Nigel bought 10 pencils and 5 erasers for 8$. The price of 2
pencils was 1$. What was the price of 2 erasers?

The solution of the system of equations is (1, -3/4)

Here we have the system of equations:

y = (1/4)*x - 1

y = -(1/2)*x - 1/4

To solve it, we use the fact that the variable "y" is the same in both equations, then we can write:

(1/4)*x - 1 = -(1/2)*x - 1/4

Now we can solve that for x:

(1/4)*x - 1 = -(1/2)*x - 1/4

(1/4)*x + (1/2)*x = 1 - 1/4

(1/4)*x + (2/4)*x =  1 - 1/4

(3/4)*x = 3/4

x = 1

To get the y-value of the solution, we just evaluate x = 1 in any of the two given lines, using the first one:

y =  (1/4)*(1) - 1 = -3/4

So the solution is (1, -3/4)

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Answer:

2.5

Step-by-step explanation:

First divide 4 by 2

Second, you want x on a side by itself. So you would move 2 over to 9.5. But since 2 is positive, you would subtract 2 from 9.5

Third, you need to get x by itself. So you would divide by 3 on both sides because division cancels out multiplication which is what 3x is. And then you end up with 2.5

3x + 4 / 2 = 9.5

3x + 2 = 9.5

3x = 7.5

3x/3 = 905/3

x = 2.5

And if you want to check it, just substitute 2.5 for x

3(2.5) + 4 / 2 = 9.5

7.5 + 4 / 2 = 9.5

7.5 + 2 = 9.5

9.5 = 9.5

Answer:

[tex]\boxed {\frac{343}{360}}[/tex]

Step-by-step explanation:

Probability Rule :

[tex]\boxed {P(A\cup B \cup C) = P(A) + P(B) + P(C) - P(A \cap B \cap C)}[/tex]

Solving :

⇒ 3/5 = 3/8 + 5/15 + 4/9 - P (A ∩ B ∩ C)

⇒ P (A ∩ B ∩ C) = 3/8 + 1/3 + 4/9 - 1/5

⇒ P (A ∩ B ∩ C) = 135/360 + 120/360 + 160/360 - 72/360

⇒ P (A ∩ B ∩ C) = (135 + 120 + 160 - 72) / 360

⇒ P (A ∩ B ∩ C) = 343/360

Answer:

2400 liters in tank

Step-by-step explanation:

Company A would take 260 minutes more than Company B for filling 2400 liters of water in Anil's tank when the rate at which Company A fills is 8 liters in 1 minute and 40 seconds, while the rate at which Company B fills is 2.2 gallons per minute.

Rate is the ratio of quantity to time.

[tex]RATE = \frac{QUANTITY}{TIME}[/tex].

In the question, we are asked to find the time which Company A takes more than Company B for filling a water tank of 2400 liters when Company A fills water at a rate of 8 liters in 1 minute and 40 seconds, while the rate at which Company B fills is 2.2 gallons per minute.

For Company A:

The capacity of the tank = 2400 liters

Rate = 8 liters in 1 minute and 40 seconds

Now, 1 minute and 40 seconds = 1 + 40/60 minutes = 1.67 minute

Therefore, the actual rate = 8/1.67 = 4.8 liters per minute.

Therefore, the time taken by Company A = 2400/4.8 minutes = 500 minutes.

For Company B:

The capacity of the tank = 2400 liters.

We know 1 gallon = 4.54 liters,

or, 1/4.54 gallons = 1 liter.

Therefore, the capacity of the tank = 2400 * (1/4.54) gallons = 528.634 gallons.

Rate = 2.2 gallons per minute.

Therefore, the time taken by Company B = 528.634/2.2 minutes = 240.288 minutes.

Therefore, the time that Company A takes more than Company B = 500 - 240.288 minutes = 259.712 minutes ≈ 260 minutes.

The given question is an incomplete question. The complete question is:

"A water tank is empty.

Anil needs to fill the tank with 2400 liters of water.

Company A supplies water at a rate of 8 liters in 1 minute and 40 seconds.

Company B supplies water at a rate of 2.2 gallons per minute.

1 gallon = 4.54 liters.

Company A would take more time to fill the tank than Company B would take to fill the tank.

How much more time?

Give your answer in minutes correct to the nearest minute."

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Option B. x-8 = 40-2x is the correct equation for the opposite angle theorem.

According to the Opposite angles theorem,

Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.

[tex]= > x-8=40-2x[/tex] ( : Because opposite vertex angles are equal)

So option B is correct in the given question

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Answer:

D.) 3y-15 =85+

Step-by-step explanation:

simply put, opposite angles theorem is where the angles are on the opposite side so the parallelogram in the photo shows that 3y-15 is on the opposite angle as 85+y (I also got this one right lol)

Answer:

oma cursos online gratis de chino para aprender a hablar y escribir en este idioma. Aprende chino con cursos de las mejores universidades en edX.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

We know that [tex]a = 4[/tex] and [tex]b = -1[/tex], as they are given in the problem. All we have to do is plug them into the equation and solve it.

[tex]5 - 2(a + 3b)/2\\ = 5 - 2(4 -3)/2\\= 5 - 1\\= 4[/tex]

Answer:

-59

Step-by-step explanation:

x = -2

4(-2)³ - 6(-2)² + (-2) - 1

= -32 - 24 - 2 - 1

= - 59

Answer:

-34s^3t - 12st^3 - t^2 + 1

Step-by-step explanation:

hope this helps

The graph is attached with the answer, This is looking like a horizontal staircase

A step function is a piece wise function whose all pieces are horizontal line or a point.

It is given in the question to graph the interval

-2 ≤x≤2

for f(x) = |x+3|

-2    1

-1     2

0     3

1      4

2     5

The graph is attached with the answer.

This is looking like a horizontal staircase

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Based on the amount saved per week and the down payment of the property, the number of months it will take to save the amount is 46 months.

First, find out the amount saved per month:

= (30% x 2,051) x 2 payments a month

= $1,230.60

The downpayment is:

= 281,700 x 20%

= $56,340

The closing cost is:

= 1.15 x 56,230

= $843.45

The number of months till the amount is saved is:

= (56,340 + 843.45) / 1,230.60

= 46 months

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Answer:

$980

Step-by-step explanation:

Given the cost of gasoline = $2.80/mile

Total Distance = 175miles x 2 (Back and forth)

= 350 miles

Total Cost = Cost of gasoline x Total Distance =

= $2.80 x 350

= $980

The total cost of the trip from Seattle to Portland and back cost in dollars will be;

⇒ $250

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The driving distance from Seattle to Portland is 175 miles.

Your car gets 25 miles per gallon and the cost of gasoline is $2.80 per gallon.

Now,

Since, The driving distance from Seattle to Portland is 175 miles.

Hence, The total distance from Seattle to Portland and back = 175 + 175

                                                                                            = 350 miles

And, Your car gets 25 miles per gallon and the cost of gasoline is $2.80 per gallon.

Hence, The cost of gallon = 350/25 x $2.50

                                        = 100 x $2.50

                                        = $250

Thus, The total cost of the trip from Seattle to Portland and back cost in dollars will be;

⇒ $250

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The multiplicative inverse of the expression 4c + 5 is 1/(4c + 5)

Given 4c + 5 ≠ 0 and c is a real number, what is the multiplicative inverse of 4c + 5

The expression is given as:

4c + 5

The multiplicative inverse of an expression x is 1/x

This means that:

The multiplicative inverse of the expression 4c + 5 is 1/(4c + 5)

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If the standard deviation for a set of data is 9.5. The margin of error is: 19.5.

Using this formula

Margin of error=Standard deviation×Mean

Let plug in the formula

Margin of error=205 × 9.5%

Margin of error = 19.475

Margin of error = 19.5 (Approximately)

Therefore If the standard deviation for a set of data is 9.5. The margin of error is: 19.5.

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By applying definite integrals and integration rules, the area bounded between the curves f(x) = x² and g(x) = -(x+2)² + 4 is equal to 8 square units.

The points of intersection between the two curves are (x, y) = (0, 0) and (x, y) = (-2, 4). The curve is f(x) = x² and upper curve is g(x) = -(x+2)² + 4. The area between the two curves is defined by this definite integral:

[tex]A = \int\limits^{0}_{-2} {f(x) - g(x)} \, dx[/tex]

[tex]A = \int\limits^{0}_{-2} {f(x)} \, dx - \int\limits^{0}_{-2} {g(x)} \, dx[/tex]

[tex]A = \int\limits^0_{-2} {[-(x+2)^{2}+4]} \, dx -\int\limits^0_{-2} {x^{2}} \, dx[/tex]

[tex]A = -\frac{(x+2)^{3}}{3}|_{-2}^{0} + 4\cdot x|_{-2}^{0}-\frac{x^{3}}{3}|_{-2}^{0}[/tex]

[tex]A = - \frac{2^{3}}{3} + 0 + 4\cdot [0 - (-2)] - 0 + \frac{(-2)^{3}}{3}[/tex]

[tex]A = -\frac{8}{3} + 8 -\frac{8}{3}[/tex]

A = 8

By applying definite integrals and integration rules, the area bounded between the curves f(x) = x² and g(x) = -(x+2)² + 4 is equal to 8 square units.

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The odds of jimmy winning a free lunch is 0.066.

Probability is the likeliness of an event to happen.

It is given that

A restaurant will select 1 card from a bowl to win a free lunch,

jimmy puts 10 cards in the bowl.

The bowl has a total of 150 cards in it

The odds of jimmy winning a free lunch is given by

= No. of chances / Total Outcomes

= 10/150

= 1/15

= 0.066

Therefore the odds of jimmy winning a free lunch is 0.066.

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Answer:

Step-by-step explanation:

1/1

Answer:

its wrong answer and question

Answer:

[tex]h(x)=\frac{1}{2}x -\frac{1}{2} .[/tex]

Step-by-step explanation:

if the initial function is f(x)=2x+1, then

x=2*h(x)+1;

2h(x)=x-1;

[tex]h(x)=\frac{x}{2} -\frac{1}{2}.[/tex]

PS. change design according the local requirements.

Answer:

[tex]y^{-1} =\frac{1}{2} x-\frac{1}{2}[/tex]

Step-by-step explanation:

To find the inverse, you want to swap the inputs with the outputs, which is why you have the swapped domain and range between a function and its range.

So, given f(x)=2x+1, its inverse would give,

x=2y+1.

Solve for y,

2y=x-1 -> y=(x-1)/2 -> y=[tex]\frac{1}{2} x-\frac{1}{2}[/tex]

Therefore, [tex]y^{-1} =\frac{1}{2} x-\frac{1}{2}[/tex]

Answer:

Given :-

Two legs of a rt. triangle : 8 and 10 respectively.

To find :-

Length of the hypotenuse

Solution :-

Using Pythagorean Theorem;

(hypotenuse)² = (8)² + (10)²

= 64 + 100

hypotenuse = √164

= 12.8 units

Answer:

12.80

Step-by-step explanation:

We have to use the Pythagoras theorem to find the value of the hypotenuse.

Let the value of the hypotenuse be c.

Let us use the below formula to find the length of the hypotenuse.

First, let us replace a and b with 8 and 10 ( the lengths of the legs of the right triangle) with a and b.

a² + b² = c²

8² + 10² = c²

64 + 100 = c²

And now let us solve the above and find the value of c.

164 = c²

√164 = c

12.80 = c

Therefore, the length of the hypotenuse is:

12.80 units

If the angle 1 and angle 2 are vertical angles, hence they must be equal to each other, therefore m∠1 = m∠2 = 72º

Angles angle are angles that are equal to equal to each other in a line geometry.

Given the following parameters

m∠1 = 72º,

If the angle 1 and angle 2 are vertical angles, hence they must be equal to each other, therefore m∠1 = m∠2 = 72º

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The equation for the red graph is f(x)=-x^2.

The question is an incomplete graph of a function is missing

For a complete question refer to the graph attached below

we have [tex]g(x)=4-x^2[/tex]

The vertex of the function g(x) is the point (0,4)

The vertex of the function f(x) is the point (0,0)

This is typically a local maximum or minimum of curvature, and some authors define a vertex to be more specifically a local extremum of curvature.

So, the rule of the translation of g(x) to f(x) is

(x,y)------> (x,y-4)

The translation is 4 units down

The equation of the function f(x) is

[tex]f(x)=g(x)-4[/tex]

[tex]f(x)=(4-x^2)-4[/tex]

[tex]f(x)=-x^2[/tex]

Therefore, The answer is f(x)=-x^2

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Answer is B.

Step-by-step explanation:

Since we know that in 30-60-90 triangle, the side corresponding to angle 90 degrees is two times the length of side corresponding to 30 degree angle. The length of side corresponding to 60 degree angle is  times the length corresponding to 30 degree angle.

We can see from our given choices that the side corresponding to 30 degree angle is 5 units.  

Therefore, the side lengths of a 30-60-90 triangle will be  and option B is the correct choice.  

PLS MARK ME AS BRAINLIEST.

Answer:

{x∈R | [tex]\frac{2x}{3\pi } +\frac{1}{2}[/tex], x∉Z}

Step-by-step explanation:

Given the function y=3tan(2/3x)

We know that tangent is a function that's continuous within it's domain but not continuous on all real numbers

Also, the roots of y=3tan(2/3x) is [tex]3\pi n/2[/tex] where n is an integer

Note that the domain of the function cannot be within [tex]3\pi n/2[/tex]

Therefore, {x∈R | [tex]\frac{2x}{3\pi } +\frac{1}{2}[/tex], x∉Z}

Answer:

D.

because 2 times 120 reduced.

Answer:

a ) cylinder

b) triangular pyramid

Answer:

Step-by-step explanation:

Comment

If 4 numbers have an average of 9, then total of the 4 numbers is 4 * 9 = 36.

If one of the 4 numbers is  a 7, then

7 + x = 36 where x is the sum of the other 3 numbers.

7 + x = 36           Subtract 7 from both sides

7- 7 +x = 36 - 7

x = 29

Answer 29

The mean absolute deviation of the number of books is 1.84

The dot plot of the number of books is in the attached figure.

From the figure, we have:

x      f

1       1

2      2

3      2

4      3

5      1

6     2

7     3

8     1

Start by calculating the mean using:

[tex]\bar x= \frac{\sum fx}{\sum f}[/tex]

So, we have:

[tex]\bar x= \frac{1 * 1 + 2 * 2 + 2 * 3 + 3 * 4 + 1 * 5 + 2 * 6 + 3 *7 + 1 * 8}{1 +2+2+3+1+2+3+1}[/tex]

Evaluate the sum and products

[tex]\bar x= \frac{69}{15}[/tex]

Divide

[tex]\bar x= 4.6[/tex]

The mean absolute deviation is then calculated as:

[tex]|\bar x| = \frac{\sum f|x - \bar x|}{\sum f}[/tex]

So, we have:

[tex]|\bar x|= \frac{1 * |1 -4.6|+ 2 * |2 -4.6| + 2 * |3 -4.6|+ 3 * |4 -4.6|+ 1 *| 5 -4.6|+ 2 * |6 -4.6|+ 3 *|7 -4.6|+ 1 * |8-4.6|}{1 +2+2+3+1+2+3+1}[/tex]

Evaluate the absolute difference

[tex]|\bar x|= \frac{1 * 3.6+ 2 * 2.6 + 2 * 1.6+ 3 * 0.6+ 1 *0.4+ 2 * 1.4+ 3 *2.4+ 1 * 3.4}{15}[/tex]

Evaluate the sum of products

[tex]|\bar x|= \frac{27.6}{15}[/tex]

Divide

[tex]|\bar x|= 1.84[/tex]

Hence, the mean absolute deviation of the number of books is 1.84

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A percentage is a way to describe a part of a whole. The relative change from last year to this year is 3.7%.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

28.6% of city employees ride the bus to work, therefore, the final value is 28.6. While Last year, 29.7% of city employees rode the bus to work, therefore, the initial value is 29.7.

Since relative change means change with respect to some value. Thus, the relative value with respect to last year is,

Relative value = (29.7-28.6)/29.7 = 0.037 = 3.7%

Hence, the relative change from last year to this year is 3.7%.

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Answer:

[tex]1.3\cdot 10^3\text{ J}[/tex]

Step-by-step explanation:

Power is defined by work over time. In physics, work can be defined as the energy transferred over from an applied force over some distance. As a formula:

[tex]W=Fd[/tex], where F = force applied and d = distance that force is applied over.

*It is worth noting that F must be parallel to the distance travelled. If it is perpendicular, no work is done, and if it is at an angle, find the parallel component and use that for F.

In this case, the force applied must counter the force of gravity on Martha, which is given by [tex]F_g=mg[/tex], where m = Martha's mass and g = gravitational constant 9.8 m/s/s. Therefore, [tex]F_g=75\cdot 9.8=735\text{ N}[/tex]. Since she raises her body 4.0 meters, the work done must be [tex]W=Fd=735\cdot 4=2940\text{ J}[/tex].

Since power is equal to work over time and t = 2.3 seconds, we have:

[tex]\displaystyle P=\frac{W}{t}=\frac{2940}{2.3}=\boxed{1278\text{ J}}\approx \boxed{1.3\cdot 10^3\text{ J}}[/tex] (to two significant figures)

Considering the given stem-and-left plot, the median = second quaritle of the data set is of 84.5.

The median of a data-set is the 50th percentile, that is, the value that separates the bottom 50% of scores from the upper 50% of scores.

This data-set has even cardinality of 26, hence the median is the mean of the 13th and 14th scores, which, considering the key for the stem-and-leaf plot, are 84 and 85, hence:

Me = (84 + 85)/2 = 84.5.

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