The granola is selling for $2.88 and weighs 18 ounces. The
flaked cereal is selling for $4.32 and contains 24 ounces.
Which is the better buy? Show your thinking.

To determine the number of solutions in a linear system without solving it, check their slopes. If the slopes are different, there is one solution; if the slopes are the same but the equations are different, there is no solution; if the equations are exactly the same, the solutions are infinite.

The 3  possible solutions of a system of equations are:

- Unique or one solution

- Infinite solutions

- No solution

In case of   a system of linear equations, we can determine the type of its solution as follows:

- If the slopes are different, then their graphs will intercept in one point. Hence, the system of linear equations will have one solution.

Example:

y = -3x - 2

5x + 2y = 15

The slopes of the line equations are different, hence the solution is unique

-  If the slopes are the same but the equation of the lines are different, the lines are parallel, hence they will not intercept. Therefore, there is no solution.

Example:

2x + 2y = 8

y = -x -5

These are parallel lines, hence, there is no solution

- If the linear equations are exactly (or can be transformed to exactly) the same equations, the solution is infinite.

Example:

2x + 2y = 8

4x = -4y + 16

Those two equations are exactly the same. Hence, the solutions are infinite.

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[tex]\angle CBE[/tex] and [tex]\angle DEB[/tex] are same-side interior angles.

There are 11 animals on a farm, some of which are goats, while others are ducks. The total number of legs on the ducks and goats is 34.

An expression, often known as an algebraic expression, is any mathematical statement that contains variables, numbers, and an arithmetic operation between them. For instance, the word m in the given equation is separated from the terms 4m and 5 by the arithmetic symbol +, as is the variable m in the expression 4m + 5.

In mathematics, an expression is referred to as an algebraic expression if it contains variables, constants, and algebraic operations (addition, subtraction, etc.). Expressions are made up of multiple terms.

Functions, variables, and numbers make up an expression (such as addition, subtraction, multiplication or division etc.) It is possible to contrast phrases and expressions.

There are 11 animals, and they have a combined total of 34 legs.

Set G and D to the number of goats and ducks, respectively.

Consequently, G = 11 - D when G + D = 11, and vice versa.

therefore 4G + 2D = 34

Using the value as a stand-in for G, we obtain 4(11 - D) + 2D = 34.

By expanding, we have 34 - 44 - 4 + 2D.

The answer is D = 5. Thus, G equals 6.

Proof (5 x 2) plus (6 x 4) equals 34.

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The graph of the given equation y=2x+1 is attached below.

There are many tools we can use to find the information of the relation which was used to form the graph.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

For example, when the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.

If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

The equation y=2x+1 gives the following information:

The slope is 2

The line intercepts is 1 on the y axis

First, we would put a point or a dot on (0,1) on the y axis. Then start making 2 points above and below my original point. IT would do this by using the slope 2/1.

By using my slope we know that (1,3) and (-1,-1).

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Answer:

x = 4, y = 12

Step-by-step explanation:

xy = -16

y = x + 8

substitute y = x + 8 into xy = -16

x(x + 8) = -16

x^2 +8x + 16 = 0

x = 4

sub x = 4 into y = x + 8

y = 4 + 8

y = 12

Answer:

It's B, -2, v/5 4, and 3².

Solving for x in the angle bisector which resulted to the proportion  x over 18 = 45 over 20 results to x = 40.5

In geometry, a line that divides an angle into two equal angles is referred to as an angle bisector.

By definition, a bisector is something that divides an object or a shape into two equal parts. A ray is said to be an angle bisector if it divides an angle into two equal portions of the same measure.

The division from angle bisectors gave rise to the proportion which is given by

x / 18 = 45 / 20

cross multiplying

x = 18 * 45 / 20

x = 40.5

hence x is solved to get 40.5

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Answer:

y = 90°

Step-by-step explanation:

Answer:

[tex]v=-18,14[/tex]

Step-by-step explanation:

[tex]2|v+2|-41=-9\\2|v+2|=32\\|v+2|=16\\\\v+2=16\\v=14\\\\v+2=-16\\v=-18[/tex]

Answer:

A = 80 cm²

Step-by-step explanation:

the area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

here b = 4 and h = 2 , then

A = 4 × 2 = 8 cm²

there are a total of 10 tiles required ( 5 black and 5 white ) , then total area is

A = 10 × 8 cm² = 80 cm²

The correct numbers to complete the statements given are 40, 400, and 4000.

This question requires you to complete a statement with a given number (40, 400 or 4000) to make the statement true by dividing the number by 40.1. To find the correct order the numbers must be place using division, let's find out the results of each of these divisions:

Based on the above, it can be concluded:

Based on this, the complete statements are:

Note: This question is incomplete; here is the complete question:

Use each of the numbers 4, 40, and 4000 once to make true statements.The value of ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯÷40.01 is close to 1

The value of ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯÷40.01 is much less than 1.

The value of ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯÷40.01 is much greater than 1.

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the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale is 4√5

What is altitude Class 9?

The altitude of a triangle is the perpendicular line segment drawn from the vertex to the opposite side of the triangle.

In geometry, a line segment is bounded by two distinct points on a line. Or we can say a line segment is part of the line that connects two points. A line has no endpoints and extends infinitely in both the direction but a line segment has two fixed or definite endpoints.

Let's call it x

According to Euclidean theorem x^2 = 5×16

x^2= 80 and

x = 4√5

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The terms of the expression are 5x², 9x and 6

Algebraic expressions are described as expressions that are composed of variables, factors, constants, coefficients and terms.

They are also known to be made up of arithmetic operation, such as;

It is also important to note that terms in algebraic expressions are seen as summands in a sum that may be different only by a actor.

They can be regrouped by the addition of  their coefficients. Like terms are those that has the same variables to the same powers or coefficients.

The types are;

5x², 9x and 6

Thus, they are 5x², 9x and 6

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The work done on the toy car is 164.4 J.

The formula for work is:

Work = force * distance

In this case, given that:

Force = 5.2 N

Distance = 32 m

So, the work is:

Work = force * distance

Work = 5.2 * 32

Work = 166.4 J

Hence, the work done is 164.4 J.

Force is described as the rate of change of momentum with respect to time, in which momentum is mass multiplied by velocity. Work is the product of displacement and the component of force in the direction of displacement. When work is done, then the kinetic energy of an object changes.

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Answer:

y = 72 and x = 36

Step-by-step explanation:

So firstly, the outside angle is 108, right? And the total of all angles in a triangle is 180 degrees. So:
180 - 108 = 72
Then the other angle, angle x, is also 72 degrees. That's because they are supplementary angles.
Now that we know x = 72 degrees. To find the y angle, you add 72 and 72 together. Which is 144.
Then you do 180 - 144. Which is 36. So, x = 72 and y = 36

I hope it helped you!

The graph of the system of equations y - 2x + 5 = 0 and y + 4x + 1 = 0 intersect at (0.667, - 3.667)

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, A system of equations y - 2x + 5 = 0 and y + 4x + 1 = 0.

Let's write the terms in the order x, y therefore,

y - 2x + 5 = 0

- 2x + y = - 5.

2x - y = 5.

And

y + 4x + 1 = 0.

4x + y = - 1.

The graph of the system of equations is attached in the image.

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a) The probability that a student will study and will pass is 0.765.

b) The probability that a student will pass is 0.715.

What is probability?

Simply put, probability is the likelihood that something will occur. When how an event will turn out is not known, one can discuss the likelihood of several outcomes.

Define some events -

A: A  student studies.

B: A student will pass.

Given that P(A)=0.85 and

P(B|A)=1-P([tex]\bar{B}[/tex]|A)

=1-0.10

=0.90

a) P(a student will study and will Pass)= P(A∩B)

= P(A)·P(B|A)

= 0.85×0.90

= 0.765

b) Given that P( student will either study or pass), the probability is -

=P(A∪B)= 0.8 then P(a student will pass)

=P(B)

It is known that P(A∪B)= P(A)+P(B)-P(A∩B)

Then P(B)=P(A∪B) -P(A) +P(A∩B)

=0.8-0.85 + 0.765

=0.715

Therefore, the probabilities are 0.765 and 0.715.

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Therefore ,we can conclude from answering the offered question that the region of the circle, triangle, and square is where the darkest area is. A=210-123 = 87 square units

A triangle is a polygon since it has three sides plus three vertices. It is one of the basic geometric forms. An illustration of a triangle with the sides A, B, and C is Triangle ABC. A distinct plane or triangle in Geometrical are discovered when the three aspects are not collinear. Three sides & three corners define a triangle as a polygon. The triangle's corners are defined as the locations where three sides converge. 180 degrees is the result of multiplying three triangle angles.

Here,

The total of the circle, triangle, and square's surface areas.

The region of the darkish area is comprised of the areas of the Circle, Triangle, and Square.

=>A = 210 – 123 = 87 square units

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The value of a is [tex]-\frac{12}{5}[/tex] if 2 is a zero of the polynomial [tex]$4 x^2-2 x+5 a$[/tex].

As per the given data, the polynomial is p(x) = [tex]$4 x^2-2 x+5 a$[/tex]

The polynomial is zero polynomial if x is 2

The places where a polynomial becomes zero overall are known as the zeros of the polynomial. The term "zero polynomial" refers to a polynomial with a value of zero (0).

Replace x with 2 we get

Therefore [tex]4(2)^2-2(2)+5 \mathrm{a}=0[/tex]

[tex]\Rightarrow[/tex] 4 (4) - 2 (2)+5 (a) = 0

[tex]& \Rightarrow[/tex] 16 - 4 + 5 (a) = 0

[tex]& \Rightarrow[/tex] 12 + 5 (a) = 0

Add -12 on both sides we get

12 + 5 (a) - 12 = 0 - 12

5 (a) = -12

Divided by 5 into both sides we get

a = [tex]-\frac{12}{5}[/tex]

Therefore the value of a is [tex]-\frac{12}{5}[/tex]

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The factors of given quadratic expression are (4a+3) and (a+6).

The factors are the polynomials which are multiplied to produce the original polynomial.

The given quadratic expression is 4a²+27a+18.

By splitting middle term method, we get

4a²+3a+24a+18

= a(4a+3)+6(4a+3)

= (4a+3)(a+6)

Therefore, the factors of given quadratic expression are (4a+3) and (a+6).

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Observational data collection might be best to study how voters might decide an upcoming ballot issue.

The majority of big data is observational data, such as bank transaction records, user viewing patterns on video streaming services, or social media posts. Observational data, however, can also be sparse data (based on just a few people).

In observational research, participants and phenomena are observed in their most natural environments. Instead of using structured environments like research labs or focus groups, this allows researchers to observe how their subjects make decisions and respond to situations in their everyday lives.

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The ratio for cos (cosine) of angle θ is: cos(θ) =  adjacent side of θ / hypotenuse

We know that in right triangle the cosine of an angle is nothing but the ratio of the side adjacent of  given angle to the hypotenuse.

In right tirnagle for an angle θ, the ratio for cosine of angle θ would be:

cos(θ) =  adjacent side of θ / hypotenuse

Consider following right triangle PQR with angle PQR = 90 degrees

Here, PR is the hypotenuse.

Assume that angle QPR measure α degrees and angle PRQ measures θ degrees.

By definition of cosine of angle θ,

cos(θ) =  adjacent side of θ / hypotenuse

cos(θ) =  QR / PR

And by definition of cosine of angle α,

cos(α) =  adjacent side of α / hypotenuse

cos(α) = PQ / PR

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a) The quadratic function is factored as follows: f(x) = 4(x - 0.5)(x + 2.5).

b) The x-intercepts of the quadratic function are given as follows: x = -2.5 and x = 0.5.

c) The end behavior of the quadratic function is given as follows: as x -> ± ∞, f(x) -> ∞.

d) The graph is constructed at the end of the answer, considering the x-intercepts, the y-intercept, the end behavior and the vertex.

The quadratic function for this problem is defined as follows:

f(x) = 4x² + 8x - 5.

Hence the coefficients are given as follows:

a = 4, b = 8, c = -5.

The discriminant is given as follows:

D = 8² - 4 x 4 x (-5)

D = 144.

Hence the x-intercepts are given as follows:

Considering the intercepts and the leading coefficient of a = 4, the function is factored as follows:

f(x) = 4(x - 0.5)(x + 2.5).

As the leading coefficient is positive, the parabola is concave up, meaning that the end behavior is that the function increases to infinity both at the left tail and at the right tail.

The y-intercept is given as follows:

f(0) = 4(0)² + 8(0) - 5

f(0) = -5.

The coordinates of the vertex are given as follows:

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On solving the provided question we can say that - here in equation we have [tex]y = 160+ 2 *t= > y = 160 + 2X 30 = > y= 160+ 60 = > y = 220 pounds[/tex]

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

[tex]y = 160+ 2 *t\\y = 160 + 2X 30\\y= 160+ 60\\y = 220 pounds[/tex]

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The family's monthly payment for their new minivan is $6,664.52

To calculate the monthly payment, we first need to find the total amount that the family is financing by subtracting the down payment from the total cost of the minivan: $45,000 - $12,000 = $33,000.

Then, we can use the monthly payment factor to calculate the monthly payment. The formula to do this is:

Monthly Payment = Financed Amount * Monthly Payment Factor

So in this case:

Monthly Payment = $33,000 * 0.202764 = $6,664.52

Therefore, the family's monthly payment for their new minivan is $6,664.52

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Answer:

Step-by-step explanation:

good

Given that,

Perimeter of kite -  38 cm

Let "x" be the one side of kite

Both of the top sides are equal

Therefore, other side = x

One side of a kite is 2 cm less than 2 times the length of another

Therefore,

One of bottom side = 2x - 2

Bottom sides are also equal

Thus, other bottom side = 2x - 5

We know that,

Perimeter = sum of all sides

38 = x + x + 2x - 2 + 2x - 2

38 = 6x - 4

6x = 38 + 4

6x = 42

x = [tex]\frac{42}{6}[/tex]

x = 7

Thus length of each side of kite is:

x = 7

2x - 2 = 2(7) - 2 = 14 - 2 = 12

Thus length of each side of kite is 7 cm , 7 cm , 12cm , 12cm

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Answer:

A

Explanation:

A line graph is a unique type of graph which is used in statistical application which represents the change in a quantity with respect to another quantity.

The price of different flavors of chocolates varies which can be represented, these variation is plotted in a two-dimensional XY plane.

If the relation include two measures can be presented by using a straight line in a graph called as linear graphs or a linear graph.

There are different types of the line graph, Simple Line Graph refers to Only one line is plotted on the graph, Multiple Line Graph where More than one line plotted on the same set of axes.

Compound Line Graph refers to the information can be divided into two or more types of data and this line graph is called a compound line graph which can be drawn to show the component.

The number of different ways is 7560 ways

From the question, we have the following parameters that can be used in our computation:

Chiefs = 1

Supporting chiefs = 2

Members = 10

Inferior officers = 2

There are 10 members.

So, the number of ways to select a chief is 10

Now, there are 9 members left

The number of ways to select a supporting chief is then represented as

Supporting chief = ⁹C₂

Now, there are 7 members left

The number of ways to select an inferior officer is then represented as

Inferior officers = ⁷C₂

So, the total number of ways is

Ways = 10 * ⁹C₂ * ⁷C₂

Evaluate

Ways = 7560

Hence, the number of ways is 7560

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The difference between the areas is 481 square miles.

Given information:

Alaska is 873 sq miles in size, as well as Rhode Island, is 392 sq miles in total.

To determine the difference between the areas in square miles, the following calculation must be performed: subtract Alaska from Rhode Island square miles then we get:

Let X be the total difference:

873 - 392 = X

481 = X

Therefore, the difference in the areas in square miles is 481.

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Answer:

1/8

Step-by-step explanation:

total probability = 1

total probability = probability of red + probability of green + probability of yellow

1 = 1/4 + 5/8 + yellow

we want to find a common denominator

in this case, we know 4 * 2 = 8, so we can multiply 1/4 by 2/2 = 1 to get

1/4 * 2/2 = 2/8

1 = 2/8 + 5/8 + yellow

1 = 7/8 + yellow

subtract 7/8 from both sides to isolate yellow

1 = 8/8

1 - 7/8 = 8/8 - 7/8 = 1/8 = yellow