Jenna bought some apples for $1.25 per pound and some avocados for $4 per pound. Altogether, she spent $14. 25 for 7 pounds of apples and avocados. What is the total number of pounds of avocados Jenna bought?

A. 1
B. 2
C. 3
D. 4
E. 5

a) The function velocity of the particle is v(t) = 0.5 · t² + 6 · t + 7, b) The distance traveled by the particle is 467 feet.

In this problem we have the equation that represents the acceleration of a particle. The function velocity (v) is obtained by integrating the function acceleration (a) and the function position is obtained by integrating the function velocity. Now we present the definitions of each function:

Velocity

v(t) = ∫ a(t) + C

Position

s(t) = ∫ v(t) + C

Where C is the integration constant.

The distance traveled during the time interval is found means of definite integrals:

Δs = [tex]\int\limits^b_a {v(x)} \, dx[/tex]= s(b) - s(a)

a) First, determine the function velocity of the particle:

v(t) = ∫ (t + 6) dt + C

v(t) = 0.5 · t² + 6 · t + C

7 = C

v(t) = 0.5 · t² + 6 · t + 7

b) Second, determine the distance traveled in the given time interval:

Δs = s(10) - s(0)

Δs = 0.167 · 10³ + 3 · 10² + 7 - 0.167 · 0³ - 3 · 0² - 7

Δs = 467

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The compound interest implies that Erica owes $10865 after 5 years

The given variables can be represented as:

The compound interest formula is given as

A = P(1 + r/n)^nt

Also from the question, we have

n = 12

This is so because the loan is compounded 12 times in a year as a result of being compounded monthly

Solving further, we replace the variables with their values in the above equation

A = 5300 * (1 + (8%/12))^(6*12)

Evaluate

A = 10865

Hence, the amount owed is $10865

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The algebraic expression √((x²-1)²) simplifies to x²-1

An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

Given: sqrt((x^(2)-1)^(2))=x^(2)-1

√((x²-1)²)

The square root will cancel out the square:

Thus, √((x²-1)²)  = x²-1

Therefore,  √((x²-1)²) simplifies to x²-1

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The value of x is 5

What are algebric expressions?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values.

The given expression is 20 - 3x = 5

We need to calculate the value of x

20 - 3x = 5

20 - 5 = 3x

15 = 3x

3x = 15

x = 5

Therefore, the value of x is in the algebric expression  is 5

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The answer to this Question is A we can use basic knowledge from linear equations to find the answer

What is Linear Equation?

Linear Equation is a equation in which degree of variables is 1 only

Yes the given case is possible only under some conditions that we can define as follows and as given in Linear Equations from Options

together cole and maggie have won 30 games and we are also given that  out of those 30 maggie has won 4 games

we should closely see at Linear Equations given in Options.

therefore cole has won 26 games which is more than 13

Hence the answer to the Question is Yes

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The area of the shaded region is calculated as: 6.88 yd²

The area of the shaded region in the diagram = area of rectangle - area of semicircle.

Given the following:

Area of the semicircle = 1/2(πr²) = 1/2 × 3.14 × 4² = 25.12 yd²

Area of the rectangle = length × width = 8 × 4 = 32 yd²

The area of the shaded region = 32 - 25.12 = 6.88 yd²

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The two quantities have proportional relationship and it's slope is 333.33

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

In this case, we have to determine is there's a uniform increase or decrease of the quantity.

The formula of proportionality is often given as

y = kx

Let's take two points and check if they share the same constant of proportionality

2000 = k(6)

k = 333.33

1000 = k(3)

k = 333.33

The relationship between sales and day is proportional.

The slope of the graph is given as

m = y₂ - y₁ / x₂ - x₁

m = 2000 - 1000 / 6 - 3

m = 333.33

NB: The slope and constant of proportionality in this case are the same quantity.

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Answer:

this 1

Step-by-step explanation:

same doubt pease any help

The maximum value of the parabola is represented by y-vertex whose value is 9.

What is a Quadratic Function?

The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

For solving a quadratic function you should find the discriminant: Δ=b²-4ac . And after that you should apply the discriminant in the formula:[tex]x=\frac{-b\pm\sqrt{\Delta} }{2a}[/tex] .

The question gives a quadratic equation and two points, but you do not know some coefficients. Then, you should find the unknown coefficients and after that, you should find the y-vertex of the parabola ([tex]y_v=\frac{-{\Delta} }{4a}[/tex]).

             y = a(x - 1)² + k  ->  points (2, 6.5) and (-1, -1), thus

            6.5=a(2-1)² + k (1)

            -1=a(-1-1)² + k   (2)

         Simplifying the equations

             6.5=a(1)² + k  ( 1 )

            -1=a(-2)² + k  (2)

            6.5=a+ k      ( 1 )

            -1=4a+ k      (2)

         Multiply equation 1 by -1

            -6.5=-a- k    ( 1 )

            -1=4a+ k      (2)

          Sum equations 1 and 2

           -7.5=3a

              a= -2.5

        If a= -2.5, from equation 1, you have

            -6.5=-a- k    

            -6.5=-(-2.5)- k  

            -6.5=2.5- k

            k=2.5+6.5

            k=9

Then , the parabola equation is y= -2.5 (x-1)² +9. You can rewrite it as:

y=-2.5(x²-2x+1)+9

y= -2.5x²+5x-2.5+9

y= -2.5x²+5x+6.5

[tex]y_v=\frac{-{\Delta} }{4a}=y_v=\frac{-{(b^2-4ac)} }{4a}=\frac{-{(5^2-4*(-2.5)*(6.5))} }{4*(-2.5)}=\frac{-90}{-10} =9[/tex]

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Answer:___(-4x⁴+9)x⁶  

                    3

Answer: I hope this is helpful mark me brainlist if this apply to you

Step-by-step explanation:

The square meter, also called the meter squared, is the International System of Units (SI) unit of area. The symbol for square meters is m2. Less formally, square meter is sometimes abbreviated as sq m.A metre square is a square with sides one metre in length – it refers to the shape and the side length, not the area. By contrast, a square metre is an area and can be any shape.The basic unit of length is the meter and is denoted as. In geometry, can be used as a variable to denote a line and can be used to name a point. In algebra, denotes the slope of a line in the equation y = m x + c .

A function is defined as a relation between a set of inputs having one output each.

Say, there is an element x in the sets of input, now it can be paired with no more than one y in the sets of output. We should note that the same y can be paired with different x's, but not the reverse. All linear equations, with the exception of vertical and horizontal lines, are functions.

The function is generally written as "f(x)" where x is the input value.

let us take an example-

f(x) = x/2

here, f(x) is a function because each input "x" has a single output "x/2":

• f(2) = 1

• f(5) = 2.5

• f(−12) = −6

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Answer: [tex]\frac{11+\sqrt{146}}{5}[/tex] seconds

Step-by-step explanation:

[tex]10=-5t^2 +22t+15\\\\5t^2 -22t-5=0\\\\t=\frac{22 \pm \sqrt{(-22)^2 -4(5)(-5)}}{2(5)}\\\\t=\frac{11+\sqrt{146}}{5} \text{ } (t > 0)[/tex]

The value of the variable x and the measures of each side of the triangle ΔDEF found using the definition of an isosceles triangle are;

x = 9

DE = 13

EF = 28

DF = 28

An isosceles triangle is a triangle that has two angles in the triangle that are congruent  and two congruent sides.

The specified parameters are;

∠D is congruent to ∠E in triangle ΔDEF

The length of the segments of ΔDEF are;

DE = x + 4

EF = 4·x - 8

DF = 7·x - 35

The (base) angles ∠D and ∠F of ΔDEF are congruent, therefore, ΔDEF is an isosceles triangle (definition)

Therefore;

EF = DF (Definition of an isosceles triangle)

4·x - 8 = 7·x - 35

7·x - 4·x = 3·x = 35 - 8 = 27

3·x = 27

x = 27 ÷ 3 = 9

x = 9

DE = x + 4

Therefore;

DE = 9 + 4 = 13

EF = 4·x - 8

Therefore;

EF = 4 × 9 - 8 = 28

DF = 7·x - 35

Therefore;

DF = 7 × 9 - 35 = 28

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For any two members of the set, addition will result in a value that is also a member of the set, if the set is closed.

It is speaking of a set, (the mathematical concept) and the operation, here, addition. For any two members of the set, addition will result in a value that is also a member of the set, if the set is closed.

Yes, whole numbers are closed under addition

It is speaking of a set, (the mathematical concept) and the operation, here, addition. For any two members of the set, addition will result in a value that is also a member of the set, if the set is closed.

So the set of whole numbers are closed under addition

Addition of the set of positive integers is closed because the sum of any two integers is also an integer.

Consider subtraction. Positive numbers are not closed under subtraction because picking a larger number to subtract from a smaller one results in a negative number result.

Therefore,  For any two members of the set, addition will result in a value that is also a member of the set, if the set is closed.

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Answer:19.26%

Step-by-step explanation: yeah

Answer:

19%

Step-by-step explanation:

There are only 5 steps here they are:

1. Divide 144.77 by 179.30

2. You get the answer 0.80741773...

3. You round it to 0.81.

4. You turn it into a percent by moving the dot(decimal) to the right four times.

5. And then you subtract it from 100 and you get 19% for the discount.

so therefore the answer is 19%

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Answer:

Step-by-step explanation:

its a

During the time period of 20 years the percent decreases in the country's population is 3.28%.

Percentage is a number or ratio which is a fraction of hundred.

Given,

Population of the country in 1990 = 152 million

Population of the country in 2010 = 147 million

Percent decrease in the population will be ,

= [ (1990's population - 2010's population)/1990's population ]*100

= [ (152 - 147 )/152]*100

= [5/152]*100

= 3.28%

Hence , the decrease in the population will be 3.28%.

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Inequalities to support the questions

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

Each factory operates for at most 12 hours each day.

let maximum profit by factory A be x and Factory B be y.

Then, Inequalities to support the questions

2x + y ≤ 12

and, 2x+ 3y ≤ 12

and, x ≥ 0, y ≥ 0

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Answer:

0

Step-by-step explanation:

0 = 0×0.1+8×0

0 = 0+8×0

0= 8×0

0=0

The points of a triangle are known as vertices, and various triangle points are centroid, circumcenter, incenter and orthocenter.

A triangle is a three-sided polygon.

The triangle's three points are known as vertices.

Several triangle-related points:

Thus, the points of a triangle are known as vertices, and various triangle points are centroid, circumcenter, incenter and orthocenter.

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Answer:

m<8=1024

Step-by-step explanation:

Since they are asking for m<8, we do 128*8=1024.

It is Growing Exponential function because the base is greater than 1 and the exponent has a positive sign.

What is exponential decay function?

A exponential decay is a function that, as the name implies, decays exponentially. So it decays fast at the beginning and slower as the value of the variable increases.

[tex]y=5^x[/tex]

It is a function called "Exponential function". The base determines the growth or decay of the function.

If  base > 1, then the function grows, otherwise if base is between 0 and 1, the function decays.

Here, the  base is positive and it's not 1 or 0.

If we have

[tex]y=5^{-x}[/tex]

this function can be rewritten in this way:

[tex]y=(1/5)^x[/tex]

Here, base between 0 and 1, the function decays

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To match equivalent expression is the fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.

In mathematics, equivalent fractions are those with the same denominator and differing numerators.

According to equivalent fractions, two or more fractions are considered to be equal if both provide the same fraction following simplification. Let's imagine that two fractions, a/b and c/d, were simplified to provide comparable fractions, e/f. In this case, the two fractions are equal to one another.

For instance, if we simplify 5/15, we get a fraction that is equal to 1/3, which is equal to 5/15.

We have to find how do we match equivalent expression.

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The value of a function f at an element x of X, denoted by the symbol f(x), is regarded to as the picture of x as per f or the value of f implemented to the input x.

In the given question we have to define which symbol is represent function.

The notation f: X→Y denotes a function, its domain, and its codomain. The value of a function f at an element x of X, denoted by the symbol f(x), is regarded to as the picture of x as per f or the value of f implemented to the input x.

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Hence, yes we can solve the triangle with the help of Law of Cosines.

What is trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Here given that,

Some people are saying it is possible to use the Law of Cosines to solve a triangle if given only three angles, and some are saying it is not possible.

Yes, with the help of Law of Cosines we can solve the triangle and the formula for it is

[tex]c^2=a^2+b^2-2abcos(C)[/tex]

where, [tex]a,b,c[/tex] are the side lengths of the triangle and [tex]C[/tex] is the angle.

Hence, yes we can solve the triangle with the help of Law of Cosines.

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Answer:

Step-by-step explanation:

3< 0 + 2

3 < 2

the inequality is false because 3 is greater than 2, so the ordered pair (0,3) can’t be a solution of the inequality

Answer:

(0, 3) is not a solution to y < x + 2.

Step-by-step explanation:

Plug the given coordinates in to the inequality:

(0, 3)  →  x = 0,  y = 3

y < x + 2

3 < 0 + 2

3 ≮ 2

(0, 3) is not a solution to y < x + 2.

The Incenter of triangle ABC is I =  (ax1+bx2+cx3 / a+b+c , ay1+by2+cy3 / a+b+c).

Given:

Let I be the incenter of triangle ABC.

Let A(x1,y1) ,B(x2,y2) and C(x3,y3) are vertices.

Let a,b and c are lengths of the sides AB,BC and AC.

we know that:

Incenter I = (ax1+bx2+cx3 / a+b+c , ay1+by2+cy3 / a+b+c)

we can find a, b and c values using the distance formula between the vertices.

AB = a =  [tex]\sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]

BC = b = [tex]\sqrt{(x3-x2)^2 + (y3-y2)^2}[/tex]

AC = c = [tex]\sqrt{(x3-x1)^2 + (y3-y1)^2}[/tex]

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The system of linear equations have variable unique solutions, infinitely many solutions and no solutions.

In algebra, a system of equations comprises two or more equations and seeks common solutions to the equations. "A system of linear equations is a set of equations which are satisfied by the same set of variables."

A system of equations as discussed above is a set of equations that seek a common solution for the variables included.

1.

y = -2x + 3 ...eq(i)

y = 1/2x - 7 ...eq(ii)

The solutions to the linear equations (x,y) are (4, -5)

2.

y = 2x - 7 ...eq(i)

y = 5x + 5 ...eq(ii)

The solutions to the linear equations (x,y) are (-4, -15)

3.

3y = -12x + 6 ...eq(i)

y = -4x + 2 ...eq(ii)

The linear equations (x, y) have infinitely many solutions

4.

y = -2x + 3 ...eq(i)

y = 2x - 1 ...eq(ii)

The linear equations (x,y) have solutions of (1, 1)

5.

y = 5x + 4 ...eq(i)

y = 5x - 2 ...eq(ii)

The linear equations have no solutions

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Answer:

Rate = 72 km per hour
Distance traveled in 2 hours = 144 km

Step-by-step explanation:

The car speed is given as 20 meters per second

There are 3600 seconds in an hour

So in 1 hour the car would travel 20 x 3600 = 72,000 meters. This is equivalent to 72,000 meters per hour

There are 1000 meters in a kilometer

So, in terms of kilometers, the car would travel 72,000/1000 = 72 km i one hour. This is equivalent to a speed of 72 km per hour

In 2 hours the car would travel 72 x 2 = 144 km