Sequences of congruence transformations:

Triangle T'U'V' is the image of triangle TUV under a rotation followed by a reflection across the y-axis.

The number of ants that are more than people will be 9800000.

It should be noted that based on the information, it was stated that on earth, there are about 1 quadrillion ants and about 8 billion people.

Therefore, the difference between the values illustrated will be:

= 1 quadrillion - 8 billion

= 1 × 10^15 - 8 × 10^9.

= 9.2 × 10^5

Therefore, the number of ants that are more than people will be 9800000

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Use the following information to fill in the blanks. On earth, there are about 1 quadrillion ants and about 8 billion people.

On Earth, there are about ...... more ants than people.

ANSWER- X is  2.52083333 or 2.52083 rounded

265-23 is 242. 242 divided into 96 is 2.52083333

(96 x 2.52083333)+23 = 265

This means our X is 2.52083...

HOPE THIS HELPS & GOOD LUCK

Answer:

[tex]\displaystyle \frac{121}{48}[/tex]

or

[tex]2.5208\bar3[/tex]

To begin, subtract 23 from both sides of the equation. This will move the constants to the right side.

[tex]96x=242[/tex]

Then, divide both sides of the equation by 96. This will isolate the unknown, x, and allow you to solve the equation.

[tex]\displaystyle \frac{96x}{96}=\frac{242}{96}[/tex]

[tex]\displaystyle x=\frac{121}{48}[/tex]

There are two different answers that are equivalent but will depend on what you are looking for.

For a fraction answer, your final answer is [tex]\displaystyle \frac{121}{48}[/tex].

For a decimal answer, your final answer is [tex]2.5208\bar3[/tex].

Answer: A quadrilateral that has 4 sides is known as a rectangle.

Answer:

Step-by-step explanation:

This is either a rectangle or a square.

(A square is a special type of rectangle, with 4 equal sides).

After solving the given equation log₃x = 4, the value of x = 81.

So,

Then,

Therefore, after solving the given equation log₃x = 4, the value of x = 81.

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The equation that shows the different and incorrect relationship is C. b = ✓(a² + c²)

It should be noted that from the information the Pythagoras theorem was illustrated and given as c² = a² + b²

Therefore, the equations that can be gotten from it include b² = c² - a².

It should be noted that the equation that shows the different and incorrect relationship is b = ✓(a² + c²)

In conclusion, the correct option is C.

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The reasonable class intervals for a frequency table in between 120-269 with 14 class interval in between is shown .

Frequency refers to the number of times an event or a value occurs. A frequency table is a table that lists items and shows the number of times the items occur.

Given:

The weights of 100 main subjects as a part of a nutrition study.

The values ranging from a low of 121 pounds to a high of 263 pounds.

According to given question we have

Total span =263 pounds- 121 pounds

                  =142 pounds

Interval             frequency

120-134                4

135-149                14

150-164                16

165-179                 28

180-194                 17

195-209                8

210-224                 7

225-239                6

240-254                 2

255-269                3

Therefore, the reasonable class intervals for a frequency table in between 120-269 with 14 class interval in between is shown .

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The composite discount = 32%

The store offers 15% which  on all items and employees get a 20% discount.

The composite discount formula is:

 -x - y + ( x ×y / 100)

Here x = 15% and y = 20%

So by putting the value of x and y we get

- 15 - 20 + ( 15 × 20 /100)

- 15 -20 + 3

- 35+ 3

-32  

Therefore we get the composite discount i.e., 32%

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The slope of the line that passes through  (8, 0) and (-4, -8) is calculated as: m = 2/3.

The slope (m) formula is given as:

Slope (m) = change in y/change in x = y2 - y1/x2 - x1.

Given the following points on the line:

(8, 0) = (x1, y1)

(-4, -8) = (x2, y2)

Plug in the values into the slope formula, x = y2 - y1/x2 - x1:

Slope (m) of the line = (-8 - 0) / (-4 - 8)

Slope (m) of the line = (-8) / (-12)

Slope (m) of the line = 2/3

Thus, the slope of the line that passes through  (8, 0) and (-4, -8) is calculated as: m = 2/3.

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The solution for the equation √x + 6 + 2 = x + 6 is 4.

An extraneous solution is one that results from the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.

A formula known as an equation uses the equals sign (=) to express how two expressions are equal.

Consider the equation,

√x + 6 + 2 = x + 6

Subtracting 6 from each side of the equation.

√x + 6 + 2 -  6 = x + 6 - 6

√x + 2 = x

Subtracting 2 from each side.

√x + 2 - 2 = x - 2

√x = x - 2

Squaring the above equation.

( √x )² = ( x - 2 )²

x = x² - 4x + 4

x² - 5x + 4 = 0

x² - x - 4x + 4 = 0

x( x - 1 ) - 4( x - 1 ) = 0

( x - 1 )( x - 4) = 0

x = 1, 4

Checking for extraneous solutions,

x = 1

√x + 6 + 2 = x + 6

√1 + 6 + 2 = 1 + 6

9 ≠ 7

Hence, x = 1 is not a solution.

For, x = 4

√x + 6 + 2 = x + 6

√4 + 6 + 2 = 4 + 6

2 + 6 + 2 = 4 + 6

10 = 10

The solution of equation √x + 6 + 2 = x + 6 is x = 4.

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Answer:

The dimensions of the rectangle are length = 22 meters and width = 13 meters.

Step-by-step explanation:

It is given that the length of a rectangle is 4 meters less than twice the width and if the area of the rectangle is 286 square meters we need to calculate the dimensions.

Firstly, let us look at the dimensions of the rectangle;

=> Let 'l' be the length and 'b' be the width of the rectangle.

Now, let us look at the area of a rectangle;

=> l × b

So, we get an equation from the above condition;

=> l = 2b - 4

Now, the area of the rectangle is given that is 286 square​ meters;

=> A = 286 sq. m.

Using the above-mentioned formula for the area of the rectangle we get;

=> A = l × b

=> 286 = (2b - 4) × b

=> 286 = 2b² - 4b

=> 2b² - 4b - 286 = 0

After solving it further we get;

=> 2b² - 4b - 286 = 0

=> b² - 2b - 143 = 0

=> b² - 13b + 11b - 143 = 0

=> (b - 13) + (b + 11) = 0

Now, after equating both the sides we get;

=> (b - 13) = 0

=> b = 13

and

=> (b + 11) = 0

=> b = -11

But, b = -11 is not possible so, the width of the rectangle is 13 meters.

And the length of the rectangle would be,

=> l = 2b - 4

=> l = 2 × 13 - 4

=> l = 22

Therefore, the dimensions of the rectangle are length = 22 meters and width = 13 meters.

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No extraneous solutions to this equation.

The equation is

[tex](5x- 4)^{1/2}[/tex] - x = 0

To find the value of x

[tex](5x- 4)^{1/2}[/tex] = x

Now square on both sides of the equation.

We get

5x - 4 =[tex]x^{2}[/tex]

[tex]x^{2}[/tex] - 5x + 4= 0

[tex]x^{2}[/tex] - 4x - x + 4 =0

x( x -4 ) - 1 ( x - 4) =0

( x- 4 ) ( x - 1)= 0

x = 4, 1

We get the value of x as 4 and 1

Now we have to put the value of x in the equation

First, put 4

[tex](5x - 4)^{1/2}[/tex] -x =0

[tex](5 * 4 - 4)^{1/2}[/tex] - 4= 0

[tex](20 - 4)^{1/2}[/tex] - 4 =0

[tex]16^{1/2}[/tex] - 4 = 0

4-4 =0

0 = 0

Now put 1

[tex](5 * 1 - 4)^{1/2}[/tex] - 1 = 0

[tex](5 -4)^{1/2}[/tex] - 1=0

1 - 1=0

0=0

Hence we get that both the value of x is not an extraneous solution.

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I think the answer is x=4

Answer: x=4

Step-by-step explanation:

2x+3(5x-7)=47

2x+15x-21=47

17x-21=47

  +21  +21

17x= 68

17     17

x=4

Hey there!

x^2 * y

= 7^2 * 9

= 7 * 7 * 9

= 49 * 9

= 441

Thus, the answer should be:

441

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The value of x is 12.

What is triangle proportion?

According to the Triangle proportion rule, When a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

In the diagram;

The side with x is a reflexive side of both triangles and as such from triangle proportionality theorem we can say that;

⇒6/x = 3/6

⇒ 36 = 3x

⇒ x = 12

Hence, The value of x is 12.

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The unknown angle in the triangle is as follows:

m∠A = 52°

External angle theorem states that If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

Therefore,

m∠D = m∠A + m∠B

m∠D = 116°

m∠A =  (2x)°

m∠B = (x + 38)°

Hence,

116 = 2x + x + 38

116 = 3x + 38

3x = 116 - 38

3x = 78

divide both sides by 3

x = 78 / 3

x = 26

Therefore,

m∠A = 2(26)

m∠A = 52°

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Answer:

[tex]1.93475*10^{-10}[/tex]

Step-by-step explanation:

To multiply the decimal numbers in scientific notation, multiply the decimals and add the powers of the 10.

  [tex]\sf 5.45 * 10^{-4}* 3.55*10^{-7}=5.45*3.55 * 10^{(-4)+(-7)}[/tex]

                                         [tex]\sf = 19.3475*10^{-11}[/tex]

Now, write the decimal 19.3475 in scientific notation.

As we have to move the decimal one count towards left, add 1 to the power.

                                         [tex]\sf = 1.93475*10^{-11+1}\\\\ = 1.93475*10^{-10}[/tex]

The value of the expression log 10,000 is 4.

The logarithmic function is the inverse of the exponential function. This means that the logarithm of a given number, say x, is the exponent to which another fixed number that is the base b, must be raised, so as to produce that number x.

Log a to the base b can be written as- log a/ log b.

Moreover, log [tex]a^{k}[/tex] = k log a, for all non negative values of a

Here, we are given a logarithmic expression- log 10,000

As the base is not given, we always assume it to be 10.

We can expand this as-

log 10,000 = log 10,000/ log 10

= log [tex]10^{4}[/tex]/ log 10

= 4 log 10/ log 10

= 4

Thus, the value of log 10,000 is 4.

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The new coordinates after transformation of the original coordinates using the transformation rule (x, y) → (x, -y) are;

P(6, -4) → P'(6, 4)

Q(2, -2) → Q(2, 2)

R(2, -6) →  R(2, 6)

S(6, -6) → S(6, 6)

The given reflection transformation of (x, y) → (x, -y) simply means a reflection across the x-axis.

Thus, the new coordinates after undergoing the above transformation are;

P(6, -4) → P'(6, 4)

Q(2, -2) → Q(2, 2)

R(2, -6) →  R(2, 6)

S(6, -6) → S(6, 6)

Thus, we conclude that the new coordinates after transformation of the original coordinates using the transformation rule (x, y) → (x, -y) are;

P(6, -4) → P'(6, 4)

Q(2, -2) → Q(2, 2)

R(2, -6) →  R(2, 6)

S(6, -6) → S(6, 6)

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The area of stained glass with a parallelogram shape is 108cm².

So, Area of parallelogram = Base × Height

Now, in △LMN use the Pythagorean theorem:

Using the parallelogram area formula:

Then,

Therefore, the area of stained glass with a parallelogram shape is 108cm².

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A pictorial representation or a diagram that represents data or values in an organized manner. For function f(x)=-x+3, -3≤x≤3 the graph is in attachment.

A pictorial representation or a diagram that represents data or values in an organized manner.

Given f(x)=-x+3, -3≤x≤3

It means x values lies from -3 to 3

x        -3         -2      -1      0     1       2      3

f(x)      6         5       4       3     2      1       0

By taking the table values we can draw a graph.

Therefore the attached graph is the graph for f(x)=-x+3.-3≤x≤3.

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Answer:

-18k

Step-by-step explanation:

-> -8k+ 10k

-> minus and plus is = minus

-> 8k+10k

-> -18k(ans)

The Magnitude of earthquake that hit Texas is 5.8; With the help of the logarithmic equation so found, we can get the value of M, with which we can get the magnitude of the Texas earthquake.

Given:

To find: Magnitude of earthquake that hit Texas.

Finding:

=>  [tex]\frac{I_2}{I_1}[/tex] =  [tex]30^M[/tex]

For  [tex]\frac{I_2}{I_1}[/tex] = 74900, the above expression becomes:

=> 74900 = [tex]30^M[/tex]

Taking logarithm on both sides, with base 10 gives:

=> log (74900) = log ([tex]30^M[/tex])

As [tex]log_b(a)^m = m(log_b(a))[/tex],

=> log (74900) = M ( log (30))

=> [tex]\frac{log(74900)}{log (30)}[/tex] = M

=> M ≈ 3.3, i.e., the increase in magnitude difference is approximately 3.3.

Thus, the magnitude of the earthquake that hit Texas = 9.1 - 3.3 = 5.8.

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Answer:

E) (0, 1)

Step-by-step explanation:

We can equalize the first two equations to find a certain point they share. We can then check if the third line also passes through this point if substituting that point's x coordinate into the third line's equation returns the point's correct y value.

[tex]2x + 1 = 3x + 1 \\\to 0 = x[/tex]

Therefore, the point is (0, 1) as substituting [tex]x = 0[/tex] into the first equation returns [tex]y = 1[/tex].

Substituting [tex]x = 0[/tex] into the third equation does also return [tex]y = 1[/tex], therefore, that line passes through the shared point (0, 1).

Answer: Evaluate x[tex]\frac{8}{3}[/tex]

DIFFERENTIATE W.R.T. X

[tex]\frac{8x\frac{5}{3} }{3}[/tex]

​

Step-by-step explanation:

From 100 yards away, a marksman hit  probability of It means 90% of the targets were hit .

What is the probability?

Total no of targets = 10

number of targets hit = 9

                                    = 100/10  = 10

                                   = 10 * 9   ⇒ 90

It means 90% of the targets were hit .

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