1. Find the length of a.

The addition equation to represent how their charges combine to make the overall charge of the atom is + 1 + - 1 = 0

A hydrogen atom has one positively charged proton and one negatively charged electron.

An atom of every elements has an electron(negatively charged) and positively charge(proton) part.

An atom as a whole is electrically neutral if the number of proton and electron are equal. They will cancel each other to make the atom neutral.

Therefore, the addition equation to represent how their charges combine to make the overall charge of the atom is as follows;

+ 1 + - 1 = 0

1 positively charged proton plus single negatively charged electron  = zero(neutral)

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13.1 = 13.10

---> 13.1 > 13.01

---> 13.01 < 13.1

The correct answer is <

Answer:

  s = -24

Step-by-step explanation:

This is a 2-step linear equation, so can be solved the way all 2-step equations are solved.

Step 1

Identify the constant term on the side of the equation with the variable term, and add its opposite to both sides.

  [tex]7 = \dfrac{1}{6}s+11\qquad\text{given}\\\\7-11=\dfrac{1}{6}s+11-11\qquad\text{add $-11$ to both sides}\\\\-4=\dfrac{1}{6}s\qquad\text{simplify}[/tex]

Step 2

Multiply both sides by the inverse of the coefficient of the variable.

  [tex](6)(-4)=(6)\left(\dfrac{1}{6}s\right)\qquad\text{multiply both sides by 6}\\\\\boxed{-24=s}\qquad\text{simplify}[/tex]

Often, when equations contain fractions, you are advised to "eliminate fractions" as a first step. That generally means you multiply both sides of the equation by a suitable common denominator.

Here, the only denominator is 6, so the fraction can be eliminated by multiplying both sides of the equation by 6.

  [tex]7=\dfrac{1}{6}s+11\qquad\text{given}\\\\6(7)=6\left(\dfrac{1}{6}s+11\right)\qquad\text{multiply both sides by 6}\\\\42=s+66\qquad\text{simplify}\\\\42-66=s+66-66\qquad\text{add the opposite of 66 to both sides}\\\\\boxed{-24=s}\qquad\text{simplify}[/tex]

You will note this requires the same number of steps, but you don't have to mess with fractions after the first step.

The value we found for the variable can be checked in the original equation.

  [tex]7=\dfrac{1}{6}(-24)+11\\\\7=-4+11\qquad\text{true}[/tex]

Answer:

  (c)  f(g(3)) > g(f(3))

Step-by-step explanation:

The relationship between the function values can be found by evaluating the functions.

The order of operations tells us we must first evaluate g(3).

  g(x) = -3x +15

  g(3) = -3(3) +15 = 6

Then we can evaluate f(x) for x=6:

  f(x) = 7x

  f(6) = 7(6) = 42

So, the composition is ...

  f(g(3)) = 42

As above, we must first evaluate f(3):

  f(3) = 7(3) = 21

Then we can evaluate g(x) for x=21:

  g(21) = -3(21) +15 = -63 +15 = -48

That means the composition is ...

  g(f(3)) = -48

The first is greater than the second.

  42 > -48

  f(g(3)) > g(f(3))

The number of ways people can get off the elevator is 604800 ways.

In this question,

Number of people, n = 7

Number of floors, r = 10

The first person can leave elevator in one of 10 ways. Then second person has to choose from one of remaining 9 floors. Then third person in 8, fourth in 7 ways and so on.

Number of ways people can get off the elevator can be calculated as

⇒ [tex]nP_r=\frac{n!}{(n-r)!}[/tex]

⇒ [tex]10P_{7}=\frac{10!}{(10-7)!}[/tex]

⇒ [tex]10P_{7}=\frac{10!}{(3)!}[/tex]

⇒ [tex]10P_{7}=\frac{(10)(9)(8)(7)(6)(5)(4)3!}{(3)!}[/tex]

⇒ [tex]10P_{7}=(10)(9)(8)(7)(6)(5)(4)[/tex]

⇒ 604800 ways.

Hence we can conclude that the number of ways people can get off the elevator is 604800 ways.

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The answer is.........

25.99

Each side of equilateral triangle will have the length equals to 42.7 cm.

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, in a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

The perimeter of a geometric figure is the sum of its sides. Thus, for a rectangle, the perimeter is 2L+2W.

You should find the perimeter of the rectangle.

2P=23+23+41+41= 128 cm

The equilateral triangle will have the same perimeter of the rectangle. An equilateral triangle presents the equal three sides, thus,

128= 3L

L=128/3=42.7 cm

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Answer:

Step-by-step explanation:

Begin by changing the radical form to exponential form:

[tex]((1024w^{-2}x^{-3}y^6z^{-1)^2)^{\frac{1}{5} }[/tex]  There are a couple of ways to do this, but let's distribute the power of 2 into the parenthesis first by using the power to power rule of multiplication:

[tex](1024^2w^{-4}x^{-6}y^{12}z^{-2})^{\frac{1}{5}[/tex]  Now we can use the same rule of power to power and distribute the power of 1/5 in:

[tex]1024^{\frac{2}{5}}w^{-\frac{4}{5}}x^{-\frac{6}{5}}y^{\frac{12}{5}}z^{-\frac{2}{5}[/tex]

The first term simplifies down to 16, and then in order to make the negative exponents positive, we move them to the denominator of a fraction, leaving the positive one where it is:

[tex]\frac{16y^{\frac{12}{5}} }{w^{\frac{4}{5}}x^{\frac{6}{5} }z^{\frac{2}{5} } }[/tex] which is the third choice down

Answer:

A: (4,7)

B: (2,1)

C: (6,1)

Step-by-step explanation:

To plot the points, go along the x-axis (the horizontal line with the x on the end) and stop where the dot is. Whatever number the dot is above is the   x-coordinate. Then, however many numbers you go up by to reach the dot is your y-coordinate.

hope this helps :)

The complete proof from the figure is:

The given parameter is:

AC ≅ DF; AB ≅ DE; ∠1 ≅ ∠6

Angles 1 and 2, & Angles 5 and 6 are vertical angles

So, we have: ∠1 ≅ ∠2; ∠5 ≅ ∠6 by the definition of vertical angles.

From the figure, triangles ABC and DEF are congruent by the SAS postulate.

So, we have: ΔABC ≅ ΔDEF by the definition of SAS postulate

Angles 3 and 4 are corresponding angles

So, we have: ∠1 ≅ ∠2; ∠5 ≅ ∠6 by the definition of corresponding angles.

Hence, the lines BC and EF are parallel lines

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Answer: 1.71, 1 3/4, 16/9, pie

Step-by-step explanation: We convert all the numbers to improper fractions. 1.71 = 171/100. 1 3/4 = 175/100 because 3/4 is 0.75. pi is 3.14... which is larger than all of the other numbers. So, pi is the largest. For 16/9, we can just divide to find the solution. Once you divide, you will notice that the answer is 1.77777777... This means that it is larger than 1.71 and 1.75 so 16/9 is the second largest. 1.71 is smaller than 1.75 so the order is 1.71, 1 3/4, pie, 16/9

Answer:

The second choice is correct.

Step-by-step explanation:

As we go right on the number line, we are getting to larger and larger values.

D is greater than C because it is to the right of C, so the first choice is not correct.

The third choice is showing absolute value.  This is saying that the letters C and D are both the same distance from zero. They are not.

The last choice says that A is to the right of B and it is not.

The second choice that is B≥ C is correct.

The basics of this question requires us to read the number line perfectly

As we go right on the number line, we are getting to larger and larger values.

D is greater than C because it is to the right of C, so the first choice is not correct.

The third choice is showing absolute value.  This is saying that the letters C and D are both the same distance from zero. They are not.

The last choice says that A is to the right of B and it is not.

Thus option 2) is correct

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Using the normal distribution, the z-score that separates the bottom​ 70% from the top​ 30% is z = 0.525.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score that separates the bottom​ 70% from the top​ 30% is z with a p-value of 0.7, hence z = 0.525.

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Answer:

20 percent

40 percent

20 percent

20(.008) percent

Step-by-step explanation:

6) 54 - 45 = 9

45 / 9 = 5

100 / 5 = 20

20 percent

7) 60 - 36 = 24

60 / 24 = 2.5

100 / 2.5 = 40

40 percent

8) 30 - 24 = 6

30 / 6 = 5

100 / 5 = 20

20 percent

9) 24.99 - 19.99 = 5

24.99 / 5 = 4.998

100 / 4.998 approx. = 20.008

20.008 percent (or rounded 20 percent)

Answer:

[tex]\textsf{A. } y=3x^2+10x-8[/tex]

Step-by-step explanation:

We are given the information that a function has zeros at x = ⅔ and x = -4. In order to find the function that has those zeros, we can substitute the value of the zeros into each function. If the value of a function equates to zero with both values, then that is the function we are looking for.

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

Standard Form of a Quadratic: ax² + bx + c = 0.

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

[tex]\large \text{$y = 3x^2+10x-8 \implies 0=3x^2+10x-8$}[/tex]

[tex]\boxed{\begin{minipage}{15 em}{\text{$x=\dfrac{2}{3}$}} \\ \\\implies 0=3\left(\dfrac{2}{3}\right)^2+10\left(\dfrac{2}{3}\right)-8\\\\\implies 0=3\left(\dfrac{4}{9}\right)+10\left(\dfrac{2}{3}\right)-8\\\\\implies 0=\not{3}\left(\dfrac{4}{\not{9}\ 3}\right)+\dfrac{20}{3}-8\\\\\implies 0=\dfrac{4}{3}+\dfrac{20}{3}-8\\\\\implies 0=\dfrac{24}{3}-8\\\\\implies 0=0\ \checkmark\end{minipage}}[/tex]    [tex]\boxed{\begin{minipage}{15 em}{\text{$x=-4$}} \\ \\\implies 0=3(-4)^2+10(-4)-8\\\\\implies 0=3(16)-40-8\\\\\implies 0=48-48\\\\\implies 0=0\ \checkmark\end{minipage}}[/tex]

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

[tex]\large \text{$y = 2x^2-5x-12 \implies 0=2x^2-5x-12$}[/tex]

[tex]\boxed{\begin{minipage}{15 em}{\text{$x=\dfrac{2}{3}$}} \\ \\\implies 0=2\left(\dfrac{2}{3}\right)^2-5\left(\dfrac{2}{3}\right)-12\\\\\implies 0=2\left(\dfrac{4}{9}\right)-\dfrac{10}{3}-12\\\\\implies 0=\dfrac{8}{9}-\dfrac{10}{3}-12\\\\\implies 0=\dfrac{8}{9}-\dfrac{10\times3}{3\times3}-\dfrac{12\times9}{9}\\\\\implies 0=\dfrac{8}{9}-\dfrac{30}{9}-\dfrac{108}{9}\\\\\implies0=-\dfrac{22}{9}-\dfrac{108}{9}\\\\\implies 0=-\dfrac{130}{9}\ \textsf{X}\end {minipage}}[/tex]    [tex]\boxed{\begin{minipage}{15 em}{\text{$x=-4$}} \\ \\\implies 0=2(-4)^2-5(-4)-12\\\\\implies 0=2(16)+20-12\\\\\implies 0=32+20-12\\\\\implies 0=40\ \textsf{X}\end{minipage}}[/tex]

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

[tex]\large \text{$y = 2x^2+5x-12 \implies 0=2x^2+5x-12$}[/tex]

[tex]\boxed{\begin{minipage}{15 em}{\text{$x=\dfrac{2}{3}$}} \\ \\\implies 0=2\left(\dfrac{2}{3}\right)^2+5\left(\dfrac{2}{3}\right)-12\\\\\implies 0=\dfrac{8}{9}\right)+\dfrac{10}{3}-12\\\\\implies 0=\dfrac{8}{9}\right)+\dfrac{10\times3}{3\times3}-\dfrac{12\times9}{9}\\\\\implies 0=\dfrac{8}{9}+\dfrac{30}{9}-\dfrac{108}{9}\\\\\implies0=\dfrac{38}{9}-\dfrac{108}{9}\\\\\implies 0=-\dfrac{70}{9}\ \textsf{X}\end{minipage}}[/tex]    [tex]\boxed{\begin{minipage}{15 em}{\text{$x=-4$}} \\ \\\implies 0=2(-4)^2+5(-4)-12\\\\\implies 0=2(16)-20-12\\\\\implies 0=32-32\\\\\implies 0=0\ \checkmark\end{minipage}}[/tex]

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

[tex]\large \text{$y = 3x^2-10x-8 \implies 0=3x^2-10x-8$}[/tex]

[tex]\boxed{\begin{minipage}{15 em}{\text{$x=\dfrac{2}{3}$}} \\ \\\implies 0=3\left(\dfrac{2}{3}\right)^2-10\left(\dfrac{2}{3}\right)-8\\\\\implies 0=3\left(\dfrac{4}{9}\right)-\dfrac{20}{3}-8\\\\\implies 0=\not{3}\left(\dfrac{4}{\not{9}\ 3}\right)-\dfrac{20}{3}-8\\\\\implies 0=\dfrac{4}{3}-\dfrac{20}{3}-\dfrac{8\times3}{3}\\\\\implies 0=-\dfrac{16}{3}-\dfrac{24}{3}\\\\\implies 0=-\dfrac{40}{3}\ \textsf{X}\end{minipage}}[/tex]    [tex]\boxed{\begin{minipage}{15 em}{\text{$x=-4$}} \\ \\\implies 0=3(-4)^2-10(-4)-8\\\\\implies 0=3(16)+40-8\\\\\implies 0=48+40-8\\\\\implies 0=80\ \textsf{X}\end{minipage}}[/tex]

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

Therefore, the function whose zeros are ⅔ and -4 is [tex]y=3x^2+10x-8[/tex].

The solution to the system and the solution that fills the blank space is (6, 1)

This are also known as a set of simultaneous equations, also known as a system of equations which is a finite set of equations for which common solutions

Given the following system of equations

2y − x = 8, and

y − 2x = −5.

From equation 2;

y = -5 + 2x ............. 3

Substitute equation 2 into equation 1 to have:

2(-5+2x) - x = 8

Expand to have:

-10 +4x -x = 8

-10 + 3x = 8

3x = 8 + 10

3x = 18

Divide both sides

by 3

3x/3 = 18/3

x = 6

Substitute x = 6 into equation 3

y = -5 + 2x

y = -5 + 2(3)

y = -5 + 6

y = 1

Hence the solution to the system and the solution that fills the blank space is (6, 1)

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Answer:

Its D (6,7)

Step-by-step explanation:

Answer:

A.  y = 1/3x^2

Step-by-step explanation:

The red graph is stretched horizontally by a factor 1/3  to give the blue graph

In the given diagram, the measure of arc QS is 168°

From the question, we are to determine the measure of arc QS

The measure of the arc is the angle subtended by the arc at the center of the circle.

From one of the circle theorems, we have that

The angle subtended by an arc of a circle at its center is twice the angle it subtends anywhere on the circle's circumference

In the given diagram,

The angle subtended by arc at the circumference of the circle = 84°

∴ The angle subtended by the arc QS at the center = 2 × 84°

The angle subtended by the arc QS at the center = 168°

Hence, in the given diagram, the measure of arc QS is 168°

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Answer:  168°

Step-by-step explanation:  TRUST ME!!!  Answer is correct in Edge!  :)

Answer: 8π mm (in terms of π)

Step-by-step explanation:

1) The formulas for solving the circumference of a circle is πd (π times diameter).

2) 8 times π equals 8π mm.

Hopes this helps!

Answer:

12.56 [tex]mm^{2}[/tex]

Step-by-step explanation:

c = 2[tex]\pi[/tex]r

or c =[tex]\pi[/tex]D

The diameter is the measure of a line segment going from one side the circle to the other and going through the middle of the circle.  A radius is a line 1/2 a diameter.  It is a line segment that goes from the center of a circle to a point on the edge of the circle.

C = (3.14)(4)

C = 12.56

In the given right triangle, the trigonometric ratio, sin J has a fractional value of 5/13 and a decimal value of 0.39.

In trigonometry, for a right triangle, the sine (sin) of any angle θ is given as the ratio of its opposite side to the hypotenuse of the triangle, that is, sin θ = (opposite side)/(hypotenuse).

In the question, we are asked to find the trigonometric ratio, sin J, for the given right triangle JKL.

The side opposite to angle J is KL, which has a value of 3 units.

The hypotenuse of the given right triangle is JK, which has a value of 7.8 units.

Thus, sin J can be calculated as:

sin J = KL/JK = 3/7.8 = 5/13 = 0.39.

Thus, in the given right triangle, the trigonometric ratio, sin J has a fractional value of 5/13 and a decimal value of 0.39.

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The first quartile of the dataset {1, 2, 3, 4, 5, 6} is 2.

Given data set: {1,2,3,4,5,6}

Median of the given data set =3.5

The data set can be split into 2 parts as, {1,2,3} and {4,5,6}. The first quartile is calculated by simply finding the median of the first part of the data set.

Thus, the first quartile is 2.

The quarter divides the distribution into four groups and calculates the range of values above and below the mean.

A quartile separates the dataset into four categories by dividing the data into three points: the lowest, median, and upper quartiles.

The interquartile range, a measurement of variation around the median, is calculated using quartiles.

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Answer:

109x

Step-by-step explanation:

We know that there are 109 students in the fourth grade, who each have x cupcakes. In order to find the total amount of cupcakes, we could add all of the cupcakes together to get:

x + x + x + x + .... x

109 times because there are 109 students.

This can be simplified to become 109x.

Answer:

Step-by-step explanation:

The most basic quadratic function is f(x) = x2, whose graph appears below. ... us to graph an entire family of quadratic functions using transformations.

The answer is A. Winter.

As the pattern is : F, W, Sp, Su, F... (letters used for convenience), then the next word in the pattern will be Winter, because that was shown in the previous sequence.

Answer:

D. 13

Step-by-step explanation:

54 ÷ 3 = 18 (your age in 5 years)

18 - 5 = 13 (your age now)

Given: [tex]2x^2 - 12x + 1 = 0[/tex]

Step 1: [tex]2(x^2- 6x + 3^2) + 1 - 2(3^2) = 0[/tex]

Step 2: [tex]2(x^2 - 6x + 9) + 1 - 18 = 0[/tex]

Second answer:  [tex]2(x - 3)^2 - 17 = 0[/tex]

Explanation in detail:

The quadratic equation a[tex]x^{2} + bx + c = 0[/tex]'s vertex form is

where a[tex](x - h)^{2} + k[/tex] equals zero

A is the [tex]x^{2}[/tex] coefficient, and h is the vertex's x-coordinate on the equation's graph.

The vertex of the equation's graph, k, has the y-coordinate.

The completing square can be used to determine the vertex form.

[tex]2x^{2} - 12x + 1 = 0[/tex] is the equation.

Put[tex]2x^{2} -12x[/tex] in a bracket and subtract 2 from them as a common component to utilize the completing square.

∵ [tex]2(x^{2} - 6x) + 1 = 0[/tex]

To determine the product of the first and second terms in the binomial, divide the second term by two.

∵ [tex]6x / 2 = 3x[/tex]

∵[tex]3x = 3 * x[/tex]

∴ The binomial's first and second terms are x and 3, respectively.

The phrase in the bracket's middle is (-)

∴ Middle of the binomial's sign is (-)

∴ The binary value is [tex](x - 3)^2[/tex]

Square 3 is nine.

To keep the equation from altering, you must deduct the same number from the bracket after adding 9 there.

∴ [tex]2(x^2 - 6x + 9 - 9) + 1 = 0[/tex]

- Remove the brace and multiply -9 by 2.

∵ [tex]2 *-9 = -18[/tex]

∴ [tex]2(x^2- 6x + 9) + 1 - 18 = 0[/tex]

- Construct a square binomial from [tex](x^{2} - 6x + 9)[/tex]

∵ [tex]x^2 - 6x + 9 = (x - 3)^2[/tex]

∴ [tex]2(x - 3)^2 + 1 - 18 = 0[/tex]

Include related terms.

∴[tex]2(x - 3)^2 - 17 = 0[/tex]

∴ The equation's vertex form is[tex]2(x - 3)^2 - 17 = 0.[/tex]

Given that: [tex]2x^2 - 12x + 1 = 0[/tex]

Step 1: [tex]2(x^2- 6x + 3^2) + 1 - 2(3^2) = 0[/tex]

Step 2: [tex]2(x^2 - 6x + 9) + 1 - 18 = 0[/tex]

Step 3:  [tex]2(x - 3)^2 - 17 = 0[/tex]

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The correct unscrambling of whyrot is worthy.

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Answer:

y^2 = -8x  for example.

Step-by-step explanation:

General form is y^2 = -4ax

The focus of this parabola will be at (-a , 0) on the x axis.

So the parabola might be:

y^2 = -4x

y^2 = -12x

y^2 = -0.9x  and so on......