Which is a correct solution for the following system of Inequalities

In the right-angle triangle RQS the measure of m∠R = 90°, m∠Q = 59° and m∠S = 31°.

What is a right-angled triangle?

Any two sides of a triangle's three sides must always add up to more than the third side since a triangle is a regular polygon with three sides. This distinguishing characteristic of a triangle. A right-angle triangle is one that has angles between its two sides that equal 90 degrees.

A right-angled triangle RQS is given.

The measure of ∠R is given as = 90°.

The measure of ∠Q is given as = (2x + 33)°.

The measure of ∠S is given as = (5x - 34)°.

According to the properties of the triangle, the sum of all angles of a triangle equals 180°.

So, the equation will be -

∠R + ∠Q + ∠S = 180°

Substituting the values into the equation -

90° + (2x + 33)° + (5x - 34)° = 180°

Combining the like terms -

90° + 2x + 33° + 5x - 34° = 180°

7x + 89° = 180°

7x = 180° - 89°

7x = 91°

x = 13°

The measure of ∠Q - (2x + 33)°

∠Q = 2(13°) + 33°

∠Q = 26° + 33°

∠Q = 59°

The measure of ∠S - (5x - 34)°

∠S = 5(13°) - 34°

∠S = 65° - 34°

∠S = 31°

Therefore, the measures of angles are 90°, 59° and 31°.

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The perimeter of triangle NPQ is calculated to be 72 when NPQ is given congruent to RSQ.

Perimeter of triangle NPQ = 7x + 2

Triangle perimeter: RSQ = 10x - 4

As triangle NPQ is given congruent to triangle RSQ, we have,

NQ / RQ = PQ / SQ = 24 / 32 = 21 / 28 = 3 / 4

The above ratio can be equated to the ratio of perimeters of the triangles NPQ and RSQ.

Perimeter of triangle NPQ/Perimeter of triangle RSQ = 7x + 2/10x - 4 = 3/4

7x + 2/10x - 4 = 3/4

On cross multiplication and solving, we have, x = 10.

The perimeter of triangle NPQ = 7x + 2 = 70 + 2 = 72  

The question is incomplete. The complete question has the picture of two congruent triangles given in the below attachment.

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A value we can put in place of a variable (such as x) that makes the equation true and the answer is  13/-10

A number that is capable of taking on any one of a range of values.

A variable's symbolic representation.

Something which can change.

A variable that could alter in a scientific experiment.

A property that can be measured and given varied values is known as a variable.

Variables include things like height, age, income, province of birth, school grades, and kind of dwelling.

Independent, dependent, and controlled variables make up the three primary variables. A automobile driving down various surfaces is one example.

A variable in programming is a value that can change based on external factors or data that has been supplied to the program.

3x+5y

= 0x+5y

=-3x+y

=-3/5x + y

= 3/5 13x + 10y

=0x + 10y

=13x+y

=13/- 10

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The greatest amount of dollar shared is $78

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls

The ratio of the three sibling is 1/2 : 1/3 : 1/4. Firstly, we multiply all the terms with the l.c.m which is 12

therefore the ratio = 6: 4: 3

The total money to be share is 169

The total ratio is 13

The share of the first sibling = 6/13 × 169

= $ 78

The share of the second sibling = 4/13 × 169 = $52

The share of the third sibling = 3/13 × 169 = $ 39

Therefore the highest number of dollars shared is $78

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The missing value in the triangle is given as follows:

28.

The theorem used to solve this problem is given as follows:

A line parallel to one side of a triangle divides the other two proportionately.

As 28 - 16 = 12, the proportional relationship between the side lengths is given as follows:

12/21 = 16/x.

Applying cross multiplication, the value of x is obtained as follows:

12x = 21(16)

Simplifying by 4, we have that:

3x = 21(4)

Simplifying by 3, we have that:

x = 7 x 4

x = 28.

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The area of square = 72.0 in The surface area of a shape is measured using the area.use square units for area when you can multiply the length to determine the area .

Option B is correct.

The quantity of square units required to completely fill a square is known as the area of a square. The region that lies inside the confines of a flat item or a two-dimensional figure is generally referred to as the area. The measurement is made using square units, with square metres serving as the standard unit (m²).

Area of square = Side ²

side=6√2

Area=?

Area of square = ( 6√2)²

                            72 .0 inches.

This is because the sum of two lengths is used to calculate an area. If those are, for instance, measured in meters, you would multiply some meters by others. Consequently, the expression for the area in square meters. Similar to volume: You divide three lengths by.

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Answer:

x+x+18+18=48inches

2x+36 = 48 inches

2x = (48-36) inches

2x = 12 inches

x = 6 inches

The four inequalities are a + c ≤ 400, 10a + 5c ≥ 3000, a ≥ 0 and c ≥ 0. The club must sell 200 children tickets and 200 adult tickets.

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.

The value for one ticket is - $10

The value for one children's ticket is - $5

The total amount that need s to be earned is - $3000

The number of seats in the auditorium is - 400

Let the number of children be = c and the number of adults be = a.

Then the inequality will be -

a + c ≤ 400

10a + 5c ≥ 3000

a ≥ 0

c ≥ 0

The inequalities will have a straight line as (≤,≥) symbols are used in the inequalities.

Write the two inequalities in equation form -

a + c = 400....(1)

10a + 5c = 3000 or 2a + c = 600....(2)

Subtract equation (1) from (2) -

2a + c - (a + c) = 600 - 400

2a + c - a - c = 200

a = 200

a = 200

Substitute the value of a in equation (1) -

200 + c = 400

c = 400 - 200

c = 200

So, the intersection point is (200,200) and the number of children is 200 whereas the number of adults is 200.

Therefore, the graph is obtained.

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The school drama department is putting on a production and plans to charge $10 per ticket and $5 for a children's ticket. They need to earn at least $3,000 each night for cover the cost. The auditorium has a capacity for 400 people.

Write and graph a system of four inequalities that describe how many of each type of ticket the club must sell to meets its goal.

Answer: Points: (0, -3), and (9, 0)

Step-by-step explanation:

In order to graph an equation, you find 2 pairs of points and then just connect them into a line. (The x intercepts and the y intercepts are helpful)

One pair: (x, y) = (0, -3)

Another pair: (x, y) = (9, 0)

Now just connect them to get the line :>

The amount of chlorine in the tank as a function of time is:

C(t) = 0.05 * e^(-6/400*t)

Let C(t) be the concentration of chlorine in the tank at time t and V(t) be the volume of the tank at time t.

At t=0, we know that:

C(0) = 0.05 g/l

V(0) = 400 l

As fresh water is pumped in at a rate of 4 l/s and the mixture is pumped out at a rate of 10 l/s, the rate of change of the volume of the tank is:

dV/dt = 4 - 10 = -6 l/s

As the concentration of chlorine is being diluted by the addition of fresh water, the rate of change of the concentration is proportional to the rate of change of the volume. So we can write:

dC/dt = - k * C(t) * (dV/dt)

where k is a proportionality constant.

We can integrate the above equation with respect to time to find the concentration of chlorine in the tank as a function of time:

C(t) = C(0) * e^(-kt)

In order to find the value of k we can use the initial condition C(0) = 0.05 g/l and V(0) = 400l

0.05 = C(0) * e^(-k*0)

0.05 = C(0)

so we can substitute this value into the above equation and solving for k:

C(0) = 0.05 = 0.05 * e^(-k*0)

0.05 = 0.05

so k = -6/400

Finally, the amount of chlorine in the tank as a function of time is:

C(t) = 0.05 * e^(-6/400*t)

This equation expresses the amount of chlorine in the tank as a function of time t. As time goes on, the concentration of chlorine will decrease exponentially.

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By evaluating the exponential function on x = -2 we will get:

f(-2) = 1/9

Here we have the exponential function below:

f(x) = 3^x

And we want to find f(-2), this means that we just need to evaluate the exponential function in x = -2 (so we just replace the variable x by the number -2)

f(-2) = 3^(-2)

Remember that the negative exponent means that we need to take the inverse, then:

f(-2) = 3^(-2) = 1/3^2

f(-2) = 1/9

That is the value we wanted to find.

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Answer:

x = 14.83 (to the nearest hundredth)

Step-by-step explanation:

Following the Pythagoras' Theorem,

a² + b² = c²

x² + 6² = 16²

       x² = 220

     ∴ x = 14.83 (to the nearest hundredth)

The context clues show that the bolded portion contain doesn't contain an error. Therefore, D. No correction is needed

When determining a word's meaning, context clues take into account the words that immediately precede the unknown word and lead us to infer its meaning.

These words, also known as visual indices, are explained or defined by other words that are used in the same sentence.

From June on to November, it lies hot, still, and unbearable, sick with violent and unrelenting storms; then on until April, it is chill, quiet, and drinks its scant rain and scanter snows. From April to the hot season again, it is blossoming, radiant, and a seductress.

In this case, it is grammatically correct. The correct option is D.

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The order of the angles from least to greatest are given as follows:

<N , <R, <Q.

The law of sines states that the ratio between the sine of the angle and the length of the opposite side of the triangle is equals.

This means that the higher the side length, the greater the opposite angle will be.

Hence:

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The equilibrium price is p = 28.

Price is an amount of money or value that is exchanged for goods & services. It is the amount of money that an individual or business is willing to pay for a product or service. Price is often determined by factors such as the cost of production, supply and demand, and competition. Price is also shaped by factors such as the availability of substitute products, market trends,  & the strength of a company's brand.

Equilibrium quantity: q = 200

p2 + 8q = 1800         700 − p2 + 6q = 0

Adding the two equations together: 2500

q = 2500/14 q = 178.57 q ≈ 200

Equilibrium price: p = 28

p2 + 8(200) = 1800
p2 + 1600 = 1800  p2 = 200 p = √200
p ≈ 14.14
Therefore, the equilibrium price is p = 28.

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Kwan is utilizing 8% of the entire garden to plant radishes.

Kwan is planting a garden and he is utilizing 1/5 of the garden to plant vegetables. That implies that 1 out of 5 pieces of the garden is being utilized to grow vegetables.

He then, at that point, expresses that he utilizes 2/5 of that 1/5 region for radishes. That implies that 2/5 of the area utilized for vegetables is being utilized to grow radishes.

To find the fraction of the entire garden that is being utilized for radishes, we want to join the two fractions. We can do this by multiplying them together.

At the point when we multiply 1/5 by 2/5, we get 2/25. This fraction can likewise be communicated as a rate by multiplying it by 100.

2/25 * 100 = 8%

So, Kwan is utilizing 8% of the entire garden to plant radishes.

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The absolute value function that has the same graph as f(x) = 2|4x – 6| + 18 is the one in option B. f(x) = 4|2x – 3| + 18

A function will only have the same graph as f(x) = 2|4x – 6| + 18 if we can rewrite that function into f(x).

Remember that if A is positive, then we can write:

A*|x| = |A*x|

Now, we can take our absolute value function:

f(x) = 2|4x – 6| + 18

We can rewrite it into:

f(x) = 2|2*2x – 2*3| + 18

f(x) = 2*| 2*(2x - 3)| + 18

f(x) = 2*2*|2x -3 | + 18

f(x) = 4*|2x - 3| + 18

Thhis is what we can see on option B, so that is the correct one.

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The expression 1/14 x³y + 8/14 xy² can be rewritten as one fourteenth xy (x² + 8y).

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The given expression is [tex]\frac{1}{14}[/tex] x³y + [tex]\frac{8}{14}[/tex] xy².

We have to take the common factor of both the terms  [tex]\frac{1}{14}[/tex] x³y and [tex]\frac{8}{14}[/tex] xy² outside.

The common factor of both terms is  [tex]\frac{1}{14}[/tex] xy.

[tex]\frac{1}{14}[/tex] x³y + [tex]\frac{8}{14}[/tex] xy² =  [tex]\frac{1}{14}[/tex] xy (x² + 8y)

Hence the given expression can be rewritten as   [tex]\frac{1}{14}[/tex] xy (x² + 8y).

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2880 ways are there to list the digits { 1, 2, 2, 3, 4, 5, 6 } so that identical digits are not in consecutive positions.

The list of the digits is: { 1, 2, 2, 3, 4, 5, 6 }

Here we have to determine how many ways are there to list the digits { 1, 2, 2, 3, 4, 5, 6 } so that identical digits are not in consecutive positions

We have one number in consecutive positions in this question

That is: (2, 2)

Number of ways that (2,2) are in consecutive positions = [tex]$\frac{6!}{2!}[/tex] = 360

The permutation of 1, (2, 2), 3, 4, 5, 6 = 6!

6! = 720

To get the total number of permutations

= [tex]$\frac{7!}{2!}[/tex]

= [tex]$\frac{5040}{2}[/tex]

= 2520

The number of ways that 2 identical digits are not consecutively positioned

= 2520 - 360 + 720

= 2880

There are 2880 ways to list the digits { 1, 2, 2, 3, 4, 5, 6 }.

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The total number of possible passwords is 46,620, if the lock requires a three digit sequence of left-right-left and the number can not be repeated.

We have to find the total number of possible passwords, if the lock requires a three digit sequence of left-right-left and the number can not be repeated.

A school lock has a lock of 37 numbers from 0 to 36.

The possible different possibilities is;

At the first position have 37 choices.

At the second position have 36 choices because the first number is not be repeated.

At the third position also have 35 choices because the first and second number is not be repeated.

So, The total number of possible passwords = 37 × 36 × 35

The total number of possible passwords = 46,620 ways

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If the dimensions of the rectangular fish tank are n , 6 and 18 , then the polynomial in the standard form for Volume of fish tank is  V = 108n .

The dimensions of the fish tank in shape of rectangular prism re :

length = n , width = 6 and height = 18 ;

the formula to be used to calculate the volume of rectangular fish tank is written as : Volume = length × Width × Height ;

substituting the values in the volume formula ,

we get ;

Volume of tank = n × 6 × 18 ;

= n × 108 ;

= 108n .

Therefore , the polynomial in the standard form can be written as V = 108n .

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The required selling price of the game after two discount is $63.75.

The term discount designates a sum or a percentage subtracted from an item's usual selling price. Make sure you need all of the items you plan to get before waiting until after the holiday to make a purchase. A discount is a decrease in the cost of a commodity or service. ​

Discount = 25%,

Additional discount = 15%

Then,

Net discount is = 36.25%

We have,

Price of game = $100

Discount amount = 36.25% of $100 = $36.25

So, the selling price of the game after discount = $100 - $36.25

= $63.75

Thus, required selling price of the game is $63.75.

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The equation of the total cost for the cover charge and drinks in point-slope form is y = 6x + 5.

The point-slope form of a linear equation is given by -

 [tex]y - y_1 = m(x- x_1)[/tex]

where m is the slope and [tex](x_1, y_1)[/tex] is a point on the line.

Here, the total cost for the cover charge and drinks can be represented by the equation y = mx + b, where y is the total cost, x is the number of drinks, m is the cost per drink, and b is the cost of the cover charge.

We know that the cover charge is $5 and drinks are $6 each, so, we can find the slope (m) of the equation by using the cost per drink which is m = 6.

We can also find the point [tex](x_1, y_1)[/tex] by using the cover charge cost which is (0,5).

Therefore, the equation in point-slope form of the total cost for the cover charge and drinks will be -

y - 5 = 6(x-0)

y - 5 = 6x

y = 6x + 5

Where x is the number of drinks and y is the total cost i.e. cover charge + drinks.

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Answer: 1/3 per friend.

Step-by-step explanation:1/3 1/6*4= 3/3 or 1 whole bag. to find the 1/6, 2/3 multiply by 1/4= 2/12 or 1/6 of popcorn per friend

The system that has the solution (-2, -2, -2) is the one in option C.

x + 2y = -6

y + 2z = -6

x - y - z = 2

We want to see which of the given systems has the solution (-2, -2, -2).

To check that, we only need to evaluate all the equations of the system on these values and see if all the equations are true.

If we look at the third system we will get:

x + 2y = -6

y + 2z = -6

x - y - z = 2

Replacing all the values of the point we get:

-2 + 2*(-2) = -6

-2 + 2*(-2) = -6

-2 + 2 + 2 = 2

All these equations are true, thus, the correct option is C.

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Figure ABCDE has vertices A(−3, 3), B(2, 3), C(5, −2), D(0, −3), and E(−3, −2) So the Area of figure = 36.5 sq units

To Find: Plot the points  

Decompose Figure ABCDE into rectangles and triangles.

lengths of Sides AB and AE.

area of Figure ABCDE

Plot ( x , y) ( x , y)

If x is positive, start right away from the origin. If it's negative, turn left.

If +ve, move y upward; if -ve, move y downward.

Plotted and labeled points

A(−3, 3), B(2, 3), (2, 3),

AB's length is five.

A(−3, 3) E(−3, −2).

AE length is 5

two triangles and one rectangle

area of a rectangle equal 5 * 5, or 25 square units.

The right angle triangle's area is equal to (1/2) * 5 * 3 = 7.5 square units.

another triangle's area is equal to (1/2) * 8 * 1 square units.

Figure's surface area is 25 + 7.5 + 4 = 36.5 sq units.

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The bag can hold a maximum of 53 pounds before breaking, and Ani has already placed 29 pounds in the bag. To find out how many more pounds she can place in the bag, we can subtract the weight already in the bag from the maximum weight the bag can hold:

53 - 29 = 24

So Ani can place 24 more pounds in the bag before it breaks.

The inequality to represent this situation is:

weight in bag + x <= 53 (x represents the amount of weight Ani can put in the bag before it breaks)

To find the solution, we can substitute the value of weight in bag and get

29 + x <= 53

Now we can solve the inequality for x

x <= 24

The solution is x <= 24, which means Ani can place 24 more pounds or less in the bag before it breaks.

To graph the solution, we can start with the number line, and plot the point 24 to the right of the origin, and shade the region to the left of the point. This represents the solution set of x <= 24, which means Ani can place 24 more pounds or less in the bag before it breaks.

The distance travelled by the car during this time  by using single  appropriate trapezium is  26.25 and the answer provided is an underestimate

A) Using a single appropriate trapezium, the estimated distance travelled by the car during the 30 seconds is approximately 55 metres.

This is calculated by taking the area of the trapezium formed by the two points of the speed graph: 8m/s and 6m/s.

The area is calculated by taking the average of the two points, multiplied by the time duration:

Area = (8+6/2) * 30

Area = 7*30

Area = 210

The area of the trapezium is then divided by the speed of the car at the start of the journey (8m/s) to get the estimated distance travelled:

Distance = 210/8

Distance = 26.25

This is rounded up to give an estimated distance travelled of 55 metres.

B) The answer of 55 metres is an underestimate of the actual distance travelled by the car. This is because the trapezium method only takes into account the start and end points of the graph, and not any of the other points in between. The actual distance travelled by the car is likely to be higher as the speed of the car is likely to have been greater at points in between the start and end points.

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