Students in band are selling oranges and grapefruit to earn money for a trip. Mrs.Whitten purchased three boxes of oranges and two boxes of grapefruit from a student for a total of $22.50. Mr. Rutig purchased one bag of oranges and four boxes of grapefruit, spending a total of $28.50. How much is one box of oranges?

4x - 3y = 16

x + y = -3

Subtract y from both sides of the 2nd equation.

x = -3 - y

Now that we have a value of x, we can plug it into the first equation to solve for y.

4(-3 - y) - 3y = 16

Distributive property.

-12 - 4y - 3y = 16

Combine like terms.

-12 - 7y = 16

Add 12 to both sides.

-7y = 28

Divide both sides by -7.

y = -4

The value of y is -4, and now we can solve for the value of x.

Plug this value into either equation.

x + (-4) = -3

Add 4 to both sides.

x = 1

The value of x is 1.

To solve the linear equations 4x-3y=16 and x+y=-3, we can use substitution. The solution is x = 1 and y = -4.

To solve the linear equations 4x-3y=16 and x+y=-3, we can use the method of substitution or elimination. Let's use substitution:

From the second equation, we have x = -3-y. Now substitute this value for x in the first equation:

4(-3-y) - 3y = 16

-12 - 4y - 3y = 16

-7y = 28

y = -4

Substitute the value of y back into the second equation to find x:

x + (-4) = -3

x = -3 + 4

x = 1

Therefore, the solution to the linear equations is x = 1 and y = -4.

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (3, 5) and (4, 6). Substitute:

[tex]d=\sqrt{(4-3)^2+(6-5)^2}=\sqrt{1^2+1^2}=\sqrt{1+1}=\sqrt2\approx1.4[/tex]

The distance between the two points is 1.4.

Option D is the correct answer.

The distance between two points of a line is given as:

Distance =  √(c - a)² + (d - b)²

We have,

To find the distance between the two points (3, 5) and (4, 6)

We can use the distance formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Substituting the given values, we get:

d = √((4 - 3)² + (6 - 5)²)

d = √(1² + 1²)

d = √2

To the nearest tenth, the distance is approximately 1.4.

Therefore,

The distance between the two points is 1.4.

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[tex]sin30^o=\frac{9}{a}\\\frac{9}{a}=\frac{1}{2}\\a=2\cdot9\\a=18[/tex]

Answer:

B. 18  

Step-by-step explanation:

We have been given a diagram of a right triangle and we are asked to find the value of a.

Since we know that Sine relates the opposite with hypotenuse of a right triangle.  

[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

Upon substituting our given values we will get,

[tex]sin(30^o)=\frac{9}{a}[/tex]

Upon substituting [tex]sin(30^o)=\frac{1}{2}[/tex] in above equation we will get,

[tex]\frac{1}{2}=\frac{9}{a}[/tex]

Now let us cross multiply our equation to solve for a.

[tex]1\cdot a=9\cdot 2[/tex]

[tex]a=18[/tex]

Therefore, the value of a is 18 and option B is the correct choice.

Answer:

n=6

Step-by-step explanation:

n= the amount of boxes he needs

so if he puts 30 toys in each box out of 180 you divide 180 by 30 and you get your answer.

so the amount of boxes he needs = 6

Final answer:

To find the number of boxes needed to pack 180 cat toys with 30 toys in each box, divide the total number of toys by the number of toys per box to get the answer of 6 boxes.

Explanation:

The number of boxes Aroon needs can be calculated by dividing the total number of cat toys by the number of toys packed in each box.

Let n represent the unknown factor, which is the number of boxes he needs.

The equation representing this situation is n = 180 ÷ 30.

Solving n = 6, Aroon needs 6 boxes to pack all 180 cat toys.

Answer:

slope =4

Step-by-step explanation:

The slope intercept equation of a line is written in the form

y= mx+b

where m is the slope and b is the y intercept.

Since y =4x+5 is written is this form, we can see that 4 is the slope and 5 is the y intercept

Answer:

D 72/27

Step-by-step explanation:

both are divisible by 9

Answer:

D. 72/27

Step-by-step explanation:

8/3

We will try to match the denominator

to get to 9 we will multiply by 3/3

8/3 *3/3 = 24/9

To get to 27 we will multiply by 9/9

8/3 *9/9 = 72/27  

A. 24/25

B. 16/9  

C. 28/9

D. 72/27  Yes

Counting in early childhood settings is best described as the D) basic ordering of numbers and identification by written number.

The question relates to the concepts children learn during their early mathematical development. The answer to the question is Basic ordering of numbers and identification by written number. This encompasses the fundamental process of recognizing numerical order and associating the spoken number with its written symbol. Counting in the early childhood setting involves learning the sequence of numbers, recognizing the relationship between the number and the quantity it represents, and connecting spatial understanding with numerical concepts.

Activities such as playing numerical board games, like Chutes and Ladders, are particularly beneficial as they involve working with numbers in a variety of ways - verbally, spatially, kinesthetically, and concerning time. This multisensory approach supports the development of numerical magnitudes, which are crucial for later mathematics achievement. The cognitive development in the area of mathematics reveals that engaging in numerical activities helps bridge the mathematical knowledge gap often observed between children from different socioeconomic backgrounds.

Answer: 3(7+q)

Step-by-step explanation:

Answer:

The simplified form of [tex]3(2+q) + 15[/tex] is 3(7+q)

Step-by-step explanation:

Given: 3(2+q) + 15

Step 1: Multiply bracket with 3

[tex]=3\times (2+q)+15[/tex]

Step 2: Now combine like terms

[tex]=6+15+3q[/tex]

Step 3: Add the combined terms

[tex]=21+3q[/tex]

Step 4: taking 3 common :

[tex]=3(7+q)[/tex]

The simplified form of [tex]3(2+q) + 15[/tex] is 3(7+q)

Answer:

The rangers

Step-by-step explanation:

Their number of wins didn't go up. In fact their wins decreased the most.

Answer:

D

Step-by-step explanation:

Improvement means positive change. The one with the least positive difference is the Rangers because they became WORSE by more than 10, which is bigger than even the Jets' negative amount.

Answer:46

Step-by-step explanation:Regular polygons are shapes made of straight lines with certain relationships among their lengths. For instance, a square has 4 sides, all the same length. A regular pentagon has 5 sides, all the same length. For these shapes, there are formulas for finding the area. But for irregular polygons, which are made of straight lines of any length, there are no formulas, and you need to be a little creative to find the area. Fortunately, any polygon may be divided into triangles, and there is a simple formula for the area of triangles.

Label the vertices (points) of the polygon starting with 1 at an arbitrary vertex and continuing clockwise around the polygon. There should be as many vertices as there are sides. E.g. for a pentagon (five sides) there will be five vertices.

Draw a line from vertex 1 to vertex 3. This will make one triangle, with vertices 1, 2, and 3. If there are only 4 sides, it will also make a triangle with vertices 1, 3 and 4.If the polygon has more than 4 sides, draw a line from vertex 3 to vertex 5. Continue in this way until you run out of vertices.

Compute the area of each triangle. The formula for the area of a triangle is 1/2 * b * h, where b is the base and h is the height.

Add up the areas, and this is the area of the polygon.

Answer:

98 sq yd

Step-by-step explanation:

46 is NOT the right ans n the method of dividing into triangles is not the best way.

the polygon is a rectangle minus a triangle.

the triangles sides are 3,4 n 5

it is a right-angle triangle cuz' 3^2 + 4^2 = 5^2

so the triangle area = base x height /2

= 3x4/2 = 6

rectangle area = length x width

= 13*8 = 104

so the polygon's area = 104 - 6

= 98 sq yd

The completed table would look like this:

Snack Type                Number Sold                 Percentage

Fruit Cup                          6                        18.75%

Veggie Sticks                         6                        18.75%

Chips                                 14                        43.75%

Water                                 4                          12.5%

Veggie Sticks:

Look at the "number of items sold" column for veggie sticks. It shows 6.

Divide the number of veggie sticks sold by the total number of snacks sold (32) and multiply by 100% to find the percentage.

(Number of veggie sticks) / (Total number of snacks) * 100%

= 6 / 32 * 100%

= 0.1875 * 100%

= 18.75% (round to two decimal places)

Chips:

Look at the "number of items sold" column for chips. It shows 14.

Follow the same steps as for veggie sticks:

(Number of chips) / (Total number of snacks) * 100%

= 14 / 32 * 100%

= 0.4375 * 100%

= 43.75% (round to two decimal places)

Water:

Look at the "number of items sold" column for water. It shows 4.

Follow the same steps as for veggie sticks and chips:

(Number of water bottles) / (Total number of snacks) * 100%

= 4 / 32 * 100%

= 0.125 * 100%

= 12.5% (round to two decimal places)

Therefore, the completed table would look like this:

Snack Type Number Sold Percentage

Fruit Cup 6 18.75%

Veggie Sticks 6 18.75%

Chips 14 43.75%

Water 4 12.5%

For complete question refer to image:

Answer:

PLEASE GIVE BRAINLIEST

Step-by-step explanation:

30% + 25% =55%

55/100 = 11/20

Final answer:

The cabinet is 52 inches tall and the football team scored 5 field goals.

Explanation:

1)To find out how tall the cabinet is with 4 drawers each being 13 inches tall, you would multiply the number of drawers by the height of each drawer. So it would be 4 drawers into 13 inches per drawer.
2)For the football team scoring question, since a field goal is worth 3 points and the team scored 15 points from field goals, you would divide the points scored by field goals by the number of points a single field goal provides. It would be 15 points ÷ 3 points per field goal.

Answers:

1)The cabinet is 52 inches tall.

2)The team scored 5 field goals.

Final answer:

Marcus's final elevation after the hike, starting from 3712 feet and dropping 50 feet, is 3662 feet.

Explanation:

Marcus starts his hike at an elevation of 3712 feet. If the trail drops 50 feet in elevation from beginning to end, we can find his final elevation by subtracting that drop in elevation from his starting elevation.

The calculation would be:
Starting elevation - Elevation drop = Final elevation

So, it will look like this:
3712 feet - 50 feet = 3662 feet

Therefore, Marcus's final elevation would be 3662 feet.

Answer:

2n/7=20

Step-by-step explanation:

let n be the number

Answer: 2x/7 =20

Step-by-step explanation:

Hi, to answer this question we have to write an equation.

Quotient means the result of the division of 2 numbers. In this case we have to divide twice a number (a number "x" multiplied by 2) by 7.

Mathematically speaking:

2x/7

That quotient is equal to 20.

So, the final equation is:

2x/7 =20

Feel free to ask for more if needed or if you did not understand something.

Answer:

[tex]A=\frac{C^2}{4\pi ^2}[/tex]

Step-by-step explanation:

Recall to find the circumference of a circle the formula is [tex]C=\pi d[/tex] or [tex]C=2\pi r[/tex]. We will also need the formula for the area of a circle which is [tex]A=\pi r^{2}[/tex]. Since the area formula is in terms of r we will use the second formula for circumference.

We start by solving for r in the Circumference formula.

[tex]C=2\pi r\\\frac{C}{2\pi } =r[/tex]. We input this value of r into the area formula.

[tex]A=\pi r^{2} \\A=\pi (\frac{C}{2\pi })^2\\A=\pi (\frac{C^2}{4\pi ^2 })\\A=\frac{C^2}{4\pi ^2}[/tex]

The formula for the area of a circle in terms of its circumference is A = (C²) / (4π), by substituting the expression for the radius r = C / (2π) into the area formula A = πr².

The student has asked how to use the formula for the circumference of a circle to write a formula for the area of a circle in terms of its circumference. The formula for the circumference (C) of a circle is C = 2πr, where π (pi) is approximately 3.14159 and r is the radius of the circle.

To write the formula for the area (A) in terms of the circumference, we first solve the circumference formula for r: r = C / (2π). Then we substitute this expression for r into the formula for the area of a circle, which is A = πr². This gives us A = π (C / (2π))², simplifying, we get A = (C²) / (4π).

Thus, the formula for the area of a circle in terms of the circumference is A = (C²) / (4π).

Answer:

The answer is 231

Step-by-step explanation:

Answer:

231

Step-by-step explanation:

Answer:

(a)

let m represents renting movie and c represents the total cost of buying a rental card.

As per the given statement: A video store charges $10 for a rental card plus $2 per movie.

⇒ c(m) = 2m + 10                      ......[1]

which implies that this equation represents the slope intercept form(i.e y = ax+b) where 2 is the slope and a y-intercepts of 10.

(b)

Graph of the given equation:

c(m) = 2m + 10

you can see in the figure given below.

(c)

now, to find the cost of buying a rental card and renting 6 movies.

⇒ m = 6 [ as m represents renting movie]

Substitute this m =6 in equation [1];

c(6) = 2(6) + 10

c(6) = 12 + 10

c(6) = 22.

Therefore, the total cost of buying a rental card and renting 6 movies is, $22.

Answer: If the rate of change is $1 = 78p, then if you have 160p, how much dollars you will get?

(if p are penys)

100p = 1 pound

if $1 = 78p = 0.78 pound

→ 1  pound = $1/0.78 = $1.28

→ 160*1 pound = $160/0.78 = $205.13

So if you change 160 pounds, you will get 205 dollars and 13 cents.

The number of dollars when 160 pounds is exchanged will be 205.13.

You may multiply the pounds by the exchange rate to get how many dollars you will receive for 160 pounds if the exchange rate is $1 = 78p.

160 pounds multiplied by the 78p to the dollar conversion rate results in:

160 pounds multiplied by 100 pence equals 16,000 pence.

Since there are 100 pence in a pound, we divide the amount in pence by 100 to get dollars:

16,000 p divided by 78p is $205.13

Consequently, if you convert 160 pounds to dollars at the current exchange rate of $1 = 78p, you will get around 124.80 dollars in return.

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Answer: Two sides are 7in, and the two other sides are 9.5 in.

Step-by-step explanation:

Since there are two sides that will be longer than the other two, 2.5 will be subtracted twice:

33in -2.5in -2.5in = 28in

Since there are 4 sides, 28in is divided by 4:

28in/4 = 7in

To find the 2 larger sides, add 2.5 back to the side length:

7in +2.5in = 9.5in

Parallelogram is a closed shaped quadrilateral in which the opposite sides are equal and parallel. The length of the parallelogram tile of the shorter side is 7 in and the length of the longer side is 9.5 in.

A store sells tiles in the shape of a parallelogram.

The perimeter of each tile is 33 inches.

One side of each tile is 2.5 inches longer than another side.

Parallelogram is a closed shaped quadrilateral in which the opposite sides are equal and parallel. As the opposite sides are equal in parallelogram thus the perimeter of the parallelogram is twice the sum of the two different sides.

Let l be the length of the shorter side. Thus longer side will be (2.5+l ).

Now the perimeter [tex]P[/tex] of the parallelogram tile can be given as,

[tex]P=2[l+(2.5+l)}[/tex]

[tex]33=4l+5[/tex]

[tex]4l=33-5[/tex]

[tex]l=\dfrac{28}{4}[/tex]

[tex]l=7[/tex]

Thus the length of the parallelogram tile of the shorter side is 7 in and the length of the longer side is 9.5 in.

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Answer:

she has a 70 percent chance of getting a yellow one

Step-by-step explanation:

Answer:

7/10 is your answer.

To find the perimeter of a rectangle in terms of x, add up the length and width and multiply by 2.

The perimeter of a rectangle can be found by adding up all four sides. In this case, the length and width of the rectangle are represented by the factors of the area measure:

10x² + 13x - 3 = (2x - 1)(5x + 3)

So the length is (2x - 1) and the width is (5x + 3). The perimeter can be calculated using the formula:

Perimeter = 2(length + width)

Substituting the values, the perimeter in terms of x is:

Perimeter = 2((2x - 1) + (5x + 3))

Simplifying further:

Perimeter = 2(7x + 2)

Perimeter = 14x + 4

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Answer:

D: y=2|x|-1

Step-by-step explanation:

We need to find the equation which describes the graph

The general form of equation for this graph is y=|x|

The graph opens upwards so its positive

We cannot choose option (a) and option (d) because it has -2

Lets check with option b  and d

In the graph, the y values starts at -1. (0,-1) is the vertex.

Lets plug in (0,-1)  and check with option b

y=2|x|+1

-1= 2|0|+1

-1=+1, its false.

Lets check with option (d)

y=2|x|-1

-1= 2|0|-1

-1=-1, its true

Option D is the answer

Answer:

10.8

Step-by-step explanation:

7.2 X 1.5 = 10.8

Assuming  two houses are 1.5 inches apart on the map. The actual distance between the houses is 10.8 miles.

Let x represent the actual distance

Given:

1 inch = 7.2 miles

1.5 inch =? miles

Hence:

1/ 7.2 = 1.5/ x

x= 7.2×1.5

x=10.8 miles

Inconclusion assuming  two houses are 1.5 inches apart on the map. The actual distance between the houses is 10.8 miles.

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The question is about coordinates on a coordinate plane, and the answer explains the concept of a coordinate plane and how to interpret coordinates.

The given question provides a set of coordinates: P(-4, 2), Q(6, 4), R(11, -2), and S(2, -3). These coordinates represent points on a coordinate plane.

In mathematics, a coordinate plane is a two-dimensional plane formed by two number lines, the horizontal x-axis and the vertical y-axis. The x-coordinate represents the horizontal position of a point, and the y-coordinate represents the vertical position of a point.

For example, point P is located at -4 on the x-axis and 2 on the y-axis. Similarly, point Q is at 6 on the x-axis and 4 on the y-axis. By understanding the coordinates of each point, we can determine their positions on the coordinate plane.

Answer:

7(50 + 3)

7(50) + 7(3)

371

Step-by-step explanation:

7(53)

50 can be written as (50 + 3)

∴7(53) = 7(50 + 3)

Proceeding with the above expression we get;

7(53) = 7(50 + 3)

         = 7(50) + 7(3)

Completing the above expression we get;      

  7(53) = 7(50) + 7(3)

            = 350 + 21

            = 371        

The polynomial x³-2x²+x-2 can be completely factorized by applying the technique of grouping and difference of squares, resulting in the complete factorization as (x-2)(x-1)(x+1).

The complete factorization of the polynomial x³-2x²+x-2 can be found by first factorizing it into simpler polynomials. The given polynomial can be rewritten as x³-2x²+x-2. It is now possible to apply grouping, pair the terms as (x³-2x²) and (-x²+x-2). This gives us x²(x-1)-1(x-2). Now, you can clearly see that you have a common factor (x-1) that you can take out from each set. This gives you your final answer of (x-2)(x²-1). Then apply further factorization on x²-1 to get (x+1)(x-1), because x²-1 is a difference of two squares. So, the complete factorization is (x-2)(x-1)(x+1).

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The complete factorization of the polynomial x^3 - 2x^2 + x - 2 is (x + 1)(x - 1)(x - 2).

The polynomial x^3 - 2x^2 + x - 2 can be factorized completely by using the Rational Root Theorem and synthetic division.

By testing various factors of the constant term -2 (±1 and ±2) and the leading coefficient 1, we find that x = -1 is a root of the polynomial.

Using synthetic division, we can divide the polynomial by (x + 1) to obtain the quotient x^2 - 3x + 2. This quadratic polynomial can be further factorized as (x - 1)(x - 2).

Therefore, the complete factorization of the original polynomial is (x + 1)(x - 1)(x - 2).

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Answer:

Option B - {(-3, 16), (0, 15), (3, 14)}

Step-by-step explanation:

Given : Equation [tex]\frac{1}{3}x+y=15[/tex].

To find : Which if the following are ordered pairs of this equation?

Solution :

Re-write the equation in linear equation format,

[tex]y=-\frac{1}{3}x+15[/tex]

Taking point, (-3,16)

We substitute x=-3,

[tex]y=-\frac{1}{3}(-3)+15[/tex]

[tex]y=1+15[/tex]

[tex]y=16[/tex]

It is true.

Taking point, (0,15)

We substitute x=0,

[tex]y=-\frac{1}{3}(0)+15[/tex]

[tex]y=0+15[/tex]

[tex]y=15[/tex]

It is true.

Taking point, (3,14)

We substitute x=3,

[tex]y=-\frac{1}{3}(3)+15[/tex]

[tex]y=-1+15[/tex]

[tex]y=14[/tex]

It is true.

Therefore, the ordered pairs are {(-3, 16), (0, 15), (3, 14)}.

So, option B is correct.

Answer:

Before cooling begins, the temperature of the water is 22°C.

Step-by-step explanation:

I think this is right

Answer:

Before cooling begins, the temperature of the water is 22°

22

°

C

.

Step-by-step explanation:

Answer:

A. 54 tenths

Step-by-step explanation:

The 4 is in the tenths place. 54 is read as fifty-four, so it is 54 tenths.