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On solving the inequalities a ≥ 10, y ≥ 55, 7a + 10y ≥ 690, the solution is obtained as (20,55).

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

Use the variables a and y to represent the number of student and adult tickets sold, respectively.

Then write the following system of inequalities -

a ≥ 10 (they must sell a minimum of 10 student tickets)

y ≥ 55 (they must sell at least 55 adult tickets)

7a + 10y ≥ 690 (they must make no less than $690 from ticket sales)

The first two inequalities are constraints on the number of tickets sold, and the third inequality represents the revenue constraint.

To find a possible solution, graph these inequalities on a coordinate plane and look for the feasible region that satisfies all three inequalities.

Alternatively, solve the system of inequalities using algebra.

First, simplify the third inequality by subtracting 7a from both sides -

10y ≥ 690 - 7a

Then, divide both sides by 10 -

y ≥ (690 - 7a)/10

This inequality represents the revenue constraint in terms of the number of student tickets sold.

Now combine the revenue constraint with the other two constraints -

a ≥ 10

y ≥ 55

y ≥ (690 - 7a)/10

Use substitution to solve for a in terms of y -

y ≥ (690 - 7a)/10

10y ≥ 690 - 7a

7a ≥ 690 - 10y

a ≥ (690 - 10y)/7

To find a possible solution, substitute a = (690 - 10y)/7 into the other two constraints -

(690 - 10y)/7 ≥ 10

y ≥ 55

These inequalities can be simplified -

690 - 10y ≥ 70

y ≥ 55

The first inequality can be solved for y -

-10y ≥ -620

y ≤ 62

Since it is known y ≥ 55, the feasible values for y are between 55 and 62, inclusive -

55 ≤ y ≤ 62

Now use the expression for a in terms of y to find the corresponding values of a -

a = (690 - 10y)/7

For each value of y between 55 and 62, inclusive, we can calculate a and check whether it satisfies the constraints -

a ≥ 10

y ≥ 55

7a + 10y ≥ 690

For example, when y = 55 -

a = (690 - 10(55))/7 = 20

7a + 10y = 7(20) + 10(55) = 690

Therefore, these values satisfy all three constraints, so one possible solution is a = 20 and y = 55.

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Answer:

312

Step-by-step explanation:

Add the area of each face together

Don't forget the units!

Let's start by finding the right face (12 by 3). From your picture, we can tell its 12m long, and 3m tall. To find the aria of any face, we multiply the length, times the width.
12 x 3 = 36.
Now let's look at where it says 8m. Since that face is just as tall as the first one, we can tell its 3m tall.
8 x 3 = 24.

We can continue this for the top face.
Since the width of the second face we did is 8m, and the width of the first one is 12m, we can tell that the top one is 8 x 12. (96).

We can do this again for the other 3 sides.
A shortcut i like to take, is to do 3 of the sides, (Like the ones we did) and add them together, then double the sum.

36+24+96=156.

156x2=312.

This shortcut should work, because by adding the aria of half the sides together, we get exactly half the answer.

When doing this, it only works to do 3 different sides. it will not work if you do the same side twice, or a parallel side.

I encourage you to let me know if this method works for you! I hope this helps!

a) Since we have seven possible outcomes and for each performer we have that the probability to perform first is 1/7, therefore, the probability that C will perform first is 1/7

b) For the probability that F or G will perform first, we have to add both probabilities to get the following:

therefore, the probability that F or G will perform first is 2/7

The amount you will have $6,500 with 5% in six years using continuous compounding is of:

$8,774.

The amount you will need to have the entire $32000 in the 6 years is of:

$18,890.46.

The balance of an account after t years, using continuous compounding, is given as follows:

\(B(t) = Pe^{kt}\)

In which the parameters are given as follows:

Putting the $6,500 into the account, the values of the parameters are given as follows:

P = 6500, k = 0.05, t = 6.

Hence the balance will be of:

B(6) = 6500 x e^(0.05 x 6) = $8,774.

The balance to have the entire $32,000, considering what you already have, will be of:

32000 - 6500 = 25500

Hence the principal is obtained as follows:

Pe^(0.05 x 6) = 25500

P = 25500/e^(0.3)

P = $18,890.46.

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The perimeter of the square is 16√5 mm, and the area of the square is 80 mm².

To calculate the perimeter and area of the square, we can use the formulas:

Perimeter = 4 * side length

Area = side length * side length

Substituting the given side length of 4√5mm into the formulas, we have:

Perimeter = 4 * 4√5mm = 16√5mm

Area = (4√5mm) * (4√5mm) = 16 * 5mm = 80mm²

Therefore, the perimeter of the square is 16√5mm, and the area of the square is 80mm².

Please note that the values are based on the provided side length of 4√5mm. If there are any changes to the side length, the perimeter and area will differ accordingly.

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The perimeter of the square is 16√5 mm, and the area of the square is 80 mm².

I took the test on plato.

Answer:

HL

Step-by-step explanation:

The axis of symmetry of the function f(x) = x² - 6x-1 is equal to 3.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry, Xmin = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

By substituting the parameters, we have the following:

Axis of symmetry, Xmin = -b/2a

Axis of symmetry, Xmin = -(-6)/2(1)

Axis of symmetry, Xmin = 6/2

Axis of symmetry, Xmin = 3.

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Answer:

The distance from the flagpole to the tree is 27 ft

Step-by-step explanation:

Answer:

2  1/40  hours = 2.025  hours

Step-by-step explanation:

1300 + 655 + 285 x  3 = 2810 calories

2810 - 2000 = 810 calories

810 / 400 = 2 1/40 hours

16. Circle F

17. BF

18. CD

19. BE

20. FA

Answer:

16.  F

17.  FA

18.  CD

19.  BE

20.  FA

Step-by-step explanation:

Question 16

A circle is named by its center.

The center of the given circle is F, therefore the name of the given circle is F.

Question 17

The radius of a circle is a straight line segment from the center to the circumference.  

Therefore, the radii of the given circle are:

Question 18

A chord is a straight line segment joining two points on the circumference of the circle.  

Therefore, the chords of the given circle are:

Question 19

The diameter of a circle is the width of the circle at its widest part. It is a straight line segment that passes through the center of the circle and whose endpoints lie on the circumference.

Therefore, the diameter of the given circle is:

Question 20

As the diameter is BE, it contains the radii FB and FE.

Therefore, the radius that is not contained in the diameter is:

Answer:

1the answer for this is easy it is 4.4

The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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Answer:

(-4,-1)

All you have to do to find it is subtract x by 5 and subtract y by 5. :)

Answer: any negative value

Step-by-step explanation:

g(x)= ax², inc on x<0 & dec on x>0

Firstly we need to get the derivative of g(x)

g'(x)=2ax

for inc interval g'(x) should be +ve

x<0 (i.e. x= -ve), then a must be -ve

for dec interval g'(x) should be +ve

x>0 (i.e. x= +ve), then a must be -ve

so in both cases a must be a negative constant

Answer:

71.8962°

Step-by-step explanation:

In order to find the angle given 2 sides, you need to identify the 2 sides with the given measure.

Since we need to find X, the 2 sides are 52 (the opposite side) and 17 (the adjacent side)

The only way to find X with an opposite and adjacent side is by using tan.

In order to find the angle, you will need to use the tan^-1 (52/17)

That will give you 71.8962°

Answer:

x = 71.9°

Step-by-step explanation:

The given diagram shows a right triangle with an unknown angle, x.

We have been given the measures of the sides that are opposite and adjacent the unknown angle. Therefore, we can use the tangent trigonometric ratio to find the value of x.

\(\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}\)

The unknown angle is x, so θ = x.

The side opposite the angle measures 52 units, so O = 52.

The side adjacent the angle measures 17 units, so A = 17.

Substitute the values into the ratio and solve for x:

\(\tan x=\dfrac{52}{17}\)

     \(x=\tan^{-1}\left(\dfrac{52}{17}\right)\)

     \(x=71.8962369...\)

     \(x=71.9^{\circ}\; \sf (nearest\;tenth)\)

Therefore, the value of x is 71.9°.

Answer:

2.4*18 = $43.2

stock price is $43.2

Step-by-step explanation:

Standard form of a linear equation is an equation that shows the form a straight line. It has three constants which are A,B, and C. The two variables being X and Y.

Here is the linear equation.

Ax+By=C

Answer:

8.8

Step-by-step explanation:

Akhtar's bonus = 20% × £70 = £14

karl's bonus = 20% × £26 = £5.2

Difference = £14 - £5.2 = 8.8

**I'm not sure about the answer sorry, please get it checked.

Answer:

The polynomial equation that cannot be solved using the quadratic formula: Option2: \(x^2-2x^3-5=0\)

Step-by-step explanation:

First of all we have to learn what a quadratic polynomial is.

A polynomial or equation of degree 2 is called a quadratic equation. Quadratic formula is used to solve quadratic equations.

The quadratic equation is of the form:

\(ax^2+bx+c = 0\)

From the given options, only option 2 doesn't have degree 2 so it is not a quadratic polynomial.

Hence,

The polynomial equation that cannot be solved using the quadratic formula: Option2: \(x^2-2x^3-5=0\)

Answer:

x^5 - 2x^3 - 5 = 0

Step-by-step explanation: Just did this problem and got it right.

Answer:

8/15

Step-by-step explanation:

(-4/5) ÷ (-3/2)

= 4/5 × 2/3

= 8/15

Answer:

\(\frac{8}{15}\)

Step-by-step explanation:

1. apply the fraction rule \(\frac{a}{-b}=-\frac{a}{b}\)

\(=\frac{\frac{4}{5}}{\frac{3}{2}}\)

2. divide fractions, multiply the corresponding values

\(= \frac{4\cdot \:2}{5\cdot \:3}\)

3. simplify: 4x2 = 8, 5x3 = 15

answer is 8/15

Let N be the middle number of 3 consecutive even integers. The sum of these integers expression are 2N + 4.

Integers are whole numbers that are either positive, negative, or zero. They are the basic building blocks of mathematics and are used to represent any quantity or amount. Examples of integers include -3, -2, -1, 0, 1, 2, 3, and so on. Integers are used in many different fields, such as economics, physics, and computer science. They are also used to describe mathematical operations and equations, as well as for counting and measuring objects. Integers are also used in everyday life, such as when counting money, measuring distances, and counting objects.

N represents the middle number of the three consecutive even integers; adding 2N to both sides of the equation yields 2N + 2N, which is equal to 4N; finally, adding 4 to 4N yields the expression 2N + 4.

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Answer:

did not list

Step-by-step explanation:

Answer:

The probability that one marble drawn at random is not blue is 70%

Answer:

It will take 8 days to complete the trip.

Step-by-step explanation:

3104 miles total

388 miles a day

3104/388 = 8

The correct answer is:

a = 43%

b = 88%

To determine the values of a and b in the relative frequency table, we need to analyze the information provided in the Venn diagram and the given table.

From the Venn diagram, we can gather the following information:

The circle labeled "satellite" has a value of 55.

The circle labeled "cable" has a value of 75.

The overlap between the two circles is labeled as 12.

Using this information, we can complete the table:

First column - "Satellite":

Entries: Satellite, Not satellite, Total

Total: 55 (as given in the Venn diagram)

Second column - "Cable":

Entries: Blank, 51%, Blank

To find the value for the "Cable" entry, we need to subtract the overlap (12) from the total number of cable users (75).

Cable: 75 - 12 = 63

Therefore, the entry becomes: Blank, 51%, Blank

Third column - "Not Cable":

Entries: a, b, Blank

To find the value for "a," we subtract the overlap (12) from the total number of satellite users (55).

a: 55 - 12 = 43

To find the value for "b," we subtract the overlap (12) from the total number of households (100).

b: 100 - 12 = 88

Therefore, the entries become: 43, 88, Blank

Fourth column - "Total":

Entries: Blank, Blank, 100%

The total number of households is given as 100% (as stated in the question).

Therefore, the values of a and b in the relative frequency table are:

a = 43% (rounded to the nearest percent)

b = 88% (rounded to the nearest percent)

Hence, the correct answer is:

a = 43%

b = 88%

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Answer:

x is 64 , y is18 and z is 98

Step-by-step explanation:

these angles are congruent and u get z by adding 64 and 18 then subtracting it for 180 since it makes a straight line

Answer:

(-3, -2)

Step-by-step explanation:

When a point is translated, the key words are very important to look at.

Up/down means you are translating the y axis.

Left/right means you are translating the x axis.

So using this key, we can solve.

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

A point located at (-3, 2) is translated down 4 units.

Since the point is going down, we will be translating the y axis. 2-4 is -2.

Since the x is staying the same, the x will be -3.

So your translated points are (-3, -2)

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I hope this helps!

-No one

The angles that are congruent are as follows:

Vertical angles are angles that are opposite of each other when two lines cross. In other words, vertical angles are formed when two lines meet each other at a point.

Vertically opposite angles are congruent.

Therefore, let's find the angles that are congruent in the diagram.

When lines intersect angle relationship such as vertically opposite angles are formed.

Therefore, the following angles are congruent because they are vertically opposite angles.

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