You have a cup with 17 coins inside. The total inside the cup is $5. 50. Determine how many half dollars and quarters are inside the cup. Use a system of equations. Be sure to define the variables and show all work

The graph of the given line 2x+3y=6 intersects the Y-axis at (0,2).

For the graph of linear equation to intersect the Y-axis, its X-co-ordinate should be zero or the abscissa is zero as Y-axis as the equation of Y-axis is x=0. Also the set of coordinates should satisfy the equation.

According to the first condition the x-coordinate of the equation should be zero so in equation 2x+3y=6 substituting the value of x as zero  2(0)+3y=6

3y=6  

y=6/3=2

So at point (0,2), the graph of the given line 2x+3y=6 intersects the Y-axis.

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The mass of the second object will be 3.5 kg.

In Newtonian mechanics, momentum is calculated as the sum of an object's mass and velocity. It has both a magnitude and a direction, making it a vector quantity.

According to the collision theory, for a chemical reaction to take place, the reacting particles must come into contact with one another. The frequency of collisions affects the reaction's rate. According to the idea, responding particles frequently encounter without reacting.

The final momentum will be calculated by the expression given below,

(m₁ + m₂ ) V=250

( 1.5 + m₂ 0 x 50 = 250

1.5 + m₂ = 5

m₂ = 5 - 1.5

m₂ = 3.5 kg

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On solving the provided question, we can say that by equation 60 miles from his home is the appointment

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

for d and t

60 = d/t

45 = d / t + 0.33

60t = d

45( t + 0.33) = d

60t = 45t + 15

t = 1 hour

d = 60 X 1 miles = 60 mile

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The value of x in the similar polygons is 7.

Two polygons are similar if their corresponding angles are congruent and their corresponding sides are in proportion.

Therefore, the polygons WXY and STU are similar.

Hence, using proportion, let's find the value of x

3 / 9 = 4 / x + 5

cross multiply

3(x + 5) = 9 × 4

3x + 15 = 36

subtract 15 from both sides of the equation

3x + 15 - 15 = 36 - 15

3x = 21

divide both sides by 3

x = 21 / 3

x = 7

Therefore,

x = 7

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The distance from point A to point B is 781.5 ft.

Since the angle of elevation from point A to the lighthouse is 15 degrees, use the tangent function to find the height of the lighthouse. Let x be the height of the lighthouse,

tan(15°) = x / 862

Solve for x.

x = 862 (tan(15°))

Similarly, let y be the distance from point B to the lighthouse,

tan(8°) = x / y

Solve for y.

tan(8°) = 862 (tan(15°)) / y

y = 862 (tan(15°)) / tan(8°)

y = 1643.45 feet

Subtract 862 from 1643.45 to get the distance from point A to point B.

distance from point A to point B = 1643.45 - 862 = 781.45 ft = 781.5 ft

Therefore, the distance from point A to point B is 781.5 ft.

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Answer:

The fixed cost to insure jewellery is $0.602.

Step-by-step explanation:

We can use the information provided to set up a system of two equations in two variables, and then use the system to solve for the fixed cost of insuring the jewellery. Let x be the fixed cost and y be the percentage of the value of the jewellery. Then we can write the following two equations:

1000x + 1000y = 32 (1) (cost equation for insuring $1000 worth of jewellery)

3500x + 3500y = 44.5 (2) (cost equation for insuring $3500 worth of jewellery)

We can use either of these equation to solve for the fixed cost(x), to do that we can first solve for y from either of the equation, and then substitute it in other equation.

From equation (1)

y = (32 - 1000x) / 1000

then substitute this in equation (2)

3500x + 3500((32-1000x) / 1000) = 44.5

3500x + 32 - 3500x =44.5 - (1000x)

-20x = -12.05

x = 0.602 $

So, the fixed cost to insure jewellery is $0.602.

That means you have to pay $0.602 as a fixed cost, in addition to 0.01(y) as a percentage of the value of jewellery to insure it.

Kate needs to buy 453.6 ft2 of mulch for her 12 ft radius garden, which is equal to 76.3 cubic feet when multiplied by the desired depth.

Kate needs to purchase 453.6 cubic feet of mulch for her garden. To figure this out, she needs to first calculate the area of her garden using the formula A = πr2, where A is the area of the garden and r is the radius. In this case, the area of Kate’s garden is 453.6 ft2. For example, if she wants to put down 2 inches of mulch, she would need to purchase 453.6 ft2 x 0.167 ft = 76.3 cubic feet. This calculation can be adjusted depending on the depth of mulch desired. For example, if Kate wants to put down 3 inches of mulch, she would need to purchase

453.6 ft2 x 0.25 ft = 113.4 cubic feet

A = πr2

A = π(12)2

A = 453.6 ft2

Mulch = A x depth

Mulch = 453.6 ft2 x 0.167 ft

Mulch = 76.3 cubic feet

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The solutions of the quadratic equation 3x² − x + 8 = 0 are as follows;

x = 0.1667 + 1.6245i

x = 0.1667 - 1.6245i

In Mathematics, the standard form of a quadratic equation is given by this mathematical expression;

ax² + bx + c = 0

Mathematically, the quadratic formula is modeled or represented by this mathematical expression:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]

From the information provided above, we can logically deduce the following data values (parameters);

3x² − x + 8 = 0

Where:

Substituting the data values (parameters) into the quadratic formula, we have the following;

[tex]x = \frac{-(-1)\; \pm \;\sqrt{(-1)^2 - 4(3)(8)}}{2(3)}\\\\x = \frac{1\; \pm \;\sqrt{1\; - \;4(3)(8)}}{2(3)}\\\\x = \frac{1\; \pm \;\sqrt{1\; - \;96}}{6}[/tex]

x = (1 ± √95)/6

x = (1 + √95)/6 = 0.1667 + 1.6245i

or

x = (1 - √71)/6 = 0.1667 - 1.6245i

In conclusion, i represents a complex number.

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Complete Question:

Find the solutions of the quadratic equation 3x² − x + 8 = 0.

The question is asking for the value of a quantity that decays continuously at a rate of 0.1% per hour. We are given that the initial value of the quantity is 7800 and are asked to find the value after 1.25 days (30 hours).

What is a ratio in mathematics?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).

We can use the following formula to find the final value of the quantity after a certain amount of time:

final value = initial value * (1 - decay rate)^time

Where decay rate is given as a decimal (0.1% = 0.001)

Plugging in the given values, we get:

final value = 7800 * (1 - 0.001)^30

The final value is around 7396.65

Rounding the final value to the nearest hundredth, the final value after 1.25 days is:

7396.65 ≈ 7396.66

The value of the quantity after 1.25 days, to the nearest hundredth is 7396.66.

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The answer to the given that is 7x 5 2x question is  70

Explanation: In this case the answer is calculated by performing the operations in the order they are written. First, we multiply 7 and 5, which gives us 35. Then, we multiply 2 and x, which gives us 2x. Finally, we add 35 and 2x, resulting in 70

Multiplication is an arithmetic operation that involves multiplying two numbers together to produce a third number. It is usually represented by the multiplication sign (×) and is one of the four basic operations in mathematics. Hence the correct answer is 70.

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x = 6 does not satisfy the given equation.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that an equation, 5(x – 3) = x + 13

Checking if x = 6 satisfy the equation or not,

5(x – 3) ? x + 13

5(6-3) ? 6+13

5×3 ? 19

15 ≠ 19

Hence, x = 6 does not satisfy the equation.

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Recursive formula for a(n) , the nth term of the sequence is

⇒ a(n) = 125 × (5)ⁿ⁻¹

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

We have to given that;

The sequence is,

⇒ 125, - 25, 5 , ....

Clearly, The sequence is a geometry sequence with common ratio - 5 and first term 125.

We know that;

The nth term of geometry sequence is,

⇒ a(n) = a rⁿ⁻¹

Where, 'r' is common ratio and 'a' is first term of the sequence.

Substitute all the values, we get;

The nth term of the given sequence is,

⇒ a(n) = a rⁿ⁻¹

⇒ a(n) = 125 × (5)ⁿ⁻¹

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The equation of the straight line in slope - intercept form will be y = (1/4)x - 2.

The slope - intercept form of a line is -

y = mx + c                                                     ... { 1 }

where -

{m} is slope of line.
{c} is y - intercept of the line.

Given is the slope of the line as {m} = 1/4 and the y - intercept as {c} = -2.

From Eq { 1 }, we can write the slope - intercept form as -

y = mx + c

y = (1/4)x - 2

Therefore, the equation of the straight line in slope - intercept form will be y = (1/4)x - 2.

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Answer:

Answer: Tomatoes If you multiply 10 x 0.69 (for onions) it would be 6.9If you multiply 100 x 0.99 (for tomatoes) it would be 99Lastly, if you multiply 100 x 0.69 (for lettuce) if would be 69Which are the most? Tomatoes.~ Hope this helps

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Based on the information provided, it seems that the product that should be displayed in the window in July is Product 5.

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the dataset's total number of values by the sum of all of those values yields this result. Both raw data and data that have been combined into frequency tables can be used for calculations. Average refers to a number's average. It is straightforward to calculate:

Divide by how many digits there are after adding up all the digits. the total divided by the count.

Based on the information provided, it seems that the product that should be displayed in the window in July is Product 5. This can be determined by looking at the sales data for each product over the months of January through June.

In every month, Product 5 has the highest sales figures among all the products. This suggests that Product 5 is the most popular among customers and would likely attract the most attention if it were to be placed in the window.

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12.57 cm is the length of the label on bottle.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that a  bottle of Buckley's has a radius of 2cm

You need to create a label for this product

We need to find the length of this label.

Means we need to find the circumference of the bottle.

The formula for circumference is

C=2πr

Given radius is 2cm

C=2×3.14×2

C=12.57 cm

Hence, 12.57 cm is the length of the label on bottle.

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Answer:

<1 and  <2  are Complementary Angles

m<1  + <2  = 90 degrees

Step-by-step explanation:

<1 and  <2  are Complementary Angles

m<1  + <2  = 90 degrees

Have a great day!

Since, angle 1 and 2 sums up to make 90 degrees, hence Angle 1 and 2 are complementary angles.

Complementary angles are those whose combined angle is exactly 90 degrees. 30 degrees and 60 degrees, for instance, are complementary angles.

Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°. In the same way, complementary angles sum to 90 degrees.

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Radical expression can be defined as the expression containing square root and rational exponent , which is in the form of p/q form.

What is an Algebraic expression ?

Algebraic expression can be defined as combination of variables , constants and exponents.

Radical expression, in which if the expression contains square root than it called as the radical expression.

Examples are  : - [tex]\sqrt{7}[/tex] , [tex]\sqrt{x}[/tex] and etc .

Rational exponent , in which it is in the form of p/q is called as the rational exponent .

Examples are :- 5/8 , 6/9,8/7 and etc .

Hence, Radical expression can be defined as the expression containing square root and rational exponent , which is in the form of p/q form.

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Answer: Jana

Step-by-step explanation: because she has the highest ratio 48 over 60 > 45 over 60

I did the test

On solving the provided question, we can say that - the each angle of pentagon is x = 108

A pentagon is a polygon with five sides that is used in geometry. The inner angles of a straightforward pentagon add up to 540°. Simple or self-intersecting pentagons are both possible. A pentagram is a self-intersecting regular pentagon. Five angles and all sides of a regular pentagon are equal. It is referred to as an irregular pentagon if the side lengths and angle measurements do not match. All outside angles, as far as we are aware, balance out inside angles. The polygon's exterior angle total is therefore equal to n(360°/n). There are five sides to a pentagon, therefore n must equal five. Consequently, 5(360°/5) = 360° is the sum of the pentagon's outer angles.

since all sum of pentagon is 540

so, 5x = 540

x = 108

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For the provide inquilty problem,

a) The feasible region lies in between the following equations,

b) The extreme points of feasible region are (2,5) , (6,1) ,(0,0),(6,0),(0,5).

Let consider, x = A and y = B, this changes your inequalities and equations as follows: Maximize x + 2y, such that:

x ≤ 6

y ≤ 5

2x + 2y = 14

x,y ≥ 0

We use graphical method, for getting the solution of problem. So, first change the Inequalities into equality equations.

we would then find the region of feasibility by looking at the areas on the graph that satisfy the inequalities and equations,

x ≤ 6

y ≤ 5

2x + 2y = 14 (this is an equation)

x ≥0

y ≥ 0

a) The graph will look like as present above : we can see that the feasible region is the area on the graph that is:

on or below the line y = 5

on or to the left of the line x = 6

on or above the line y-axis , y = 0

on or to the right of the x-axis, x = 0

on the line 2x + 2y = 14

This says is that your solution has to be on the line of 2x + 2y = 14, have an x-coordinate that is greater than or equal to 0 and less than or equal to 5 and have a y-coordinate that is greater than or equal to 0 and less than or equal to 5. The maximum or minimum value should be at the corner points of the feasible region.

b) The corner points would be at (x,y) = (2,5) and (x,y) = (6,1). Also, plotted some other points on the line just to show the max/min value of function on the corner points of the feasible region.

(2,5) = 12

(4,3)= 10

(3,4) = 11

(6,1) = 8

the maximum solution is at the coordinate of (2,5) and all of your constraints have to be satisfied at the this point. The solution is that the maximum value is when x = 2 and y = 5, that is one of the corner points of the feasible region.

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Complete question:

Consider the following linear program:

Max. 1A+2B , s.t.

1A ≤6

1B≤5

2A+2B=14

A,B>0

a. Show the feasible region.

b. What are the extreme points of the feasible region?

Answer:

2,30

the difference between 3,45 and 4,60 is 1,15. So if you add 1,15 and 1,15 it will be 2,30. you can't do 1,10 because the rate is 1,15 neither can you do 6,85 because 5,75 plus 1,15 is 6,90 not 6,85 so 2,30 is the final choice.

In the recorded test scores 90 is the mode, as it appears most frequently in the set of ff test scores.

Job applicants submitted their ff test results, which were as follows: 65, 68, 70, 75, 88, 90, 90, 91, and 92. Following that, the Mean (Average) is 81, Median (Middle) is 88, and Mode (Most Common) is 90. The mode can be calculated quite easily.

After sorting the numbers in a set according to their order—lowest to highest or highest to lowest—count how many times each number appears in the group.

The mode is the one that is most prevalent. the quantity that happens the most frequently, or the quantity that appears the most frequently overall. The mode of the numbers 4, 2, 4, 3, 2, and 2 is 2, since it appears three times, more than any other number. The most frequent number in a set of numbers is called the mode.

To find the mode, we first need to put the test scores in order from lowest to highest:

65, 68, 70, 75, 88, 90, 90, 91, 92

Then we can count how many times each number appears:

65: 1 time

68: 1 time

70: 1 time

75: 1 time

88: 1 time

90: 2 times

91: 1 time

92: 1 time

As we can see, the number 90 appears the most with 2 times, so the mode of this set of data is 90.

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Answer:

1. FC = 6

2. BC = 10

3. EC = 7

4. BA = 12

5. BC = 7

Step-by-step explanation:

⭐What is the centroid of a triangle?

Using the properties of a centroid, we can determine the lengths the problem is asking us for.

1. If CD = 12, find FC.

So if the median we need to look at is FD,

then CD : FC = 2:1

[tex]\frac{CD}{FC} = \frac{2}{1}\\\\\\\\[/tex] . . . . . . . . write the proportion

[tex]\frac{12}{FC} = \frac{2}{1}[/tex] . . . . . . . . . substitute the known values

[tex]12 = 2FC[/tex] . . . . . .  cross multiply

[tex]FC = 6[/tex] . . . . . . divide both sides by 2 to isolate FC

∴ FC = 6

2. If BG = 15, find BC

So if BG = 15, and BC is the distance from a vertex to the centroid, then BC is 2/3 of BG.

[tex]BC = \frac{2}{2}BG[/tex] . . . . . write equation

[tex]BC = \frac{2}{3}(15)[/tex] . . . . . substitute known values

[tex]BC = \frac{30}{3}[/tex] . . . . . . . . multiply numerators

[tex]BC = 10[/tex] . . . . . .  . . compute

∴ BC = 10

3. If AE = 21, find EC

So if AE is the full median, and EC is the distance from the centroid to the opposite side of a vertex, then EC is 1/3 of AE.

[tex]EC = \frac{1}{3}AE[/tex] . . . . . . . . write equation

[tex]EC = \frac{1}{3}(21)[/tex] . . . . . . . . substitute known values

[tex]EC = \frac{21}{3}[/tex] . . . . . . . . . . . multiply the numerators

[tex]EC = 7[/tex] . . . . . . . . . . . . compute

∴ EC = 7

4. If FA = 6, find BA

If BA is a side length that is bisected by a median, then FA is 1/2 of BA.

[tex]FA = \frac{1}{2}BA[/tex] . . . . . . . make equation

[tex]FA = \frac{1}{2}(6)[/tex] . . . . . . . . substitute known values

[tex]FA = \frac{6}{2}[/tex] . . . . . . . . . . . multiply the numerators

[tex]FA = 3[/tex] . . . . . . . . . . . compute

∴ FA = 3

5. If CG = 3.5, find BC

So if the median we need to look at is BG,

then BC : CG = 2:1

[tex]\frac{BC}{CG} = \frac{2}{1}[/tex] . . . . . . . . . . create the proportion

[tex]\frac{BC}{3.5} = \frac{2}{1}[/tex] . . . . . . . . . . substitute the known values

[tex]BC = 2(3.5)\\[/tex] . . . . . . . . cross multiply

[tex]BC = 7[/tex] . . . . . . . . . . . . . compute

∴ BC = 7

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Answer:

To enclose the rectangular garden, Owen will need to put fencing along the length of the garden, which is 25 feet, and along the width of the garden. He wants to use less than 8 feet of fencing, so the width of the garden must be less than 8 feet.

The total amount of fencing needed will be equal to the length of the garden plus the width of the garden, multiplied by 2 (since there are two sides to the garden for each of the length and width).

For example, if the width of the garden is 5 feet, the total amount of fencing needed will be 25 + 5 + 25 + 5 = 60 feet, which is less than 8 feet.

So, the width of the garden can be any value less than 8 feet.

Step-by-step explanation:

Fourteen types of angles are Acute Angles, Obtuse Angles, Right Angles, Straight Angles, Reflex Angles, Positive Angles, Negative Angles, Complementary angles, Supplementary angles, Linear Pair, Adjacent angles, Vertically Opposite angles,  Alternate interior angles and Alternate exterior angles.

There are mainly 5 types of angles based on their magnitude. They are Acute Angles, Obtuse Angles, Right Angles, Straight Angles and Reflex Angles.

Positive Angles and Negative Angles are the angles based on the direction of measurement or the direction of rotation.

When two angles are paired, then there exist different angles, such as Complementary angles, Supplementary angles, Linear Pair, Adjacent angles, Vertically Opposite angles,  Alternate interior angles and Alternate exterior angles.

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Answer: Let x be the number of players who can attend the game. The total cost for the tickets is $45 per ticket * x tickets + $4 per ticket * x tickets + $20 flat fee = $49x + $20. We can write this as an inequality as follows:

49x + 20 <= 1500

To solve this inequality, we need to isolate the x term on one side of the inequality. We can do this by subtracting 20 from both sides:

49x <= 1480

Then, we can divide both sides by 49 to find the value of x:

x <= 30

Thus, if their budget is $1500, the football team can purchase tickets for at most 30 players to attend the game.

Step-by-step explanation: