Susan makes purple paint by mixing red and blue paint in the ratio 2:3
She has 12ml of red and 15ml of blue
What is the maximum amount of purple she can make?

Answer: Choice D) x is a real number

Reason:

We can replace x with any number we want without any restriction. There's no issues dealing with division by zero errors for instance, and we also don't have negatives under square roots to worry about. The domain of any linear function is always "the set of all real numbers".

Extra info: The domain in interval notation is [tex](-\infty, \infty)[/tex] which could be thought of as [tex]-\infty < x < \infty[/tex], i.e. x is between negative infinity and positive infinity.

Answer:

d

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The slope-intercept form is the equation of a straight line (y=mx+b)

m= gradient and b= y-intercept

m=2/3 (rise over run)  b= 4 (it goes through the point (0,4)

y=(2/3)x+4

Get rid of the fraction by multiplying everything by 3

3y=2x+12

which is also -2x+3y=12

La operación que representa 147.3 = 441 es dada por una multiplicación, por eso opción c es correcta.

El resultado del producto entre 147 y 3 es de 441, por lo que se hace una operación de multiplicación.

Así, hay que la opción c es correcta.

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Answer:

y=-4 is a function

Step-by-step explanation:

It passes the vertical line test, and each x has only one y, so it is a function.

x = -4 is NOT a function because one x has multiple y values. It does not pass the vertical line test.

Step-by-step explanation:

if I understand the question, write an equation for n in terms of i for number of Id cards an d for number driver license.

n = 15i + 20d

The value of n for a total minutes processing id card applications and driver's license applications would be 35 minutes.

Used the concept of addition that states,

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that,

For her job, Natasha spent a total of n minutes processing id card applications and driver's license applications.

And, it takes Natasha 15 minutes to process an id card application and 20 minutes to process a driver's license application.

Now by the given condition, we get;

n = 15 minutes + 20 minutes

n = 35 minutes

Therefore, the value n is 35 minutes.

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The magnitude of the electric field at the point (-2, 2, 0) is 46.52 V/m

Since in a certain region of space, the potential is given by v = 2x − 5x²y 3yz²,

The electric field, E = -grad(V) where grad(V) = (dV/dx)i + (dV/dy)j + (dV/dz)k

Since V = 2x − 5x²y + 3yz²

dV/dx = d(2x − 5x²y + 3yz²)/dx

= d2x/dx - d5x²y/dx + d3yz²/dx

= 2 - 10xy + 0

= 2 - 10xy

dV/dy = d(2x − 5x²y + 3yz²)/dy

= d2x/dy - d5x²y/dy + d3yz²/dy

= 0 - 5x² + 3z²

=  - 5x² + 3z²

dV/dz = d(2x − 5x²y + 3yz²)/dz

= d2x/dz - d5x²y/dz + d3yz²/dz

= 0 - 0 + 6z

=  6z

So, E = -grad(V)

= -[(dV/dx)i + (dV/dy)j + (dV/dz)k]

= -[(2 - 10xy)i + (- 5x² + 3z²)j + (6z)k]

So, the electric field at (-2, 2, 0) is

E = -[(2 - 10xy)i + (- 5x² + 3z²)j + (6z)k]

E = -[(2 - 10(-2)(2))i + (- 5(2)² + 3(0)²)j + (6(0))k]

E = -[(2 + 40)i + (- 5(4) + 0)j + (0)k]

E = -[42i + (-20 + 0)j + (0)k]

E = -[42i - 20j + 0k]

E = -42i + 20j - 0k

So, the magnitude of E at (-2, 2, 0) is

|E| = √[(-42)² + 20² + 0²]

=  √[1764 + 400 + 0]

= √2164

= 46.52 V/m

So, the magnitude of the electric field at the point (-2, 2, 0) is 46.52 V/m

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Answer:

Step-by-step explanation:

Answer:

C. m∠1 = m∠4

Step-by-step explanation:

A. m∠2 + m∠4 = 180°

∠2 and ∠4 are vertically opp. angles which means m∠2 = m∠4.

Hence, it's a false statement.

B. m∠2 + m∠3 = 180°

∠2 and ∠3 are corresponding angles which means m∠2 = m∠3.

It's a false statement.

C. m∠1 = m∠4

∠1 and ∠4 are another pair of corresponding angles which clearly states that m∠1 = m∠4.

Therefore, it's a true statement.

D. m∠1 = 90°

As clearly visible in the diagram;

It's a false statement.

Answer:

700 kWh which is more than 200 so

0.10(x - 200) + 30

0.10( 700 -200)+ 30

0.10( 500) + 30

50 + 30

80

$80

Answer: The range of the function is all real numbers less

than or equal to 0.

The correct statement for the given function f(x) = -√x is "The range of the function is all real numbers less than or equal to 0." So, the correct option is C.

The domain of the function is all real numbers that are greater than or equal to 0 but we know that the square root of a negative number is in the real number system.

The graph of the function shows that for each positive input i.e. the range values we get the output values that are negative or zero.

Therefore, the range of the function is all real numbers less than or equal to 0, which is option C.

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Answer:

Step-by-step explanation:

a. 4cm * 9cm * 2cm = 72 cm^3

b. 5m * 4m * 9m = 180 m^3

c. 10dm * 36 dm^2 (because the square could also be represented as 6cm * 6cm) =360 dm^3

d. (56mm)^3 =  175616 mm^3

e. 10 m * 1 m^2 (because of the square) = 10m^3

To tell which cubic unit of measure that should be used:

   ⇒ we should examine the unit of the side lengths

First question (a):

            ⇒ must use cm³ as cubic unit of measure

               ⇒ as all sides are centimeters

                  ⇒Answer: cubic centimeters or cm³

Second question(b):

            ⇒ must use m³ as cubic unit of measure

               ⇒ as all sides are meters

                  ⇒Answer: cubic meters or m³

Third question(c):

              ⇒must use dm³ as cubic unit of measure

                 ⇒ as all of the sides given are in decimeter

                     ⇒Answer: cubic decimeter or dm³

Fourth question(d):

              ⇒ must use mm³ as cubic unit of measure

                  ⇒ as all the given sides with side lengths are in millimeters

                      ⇒ Answer: cubic millimeters or mm³

Fifth question(e):

              ⇒ must use m³ as cubic unit of measure

                  ⇒ as all given sides with side lengths are in meter

                      ⇒Answer: cubic meter or m³

In general:

⇒ when faced with these problems

   ⇒ look to the unit of measure of the majority of the side lengths

   ⇒ look to the unit of measure that the problem wants for the answer

Hope that helps!

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Answer:

y

Factor:4x^3-7x^2-30/y+15:

⬇

4x^3y-7x^2y+15y-30

y

Answer:

y = 4x

Step-by-step explanation:

Equation of line in point -y intercept form:

    [tex]\sf \boxed{\bf y-y_1=m(x- x_1)}[/tex]

[tex]\sf x_1 = 1 \ ; \ y_1=4 \ \& \ m = 4[/tex]

  y - 4 = 4(x -1)

  y - 4 = 4*x - 4*1

  y - 4 = 4x - 4

Add 4 to both sides

       y = 4x - 4 + 4

      y =4x

Answer:

[tex]3[/tex] and perpendicular

Step-by-step explanation:

It's important to remember that equations of lines are always set up in the format of [tex]y=mx+c[/tex].

[tex]y[/tex] is the [tex]y[/tex] value, [tex]m[/tex] is the gradient/slope, [tex]x[/tex] is the [tex]x[/tex] value and [tex]c[/tex] is the y-intercept.

Therefore, we must always rearrange our line equations so that [tex]y[/tex] is the subject.

In the first question, we are given the equation [tex]2x+6y=12[/tex].

We rearrange to make [tex]y[/tex] the subject:

[tex]6y = 12-2x[/tex]

Then, we divide both sides by 6 to have the [tex]y[/tex] isolated:

[tex]\frac{6}{6} y = \frac{12}{6} - \frac{2}{6}x\\\\ y = 2 - \frac{1}{3}x[/tex]

To find a perpendicular slope, we use the negative reciprocal of the original slope. The negative part of that means we negate the value (it becomes inverse) and the reciprocal part means that we flip the fraction.

So here, the slope is [tex]-\frac{1}{3}[/tex].

So, the negative reciprocal of that would be [tex]3[/tex] because we inverse the sign (the negative becomes positive) and the fraction is flipped to create [tex]\frac{3}{1}=3[/tex].

So, the perpendicular slope is [tex]3[/tex].

In the second question, we have two equations. They both need to be rearranged to isolate the [tex]y[/tex].

[tex]4x-y=5\\4x = 5 + y\\y = 4x - 5\\\\4y = -x-12\\y = -\frac{1}{4}x - 3[/tex]

Look at the slopes of the two equations. If you look carefully, you will see that they are inverse of each other (one is positive and one is negative) and if you imagine [tex]4 = \frac{4}{1}[/tex], the fraction is flipped.

This means that the values are negative reciprocals of each other, meaning the lines are perpendicular.

Step-by-step explanation:

I think 1 is true.

3 is false. it's $10 per hour

Answer:

f(x)=15x+120

Step-by-step explanation:

trust

Answer:

k = 4

Explanation:

[tex]\sf 10^{k-2}=100[/tex]

make bases similar

[tex]\sf 10^{k-2}=10^2[/tex]

cancel out the bases

[tex]\sf k-2=2[/tex]

add '2' on both sides

[tex]\sf k-2+2=2+ 2[/tex]

simplify the following

[tex]\sf k =4[/tex]

Answer:

1 and -2 (has a multiplicity of 2)

Step-by-step explanation:

so since x=-2 is a root then (x+2) is a factor of the polynomial. This means you can divide the polynomial by (x+2) by using synthetic or long division. So for this example I'll using synthetic division which is much more simple than long division

-2 | 1   3    0   -4

         -2   -2    4

     1    1    -2   0

(x+2)(x²+x-2)

Now you can factor the quadratic into

(x+2)(x-1)

x+2 = 0

x = - 2

x-1 =0

x = 1

Answer:

Width is 46 meter

Length is 86 meter

Given:

Formula:

Trial and improvement:

1st try with w = 50

w(w + 40) = 4000

50(50 + 40) = 4000

4500 ≠ 4000

Value too high.

2nd try with w = 45

w(w + 40) = 4000

45(45 + 40) = 4000

3825 ≠ 4000

Value too small

3rd try with w = 46

w(w + 40) = 4000

46(46 + 40) = 4000

3956 ≠ 4000

This value is somewhat near to the area value.

It is found that width = 46 m then length = (w + 40) = (46 + 40) = 86 m

Two planes that do not intersect are always parallel.

Answer:

Area = 20 units

Step-by-step explanation:

A (-1,0)

B (0,4)

C (4,4)

D (4,-1)

i hope this is right

Answer:

Area = 20

Step-by-step explanation:

A (0,-1)

B (0, 4)

C (4, 4)

D (4, -1)

At x = -1 , 0 ,1 ,2 , the y value = 0, 1, 2, 3, Option C is the correct answer.

A function is a law that relates a dependent variable to an independent variable.

The points of line are

(- 1, 0), (0, 1),(1, 2).

The equation of the line formed will be

y = mx +c

[tex]\rm m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

m = 1

y = x +c

at x = 0 , y =1

c = 1

The equation is

y = x+1

The option 1 is

x = - 1, 0, 1, 2.

y1 = 0, 4, 6, 8.

y2= 0, 2, 4, 6

y3 =0, 1, 2, 3.

From the equation

at x = -1 , 0 ,1 ,2

the y value = 0, 1, 2, 3

Therefore Option C is the correct answer.

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The diagonal of the square pyramid will be equal to 33.10 centimetres.

The lines which connect the two opposite corners of any quadrilateral are called diagonal. here we have a square pyramid whose slant height and the vertex height are given and we have to find the diagonal length of the base.

Let the side of the square base of the pyramid is "a". Now the side will be calculated by the following relation.

[tex](\dfrac{a}{2})^2[/tex] =  s² - H

[tex](\dfrac{a}{2})^2[/tex]  = 12² - 7 = 137

a²   = 137 x 4  = 548

a  =  √548 = 23.40 cm

Now the diagonal will be calculated by using the Pythagorean theorem

D² = 23.04²  + 23.40²

D² = 548 + 548

D  = √1096

D  = 33.10 centimeter

Therefore the diagonal of the square pyramid will be equal to 33.10 centimetres.

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The domain is (-∞,∞) and the range is [-2,∞)

From the graph, we can see that the x values extend at both sides of the graph.

This means that the domain is the set of real values i.e. (-∞,∞)

However, the minimum y value is -2 and it increases from their

This means that the range is [-2,∞)

Hence, the domain is (-∞,∞) and the range is [-2,∞)

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The solution to the exponential expression is as follows:

Exponential expressions are convenient ways to express the mathematical power of a number in short forms.

Simplifying the following expressions given:

1.

[tex]\mathbf{\dfrac{(2\times 3^{-2})^3(5\times 3^2)^2}{(3^{-2})(5\times 2)^2} }[/tex]

Applying the exponent rule: [tex]\mathbf{(a\times b)^n = a^n b^n}[/tex]

[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 5^2\times 81}{3^{-2}\times 5^2\times2^2} }[/tex]

cancel out the common factor, we have:

[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 81}{3^{-2}\times2^2} }[/tex]

[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 3^4}{3^{-2}\times2^2} }[/tex]

[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 3^6}{2^2} }[/tex]

[tex]\mathbf{\implies \dfrac{2^3 \times \dfrac{1}{729} \times 3^6}{2^2} }[/tex]

[tex]\mathbf{\implies \dfrac{2^3 \times \dfrac{1}{729} \times729}{2^2} }[/tex]

[tex]\mathbf{\implies \dfrac{2^3 }{2^2} = 2}[/tex]

2.

[tex]\mathbf{=(3^3)(4^0)^2(3\times 2)^{-3}(2^2)}[/tex]

= [tex]\mathbf{\dfrac{1}{2}}[/tex]

3.

[tex]\mathbf{\dfrac{(3^7\times 4^7)(2 \times 5)^{-3}(5^2)}{12^7\times 5^{-1}\times 2^{-4}} = 2}[/tex]

4.

[tex]\mathbf{\dfrac{(2\times 3)^{-1}\times 2^0}{(2\times 3)^{-1}}= 1}[/tex]

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The equation represents a side that is perpendicular to side d is y = -2x+5. Option B is correct.

A numerical assessment of a line's angle relative to the ground is known as the slope.

The inclination of any line, ray, or line segment is the fraction of the perpendicular to the horizontal distance between any two positions on it.

The given linear equation in the problem is;

y = 2x+5

Compare the equation with the standard equation;

[tex]\rm y = mx+ c[/tex]

where,

m is the slope and c is the intercept. After comparing, we will get; Hence, the slope and y-intercept will be;

m = 2

The product of the slope of the two-line perpendicular to each will be -1.

m₁×m₂ = -1

The equation represents a side that is perpendicular to side d is;

y = -2x+c.

m₁=2

m₂=-2

m₁×m₂ = -1

The equation represents a side that is perpendicular to side d is y = -2x+5.

Hence, option B is correct.

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The value of x in the equation [tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex] is x = -1 or x = -2

The equation is given as:

[tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex]

Start by taking the LCM

[tex]\frac{4x(x - 2) - 5x(x - 1)}{(x - 1)(x -2)} = \frac{2}{x^2 - 3x + 2}[/tex]

Expand the denominator

[tex]\frac{4x(x - 2) - 5x(x - 1)}{x^2 -3x +2} = \frac{2}{x^2 - 3x + 2}[/tex]

Cancel out the common factor

4x(x - 2) - 5x(x - 1)= 2

Expand

[tex]4x^2 - 8x - 5x^2 + 5x = 2[/tex]

Evaluate the like terms

[tex]-x^2 - 3x = 2[/tex]

Rewrite as:

[tex]x^2 + 3x + 2 = 0\\[/tex]

Expand

[tex]x^2 + 2x + x + 2 = 0[/tex]

Factorize

x(x + 2) + 1(x + 2) = 0

Factor out x + 2

(x + 1)(x + 2) = 0

Solve for x

x = -1 or x = -2

Hence, the value of x in the equation [tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex] is x = -1 or x = -2

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