Word problem involving average rate of change

Answer:

0.03x+0.05=1.50

Hopely this can help you

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Substitute x with 8 :

6(8-5) =

8-5 = 3

6(3) = 6 × 3 = 18

Therefore 18 is our final answer

Hope this helped and have a good day

Hey there!

6(x - 5)

= 6(8 - 5)

= 6(8) + 6(-5)

= 48 - 30

= 18

OR EVEN:

6(x - 5)

= 6(8 - 5)

= 6(3)

= 18

18 = 18

Therefore, your answer should be:

18

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

The simplified expression of -35 / (-5) is 7.

Let the given expression be -35 / (-5) then

-35 / (-5) = -35/-5

simplifying the above equation, we get

= 35/5

= 7

Therefore, the value of -35 / (-5) is 7.

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The first five terms of the sequence an =5 n-3 are 2, 7, 12, 17  and 22.

According to the question.

We have a formula or a rule for finding the terms of a sequence i.e.

an = 5n -3.

The first term of the sequnence an = 5n - 3 is given by

a(1) = 5(1) -3 = 5 -3 = 2

The second term of the sequence an = 5n - 3 is given by

a(2) = 5(2) - 3 = 10 - 3 = 7

The third term of the sequence an = 5n -3 is given by

a(3) = 5(3) - 3 = 15 - 3 = 12

The fourth term of the sequence an = 5n - 3 is given by

a(4) = 5(4) - 3 = 20 - 3 = 17

The fifth term of the sequence an = 5n - 3 is given by

a(5) =  5(5) - 3 = 25 - 3 = 22

Hence, the first five terms of the sequence an =5 n-3 are 2, 7, 12, 17  and 22.

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Answer:

The value of the given series is 49.75

Step-by-step explanation:

This is a problem from geometric progression ,

As we know the formula for geometric progression is aₙ = a₁ r ⁿ⁻¹

Where , a₁ is the first term and r is the ratio , and n is the number of terms.

Ratio is , 40/80 = 1/2

Here , a₄ = 80 . (1/2)⁴ ⁻ ¹ = 80 / 8  = 10

a₅ = 80 . (1/2)⁵ ⁻ ¹ = 80 / 16 = 0.5

a₆ = 80 . (1/2)⁶ ⁻ ¹ = 0.25

a₇ = 80 . (1/2)⁷ - ¹ = 0.125

a₈ = 80 . (1/2) ⁸ ⁻ ¹ = 0.625

Now the series can be written as .

80-40+20- 10 + 0.5 - 0.25 + 0.125 - .625 = 49.75

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The slope intercept form is y = 1/4x + 13/4

The general expression for slope intercept form is given as follows

                 y = mx + c

        where, m = slope of the line

                       c = intercept

We have been given the equation that is,

         y – 2 = 1/4(x+ 5)

We will solve this step by step to convert it into the general form that is,

       y – 2 = 1/4(x+ 5)

       y – 2 = 1/4x + 5/4

          y = 1/4x + 5/4 + 2

          y = 1/4x +13/4

which is in the general form of   y= mx + c where m = 1/4 and c = 13/4

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Answer:

22 divided by 2 equals 11, so each shirt at store one, you are getting for $11. Store 2 is having a sale of 10% off 12.99 is 11.69, so each shirt is $11.69. So, Store 1 is a better deal.

Step-by-step explanation:

Answer:

1.38$

Step-by-step explanation:

QUESTION

Two stores are having sales on the same shirt. the sale at store 1 is "2 shirts for $22" and the sale at store 2 is "each $12.99 shirt is 10% off". explain how much will you save by buying at store 1.

EXPLANATION

store one 2 shirts 22$

store 2 1 shirt 12.99/10=1.30 so 12.99-1.30=11.69x2=23.38

23.38-22=1.38

Answer: Option (4)

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals of each other, so the slope of the line we want to find is -5/3.

Of the options, the only one that satisfies this is choice 4.

If AB = 6y - 14, BC = 10 - 2y then the value of AC = 8.

In geometry, the midpoint is the point in the middle of a line segment. It is equidistant from both endpoints and serves as the segment and endpoint centroid. It cuts the segment in half.

Given: AB = 6y - 14, BC = 10 - 2y

Since B is the midpoint of AC, AB = BC then

6y - 14 = 10 - 2y

Add 14 on both sides of the equation, and we get

6y - 14 + 14 = 10 - 2y + 14

6y = - 2y + 24

Add 2y on both sides of the equation

6y + 2y = - 2y + 24 + 2y

simplifying the above equation, we get

8y = 24

y = 24/8

y = 3

Substitute the value of y in AC then we get

AC = 2(6(3) - 14)

= 2(4)

AC = 8

Therefore, the value of AC = 8.

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Answer:

x > 2

Step-by-step explanation:

because , you have to use inverse operation to check your answer .

-6x-4< 2x-20

-6x-4+4<2x-20=4

-6x<2x-16

-6x-2x<2x-16-2x

-8x<-16

(-8x)(-1)>(-16)(-1)

8x>16

8x/8 > 16/8

x>2

The solutions of the quadratic equation [tex]x^{2}[/tex]-20=8 x are -2 and 10.

The given quadratic equation is [tex]x^{2}[/tex] - 20 = 8 x . To get the solutions of the given quadratic equation we need to simplify the quadratic equation. The step wise simplification of the given quadratic equation is,

[tex]x^{2}[/tex] - 20 = 8 x

[tex]x^{2}[/tex] - 8x -20 =0

on breaking -8x in two parts as -10x + 2x , we will get

[tex]x^{2}[/tex] -10x + 2x -20 = 0

x (x - 10) + 2 (x - 10) = 0

On taking (x-10) as common, we get

(x-10) (x+2) = 0

x = -2 , 10

The solutions of the quadratic equation [tex]x^{2}[/tex]-20=8 x are -2 and 10.

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 The full quadratic expression is expressed as follows:

x² - 5x + 6.25

An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.

  Equations can be graphed, just like a function.

   To solve this problem we must complete square in the expression, it is necessary to note that perfect square trinomial has the form of:

(a - b)² = a² - 2ab + b²

x² - 5x + ?

5x = 2xb

2b =5

b = 5/2

   Let's complete the square

x² - 5x + (5/2)²

x² - 5x + 25/4  

x² - 5x + 6.25

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The value of the expression [tex]5c^{3} -6c\sqrt{-2c}[/tex] at c = -5 is [tex]5(-125 +6\sqrt{10})[/tex]  .

An algebraic expression is an expression having constant and variable joined with algebraic operation(+,-,×,÷).

For Example , 2c+5x+6 is an algebraic expression.

In the given expression

[tex]=5c^{3} -6c\sqrt{-2c}[/tex]

Substituting the value of c = -5 .

We get ;

[tex]=5(-5)^{3} -6(-5)\sqrt{-2(-5)}[/tex]

[tex]=5(-125) +30\sqrt{-2(-5)}\\ \\ =-625 +30\sqrt{10}[/tex]

taking 5 common from both the terms

[tex]=5(-125 +6\sqrt{10})[/tex]

Therefore , the value of the expression [tex]5c^{3} -6c\sqrt{-2c}[/tex] is [tex]5(-125 +6\sqrt{10})[/tex].

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1,2,5 square root both sides

The sum of the solutions are 32/3.

The modulo (or "modulus" or "mod") is the remainder after dividing one number by another.

Example: 100 mod 9 equals 1

Because 100/9 = 11 with a remainder of 1

Another example: 14 mod 12 equals 2

Because 14/12 = 1 with a remainder of 2

12-hour time uses modulo 12 (14 o'clock becomes 2 o'clock)

It is where we end up, not how many times around.

|3y-4|=9

3y-4=9 or 3y-4=-9

3y=13 or 3y=-5

y=13/3 or y-5/3

|y-4|=3

y-4=3 or y-4=-3

y=7 or y=1

The solutions are y=13/3, y=-5/3, y=7, y=1

Hence the sum of the solutions are 32/3.

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The inequality that shows the number of shirts that Lisa buys is given as 15x + 35 ≤ 137

An equation is an expression that shows the relationship between two or more numbers and variables.

Let s represent the number of shirts that Lisa buys. Lisa only has $137 to spend, therefore:

15x + 35 ≤ 137

The inequality that shows the number of shirts that Lisa buys is given as 15x + 35 ≤ 137

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The point P which partitions the line segment AB have coordinates as P(0,3)

Line Segment is a line which joins together two points to form a straight line. It can be extended in either side.

It is given that,

A line segment AB having coordinates such as A(0,0) and B(0,6) respectively

The line segment AB is partitioned by a given point P in two minor line segments AP and PB

We need to find, the coordinates of the partitioning point i.e. P

The given formula will be used,

The coordinates of the point P = ([tex]\frac{x1+x2}{2}[/tex], [tex]\frac{y1 + y2}{2}[/tex])

Now, x1 = 0, x2 = 0, y1 = 0, y2 = 6

Putting values in the formula, we get

([tex]\frac{0+0}{2}[/tex], [tex]\frac{0+6}{2}[/tex])

(0,3)

Hence, the point P which partitions the line segment AB have coordinates as P(0,3)

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Check the picture below.

The statement, m∠A ≅ m∠B, represents the congruence property.

The congruency property of equality states that if two angles have measures that are equal to each other, then both angles are said to be congruent to each other.

Given that:

The measure of angle A = 29 degrees

The measure of angle B = 29 degrees.

Since both angles have the same measure, then both angles are congruent to each other.

Therefore, the statement, m∠A ≅ m∠B, represents the congruence property.

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The standard deviation is 7.35.

Standard deviation is used to determine how the values in a group differs from the mean of the values in the group

In order to determine the standard deviation, take the following steps:

Determine the mean of the observation: (87 + 91 + 74 + 73 + 80 + 84 + 68 + 75) / 8 =79

Determine the difference between each value and the mean and then square the result:

(87 - 79)² + ( 91 - 79) ² + (74 - 79)² + (73 - 79)² + (80 - 79)²  + (84- 79)²  + (68 - 79)²  +( 75- 79) ²

64 + 144 + 25 + 36 + 1 + 25 + 121 + 16 = 432

Determine the mean of the sum of the squared differences and then find the square root of the mean:

√432 / 8 = 7.35

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Answer:

the square root rounded up is around 8

Step-by-step explanation:

because if the 5 is not beside the number it rounds down and the number was 3 so its 8

The equation that has no solution is 24x+32-2.1x = 20.9x+30+x-2

Part A

24x+32-2.1x = 20.9x+30+x+2

Add like terms

24x-2.1x-20.9x-x = 30+2-32

0x = 0

Infinitely many solutions

Part B

24x+32-2.1x = 20.9x+30+x-2

Add like terms

24x-2.1x-20.9x-x = 30-2-32

0x = -4

There is no solution

Part C

24x+32-2x = 20.9x+30+x-2

Add like terms

24x-2x-20.9x-x = 30-2-32

0.1x = -4

x = (-4)/0.1

x = -40

It has only one solution

Part D

24x+32 = 20.9x+30

Add like terms

24x-20.9x = 30-32

3.1x = -2

x= (-2)/3.1

x = -0.64

It has only one solution

Hence, the equation that has no solution is 24x+32-2.1x = 20.9x+30+x-2

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Variable - These are the unknown quantities that expected to estimate it as an output.

Example:- In an optimization model for labor scheduling, the number of nurses to employ during the morning shift in an emergency room may be a Decision variable.

Constraints - the restrictions on the variable open linear programming problem are called constraints.

The conditions x ≥ 0, y ≥ 0 called non negative restrictions.

Objective equation - the objective equation should be specified in a quantitative way.

It is of the form Z = ax + by

where x and y are decision variable.

Z is to be maximized or minimized to find the solution.

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Answer: 146 cm

Step-by-step explanation:

A simple way to find the perimeter of a rectangle is to double both sides and add them.

(49.5 * 2) + (23.5)

= 99 + 47

= 146

Answer:

m1 = 122°

m2= 58°

Step-by-step explanation:

M1 is an alternate interior angle, of 122°, which means that that angle is also 122°.

The line with m1 and m2 added together equal 180°, so we can subtract 122 from 180 to find m2.

180-122= 58

The standard equation for the given slope is y - 2 = 0

These are two methods for finding the equation of a line given a point and slope. Create the equation y = mx + b.

We just solved using the m given in the problem and the b. Point-slope form = y-y1 = m (x-x1), where (x1, y1) is the specified point and m is the specified slope. "x" and "y" remain as variables.

Putting (0,2) for (x1, y1) and m=0, we get

y-2=0(x-0)

(y-2) =

y-2=

+y-2=0

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The AA criterion for triangle similarity states that if two triangles have two pairs of congruent angles, then the triangles are similar.

What is a triangle similarity criterion?

According to the Angle-Angle (AA) criterion, two triangles are considered comparable if "two angles of one triangle are respectively equivalent to two angles of another triangle."

What distinguishes AA similarity from AAA similarity?

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Step-by-step explanation:

A and B are similar but not congruent

similar=same shape

congruent=same shape and same size