A triangle is translated by using the rule (x,y) (x-4,y+1). Which describes how the figure is moved?​

The rate of change of stamp collection was $57.5 per year.

Rate is comparison of two related quantities.

Often the second quantity is time (per second, per hour, etc) but it can be anything.

Can be in the style "this per that" or as a single number calculated using division.

Example: Sam makes 3 pancakes every 6 minutes, that is a rate of:

• 3 pancakes per 6 minutes

• 0.5 pancakes per minute

• 30 pancakes per hour

• an hourly rate of 30

By formula the rate of change = Change in cost/ Time taken

=( $980 - $420)/ 8years

= $460/ 8 years

= $57.5 per year

Thus the rate of change of stamp collection was $57.5 per year.

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Answer:

Should be 3.9

Step-by-step explanation:

prove me wrong

The common difference is (1,0.38).

An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the same. In this type of progression, there is a possibility to derive a formula for the nth term of the AP. For example, the sequence 2, 6, 10, 14, … is an arithmetic progression (AP) because it follows a pattern where each number is obtained by adding 4 to the previous term.

x1 = 1 , y1 = 24

x2 = 2, y2 = 24.38

x3 = 3 , y3 = 24.76

x4 = 4 , y4 = 25.14

Thus the common difference equals :-

x2 - x1 = x3 - x2 = x4 - x3 = 1

y2 - y1 = y3 - y2 = y4 - y3 = 0.38.

Thus the common difference is (1,0.38).

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Answer:

y = 60

Step-by-step explanation:

"The ratio of y to x is 3"

This means that, [tex]y\div x=3[/tex]

"The sum of y and x is 80"

This means,  [tex]x+y=80[/tex]

If [tex]y\div x=3[/tex], then [tex]y = (3*x)[/tex].

We can plug this into the other equation by substitution:

[tex]x + (3 * x)=80[/tex]

This simplifies to:

[tex]4x = 80[/tex]

Which we can solve out and get:
[tex]x=20[/tex].

We solved for x, but we need the value of y.

So, we go back to the equation we first derived: "[tex]y = (3*x)[/tex]".

And now we substitute the value of x, into this.

[tex]y = (3 * (20))[/tex]

By solving this out, we get:
[tex]y=60[/tex]

So, the value of y is 60.

The length of side DF is 3.75.

Given that within the figure there are two triangles that are similar.

Congruent triangles will be triangles that have a comparable measure and shape. This infers that the comparing sides are comparable and the relating focuses are equivalent.

Two comparative triangles are given.

If two triangles are comparable at that point their comparing sides are relative and comparing points are congruent.

DF/AB=EF/BC

Substitute the values from the given figure

DF/15=6/24

Cross multiply both sides, and we get

DF×24=6×15

DF×24=90

Divide both sides by 24, we get

(DF×24)/24=90/24

DF=15/4

DF=3.75

Hence, the length of side DF from the given figure is 3.75.

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For a person to be able to create a coordinate proof to show that the two triangles are congruent by the SSS Triangle Congruence Theorem one can simply use the distance formula.

Given that the distance formula =

[tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1}^{2} )}[/tex]

Let say that Angle ABC has the vertices of A (-4, -2),  B (-5,1). C (0,2) and Angle DEF   has the vertices of D (7, -4), E (4,-5), F (3,0)

So lets prove it:

AC = [tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1}^{2} )}[/tex]

=[tex]\sqrt{(-4-0)^2 + (-2-2)^2}[/tex]

=[tex]\sqrt{32}[/tex]

= 4[tex]\sqrt{2}[/tex]

Do the same for DF:

DF = [tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1}^{2} )}[/tex]

= [tex]\sqrt{(7-3)^2 + (-4-0)^2}[/tex]

=[tex]\sqrt{32}[/tex]

= 4[tex]\sqrt{2}[/tex]

Looking at the above, one can see the values are the same and as such this proves that AC is the same to DF. If you do the same for the other part of the angles, you will see that they are congruent.

Therefore, For a person to be able to create a coordinate proof to show that the two triangles are congruent by the SSS Triangle Congruence Theorem one can simply use the distance formula.

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The purpose of the coordinate graphing system described by Descartes in his book "Discourse on Method" is to use algebraic methods to solve geometric problems. That is option A.

The coordinate graphing system is used on graphical systems to describe the relationship or location between two points on different axes such as X and y axis.

According to Descartes in his book "Discourse on Method" he developed a connection between Algebra and geometry.

Therefore, the main purpose for the coordinate graphing system is to use algebraic methods to solve geometric problems.

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Answer:

The answer that you are looking for is A.

Have a great day!

Step-by-step explanation:

Please mark me brainliest!

The volume of the composite figure shown in the picture is equal to 375 cubic meters.

The volume is the space occupied by a solid, the volume of the composite figure is sum of the volumes of the two elements, the one is a square prism and the other, a triangular prism. The volume of the entire figure is:

V = (5 m)² · (13 m) + (1/2) · (5 m)² · (4 m)

V = 375 m³

The volume of the composite figure shown in the picture is equal to 375 cubic meters.

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Answer:

t = 60/n

Step-by-step explanation:

The original equation we know is y = k/n

Since 12 people can assemble the set in 5 hours, when y is 5, n will be 12.

We can now input that value into the equation.

--> 5 = k/12

--> 5(12) = k/12 (12)

--> 60 = k

--> k = 60

The equation to represent the situation can be written as:

t = 60/n

and that is our final answer!

12 people can assemble in 5hours

So

Equation

Or

Answer:

b = 3.5

a = 7

Step-by-step explanation:

Hello!

This triangle is a 30°-60°-90° triangle, as the missing angle is 30° and the other two angles are 60° and 90°.

There are some important Rules:

We can first solve for the leg that is opposite to the 30° angle.

Since [tex]\frac{7\sqrt3}{2}[/tex] is [tex]b\sqrt3[/tex]:

The length of b is 3.5.

We can multiply 3.5 by 2 to find the length of a.

The length of a is 7.

Answer:

A

Step-by-step explanation:

The rule for a 180 degree clockwise rotation is (-x, -y). After applying this to the figure, it must be translated one unit right to match the image.

Answer:

Step-by-step explanation:

hello :

4lnx - 8 = 12

4lnx - 8 +8= 12+8

4lnx =20

lnx =5

coclusion : x =e^5

A. x = 148.4

Answer:

  14400 cm³/s

Step-by-step explanation:

Find the rate of change of volume in terms of edge length, and evaluate the expression for the given conditions.

  V = s³ . . . . volume in terms of edge length (s)

  dV/dt = 3s²·ds/dt . . . . . . derivative of volume with respect to time

For the given values of s and ds/dt, this is ...

  dV/dt = 3(40 cm)²(3 cm/s) = 14400 cm³/s

Answer:

x = y = 6.5[tex]\sqrt{2}[/tex]

Step-by-step explanation:

the triangle is isosceles, both base angles are 45° then the 2 legs are congruent , that is x = y

using the sine ratio in the right triangle and the exact value

sin45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{13}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )

2x = 13[tex]\sqrt{2}[/tex] ( divide both sides by 2 )

x = y = 6.5[tex]\sqrt{2}[/tex]

Step-by-step explanation:

as the graphic shows, there are 2 objects : 1 block and 1 triangular shaped half-block.

the block is

7cm × 6cm × 2cm

the half-block is

8cm × 7cm × 6cm

with 10cm being the length of the tilted "roof" area.

the 2 sides facing each other are not visible to the observer, so, they are not part of the surface area of the composite figure.

let's start with the block :

top and bottom 7×2

front and back 6×2

no left (fully covered by the half-block)

right 6×7

that gives us :

2 × 7×2 = 2×14 = 28 cm²

2 × 6×2 = 2×12 = 24 cm²

6×7 = 42 cm²

in total : 94 cm²

the half-block :

top 10×7

bottom 8×7

front and back (triangles) 8×6/2

no left (due to being a half-block)

no right (fully covered by the block)

that gives us :

10×7 = 70 cm²

8×7 = 56 cm²

2 × 8×6/2 = 2×24 = 48 cm²

in total : 174 cm²

so, the complete surface area of the composite figure is

94 + 174 = 268 cm²

Answer:

no solution

Step-by-step explanation:

Your question is in the form:

absval of something

= a NEGATIVE number



The absolute value is always positive. So it can never be negative.

There are no values that x can be that will make this math sentence true.

It's not really a trick question, but the course/teacher/book/program just wants you to recognize that an absolute value CANNOT be negative.

Answer:

Step-by-step explanation:

a = number of successful events

b = total number of events.

Using Algebraic equation, Kathy worked 22 hours at job A and 12 hours at job B, the week she made US $ 140.60.

Let's review all the information given for solving this question:

Rate per hour of Job A = US$ 6.20

Rate per hour of Job B = US$ 6.50

Earnings received by Kathy during the week = US$ 140.60

Total time worked by Kathy during the week = 22hours

Hours at job A = x

Hours at job B = 22 -x

In order to find how many hours Katy worked at each job: This is the Algebraic equation that we'll use:

6.20x + 6.50 (22 - x) = 140.60

6.20x + 143- 6.50x = 140.60

-0.3x = 140.60 - 143

-0.3x = - 2.4

    x = -(2.4)/-(0.3)

x = 14.3/0.3 = 8 (Dividing by 0.3 at both sides)

Kathy worked 8 hours at job A.

Hours at job B = 22 - x. Put x = 11 we get

Hours at job B = 22 -11

= 11

Hence, using Algebraic equation Kathy worked 22 hours at job A and 12 hours at job B, the week she made US $ 140.60.

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The  truncation error for s3  is 0.008

The  truncation error serves as the  difference between a truncated value as well as  the actual value.

This truncated quantity can be a numeral having a fixed number of allowed digits.

Therefore the value of S_3=0.008

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Answer:

y = -1.5x + 3.5

Step-by-step explanation:

Slope intercept form is y=mx+b.

3x + 2y = 7

2y = -3x + 7

y = -1.5x + 3.5

Answer:

-3/2x+7/2=y

Step-by-step explanation:

Answer:

They all equal zero

Step-by-step explanation:

A number cannot equal itself times any number that isn't zero, unless it itself is zero.

[tex]4x - 7x - 4x + 7 \sqrt{x} + \sqrt{x} [/tex]

[tex] - 7x + 8 \sqrt{x} [/tex]

Answer:

72

Step-by-step explanation:

This shape is a prism; it's a 3-D shape with 6 sides. Basically, it's a box.

All 6 sides are rectangles.

Surface area means that we'll find the area of all 6 rectangles and add them up.

There's a front and back, left and right, and a top and bottom.

The area of a rectangle is length×width or base×height.



The front and back are identical.

Area = length×width

Area = 6×3 = 18

Since the front and back are the same, two of the rectangles have area = 18.



The left and right are the same:

Area = 3 × 2

Area = 6

Two faces have area = 6.

The top and bottom are the same.

Area = 6 × 2

Area = 12

Again, two faces have area = 12.

To find the total surface area, add up all 6 areas.

A =18+18+6+6+12+12

A = 72

The volume of air inside the cube is 1887.376 cubic inches

The volume of a shape or an object is the amount of space in the object

The given parameters are:

The volume of the cube is calculated using

Volume = (Side length)^3

Substitute 12.6 for Side length

Volume = 12.6^3

Expand the exponent

Volume = 12.6 * 12.6 * 12.6

Evaluate the product

Volume = 2000.376

The volume of air inside the cube is calculated using

Volume of the air = Volume of the cube - Volume of the ball

So, we have

Air = 2000.376 - 113

Evaluate

Air = 1887.376

Hence, the volume of air inside the cube is 1887.376 cubic inches

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The new values for the mean and the standard deviation are 38 and 5 respectively.

The mean of a population is given as [tex]\mu = \frac{\sum_{N}^{i}x_i}{N}[/tex] and its standard deviation is given as [tex]\sigma = \sqrt{\frac{\sum_{N}^{i}(x_i-\mu)^2}{N}}[/tex].

In the question, we are given that a population has a mean of μ = 35 and a standard deviation of σ = 5, and are asked for the new values for the mean and standard deviation when 3 points are added to every score in the population.

We let the new population formed be over the variable k.

Thus, [tex]k_i = x_i + 3[/tex], for all i from 1 to N.

Thus, the new mean can be calculated as:

[tex]\mu_k = \frac{\sum_{N}^{i}k_i}{N}\\\mu_k = \frac{\sum_{N}^{i}(x_i + 3)}{N}\\\mu_k = \frac{\sum_{N}^{i}x_i + 3N}{N}\\\mu_k = \frac{\sum_{N}^{i}x_i}{N} + 3\\\mu_k = \mu + 3\\\mu_k = 35 + 3 = 38 [Since, \mu = 35].[/tex]

Thus, the new mean is 38.

Thus, the new standard deviation can be calculated as:

[tex]\sigma_k = \sqrt{\frac{\sum_{N}^{i}(k_i-\mu_k)^2}{N}}\\\sigma_k = \sqrt{\frac{\sum_{N}^{i}(x_i + 3-38)^2}{N}}\\\sigma_k = \sqrt{\frac{\sum_{N}^{i}(x_i-35)^2}{N}}\\\sigma_k = \sqrt{\frac{\sum_{N}^{i}(x_i-\mu)^2}{N}} [Since, \mu = 35]\\\sigma_k = \sigma = 5.[/tex]

Thus, the new standard deviation is 5.

Thus, the new values for the mean and the standard deviation are 38 and 5 respectively.

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In the given diagram, the value of x is 90°

From the question, we are to determine the value of x

In the given diagram,

Using the linear pair theorem, we can write that

x + 90° = 180°

x = 180° - 90°

x = 90°

Hence, the value of x is 90°

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Answer: K

Step-by-step explanation:

I. Correct. When t=0, h=c, so if you alter the value of c, the h-intercept changes.

II. Correct, the maximum value of [tex]-at^2 +bt[/tex] will stay the same, but you are changing c, which is the amount you are always adding to it, meaning the maximum will change.

III. Correct. If you plug into the quadratic formula setting h=0, it is easy to see changing the value of c will change the solutions.

The correct statement regarding the quadratic function is:

K. I, II and III.

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

If a > 0, it has a maximum value, and if a < 0, it has a minimum value.

The extreme value is [tex](x_v,y_v)[/tex], in which:

The solutions are:

In this problem, we have a function h(t). Changing the coefficient c, the h-intercept h(0) changes. Looking at the formulas in the bullet point, the value of [tex]\Delta[/tex] changes, meaning that both the maximum value [tex]y_v[/tex] and the t-intercepts [tex]t_1[/tex] and [tex]t_2[/tex] will change, so option K is correct.

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Answer:

m = [tex]\frac{1}{2}[/tex] , m = 5

Step-by-step explanation:

assuming you mean

2m² - 11m + 5 = 0

consider the product of the factors of the m² term and the constant term which sum to give the coefficient of the m- term

product = 2 × 5 = 10 and sum = - 11

the factors are - 10 and - 1

use these factors to split the m- term

2m² - 10m - m + 5 = 0 ( factor the first/second and third/fourth terms )

2m(m - 5) - 1(m - 5) = 0 ← factor out (m - 5) from each term

(m - 5)(2m - 1) = 0 ← in factored form

equate each factor to zero and solve for m

2m - 1 = 0 ⇒ 2m = 1 ⇒ m = [tex]\frac{1}{2}[/tex]

m - 5 = 0 ⇒ m = 5

Answer:

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