In a soccer game, 1/5 of the players on Team A and 1/11 of the players on Team B score a goal. A total of 5 players on Team A and 2 players on Team B score a goal. How many players are on each team?

The required solution of the given equation is x = -7.

"Multi-step equation" means an equation that requires more than one step to be solved.

"Like terms" refers to terms that have the same variables raised to the same powers. In this equation, there are no like terms, so no simplification of the equation is needed in that regard.

"Negative coefficients" refers to the fact that some of the coefficients in front of the variables in the equation are negative. For example, in this equation, the coefficient of x is -3, and the coefficient of -9 is also negative.

To solve this equation, you can simplify both sides by combining like terms:

-9 + x -3x = 5

-9 - 3x + x = 5

-9 - 2x = 5

Next, isolate the variable on one side of the equation by adding 9 to both sides:

-9 - 2x + 9 = 5 + 9

-2x = 14

Finally, divide both sides by -2 to find x:

(-2x) / -2 = 14 / -2

x = -7

So the solution is x = -7.

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Answer:

If we remove 9 from the data set, the mean reduces by 0.5 from 6 to 5.5

Step-by-step explanation:

Answer
If we remove 9 from the data set, the mean reduces by 0.5 from 6 to 5.5

$0.04  is the unit price (per ounce) for the sports drink.

A division is a process of splitting a specific amount into equal parts.

Given that  local grocery store is having a sale on sports drinks.

For a particular brand of sports drink, a 6 -pack of 20 -ounce bottles costs $4.96

We need to find the the unit price (per ounce) for the sports drink.

6×20

120 ounce bottles in total which cost $4.96.

Now 4.96/120 is the cost of each bottle

$0.04 is the unit price of the sport drink.

Hence, $0.04  is the unit price (per ounce) for the sports drink.

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The fourth year increase in salary is 4.5 percent.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, Inka's starting annual salary was $55,600.

After her first year she received a 2% pay rise.

Now, 2% of 55,600

= 2/100 ×55,600

= 1112

So, salary of 2nd year is 55,600+1112=$56712

The next year she received a 3% pay rise.

Now, 3% of 56712

= 3/100 ×56712

= 1701.36

So, salary of 3rd year is 56712+1701.36=$58413.36

Last year she received an x% pay rise.

Now, x% of 58413.36+58413.36=61,042

x/100 ×58413.36=61,042-58413.36

584.1336x=2628.64

x=2628.64/584.1336

x=4.5%

Therefore, the fourth year increase in salary is 4.5%.

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Answer:

Step-by-step explanation:

4(4y+5)=3(y+7)

16y+20=3y+21

13y=1

y=1/13

Answer:

y = 1/13

Step-by-step explanation:

 (4y + 5) : 3 = (y+7) :4

Product of extremes = (4y + 5) * 4

                                  = 4y *4 + 5*4

                                  = 16y + 20

Product of mean = 3*(y +7)

                            = 3*y + 3*7

                            = 3y + 21

Product of extremes = product of mean

          16y + 20 = 3y + 21

Subtract 20 from both sides,

                  16y = 3y + 21 - 20

                  16y = 3y + 1

Subtract 3y from both sides,

               16y - 3y = 1

                     13y = 1

                        [tex]\boxed{\bf y =\dfrac{1}{13}}[/tex]          

Answer:

Step-by-step explanation:

Hope this helps : )

A geometric method is known as "stereographic projection" involves projecting a flat map of a sphere onto a three-dimensional surface with a point at its center.

This is one way to construct a sphere. The construction of geodesic domes, which gained popularity in the 1960s, is one example of an art and construction project that frequently makes use of this approach.

Using a solid material and carving it into the shape you want is another way to make a sphere. This can be accomplished using stone, clay, wood, and other materials. To produce a sphere with perfect symmetry, this method necessitates considerable skill and precision.

A third approach is to construct a sphere from numerous small, flat pieces. Paper or fabric can be used to accomplish this, with each piece being cut into a curved shape and glued together to form the sphere. Origami balls, for example, are a common decorative item made using this method.

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Answer:

Step-by-step explanation:

The two trains are moving apart from each other, so we can add their speeds to find their relative speed:

Relative speed = 75 + 95 = 170 miles per hour

We want to know how long it will take for the trains to be 204 miles apart. We can use the formula:

distance = rate × time

to solve for the time. Let t be the time in hours:

204 = 170t

Solving for t, we get:

t = 204/170

t ≈ 1.2 hours

Therefore, it will take approximately 1.2 hours for the two trains to be 204 miles apart.

Answer:

60%

Step-by-step explanation:

Answer:

Step-by-step explanation:

A.) To find out how many pages Celina reads per minute, you would have to divide 16 by 8 = 2.

B.) Now that we know she reads two pages every one minute, we are able to calculate how many minutes it takes her to read one. You need to divide 2 by 2 = 1.

A.) = 2

B.) = 1

The correct equation to show the cost of meat per pound at Sam's Grocery Store is x = 2y, where x is the cost of meat per pound at Sam's Grocery Store and y is the cost of meat per pound at Lane Grocery Store.

This equation represents the fact that the cost of meat per pound at Sam's Grocery Store is twice the cost of meat per pound at Lane Grocery Store.

For example, if the cost of meat per pound at Lane Grocery Store is $5, then the cost of meat per pound at Sam's Grocery Store would be 2 * $5 = $10.

So, the equation x = 2y accurately shows the relationship between the cost of meat per pound at Sam's Grocery Store and the cost of meat per pound at Lane Grocery Store.

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The required correct values for A, B, and C is 9, 52, and 130 respectively.

Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Since a standard piano has a ratio of white to black keys is given as,
= 91/63
= 13/9

Now,
13/A =91/63
A = 9

Similarly,
B = 52

C = 130

Thus, the required correction values for A, B, and C is 9, 52, and 130 respectively.

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Answer:

Step-by-step explanation:

If LP represented the height of the triangle, then the segment would be the vertical leg of a right triangle. This is due to the fact that the altitude of an isosceles triangle is perpendicular to the base MN.

Thus, by the Pythagorean Theorem, (1.3)^2 + (3.5)^2 = (3.7)^2 if and only if segment LP is the height of the triangle. Calculate for yourself whether this is true.

Answer:

Below

Step-by-step explanation:

From mile 3 to mile 18 is 15 miles

   He needed   2 hrs - .75 hr  = 1.25 hr to run 15 miles

15 miles / 1.25 hr =  12 miles per hour    ( VERY fast !)

Answer:

Step-by-step explanation:

x = # of adults

y = # of students

6x + 4y = 72

x + y = 12

Answer: No, you can prove it

Step-by-step explanation:

It is a right angle at both triangles and the sides to points toward the vertex of the triangle have to be the same. So, the bottom side must be the same and the angles are the same. It is congruent.

The part of the whole brownies that Jiah eat will be 1/8.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Fractions help to distribute and judge the numbers easily and make the calculation faster. Instead of using decimal values, the representation of fractions looks simpler.

Jia's mom = 1/4

Jia's sister = 1/4

Jia's brother = 1/4

Jia's share = 1 - (1/4 + 1/4 + 1/4) = 1 - 3/4 = 1/4( of her share)

Jia's share in relation to the whole = 8/8 - 7/8 = 1/8

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Answer:

y ≤ 3/4x-2

The 3/4 is the slope, and -2 is y intercept

Answer:

The answer is the equation for the function describing the movement of the buoy:

f(x) = 5 * sin(2 * pi * x / 16) + 8

Step-by-step explanation:

To graph the function, we need to find an equation that describes the buoy's movement. Since the buoy bobs up and down 5 meters from the ocean's depth, we can use the sine function. The amplitude of the function is 5, since the buoy moves 5 meters from the normal ocean depth. The period of the function is 16 seconds, since it takes 16 seconds for the buoy to go from its highest point to its lowest point.

Using this information, we can write the equation for the function as:

f(x) = 5 * sin(2 * pi * x / 16) + 8

where x is the time in seconds.

The first point on the graph would be (0, 8), since at x = 0 the buoy is at normal ocean depth. The second point would be either a maximum or minimum value on the graph closest to x = 0, which can be found by finding the derivative of the function and setting it equal to zero.

The graph of the function would look like a wave that oscillates up and down, with a maximum value of 5 meters above the normal ocean depth and a minimum value of 3 meters below the normal ocean depth.

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The graph of f(x) = -0.1 |x| opens. The point (-100, -10) or (100, -10) is on the graph.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

We know that the graph of the function f(x) = a|x| opens upwards if the value of a > 0 and it opens downwards for a< 0.

For the given function the value of a = -0.1 < 0.

So, the graph of f(x) opens downwards.

The coordinates of the graph are determined by substituting the value of y in the given function:

f(x) = -0.1 |x|

-10 = -0.1 |x|

x = -100 or x = 100

So, the two points are (-100, -10) or (100, -10).

Hence, the graph of f(x) = -0.1 |x| opens. The point (-100, -10) or (100, -10) is on the graph.

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Answer:

120.010

Step-by-step explanation:

The perimeter of the 6-sided shape given the length and width of the rectangle is 48 cm

The perimeter of a rectangle= 2(length + width)

Length of the rectangle= 7 cm

Width of the rectangle= 5 cm

The perimeter of a rectangle= 2(length + width)

= 2(7 + 5)

= 2(12)

= 24 cm

The 6-sided shape is the combination of two rectangles

So,

Perimeter of the 6-sided shape = 24 cm + 24 cm

= 48 cm

Therefore, the 6-sided shape has the perimeter 48 cm.

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Answer:

  314 yd²

Step-by-step explanation:

You want the area of a circle that has a diameter of 20 yards.

The usual formula for the area of a circle is ...

  A = πr² . . . . . . where r is the radius

The radius of the circle is half the diameter, so is (1/2)(20 yd) = 10 yd.

Using this value in the formula, we find the area to be ...

  A = 3.14(10 yd)² = 314 yd²

The three-digit palindromes that can be created using the digits are 16 numbers.

A word, number, phrase, or other group of characters that reads the same backwards as it does forwards is called a palindrome. Examples include the words "madam" or "racecar," the date and time 12/21/33 12:21, and the phrase "A man, a plan, a canal — Panama."

The three-digit palindromes are of the form: ABA.

Here, A can be selected in 4 ways.

Digits can be repeated hence, B can be selected in 4 ways.

The last A is the same number as the first A, hence the selection is 1 way.

The number of three digits palindrome that we can form is:

(4)(4)(1) = 16 ways

Hence, the three-digit palindromes that can be created using the digits are 16 numbers.

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In light of this, Liam's earnings after six years will be roughly $47,139.92.

Profits from Liam's company have reached $43,200, and they are growing at a 1.2% annual rate.

We can use the compound interest calculation to calculate the number of profits after six years.

The formula is P = P0 *[tex](1 + r/100)^t[/tex], If t is the number of years, which is 6, P0 is the initial sum of $43,200, r is the yearly interest rate of 1.2%, and t is the number of years.

By substituting these values into the formula,

we can calculate the final amount as P = 43,200 * [tex](1 + 1.2/100)^6[/tex] = 43,200 * [tex]1.012^6[/tex] = 43,200 * 1.07711 = $47,139.92.

In light of this, Liam's profits after six years will be roughly $47,139.92.

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The simple interest on a principal amount is the function on time t.

Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans. It's also the type of interest that banks pay customers on their savings accounts.

Given here: Principal=$3200, Annual rate of interest =8% and time=5 years

Thus Simple interest is S.I= 3200×8×5 / 100

                                           =$1280

Which is equal to the interest given in the question.

Thus the the interest rate forms a linear function or

Simple Interest is calculated using the following formula: SI = P × R × T /100,

where r and P are constant then S.I can be written as the function of time t

SI(t)= P×r×t/100

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The answer to the expression 2b x b is simply 2b^2. Exponentiation is a mathematical operation that raises a number to a power, and in this case, b is raised to the power of 2.

Alternatively, if exponentiation is not allowed, the answer to the expression is simply 2b * b, which can be simplified to 2b^2 as well.

So, the answer to the expression 2b x b is 2b^2, regardless of whether or not exponentiation is used.

The expression 2b x b represents the product of two scalars, 2 and b, multiplied by a scalar b.

The expression could represent a variety of quantities in mathematics and science, including the area of a rectangle, the volume of a cube, or the kinetic energy of an object, among others.

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The values of the variables are -4 and -9

From the information given, we have the equations:
y = 2x - 1

y = x -5

Now, from substitute the value of y in equation 2 to equation 1, we get;

x - 5 = 2x -1

collect the like terms

x -2x = -1 + 5

Add or subtract the like terms

-x = 4

Make 'x' the subject

x = -4

Substitute the value into equation 2

y = -4 - 5

y = -9

Then, the values are-4 and -9

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Answer:

[tex]3\left(x-\dfrac{5}{6}\right)^2-\dfrac{49}{12}[/tex]

Step-by-step explanation:

Given quadratic expression:

[tex]3x^2 - 5x - 2[/tex]

To complete the square, factor out the coefficient of the leading term:

[tex]\implies 3\left(x^2-\dfrac{5}{3}x-\dfrac{2}{3}\right)[/tex]

Add and subtract the square of half the coefficient of the term in x inside the parentheses:

[tex]\implies 3\left(x^2-\dfrac{5}{3}x+\left(\dfrac{\frac{-5}{3}}{2}\right)^2-\left(\dfrac{\frac{-5}{3}}{2}\right)^2-\dfrac{2}{3}\right)[/tex]

Simplify:

[tex]\implies 3\left(x^2-\dfrac{5}{3}x+\left(\dfrac{-5}{6}\right)^2-\left(\dfrac{-5}{6}\right)^2-\dfrac{2}{3}\right)[/tex]

[tex]\implies 3\left(x^2-\dfrac{5}{3}x+\dfrac{25}{36}-\dfrac{25}{36}-\dfrac{2}{3}\right)[/tex]

Factor the perfect square trinomial formed by the first three terms inside the parentheses:

[tex]\implies 3\left(\left(x-\dfrac{5}{6}\right)^2-\dfrac{25}{36}-\dfrac{2}{3}\right)[/tex]

Distribute:

[tex]\implies 3\left(x-\dfrac{5}{6}\right)^2-\dfrac{75}{36}-\dfrac{6}{3}[/tex]

[tex]\implies 3\left(x-\dfrac{5}{6}\right)^2-\dfrac{25}{12}-2[/tex]

Simplify:

[tex]\implies 3\left(x-\dfrac{5}{6}\right)^2-\dfrac{25}{12}-\dfrac{24}{12}[/tex]

[tex]\implies 3\left(x-\dfrac{5}{6}\right)^2-\dfrac{49}{12}[/tex]