Solve the system of linear equations by substitution.
5x+2y=9
x+y=-3

The ΔABC reflects across x-axis with point a=2 and scale factor of x+2 to form the ΔA'B'C'.

What is reflection?

A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.

The vertices of ΔABC is given as -

A(–4, –2), B(–2, 6), and C(4, 4)

The vertices of ΔA'B'C' is given as -

A′(–2, –2), B′(0, –10), and C′(6, –8)

To find the scale factor of the reflection use the formula -

x + a = x' and y + b = y'

Substitute the values in the equation.

For vertex A and A' -

x1 + a = x1'

-4 + a = -2

a = -2 + 4

a = 2

y1 + b = y1'

-2 + b = -2

b = -2 + 2

b = 0

For vertex B and B' -

x2 + a = x2'

-2 + a = 0

a = 0 + 2

a = 2

y2 + b = y2'

6 + b = -10

b = -10 - 6

b = -16

For vertex C and C' -

x3 + a = x3'

4 + a = 6

a = 6 - 4

a = 2

y3 + b = y3'

4 + b = -8

b = -8 - 4

b = -12

It can be seen that the values of a is constant whereas the values of y varies. This happens due to reflection of coordinates across the x-axis.

Therefore, the reflection happens across the x axis.

To learn more about reflection from the given link

https://brainly.com/question/26642069

#SPJ1

The new computer will take to loading a document with 2 graphics and 1 paragraph is 43.99 seconds.

Time taken can be calculated using percentages by determining the percentage of time that has already passed, then calculating the remaining time based on the percentage of time remaining.

For example, if you are asked to calculate the time taken for a project that is 50% complete, you would first need to determine the total length of the project. Let's say it is a project with a timeline of two months.

Next, you would need to calculate the percentage of time that has already passed. In this case, since the project is 50% complete, 50% of the two months has already passed. This means that one month has passed.

Finally, you can determine the time taken by subtracting the time that has already passed from the total length of the project. In this case, the time taken would be one month, since one month has already passed and there is one month remaining until the project is completed.

The old computer would load 2 graphs and one paragraph in:

22 × 2 seconds + 9 seconds = 53 seconds

The new computer is 17% faster so:

53 - (17% × 53) = 43.99 seconds

To learn more about time taken problems, visit

brainly.com/question/29438900

#SPJ1

Answer: Let's call the first number "x" and the second number "y".

From the problem statement, we know that:

x = 3y - 6 (because one number is six less than three times the other number)

x + y = 38 (because the sum of the numbers is 38)

We can substitute the first equation into the second equation to solve for one of the variables:

3y - 6 + y = 38

4y - 6 = 38

4y = 44

y = 11

Now we can substitute this value of y back into the first equation to find the value of x:

x = 3(11) - 6

x = 29

So the two numbers are:

x = 29

y = 11

Step-by-step explanation:

The simplified form of the given expression is x raise to the power of one-thirty.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

Simplifying indices expressions

Given the indices expression (x^1/2/(x^1/3)^1/5

Using the indices law below:

a^m/a^n = a^m-n

(a^m)^n

Applying the law above to the given equation

(x^1/2/(x^1/3)^1/5 = (x^1/2-1/3)^1/5

(x^1/2/(x^1/3)^1/5 = (x^1/6)^1/5

(x^1/2/(x^1/3)^1/5 = x^1/30

Hence the simplified form of the given expression is x raise to the power of one-thirty.

Learn more on indices here:

brainly.com/question/10339517

#SPJ1

The expression after simplification is -6x¹¹.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The given expression is (-4x²) (3x⁵) / (2x⁻⁴).

We have the rule for exponents,

xᵃ . xᵇ = xᵃ⁺ᵇ

xᵃ / xᵇ = xᵃ⁻ᵇ

(-4x²) (3x⁵) = (-4 × 3) x²⁺⁵ = -12x⁷

-12x⁷ / 2x⁻⁴ = (-12 / 2) x⁷⁻⁻⁴

                   = -6x¹¹

Hence the simplification of the expression (-4x²) (3x⁵) / (2x⁻⁴) is -6x¹¹.

Learn more about Expressions here :

https://brainly.com/question/28172855

#SPJ1

Answer: 15 + x, or x + 15

Step-by-step explanation:

The perimeter of triangle QTS is represented as line segments QT + TS + QS.  This means:

6 + 6 + ((3x - 1) + (4 - 2x))

You can first simplify 6 + 6, 6 + 6 = 12

12 + ((3x - 1) + (4 - 2x))

Next, focus on ((3x - 1) + (4 - 2x))

3x + (-1) + 4 + (-2x), addition is commutative, so use addition
3x + (-2x) + 4 + (-1)
(3x - 2x) + (4 - 1)
x + (4 - 1)
x + 3

The equation is now:

12 + x + 3

You can simplify this more by adding 12 + 3

15 + x

The answer is 15 + x or x + 15 because that is as simplified as the equation can be.

I hope this helps!

Answer:

Yes, a transformation of f in the form g(x) =f(x)+k can have no x-intercepts. This will occur if the constant k is added to the y-value of every point on the f(x) graph, resulting in the chart of g(x) being shifted upward by k units. If the original diagram of f(x) had no x-intercepts, then the graph of g(x) would also have no x-intercepts because the x-coordinate of each point on the graph of f(x) is unchanged by the transformation.

Step-by-step explanation:

Answer: To find the number of cords of wood that can fit in a room, we need to find the volume of the room and then divide that by the volume of a cord of wood.

A cord of wood is a unit of measurement that is equal to 128 cubic feet.

The volume of the room can be found by multiplying the length by the width by the height:

V = 4 x 4 x 2 = 32 cubic yards

To convert cubic yards to cubic feet, we can use the conversion factor of 1 cubic yard = 27 cubic feet.

So, the volume of the room in cubic feet is:

V = 32 x 27 = 864 cubic feet

To find the number of cords of wood that can fit in the room, we divide the volume of the room by the volume of a cord of wood:

cords = 864 / 128

cords ≈ 6.75

So, you could fit approximately 6.75 cords of wood in a room that is 4 yards long, 4 yards wide, and 2 yards high, to the nearest hundredth.

Step-by-step explanation:

The person walks 128 feet if she walked around the square pathway.

The plane forms that can be sketched on a flat (or plane) surface or a piece of paper are known as 2D shapes. Every 2D shape has different attributes, like area and perimeter. Some of the two-dimensional objects have sides and corners, while others have curved edges.

Given two pathways,

circular and square, and the circular pathway is inscribed inside of a square pathway,

area of circular pathway = 768 square feet

area of circle = π/4*d²

where d is the diameter

768 = π/4*d²

768*4 = πd² (π = 3)

3072/3 = d²

d = √1024

d = 32 feet

since the circle is inscribed in a square the length of a side of square is equal to the diameter of the circle,

d = a = 32 feet

to find the perimeter of the square path,

perimeter of square = 4a

perimeter of square = 4*32

perimeter of square = 128 feet

Hence the person has to cover 128 feet if she walked around the square pathway.

Learn more about 2D shapes;

https://brainly.com/question/30162250

#SPJ1

(i) 0

(ii) inifinity(very large value)

(iii) undefined

(iv) positive value

(v) negative value

A limiting value of a function is a value that the function approaches as the input (or independent variable) approaches a certain value. It is also called the function's limit at that point. This concept is used in calculus to understand the behavior of functions and their derivatives.

so in all the cases we have to find the limiting value of f(x)

1. if the value of f(b) is very large the 1/f(b) is very small.

2. if f(b) is small then the value of 1/f(b) is very large

3. if f(b) is 0 then 1/f(b) is not defined.

4. if f(b) is positive then its reciprocal is also positive.

5. if f(b) is negative then its reciprocal is also negative.

To know more about limiting value click on below link:

https://brainly.com/question/28423573#

#SPJ4

(I) 0

(ii) The infinite (very large value)

IIII, undefinable

(iv) A favorable value

(v) negative value

A function's limiting value is a point that the function approaches as the input (or independent variable) gets closer to a particular value. At that time, it is also known as the function's limit. Calculus makes use of this idea to comprehend how functions behave and how their derivatives work.

Therefore, we must always determine the limiting value of f. (x)

1. The value of 1/f(b) is very small if the value of f(b) is very large.

2. The value of 1/f(b) is very large if f(b) is tiny.

3. 1/f(b) is not defined if f(b) is 0.

Learn more about function Visit: brainly.com/question/22340031

#SPJ4

The solution to the system is (7.5, 1)

From the question, we have the following parameters that can be used in our computation:

2x−3y=12

−12y+8x=48

divide the first equation by 2

So, we have

x - 1.5y = 6

This gives

x = 6y + 1.5

By substitution, the second equation becomes

-12y + 8 (6y + 1.5) = 48

So, we have

-12y + 48y + 12 = 48

Evaluate

36y = 36

Divide by 36

y = 1

So, we have

x = 6 + 1.5

x = 7.5

Hence, the solution is (7.5, 1)

Read more about system of equation at

https://brainly.com/question/13729904

#SPJ1

Answer:

4.5

Step-by-step explanation:

4.5 times 2 = 9

9 divided by 2 =4.5

Answer: -56/55

Step-by-step explanation:

2 4/5x = -11/4

14/5x = -11/4

Cross multiply:

-55x = 14 * 4 = 56

x = -56/55

The measure of the angle ABC and angle CBD are 48 and 42 degrees

As a general rule:

Complementary angles add up to 90 degrees

This means that

we get: ∡ABC + ∡CBD = 90

3x + 6 + 4x - 14 = 90 ------ Substituting 3x + 6 and 4x - 14 for ∡s ABC and CBD

Evaluate the like terms

7x = 98

Divide both sides by 7

x = 14

So, we have

Measure of ∡ABC: 3 * 14 + 6 = 48

Measure of ∡CBD:  4 * 14 - 14 = 42

Read more about angles at

https://brainly.com/question/25716982

#SPJ1

Complete question

Find the measure of each angle

angle ABC and angle CBD are complementary angles, m angle ABC=(3x+6)degrees, and m angle CBD=(4x-14)degrees

Using what we know about lines and vertical angles we will see that:

m∠3 = 35°.

Remember that when two lines intercept and 4 angles are formed, the vertical angles (these ones connected only by the vertex) have the same measure.

For example, 2 and 5 are vertical angles in this case.

Angles 6 and 3 also are vertical angles, and if both white lines are parallel, then the measures of angle 1 and 6 will be equal (because both are on the same quadrant) then:

m∠6 = 35°

Then the measure of angle 3 is:

m∠3 = 35°.

Learn more about vertical angles by reading:

https://brainly.com/question/14362353

#SPJ1

Answer:

f(x) = 0.5x

Step-by-step explanation:

For this problem, we simply have to find the constant of proportionality between x and f(x). In other words, what x is multiplied by to get f(x).

Since this proportion is constant (meaning it doesn't change), all we have to do is divide an f(x) value in the table by its corresponding x value.

p = f(x) / x

p = -2 / -4

p = 1/2 = 0.5

We can show the relationship of x to f(x) with the equation f(x) = px, which can be simplified using the constant of proportionality that we just solved for.

f(x) = 0.5x

Step-by-step explanation:

based on you input, I would suggest you divide 70 by 4 to get 17.5.

that is the answer. trust.

#quanta #vesperdiagram

Answer:

111

Please mark brainliest

Step-by-step explanation:

The absolute value function for f(e) is given as follows:

f(e) = |e|

The piece-wise definition of the function is given as follows:

The absolute value of a number is the number without the signal, representing the difference between the number and zero.

This means that the elevation function gives just elevation, without considering if the elevation is positive or negative, and thus the function is defined as follows:

f(e) = |e|

More can be learned about the absolute value of a number at brainly.com/question/24368848

#SPJ1

Answer:

uh 6

Step-by-step explanation:

10??????????????????????????6????

The interquartile range?

I believe it is 65.

Answer: To graph the equation y = 2/3x - 1, we can start by finding some points that satisfy the equation.

We can pick any value for x and substitute it into the equation to find the corresponding y-value.

For example:

When x = 0, y = (2/3)(0) - 1 = -1

When x = 1, y = (2/3)(1) - 1 = -1/3

When x = 2, y = (2/3)(2) - 1 = 1/3

When x = 3, y = (2/3)(3) - 1 = 2/3

We can plot these points on a coordinate plane and then connect them with a straight line to graph the equation.

The graph will be a line that passes through the points (0, -1), (1, -1/3), (2, 1/3), and (3, 2/3).

Step-by-step explanation:

Answer:

Step-by-step explanation:

O gráfico  de g(x) = [x+3] é uma Reta que passarum pelo pno (3,0) e tem inclinação 1.

The distance of EH is 4.1866 meters.

Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.

From the question, we have,

Radius of the circle = 5.3 meters

EF = EI = 5.3 meters

FG = 6.5 meters

Also, we have, HE is a perpendicular bisector of FG.

FH = HG = 6.5 / 2 = 3.25

We have to calculate EH.

We have, FH is the projection of EF in the vertical axis.

FH = EF sin (θ), where θ is the angle FEH.

3.25 = 5.3 sin (θ)

sin (θ) = 0.6132

θ = sin⁻¹ (0.6132)

θ = 37.82°

We have,  EH is the projection of EF into the horizontal axis.

EH = EF cos (θ)

     = 5.3 cos (37.82°)

     = 5.3 × 0.7899

     = 4.1866 meters

Hence the length of EH is 4.1866 meters.

Learn more about Circles here :

https://brainly.com/question/17357009

#SPJ1

The linear function that gives the number of matchsticks required to make the nth pattern is given as follows:

M(n) = 15n.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

When a linear function represents a proportional relationship, it means that the intercept is of zero.

As for each pattern the number of sticks is increased by 15, the slope is of 15 and the equation is given as follows:

M(n) = 15n.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Answer: Lisa will receive 475 Euros.

Step-by-step explanation: 500x0.95 = 475.

Answer:

Step-by-step explanation:

2

Answer: So Here you go I got the perfect answer with a explanation

Step-by-step explanation:

A unit rate is a rate in which the second term is 1. To find a unit rate, we need to divide the first term by the second term.

A) 40:5 has a unit rate of 8 (40/5 = 8)

C) 96:12 has a unit rate of 8 (96/12 = 8)

D) 48:6 has a unit rate of 8 (48/6 = 8)

So options A, C and D has a unit rate of 8.

Answer:

the ration has a unit rate of 8 A - 40:5C - 96:12 D - 48:6Dividable by 8

Step-by-step explanation:

Answer:

-13a +10b

Step-by-step explanation:

          [tex]-3a-4b-2(5a-7b)[/tex]

[tex]=-3a-4b-10a+14b[/tex]

[tex]=-13a+10b[/tex]

Hope this helps