add (3x + 9 / 2x + 6) + (8x + 12 / x^2 + 6x + 9)

Answer:

Q=9

Step-by-step explanation:

if we get the bottom lengths of both triangles and divide them by eachother we can find the scale factor. so 12/4=3 meaning the scale factor is 3 meaning the bigger triangle is 3 times bigger so if we have the smaller version of the length of Q we just have to multiply 3 by 3 to get the enlarged version so Q=9inch

(its a lot of words but i wanted to make sure you understand)

Answer:

30

Step-by-step explanation:

each of the boxes is 2*2

so 30 :D

The complete table is as shown below

x         y

-2       -4

-1       -2

0        0

1        2

2       4

The similarity between y = 2x and y = x is that they are proportional relationship

The difference between y = 2x and y = x is that they are have different slopes

In mathematics, a proportional relationship is a type of relationship between two quantities where their ratio always remains the same.

How to fill the table

for x = -2, y = 2 * -2 = -4

for x = -1, y = 2 * -2 = -2

for x = 0, we solve for A; y = 2 * 0 = 0

for x = 1, y = 2 * 1 = 2

for x = 2, we solve for B; y = 2 * 2 = 4

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The per capita emissions for each country is:

Using this formula to find the  Per capita emissions for each country

Per capita emissions = C02 Emission (tons of carbon dioxide ) /  Total emissions by population

China

Per capita emissions =8,782,000,000/1,359,750,000

Per capita emissions = 6.46

United States

Per capita emissions =5,144,000,000/316,597,000

Per capita emissions= 16.25

India

Per capita emissions = 2,185,000,000 /1,233,460,000

Per capita emissions = 1.77

Russia

Per capita emissions=1,646,000,000/143,400,000

Per capita emissions = 11.48

Japan

Per capita emissions = 1,232,000,000/127,310,000

Per capita emissions = 9.68

Germany

Per capita emissions = 733,000,000/80,523,700

Per capita emissions = 9.10

Iran

Per capita emissions = 583,000,000/76,876,000

Per capita emissions = 7.58

South Korea

Per capita emissions = 576,000,000/50,219,669

Per capita emissions = 11.47

Indonesia

Per capita emissions = 535,000,000/237,641,326

Per capita emissions = 2.25

Canada

Per capita emissions = 528,000,000/35,141,542

Per capita emissions =15.02

Therefore China per capita emissions is 6.46.

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A)  Formula for r  is r = I/p*t

B) The annual interest rate on the account  is 0.05%

Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal  and by the number of days that elapse between payments.

For part A of the question, I=p*r*t

Therefore, r =  I/p*t    ( by taking interest rate on one side and moving rest of the terms on the other side of the 'equals to'. As we know that when we move a term which is being multiplied on one side to the other side, it is then used as a divisor.)

For part B of the question, put values in the above formula

simple interest earned =  $125,00

principal deposit =  $5,000,00

time period in years = 6 months that is 1/2 years

r =  I/p*t

r = 125,00/5,000,00*1/2

r = 0.05%

Therefore, The formula solved for r is r =  I/p*t and the annual interest rate on the account that earned $125,00 in simple interest after 6 months with principal deposit of $5,000,00 is 0.05%.

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Answer:

\(\frac{11}{12}\)

Step-by-step explanation:

\(Rule: \frac{x}{y} \pm \frac{a}{b} = \frac{x \pm y}{z}\\\frac{1}{4}+\frac{2}{3} = \frac{3}{12}+\frac{8}{12} (LCM)\\=\frac{3+8}{12}\\=\frac{11}{12}\\\)

Answer:

Since an isosceles triangle has two congruent angles (the base angles), let x be the measure of each base angle. Then we know that the sum of the three angles in a triangle is 180 degrees, so:

vertex angle + base angle + base angle = 180

66 + x + x = 180

2x + 66 = 180

2x = 114

x = 57

Therefore, each base angle measures 57 degrees.

The expression that represents the pattern is n = x² + 2.

It should be noted that it's a quadratic equation.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.

The number of blocks for design 8 will be:

= 8² + 2

= 66

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The maximum number of pens and pencils she can purchase is 10 pens and 30 pencils. The result is obtained by using substitution method on inequality problem.

The most important thing in inequality problem is the inequality symbol. The symbols are:

Teri wants to buy as many pencils and pens as possible by spending no more than $6.50. She wants three pencils for every pen. Each pencil costs $0.15 and each pen costs $0.20.

Find the maximum number of pens and pencils she can purchase?

Let's say:

The money spent is no more than $6.50. It means the maximum money spent is $6.50. We got the inequality.

0.15x + 0.20y ≤ 6.50

She wants 3 pencils for 1 pen. We have x = 3y.

Substitute x with 3y!

0.15(3y) + 0.20y ≤ 6.50

0.45y + 0.20y ≤ 6.50

0.65y ≤ 6.50

y ≤ 10

x = 3y = 3(10) = 30

Hence, Teri can purchase 10 pens and 30 pencils with the money she can spend.

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The Propositions are resulting

(a) ∀x∃y(x = y²) is False

(b) ∀x∃y(x² = y) is True.

(c) ∃x∀y(xy = 0) is True.

(d) ∀x∃y(x + y = 1) is True.

(a) ∀x∃y(x = y²)

This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².

Therefore, the proposition (a) is false.

(b) ∀x∃y(x² = y)

For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.

Therefore, the proposition (b) is true.

(c) ∃x∀y(xy = 0)

The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.

Therefore, the proposition (c) is true.

(d) ∀x∃y(x + y = 1)

To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.

Therefore, the proposition (d) is true.

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Answer:

The equation of the line will be:

\(y=-\frac{1}{2}x-6\)

Step-by-step explanation:

Given

Point slope form:

\(y-y_1=m\left(x-x_1\right)\)

substituting the values m = -1/2 and the point (4,-8)

\(y-\left(-8\right)=\frac{-1}{2}\left(x-4\right)\)

\(y+8=\frac{-1}{2}\left(x-4\right)\)

subtract 8 from both sides

\(y+8-8=\frac{-1}{2}\left(x-4\right)-8\)

\(y=-\frac{1}{2}x-6\)

Therefore, the equation of the line will be:

\(y=-\frac{1}{2}x-6\)

The sum of the first 20 terms of the arithmetic sequence is equal to 550.

In Mathematics, the sum of an arithmetic sequence can be calculated by using the following mathematical equation:

Sn = n/2(2a₁ + (n - 1)d) or Sn = n/2(a₁ + L)

Where:

By substituting the given terms into the formula for the sum of an arithmetic sequence, we have the following;

Sn = n/2(a₁ + L)

S₂₀ = 20/2(-1 + 56)

S₂₀ = 10(55)

S₂₀ = 550.

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The population of town B in 1995 was 25% of the population of town A in 1995.

Let's assume that the initial population of both town A and town B in 1985 is P.

From 1985 to 1995, the population of town A increased by 60%, which means the population of town A in 1995 is P + 0.60P = 1.60P.

On the other hand, the population of town B decreased by 60%, which means the population of town B in 1995 is P - 0.60P = 0.40P.

To find the percentage of town B's population compared to town A's population in 1995, we divide the population of town B by the population of town A and multiply by 100.

Population of Town B in 1995 / Population of Town A in 1995 * 100

(0.40P) / (1.60P) * 100

0.25 * 100

25%

This means that town B's population in 1995 was 25% of the population of town A in 1995.

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Answer:

D

Step-by-step explanation:

Just apply the rules for exponents. I hope it helps.

The value of t₄ in the arithmetic sequence is 103/8.To determine the value of t₄ in an arithmetic sequence, we need to use the given information that t₁ = 11 (the first term of the sequence) and S₉ = 243 (the sum of the first 9 terms of the sequence).

We know that the formula for the sum of an arithmetic sequence is Sₙ = (n/2)(2a + (n-1)d), where Sₙ is the sum, a is the first term, n is the number of terms, and d is the common difference.

From the given information, we have S₉ = 243, a = 11, and n = 9. Plugging these values into the sum formula, we can solve for d:

243 = (9/2)(2(11) + (9-1)d)

243 = 9(22 + 8d)

243 = 198 + 72d

45 = 72d

d = 45/72 = 5/8

Now that we have the common difference, we can find t₄ using the formula for the nth term of an arithmetic sequence:

tₙ = a + (n-1)d

t₄ = 11 + (4-1)(5/8)

t₄ = 11 + 3(5/8)

t₄ = 11 + 15/8

t₄ = 88/8 + 15/8

t₄ = 103/8

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Answer:20

Step-by-step explanation:this is wrong

Answer:

40

Step-by-step explanation:

subtract median of dogs and median of cats

Answer:

\( \frac{ \sqrt{3} }{3} \)

Step-by-step explanation:

\((sin30 + \cos(60) )( \tan(60) - \sec(30) \)

\(( \frac{1}{2} + \frac{1}{2} )( \sqrt{3} - \frac{2 \sqrt{3} }{3}) \)

\((1)( \sqrt{3} )\) over 3

\( = \frac{ \sqrt{3} }{3} \)

Answer:

i hope this will help you

Answer:

b-3

c-40

Step-by-step explanation:

Answer:

The three interior angles of a triangle must equal 180 degrees. The base angles must be the same degree for a triangle to be isosceles. We can set x as the measure of one base angle, and write an equation.

40 + 2x = 180

Subtract 40 from both sides.

2x = 140

Divide both sides by 2.

x = 70

The measure of a base angle is 70 degrees.

:)

The length of the side opposite to the reference angle is 7.77 units.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

If we take the reference angle 45°, The side 'x' is opposite and the side having a length of 11 units is the hypotenuse.

We know, sin = opposite/hypotenuse.

Therefore,

sin45° = x/11.

1/√2 = x/11.

x = 11/√2.

x = 7.77 units.

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Answer:

\(-\frac{3(\sqrt{6}-\sqrt{2})}{2}\text{ or } \frac{-3\sqrt{6}+3\sqrt{2}}{2}}\text{ or }\frac{3(\sqrt{2}-\sqrt{6})}{2}\)

Step-by-step explanation:

There are multiple ways to achieve and even express the exact answer to this problem. Because the exact value of \(6\cos(105^{\circ}})\) is a non-terminating (never-ending) decimal, it does not have a finite number of digits. Therefore, you cannot express it as an exact value as a decimal, as you'd either have to round or truncate.

Solution 1 (Cosine Addition Identity):

Nonetheless, to find the exact value we must use trigonometry identities.

Identity used:

\(\cos(\alpha +\beta)=\cos \alpha \cos \beta-\sin \alpha \sin \beta\)

Notice that \(45+60=105\) and therefore we can easily solve this problem if we know values of \(\cos(45^{\circ})\), \(\cos(60^{\circ})\), \(\sin (45^{\circ})\), and \(\sin(60^{\circ})\), which is plausible as they are all key angles on the unit circle.

Recall from either memory or the unit circle that:

Therefore, we have:

\(\cos(105^{\circ})=\cos(45^{\circ}+60^{\circ}}),\\\cos(45^{\circ}+60^{\circ}})=\cos 45^{\circ}\cos 60^{\circ}-\sin 45^{\circ}\sin 60^{\circ},\\\cos(45^{\circ}+60^{\circ}})=\frac{\sqrt{2}}{2}\cdot \frac{1}{2}-\frac{\sqrt{2}}{2}\cdot \frac{\sqrt{3}}{2},\\\cos(105^{\circ})=\frac{\sqrt{2}}{4}-\frac{\sqrt{6}}{4},\\\cos(105^{\circ})={\frac{-\sqrt{6}+\sqrt{2}}{4}}\)

Since we want the value of \(6\cos 105^{\circ}\), simply multiply this by 6 to get your final answer:

\(6\cdot {\frac{-\sqrt{6}+\sqrt{2}}{4}}=\frac{-3\sqrt{6}+3\sqrt{2}}{2}}=\boxed{\frac{3(\sqrt{2}-\sqrt{6})}{2}}\)

Solution 2 (Combination of trig. identities):

Although less plausible, you may have the following memorized:

\(\sin 15^{\circ}=\cos75^{\circ}=\frac{\sqrt{6}-\sqrt{2}}{4},\\\sin 75^{\circ}=\cos15^{\circ}=\frac{\sqrt{6}+\sqrt{2}}{4}\)

If so, we can use the following trig. identity:

\(\cos(\theta)=\sin(90^{\circ}-\theta)\) (the cosine of angle theta is equal to the sine of the supplement of angle theta - the converse is also true)

Therefore,

\(\cos (105^{\circ})=\sin (90^{\circ}-105^{\circ})=\sin(-15^{\circ})\)

Recall another trig. identity:

\(\sin(-\theta)=-\sin (\theta)\) and therefore:

\(\sin (-15^{\circ})=-\sin (15^{\circ})\)

Multiply by 6 to get:

\(6\cos (105^{\circ})=-6\sin (15^{\circ})=-6\cdot \frac{\sqrt{6}-\sqrt{2}}{4}=\boxed{-\frac{3(\sqrt{6}-\sqrt{2})}{2}}\) (alternative final answer).

The level curve for c = 0 is the union of the x-axis and y-axis, while the level curve for c = 1 is a hyperbola that passes through the origin and is symmetric about both axes.

To sketch the level curves of the function f(x,y) = xy for c = 0 and c = 1, we need to find the set of points (x,y) where f(x,y) takes on these values.

For c = 0, we have xy = 0, which means that either x = 0 or y = 0. So the level curve for c = 0 is the union of the x-axis where y = 0 and the y-axis where x = 0. Refer the graph attached.

For c = 1, we have xy = 1, which means that y = 1/x (when x is not equal to 0). So the level curve for c = 1 is the set of all points (x,y) such that y = 1/x. This is the graph of a hyperbola that passes through the origin and is symmetric about both axes. Refer the graph attached.

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Answer:

Sales from products.

Population.

Voting.

The value of x is x= π/8

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

2tan x/1-tan² x= 1

We know that tan π/4= 1

So, 2tan x/1-tan² x= tan π/4

Also, we know that tan 2x=  2tan x/1-tan² x

Again, 2tan x/1-tan² x= tan π/4

tan 2x= tan π/4

Now comparing we get

2x= π/4

x= π/8

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Answer:

the angle is acute angle

Answer:

The type of angle shown is an acute angle

Step-by-step explanation:

there are 4 main types of angles. this is an acute angle as it is less than 90°.

Types of angles:

The 4 main types of angles are: acute, obtuse, right angles, reflex angles.

Acute angles- Acute angles are angles less than 90°.

Obtuse Angles-Obtuse angles are angles greater than 90° but less than 180°.

Right Angles- Right angles are angles of 90°.

Reflex Angles- Reflex angles are angles greater than 180° but less than 360°.

Answer:

what? hshwjjwjdjdd jwhbebdhd

Answer:

4.5

Step-by-step explanation:

Graph y=3x then find two points from the graph, then find the distance between them two and round 4.47 to 4.5

Answer:

3.2

Step-by-step explanation:

the answer was in the back of my textbook