There are 1000 rabbits and chickens on a farm, and together they have 3150 legs. How many rabbits and how many chickens are there on the farm?.

The quadratic function is f(x) = x² -6x + 16.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Let the standard form of quadratic function polynomial is ax² + bx + c = 0

And the zeros of the equation is (x +2) and (x-8)

Now to find the polynomial,

we multiply both zeros

(x +2)(x -8)

= x² + 2x -8x + 16

= x² -6x + 16

And the function in the standard form.

Therefore, the quadratic function is f(x) = x² -6x + 16.

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Answer: A

Step-by-step explanation:

adding two circles to the left side would result in square triangle circle circle and if you add a square to the right it would be circle circle triangle square thus balancing it

open image below.

Step-by-step explanation:

a) The co-efficient of x⁴y³ = -241920

b) The coefficient of x²y⁷ =  900

What Does an Expression Coefficient Mean?

The expansion is given by the following formula:

(a + b)ⁿ = Σⁿₓ=₀(ⁿₓ) aⁿ⁻ˣ bˣ, where

(ⁿₓ) = n! / (n-x)! k! and n! = 1.2..3.....n.

a) (-3x+4y)⁷ = ⁷C₀ (-3x)⁷(4y)⁰ + ⁷C₁ (-3x)⁶(4y)¹ + ⁷C₂ (-3x)⁵(4y)¹ + ⁷C₃ (-3x)⁴(4y)³ + ⁷C₄ (-3x)³(4y)⁴ + ⁷C₅ (-3x)²(4y)⁵ + ⁷C₆ (-3x)¹(4y)⁶ + ⁷C₇ (-3x)⁰(4y)⁷

The co-efficient of x⁴y³ = 35x - 27x³ * 256y⁴

= -241920x³y⁴

Hence, the coefficient of x⁴y³ = -241920.

b) (5x - y)⁹ = ⁹C₀(5x)⁹(-y)⁰ + ⁹C₁(5x)⁸(-y)¹ + ⁹C₂(5x)⁷(-y)² + ⁹C₃(5x)⁶(-y)³ + ⁹C₄(5x)⁵(-y)⁴ + ⁹C₅(5x)⁴(-y)⁵ + ⁹C₆(5x)³(-y)⁶ + ⁹C₇(5x)²(-y)⁷ + ⁹C₈(5x)(-y)⁸ + ⁹C₉(5x)⁰(-y)⁹

The coefficient of x²y⁷ = 36 * 25x² * y⁷

= 900x²y⁷

Hence, the coefficient of x²y⁷ = 900.

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The required mean and standard deviation of height J is 69.6 inches and 2.88 inches.

The mean of the values is the ratio of the total sum of values to the number of values.

here,
1 foot = 12 inches,
Mean  = 5.8 feet
Mean = 5.8 (12 inches)
mean  = 69.6 inches,

Now,
Standard deviation = 0.24 (feet)
Standard deviation  = 0.24 (12 inches)
Standard deviation = 2.88 inches

Thus, the required mean and standard deviation of height J is 69.6 inches and 2.88 inches.

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It will take 5 weeks for every member to play each of the other members of the club.

What are the arrangements?

A strategy or preparation for something, especially for it to occur in a certain way: Two days a week, she had the plan to work from home. The motel was filled, so we had to find another place to stay.

Here, we have

A chess club meets every week and has 6 members.

Each member of the club plays one opponent each week.

We have to find out how many weeks will it take for every member to play each of the other members of the club.

Total number of matches played = (6×5)/2 = 15

Games per week = 3

Every member is to play each of the other members of the club = 15÷3= 5.

Hence, it will take 5 weeks for every member to play each of the other members of the club.

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Answer:

x= 24 − 9y

x= 3/2 − 3y/2

Step-by-step explanation:

The equation of the line that is parallel to the line y = -2x + 1 and passing through (-6, -7) will be y = -2x - 13.

Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.

The slope of the parallel line will remain the same. Then the equation of the line that is parallel to the line y = -2x + 1 will be given as,

y = -2x + c

The equation passes through (-3, -7), then the value of the variable 'c' is given as,

- 7 = -2(-3) + c

-7 = 6 + c

c = - 13

Then the equation of the line that is parallel to the line y = -2x + 1 and passing through (-6, -7) will be y = -2x - 13.

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Juan sells 1148 more surfboards than beach toys and sells 1435 fewer bathing suits than beach toys.

As of the mentioned data, Juan has three different surf shops at Sunny Beach. Where he sold 12,195 surfboards, 9,612 bathing suits, and 11,047 beach toys.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

here,
The difference in beach toys and surfboard sell = 12,195 - 11,047 = 1148
Differences in beach toys and bathing suit seel = 9612 - 11047 = -1435

Thus, Juan sells 1148 more surfboards than beach toys and sells 1435 fewer bathing suits than beach toys.

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Answer:

option 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (4, 0) ← 2 points on the line

m = [tex]\frac{0-(-2)}{4-0}[/tex] = [tex]\frac{0+2}{4}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = [tex]\frac{1}{2}[/tex] x - 2

Answer:

When a triangle is enlarged using a scale factor of 1/2 and center (1,9), the resulting triangle will be similar to the original triangle. This means that the angles of the new triangle will be the same as the angles of the original triangle, but the lengths of the sides will be scaled down by a factor of 1/2.

For example, if triangle ABC has vertices at (0,0), (3,0), and (3,4), then the coordinates of the vertices of triangle A'B'C' would be (1,9), (1.5, 9), and (1.5, 9.2), respectively. The side lengths of triangle A'B'C' would be half the length of the corresponding sides of triangle ABC, but the angles would be the same.

It is important to note that the center of the enlargement, (1,9), will not be a vertex of triangle A'B'C'. Instead, it will be the point at which the enlargement is centered, and the resulting triangle will be positioned relative to this point.

Step-by-step explanation:

The remainder will be constant if the divisor of a polynomial is a factor.

Given,

Polynomial division;

Divide the first term of the dividend by the first term of the divisor to divide polynomials using long division. The quotient's initial term is this. Dividend is calculated by multiplying the new term by the divisor. The new dividend is this difference.

We have to find the remainder if the divisor of a polynomial is a factor;

Here,

You know, from long division of regular numbers, that your residue (if there is one) has to be smaller than whatever you divided by. Since we're dividing by a linear factor (i.e., a factor whose degree on x is just an understandable "1"), the remainder in polynomial terms must be a constant value.

That is,

If a polynomial's divisor is a factor, the residual will always be a fixed number.

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To make a scale drawing with scale of 1:1 means a full size image .

Scale drawings are images that depict objects at a scale different from their actual size.

Depending on the size of the object being represented and how the drawing will be used, they can depict objects at either a bigger or smaller scale than full size.

The scale gives the proportion of a distance at full size to the distance that, at the scale in use, would have the same length.

The notation " : " is used to denote the scale of drawings as a ratio.

So, According to the question,

In full size drawings, the ratio is 1:1 (or occasionally 1/1 or "one to one").

Hence , a full size drawing is made by scale 1:1

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The best approximation for the area of this circle with a radius of 8in is 201.0 in².

A circle is a two-dimensional object made up of points that are spaced out from a given point (center) on the plane by a fixed or constant distance (radius). The area, a circle occupies in a two-dimensional plane is known as the area of the circle. Therefore, the area that a circle with radius r encloses is πr².

Given the radius r of the circle is 8 in. Then, the area is,

A = 3.14×(8 in)² =200.96 in²=201.0 in²

The answer is 201.0 in² and the correct option is option c.

The complete question is -

What is the best approximation for the area of this circle? Circle with radius labeled 8 in. Use 3.14 to approximate pi.  a) 25.1 in² b) 50.2 in² c) 201.0 in² d) 803.8 in²

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In 2021, 65.6 percent of mothers with children under age 6 participated in the labor force

Percentages are fundamentally fractions with 100 as the denominator. To show that a number is a percentage, the percent symbol (%) is placed next to it. For instance, if you answered 45 out of 100 questions on a test accurately (45/100), you would have gotten a 45% mark.

According to the given information

In 2021, 65.6 percent of mothers with children under age 6 participated in the labor force compared with 75.5 percent of mothers whose youngest child was age 6 to 17.

In 2021, 65.6 percent of mothers with children under age 6 participated in the labor force

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There are 28 ways can-the coach select this pair.

A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Given that;

A coach selects 2 of his 8 team members to gather the equipment.

Now,

Since, A coach selects 2 of his 8 team members to gather the equipment.

Hence, Number of ways = [tex]^{8} C_{2}[/tex]

                                      = 8! / 2! 6!

                                      = 8 × 7 / 2

                                     = 28

Thus, Number of ways = 28

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The ratio is 7:4 for the line joining the points (- 5 1) and (2 3)

In mathematics, a ratio shows how many times one number is represented by another. TA ratio can have quantities of any kind, such as counts of persons or objects, measurements of lengths, weights, or times, etc. Both numbers must be positive in the vast majority of situations.

We can calculate the ratio by subtracting the x-values and y-values of the given points:

(2 + 5) : (3 - 1)

= 7 : 4

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Answer:

The answer is 2/3x - y = 15

Step-by-step explanation:

The remainder is 5. To calculate this, first, divide 599 by 9 to get the largest multiple of 9 before 599. 5/9 < 1, so carry the 5 to the tens, 59/9 = 6 r 5, so carry the 5 to the digits. 59/9 = 6 r 5 again, so the largest multiple is 66. Multiply 66 by 9 to get 594, and subtract this from 599 to get 5, the remainder.

Answer:

22

Step-by-step explanation:

The surface area of the plane is π√14 sq. units.

Given plane = x+2y+3z=1 and cylinder = x² + y² = 9

Let J be the projection on the plane x+2y+3z=1

We know that the surface area of an equation is

∫∫j  √{1+(∂z/∂x)² + (∂z/∂y)²} dA

It is given that the plane is inside the cylinder.

We can use the coordinates of the cylinder to get

x = r cosθ and y = rsinθ

Therefore,

x² = r²cos²θ

y² = r²sin²θ

Therefore,

x² + y² =  r²cos²θ + r²sin²θ

= r²(cos²θ + sin²θ)

=  r²                                         [Since cos²θ + sin²θ = 1]

Putting the value of x² + y² in the initial equation we get

r² =  9

or, r = 3

Therefore,

J = {(r,θ)/ 0 ≤ r ≤ 3, 0 ≤ θ ≤ 2π}

Now,

x +2y + 3z =1

or, z = 1/3(1 - x - 2y)

Partially differentiating z with respect to x gives us

∂z/∂x = -1/3

Partially differentiating z with respect to y gives us

∂z/∂y = -2/3

Hence,

Surface Area = ∫∫j √{1+(∂z/∂x)² + (∂z/∂y)²} dA

= ∫∫j √{1+ (-⅓) ² + (-⅔) ²} dA

= ∫∫j √(9+1+4)/√9 dA

= √14 /3∫∫j dA

=√14/2 [2π - 0]

= π√14 sq units

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Answer:

g(x) = (1/2x)^2

Step-by-step explanation:

The function of g(x) is stretched in the graph, so the value is going to be less than 1, which eliminates choice A.

Because the graph g(x) lands on the point (2,1), input this in each of the expressions and see which one is true. C is the only one that truly works.

The translation from the triangle ABC to triangle A'B'C' is 3 units right and 2 units up.

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.

Given that,

The coordinates of triangle ABC are A(-3, 1), B(-1, 2) and C(1, 1)

The coordinates of triangle A'B'C' are A'(0, 3), B'(2, 4) and (4, 3).

When the shape is moved towards the right by k units, then replace x with x + k.

When the shape is moved up by k units, then replace y with y + k.

A(-3, 1)→A'(-3+3, 1+2)

B(-1, 2)→B'(-1+3, 2+2)

C(1, 1)→C'(1+3, 1+2)

Therefore, the translation is 3 units right and 2 units up.

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The maximum period of time they could reserve the meeting space is 9 hours.

Mathematical expressions with the symbols > and are known as inequality. Finding a range, or ranges within ranges, of values that an unknown x can have while still satisfying the inequality is referred to as "solving" an inequality. In this lesson, inequalities are resolved using graphs and algebra.

An algebraic inequality expression is a mathematical statement that uses the it as a sign to connect an expression to a value, a variable, or another expression. One type of variable inequalities can have solutions that can be graphed either in a coordinate plane or on a number line.

Inequality expression is 31 + 5.9*t < 84.10.

To understand it, collect all constant on the right side:

5.9*t < 84.10 - 31 = 53.10,

Hence, t < 53.10 % 5.9 = 9 hours.

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Correct Question:

To rent a certain meeting room, a college charges a reservation fee of $31 and an additional fee of $5.90 per hour. The chemistry club wants to spend less than $84.10 on renting the meeting room. What are the possible amounts of time for which they could rent the meeting room? Use t for the number of hours the meeting room is rented, and solve your inequality for t.

Scale factor of greater than 1 indicates the size of the shape will increases

The scale factor is defined as the ratio between the original size of the figure and the new size of the figure.

The scale factor of the figure maybe greater than 1 or the between 0 and 1

If the scale factor of the figure is between 0 and 1, then the size of the figure will decreases, the new size of the figure will be less than original figure

Similarly, if the scale factor is greater than 1, the size of the figure will increase, new figure will be larger than original figure

Therefore, if the scale factor is greater than 1  the figure will enlarge

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The expression equivalent to the given expression is 7.5 - 10x

From the question, we are to create an equivalent expression to the given expression

The given expression is

-2.5(4x - 3)

To determine the equivalent expression, we will simplify the expression by applying the distributive property.

Simplifying the expression

-2.5(4x - 3)

Apply the distributive property

-10x + 7.5

= 7.5 - 10x

Hence, the expression is 7.5 - 10x

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Answer:6 3/10

Step-by-step explanation:

use Desmos calculator

Therefore, [tex]x^{2}[/tex] + 3 x -5 = 0 ,[tex]x^{2}[/tex] - x =0 and 7 [tex]x^{2}[/tex] + 14 x = 0  are quadratic equation.

Equation: a claim that two expressions with variable- and/or number-filled expressions are equivalent. Mathematical development has been sparked by the desire to find solutions to equations, which are really just questions.

Here,

Given:

[tex]x^{2}[/tex] + 3 x -5 = 0

[tex]x^{2}[/tex] - x =0

3 x + 7 .5 x - 7 = 0

7 [tex]x^{2}[/tex] + 14 x = 0

[tex]x^{3}[/tex]- 3 x2 + 1 = 0

x - 5 = 9 x + 7

The [tex]x^{2}[/tex] is present in equation which are quadratic

thus,

[tex]x^{2}[/tex] + 3 x -5 = 0

[tex]x^{2}[/tex] - x =0

7 [tex]x^{2}[/tex] + 14 x = 0

these following above equations are quadratic equation .

Therefore, [tex]x^{2}[/tex] + 3 x -5 = 0 ,[tex]x^{2}[/tex] - x =0 and 7 [tex]x^{2}[/tex] + 14 x = 0  are quadratic equation.

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The equation which can be used to find the number is 2n = -4, and the number is -2.

What do you mean by equation?

A mathematical statement which is known as an equation makes two expressions' values equal to each other. It is mathematical statement which says "this is equivalent to that," in different words. It appears to have an equal sign in the centre, with a mathematical expression on the right side, and a mathematical expression on the left side.

Let the number be n,

we have given that the number is being twice.

So, the number becomes 2n

And, it is also given that the this twice of the number is equal to -4.

So the equation becomes as:

2n = -4

on solving this equation, we get n = -2

Therefore, the equation is 2n = -4 and the number is -2.

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To dilate a rectangle by 2 , multiplied by the scale factor with every coordinates of rectangle

Assume that, the origin (0, 0) be the center of dilation in the coordinate plane.

Let ABCD be a Rectangle in the coordinate plane. The points in the coordinate planes are A(-2, 2), B(3, 2), C(3, -2), D(-2, -2)

We have to dilate by scale factor 2, then every coordinate point of the original triangle will multiplied by the scale factor

Coordinates of new rectangles : A'(-4,4) , B'( 6, 4) ,C(6, -4) and D'(-4,  -4)

Therefore, When we dilate a rectangle by scale factor 2 ,

The dilated triangle will be A’B’C’D’ and the coordinate points obtained are  A'(-4,4) , B'( 6, 4) ,C(6, -4) and D'(-4,  -4)

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