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x + 2y = 12 and x = 4y represents the given word problem in equations

How to form an equation for a word problem?

Here are some steps to follow:

1. Understand all the words used in stating the problem. Understand what you are asked to find.

2. Translate the problem to an equation.

Assign a variable (or variables) to represent the unknown. Clearly state what the variable represents.

3. Carry out the plan and solve the problem.

Use substitution, elimination or graphing method to solve the problem.

According to the given question:

Isaiah scored a total of 12 points. In this game, he made some free throws (worth one point each) and some two point shots.

Let number of free throws be x and number of two point shots be y.

x(1) + y(2) = 12

x + 2y = 12

This equation defines the total number of points scored with free throws and two point shots.

He made 4 times as many free throws as two point shots.

Using the pre defined variables to form the equation as

x = 4y

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The slope of equation 3x-4y = 5 is 3/4.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Slope-intercept form:

y = mx+b,

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

Given equation:

3x-4y = 5

To find the slope:

First, we simplify the equation.

-4y = 5 -3x

Divide by -4.

(-4/-4)y = 5/-4 + (-3/-4)x

y = (3/4)x -5/4

Now, we know the slope-intercept form:

y = mx+b,

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

Comparing, both the equation,

we get,

m =3/4.

So, the slope is 3/4.

Therefore, the slope is 5/3.

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Answer:

A dog eating 4 cups each day

Step-by-step explanation:

Because the unit rate is like a unit number over 1.

Example: 3 miles per hour

So, I think the answer is A dog eating 4 cups each day

Answer:

Step-by-step explanation:

28/4 = 7

40/4 = 10

Then:

28:40 in simplest terms is:

7:10

Answer:

[tex] \sf \: 7 : 10 [/tex]

Step-by-step explanation:

Now we have to,

→ simplify ratio into simplest form.

The given ratio,

→ 28 : 40

Let's simplify the given ratio,

→ 28 : 40

→ (28) ÷ 4 : (40) ÷ 4

→ (7) : (10)

→ 7 : 10

Therefore, the ratio is 7 : 10.

The value of g'(t) is  ([tex]e^t[/tex], -sin t, cos(t)).

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x, y, z) = xz + yz + xy,

g(t) = ([tex]e^t[/tex], cos(t), sin(t))

Now, differentiating g(t) w.r.t t

g'(t) =  ([tex]e^t[/tex], -sin t, cos(t))

Hence, the g'(t) =  ([tex]e^t[/tex], -sin t, cos(t)).

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As per the Maclaurin series, the value of the function is written as 2.8521

The term Maclaurin series is defined as  a function that has expansion series that gives the sum of derivatives of that function.

Here we have given that the function is [tex]\sum\frac{(-1)^n\pi^{2n}}{4^{2n}(2n)!}[/tex]

And we need to find the sum of series by using the Maclaurin series as

Now, the sum of series is calculated as,

=>f(n) =  [tex]\sum\frac{(-1)^n\pi^{2n}}{4^{2n}(2n)!}[/tex]

When we put the value on n = 0, then we get,

=> f(0) = [1 x 3.14]/1] =  3.14

Now, we have to put the value of the function, the value of x as 1,

Then we get,

=> f(1) = [-1 x 9.8596] / [16 x 2]

=> f(1) = -0.308

And then we have to put the value of function for the value of x as 2,

Then we get,

=> f(2) = [1 x 30.959] / [64 x 24]

=> f(2) = 0.0201

Then the sum of the series is

=> 3.14 - 0.308 + 0.0201

=> 2.8521

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The coefficient of x in the expression 4x+ 3y is 4. This means that for every x there is 4 times as much as for every y. The coefficient of x is the number that is multiplied by x in the expression.

In the expression 4x+ 3y, the coefficient of x is 4. This means that the x is multiplied by 4. The coefficient of a term is the number that is multiplied by the variable. In this expression, the x is multiplied by 4 and the y is multiplied by 3. This means that for every x there is 4 times as much as for every y. In order to find the coefficient of x in the expression, we must look at the number that is multiplied by x. In this case, the number is 4. This means that the coefficient of x is 4. For example, in this expression, the coefficient of x is 4 which means that for every x there is 4 times as much as for every y.

4x + 3y

Coefficient of x = 4

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Area of rectangle= [tex]12x^{2} y^{4}[/tex] id from given breadth and length of rectangle that are given in form of monomial.

The result of non-negative powers of variables is a monomial. A monomial will only have one term and no variables in the denominator.

A binomial, which is the product of two monomial, has two dissimilar terms.

The area of a rectangle with length l and width w is given by the formula

A = l×w.

In this case,

length of the rectangle = 3x²y

width = 4y³

Therefore, the area of the rectangle is given by A = 3x²y * 4y³

                                                                                   = [tex]12x^{2} y^{4}[/tex]

This is a monomial because it is a single term that contains only variables and their exponents.

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The required median of the given data set is 8.

Finding the middle number requires sorting all the data points and choosing the center one (or if there are two middle numbers, taking the mean of those two numbers).

Example: When the numbers are arranged (1, 4, 7), the number 4 lies in the middle, making it the median of 4, 1, and 7.

So, we have the data:

4, 8, 10, 5, 9

Arrange in ascending order as follows:

4, 5, 8, 9, 10

Since 8 is the number in the middle then it is the median.

Therefore, the required median of the given data set is 8.

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Answer:

The area of the irregular shape is 268.8.

Step-by-step explanation:

To find the area of an irregular shape, we first have to break it into common shapes, here, in this case, we will break it into a rectangle with sides 14 and 8 and a triangle with a base length equal to 14 and the opposite angle to the base is equal to 32°.

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A symbol (often a letter) used in mathematics to represent an unknowable numerical value in quite an equation or algebraic statement.

Example:

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When constructing an angle bisector using a compass, all three arcs do not need to have the same radius.

To construct an angle bisector, you first place the point of the compass on one of the angle's vertices and draw an arc that intersects both sides of the angle. Next, you place the point of the compass on the other vertex of the angle and draw another arc that also intersects both sides of the angle. Finally, you draw a straight line through the point where the two arcs intersect, which will bisect the angle.

The radius of the compass does not affect the construction of the angle bisector, as long as the compass is set to a radius that is large enough to intersect both sides of the angle at some point. As long as the arcs intersect, the angle bisector can be accurately constructed, regardless of the radius of the arcs.

The complete question is:-

When constructing an angle bisector, the compass must be used to make three arcs. Do all three arcs need to have the same radius? Explain.

- Yes, because then the marks are equidistant from each other.

- Yes, because you need the points of intersection of the angle and arcs to form a parallelogram.

- No; the second two arcs must have the same radius but it can be different from the first.

- No; any three radii will work.

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Answer:

8/15

Step-by-step explanation:

There are 15 equal-sized sectors:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15

The odd ones are:

1, 3, 5, 7, 9, 11, 13, 15

There are 8 odd numbered sectors.

p(event) = (number of desired outcomes)/(total number of possible outcomes)

p(odd) = 8/15

Answer: Angle C

Step-by-step explanation:

The length of C-T and T-B would be longer then C-B and push C-B out making angle C the biggest.

Answer:

----------------------

Given options:

A) f(x) = 2x² + 5x − 12,

B) f(x) = 2x + 5,

C) f(x) = 2(x + 5)² − 12,

D) f(x) = 2(x + 5)(x − 12),

The greatest product that can be obtained by multiplying two of these 36 integers is; 306

We are told that when 36 consecutive integers are added, the product is -18.

Now, the sequence for these integers would be;

x, (x + 1), (x + 2), (x + 3),......(x + 35)

Now, since the addition of these integers gives a negative number, then it suggests to us that the sequence starts with a negative integer and then ends with a positive integer.

Thus, we have;

x + (x + 1) + (x + 2) +(x + 3) + (x + 35) = -18

The formula for sum of an arithmetic sequence is;

Sₙ = (ⁿ/₂)(2a + (n - 1)d)

where a is first term and d is common difference

Thus;

-18 = (36/2)(2x + (36 - 1)1)

-18 = 18(2x + 35)

-18/18 = 2x + 35

2x + 35 = -1

x = -34/2

x = -17

Thus;

The first term = -17

Last term = -17 + 35 = 18

Thus, the greatest product that can be obtained  = 18 * 17 = 306

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Answer:

306

Step-by-step explanation:

Answer:  4 2/3

Step-by-step explanation:

14/3 is an improper fraction. Let's take the numerator and divide it by the denominator.

Divide 14 by 3. The quotient digit is 4.

Multiply the quotient digit 4 by the divisor 3.

Subtract 12 from 14.

The result of 14 divided by 3 is 4 with a remainder of 2.

Thus, 14/3 as a mixed number can be written as 4 2/3.

14/3 as it can't further cut out.

Because in a mixed number it is 4 2/3. This can be expressed as a fraction by multiplying the whole number (4) by the denominator (3) and adding it to the numerator (2), giving a fraction of 14/3.

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Obtuse angles, right angles (90 degrees), and acute angles are the three sorts of angles that we can distinguish in order from largest to smallest (smaller than a right angle).

In Euclidean geometry, an angle is made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively. Angles can be formed by two rays in the plane where they are placed.

Additionally, when two planes overlap, angles are created.

Dihedral angles are what they are called.

The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation.

A geometrical shape called an angle is created by connecting two rays at their termini. In most cases, an angle is expressed in degrees.

Order of angles from largest to smallest: obtuse angles are the three types of angles that we can recognize (larger than a right angle), Right angles (90 degrees), and acute angles (smaller than a right angle).

Therefore, the order of angles from largest to smallest: obtuse angles are the three types of angles that we can recognize (larger than a right angle), Right angles (90 degrees), and acute angles (smaller than a right angle).

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Yes, 3x²A5y is a polynomial.

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

we need to check whether 3x²A5y is a polynomial.

An expression is combination of variables, numbers and operators.

For an expression to be a polynomial term, it must contain no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions.

3x²A5y is a polynomial.

Hence,  3x²A5y is a polynomial.

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Answer: 1.5 and 20

Step-by-step explanation:

Answer:

∠MGN = 24°

∠NGO = 24°

Step-by-step explanation:

⭐What is an angle bisector?

Thus, ∠MGN ≅ ∠NGO.

To solve for ∠MGN and ∠NGO, we need to:

1. Create an equation about their relationship:

If ∠MGN ≅ ∠NGO, then...

[tex]5x-6 = 11x -42[/tex]

2. Solve for "x":

[tex]5x - 6 = 11x -42[/tex]

[tex]42 - 6 = 11x - 5x[/tex]

[tex]36 = 6x[/tex]

[tex]6 = x[/tex]

3. Substitute "x" back into the equations to find the angle measures:

[tex]< MGN = 5x - 6[/tex]

[tex]< MGN = 5(6) - 6[/tex]

[tex]< MGN = 30 - 6[/tex]

[tex]< MGN = 24[/tex]

❗❗❗At this point, you could write that ∠MGN and ∠NGO = 24°, as they are congruent, but you should still substitute "x" into  ∠NGO to make sure "x" is correct.❗❗❗

[tex]< NGO = 11x - 42[/tex]

[tex]< NGO = 11(6) - 42[/tex]

[tex]< NGO = 66 - 42[/tex]

[tex]< NGO = 24[/tex]

∴ ∠MGN = 24°

∴ ∠NGO = 24°

To find potential rational roots, we make use of the rational root theorem

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

Task: How the potential rational root is calculated

To make use of the potential rational root, we use the rational root theorem using the following steps

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(x+1) & (x-5) are the factors of given equation.

The given Equation is,

x3- [tex]3x^{3}[/tex] - 9

Here, If we substitute x =5, in the given equation, then we find

     (5)3 - 3(5)3 - 9*5 -5 = 0

x-5 is factor of given equation to find another factor dividing given equation by x-5

    we will get =(x2+2x+1) after dividing the equation by x - 5

Hence x3- [tex]3x^{3}[/tex] - 9 =(x2+2x+1) (x-5)

                            =(x+2)2 (x-5)

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Answer: Since all the corresponding sides of two congruent polygons will be equal, their scale factor will be 1.

Step-by-step explanation:

Answer:

y + 2y = 3y

Explanation:

y and 2y are like terms. Their sum is 3y

Parallel lines are defined as lines that do not intersect or meet at any point in a plane. They are always parallel and equidistant from one another.

What is answer parallel line?

In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet. They can be both horizontal and vertical.

Parallel lines are two lines in the same plane that are equal distance apart and never intersect.

Real-world parallel line examples include railroad tracks, sidewalk edges, street markings, zebra crossings, the surface of pineapple and strawberry fruit, staircases and railings, and so on.

Parallel lines are lines in a plane that never meet, no matter how far they are extended. The distance between the parallel lines is constant because they never meet.

Parallel lines are defined as lines that do not intersect or meet at any point in a plane. They are always parallel and equidistant from one another.

these are 8 parallel lines

2x+3y = 6

2x+3y = 4

2x+3y = 1

2x+3y = 2

2x+3y = 3

2x+3y = 8

2x+3y = 7

2x+3y = 5

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Answer:

The solution on a graph is the point where two lines interesect

Step-by-step explanation:

Prakash's total score in math and science is (x+90)marks

This word problem will need as to write what we have been given and analyze and come up with an equation to solve it

We are given that Prakash's score in science is = x marks

and that Prakash's score in mathematics = 90 marks

Therefore to get the total score in both math and science will we have to add the score Prakash scored in math and the score Prakash scored in science:

This will translate to (x) +(90)

We will get the total as x+90

hence the total score will be x+90 marks

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The correct statement regarding the proportional relationships is given as follows:

B. Karleigh ran a greater distance. The slope of the line described by the data in her table increased at a rate of 1/10, compared to 1/12 for Andrew.

To obtain the person who runs faster, we need to look at their rates, as the time and the distance form a proportional relationship.

Andrew ran 1.5 miles in 18 minutes and 2 miles in 24 minutes, hence his rate is given as follows:

k = 1.5/18 = 2/24 = 1/12 = 12 minutes per mile.

Karleigh ran 3 miles in 30 miles and 4 miles in 40 minutes, hence her rate is given as follows:

k = 3/30 = 4/40 = 1/10 = 10 minutes per mile.

Due to the lower number of minutes per mile, Karleigh ran faster, and the correct option is given by option B.

Andrew ran 1.5 miles in 18 minutes and 2 miles in 24 minutes.

Karleigh ran 3 miles in 30 miles and 4 miles in 40 minutes.

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Answer: x-intercepts

Step-by-step explanation:

basic math

Answer: X intercept

Step-by-step explanation:

The x-intercept is the point at which a graph crosses the x-axis. The y-intercept is the point at which the graph crosses the y-axis. To find the x-intercept of a line, substitute 0 for y into the equation and solve for x.