System of Inequalities Problem Solving Task
Wait!! I Need my Weights!

Eric runs a dive boat named the Lois Ann. He has been struggling to fill his boat and he doesn't understand why. Eric provides weights for the scuba divers that go out on the boat. He has a maximum of 220 pounds of weight available for the divers to use and estimates that the average adult needs 20 pounds of weight and the average child needs 10 pounds of weight. Eric also likes to provide his divers with tanks to use. For each trip each adults requires 2 tanks and each child requires only 1 tank. The Lois Ann can accommodate at most 30 tanks and can hold a maximum of 20 scuba divers on any trip.
1) Write inequalities to represent all of the constraints in Eric's problem. Use x for the number of adults and y for the number of children.

Please help!!! I WILL GIVE BRAINLIEST​

Answer:$10

Step-by-step explanation:

Assume 20% = 0.20

50 x 0.20 = 10

OR

Move the decimal one place to the left for 10 percent, and double it to get 20 percent.

Answer:

Suppose 20% Equals 0.20.

50 x 0.20 = 10

To acquire 10%, move the decimal one position to the left, and to reach 20%, double it.

Step-by-step explanation:

The correct term for each term is -

Federal Fund Rate

Bank holding company

Check clearing

Net worth

Discount rate

What is an account?

A certain kind of financial asset or debt that is kept and owned in your name.

When a bank borrows money from another bank, the interest rate it pays is called the Federal Fund Rate.

Ownership of more than one bank constitutes a bank holding company.

When a bank customer writes a check, the check will go through the process of check clearing.

A bank's total assets minus its total liabilities make up its net worth.

Banks repay loans from the Federal Reserve at a rate of interest called the discount rate.

Therefore, these are the key terms used in banking.

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Answer:

A [tex]180^{\circ}[/tex] rotation about the origin, then a dilation by a scale factor of [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

The preimage is larger than the image.

Also, the orientiation of the triangle didn't change.

Answer:

Step-by-step explanation:

Use the formula for circles.

[tex]x^{2} + y^{2} = r^{2}[/tex]

Since we already have the values of x and y in the given problem (-2,3), substitute the values in the fomula.

[tex]x^{2} + y^{2} = r^{2}[/tex]

[tex](-2)^{2} + (3)^{2} = r^{2}[/tex]

[tex]4 + 9 = r^{2}[/tex]

[tex]13 = r^{2}[/tex] (square both sides to get the radius)

[tex]\sqrt{13} = \sqrt{r^{2} }[/tex]

[tex]\sqrt{13} = r[/tex]

Answer:

4x+5 = 13

Step-by-step explanation:

2x-7= 5

Answer: Root 16 = 4, 4*1/2= 2

5/9*1/2= 5/18

Root 3 = 1.73205...*1/2= 0.866025...

Root 3 is the answer

Step-by-step explanation:

(e) = number of erasers she had originally.

now she has 38.

so,

A

38 = (e) + 10

B

38 - 10 = (e) + 10 - 10

28 = (e)

she had originally 28 erasers.

The number of hot cocoas the Ai Mi would be expected to sell with a high temperature of 64 ºF is given as follows:

60.

As the graph of the linear function is given, the most practical way to define the function is using the slope-intercept format, as follows:

y = mx + b.

In which the coefficients are given as follows:

From the graph, when x = 0, y = 111, hence the intercept b is given as follows:

b = 111.

When x increases by 5, from 0 to 5, y decays by four, from 111 to 107, hence the slope m is obtained as follows:

m = -4/5

m = -0.8.

Hence the function that predicts the amount of hot cocoa sold for a high temperature of x ºF is given as follows:

y = -0.8x + 111.

The prediction for a high temperature of x = 64 is given as follows:

y = -0.8(64) + 111

y = 60 hot cocoas, rounded.

The graph is given by the image presented at the end of the answer.

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Answer:

7 ≤ x ≤ 25

Step-by-step explanation:

Triangle Inequality Theorem

The sum of any two sides of a triangle is greater than or equal to the third side:

Therefore, the longest side of the triangle is "c".

Let the longest side be "x":

Therefore:

Let the longest side be 16:

Therefore:

As 9 < 16, the longest side cannot be 9.

Therefore, the length of the third side of the triangle, given that the other two sides are 9 ft and 16 ft is greater than or equal to 7, and less than or equal to 25:

answer: none it is  -3

On solving the provided question, we can say that unlike other shapes, which all have parallel lines, only has one parallel side.

Parallel lines in geometry are coplanar infinite lines that don't intersect anywhere. In a given three-dimensional space, parallel planes are those that never cross. Curves with a constant minimum distance between them and no points of contact or intersection are said to be parallel. Two lines that are in the same plane, equally spaced apart, and never intersect are referred to as parallel lines in geometry. Either horizontal or vertical can apply. Parallel lines can be noticed in everyday objects like railroad tracks, rows of notebooks, and pedestrian crossings.

unlike other shapes, which all have parallel sides, only has one parallel side.

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The length of each diagonal is of: 11 units.

The diagonal lengths are defined as follows:

As the figure is a rectangle, the diagonal lengths are the same, and thus the value of x is obtained as follows:

WY = XZ

6x - 7 = 3x + 2

3x = 9

x = 9/3

x = 3.

Hence the diagonal length is given as follows:

XZ = 3(3) + 2 = 9 + 2 = 11 units.

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Answer:

2023

Step-by-step explanation:

3 + 4x = y

y = 3 + 4(505)

y = 3 + 2020

y = 2023

An absolute value equation may have one solution, two solutions, or no solutions.

Absolute value means "distance from zero" on a number line. To represent the absolute value of a number, we use a vertical bar on either side of the number.

The absolute value is the distance from zero, It is the non-negative quantity, which defines the number as the distance of the number from zero on the number line.

The absolute value has only one solution when it is compared to 0.

When the absolute value equation is compared with any positive number, then the number of solutions is two.

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Answer:

true

Step-by-step explanation:

i had the same question on a quiz.

The value of x for the equation 34+x4=1 is [tex]\frac{-33}{ 4}[/tex]

As we have [tex]34+4x=1[/tex]

Subtracting [tex]34[/tex] from both sides we get

[tex]4x=1-34[/tex]

[tex]4x=-33[/tex]

Dividing with [tex]4[/tex] both sides

we get the answer [tex]x=\frac{-33}{4}[/tex]

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Zach is trying to find out the hypotenuse value of the right-angle triangle.

What is the right triangle?

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

The Pythagorean theorem states that "in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides".

Zach is most likely trying to find the length of the hypotenuse of a right triangle, which is the side opposite the right angle, given the lengths of the other two sides.

In this case, given 32 inches, 20 inches, and 20 inches values, he's trying to find out the hypotenuse value of the right-angle triangle.

Hence, Zach is trying to find out the hypotenuse value of the right-angle triangle.

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Answer:

37 and -18

Step-by-step explanation:

Answer:

let x and y be two numbers

The required, relation shown in graphs A and D is functions.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
The curves shown in graphs B and C are not functional, as both graphs consist of only one variable.

While curve shown in graph A and D are function because it shows the relationship between two variables x and y.

Graph A shows, Absolute value function,
Graph D shows the quadratic function.

Thus, the Relation shown in graphs A and D is functions.

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Answer:

The answer is B -2x +24

Step-by-step explanation:

I will show you how I got this answer step by step

-3(2x-8) + 4x

step 1

distribute the -3 through the parentheses

step 2

collect like terms

so -6x+4x = -2x

ANSWER: -2x+24

The expression is equivalent to the given expression is -2x +24

An expression in math is a statement having minimum of two numbers, or variables, or both and an operator connecting them.

Given that, is an expression -3(2x-8)+4x, we need to find an expression equal to the given,

Simplifying the expression,

= -3(2x-8) + 4x

= -6x + 24 + 4x

= -6x+4x = -2x

Hence, the expression is equivalent to the given expression is -2x +24

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No, the absolute value of equations does not always have two answers

Understanding the absolute value is crucial for mathematicians. We place vertical bars on either side of a number to show its absolute value. On a number line, absolute value refers to distance from zero. A negative number's absolute value is a positive number. A positive number has the same absolute value as another positive number.

There are not always two solutions to an equation's absolute value. An equation involving fundamental values may have one or more solutions, depending on the equation's overall structure and the values that are being entered. For example, whereas the equation |x| = 2x has no solutions, but the equation |x| = 1 has two solutions (x = 1 and x = -1).

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I would recommend taking this bet, as the expected value of the bet is Positive.

The expected value of a bet is the sum of the product of each possible outcome and its corresponding probability. In this case, the probability of getting two heads is 0.25, and the payout for that outcome is $10. The probability of not getting two heads is 0.75, and the payout for that outcome is -$2. When you multiply each outcome by its corresponding probability and sum them together, the expected value of the bet is $1.0. Because the expected value of the bet is positive, it is  a good bet to take. It is more likely that you will gain money .

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Answer:

Step-by-step explanation:

all internal angles in a triangle add to 180 degrees.

77+36=113

180-113=67

we know that the final angle in the triangle is 67 degrees

the left parallel line makes another triangle in the bottom left. we know that one angle is 41 and we just calculated that the other is 67.

41+67=108

180-108=72

so now we know that the small triangle in the bottom left has angles of 41,67 and 72.

all straight lines are 180 degrees, and we just figures out that the left side of the left parallel line is 72 degrees. therefore the other side is 108 degrees.

since they are parallel lines, the left angle of both of them on the bottom line is 72, while the right angle is 108.

this means that x=108 degrees

i hope this is right and it helps if it is correct. really sorry if it is wrong. have a good day :)

The probability that the entire batch will be accepted will be 9339

4000-90 = 3910 (non-defective) (non-defective)

If P(first not defective) = 3910/4000 and it is not changed (1 less to choose from and 1 less not defective)

P(second is not flawed if first is flawed) = 3909/3999 If the item is also not replaced (a total of 2 less to choose from and 2 less not defective)

P

(1st and 2nd are not defective, so the third is also not defective)) = 3908/3998

Simply multiply these three fractions to get the answer: 3910(3909>)(3908)) / (4000(3999)(3998)).

=9339

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Answer:

The ratio of boys to girls is 4:5, which can be simplified to 4/5.

The fraction of the class that is boys is 4/5 (or 0.8), and the fraction of the class that is girls is 5/9 (or 0.5555).

So, 4/9 of the class is boys.

The supplied statement states that the iterated integral after being converted to interpolation is 32/3.

In mathematics, an integral is either a number representing the region beneath a function's graph over a certain interval or just a new function, the reverse of which contains the original mechanism (indefinite integral). To complete the whole, an essential component is required. The term "essential" is almost a synonym in this context. Trigonometric functions of functional and equations are a concept in mathematics. Integral is a derivative of Middle English, Latin integer, and Medieval Latin integralis, each of which mean "making up a whole."

Therefore, the area is,

[tex]R=\left\{(x, y) \mid 0 \leq x \leq 2,0 \leq y \leq \sqrt{2 x-x^2}\right\}[/tex]

So,

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

y² = 2x - x²

x² - 2x + y² = 0

x² - 2x + 1 + y² = 1

(x-1)² + y² = 1

In other words, the area is the middle section of the disk with a radius of 1 and a center at (0,1).

Region R's polar coordinates are

x = r cos∅, y = r sin∅

So,

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

y² = 2x - x²

x² + y² = 2x

r² = 2r cos∅

r = 2 cos∅

The polar coordinates of the sphere of integration as,

[tex]R=\left\{(r, \theta) \mid 0 \leq \theta \leq \frac{\pi}{2}, 0 \leq r \leq 2 \cos \theta\right\}[/tex]

The provided integral then becomes,

[tex]\begin{aligned}& \int_0^2 \int_0^{\sqrt{2 x-x^2}} 6 \sqrt{x^2+y^2} d y d x \\= & \int_0^{\frac{\pi}{2}} \int_0^{2 \cos \theta} 6 r \cdot r d r d \theta \\= & \int_0^{\frac{\pi}{2}} \int_0^{2 \cos \theta} 6 r^2 d r d \theta \\= & \int_0^{\frac{\pi}{2}} 6\left(\frac{r^3}{3}\right)_0^{2 \cos \theta} d \theta\end{aligned}[/tex]

[tex]\begin{aligned}& =\int_0^{\frac{\pi}{2}} 2\left(8 \cos ^3 \theta-0\right) d \theta \\& =16 \int_0^{\frac{\pi}{2}} \cos ^2 \theta \cdot \cos \theta d \theta \\& =16 \int_0^{\frac{\pi}{2}}\left(1-\sin ^2 \theta\right) \cdot \cos \theta d \theta\end{aligned}[/tex]

Let u = sin∅ then du = cos ∅ d∅

If ∅ = 0 then u = 0 and if ∅ = π/2 then u = 1.

The above integral thus becomes,

[tex]\begin{aligned}& \int_0^2 \int_0^{\sqrt{2 x-x^2}} 6 \sqrt{x^2+y^2} d y d x \\= & 16 \int_0^1\left(1-u^2\right) d u \\= & 16\left(u-\frac{u^3}{3}\right)_0^1 \\= & 16\left(1-\frac{1}{3}\right)\end{aligned}[/tex]

= 32/3

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To complete the given statement, we have;

i. SM > DM

ii. <PQS < <RQS

iii. AS > RM

iv. m<1 = m<2

Any given shape which is bounded by straight side is referred to as a plane shape. Examples include: triangles, rectangle, trapezium, parallelogram etc.

It can be observed in the given question that the shapes have different properties regarding their length of sides and measure of internal angles. Each of the statement can be completed as thus;

1. From triangle SJD,

m<SJM > m<DJM

Then, it can be deduced that;

SM > DM

2. From quadrilateral PQRS,

RS > PS

It can be deduced that;

<PQS < <RQS

3. From triangle AMS, it can be deduced that AS > RM.

4. From quadrilateral ABCD,

AD II BC

Then,

m<1 = m<2             (by alternate angle property)

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Answer:

Step-by-step explanation:

An isosceles triangle with sides of 3/6, 3/6 and an unknown length, and a circle tangent to the two sides with a given radius can be solved using the Pythagorean theorem, trigonometry and the circle area formula.

We know that the triangle is isosceles, so the angle at point B is congruent to angle at point C, and let's call it x. Now we know that angle BAC = 90- x. Since the circle is tangent to the side AB and AC at B and C respectively, we can use the property of tangents that says that the radius of a circle that is tangent to a line is perpendicular to that line, and we can use the triangle formed by the radius, the side and the angle at that point to apply the Pythagorean theorem.

3/6^2 + r^2 = (3/6/sin(x))^2

r^2 = (3/6)^2 (1/sin^2(x) -1)

Now we can use the area of the circle formula A = πr^2, to find the area of the circle that passes through the vertices A, B, and C:

A = π r^2 = π(3/6)^2 (1/sin^2(x) -1)

Using the values of the problem we get

A = π(3/6)^2 (1/sin^2(90- x) -1) = π(3/6)^2 (1/cos^2(x) -1) = π(52^2) = 2701π = 27.01 (D)

Therefore the area of the circle that passes through vertices A, B, and C is 27.01.

Answer:

  a ≠ 0

Step-by-step explanation:

You want to know the restriction applicable to 2(y+a)/a(x-3).

A rational expression is undefined when its denominator is zero. The restrictions are applied so that no denominator is zero.

Here, the expression is ...

  [tex]\dfrac{2(y+a)}{a}(x-3)[/tex]

The only denominator is 'a'. It cannot be zero.

The restriction is a ≠ 0.

__

Additional comment

If we assume this is a relation in which x- and y- are the only variables, there is no restriction on the relation as written.

Perhaps you intend that (x-3) be a denominator factor. Then the relation would have the restriction x≠3. Such an expression would need to be written as ...

  2(y+a)/(a(x-3)) . . . . . . using parentheses around the denominator

<95141404393>

The system of inequalities to represent the maximum amount of flooring needed and the maximum amount of money Samuel wants to spend is x + y <= 2000 and 4.50x + 8.25y <= 10000.

Let x be the number of square feet of carpet and y be the number of square feet of hardwood.

The most amount of flooring area he can cover is 2000 square feet. So the first inequality represents the maximum amount of flooring area that Samuel can cover:

x + y <= 2000

The carpet is $4. 50 per square foot and the hardwood is $8. 25 per square foot and Samuel has a budget of $10,000. So the second inequality represents the maximum amount of money that Samuel wants to spend:

4.50x + 8.25y <= 10000

So the system of inequalities is:

x + y <= 2000

4.50x + 8.25y <= 10000

This system represents the possible combinations of carpet and hardwood that Samuel can use while staying within his budget and the maximum amount of flooring area he can cover.

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By distributive property for real numbers, the expression (- 4 + v + 4 · x) · (- 6) is equivalent to the expression 24 - 6 · v - 24 · x.

In real algebra, distributive property is an algebraic property where a real number is "distributed" on every term of a sum of real numbers. This property is described below:

c · (a + b) = a · c + b · c

Where a, b, c are real numbers.

Now we proceed to use distributive property in the following case. First, write the entire expression:

(- 4 + v + 4 · x) · (- 6)

Second, apply distributive property:

(- 6) · (- 4) + (- 6) · v + (- 6) · (4 · x)

Third, use associative property:

(- 6) · (- 4) + (- 6) · v + [(- 6) · (4)] · x

Fourth, use sign laws and multiply on each term:

24 - 6 · v - 24 · x

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