10) x - (9.6 × 10)

∴ 960y = 10x - 96

- Add the two sides by 96

∴ 960y + 96 = 10x

- Subtract 960y from both sides

∴ 96 = 10x - 960y

∴ The standard form of the equation is 10x - 960y = 96, where

  A = 10 , B = -960 , C = 96

Steps for the box plot are given below.

Since they are already in the order you know the 22 and the 61 are the upper and lower extremes.

To find the median you find the number that is in the middle which is 42.

We have to find the lower quartile find the middle number starting from the first number and the number to the left of the median (22 and 36 in this case). The lower quartile is 25.

a quartile is a type of quantile that divides the number of data points into four parts, or quarters, of more or less equal size. The data must be ordered from smallest to largest to compute quartiles; as such, quartiles are a form of order statistic

To find the upper quartile, fine the middle number between the number to the right of the median and the last number (44 and 61 in this case.) If the upper quartile is 57 you then just plot it and graph it.

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Answer:

4.847

Step-by-step explanation:

divide 8.24 by 1.7

8.24 /1.7 = 4.847

For this case we have the following operation:

[tex]\frac{8.24} {1.7}[/tex]

We must find the final result after the division.

To do this, we can use a calculator or a computer program.

We then have to do the division:

[tex]\frac{8.24} {1.7} = 4.94[/tex]

Answer:

The total ratio is given by: 4.94.

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

Explanation:

The letter T is the 20th letter in the English alphabet. This means that there are 20 letters to pick from to go with the 10 single digit numbers to pick from. We have 20*10 = 200 different combinations (eg: one combination is K4).

Out of these 200 combinations, there is exactly one winning match.

The probability of winning is therefore P(W) = 1/200 = 0.005 and the probability of losing is P(L) = 1-P(W) = 1-0.005 = 0.995 where W and L represent winning and losing respectively.

The net value of winning is V(W) = 250 - 1 = 249 because the player wins $250 but they lose $1 (which is the cost of the ticket). The net value of losing is V(L) = -1, indicating the player has lost that $1 and hasn't gained any money at all.

-----------

To summarize so far:

P(W) = 0.005

P(L) = 0.995

V(W) = 249

V(L) = -1

Multiply the probability P values with the corresponding net values V, then add up the products to get the expected value:

E(X) = P(W)*V(W) + P(L)*V(L)

E(X) = 0.005*249 + 0.995*(-1)

E(X) = 0.25

The expected value is 0.25 dollars or 25 cents

This positive expected value means that the game is favored toward the player, because over the long run, the player gains an average of 25 cents each time they play. On the other side of the spectrum, the lottery company loses on average 25 cents each time. The nonzero expected value means that the game is not fair.

Answer:

Assign numbers to each client and then use a random number generator to choose one hundred clients to survey.

Step-by-step explanation:

I think the best method would be:

Assign numbers to each client and then use a random number generator to choose one hundred clients to survey.

It is the best way to choose a random sample as it is a fair representation of her all customers. In this sample all of her costumers will be assigned numbers and will be chosen randomly. ...

Answer:

(x - 2)² + (y + 5)² = 16

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (2, - 5) and r = 4, hence

(x - 2)² + (y - (- 5))² = 4², that is

(x - 2)² + (y + 5)² = 16 ← is the equation of the circle

First you must solve system of equations.

Multiply the first equation by 4 and second one by 3.

You result with,

[tex]

16x-12y=4 \\

15x+12y=27

[/tex]

Add the equations so y terms cancel out.

[tex]31x=31\Longrightarrow x=1[/tex]

Insert x that was found in either one of the equations. I'll pick first one.

[tex]4\cdot1-3y=1[/tex]

Solve for y.

[tex]

-3y=-3 \\

y=1

[/tex]

The solutions to the system of equations are,

[tex]\boxed{x=1},\boxed{y=1}[/tex]

Therefore the number missing is 1.

Hope this helps.

r3t40

Answer:

(1,1)

Step-by-step explanation:

Answer:

32.27°

Step-by-step explanation:

Convert 32° 15' 66'' to the nearest hundredth of a degree

we know that

1 degree=60 minutes

1 minute=60 seconds

1 degree=3,600 seconds

step 1

Convert 15' to degrees

15'=15/60=0.25°

step 2

Convert 66'' to degrees

66''=66/3,600=0.02°

substitute

32° 15' 66''=32° +0.25°+0.02°=32.27°

Answer:

[-1,1]

Step-by-step explanation:

The question in English is

which of the following intervals contains the number 0?

case A) (0,1]

All real numbers greater than zero (the number 0 is not included) and less than or equal to 1 (the number 1 is included)

case B) [-1,1]

All real numbers greater than or equal to -1 (the number -1 is included) and less than or equal to 1 (the number 1 is included)

In this interval is included the number 0

case C) [-1,0)

All real numbers greater than or equal to -1 (the number -1 is included) and less than 0 (the number 0 is not included)

Answer:

The answer is the attached figure

Step-by-step explanation:

* Lets explain mutually exclusive and non-mutually exclusive

- The mutually exclusive means events cannot happen  at the

 same time

# P(A or B) = P(A) + P(B)

- The non-mutually exclusive means they  have at least one

 outcome in common

# P(A or B) = P(A) + P(B) - P(A and B)

* Lets solve the problem

∵ Events A and B are mutually exclusive

∵ Circle A represents the event A

∵ Circle B represents the event B

∴ There is no intersection between the two circles A and B

∵ Events B and C are non-mutually exclusive

∵ Circle C represents the event C

∴ There is an intersection between the two circles B and C

* The answer is the attached figure

Answer: D. image 4.

Just did assignment.

Answer:

C. 18

Step-by-step explanation:

Both triangle are same (compared with angles), but are different size.

This is based on simple ratio.

AB/AC = DE/DF

27/15 = x/10 //Multiply both sides by 10

270/15 = x

x = 18

Therefore DE is 18.

Hence, the length of DE is 18.

Length is defined as the measurement or extent of something from end to end. In other words, it is the larger of the two or the highest of three dimensions of geometrical shapes or objects.

It can be observed that the given 2 triangles are similar.

we know, for similar triangles, the ratio of corresponding sides is equal.

Hence,

          [tex]\frac{15}{10} = \frac{27}{x}[/tex]

          [tex]x = 18[/tex]

Therefore, the value of x is 18.

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ANSWER

(10,100) is the correct answer

Answer:

The correct option is 3. The possible domain and range of the function is (10, 100).

Step-by-step explanation:

It is given that a bakery's production is modeled by function f(x), where

f(x) = The number of donuts made in a day

x = The number of bags of flour needed.

The number of donuts made in a day and the number of bags of flour needed can not be a fraction value of a negative number. So, the values of x and f(x) can not defined by negative or decimal numbers.

In ordered pair (-1,15), the value of x is negative, so option 1 is incorrect.

In ordered pair (5,92.75), the value of y is in decimal, so option 2 is incorrect.

In ordered pair (10,100), both coordinates are positive integers, so option 3 is correct.

In ordered pair (-5,110.5), the value of x is negative and the value of y is in decimal, so option 4 is incorrect.

The possible domain and range of the function is (10, 100). Therefore the correct option is 3.

Answer:

I will assume

h = 82.5 sin (3 pi (t+0.5) )+97.5 , (you had no equation and no h)

so when t = 6

h = 82.5 sin (3π(6.5)) + 97.5

= 82.5(-1) + 97.5 = 15

check: period = 2π/(3π) = 2/3 minutes (that is a fast ride considering how huge it is)

So 6 ÷(2/3) = 9 , at the 6 minute mark, the last passenger has just completed 9 rotations.

the min height of the basket is -82.5 + 97.5 = 15

( the min value of 82.5 sin(anything) = 82.5(-1) )

so the last passenger must be at the platform level.

how did you get 79 ???

Step-by-step explanation:

You could multiply 19.45 by 0.2 to solve for it, but if you're not using a calculator, then 19.45/5 would be much more convenient and easier.

0.2 is 1/5 in fraction form, which is why we can do that.

19.45/5 = 3.89

Dino should leave $3.89 as a tip.

Answer:

$3.89

Step-by-step explanation:

X = 20

19.45 = 100

19.45*20=389

389/100=$3.89

Answer:

B

Step-by-step explanation:

you add the like terms together and find the value of x multiple by 4

Answer:

Step-by-step explanation:

The formula of a volume of a cube:

[tex]V=a^3[/tex]

a - edge

We have a = 8cm.

Substitute:

[tex]V=8^3=512\ cm^3[/tex]

Answer:

512 square centimeters

Step-by-step explanation:

have a great day :)

[tex]\huge{\boxed{66}}[/tex]

Start by substituting in the values. [tex]3(2)+6(8+2)[/tex]

Add. [tex]3(2)+6(10)[/tex]

Multiply. [tex]6+60[/tex]

Add. [tex]\boxed{66}[/tex]

Answer:

Step-by-step explanation:

3a+6(b+2)

=3(2)+6(8+2)

=6+6(10)

=6+60

=66

Answer:

f(x)=(7(x-2)(x+5))/((x-1)(x+1))

Step-by-step explanation:

The vertical asymptotes should be in the denominator. The x-interceps should be in the numerator. Because the horizontal asymptote is y=7, you have to put 7 in the numerator because the horizontal asymptote is the coefficient of the numerator ÷ the coefficient of the denominator, when we have the same degree of the numerator and the denominator.