How are translations and reflections represented as a function?​


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The solution of the equation is x= -6 or x = 2.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

We have the Equation x²+ 4x -4 - 8 or x² + 4x - 12.

Now Factorizing the equation we get

x² + 4x - 12

= x² + 6x - 2x  - 12.

= x (x+ 6) - 2( x+ 6)

= (x -2) (x+ 6)

So, x-2 = 0 or x+ 6= 0

x= 2 or x= -6

Thus, the solution of the equation is x= -6 or x = 2.

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Answer:

t = 32

Step-by-step explanation:

The given equation is :

[tex]24=\dfrac{3}{4}t[/tex] ....(1)

Where

t is the number of guests attending the catered event.

The reciprocal of [tex]\dfrac{3}{4}[/tex] is [tex]\dfrac{4}{3}[/tex].

Multiplying both sides by the reciprocal of [tex]\dfrac{3}{4}[/tex].

[tex]24\times \dfrac{4}{3}=\dfrac{3}{4}\times \dfrac{4}{3}t\\\\t=8\times 4\\\\t=32[/tex]

Hence, 32 guests will attend the catered.

Answer:

x = 4

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

B. $137.20

Step-by-step explanation:

Answer:

x = -2.3

Step-by-step explanation:

4x + 1.3 = -7.9

First we want to combine the like terms.

Subtract 1.3 from both sides.

4x = -9.2

Now we want to isolate x by dividing both sides by 4.

x = -2.3

Check your answer by plugging x back into the original equation.

4x + 1.3 = -7.9

4(-2.3) + 1.3 = -7.9

Multiply.

-9.2 + 1.3 = -7.9

Add.

-7.9 = -7/9

Your answer is correct.

Hope this helps!

Step-by-step explanation:

4x + 1.3 = - 7.9

4x = - 7.9 - 1.3

4x = - 9.2

x = - 9.2/4

= - 2.3

9514 1404 393

Answer:

  5/8 or 5/9

Step-by-step explanation:

The fraction will be exactly ...

  5/(8 1/2) = 10/17   ⇒   (8 1/2)×(10/17) = 5

__

The fraction will be approximately ...

  5/8 or 5/9

The denominator will be a number that makes (8 1/2)/(denominator) ≈ 1. For that denominator, the numerator will be 5, so that we have ...

  (8 1/2) × (5/denominator) ≈ 5

  (8 1/2)/(denominator) ≈ 1 .  . . . . . . . divide by 5

If we want the denominator to be an integer, we could choose either 8 or 9. If we choose 8, the result will be slightly more than 5; if we choose 9, the result will be slightly less.

  (8 1/2) × (5/8) = 5.3125 ≈ 5

  (8 1/2) × (5/9) = 4.722... ≈ 5

Either 5/8 or 5/9 will give a product of about 5.

Answer:

Step-by-step explanation:

Answer:

keiko- x

imelda- x+ 36

Sarah- x- 38

Step-by-step explanation:

Answer:

a. the line that passes through the most data points.

Step-by-step explanation:

The least-squares regression line is the line that passes from mostly all the data points also this line would be located on a scatterplot that minimizes the distance square from the points to the line

Therefore as per the given situation, the option a is correct

Hence, the rest of the given options would be wrong

Step-by-step explanation:

[tex] \frac{360 - 2(x + 30)}{2} = x \\ 360 - 2x - 60 = 2x \\ 300 - 4x = 0 \\ 4x = 300 \\ x = 300 \div 4 = 75[/tex]

Answer:

75 degrees

Step-by-step explanation:

In a parallelogram, adjacent angles always add up to 180 degrees. So, for example, A+B=180 and C+B=180.

Therefore, A+D=180.

Because we're given that angle A is (x+30) degrees and angle D is x degrees, we can plug them into the below equation:

[tex](x+30)+x=180[/tex]

Open up the parentheses

[tex]x+30+x=180\\2x+30=180[/tex]

Subtract both sides by 30

[tex]2x-30=180-30\\2x=150[/tex]

Divide both sides by 2

[tex]\frac{2x}{2} =\frac{150}{2} \\x=75[/tex]

Therefore, x is equal to 75 degrees.

I hope this helps!

Answer:

$1,045

Step-by-step explanation:

40×22=880

22÷2=11

11+22=33

33×5=165

165+880=1,045

Answer:

15 dollars each pizza

Step-by-step explanation:

2 pizzas (15 + 15 = 30)

30 + 6 = 36

Answer:

15

Step-by-step explanation:

15+15=30+6 =36

Answer:

Step-by-step explanation:

Answer:

x= 7/20

Step-by-step explanation:

(5+2×8)/6=x(4+6)

(5+16) /6 = 4x+6x

21/6=10x (divide 21/6 by 3)

7/2=10x

7/2×1/10= x

x= 7/20

Hope this helps :)

Keep Smiling

Answer: C

Step-by-step explanation:

Answer:

x = 3.5

y = 8x + 12

Step-by-step explanation:

1) Given the equation

12x = 4(x+2)+20

Expand

12x = 4x+8+20

12x - 4x = 28

8x = 18

x = 28/8

x = 3.5

Hence the value of x is 3.5

2) The standard form of equation in slope intercept form is y = mx+c

m is the slope

c is the y intercept

Get the y-intercept

Substitute m = 8 and (0, 12) into y = mx+c

12 = 8(0)+c

12 = c

c = 12

Get the required equation

Recall that y = mx+c

y = 8x + 12

This gives the required equation

Answer:

(a) Yes, it does not matter if f is continuous or differentiable; every function satisfies the Mean Value Theorem.

(b) [tex]c =0.51995[/tex]

Step-by-step explanation:

Given

[tex]f(x) = e^{-4x};\ [0,2][/tex]

Solving (a); Does the function satisfy M.V.T on the given interval

We have:

[tex]f(x) = e^{-4x};\ [0,2][/tex]

The above function is an exponential function, and it is differentiable and continuous everywhere

Solving (b): The value of c

To do this, we use:

[tex]f'(c) = \frac{f(b) - f(a)}{b - a}[/tex]

In this case:

[tex][a,b] = [0,2][/tex]

So, we have:

[tex]f'(c) = \frac{f(2) - f(0)}{2 - 0}[/tex]

[tex]f'(c) = \frac{f(2) - f(0)}{2}[/tex]

Calculate f(2) and f(0)

[tex]f(x) = e^{-4x}[/tex]

So:

[tex]f(2) = e^{-4*2} = e^{-8} = 0.00033546262[/tex]

[tex]f(0) = e^{-4*0} = e^{0} = 1[/tex]

This gives:

[tex]f'(c) = \frac{0.00033546262 - 1}{2}[/tex]

[tex]f'(c) = \frac{-0.99966453738}{2}[/tex]

[tex]f'(c) = -0.4998[/tex]

Note that:

[tex]f'(x) = (e^{-4x})'[/tex]

[tex]f'(x) = -4e^{-4x}[/tex]

This implies that:

[tex]f'(c) = -4e^{-4c}[/tex]

So, we have:

[tex]f'(c) = -0.4998[/tex]

[tex]-4e^{-4c} =-0.4998[/tex]

Divide both sides by -4

[tex]e^{-4c} =\frac{-0.4998}{-4}[/tex]

[tex]e^{-4c} =0.12495[/tex]

Take natural logarithm of both sides

[tex]\ln(e^{-4c}) =\ln(0.12495)[/tex]

[tex]\ln(e^{-4c}) =-2.0798[/tex]

Apply law of natural logarithm

[tex]\ln(e^{ax}) =ax[/tex]

So:

[tex]-4c =-2.0798[/tex]

Solve for c

[tex]c =\frac{-2.0798}{-4}[/tex]

[tex]c =0.51995[/tex]

Answer:

0.48 = 48% probability that an employee selected at random will need either corrective shoes or major dental work

Step-by-step explanation:

I am going to solve this question treating these events as Venn probabilities.

I am going to say that:

Event A: Employee needed corrective shoes.

Event B: Employee needed major dental work.

22% of the employees needed corrective shoes

This means that [tex]P(A) = 0.22[/tex]

29% needed major dental work

This means that [tex]P(B) = 0.29[/tex]

3% needed both corrective shoes and major dental work.

This means that [tex]P(A \cap B) = 0.03[/tex]

What is the probability that an employee selected at random will need either corrective shoes or major dental work?

This is:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

Replacing the values that we have:

[tex]P(A \cup B) = 0.22 + 0.29 - 0.03 = 0.48[/tex]

0.48 = 48% probability that an employee selected at random will need either corrective shoes or major dental work

Answer:

10 is A

11 is D

12 is C

and 13 is B

Answer:

With algebraic expressions, you can’t add and subtract any terms like you can add and subtract numbers. Terms must be like terms in order to combine them. So, you can’t always simplify an algebraic expression by following the order of operations. You have to use the distributive property to rewrite the expression and then combine like terms to simplify. With numeric expressions, you can either simplify inside the parentheses first or use the distributive property first.

Step-by-step explanation:

Answer:

Algebraic expressions have terms, Terms must be like to add and subtract,    You can’t always follow the order of operations with algebraic expressions.

Step-by-step explanation:

Answer :A

explaination: when we reflect an ordered pair over the origin, we can it write like this (0,y)

{y; 0<y<infinite }

ex: (0,1)

(0,2)

(0,3) etc

Answer:

21.4

Step-by-step explanation:

Answer:

A or top left

Step-by-step explanation:

Isosceles triangles should have a perpendicular bisector from an angle to the opposite base.

The top left has that factor.

Answer:

x² - 12x + 36

factored: (x - 6)(x - 6)

Answer:

yes it's a inverse function

Answer:

Yes it is

Step-by-step explanation:

To remeber, if none of the lines overlap or crosses each other, its a function.

Answer:

I think its y-x, if y >x.

Step-by-step explanation:

Answer:

I think it's the second one y=400x I'm not sure . I hope that I helped you

Answer:

[tex]y=50x[/tex]

Why:

We can tell the slope because for every hour, the car travels 50 miles by simply looking at the graph. This would be a slope of [tex]\frac{50}{1}[/tex], or 50. Because the y-intercept is 0, no intercept appears on the equation. Good luck!

Answer:

it should be the graph on the bottom right

Step-by-step explanation:

The income should be more than the cost in order to make a profit and that happens for Leanne when she sells 8 quilts, so the 8 should be on the x-axis (the axis named "Quilts Sold")

The income should be 0 in the beginning bc when she sells 0 quilts she will be earning 0.

after selling 8 quilts her income will be higher than her costs

(Though naming the y-axis as "profit" is not accurate bc when she sells 0 quilts she will lose money since she will be spend money to make the quilts but not earn the money to compensate for the cost).

with all of these reasons combined the correct should be the one on the bottom right

Answer:

Step-by-step explanation:

height after x seconds = -16x² - 2x + 600

-16x² - 2x + 600 = 450

16x² + 2x - 150 = 0

8x² + x - 75 = 0

Quadratic formula

x = [-1 ± √(1² – 4·8(-75))] / [2·8]

 = [-1 ± √2401] / 16

 = [-1 ± 49] /16

 = 3, -3⅛

-3⅛ is an extraneous solution, so x = 3 seconds.

Answer:

a) x= 29, y= 87

b) x= 19, y= 45

Step-by-step explanation:

Q5. a) Let the first number be x and the second number be y.

The sum of 2 integers is 116.

x +y= 116 -----(1)

The second number is three times the first number.

y= 3x -----(2)

Substitute (2) into (1):

x +3x= 116

4x= 116

x= 116 ÷4

x= 29

Substitute x= 29 into (2):

y= 3(29)

y= 87

b) Let the smaller number be x and the larger number be y.

x +y= 64 -----(1)

y -x= 26 -----(2)

Since we have to use substitution to solve the equations, let's first rewrite an equation to make one of the variables the subject of the equation.

From (1):

x= 64 -y -----(3)

Substitute (3) into (2):

y -(64 -y)= 26

y -64 +y= 26 (expand bracket)

2y= 26 +64 (simplify, +64 on both sides)

2y= 90

y= 90 ÷2

y= 45

Substitute y= 45 into (3):

x= 64 -45

x= 19