Mathematics High School

## Answers

**Answer 1**

The **rate of change**, y=−√x−4 +5, is expressed as 1/5−2i/5 .The square root of a number is the number itself.

what is a square root ?

A number can be obtained by **multiplying** the square root by itself. Square root is represented by the symbol sqrt, which stands for square root of, end square root. The reverse of squaring an** integer** is finding its square root. The result of multiplying a number by itself yields its square value, whereas the square root of a number can be found by looking for a number that, when squared, yields the original value. If 'a' is the square root of 'b,' then a a = b.

given

Use the average rate of change formula to substitute.

(√1)−(√−4) / (1)−(−4)

Condense the phrase.

1/5−2i/5

The rate of change, y=−√x−4 +5, is expressed as 1/5−2i/5 .The square root of a number is the number itself.

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## Related Questions

Start with a circle whose equation is (x-a)^2 + (y-b)^2=r. Dilate that circle by a scale factor of 1/r with center of dilation (a,b). What does this transformation demonstrate

### Answers

The **dilation** of the circle with a scale factor 1/r and center at (a,b) will transform the **circle** into a point at (a,b).

A dilation is a **transformation** that results in an image with the same shape as the original but a different size. • An enlargement is a dilation that produces a larger image. • A reduction is a dilation that produces a smaller image.

To solve this we will use the transformation formula for a dilation with center (a,b) and **scale factor**

k, (x,y) --> (a + k(x-a), b + k(y-b)).

Substituting in our values, we get

(x,y) --> (a + (1/r)(x-a), b + (1/r)(y-b)).

Setting this equal to (a,b), we get

(a + (1/r)(x-a) = a, b + (1/r)(y-b) = b).

Solving for x and y gives x = a and y = b. Therefore, the dilation of the circle with a scale factor of 1/r and center at (a,b) will transform the circle into a point at (a,b).

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What is the length of the short side of one of the 30 60 90 triangles?

### Answers

Remembering the ratio of** 1: 3: 2** and understanding that the smallest side length is always opposite the **shortest angle (30°)** and the longest side length is always opposing the **greatest angle (90°) **can help you recall the **30-60-90 triangle **principles.

According to the **30-60-90 triangle theorem,** the **hypotenuse** is twice as long as the **shorter leg**. Additionally, the sides of this particular triangle have a ratio of 1:2: [tex]\sqrt{3}[/tex].

A **30-60-90 triangle** can have** three sides**, and if you only know one, you can use shortcuts to discover the other two. The three scenarios you encounter when performing these computations are as follows:

You are aware of the **short leg **(the side across from the** 30-degree angle**). To find the** hypotenuse**, multiply the length by two. The long leg can be calculated by multiplying the short side by the **square root of 3**.You are aware of the **hypotenuse**. To get the** short side**, divide the hypotenuse by two. To determine the long leg, multiply this response by the **square root of 3**.You are aware of the** long leg **(the side across from the 60-degree angle). To determine the **short side**, divide this side by the **square root of 3**. To find the** hypotenuse**, multiply that amount by two.

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PLEASE HELP ASAP. I WILL GIVE BRAINLIEST!!!

Which of the following is not an expression

A. 7 - 5x

B. 2 + 3x = 8

C. x/2 + 1

D. 2x + 6

### Answers

B because it’s the only one with an equal sign

**Answer:**

B) 2 + 3x = 8

**Step-by-step explanation:**

Option B is not an expression as expressions do not have equal signs.

David drives from his home to the airport to catch a flight. He drives 35 miles in the first hour,

but realizes that he will be 1 hour late if he continues at this speed. He increases his speed by 15

miles per hour for the rest of the way to the airport and arrives 30 minutes early. How many miles

is the airport from his home?

(A) 140 (B) 175 (C) 210 (D) 245 (E) 280

### Answers

If **David** drives from his home to the airport to catch a flight. He drives 35 miles in the first hour, but realizes that he will be 1 hour late if he continues at this speed. The number of **miles **that is the airport from his home is 210.

How to find the distance?

Let **d** represent the **distance** that is needed to travel 1 hour

1 hour late decreased to 0.5 hours early = 1.5

Hence,

d/50 + 1.5 = d/35

**Simplify**

7d + 525 =10d

Collect like terms

525 = 10d - 7d

525 = 3d

Divide both side by 3d

d = 525/3

d = 175

Total number of **miles** :

Total number of miles = 175 + 35

Total number of miles = 210

Therefore we can conclude that the correct option is **C.**

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The value of x is -1/4 Order these expressions from least to greatest:

X

1-x

x-1

-1÷x

### Answers

**Answer:**

**Step-by-step explanation:**

-1 divided by x

1 - x

X - 1

In altitude BH and angle bisector AL intersect at point M. Given m∠HML = 100° and m∠MLC = 110°. Find angles of △ABC

### Answers

The **angles** of triangle ABC are 60 degrees when altitude BH and bisector AL intersect at point M.

**What is equilateral triangle?**

An **equilateral** **triangle** in geometry is a triangle with equal-length sides on all three sides.

Given that:

[tex]\angle HML = 100 \\\\\angle MLC = 110[/tex]

Since, BH is the altitude [tex]\angle MHC= 90[/tex].

The total angle of a quadrilateral is 360, hence:

100 + 110 + 90 + C = 360

C = 60 degrees.

Now consider triangle BHC:

The sum of angle of a triangle is 180, hence:

90 + 60 + B = 180

B = 30

Since the half angle B = 30, the entire [tex]\angle ABC = 60[/tex].

Consider triangle ABC:

Using sum of triangles, we have:

[tex]\angle A + \angle B + \angle C = 180\\\\\angle A + 60 + 60 = 180 \\\\\angle A = 60[/tex]

Hence the measure of angles of triangle ABC is 60 degrees.

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How do you draw a line segment equal to a given segment?

### Answers

draw a line from the starting point of the **segment** to the endpoint using the same angle and **length**.

1. Place a ruler or straightedge on the given segment and draw a line along the length of the ruler.

2. Use a compass to create a line segment equal to the given segment. Set the compass to the length of the given segment, place the point of the compass on one end of the segment, and draw an arc to the other end of the segment.

3. Use a protractor to measure the **angle** and **length** of the given segment. Then, draw a line from the starting point of the segment to the endpoint using the same angle and length.

The answer explains three methods for drawing a line segment equal to a given segment: using a ruler or **straightedge**, using a **compass**, and using a protractor.

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What is the vector equivalent to the directed line segment from the point?

### Answers

The **vector** equivalent to the directed line **segment** from the point (x1, y1) to the point (x2, y2) is the vector <x2-x1, y2-y1>.

The vector of a directed **line** segment is the difference between the two endpoints of the line segment. In this case, the endpoints are the points (x1, y1) and (x2, y2). Therefore, the vector of the directed line **segment** is equal to the vector <x2-x1, y2-y1>.

The vector equivalent of a directed line segment from the point (x1, y1) to the point (x2, y2) is the vector with initial point (x1, y1) and terminal point (x2, y2). This vector is equal to the vector form <x2-x1, y2-y1>, which describes the displacement from the initial point to the terminal point. This vector can also be written in component form, meaning the magnitude of the vector in the x-**direction** is x2-x1, and the magnitude of the **vector** in the y-direction is y2-y1.

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What are the real roots of the equation x2 3 x1 3 âˆ’ 2?

### Answers

The **real roots** of the equation x^(2/3) + x^(1/3) - 2 = 0 are 1 and -8.

The equation x^(2/3) + x^(1/3) - 2 = 0 does not have any **real roots**. Since the **exponents** are not integers, x^(2/3) and x^(1/3) are not defined for negative values of x, and so the equation has no solutions for real values of x.

But,

Let y = x^(1/3)

The equation x^(2/3) + x^(1/3) - 2 = 0 will become y² + y - 2 = 0.

Solving for the roots of this equation,

y² + y - 2 = 0

(y + 2)(y - 1) = 0

y = -2 ; y = 1

Substitute the value of y and solve for x.

y = x^(1/3)

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

x = -8 ; x = 1

Therefore, the real roots of the equation is 1 and -8.

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What is the angle of turn clockwise from South East to North?

N

A 45°

B 135°

C 225°

D 315°

### Answers

The **angle** of a turn **clockwise **from South East to North is Option B 135°.

When determining the **angle **of turn, it is important to consider the direction of **rotation **(in this case, clockwise) and the starting and ending points (in this case, South East to North).

If we imagine the **compass **as a clock, with North at the 12 o'clock position, South at the 6 o'clock position, East at the 3 o'clock **position**, and West at the 9 o'clock position. Then South East would be at the 4:30 position and the **North **would be at the 12 **o'clock **position. To **rotate **from 4:30 (South East) to 12 o'clock (North) in a clockwise direction, we would have to rotate 135 degrees. Thus, the angle of a turn **clockwise** from South East to North is 135 degrees.

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How do you draw a logarithmic graph?

### Answers

Choose the range of values for the x-axis and the y-axis , Plot the points on the **graph**, using the **logarithmic formula **, Connect the points with a smooth curve and Label the axes and add any other details you want to include.

1. Choose the range of values for the x-axis and the y-axis. Select the minimum and maximum values for both the x-axis and the y-axis.

2. Plot the points on the **graph**, using the **logarithmic formula.** Use the formula log(x) = y to calculate the points that should be plotted on the graph. For example, if the x-axis range is from 1 to 10, and the y-axis range is from 0 to 10, then the first point would be (1,0).

3. Connect the points with a **smooth curve.** Once all the points have been plotted, use a ruler or a graphing calculator to connect them with a smooth curve.

4. Label the axes and add any other details you want to include. Use a **ruler** or a graphing calculator to label the axes and add any other details you want to include, such as a title, a legend, or a grid.

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Determine the vertical distance and the horizontal distance of point P and point Q. (a) P=4m Q=6m.

### Answers

if you dog like something

What i the cartoonit' purpoe in thi cartoon?

to convince people that fungal band are dangerou for beetle

to convince people that beetle are damaging to tree

to make people laugh at a play on word

to make people believe that longhorn beetle hate fungi

### Answers

The **cartoonist's purpose** of the given cartoon is C: **"to make people laugh at a play on the words".**

Though the **cartoon** in the picture is designed based on the concept that **fungal bands** are an effective way of the biological control of Asian longhorn beetles, the core purpose of the cartoonist in designing this cartoon is to portray the idea in a comical way, indicating how these fungi actually form a **music band** called 'the fun guy' and they remove the beetles by playing their music, that awful racket as the beetle says.

Thus, the cartoonist's purpose of this cartoon is to make people laugh at a play on the words.

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-35PTS- what theorem can be used to prove these triangles are congruent

### Answers

**Answer:**

Neither

----------------------------

We see **two sides and one angle** marked as **congruent** on both triangles.

The congruent **angle is not included.**

It means we can **neither state it is ASA nor SAA** as both of these require two congruent angles.

The mean length of 10 childrens' index finger is 6.8cm.

The mean length of 7 adults' index finger is 12.8cm.

What is the mean length (rounded to 2 DP) of these 17 people's index finger?

### Answers

Answer:

hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Step-by-step explanation:

What is the coefficient of xÂ³?

### Answers

Let x equal the x³-1 **coefficient**. Thus,** x=1 **is the **coefficient** of the given function.

**Coefficient** **definition**.

A number or symbol that **multiplies** another number or symbol is referred to as a "coefficient" (used as a mathematical variable).

Give a co-efficient example in writing.

A coefficient is a result of multiplying an amount by a variable. **6z**, for instance, is short for six times z. 6 is a coefficient since z is a variable. The coefficient is one for variables that don't have a value.

Let x equal the** x³-1** coefficient. Thus, x=**1** is the coefficient of the given function.

The expression's coefficient is the term **multiplied** by x³. Since x³ is not a word, the **answer** is** 1**.

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The full **question** should be:

What is the coefficient form of XÂ³ 2 *?

15) 3x2 - x - 10 When this trinomial is factored completely, one of its factors is A) x 2 B) x - 5 C) 3x 5 D) 3x - 2

### Answers

When the **trinomial** 3x² - x - 10 is **factored completely**, one of its **factors** is 3x+5.

Solving the given **trinomial** 3x² - x - 10.

=>3x² - 6x+5x - 10

=>3x(x-2)+5(x-2)

=>(3x+5)(x-2)

The **two factors **of the given trinomial 3x² - x - 10 is (3x+5) and (x-2), but according to the given **options**, the correct answer is option C - 3x+5.

Thus, When the trinomial 3x² - x - 10 is **factored completely**, one of its **factors** is 3x+5.

Complete question: 3x² - x - 10

When this trinomial is factored completely, one of its factors is

A) x + 2

B) x - 5

C) 3x + 5

D) 3x - 2

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solve 2+n=0(mod6)

solve2+(3+n)=1 (mod6)

### Answers

Solving the **modular arithmetic **will result to

2 + n = 0 (mod 6): n = -22 + (3 + n) = 1 (mod 6): n = -4

What is modular arithmetic?

The term **modular arithmetic **is the arithmetic that works with whole numbers in a such that, following division by a modulus, all numbers are replaced by their **remainders**.

Solving the **modular arithmetic**: 2 + n = 0 (mod 6)

2 + n = 0 (mod 6)

n = -2

Solving the modular arithmetic: 2 + (3 + n) = 1 (mod 6):

2 + (3 + n) = 1 (mod 6)

5 + n = 1 (mod 6)

n = 1 - 5

n = -4

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Ellie bought snacks for her team's practice. She bought a bag of oranges for

$2. 66 and a 5-pack of juice bottles. The total cost before tax was $7. 46. Write

and solve an equation which can be used to determine j, how much each

bottle of juice costs?

### Answers

The ** linear equation **for jj is ($7.46 - $2.66) / 5 and the cost of each bottle of juice is $0.96.

**What in mathematics is a linear equation?**

**A linear equation** is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the** variables.**

The first step to take in order to determine jj, is to determine the total cost of the 5-pack of juice bottles.

Cost of the 5-pack of juice bottles = Total cost before tax - cost of the bag of oranges

Cost of the 5-pack of juice bottles = $7.46 - $2.66 = $4.80

The second step is to determine the cost of each bottle of juice

The cost of each bottle of juice = Cost of the 5-pack of juice bottles / total number of bottles

$4.80 / 5

= $0.96

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“Theresa’s Transportation” rental car company charges $30 to rent a car and $0.60 per mile for each rental. “Pete’s propulsions” rental car company charges $20 to rent a car and $0.85 per mile. After how many miles will it be more expensive to rent from Pete’s Propulsions than Theresa’s Transportation

### Answers

On solving the provided question, we got to know that he **fraction **can bake 200/57 loaves or 3 29/57 loafs.

what is fraction?

Mathematically speaking, fractions are represented by **integers **that indicate a portion of a whole. In the same way that a whole can be any quantity, **value**, or object, a fraction can be a portion or subset of any quantity of a whole. As an example, let's try to comprehend this idea. The pizza in the picture below is cut into 8 equally sized pieces. The chosen slice of pizza might now be expressed as 1/8 if we wanted to. This indicates that we are talking about one of eight equally sized sections. It denotes a ratio of 1/8. Reading options include: One-eighth, or

1 by 8

13 1/3 divided by 3 4/5

Let's first convert these mixed numbers to incorrect fractions.

13 1/3 = 13(3) + 1 = 39 + 1 = 40/3

3 4/5 = 3(5) + 4= 19/5

Now that we have divided 40/3 by 19/5, we can just switch the operation to multiplication and flip the second fraction because we know how to divide fractions.

40/3 x 5/19 = 200/57

he can bake 200/57 loaves or 3 29/57 loafs.

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What are the values for the coefficients and constant term of 0 2 3xÂ² 5x?

### Answers

The coefficient of the **expression **3x² is the number 3 and **constant **term is 20

What are the **coefficients**?

The coefficients are the numbers on the left side or before each variable.

What is an** algebraic expression**?

Is a set of numbers and letters that make up an expression that has a meaning, the letters are **variables **and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model **mathematical **processes.

If the expression of a single term is:. 3x²

Then the only coefficient will be the number that is placed before it and it is:

Number 3

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PLEASE HELPP

mia has 3 bags the number of toys in each bag is 6, 8 and x what is the number of toys in the third bag if the average number of toys in the three bags is 6?

a. 3

b.6

c.4

d.8

### Answers

**Answer:**

b

**Step-by-step explanation:**

i think b because it makes more sense than a or c

The answer here is b here’s hii

Which functions have an axis of symmetry of x = –2? Check all that apply.

f(x) = x2 + 4x + 3

f(x) = x2 – 4x – 5

f(x) = x2 + 6x + 2

f(x) = –2x2 – 8x + 1

f(x) = –2x2 + 8x – 2

### Answers

The quadratic functions that have an **axis of symmetry** at x = -2 are given as follows:

f(x) = x² + 4x + 3.f(x) = -2x² - 8x + 1.

How to obtain the axis of symmetry of a quadratic function?

The standard **definition **of a quadratic function is given by the rule presented as follows:

y = ax² + bx + c, in which a is different of zero.

The **axis of symmetry** is given by the x-coordinate of the vertex, hence it's equation is defined as follows:

x = -b/2a.

Meaning that the correct options are given by the **first **and by the **fourth options** in this problem.

For the **first **function, we have that:

a = 1, b = 4.

Hence the axis of symmetry is **obtained **as follows:

x = -4/2 = -2.

For the **fourth **function, we have that:

a = -2, b = -8.

Hence:

x = -8/4 = -2.

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Seth built a wooden step stool out of two rectangular prisms and two cubes. Before fastening the components together, he stained each component to give it its final color.

To completely stain the bottom rectangular prism, Seth had to cover

square inches of wood. For one of the cubes to be completely stained, he had to cover

square inches of wood. To completely stain the top rectangular prism, he had to cover

square inches of wood.

Once the stool was fastened together, he applied a coat of sealant to all exposed surfaces of the stool, including the bottom, to cover a total of

square inches.

### Answers

To complete stain the bottom **rectangular prism**, he needs to cover 624 square inches.

What is surface area?

A solid object's **surface** **area** is a measurement of the overall space that the object's surface takes up.

Given that:

Bottom rectangular prism:

Length = 22 in

Width = 8 in

Height = 6 in

The surface area of the rectangular prism is:

SA = 2( lh + wh + lw)

SA = 2((22)(6) + (8)(6) + (22)(6))

SA= 624 square inches.

To complete stain the bottom rectangular prism, he needs to cover 624 square inches.

Square:

Side = 4 in

The surface area of the cube is:

[tex]SA = 6a^2[/tex]

[tex]SA = 6 (4)^2\\\\SA= 96[/tex]square inches.

To completely stain two squares, he needs to cover 96 * 2 = 196 square inches.

Top rectangular prism:

Length = 18 in

Width = 5 in

Height = 2 in

The surface area of the rectangular prism is:

SA = 2( lh + wh + lw)

SA = 2((18)(2) + (5)(2) + (18)(5))

SA = 136 square inches

Hence to completely stain top rectangular prism, he needs to cover 136 square inches.

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3 Write an equation for each function, where x is the

number of months and y is the amount owed.

Mr. Allen's plan:

Mr. Jessup's plan:

rriculum Associates, LLC Copying is not permitted.

In

-L-

ODPPY LINAL

### Answers

The **y-intercept** represents the loan amount initially. And the rate of change of the **function **will be negative The equation of Mr. Allen's plan will be y = - 80x + 560 and Mr. Jessup's plan will be y = - 40x + 400.

What is a linear equation?

A **connection **between a number of variables results in a linear model when a graph is displayed. The **variable **will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the **slope **of the line and c is the y-intercept of the line.

From the graph, the **y-intercept** of the line represents the value of the loan initially.

From the graph, the **slope **of both lines is negative, then the **rate **of **change **of the function will be **negative**.

Let 'x' be the number of **months **and 'y' be the amount **owed**.

The **two **points are (0, 560) and (1, 480). Then the equation of the line is given as,

(y - 560) = [(560 - 480) / (0 - 1)](x - 0)

y - 560 = - 80x

y = - 80x + 560

And the **equation **of the line for Mr. Jessup's plan will be given as,

y = - 40x + 400

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What are the factors of the expression xÂ² 4x 3?

### Answers

The factors of the **expression** x² 4x 3 are (x + 3)(x − 3).

What is factor?

**Factor** is a number that can be multiplied to produce another number. Factors are used to find the greatest common factor (GCF) and least common multiple (LCM) of two or more numbers. Factors are also used in equations to find solutions and in algebra to solve polynomials. Factors are also important in computing, since they are used to identify prime numbers and prime **factorisation**.

This is determined by using the factoring technique called factoring by grouping.

First, the expression is written in two groups: x2 and 4x 3. Then, each group must be factored. For the first group, the factors are x and x, since any number multiplied by itself results in the number itself. For the second group, the factors are 4 and 3, since 4 multiplied by 3 equals 12.

Next, the two factors of each group must be multiplied together. The product of x and 4 is 4x, and the product of x and 3 is 3x. The product of 4 and 3 is 12.

Finally, the two groups of factors are combined to form the final expression: (x + 3)(x − 3).

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These tables correspond to inputs and outputs. Which of these input and output tables could represent a function rule, and which ones could not?

### Answers

Table **A **is a function.

Table **B **is not a function.

Table **C **is a function.

Table **D **is not a function.

What is a function?

A function can be defined as the **outputs **for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the **dependent **variable.

We know a relation is a function if it is one-to-one or many-to-one.

But a **relation **is not a function if it is one to many.

Table A is a function and it is a many-to-one function.

Table B is not a function as input 1 leads to two different outputs 1, - 1.

Table C is a function and it is a one-to-many function.

Table D is not a function as one input leads to 3 different outputs.

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The ratio of the sides of a triangle is 3:5:6. If the perimeter of the triangle is 154 feet, what are the side lengths?

### Answers

The **side length **of the **triangle **are

33 feet55 feet66 feet

How to find the side length of the triangle

A **triangle **with given **ratio **of sides as 3 : 5 : 6 and a perimeter of 154 feet is calculated from the formula of **perimeter **which is

= a + b + c

where

a, b, and c are the **dimensions **of the side length of the triangle:

Using the values given in the problem we have

let the ratio be a multiple of x such that

154 = 3x + 5x + 6x

154 = 14x

x = 11

a = 3 * 11 = 33 feet

b = 5 * 11 = 55 feet

c = 6 * 11= 66 feet

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Luc is investigating dilations of scale factor 2 of the line y = -4x +3. He claims that for some centers of dilation, the line will remain the same. Which centers of dilation could be used to support Luc's claim? Select ALL that apply.

### Answers

Luc is correct in stating that the line will remain the same with certain dilation centers, such as the origin (0, 0) and the point (3, -4). These **centers **of dilation will cause a scale **factor **of 2, but the line will remain the same.

To check if Luc is correct, we can calculate the points of the dilation with scale factor 2.

For the **origin **(0, 0):

**Point **A: (x, y) = (0, 3)

Point B: (x, y) = (-4, -3)

Dilated Point A: (x, y) = (0, 6)

Dilated Point B: (x, y) = (-8, -6)

Equation of the dilated line: y = -4x + 6

This shows that the line is dilated with scale **factor **2, but is the same line.

For the point (3, -4):

Point A: (x, y) = (3, -1)

Point B: (x, y) = (-1, -7)

Dilated Point A: (x, y) = (6, -2)

Dilated Point B: (x, y) = (-2, -14)

**Equation **of the dilated line: y = -4x + 3

This shows that the line is dilated with scale factor 2, but is the same line.

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Simplify: [tex]\frac{32a^2bc^3}{20abc}[/tex]

### Answers

The **fractions **is **simplified **to 8ac²/ 5

What is a fraction?

A **fraction** can be described as the **part **of a **whole** element, number or variable.

There are different types of fractions, which includes;

Improper fractionsProper fractionsMixed fractionsComplex fractionsSimple fractions

Examples of improper fractions; 5/3, 7/5

Examples of proper fractions; 3/4, 5/6

Examples of mixed fractions; 3 1/2, 4 5/6

Examples of simple fractions; 1/2 , 1/ 4

From the information given, we have that;

[tex]\frac{32a^2bc^3}{20abc}[/tex]

This is simplified to;

32 × a × a × b × c × c × c/ 20 × a × b × c

Divide the common terms

8ac²/ 5

Hence, the **fractions **is 8ac²/ 5

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