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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:

A = 6

Step-by-step explanation:

Look at the picture

Answer:

17.65%

Step-by-step explanation:

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

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 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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Answer: I want to say 3/4

Step-by-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:

2

Step-by-step explanation:

2/19=2:19

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

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 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.

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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Answer:

b

Step-by-step explanation:

The required differentiation of  f(x) is f'(x) = 6hx -7h -4h² - f'(x + h)

Given that,
To determine the differentiation f'(x)
f(x+h) - f(x) = -3hx² + 7hx + 4h²x - 5h² - 3h³ is given,

Differentiation is defined as the instantaneous rate of change of a particular quantity with respect to another.

Here,
f(x + h) - f(x) = -3hx² + 7hx + 4h²x - 5h² - 3h³

differentiate with respect to x
d[f(x + h)]/dx    - df(x)/ dx = -3hdx² /dx + 7hdx /dx + 4h²dx/dx - d(5h² + 3h³)/dx
f'(x + h) - f'(x) =  -6hx + 7h + 4h²
f'(x) = 6hx -7h -4h² - f'(x + h)

Thus, required differentiation of  f(x) is f'(x) = 6hx -7h -4h² - f'(x + h).

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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 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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The width and height of a newer 90 inch televison whose aspect ratio is 16:9 are 57.6 and 32.4 inches

The given parameters are

Aspect ratio = 16 : 9

Size = 90 inches

The width is calculated as

Width = 16/(16 + 9) * 90

Evaluate

Width = 57.6

This means that

height = 9/(16 + 9) * 90

Evaluate

height = 32.4

Hence, the width and height of a newer 90 inch televison whose aspect ratio is 16:9 are 57.6 and 32.4 inches

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Answer:

[tex]\textsf{23.} \quad c)\;\;y=-2x+7[/tex]

[tex]\textsf{24.} \quad 12[/tex]

[tex]\textsf{25.} \quad -2.33\:\:\sf (2\:d.p.)[/tex]

Step-by-step explanation:

Given equation:

[tex]y=\dfrac{1}{2}x-1[/tex]

If two lines are perpendicular to each other, the slopes are negative reciprocals.  

Therefore, the slope of a line perpendicular to the given equation is -2.

Substitute the found slope and the given point (3, 1) into the point-slope formula to find the equation of the line:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-1=-2(x-3)[/tex]

[tex]\implies y-1=-2x+6[/tex]

[tex]\implies y=-2x+7[/tex]

Define the variables:

Given information:

Create two equations with the given information:

[tex]\begin{cases}x+y=15\\20x+50y=390\end{cases}[/tex]

Solve the first equation for y:

[tex]\implies y=15-x[/tex]

Substitute the found expression for y into the second equation and solve for x:

[tex]\implies 20x+50(15-x)=390[/tex]

[tex]\implies 20x+750-50x=390[/tex]

[tex]\implies -30x+750=390[/tex]

[tex]\implies -30x=-360[/tex]

[tex]\implies x=12[/tex]

Therefore, Kerry received 12 twenty-dollar bills.

Given expression:

[tex]\dfrac{6^2-4^2}{-10+\sqrt{2}}[/tex]

Following the order of operations (PEMDAS), simplify the numerator:

[tex]\implies \dfrac{36-16}{-10+\sqrt{2}}[/tex]

[tex]\implies \dfrac{20}{-10+\sqrt{2}}[/tex]

Calculate the square root:

[tex]\implies \dfrac{20}{-10+1.414213...}[/tex]

Simplify the denominator:

[tex]\implies \dfrac{20}{-8.5857864...}[/tex]

Divide the numerator by the denominator:

[tex]\implies -2.3294313...[/tex]

Therefore:

[tex]\implies \dfrac{6^2-4^2}{-10+\sqrt{2}}=-2.33\:\: \sf (2\:d.p.)[/tex]

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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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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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 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 coordinates of point B, (x, y) is given by (x, y) = ((a₁ + c₁)/2, (a₂ + c₂)/2)

From the question, we are to determine how to find the coordinates of B

From the given information,

Point B is the midpoint of line AC

If the coordinates of point A are (a₁, a₂) and the coordinates of point C are (c₁, c₂)

Then,

The coordinates of the midpoint (x, y) is given by

(x, y) = ((a₁ + c₁)/2, (a₂ + c₂)/2)

Hence, the coordinates of point B, (x, y) is (x, y) = ((a₁ + c₁)/2, (a₂ + c₂)/2)

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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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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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Answer:

this game needs step to step explanation

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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