E
D
A
In the diagram above, why is m/EFD = m/BFC?
O If two angles are supplementary, then their measures are equal.
O If two angles are vertical, then they are congruent.
O If two angles are complementary, then they are congruent.
OIf two angles are a linear pair, then they have equal measure.
F
O If a ray bisects an angle, then it divides it into two congruent angles.
40°
ВА
C

The scientific notation of (4.3 × 10⁻²)(5.12 × 10⁻¹⁰) on simplifying is 2.2016 × 10⁻¹¹ which is option (A).

It is given that  (4.3 × 10⁻²)(5.12 × 10⁻¹⁰) .

On multiplying 4.3 by 5.12 , we get

4.3 × 5.12 = 22.016

Using exponent law for 10⁻² and 10⁻¹⁰ , we get

10⁻² × 10⁻¹⁰ = 10⁻²⁻¹⁰

                   = 10⁻¹²

Hence as a whole it is written as 22.016 × 10⁻¹².

In scientific notation , it is written as 2.2016 × 10⁻¹¹ .

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We're given:

To solve for t(x), we simply plug in the expressions given for f(x) and g(x):

[tex]t(x)=f(x)-g(x)\\t(x)=(3x^2+7)-(x^3+5x^2-3)[/tex]

[tex]t(x)=3x^2+7-x^3-5x^2+3\\t(x)=-x^3+3x^2-5x^2+7+3\\t(x)=-x^3-2x^2+10[/tex]

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

The unknown quantity is 512.14 percent, that is 512.14% of 140 is 717

According to the question the formula that we have to use is

                                                   R*B = A        (1)

And we have been given that

                              x%  of 140 = 717          (2)

Thus we have to find the x percent. Comparing equation (1) and (2) we get,

                R =  x%

                B = 140

                A = 717

Therefore to find the value of R we will use the formula,  R = A/B

Thus,   x% = 717/140

           x % = 5.12

           x = 512.14

Hence the unknown quantity is 512.14 percent that is, 512.14% of 140 is 717

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The equivalent expression is negative eleven sixths times n minus one twelfth. Option C

Algebraic expressions are expressions that are made up of terms, variables, factors, coefficients, constants.

They are also made up of mathematical operations.

Equivalent expressions are defined as expressions have the exact same solution but may have different arrangement of values.

Given the expression;

[ -3 1/ 3n + 1/ 6 } + { 1 3/ 6n - 3/ 12 }

simply the expression;

- 10/ 3n + 1/ 6 + 9/6n - 3/ 12

collect like terms

-10/ 3n + 9/ 6n + 1/ 6 - 3/ 12

-20n + 9n/6 + 2 - 3  /12

Add like terms

-11n/ 6 - 1/ 12

Thus, the equivalent expression is negative eleven sixths times n minus one twelfth. Option C

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The third ball weighs 15 pounds.

Given that there are three bowling balls, the balls average 14 pounds.

The first ball weighs 12 pounds.

The second ball weighs 15 pounds.

We need to find the weight of the third ball.

To find the weight of the third ball, you can use the average weight formula:

Average weight = (Sum of weights) / (Number of balls)

Given that the average weight of the three balls is 14 pounds and you know the weights of the first two balls (12 pounds and 15 pounds), you can find the weight of the third ball (let's call it "x") using the formula:

14 = (12 + 15 + x) / 3

Now, solve for x:

14 = (27 + x) / 3

Multiply both sides by 3 to eliminate the denominator:

42 = 27 + x

Subtract 27 from both sides:

x = 42 - 27

x = 15

Therefore, the weight of the third ball is 15 pounds.

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The Retained Earnings Balance as of the Beginning of the Year, January 1, 20XX is $10,260

What is net income?

The net income is the excess of fees earned by Adventure Travel  in the year ended  over its total expenses, in essence, we need to determine its total expenses first and foremost, which comprises of salaries expense, rent expense, depreciation expense, advertising expense and office supplies expense

total expenses=32,800+16,800+3960+4000+2800

total expenses=60,360

fees earned=75,000

net income =fees earned-total expenses

net income=75,000-60,360

net income=$14,640

Now the closing retained earnings comprises of beginning retained earnings plus the net income minus the cash dividends paid

Retained earnings=$14,640+$ 10,260-$1,000

Retained earnings=$23,900

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The value of "x" which will satisfy the equation [(x + 1) = (7x - 5)] is 1.

As per the question statement, we are provided with a linear equation

[(x + 1) = (7x - 5)].

We are required to determine the value of "x" for which, the above mentioned equation will be satisfied.

To solve this question, we simply need to rearrange our given equation, and bring the variable terms to one side, and the integer terms to another, and then solve for "x", as shown below.

{[(x+1)=(7 x-5)] }

or,(5+1)=(7 x-x)

or,(7-1) x=(5-1)

or, 6 x=6

or,x=6/5

or,x=1

That is, the value of "x" which will satisfy the equation [(x + 1) = (7x - 5)] is 1.

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Answer: I want to say 3/4

Step-by-step explanation:

According to the given figure, the length of interval AB can be denoted by AB =6.40312.  

Let's consider the intersecting point of A and b

is p

And

AB is c

AP is 6-2= 4 units = a

BP is 6-1 = 5 units = b

Applying the Pythagorean theorem :

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 (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2

4^2 +5^2 = 16+25

=41

c^2 = 41

C= root of 41 = 6.40312

AB is  6.40312

Algebraic proofs

The theorem can be proved algebraically using four copies of the same triangle arranged symmetrically around a square with side c, as shown in the lower part of the diagram.[5] This results in a larger square, with side a + b and area (a + b)2. The four triangles and the square side c must have the same area as the larger square,

{\displaystyle (b+a)^{2}=c^{2}+4{\frac {ab}{2}}=c^{2}+2ab,}{\displaystyle (b+a)^{2}=c^{2}+4{\frac {ab}{2}}=c^{2}+2ab,}

giving

{\displaystyle c^{2}=(b+a)^{2}-2ab=b^{2}+2ab+a^{2}-2ab=a^{2}+b^{2}.}{\displaystyle c^{2}=(b+a)^{2}-2ab=b^{2}+2ab+a^{2}-2ab=a^{2}+b^{2}.}

A similar proof uses four copies of a right triangle with sides a, b and c, arranged inside a square with side c as in the top half of the diagram.[6] The triangles are similar with area {\displaystyle {\tfrac {1}{2}}ab}{\tfrac {1}{2}}ab, while the small square has side b − a and area (b − a)2. The area of the large square is therefore

{\displaystyle (b-a)^{2}+4{\frac {ab}{2}}=(b-a)^{2}+2ab=b^{2}-2ab+a^{2}+2ab=a^{2}+b^{2}.}{\displaystyle (b-a)^{2}+4{\frac {ab}{2}}=(b-a)^{2}+2ab=b^{2}-2ab+a^{2}+2ab=a^{2}+b^{2}.}

But this is a square with side c and area c2, so

c^{2}=a^{2}+b^{2}

c^{2}=a^{2}+b^{2}

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The length of the interval AB can be expressed as AB =6.40312 using the accompanying figure.

Consider the location where A and b intersect.

is p

And

AB is c

AP is 6-2/4 units, or an.

BP equals 6-1 = 5 units + b.

Making use of the Pythagorean theorem

Pythagorean principle,

the well-known geometric theorem that states that the hypotenuse of a right triangle—the side across from the right angle—is equal to the sum of its legs' squares, or, in familiar algebraic form, a2 + b2 = c2.

4^2 +5^2 = 16+25

=41

c^2 = 41

41 divided by C equals 6.40312

AB is 6.40312

mathematic proofs

As indicated in the lower portion of the diagram, the theorem can be proven algebraically by placing four identical triangles symmetrically around a square with side c. [5] Consequently, a larger square is formed, with side a + b and area (a + b)2. The area of the larger square must be shared by the four triangles and the square side c.

{\displaystyle (b+a)^{2}=c^{2}+4{\frac {ab}{2}}=c^{2}+2ab,}{\displaystyle (b+a)^{2}=c^{2}+4{\frac {ab}{2}}=c^{2}+2ab,}

giving

{\displaystyle c^{2}=(b+a)^{2}-2ab=b^{2}+2ab+a^{2}-2ab=a^{2}+b^{2}.}{\displaystyle c^{2}=(b+a)^{2}-2ab=b^{2}+2ab+a^{2}-2ab=a^{2}+b^{2}.}

A similar proof uses four copies of a right triangle with sides a, b and c, arranged inside a square with side c as in the top half of the diagram.[6] The triangles are similar with area {\displaystyle {\tfrac {1}{2}}ab}{\tfrac {1}{2}}ab, while the small square has side b − a and area (b − a)2. The area of the large square is therefore

{\displaystyle (b-a)^{2}+4{\frac {ab}{2}}=(b-a)^{2}+2ab=b^{2}-2ab+a^{2}+2ab=a^{2}+b^{2}.}{\displaystyle (b-a)^{2}+4{\frac {ab}{2}}=(b-a)^{2}+2ab=b^{2}-2ab+a^{2}+2ab=a^{2}+b^{2}.}

But this is a square with side c and area c2, so

c^{2}=a^{2}+b^{2}

c^{2}=a^{2}+b^{2}

The probability that it is blue or red is 1

The given parameters are

Marbles = 8

Red = 2

Blue = 6

The probability that the selected marble is blue or red is calculated as

P  = P(Blue) + P(Red)

This gives

P = 6/8 + 2/8

Evaluate the sum

P = 1

Hence, the probability that it is blue or red is 1

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Complete question

A bag with 8 marbles is shown below. 2 marbles are red, and 6 are blue. A marble is chosen from the bag at random. What is the probability that it is blue or red?

Write your answer as a fraction or a whole number.

Answer:

2

Step-by-step explanation:

2/19=2:19

By factoring out the coefficient of variable, -2x+3 can be written as [tex]-2(x-\frac{3}{2})[/tex].

Factoring out means isolating a common factor from an expression. A number or a variable that is multiplied by another variable in the expression forms the coefficient. The factoring out of the coefficient of variable means taking the factor of the coefficient part of the variable term.

Given data is an expression -2x+3.

-2 is the coefficient of variable x. So, factoring out the (-2) from -2x+3:

It can be written as [tex]-2(x-\frac{3}{2} )[/tex]

Hence, -2x+3 can be written  [tex]-2(x-\frac{3}{2})[/tex] by factoring out the coefficient of variable.

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The jeans and cell phones produced by US will be 500 and 25 and jeans and cell phones produces by china will be 500 and 50 and the total number of jeans and cell phones is 1000 and 75.

Given that worker in the United States and a worker in China can each produce 1,000 pairs of jeans per week and A worker in the United States can produce 50 cell phones, and a worker in China can produce 100 cell phones in given time.

US: opportunity cost of jeans = 50/1000= 0.05;

1Jeans = 0.05 cell phones

China: opportunity cost of jeans = 100/1000= 0.1

1 jeans= 0.1cell phones

US: opportunity cost of cell phones= 1000/50= 20

1 cell phone= 20 jeans

China: opportunity cost of cell phones = 1000/100= 10

1 cell phone = 10 jeans

Each country will give equal time for producing each product.

Thus, each firm will produce half of its capacity when they combined there production.

So, pair of jeans US will produce in a week 1000/2 = 500 pair jeans a week

Cell phones US will produce in a week 50/2 = 25 cell phones in a week.

Similarly, pair of jeans china will produce in a week 1000/2 = 500 pair jeans a week

& Cell phones china will produce in a week 100/2 = 50 cell phones in a week.

The total number of jeans produced by the two countries combined is

500+500=1000

The total number of cell phones produced by the two countries combined is 25+50=75.

Hence, The jeans and cell phones produced by US will be 500 and 25 and jeans and cell phones produces by china will be 500 and 50 and the total number of jeans and cell phones is 1000 and 75 when United States and a worker in China can each produce 1,000 pairs of jeans per week.

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From the situation described, we have that:

a) The exponential function is: [tex]y(t) = 500e^{-0.041759389t}[/tex]

b) The rule is: [tex]y(t) = y(0)\left(\frac{358}{500}\right)^{\frac{t}{8}}[/tex]

c) The half-life of the element is of 16.599 days.

The exponential function for the substance's amount after t days is given by:

[tex]y(t) = y(0)e^{-kt}[/tex]

For this problem, we have that:

y(0) = 500, y(8) = 358.

Hence we can solve for k as follows:

[tex]y(t) = y(0)e^{-kt}[/tex]

[tex]358 = 500e^{-8k}[/tex]

[tex]e^{-8k} = \frac{358}{500}[/tex]

[tex]\ln{e^{-8k}} = \ln{0.716}[/tex]

-8k = ln(0.716)

k = -ln(0.716)/8

k = 0.041759389.

Hence:

[tex]y(t) = 500e^{-0.041759389t}[/tex]

For item b, 358/500 of the substance is the amount remaining each period of 8 days, hence f(t) = t/8 and the rule is given by:

[tex]y(t) = y(0)\left(\frac{358}{500}\right)^{\frac{t}{8}}[/tex]

For item c, using the rule from item a, we have to find t for which y(t) = 0.5y(0), hence:

[tex]y(t) = y(0)e^{-0.041759389t}[/tex]

[tex]0.5y(0) = y(0)e^{-0.041759389t}[/tex]

[tex]e^{-0.041759389t} = 0.5[/tex]

[tex]\ln{e^{-0.041759389t}} = \ln{0.5}[/tex]

-0.041759389t = ln(0.5)

t = -ln(0.5)/0.041759389

t = 16.599.

The half-life of the element is of 16.599 days.

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Answer:

A = 6

Step-by-step explanation:

Look at the picture

Two expressions with an equal sign is equation, The given function is 7x+2y=6, The equation when x is independent variable is x=(6-2y)/7.

Two expressions with an equal sign in between is called as equation.

The given equation is 7x+2y=6.

In the given equation x and y are two variables.

According to the question, to make x as independent variable we have to perform few operation in equation.

7x+2y=6.

Subtract 2y on both sides

7x+2y-2y=6-2y

7x=6-2y

Divide both sides by 7

x=(6-2y)/7.

Therefore the independent variable x is (6-2y)/7.

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The required evidence is used to give stand to proofs while counterexamples are used to prove the proof false.

Given that,
To specify how are evidence and counterexamples used in proofs.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
proving
a² = 1
Let assume a = 1
When squaring both sides
a² = 1
Conture an example of the proof a² = 1 to prove a = 1
a² = 1
a = ± 1
a ≠ 1 alone

Thus, the required evidence is used to give stand to proofs while counterexamples are used to prove the proof false.

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The piecewise definition for the function is

The definition of the function is given as:

f(x) = |3x^3|

Remove the absolute bracket in the above function

So, we have:

f(x) = 3x^3 and f(x) = -3x^3

The domain of the above functions are

x < 0 and x >=0

Next, we plot the graph of the function

See attachment for the graph of the piecewise definition for the function

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The total estimated weight of the three pieces of the fruit is 45 g.

Combining things and counting them as one big group is done through addition. Addition is the process of combining two or more integers in mathematics. The addends are the numbers that are added, whereas the total is the result of the operation.

Given: The weight of three pieces"

8.712 g

14.125 g

21.926 g

The estimated weight of the three fruits will be:

8.712~ 9 g

14.125 ~ 14 g

21.926 ~ 22 g

So, the total estimated weight of the three pieces of the fruit = 9 + 14 + 22

The total estimated weight of the three pieces of the fruit = 45 g                                                    

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Answer:

this game needs step to step explanation

Step-by-step explanation:

the sum of fmeasure angle of triangle is 180°

so <A + < B + <C = 180

6x - 24 = 0

x = 4

Answer:

17.65%

Step-by-step explanation:

https://www.calculatorsoup.com/calculators/financial/markup-calculator.php?cost=49.50&margin=15&action=solve

The x-intercept of the function is (-3, 0).

What is x-intercept of a function?

A function's x-intercepts are the point(s) at which its graph crosses the x-axis. The term "x-value" is commonly used to describe the x-intercept.

Where a line on a graph crosses the x-axis is known as the x-intercept. At that time, the y coordinate's value is zero. For instance, the x-intercept would be where the equation y = x + 5 crosses the x-axis at the location (-5, 0).

The x-intercept of the given function is in option (c).

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at the end the particle is at 3 units from the starting point.

Here we have one-dimensional motion, so the position of the particle is given by scalars.

We know that the particle starts at position 5. If it moves to the left, we subtract the value, if it moves to the right, we add the value.

Here we have the sequence of motions:

Then the final position will be at:

5 - 4 + 8 + 6 - 13 = 2

Then the final position is at 2, and the initial position is at 5, the difference between these is: 5 - 2 = 3

Then, at the end the particle is at 3 units from the starting point.

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꧁Helloo!꧂

・❥・・・❥・❥・・❥・・❥

It's a linear function because the formula of the linear function is

Y=mx+b

The h(x) is also considered the y its just another mathematical way of saying it.

the mx which is the slope is -2x

And since there is no B there it's only going to be considered zero

I hope iv been of help to you ^w^

・❥・・❥・・❥・・❥・・❥

Answer:

Step-by-step explanation:

[tex](\frac{720 miles}{1 hour} )(\frac{1 hour}{3600 seconds} ) (\frac{5280 feet}{1 mile} )[/tex]

Units cancel to get answer in feet per seconds.

720 x 1/3600 x 5280  = 1056 feet per seconds

1056 x 20 seconds = 21120 feet

Answer: The Function of g(x) = k[f(x)] = k |x|  

Following these rules we can define a vertical stretch or compression of any function.

Step-by-step explanation:

When a function of absolute values, f, is stretched or contracted vertically,

Define f(x) :

f(x) is the value of the function. m is the slope of the line. b is the value of the function when x equals zero or the y-coordinate of the point where the line crosses the y-axis in the coordinate plane. x is the value of the x-coordinate.

Define g(x) :

The function g (x) is called an inner function and the function f (x) is called an outer function.

When the vertical component of a function f(x) = |x| is increased by a factor k,

                     g(x) = k[f(x)] = k |x|  

where k > 1,

If the same function is compressed vertically by a factor k,

                    g(x) = k[f(x)] = k |x|  

where 0 < k < 1,

Following these rules we can define a vertical stretch or compression of any function.

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Answer:

b

Step-by-step explanation:

An equation for the function is y= -[tex](x-2)^{2}[/tex]+1.

A symmetry rotation around

x-axis:

(y= f(x) → y= −f(x))

So we have:

y= −[tex]x^{2}[/tex].

A translation to the right of a=2 units:

(y= f(x) a>0 , y= f(x−a))

So, we have:

y=− [tex](x-2)^{2}[/tex]

And finally, a vertical translation of one unit up of the graph of the function, c=1

(y = f(x) → c>0,y = f(x)+c)

That is:

y= -[tex](x-2)^{2}[/tex]+1.

Symmetry (from Ancient Greek: συμμετρία Symmetry "agreement in dimensions, due proportion, arrangement")in everyday language refers to  a way  of harmonious and beautiful proportion and balance.In mathematics, "symmetry"  features a  more precise definition, and  is typically  used to refer to an object that is invariant under some transformations; including translation, reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart,  they're  intricately related, and hence are discussed together  during this  article.

Mathematical symmetry  could also be  observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including theoretic models, language, and music.

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