You are given that f(x)=x²+4 and g(x)=3 x-1 .

a. What are the domain and range of f(x) and g(x) ?

Answer:

Step-by-step explanation:

The coordinate of the midpoint of the segment is -10

We have been given,

The coordinate of the endpoints of the segment are , -16 and -4

We need to find the coordinate of the midpoint of the segment.

Using the midpoint formula,

m = (-16-4)/2

   = -20/2

   = -10

Therefore, the coordinate of the midpoint of the segment is -10

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Answer:

m = -3

Step-by-step explanation:

According to the question, to calculate the zeros of each function. The given function is f(x) = [tex]x^{4}-5x^{2} +6[/tex]

Now, let us assume [tex]a=x^{2}[/tex]. Therefore, the above equation can be written as:

[tex]f(x)=a^{2}-5a+6[/tex]

Calculate the factors of the given equation and it can be re-written as:

[tex]f(x) = (a+2)(a+3)[/tex]

To calculate the final solution, equate it to zero.

[tex](a+2)(a+3)=0\\a=-2,-3[/tex]

Now, substitute these values in the original assumed equation:

The zeros function values are [tex]-\sqrt{2i};\sqrt{2i},-\sqrt{3i} ,\sqrt{3i}[/tex]

What is zero functions?

A zero function is a function which is almost zero everywhere on the graph. It is also known as a constant function.

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In the right triangle XYZ, angle X and angle Y are complementary angles, is angle sin z= 36/85, then the value of cos z= 77/85

In the right triangle XYZ, angle X and angle Y are complementary angles.

The complementary angle is either of two angles whose sum is 90 degrees

Therefore,

Angle X + Angle Z = 90 degrees

In trigonometry,

sinθ = Opposite side / Hypotenuse

sin z= 36/85

z= [tex]sin^{-1}(\frac{36}{85} )[/tex]

z= 25.06

Then the value of cos z is

cos 25.06 = 77/85

Hence, in the right triangle XYZ, angle X and angle Y are complementary angles, is angle sin z= 36/85, then the value of cos z= 77/85

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The summation of f (x) and g (x) = x ² + 3 x + 3

Given,

f (x) = x ² + 4

g (x) = 3 x - 1

The question states to find the summation of the function f, that is, f (x) = x ² + 4, and function g, that is, g (x) = 3 x - 1

Performing the addition operation on these functions is just like simple addition.

This implies, adding the two functions f (x) and g (x), we get

f (x) + g (x) = x ² + 4 + 3 x - 1

=> f (x) + g (x) = x ² + 3 x + 3

This assumes that the summation or addition of the two functions f (x) and g (x) gives x ² + 3 x + 3

Therefore, we get the summation of f (x) and g (x) as x ² + 3 x + 3

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The value of the x means hypotenuse according to the Pythagoras is 12.8.

According to the statement

We have to find that the value of the x.

So, For this purpose, we know that the

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse

From the given information:

The perpendicular length is 12.

And The base is a 4.5

And we have to find that the hypotenuse value.

Then

According to the theorem

Perpendicular^2 + base^2 = Hypotenuse^2

And substitute the value then

12^2 + 4.5^2 = Hypotenuse^2

144 + 20.25 = Hypotenuse^2

Then

Hypotenuse^2 = 144 + 20.25

Hypotenuse^2 = 164.25

Hypotenuse = 12.8.

So, The value of the x means hypotenuse according to the Pythagoras is 12.8.

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The solution of the equation solved for a is (D)  y c-x b / x

As it is given that

x / y = c / a + b

Calculating for a

(a + b)x = cy

a + b = cy / x

a = (cy / x) - b

a = (cy - bx) / x

a = (yc - xb) / x

The solution of the equation solved for a is (D)  y c-x b / x

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The value of a calculated by Noemi is not correct as the correct value is

     a = -1/45

We know that the general form of the quadratic equation is given as

                        y = ax² + bx + c

where, a and b are coefficients of the variable x and c is the constant term.

Now according to the question the path of the golf ball is parabola whose coordinates will be

       (0,0) = origin where it starts

       (60,80) = vertex or the maximum point

       (120,0) = end point

Now putting the value of (x,y) in the above formula to find the value of a,b and c

when (x,y) = (0,0)

       0 = a0² + b0 +c

       c = 0

when (x,y) = (60,80)

      80 = a60² + b60 +c

       80 = 3600a + 60b + 0        (1)

when (x,y) = (120,0)

      0 = a120² + b120 +c

      0 = 14400a + 120b + 0      

       120b = -14400a

          b = -120a

Putting the value of a in equation (1) we get

    80 = 3600a + 60(-120a)

    80 = 3600a - 7200a

    80 = -3600a

     a = - 1/45

 ⇒ b = 8/3

Hence the equation will be         y = -1/45x² + 8/3x

and the value of a calculated by Noemi is not correct as the correct value is a = -1/45

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The answer to the given logarithm expression is  log₁/₂ 1/2 = 1

Another technique to clarify exponents in mathematics is through logarithms. A base number's logarithm equals another number.

For instance, log10 100 = 2 if 102 = 100. A logarithm is defined as an influence by which variety must be raised to receive another value. this is often the foremost convenient thanks to represent large numbers. Logarithms have several important properties that prove that logarithmic multiplication and division is written because the logarithm of addition and subtraction. The log is named the logarithm of base e. The logarithm is represented by ln or loge. where 'e' represents Euler's constant,  approximately capable 2.71828. as an example, the log of 76 is written as ln 76. The log defines what percentage times 'e' must be multiplied to induce the required output.

Using log property logₐ a = 1log₁/₂ 1/2 = 1

Hence , we evaluated the logarithm which is log₁/₂ 1/2 = 1

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The expression that represents the temperature of the water after Raul added the ice cubes is 72.3°F + (72.3°F)

From the question, we are to write an expression that represents the temperature of the water after Raul added ice.

From the given information,

The initial temperature is 72.3°F

and

The change in temperature was -39.1°F

Thus,

The expression that represents the temperature of the water after Raul added the ice cubes is

72.3°F + (72.3°F)

Hence, the expression written as the sum of two numbers is 72.3°F + (72.3°F)

Here is the complete question:

Raul is performing an experiment. He pours water into a glass and measures the temperature of the water at 72.3°F. Then he adds a few ice cubes to the glass of water. He measures the temperature of the water again and finds that it has changed by -39.1°F. Write an expression that represents the temp of the water after Raul added the ice cubes. Write the expression as the sum of two numbers.

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Step-by-step explanation:

lily's in months=4/12

hugos in months=8/12

4/12+8/12

1/3+2/3

lily's month in simplest form=1/3

hugos month in simplest form=2/3

Answer:

7°

Step-by-step explanation:

The three angles of a triangle should sum up to 180°

→   m∠1 + 121 + 52 = 180

→   m∠1 + 173 = 180

→   m∠1 = 180 - 173 = 7°

A function that models each inverse variation is y = 24. 1/x and y when x=-5 is -24/5

Those with inverse properties cancel each other out. In other words, f(g(x)) = g(f(x)) = x if g(x) is f's inverse (x). We have a great approach we can use to achieve this given an equation for which we desire the inverse.

Not every action has an equivalent. It is obvious that f(x) will never again have the same value if it has an inverse. We designate a unique name for this resource.

Inverse variation is y = k. 1/x

given y = 12

x = 2

So, 12 = k. 1/2

So, the value of k = 24

We can conclude that the value of constant variation is 24

when x = -5, the value of y will be -

y = k.1/x

y = 24 . 1/-5

y = -24/5

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The simplification of 4+√12 / 4-√12 after rationalizing all denominators

is 7+4[tex]\sqrt{3}[/tex]

We are given the equation;

[tex]\frac{4+\sqrt{12} }{4-\sqrt{12} }[/tex]

The above equation can also be written as;

[tex]\frac{4+\sqrt{4*3} }{4-\sqrt{4*3} }[/tex]

Since our question requires us to rationalize the denominator, we will use the initial equation to rationalize the denominator. That is;

[tex]\frac{4+\sqrt{12} }{4-\sqrt{12} }[/tex]  *  [tex]\frac{4+\sqrt{12} }{4+\sqrt{12} }[/tex]

We then simplify;

4(4+[tex]\sqrt{12}[/tex])+[tex]\sqrt{12}[/tex](4+[tex]\sqrt{12}[/tex]) /  4(4+[tex]\sqrt{12}[/tex])- [tex]\sqrt{12}[/tex](4+[tex]\sqrt{12}[/tex])

= 16+4[tex]\sqrt{12}[/tex]+4[tex]\sqrt{12}[/tex]+[tex]\sqrt{12*12}[/tex] / 16+4[tex]\sqrt{12}[/tex]-4[tex]\sqrt{12}[/tex]-[tex]\sqrt{12*12}[/tex]

= 16+8[tex]\sqrt{12}[/tex]+12 /16-12

=28+8[tex]\sqrt{12}[/tex] / 4

=28+8[tex]\sqrt{4*3}[/tex] /4

= 28+8*2[tex]\sqrt{3}[/tex] /4

=28+16[tex]\sqrt{3}[/tex] /4

Divide all sides by 4;

= 7+4[tex]\sqrt{3}[/tex]

The final answer is therefore; 7+4[tex]\sqrt{3}[/tex]

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Answer:    14 min

Step-by-step explanation:

After 14 minutes more the scene will have the same amounts rendered if the computer is rendering two scenes.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

A computer is rendering two scenes. The computer has already rendered 540 thousand pixels (kpx) of a kitchen scene and renders another 90kpx each.

Let after t minutes the scene will have the same amounts rendered.

The linear equation in one variable can be framed as:

540 + 90t = 960 + 60t

After solving the above linear equation in one variable:

90t - 60t = 960 - 540

30t = 420

t = 14 minutes

Thus, after 14 minutes more the scene will have the same amounts rendered if the computer is rendering two scenes.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

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This version is much shorter, and more simpler, compared to 5 x 10^6 millimeters. It's more appropriate to use millimeters with very small objects or distances.

Note: 5 x 10^6 = 5,000,000 = 5 million

Answer:

8.8 x 10^3

Step-by-step explanation:

8.8  *  1 x 10^3  = 8.8 x 10^3      <=====  done

summing-up the values for equation of line y = x/2 + 1 in table :

x       y

-10   -4

-6    -2

-2     0

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

Here, the given equation is :

y = x/2 + 1

Now, computing the value of y corresponding to values of x by substituting values in above equation :

when x = -10 :

y = x/2 + 1

y = -10/2 + 1

y = -5 +1

y = -4

similarly, for :

x = -6 , y = -2

x = -2 , 0

summing-up the above values in table that is attached below :

x       y

-10   -4

-6    -2

-2     0

⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

Now to draw the line graph of above equation taking any two coordinates let us say (-2,0) and (-2,-6). Now drawing the line joining these two points as shown in figure attached below.

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Answer:

g(f(x)) = 4x^2 + 8x + 4

Step-by-step explanation:

If f(x) = 2x + 1 and g(x) = x² + 2x + 1, find g(f(x)).

You are asked to find g of f of x.

This means your x value for the equation g(x) is f(x), hence g(f(x)).

g(2x+1)=(2x+1)^2 + 2(2x+1) +1

g(2x+1) = 4x^2 + 4x + 1 +4x + 2 + 1

Combine like terms.

g(2x+1) = 4x^2 + 8x + 4

g(f(x)) = 4x^2 + 8x + 4

Answer:

Slope: 2/1

equation: y=2/1x+2

Answer:

z+2y

Step-by-step explanation:

z is the only z there so dont have to change

-3y+5y=2y

so u get z+2y

Hey there!

z - 3y + 5y

= 1z - 3y + 5y

COMBINE the LIKE TERMS:

= (-3y + 5y) + (1z)

= -3y + 5y + 1z

= 2y + 1z

= 2y + z

Therefore, your answer should be:

2y + z

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The solution to the given system of equations is x = 1, y = 1. That is, (1, 1)

From the question, we are to solve the given system of equations.

The given system of equations is

y = -2x + 3y  ------------- (1)

y = 5x - 4      ------------- (2)

Substitute equation (2) into equation (1)

y = -2x + 3y

5x - 4 = -2x + 3(5x - 4)

5x - 4 = -2x + 15x - `12

Collect like terms

-4 + 12 = -2x + 15x - 5x

Simplify

8 = 8x

∴ x = 8/8

x = 1

Substitute the value of x into equation (2)

y = 5x - 4

y = 5(1) - 4

y = 5 - 4

y = 1

Hence, the solution to the given system of equations is x = 1, y = 1. That is, (1, 1)

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Jack spent first a total of AED 1282.04 and when he bought the box it cost AED 205.96

To solve this problem we must perform the following algebraic operations with the given information

Information about the problem:

Calculating the total cost Jack spend before bought the box:

Total cost = (No. drill bits*cost of drill bits) +  (No. washers  *cost of washers ) +  (No. hammers *cost of hammers)

Total cost = (8 drill bits * AED 11.22/ drill bits) + (10 washers * AED 10.11 / washers) + (2 hammers * AED 545.59 / hammers)

Total cost = AED 89.76 + AED 101.1 + AED 1091.18

Total cost = AED 1282.04

Calculating the box cost:

Balance = Paid - (Total cost + box cost)

Balance = Paid - Total cost - box cost

box cost = Paid - Total cost - Balance

box cost = AED 1500 - AED 1282.04 - AED 12

box cost = AED 205.96

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

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The solution of the given equation by rounding off it to the nearest ten-thousandth is 0.0872.

What is a round-off of the digit?

In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.

For eg: 13.58 ~ 13.6

Solving the given equation log 8(2x - 1) = 1/3

We are given a logarithmic expression: log 8(2x - 1) = 1/3

We know that e^(log b) = b

a log b = (log b)^a

log a + log b = log (ab)

Using exponential on both sides, we have

e^(log 8(2x - 1)) = e^(⅓)

8(2x - 1) = 1.3956

(2x - 1) = 1.3956 / 8

2x = 0.17445

x = 0.0872

Hence, the solution of the given equation rounded off to the nearest ten-thousandth is 0.0872.

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Answer:

y = 85

Step-by-step explanation:

6x - 25 = 4x + 15

(Subtract 4x from both sides)

2x - 25 = 15

(Add 25 to both sides)

2x = 40

(Divide 40 by 2)

x = 20

6(20) - 25 = 4(20) + 15

(Solve)

95 + 95 = 190

(Subtract 360 from 190)

360 - 190 = 170

(Divide 170 by 2)

85

y = 85

Writing 2,000 words will take about 50 minutes for the average writer typing on a keyboard and 1.7 hours for handwriting.

Answer:

5 hours. the response has to be 20 characters long.