Sammi borrowed 11 DVDs from her local library for a total of 1,200 minutes. All of the DVDs were either animated or a superhero movie. Each of the animated DVDs lasted for about 90 minutes. Each superhero movies lasted about 120 minutes. How many of each type of movie did Sammi borrow?

In your handwritten work do the following:

Clearly define your variables used
Write a system of linear equations representing the scenario
Solve the system of equations algebraically either by substitution or elimination
Check your solution algebraically and describe what your solution means in context
In the textbox below:

Write your solution and describe why you chose the method you did (substitution or elimination) instead of choosing the other option. After solving, do you feel you chose the most efficient or easiest method?

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{a + b - 3}\\\mathsf{= 10 + 7 - 3}\\\mathsf{= 17 - 3}\\\mathsf{= 14}\\\\\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{14}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

At 200 miles, the cost will be the same.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Mover R U rents moving trucks for an initial fee of $45 and charges $0.25 per mile.

And, Trunks to Use rents trucks for an initial fee of $35 and charges $0.30 per mile.

Now, Let in x miles the cost will be the same.

Hence, We can formulate;

For Mover R U rents moving trucks for an initial fee of $45 and charges $0.25 per mile.

⇒ $45 + $0.25x

And, For Trunks to Use rents trucks for an initial fee of $35 and charges $0.30 per mile.

⇒ $35 + $0.30x

Equate both equation, we get;

⇒ 45 + 0.25x = 35 + 0.30x

⇒ 45 - 35 = 0.30x - 0.25x

⇒ 10 = 0.05x

⇒ x = 10/0.05

⇒ x = 1000/5

⇒ x = 200

Thus, At 200 miles, the cost will be the same.

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According to the problem this week Edward took 304 photographs.

A week is a unit of time typically spanning seven days, representing the time it takes for one cycle of the days of the week to be completed. Generally, a week is divided into seven days, beginning with Sunday and ending with Saturday. During a week, people usually work five days, with weekends off for leisure or relaxation.The term “week” is believed to be derived from the Germanic word “wih”, which means “turning” or “change”.

This week Edward took 304 photographs. This is calculated by taking the 320 photographs he took last week and subtracting 5% (or 16 photographs). 320 - 16 = 304.

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Find the midpoint of each pair of points, and then take the average of those midpoints to find the center pc. The radius r is the distance from pc to any of the given points. To find the unit normal vector n, take the cross product of any two vectors between the given points and pc.

To find the center pc, the radius r, and the unit normal vector n of the circle that goes through the three points p1=(5,0,7), p2=(1,3,6), and p3=(7,5,4) in 3D space, follow these steps:

1. Find the midpoint of each pair of points:

Midpoint of p1 and p2 = (3,1.5,6.5)

Midpoint of p2 and p3 = (4,4,5)

Midpoint of p3 and p1 = (6,2.5,5.5)

2. Take the average of the three midpoints to find the center pc:

pc = (4.33, 2.83, 6.17)

3. Calculate the radius r as the distance from pc to any of the given points:

r = √((5-4.33)2+(0-2.83)2+(7-6.17)2)

r = 2.66

4. To find the unit normal vector n, take the cross product of any two vectors between the given points and pc:

v1 = (5-4.33, 0-2.83, 7-6.17)

v2 = (1-4.33, 3-2.83, 6-6.17)

n = v1 x v2

n = (-11.67, 5.67, -7.33)

n = (-0.79, 0.37, -0.48)

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The weight of Dima in kilograms round to the nearest hundredth is: 58.51 kilograms.

A weight measuring unit: One pound equals 454 grams. One kilogram is roughly equivalent to 2.2 pounds.

One pound contains 16 ounces.

The word "poundus" means "weight" in Latin.

The £ symbol is derived from an ornate L in Libra.

We are given the weight of Dima as 129 pounds.

we know by conversion that:

1 pound= 0.453592 kilograms

Hence 129 pounds= 129×0.453592 kilograms

129 pounds=58.513368 kilograms.

Therefore, The weight of Dima in kilograms round to the nearest hundredth is: 58.51 kilograms.

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A) The expression that represents the area of the rectangle is;

18x² + 63x + 55

B) The degree of the polynomial is 2 and the classification is a quadratic polynomial.

C) The multiplication of the polynomials (3x + 5) and (6x + 11) to obtain another polynomial demonstrated the closure property of polynomials

A) The formula for the area of a rectangle is;

Area = Length * Width

We are given length of sides as (3x + 5) and (6x + 11)

Thus;

Area = (3x + 5)(6x + 11)

Area = 18x² + 63x + 55

B) The degree of the expression is the highest power which is 2 in the first term 18x².

C) In part A we multiplied 2 polynomials (3x + 5) and (6x + 11) and obtained another polynomial. This demonstrated the closure property of polynomials

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The value of the leading coefficient is equal to -1.

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression. In the term 5x, the coefficient of the number is 5. This coefficient is a whole number that is positive and real.

we know that

The formula to solve a quadratic equation of the form ax²+bx+c =0 is equal to

[tex]x = \frac{-b (+/-) \sqrt{b^{2}-4ac } }{2a}[/tex]

In this problem we have

[tex]f(x) = -x^{2} -8x-7[/tex]

Equate the function to zero

[tex]-x^{2} -8x-7 = 0[/tex]

So, a = -1

     b = -8

     c = -7

Hence, The value of the leading coefficient is equal to, a = -1.

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Answer:

11 2/3

Step-by-step explanation:

5 ÷ 3/7

When dividing with fractions, we use copy dot flip.

Copy the first number

5

Then change division to multiplication.

5 *

Then use the reciprocal of the last number.

5 * 7/3

35/3

Change the improper fraction to a mixed number.

11 2/3

The number of apples that John have is 2 if Mary has 8 apples and Jahn has 1/4 the number of apples as Mary.

Therefore the answer is 2.

This is a problem based on use of fractions. A fraction is a mathematical expression that represents a part of a whole.

John has 1/4 the number of apples as Mary, which means that for every 4 apples that Mary has, John has 1 apple.

To find the number of apples John has, you would divide the number of apples Mary has by 4. In this case, Mary has 8 apples, so John would have

1/4 * 8 = 2 apples

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The correct dot plot representation of the life spans of houseflies is option B, with the life spans ranging from 4 to 14 days and most life spans in the range of 5 to 9 days.

A dot plot is a simple and effective way of visualizing data, especially for small data sets. A dot plot represents each data point as a dot on a number line, with the position of the dot indicating the value of the data point.

Option B states that the life spans range from 4 to 14 days, with most life spans in the range of 5 to 9 days. This means that the dot plot will have a number line running from 4 to 14, with the majority of dots clustered in the 5 to 9 range. This is the correct representation of the dot plot of the life spans of houseflies.

The dot plot suggests that the distribution of the life spans of houseflies is not symmetrical and has a mode (the most frequent value) between 5 and 9 days. This indicates that most houseflies live between 5 and 9 days, with fewer houseflies living either shorter or longer lives.

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Answer: [tex]AD=33[/tex]

Step-by-step explanation:

Using the formula for the perimeter of a rectangle,

[tex]2(2z+1+3z+3)=108\\\\2(5z+4)=108\\\\5z+4=54\\\\5z=50\\\\z=10\\\\\implies BC=33 \implies AD=33[/tex]

Answer:

A; Janae and Jerome must each have only 1 marble

Step-by-step explanation:

First, let's create equations for the amount of marbles each person has:

Janae: m

Jerome: m

Gwen: 4(m+2)

John: 8m+4

Next, let's create an inequality using the statement "John has more marbles than Janae, Jerome, and Gwen combined"

John > Janae + Jerome + Gwen : 8m+5 > m + m + 4(m+2)

Lastly, let's solve for what m could be equal to. To do this, we will need to solve the inequality for m:

8m + 5 > m + m + 4(m+2)   [Distribute 4 to (m+2) on the right side]

8m + 5 > m + m + 4m + 8   [Combine like terms]

8m + 5 > 6m + 8   [Subtract 6m from both sides]

2m + 5 > 8   [Subtract 5 from both sides]

2m > 3   [Divide both sides by 2]

m > 3/2

So, for John to have more marbles than Janae, Jerome, and Gwen combined, m, or the amount of marbles Janae and Jerome have, must be less than 3/2. When looking at the answers, only one option is less than 3/2, 1. So, Janae and Jerome must each have only 1 marble.

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Answer:

68

Step-by-step explanation:

abdul＋mariya/2＝56

total abdul ＋ mariya ＝56*2＝112

112＋hari/3＝60

total 3 person＝60*3＝180

hari ＝180-112＝68

pls give brainliest if correct

Answer: 3/20

Step-by-step explanation:

3/5 x 1/4

The factored form of this polynomial x³ + 3x² - 13x - 15 will be (x - 3), (x + 5) and (x + 1).

What is factorization?

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The polynomial is given as,

⇒ x³ + 3x² - 13x - 15

Factorize the polynomial, then we have

⇒ x³ + 3x² - 13x - 15

⇒ x³ - 3x² + 6x² - 18x + 5x - 15

⇒ x²(x - 3) + 6x(x - 3) + 5(x - 3)

⇒ (x - 3)(x² + 6x + 5)

⇒ (x - 3)(x² + 5x + x + 5)

⇒ (x - 3)[x(x + 5) + 1(x + 5)]

⇒ (x - 3)(x + 5)(x + 1)

Therefore, The factored form of this polynomial x³ + 3x² - 13x - 15 will be (x - 3), (x + 5) and (x + 1).

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If Candidate A received 36 votes, the number of votes that Candidate B received is 60 votes.

The correct option is (C)

Now, According to the question:

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

The first step is to determine the relationship between the number of votes of Candidate A and B. This can be determined by expressing the number of votes in its simplest form.

12 : 20 in its simplest form is 3 : 5

18 : 30  in its simplest form is 3 : 5

27 : 45  in its simplest form is 3 : 5

Now, determine the factor second factor of 36 if the first factor is 3.

36 / 3 = 12

Now multiply 12 by 5: 12 x 5 = 60

Hence, If Candidate A received 36 votes, the number of votes that Candidate B received is 60 votes.

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The perimeter of the tabletop is 79 inches. To calculate the perimeter of a parallelogram, you would use the following formula:

In this case, the length is 30 inches and the width is 14.5 inches, so the perimeter would be 2(30 + 14.5) = 79 inches.

To calculate the perimeter of a parallelogram, use the following steps:

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Answer:

m=1

Step-by-step explanation:

The minutes does it take them to weld the railing are 50 minutes.

To find out the time it takes Nathaniel and Brenda to weld a railing together, you can follow these steps:

Find out how long it takes Brenda to weld a railing: Nathaniel takes 75 minutes, so Brenda takes 75 + 25 = 100 minutes.

Divide the time it takes to weld a railing by the number of workers: 100 minutes / 2 workers = 50 minutes.

Therefore, it takes Nathaniel and Brenda 50 minutes to weld a railing together.

This is a math problem that involves calculating the time it takes two workers, Nathaniel and Brenda, to complete a task of welding a railing. Nathaniel can weld a railing in 75 minutes, while Brenda can do it 25 minutes faster. The question asks how many minutes it takes for the two of them to weld the railing if they work together. To answer this, we need to find out how long it takes Brenda to weld a railing, then divide the total time between the two workers.

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The function f(x) is equal to x√x.

The value of a is 25/4.

What is a function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.

Given integration is

[tex]5+\int_a^x\frac{f(t)}{t^2}dt =2\sqrt{x}[/tex]

Rewrite the equation

[tex]\int_a^x\frac{f(t)}{t^2}dt[/tex]= 2√x - 5

The differentiation of 2√x is f(t)/t² at t = x.

The differentiation of 2√x is 1/√x.

Therefore, 1/√x = f(x)/x²

x²/√x = f(x)

f(x) = x√x

Putting f(t) = t√t in the given equation:

[tex]5+\int_a^x\frac{t\sqrt{t} }{t^2}dt =2\sqrt{x}[/tex]

[tex]\int_a^x\frac{1 }{\sqrt{t}}dt =2\sqrt{x}-5[/tex]

[tex][2\sqrt{t}]_a^x[/tex] = 2√x - 5

2√x - 2√a = 2√x - 5

2√a = 5

√a = 5/2

Square both sides:

a = 25/4

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The equation of the tangent line of f(x)=(x-5)/(x+1) at x=6 in the form of y = mx + b is y = (6/49)x - 29/49 .

The function whose tangent line is to be found out is f(x)=(x-5)/(x+1) ;

to find the tangent equation , we differentiate the function ;

the function f(x) is of the form g(x)/h(x) ;

On differentiating g(x) and h(x) , we get that g'(x) = h'(x) = 1 ;

We get ; f'(x) = [1(x+1))-(1(x-5)]/(x+1)² ;

⇒ f'(x) = [x+1-x+5]/(x+1)² ;

⇒ f'(x) = 6/(x+1)² ;

Now, we x = 6 in the derivative to find slope of tangent at that point.

So , ⇒ f'(6) = 6/(6+1)²

⇒ f'(6) = 6/49

Now the slope is =  6/49 ,  the value of y in (6,y) by putting in x = 6 into the original function:

⇒ f(6) = (6 - 5)/(6 + 1)

⇒ f(6) = 1/7

We currently know a point (6,1/7) = (x₁,y₁) and slope of tangent, which is 6/49.

now using  point slope form to find equation of tangent.

⇒ y-y₁ = m(x-x₁)

⇒ y - 1/7 = (6/49)(x-6)

⇒ y = (6/49)x - 29/49

Therefore , The equation of the tangent is y = (6/49)x - 29/49 .

The given question is incomplete , the complete question is

What is the equation of the tangent line of f(x)=(x-5)/(x+1) at x=6 . Enter your answer as an equation in the y = mx + b form ?

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Jamal will have 63 vacation days after working at his new job for 2 years.

To calculate the number of vacation days Jamal will have after 2 years,

We need to determine the number of months he worked

(2 years = 2 * 12 = 24 months)

And then use that in the expression for his vacation days: 51 + 0.5m.

So, for 24 months, we have:

Vacation days = 51 + 0.5 * 24

Vacation days = 51 + 12

Vacation days = 63

In arithmetic, addition is the process of adding two or more integers together. The numbers being added are known as addends, while the outcome of the addition process, or the final response, is known as the sum.

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The value of the double integral ∫r(8x 6y 48)da where r is the region: 0≤x≤3,0≤y≤4. is 864

Double integrals are a way to integrate over a two-dimensional area. In some cases, the integral of one variable function, a double integral, is defined as a limit of a Riemann sum.

Double integrals are used to calculate the area of a region, the volume under the surface, and the average value of a function of two variables over a rectangular region. In a double integral, the outer limits must be constant, but the inner limits can depend on the outer variable. This means, we must put y as the inner integration variables, as was done in the second way of computing

∬R(8x+6y+48)dA=∫04∫03(8x+6y+48)dxdy

=∫04(4x2+6xy+48x)∣03dy

=∫04(36+18y+144)dy

=∫04(180+18y)dy

=(180y+9y2)∣04

=720+144=864

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The matrix [Qr₁...Qrp] is the result of transforming each vector in R through the matrix Q.

A matrix is a collection of numbers arranged in rows and columns, with each element representing a specific value.

In this explanation, we will look at the relationship between a matrix Q and a set of vectors r₁,..., rp in Rⁿ, and how they can be combined to form a new matrix [Qr1...Qrp].

The matrix [Qr₁...Qrp] can be written as the product of two matrices: QR, where R is defined as [r₁...rp].

This means that when the matrix Q is multiplied by the matrix R, we get the matrix [Qr₁...Qrp].

The reason for this is that multiplying a matrix by another matrix is simply a way of transforming each vector in the original matrix.

In this case, Q transforms each vector r₁,..., rp in R to produce the new set of vectors [Qr₁...Qrp].

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Answer:

The y-intercept is (0, 3).

The equation is not factorable.

Step-by-step explanation:

We are given the equation:

Y=4x^2-4x+3

and we are asked to graph it.

To do this, let's first find the vertex of the parabola that a quadratic equation creates.

[tex]V(-\frac{b}{2a}),f(x))[/tex]

Here, a = 4 and b = -4. So the vertex must be:

[tex]V(-\frac{-4}{2(4)},f(x))[/tex]

[tex]V(\frac{1}{2},f(\frac{1}{2}))[/tex]

[tex]V(\frac{1}{2},2)[/tex]

Next, let's find the intercepts.

[tex]x=0[/tex]

[tex]y=4(0^{2})-4(0)+3=3[/tex]

The y-intercept is (0, 3).

The equation is not factorable.

Answer:

9 gal/day

Step-by-step explanation:

We are given 1 cup per 10 minutes. You can always change the way an expression looks without changing its value if you multiply it by 1. But here we need to change the units. So the 1 we're multiplying is:

1gal/16cups or

60min/1hr or

24hr/1day

See image. We can set it up to cancel the units we don't want and get the units we do want.

see image.

The product of (-8) and a number at most 50 will be

50 * (-8) = -400

Mathematicians use multiplication to calculate the sum of two or more numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis.

Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The components in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the result is the number 54.

a mathematical operation that accepts two integers and outputs a result that is equal to the sum of a column that has one of the values repeated the same amount of times as the other number. Eight times three equals the total of eight times eight.

The product of (-8) and a number at most 50 will be

50 * (-8) = -400

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Given - Cos^2(45) + cos ^2(60) + cos^2(y) = 1

We Know ,

Cos^2(45) = (1/[tex]\sqrt{2}[/tex])^2    ------- 1

cos^2(60)= (1/2)^2       --------2

From equation 1 &2

1/2 + 1/4 + cos^2(y) =1

cos^2(y) = 1- (1/2 + 1/4)

cos^2(y) = 4-2-1/4

cos^2(y) = 1/4

cos (y) = [tex]\sqrt{1/4}[/tex]

cos (y) = 1/2

cos (y) = cos (60)

y=60

The value of y that is being determined by the given

trigonometric equation Cos^2(45) + cos ^2(60) + cos^2(y) = 1 is y = 60

Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations in a triangle. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

Given that, Cos^2(45) + cos ^2(60) + cos^2(y) = 1

We Know that ,

cos(45) = 1/[tex]\sqrt{2}[/tex]  and cos(60) = 1/2

hence, Cos^2(45) = (1/[tex]\sqrt{2}[/tex])^2          (1)

cos^2(60)= (1/2)^2         (2)

From equation 1 &2

1/2 + 1/4 + cos^2(y) =1

cos^2(y) = 1- (1/2 + 1/4)

cos^2(y) = 4-2-1/4

cos^2(y) = 1/4

cos (y) = 1/[tex]\sqrt{4}[/tex]

cos (y) = 1/2

cos (y) = cos (60)

Therefore , y=60

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