Suppose the geographic area of Los Angeles County is 4,751 square miles. If the state of California has an
area of 1.637 x 105 square miles, that means that it would take approximately 35 Los Angeles Counties
to make up the state of California. As of 2013, the population of Los Angeles County was 1 x 107 people.
If the population were proportional to area, what would be the population of the state of California?

The angle in degrees between the two planes is approximately 159.460°.

The equation of the plane, whose form is a · x + b · y + c · z = d is equivalent to this vectorial form (a, b, c) • (x, y, z) = d, where (a, b, c) is the vector of coefficients. The angle between the two planes:

θ = cos⁻¹ [[(a₁, b₁, c₁) • (a₂, b₂, c₂)] / [||(a₁, b₁, c₁)|| · ||(a₁, b₁, c₁)||]]

If we know that (a₁, b₁, c₁) = (1, - 10, - 8) and (a₂, b₂, c₂) = (2, 5, 8), then the angle between the two planes is:

θ = cos⁻¹ [[(1, - 10, - 8) • (2, 5, 8)] / [√165 · √93]]

θ = cos⁻¹ [(-2 - 50 - 64) / √15345]

θ = cos⁻¹ (- 116 / √15345)

θ ≈ 159.460°

The angle in degrees between the two planes is approximately 159.460°.

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Using proportions, it is found that the cost per ounce is of $0.8.

The missing information is the number of ounces in the balm, that is of 20.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

The cost per ounce is given by the proportion of the cost by the number of ounces, hence:

Then:

$16/20 = $0.8.

The cost per ounce is of $0.8.

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For the system of equations y = 2 x + 3 and 2 y - x = 12, the solution will be x = 2 and y = 7.

We are given the system of equations:

y = 2 x + 3   … (1)

2 y - x = 12     …. (2)

We need to solve it to find the values of x and y.

Putting the value of y from equation (1) in equation (2), we get that:

2 y - x = 12

2 (2 x + 3) - x = 12

Multiplying the brackets, we get that:

4 x + 6 - x = 12

3 x + 6 = 12

Subtract 6 from both the sides, we get that:

3 x + 6 - 6 = 12 - 6

3 x = 6

Divide both sides by 3. we get that:

3 x / 3 = 6 / 3

x = 2

y = 2 x + 3

y = 2 (2) + 3

y = 4 + 3

y = 7

Therefore, we get that, for the system of equations y = 2 x + 3 and 2 y - x = 12, the solution will be x = 2 and y = 7.

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Answer: x=16

DF=105

Step-by-step explanation:

DF=DE+EF
9x-39=47+3x+10

9x-39=57+3x

9x=96+3x

6x=96

x=16

DF=9x-39

DF=9(16)-39

DF=144-39

DF=105

Answer:

length = 105 yd

width = 35 yd

Step-by-step explanation:

Let L = length and W = width.

L = 3W

perimeter = 2(L + W)

280 =2(L + W)

L = 3W

We have a system of 2 equations. Let's use the substitution method to solve it. Substitute 3W for L in the first equation.

280 = 2(3W + W)

140 = 4W

W = 35

L = 3W = 3(35) = 105

length = 105 yd

width = 35 yd

Rotation of a point through 189° about the origin When a point C(h, k) is rotated through 180° in either an anticlockwise or clockwise direction about the origin O, it takes the new position D(-h, -k).

The rotation formula will give us the precise location of a point after a finite degree of rotation. The rotation formula is determined by the type of rotation applied to the point in relation to the origin. A geometric two-dimensional shape can undergo four major types of transformation.

The rotation formula describes how a point rotates with respect to the origin. The rotation formula is used to determine the position of a point after it has been rotated. A rotation is a circular motion around a specific axis or point of rotation. In general, rotation can be done in two ways: clockwise and anti-clockwise or counter-clockwise.

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The total of three consecutive even numbers is 312.

The correct option is A.

Three numbers totaling 312 are consecutive, one of which being 104. Take one of the other numbers from 104=103 and add one to 104=105 for the third.

103 + 104 + 105 = 312.

Consecutive even numbers are consecutive even integers that differ by 2. If x is an even number, then x + 2, x + 4, and x + 6 are also even numbers. The difference between consecutive even numbers is two.

The formula for successive integers is quite simple. If x is the first consecutive integer, x+1 is the next, x+2 is the third, x+3 is the fourth, and so on. Consider the following example. 45 is 'x if it is the first consecutive integer in either a series of numbers.

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Answer:V≈113.1

Step-by-step explanation:

d Diameter 6

V=4

3πr3

d=2r

Solving forV

V=1

6πd3=1

6·π·63≈113.09734

Answer:

  5 + 10 + 15 = 30

Step-by-step explanation:

You want a sum of three multiples of 5 that does not end in 5.

Any odd multiple of 5 will end in 5. An even multiple will not.

In order for the sum to not end in 5, the total of the multipliers must be even:

  1×5 +2×5 +3×5 = 6×5 = 30

  5 +10 +15 = 30 . . . . . . three multiples of 5 whose sum does not end in 5

The angles of rotation will map the figure onto itself are 60, 120, 180....

In geometry, transformation involves changing the angle, position and/or size of a shape.

The figure that completes the question is added as an attachment

The given parameter is the shape in the figure

From the figure, we can see that the shape has 6 congruent sides

This means that the shape is a regular hexagon

The angle of rotation will map the figure onto itself is calculated as

Angle = 360/Number of sides

So, we have

Angle = 360/6

Evaluate

Angle = 60

The other angles must be a multiple of 60

i.e. 60, 120, 180....

Hence, the angles of rotation will map the figure onto itself are 60, 120, 180....

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The equation representing the product of theirs fractions is -

(- 2/7) x (- 3/4)  and on solving this expression, we get 3/14.

In mathematics, fractions are represented as a numerical value, which defines a part of a whole.

Given that Cassie and Amy are playing a card flash game such that Cassie has a card with the fraction - 2/7 and Amy has a card with fraction - 3/7.

The equation that represent the product of their fractions is -

(- 2/7) x (- 3/4)

Now, solving the above expression, we get -

(- 2/7) x (- 3/4)

(1/7) x (3/2)

3/14

Therefore, the equation representing the product of theirs fractions is -

(- 2/7) x (- 3/4)  and on solving this expression, we get 3/14.

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Answer:

A= (2xy^2)^3. (-1/2x^2yz) (gạch chéo là phần)

B=(-4x3y2z)(  x2y3)3xy

Step-by-step explanation:

ok :)

The value of the number is 15.

Let the first number be represented by x.

The second number will be:

(2 × x) - 2 = 2x - 2

Therefore, the addition of the numbers will be:

= x + 2x - 2 = 43

3x - 2 = 43

3x = 43 + 2

3x = 45

Divide

x = 45/3

x = 15.

Therefore, the number is 15

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Answer:

Option D: [tex]y=-2[/tex]

Step-by-step explanation:

The line is horizontal, which means the slope is 0. The line also crosses the y-axis at (0,-2). Thus y at 0 is equal to 2.

Answer:

800,000

Step-by-step explanation:

To do this, simply divide the number by 10. 8000000/10 = 800,000.

The value of (9)14+(−9)+(−9)14 is -9

The concept is used to Solve is BODMAS

(9)14+(−9)+(−9)14

126-9-126=-9

BODMAS, also known as the order of operations, is a series of operations in an arithmetic statement. Math is all about logic and certain common principles that help us with our calculations. So BODMAS is one of the basic principles for simplifying multi-operator formulations.

An expression or equation in arithmetic has two components:

Numbers \Operators

A character that combines two integers to form an expression or equation is known as an operator. The most popular operators in mathematics are Addition (+), Subtraction (-), Multiplication (), and Division (). Finding the solution to mathematical statements or equations with only one operator is rather straightforward.

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The expression for the sum of 1 cubed, 2cubed and 3 cubed is 1² + 2³ + 3³ and the value is 36.

It should be noted that the information is to find the expression for the sum of 1 cubed, 2cubed and 3 cubed.

This will be:

= 1³ + 2³ + 3³

= 1 + 8 + 27

= 36

Therefore, the correct answer is 36.

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Answer:

x=

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

The function f ( x ) = 2 x² + 5 will have the value 23 for f (- 3).

We are given the function:

f ( x ) = 2 x² + 5

We need to find the value of f ( -3 ).

We will do this by substituting the value of x = - 3 in the function and then evaluating the expression.

Putting x = -3 in the function, we get that:

f ( x = - 3 ) = 2 (- 3)² + 5

Solving the square, we get that:

f (- 3) = 2 ( 9 ) + 5

Simplifying the expression, we get that:

f (- 3) = 18 + 5

f (- 3) = 23

Therefore, we get that, the function f ( x ) = 2 x² + 5 will have the value 23 for f (- 3).

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Answer:

use a calculator

Step-by-step explanation: the calculator doesn't lie I used a calculator

Answer:

1,000,000

Step-by-step explanation:

Using translation concepts, the vertices of the triangle after the rotation are given as follows:

G'(2,-2), E'(5,-4), F'(5,-1).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

The rule for a 90º counterclockwise rotation around the origin is:

(x,y) -> (-y,x).

Hence the vertices should be given by:

The correct translation is graphed at the end of the question. You are doing a good job, just there was two small mistakes on the rule :).

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A random sample and a non-random sample for this situation are given below:

This refers to the statistical population where there is an equal chance of being selected by members of a population.

Hence, we can see that a random sample and a non-random sample for this situation are given above and this shows that each of them have equal chances of being selected (random sampling)

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Answer:4

Step-by-step explanation:4(5x+6) = 4[tex]x[/tex]5x=20x   4[tex]x[/tex]6=24

Answer:

The answer is 4.

4 * 5x = 20x

4 * 6 = 24

So the result we get is 20x + 24

The true statement about the angles of the triangle OPQ  is the third statement that is  m∠P < m∠O < m∠Q.

It is given that:-

In triangle OPQ,

PQ = 19

QO = 11

OP = 20

We have to find which one of the six statements given in the question is correct.

We know that, in a triangle, if one side of the triangle is longer than the other side, then the angle opposite to the longer side will be larger than the angle opposite the shorter side.

Hence,

In triangle OPQ,

Angle opposite to side OP = ∠Q

Angle opposite to side PQ = ∠O

Angle opposite to side QO = ∠P

As,

QO < PQ < OP , Hence,

m∠P <  m∠ O < m∠Q

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Answer:

See the answer below

Step-by-step explanation:

The dimensions of a rectangle with an area of 12 ft.² and a diagonal of 5 feet are 4 feet and 3 feet.

From the information, we are given that the dimensions of a rectangle with an area of 12 ft.² and a diagonal of 5 feet.

It should be noted that the number will be:

= 4 × 3 = 12 ft²

It should be noted that 4² + 3² = 25 and the square root will give 5 which is also the diagonal.

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Answer:

6.7

Step-by-step explanation:

√45 = 6.7

.................

the tangent is only horizontal at the critical points of the equation, so

[tex]y=2x^3+3x^2-12x+3\implies \cfrac{dy}{dx}=6x^2+6x-12\implies \cfrac{dy}{dx}=6(x^2+x-2) \\\\\\ \stackrel{\textit{setting the derivative to 0}}{0=6(x^2+x-2)}\implies 0=x^2+x-2 \\\\\\ 0=(x+2)(x-1)\implies \boxed{x= \begin{cases} -2\\ 1 \end{cases}} \\\\[-0.35em] ~\dotfill\\\\ y=2(-2)^3+3(-2)^2-12(-2)+3\implies y=-16+12+24+3\implies \boxed{y=23} \\\\\\ y=2(1)^3+3(1)^2-12(1)+3\implies y=2+3-12+3\implies \boxed{y=-4} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \text{\LARGE (-2~~,~~23)\qquad (1~~,~~-4)}~\hfill[/tex]