Write and solve a system of equations for each situation. Check your answers.A store sells small notebooks for 8 and large notebooks for 10 . If you buy 6 notebooks and spend 56 , how many of each size notebook did you buy?

The equation of line tangent is y-35x+30=0.

What is tangent of a line?

A tangent line to a circle is a line that touches the circle exactly one time in Euclidean plane geometry and never enters the interior of the circle. Tangent lines to circles are the focus of various theorems and are crucial to numerous geometric structures and mathematical arguments.

Given equation y=2x+33x-2

                       =>y=35x-2

General slope intercept form is y=mx+b

Comparing and we get m = 35

The equation of tangent is y-5=35 (x-1)

=> y-5=35x-35

=> y=35x-35+5

=>y-35x+30=0

Therefore, the equation of line tangent is y-35x+30=0.

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The solution of the given equation 5/2x - 2/3 = 1/x + 5/6 is at x = 9/11.

According to the given question.

We have an equation

5/2x -2/3 = 1/x + 5/6

Since, we have to solve the above equation for x.

Thereofore, the solution of the equation 5/2x -2/3 = 1/x + 5/6 is given by

5/2x -2/3 = 1/x + 5/6

⇒ 5/2x -1/x  = 5/6 + 2/3

⇒  (5 -2) /2x  =   5+ 2(3)/6

⇒ 3/2x = 11/6

⇒6(3)  = 11(2x)

⇒ 18 = 22x

⇒ 18/22  = x

⇒ 9/11 = x  or x = 9/11

Hence, the solution of the given equation 5/2x - 2/3 = 1/x + 5/6 is at x = 9/11.

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x=5 that's my final answer because 2(8)=4x-4

Answer:

m = 18

n = 60

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180.

We can write the following equation to find, first value of m, then the value of n:

65 + 42 + 55 + m = 180 add like terms

162 + m = 180 subtract 162 from both sides

m = 18

Now the value of n:

65 + 55 + n = 180 add like terms

120 + n = 180 subtract 120 from both sides

n = 60

Answer:

982888428848588828480484883858

Step-by-step explanation:

The subtraction equation to addition equation is as follows;

By converting the subtraction equation to addition equation, we have to change the sign from subtraction to addition but the equation overall remain the same.

Therefore,

a - 9 = 6

add 9 to both sides

a - 9 + 9 = 6 + 9

a  = 6 + 9

p - 20  = -30

add 20 to both sides

p = -30 + 20

z - (-12) = 15

open the bracket by multiplying the signs

Therefore,

z + 12 = 15

x - (-7) = -20

open the bracket by multiplying the signs

x + 7 = -20

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The Surface area of a cone is 308.647 sq. inches.

What is the Surface area of cone ?

The area occupied by the surface / boundary of a cone. It is always measured in square units. Stacking many triangles and rotating them around an axis gives the shape of a cone. As it has a flat base, thus it has a total surface area as well as curved surface area.

The surface area of the cone can be given by finding the area of the sector by using the formula,

Area of the sector (in terms of length of arc) = (arc length x radius) / 2 = ((2πr) x l) /2 = πrl.

We are given the height and radius

h = 19 inches

r = 5 inches

The formula for Surface Area is:

Surface Area = πrl

We have to find slant height first:

[tex]l=\sqrt{h^{2}+r^{2} }[/tex]

[tex]l=\sqrt{19^{2}+5^{2} }\\ l=\sqrt{361+25}\\l= \sqrt{386}[/tex]

[tex]l=19.467 inches[/tex]

Now, The Surface Area is:

SA = πrl (π = 3.14)

SA = 3.14 x 5 x 19.467

SA = 308.647 [tex]inches^{2}[/tex]

Hence, The Surface area of a cone is 308.647 sq. inches.

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The simplification of the given complex fraction [tex]1- \frac{1}{\frac{4}{2-\frac{3}{5} } }[/tex] is equal to (23)/(28).

As given in the question,

Given complex fraction is [tex]1- \frac{1}{\frac{4}{2-\frac{3}{5} } }[/tex]

Simplify the given complex fraction by taking the least common multiple,

[tex]1- \frac{1}{\frac{4}{2-\frac{3}{5} } }\\\\\\= 1- \frac{1}{\frac{4}{\frac{10-3}{5} }}\\ \\= 1- \frac{(1)(5)}{(4)(7)}\\ \\= \frac{(28-5)}{28}\\ \\= \frac{23}{28}[/tex]

Therefore, the simplification of the given complex fraction [tex]1- \frac{1}{\frac{4}{2-\frac{3}{5} } }[/tex] is equal to (23)/(28).

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23 lies between the two perfect squares 16 and 25 which are the squares of 4 and 5 respectively.

The value of √23 lies between 4 and 5.

What in mathematics is a perfect square?

Informally: A square number, perfect square, or simply "a square" is the result of multiplying an integer (a "whole" number), positive, negative, or zero, times itself. Therefore, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on are all square numbers.

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By elimination, the solution of the system of equations, 5x - y = 4 and 2x - y = 1, is (1 , 1).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.

Subtracting the two equations will eliminate the variable y.

5x - y = 4     (equation 1)

2x - y = 1     (equation 2)

3x      = 3

x = 1

Substitute the value of x to any of the two equations and solve for y.

5x - y = 4     (equation 1)

5(1) - y = 4

-y = 4 - 5

-y = -1

y = 1

Hence, the solution of the system of equations is (1 , 1).

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Based on the temperature at the beginning of the day, and the change in temperature by the end of the day, the temperature at day's end was -3°C.

The temperature started at 4°C and then dropped during the day by a temperature of 7°C.

The temperature at day's end will therefore be:
= Beginning temperature - Change in temperature

Solving gives:

= 4 - 7

= -3 °C

In conclusion, the change in temperature would lead to an ending temperature of -3°C.

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Answer:

a = 4(d - g)

Step-by-step explanation:

d - g = [tex]\frac{1}{4}[/tex] a ( multiply both sides by 4 to clear the fraction )

4(d - g) = a

The diameter of the circle is 19.8 inches.

We are given the value of side of square in the question. The diameter of the circle will be equal to the diagonal of square. The diagonal of square can be calculated using Pythagoras theorem. So, finding the diagonal of square, which will be hypotenuse.

Diagonal² = Base² + Perpendicular²

Diagonal² = side² + side²

Keep the values to find the value of diagonal

Diagonal² = 14² + 14²

Take square of values on Right Hand Side of equation

Diagonal² = 392

Diagonal = √392

Taking square root on Right Hand Side of equation

Diagonal = 19.8 inch

So, diagonal of square is diameter of circle which is 19.8 inches.

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The machine will take 6.25 minutes to grade 300 multiple choice tests.

Unitary method is a concept in which the value of a single unit is first found out and then multiplied by the necessary value to get the required answer.

Here, we are given that a grading machine can grade 96 multiple choice tests in 2 minutes.

This means that the machine will take 2/96 minutes to grade one multiple choice test

X = number of minutes taken by the machine to grade 300 multiple choice tests

Thus, we can use the proportion 2/96 to predict X in the following manner-

X = 2/96 (300)

X = 600/ 96

X = 100/ 16

X = 6.25

Thus, the machine will take 6.25 minutes to grade 300 multiple choice tests.

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The equation which correctly gives P in terms of E, O and M as required is; P = 6E - 4M - O.

It follows from the task content that the expression which represents P in terms of E, O and M be determined.

On this note, since the initial formula is;

E = (O + 4M + P)/6

Multiply both sides by 6;

6E = O + 4M + P

Subtract O and 4M from both sides;

P = 6E - 4M - O.

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There are 5 cups of 3/8 servings in 1 7/8 cups of apple cider

The number of cup servings is 3/8

The number of apple cider cups is 1 7/8

Therefore the number of cup servings can be calculated as follows

15/8 ÷ 3/8

convert to multiplication

= 15/8 × 8/3

= 15/3

= 5

Hence there are 5 cups of 3/8 servings in 1 7/8 cups of apple cider

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Answer:

50.27

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]A(-5)=4(-5)^{2} -3(-5)+2\\A(-5)=100+15+2\\A(-5)=117[/tex]

Answer:

The series third has a sum of 5 option (C) is correct because the sequence represents the sum of the infinite terms.

What is a sequence?

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have a series shown in the picture.

The geometric sequence is shown in the options.

As we know, in the geometric sequence there is a first term and common difference

In the first sequence:

First term a = 2

Common difference = 2(0.1)/2

Common difference d = 0.1

The sum of the infinite series is:

S = a/(1 - r)

S = 2/(1 - 0.1)

S = 2.22

In the second sequence:

First term a = 15

Common difference = 15(0.3)/15

Common difference d = 0.3

The sum of the infinite series is:

S = a/(1 - r)

S = 15/(1 - 0.3)

S = 21.42

In the third sequence:

First term a = 4

Common difference = 4(0.2)/4

Common difference d = 0.2

The sum of the infinite series is:

S = a/(1 - r)

S = 4/(1 - 0.2)

S = 5

Thus, the series third has a sum of 5 option (C) is correct because the sequence represents the sum of the infinite terms.

Step-by-step explanation:

Answer: 2000.18 unit^3

Step-by-step explanation:

radius = 14 / 2 = 7

V of cylinder = π x r^2 x h

= 3.14 x 7^2 x 13

= 3.14 x 49 x 13

= 2000.18 unit^3

Applying the triangle midsegment theorem, the length of BC is: 12 units.

The segment that connects the midpoints of two sides of a triangle is referred to as the midsegment of a triangle.

According to the triangle midsegment theorem, this midsegment is parallel to the third side of the triangle and also has a length that is half of the length of the third side of the triangle.

That is: length of midsegment = 1/2(length of the third side).

Given the following:

DE is a midsegment and is parallel to BC, a third side.

DE = 6 units

Thus, based on the triangle midsegment theorem, DE = 1/2(BC)

Substitute

6 = 1/2(BC)

2(6) = BC

12 = BC

BC = 12 units.

In conclusion, applying the triangle midsegment theorem, the length of BC is: 12 units.

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Answer: 2200 yards

Step-by-step explanation:

First find the unit rate, 660/3 = 220

So, Owen can jog 220 yards in one minute.

220 times 10 to find how much Owen can jog in 10 minutes.

220*10 = 2200.

Answer:

2200

Step-by-step explanation:

Answer:

22 yards

Step-by-step explanation:

Let x equal the number of yards of ribbon at $.07 per yard:

$18.46 + 0.07x = $20.00

Solve for x

Subtract $18.46 from both sides

0.07x = $1.54

Divide both sides by .07

x = 22

The two non negative real numbers with a sum of 40 have the largest possible product are 20 and 20.

Steps to find Maximum of a function f(x).

Step 1 : Differentiate the function F(x)

Step 2 : Equate f'(x) to zero to find the critical points .

Step 3 : Substitute the critical points in f''(x) , if

f''(x)< 0 them maximum value will be at the critical point.

in the given function

the sum of two non negative real numbers is 40.

Let the numbers be x and y .

So , x+y=40

y=40-x     ....(1)

We need to maximize the product i.e. x.y

Substituting the value of y from equation (1) we get

[tex]f(x)=x.y\\ \\ f(x)=x.(40-x)\\ \\ f(x)=40x-x^{2}[/tex]

Step (i) differentiating with respect to x we get

[tex]f'(x)=40-2x[/tex]

Step (ii) Equating f'(x) to 0

[tex]40-2x=0\\ \\ x=20[/tex]

x=20 will be the critical point .

Step (iii) Substituting the critical point in f''(x)

again differentiating with respect to x we get

[tex]f''(x)=-2\\ \\ f''(20)=-2[/tex]

Since -2<0. therefore , x=20 is the point where f(x) is maximum.

Substituting the value of x=20 in equation (1) we get

y=40-x

y=40-20

y=20.

Therefore , the two non negative real numbers with a sum of 40 have the largest possible product are 20 and 20.

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Answer:

Step-by-step explanation:

1-    8

3 -    8+2= 10      

The range of the data set 1 and data set 2 is 4

Data set 1

The maximum value of the data set 1 = 7

The minimum value of the data set 1 = 3

The range is the difference between the maximum value and minimum of the data set

Range = Maximum value - Minimum value

Range of the data set 1 = 7 - 3

= 4

Data set 2

The maximum value of the data set 2 = 7
The minimum value of the data set 2 = 3

The range = Maximum value - Minimum value

The range of the data set 2 = 7 - 3

= 4

Hence, the range of the data set 1 and data set 2 is 4

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The constant of variation in  y = (6)x is (6)

y = kx            (Where k is the constant)

Here,

⇒ y = (6)x

So, k = (6)

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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Step-by-step explanation:

I use a thing call

P-parenthesis

E-exponents

M D-Multiplication and division (Left to right)

A S- Addition and Subtraction (left to right)

We need to wait to use the exponents so 5x2=10, Add the 2 power to ten so 10^2.=100. 100^3.

Answer:

a) -18/3 = - 6

b) 18/-3 = - 6

c) - 18/-3 = 6

Hope this helps :)