Algebra solve the equation show work

According to the census data, the population of China is more than the population of US by a factor 4.2

Given data

population of China = 1.3x10^9

population of US = 308,745,538

population of china = 1.3x10^9. can be rewritten as = 1,300,000,000

comparing the both figures representing population. we divide the population of China by the population of US

let the number of times the population of china is greater than population of US be x, such that

308,745,538 * x = 1,300,000,000

308,745,538x = 1,300,000,000

x = 1,300,000,000 / 308,745,538

x = 4.2106

x ≅ 4.2

We therefore say that the population of china is more than the population of US by a factor 4.2

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The value of x is equal to 16.

Let A and B be angles supplementary to each other, two angles are supplementary when the sum of its measures is equal to 180°. Mathematically speaking, the geometric system is represented by the following formula:

(7 · x + 6) + (5 · x - 18) = 180

12 · x - 12 = 180

12 · x = 192

x = 16

The solution to this equation is 16.

The statement is incomplete, correct form is shown below:

Let be A and B two angles that are supplementary to each other. The measures are (7 · x + 6)° and (5 · x - 18)°, respectively. Find the value of x.

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Answer:

show working

Step-by-step explanation:

you know the area of a rectangle or square is length x width, we do the same here.

so we have a length of (x+5) and because its a square we do (x+5)(x+5) which is

[tex] {x}^{2} + 10x + 25[/tex]

and we know the area of the square is 30 so we make the expression above equal to 30 and take 25 away from both sides to get the wanted equation

Answer:

a. -10

b. -2

c. 10

d. 2

e. -2

f.  2

Answer:

a. = -10 b.=-2 c.=-2 d.=+2 e.=+2 f.=+10

The value of both x and y are 6 degrees in the given figure of arrangement.

What is angle bisector ?

angle bisector is the line which divides the given angle into two equal parts.

a) Here, the line RQ is the angle bisector of angle ∠WRV that is RQ line divides the angle ∠WRV into two equal parts and it is given that :

angle ∠WRQ is 48 degrees

and, angle ∠QRV is 7y+6

Therefore, ∠WRQ = ∠QRV

7y+6 = 48

7y = 48-6

7y = 42

y = 6 degrees

b) It is given that CR is perpendicular to PR that is angle ∠CRP will make 90 degrees and it is given as :

∠CRP = 13x + 12 degrees

90 = 13x + 12

13x = 78

x = 6 degrees

Therefore, the value of both x and y are 6 degrees.

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The solution for the expression ((8p² - 2s³) / m ) + ((58p² - 2s³) / m) + ((58p² - 2s³) / ( m + 5)) is 196.72

Given,

The expression: ((8p² - 2s³) / m ) + ((58p² - 2s³) / m) + ((58p² - 2s³) / ( m + 5))

Where,

Value of p is given as 3

Value of s is given as 2

Value of m is given as 4

Then,

((8p² - 2s³) / m ) + ((58p² - 2s³) / m) + ((58p² - 2s³) / ( m + 5))

= (8 x 3² - 2 x 2³) / 4 + (58 x 3² - 2 x 2³) / 4 + (58 x 3² - 2 x 2³) / 4 + 5

= (8 x 9 - 2 x 8) / 4 + (58 x 9 - 2 x 8) / 4 + (58 x 9 - 2 x 8) / 9

= (72 - 16) / 4 + (522 - 16) / 4 + (522 - 16) / 9

= 56 / 4 + 506 / 4 + 506 / 9

= 14 + 126.5 + 56.22

= 196.22

Therefore, the solution for the expression ((8p² - 2s³) / m ) + ((58p² - 2s³) / m) + ((58p² - 2s³) / ( m + 5)) is 196.72

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A) The type of variation between pitch and wavelength is an inverse variation. b) the pitch when the wavelength is 5 feet would be 132 hertz.

we know that the Inverse Variation is a relationship between two variables in which the product is a constant.

Let x be a pitch of a musical instrument

y be the wavelength

x*y=k

We need to find the value of k for x=220 hertz   and y=3 ft

Then x*y=k

220*3=k

k=660

And for x=165 hertz ,  y=4 ft

x*y=k

165*4=660

k=660

A) Therefore, the type of variation between pitch and wavelength is an inverse variation.

B) the pitch when the wavelength is 5 feet;

x=?

y=5 ft

k=660

x*y=k

Then solve for x

x=k/y

x=660/5

x=132 hertz

Part b) the pitch when the wavelength is 5 feet would be 132 hertz

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The complete question is;

"A musical instrument has a pitch of 220 hertz when the wavelength is 3 feet. When the wavelength is 4 feet, the pitch is 165 hertz. What is the type of variation between pitch and wavelength? What is the pitch when the wavelength is 5 feet? hertz"

The likelihood that Zoe would then strike out in her further at bat this season is calculated.

The various findings or components in a pie chart are depicted by the sectors of a circle, and the entire circle symbolizes the total of the value of each of the components. Obviously, the overall angle of 360° at the central point of the circle is divided by the component values.

Now, for the stated question; It is mentioned that-

Step 1: Last season, Zoe struck out in 10% of her at-bats.

Thus, the probability that the Zoe struck out in her at-bats is 10%.

Then, the probability that the Zoe does not struck out in her at-bats is 90%.

Step 2: The simulation will have 40 trials.

Step 3: We can employ a spinner split into two sectors, one that included 10% of the spinner's area while the other 90%. Determine the central angle of the each sector.

Zoe got thrown out =10% of 360° = 36° Sector yellow

Zoe does not strike out (90 percent of 360° = 324°).

Consider the blue sector in the graph.

Step 4: A trial consists of one spin of the spinner and one strike on the bat by Zoe.

A successful trial means Zoe did not strike out, while a failed trial implies Zoe did strike out. The simulation will include 40 trials.

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Answer:

A. 24.17.

Step-by-step explanation:

Perimeter of given triangle

= 4 + 4.5 + 6

= 14.5.

3:5 = 14.5 : P     where P is perimeter of new triangle

3/5 = 14.5/P

3P = 5*14.5

P = 14.5 * 5 / 3

  = 24,166667

  = 24.17.

By using cross mutliplication, there are 24 gallons in the water tank after 30 minutes.

According to the statement the water tank is full at constant rate, 10 % tank capacity per each 5 minutes. The tank has a capacity of 40 gallons. The gained capacity is determined by the following cross multiplication, where the water capacity is directly proportional to filling time:

x ∝ t

x = (n / 100) · V × (T / t)        (1)

Where:

x = [0.1 · (40 gal)] × (30 min / 5 min)

x = 24 gal

There are 24 gallons in the water tank after 30 minutes.

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The equation for the vertical translation of y=f(x).2/3 unit down is y=f(x)-2/3.

Using equations of the form y=f(x), you may be able to modify the graph in various ways. For example, you can move the chart up, down, left, or right, flip it around the x or y-axis, or stretch or shrink it vertically or horizontally. Understanding these transformations makes it easy to graph different functions. Start with a "basic model" and apply a series of modifications to change it to the desired function.

A point on the graph of y=f(x) has the shape (x,f(x)).

The points on the graph of y=f(x)-2/3 are of the form (x,f(x)-2/3).

So, the graph for y=f(x) -2/3 is the same as the graph for y=f(x) shifted down by 2/3 units.

The new equation is:

y=f(x)-2/3

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Answer:

2 ≤ y

Step-by-step explanation:

2 ≤ y

Answer:

Length is 26.25 and width is 21.25

Step-by-step explanation:

the length is gonna be the width but plus 15, so W+15, and we know that there's 2 widths and 2 lengths in a perimeter so were gonna start off our algebraic expression like this:

2(15+W)+2W=115

distribute the 2

30+2W+2W=115

combine like terms

30+4W=115

subtract 30 from both sides

4W=85

divide 4 from both sides

W=21.25

now plug in our width value into W+15 to find length

W+15

21.25+15=L

36.25=L

The graph of f(x) is shifted 5 units to the left to create g(x).

A parent function is an equation in the simplest form of a family of functions. A family of functions is a collection of functions that represent similar characteristics and/or transformations of its parent function. A parent function can be represented with different degree values such as degrees 1, 2, or 3.

The most basic parent function is called a constant function.

Types of Parent Functions

There are multiple forms of parent functions. Some types of parent functions are:

Constant function: A horizontal line that intersects the y-axis.

Square root function: The inverse function of a quadratic function following the form f(x)= [tex]\sqrt{x}[/tex]

Cube root function: The inverse function of a cubic function in the form f(x)= 3     [tex]\sqrt{x}[/tex]

A parent function is the simplest form that a function can be. Its basic shape is not in any way altered.

For instance, when you see a u-shaped graph that is inverted and vertically stretched, you should still recognize that it is a parabola which has undergone different transformations

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Answer:

The graph of f(x) is shifted 5 units to the left to create g(x).

Step-by-step explanation:

The area of the doghouse in square feet is calculated as 9 (13) ft2.

The formula to find the area of the dog house is 9(1/3) ft2

Area of the dog house = Length of the dog house width of the dog house

Area = (72 ft )  (83 ft )

Area = 7.82.3 ft*ft

Area = (566) ft2

Hence, the area becomes Area = 9 (13) ft2

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The scores on the statistics test was normally distributed with a mean of 86 and a standard deviation of 5. Jose scored a 93 on his test then 1.4% of the class scored less than he did.

A probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

The scores on the statistics test was normally distributed with a mean of 86, a standard deviation of 5, and Jose scored a 93 on his test.

We need to find the percentage of the class scored less than he did

z=(x-mean)/ S.D

=93-86/5

=7/5

=1.4

Therefore 1.4 percentage of the class scored less than Jose did.

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Answer: b=8

Step-by-step explanation:

Answer:

a. No

b. Yes

c. Yes

Step-by-step explanation:

Answer:

Step-by-step explanation:

Using it's concept, it is found that the percentile of 7 cakes is the 67th percentile.

When a measure is in the xth percentile of a data-set, it is greater than(or equal) x% of the measures and lesser than (100 - x)%.

In this problem, we have that:

Hence, the percentile of the measure 8 is found as follows:

8/12 = 67th (rounded).

The percentile of 7 cakes is the 67th percentile.

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Answer:

f(6) = 40

Step-by-step explanation:

f(x)=8x-8

f(6) means to evaluate the function at x = 6.

Substitute 6 for x, and evaluate the right side.

f(6) = 8(6) - 8

f(6) = 48 - 8

f(6) = 40

Answer: True

Step-by-step explanation: Because Im A Top G

Answer:

7 baskets

Step-by-step explanation:

in the first game, he shot 6 baskets so

34 - 6 = 28

she shot the same number for each of the 4 games,

so divide 28 and 4.

the answer is 7

hope this helps

 From the list of numbers presented:

 we can determine that this is a infinite serie.

      A sequence is an order of elements that are governed by a pattern, that is, it has variations between each element that remain constant and allow us to determine values before or after the known elements.

 A sequence maintains an order, and this numerical order can be finite or infinite, in the given case we have the following list:

1, 2, 4, 8, 16, 32

2ⁿ⁻¹

  In this series we have the initial value of the same, but we do not know the final value, although we know its behavior, we can say that this series has no end, it is an infinite serie.

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A rectangle as the only parallelogram that can be inscribed in a circle.

A rhombus's opposite angles are congruent. If a rhombus has an angle, it has one pair of opposite angles that are and another pair of opposite angles that are. Because opposite angles are not supplementary, this rhombus cannot be encircled.

Because not all quadrilaterals can be inscribed in circles, they are not all cyclic quadrilaterals. If and only if the opposite angles of a quadrilateral are supplementary, it is cyclic.

A rectangle is the only parallelogram that can be inscribed in a circle. The important point is that the radius of the circle is R, because every rectangle can be inscribed in a (unique circle). (I believe.) One of the properties of a rectangle is that the diagonals bisect in the 'center,' which is also the circumscribing circle's center.

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Answer:

36

Step-by-step explanation:

= 24/6+2^3*4

= 24/6+8*4

= 4+8*4

= 4+32

= 36

assuming 4x+21=6x-23

then you can get x by doing

4x+21=6x-23

21=2x-23

44=2x

x=22

4x+21= 109

6x-23= 109

We get the expression 64√2 in the form 2ⁿ as 2⁶°⁵.

An expression is a way in which numbers are written.

It can be variables, constants or a combination of both.

We are given an expression:

64 √2

We know that:

64 = 2 × 2 × 2 × 2 × 2 × 2

64 = 2⁶

Also, we can write √2 as

√2 = 2⁰°⁵

We get that:

2⁶ × 2⁰°⁵

simplifying the expression, we get that:

= 2⁶⁺⁰°⁵

= 2⁶°⁵

Therefore, we get the expression 64√2 in the form 2ⁿ as 2⁶°⁵.

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The fraction 1/3 is not equivalent to a terminating decimal

A terminating decimal can be defined as a decimal expressed in a finite number of figures.

It is also said to be a decimal having an end point.

Example;

1/ 2 is a terminating decimal having its value as 0. 5

Given the fraction;

1/ 3, the decimal value = 0. 333333333

It is not a terminating decimal as it has an indefinite decimal value.

Thus, the fraction 1/3 is not equivalent to a terminating decimal

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The approximate rate of change in attendance from 2001 to 2005 is 1657.  

Rate of Change of value is defined as the change in value over an interval of time.

Denoted by [tex]rate.of.change=\frac{change.in.value}{time}[/tex]

In the given question

Attendance in the year 2001 = 450746

Attendance in the year 2005=457373

Time = 2005-2001= 4 years .

[tex]rate.of.change=\frac{value.in.2005-value.in.2001}{2005-2001}[/tex]

rate of change = [tex]\frac{457373-450746}{4}[/tex]=[tex]\frac{6627}{4}[/tex]=1656.75≅1657

this  means that attendance increases about 1657 per year.

Therefore , the approximate rate of change in attendance from 2001 to 2005 is 1657 .

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