Select the correct answer.
Identify the axis of symmetry of the function graphed below.

A. X=1
B. X=3
C. X=5
D. X=4

Answer:

1. Assume the contrary, namely that √2 + √3 + √5 = r, where r is a rational number.

Square the equality √2 + √3 = r − √5 to obtain 5 + 2

√6 = r2 + 5 − 2r

√5. It follows

that 2√6 + 2r

√5 is itself rational. Squaring again, we find that 24 + 20r2 + 8r

√30

is rational, and hence √30 is rational, too. Pythagoras’ method for proving that √2 is

irrational can now be applied to show that this is not true. Write √30 = m

n in lowest

terms; then transform this into m2 = 30n2. It follows that m is divisible by 2 and because

2( m

2 )2 = 15n2 it follows that n is divisible by 2 as well. So the fraction was not in lowest

terms, a contradiction. We conclude that the initial assumption was false, and therefore

√2 + √3 + √5 is irrational.

Step-by-step explanation:

Answer:

Step-by-step explanation:

"The difference of two numbers is 15."

x-y = 15

x>y

"Five times the smaller number is the same as 9 less than twice the larger number."

5y = 2x-9

y = x-15

substitution

5(x-15) = 2x-9

5x-75 = 2x-9

3x = 66

x = 22

y = x-15 = 7

Answer:

David share is 36 sweets

Step-by-step explanation:

let Lucy share be x

let David share be y

Lucy has 27 more

x=y+27

total sweet is x+y

y+27 +y= 2y+27

total ratio = 4+7=11

David share=

[tex]y = \frac{4}{11} \times (2y + 27)[/tex]

[tex]11y = 4(2y + 27)[/tex]

[tex]11y = 8y + 108[/tex]

[tex]11 y- 8y = 108[/tex]

[tex]3y = 108[/tex]

y=108/3= 36

Answer:

B. Invesment

Correct me if You want If its wrong.

Answer:

y=[tex]\frac{5}{8}x[/tex]

Step-by-step explanation:

So in this equation you have to do this with the points to get the slope

M= [tex]\frac{y2-y1}{x2-x1}[/tex]

M is the slope so using this eqaution will give you the equation.

Answer:

The three ways to solve a system of equations are substitution, elimination, and graphing. You can use these methods to solve any system of equations, it just depends on which method you use.

Step-by-step explanation:

In the substitution method, you get one variable isolated on one side of an equation, then use that equation to substitute the variable with what it's equal to into the second equation to solve the equation.

In the elimination method, you get all the variables in your equations together one side, and the constant on the other. Then, multiply or divide one or two equations to get one variable with the same coefficient for both equations (be sure to multiply or divide both sides to each equation), and add or subtract the equations together to get rid of that variable (make sure to add the left sides of the equations together and the right sides of the equations together, no the opposite!) and solve the equation.

In the graphing method, you solve for y in each equation, graph both equations on a coordinate plane, and find the point of intersection for both lines to solve the equation (For example, if the point of intersection is (2, 7), the answer to your equation would be X = 2 and Y = 7).

Answer:

64

Step-by-step explanation:

37+27=64

Answer:

The vertex of f(x) is at (-5,-10).

The function g(x) is decreasing at a rate of 5%.

The zeros of h(x) are at x = -3 and x = 1.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

[tex]f(x) = ax^{2} + bx + c[/tex]

It's vertex is the point [tex](x_{v}, f(x_{v})[/tex]

In which

[tex]x_{v} = -\frac{b}{2a}[/tex]

If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]f(x_{v})[/tex]

Decaying exponential function:

A decaying exponential function has the following format:

[tex]A(x) = A(0)(1-r)^{x}[/tex]

In which A(0) is the initial quantity and r is the decay rate.

Zeros of a function:

Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] such that it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.

Vertex of f:

The function f is given by:

[tex]3(x+5)^2 - 10[/tex]

Expanding the calculations to place at the correct format:

[tex]3(x+5)^2 - 10 = 3(x^2 + 10x + 25) - 10 = 3x^2 + 30x + 75 - 10 = 3x^2 + 30x + 65[/tex]

Which means that

[tex]a = 3, b = 30, c = 65[/tex]

The x-value of the vertex is:

[tex]x_{v} = -\frac{30}{2*3} = -5[/tex]

The y-value of the vertex is:

[tex]f(-5) = 3(-5+5)^2 - 10 = -10[/tex]

The vertex of f(x) is at (-5,-10).

Decreasing rate of g(x).

We have that:

1 - r = 0.95

So

r = 1 - 0.95 = 0.05

Which means that the decreasing rate is of 5%.

The zeros of h(x) are

The zeros are

x + 3 = 0 -> x = -3

x - 1 = 0 -> x = 1

So

The zeros of h(x) are at x = -3 and x = 1.

Answer:

The third side is 17

Step-by-step explanation:

To find the hypotenuse, you square the legs of the right triangle and add the values together, and then take the square root of their sum. [tex]\sqrt{15^{2} + 8^{2} }[/tex] = [tex]\sqrt{225 + 64}[/tex] = [tex]\sqrt{289}[/tex] = 17

Answer:

[tex]\displaystyle m=\frac{1}{3}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (5, 0)

Point (-4, -3)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Answer:

44

Step-by-step explanation:

delta math

The length of t is approximately 43.60 cm, to the nearest centimeter.

The properties of the triangle are:

1. The sum of all the angles of a triangle (of all types) is equal to 180°.

2. The sum of the length of the two sides of a triangle is greater than the length of the third side.

3. In the same way, the difference between the two sides of a triangle is less than the length of the third side.

To find the length of side t in triangle RST, we can use the law of cosines, which relates the lengths of the sides and the cosine of one of the angles in a triangle:

[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]

where c is the length of the side opposite the angle C, and a and b are the lengths of the other two sides.

In this case, we know that:

r = RS = 52 cm

s = ST = 55 cm

∠T = 48°

So, we want to find the length of t, which is the side opposite the angle T.

Let's call the length of t "c". Then, applying the law of cosines, we have:

[tex]c^2 = r^2 + s^2 - 2rs cos(T)\\\\c^2 = (52 cm)^2 + (55 cm)^2 - 2(52 cm)(55 cm) cos(48^0)\\\\c^2 = 1901.57[/tex]

Taking the square root of both sides, we get:

c= 43.60 cm

Therefore, the length of t is approximately 43.60 cm, to the nearest centimeter.

Learn more about triangles here:

https://brainly.com/question/2773823

#SPJ2

Answer:

d=1

e=4/9

f=16/81

Step-by-step explanation:

Substitute x in the right column with the values in the left column to find d, e, and f.

Answer:

d = 1

e = 4/9

f = 16/81

Step-by-step explanation:

d is 1 because any term raised to the power of zero equals one

e: (2/3)² = 2²/3² = 4/9

f: (2/3)^4 = 2^4/3^4 = 16/81

Answer:

B

Step-by-step explanation:

Hope this helps

Answer:

It would be B

Step-by-step explanation:

Hope this helps

Answer:

A

Step-by-step explanation:

As 2 < a < 5, only option A suffices this condition, because 2 < 3 < 5.

Answer:

x = 16

Step-by-step explanation:

Since ∆ABC is congruent to ∆DEC, their corresponding angles would be equal to each other.

<B is congruent to <E, therefore,

<B = <E

x + 15 = 6x - 65 (substitution)

Collect like terms

x - 6x = -15 - 65

-5x = -80

Divide both sides by -5

x = 16

Answer:

f(g(x)) = 2x - 7

g(f(x)) = 2x - 2

Step-by-step explanation:

basically, you just want to plug in the g(x) function wherever you see an x in the f(x) function

f(g(x)) = 2(x - 5) + 3

         = 2x - 10 + 3

         = 2x - 7

the inverse function is doing the same thing but plugging in f(x) wherever you see an x in the g(x) function

g(f(x)) = (2x + 3) - 5

         = 2x + 3 - 5

         = 2x -2

Answer:

3

Step-by-step explanation:

Answer:

9000

Step-by-step explanation:

Answer:

C. Mitch, because he gets higher median hours of sleep

Step-by-step explanation:

Answer:

1600

Step-by-step explanation:

pls brainliest

Answer:

hope it helped have a good day mate

Answer:

I'm pretty sure the answer is B.

Step-by-step explanation:

Hope this helps u out!

Answer:

Slope Number 1 is Harry.

Step-by-step explanation:

y = -1/2 + 30

-1 being one less exercise to complete

2 being the 2 minutes spent on each exercise

and 30 being the number of exercises

Answer:

I would say 2 hours

Answer:

Reflection and Dilation

Step-by-step explanation:

These two make the most sense for this.

Hope it helps and is correct!

Answer:

c

Step-by-step explanation:

3x16=48

3+16+3+16=48

pls brainliest

Answer:

The 5 bags of pretzels.

Step-by-step explanation:

Because if you were to buy 5 individual bags you would end up paying $20.00, instead of $12.00

Answer:

The second option

Step-by-step explanation:

In order to find the unit price of each, consider the quotient of amount of money per bag:

Case 1:

$4/ 1 bag

Case2:

$12 / 5 bags = $2.4 / 1 bag

Therefore, the second option is the one with lower unit price.

Answer:

50 coffees

(and 40 empanadas)

Step-by-step explanation:

x= coffee y=empanadas

.5x+2y=105

x+y=90

Isolate a variable

x+y=90

x-90= -y

-x+90=y

Plug this in for y in the other equation

.5x+2(-x+90)=105

Solve for x

.5-2x+180=105

-1.5x= -75

x=50

we can stop here but that's lame so let's figure out how many empanadas she sold

we know that x=50 so we can just plug this into either beginning equation and solve for y

50+y=90

y=40

x = -6, 8

Find the values of x by factoring, getting

(x - 8)(x + 6) = 0

Answer:

x = -6, 8

Step-by-step explanation: