he simultaneous equations
5x + y = 21
x - 3y = 9

With working out​

Answer:

[tex](x^{4}y^{6}+1)(x^{8}y^{12}-x^{4}y^{6}+1)[/tex].

Step-by-step explanation:

We want to expand: [tex]x^{12}y^{18}+1[/tex].

We can rewrite this as the sum of two cubes.

[tex](x^{4})^3(y^{6})^3+1=(x^{4}y^{6})^3+1^3[/tex].

Recall and use the sum of cubes identity: [tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]

By comparing our newly rewritten expression to this identity, we have [tex]a=x^4y^6[/tex] and [tex]b=1[/tex].

We substitute into the identity to get:

[tex](x^{4}y^{6})^3+1^3=[x^{4}y^{6}+1][(x^{4}y^{6})^2-(x^{4}y^{6})(1)+1^2][/tex].

We now use this rule of exponents :[tex](a^m)^n=a^{mn}[/tex]  to get;

[tex](x^{4}y^{6}+1)(x^{8}y^{12}-x^{4}y^{6}+1)[/tex].

Answer:730000

Step-by-step explanation:

Follow below steps;

To round the number 726,034 to the nearest ten thousand, we must look at the thousands digit, which is 2. Since 2 is less than 5, we do not round up, and thus, leave the ten thousands place as it is.

The number 726,034 rounded to the nearest ten thousand is 720,000. We can see that the thousand's digit is less than 5, so we round down. This process aligns with the rounding rule stating that if the number you are rounding is followed by 0, 1, 2, 3, or 4, you round the number down.

Answer:

36

Step-by-step explanation:

area of trapezium is (1/2)×(6+9)×8=60

area of triangle is (1/2)×6×8=24

area of shaded =60 - 24 =36

The area of the shaded region of the trapezoid is 36.

area of trapezium is (1/2)×(6+9)×8=60

area of triangle is (1/2)×6×8=24

area of shaded =60 - 24 =36

Answer:

{196, 256, 484}

Step-by-step explanation:

14² = 196;

16² = 256;

19² = 361;   390 lies between 361 and 400, and is thus NOT a perfect square;

20² = 400;

22² = 484

564 lies between the two perfect squares 23² and 24², but is itself NOT a perfect square.

Thus, the perfect squares are {196, 256, 484}

The perfect squares out of the numbers 196, 256, 390, 484, 564 are 196, 256, and 484. A perfect square is a number that can be expressed as an integer multiplied by itself.

The perfect squares from the list you provided are: 196, 256, and 484. A perfect square is a number that can be expressed as the product of an integer with itself. For example, 256 is a perfect square because it can be expressed as 16 times 16, or 16^2. Similarly, 196 and 484 are perfect squares as they can be expressed as 14^2 and 22^2, respectively. On the other hand, numbers 390 and 564 are not perfect squares as they cannot be expressed as the product of an integer with itself.

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Answer:

(m - 6n)(3m + 2n)

Step-by-step explanation:

Given

3m² - 16mn - 12n²

Consider the factors of the product of the coefficient of the m² term and the n² term which sum to give the coefficient of the mn term

product = 3 × - 12 = - 36 and sum = - 16

The factors are - 18 and + 2

Use these factors to split the mn term

3m² - 18mn + 2mn - 12n² ( factor the first/second and third/fourth terms )

= 3m(m - 6n) + 2n(m - 6n) ← factor out (m - 6n) from each term

= (m - 6n)(3m + 2n)

Answer:

Yes

Step-by-step explanation:

The more you jump, the higher your blood flow becomes, since your heart needs to pump more blood to the working areas. This really doesn't belong in math though.

Answer: yes

Step-by-step explanation: but i am not that sure how i can explain it, here look at the guys answer above. Also thank the guy above, not me.

Answer:

15,36,39

Step-by-step explanation:

primitive pythag: 5, 12, 13 *3

Answer:

The Answer is D

Step-by-step explanation:

Answer:

1 year = 52 weeks.

Divide total weeks by 52 to get total years.

Nearest Thousandth would be 3 decimal places.

3004 weeks / 52 weeks per year = 57.769 years.

Answer:

57.769

Step-by-step explanation:

There are 52 weekends in one year

3004 divided by 52 = 57.7692

Round to the nearest thousandth 57.769

Answer:

2x + 7

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

f(x) - g(x) = 3x + 1 - (x - 6) = 3x + 1 - x + 6 = 2x + 7

Answer:it is 120 balloons  

Step-by-step explanation:

15 min = 20 balloons

6min = ????? = 20 multipyed by 6=

120                                                                 hope this helps:)

Answer: He can create 8 balloon animals in 6 minutes.

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

So, first we have to find the number of balloon animals he can create per minute by dividing the number of balloon animals created in 15 minutes (20) by the number of minutes (15).

Mathematically speaking:

20/15 = 1.3333 balloon animals per minute

Now we multiply the value obtained by 6:

1.333333 x 6 = 8 balloon animals (rounded)

Answer:

[tex]\displaystyle f^{-1}(x) = -\frac{1}{5}x - \frac{4}{5}[/tex].

Step-by-step explanation:

The question has provided an expression for the function [tex]f(x)[/tex] and is asking for its inverse, [tex]f^{-1}(x)[/tex].

Based on the definition of inverse functions,

[tex]f(f^{-1}(x)) = x[/tex].

Let [tex]y = f^{-1}(x)[/tex].

[tex]f(y) = x[/tex].

[tex]-5 y - 4= x[/tex].

Solve this equation for [tex]f^{-1}(x) = y[/tex]:

[tex]-5y = x +4[/tex].

[tex]\displaystyle y = (-\frac{1}{5})\cdot (x + 4) = -\frac{x}{5} -\frac{4}{5}[/tex].

However, [tex]f^{-1}(x)=y[/tex] As a result,

[tex]\displaystyle f^{-1}(x) = -\frac{x}{5} -\frac{4}{5}[/tex].

Answer:

[tex]\large\boxed{f^{-1}(x)=-\dfrac{x+4}{5}}[/tex]

Step-by-step explanation:

[tex]f(x)=-5x-4\to y=-5x-4\\\\\text{Exchange x to y and vice versa:}\\\\x=-5y-4\\\\\text{Solve for}\ y:\\\\-5y-4=x\qquad\text{add 4 to both sides}\\\\-5y=x+4\qquad\text{divide both sides by (-5)}\\\\\dfrac{-5y}{-5}=\dfrac{x+4}{-5}\\\\y=-\dfrac{x+4}{5}[/tex]

Answer:

(fog)(x) = x^2

Step-by-step explanation:

Here g(x) = x^2 + 14 becomes the input to f(x):

(fog)(x) = [x^2 + 14] - 14

(fog)(x)  = x^2 (answer)

If the function are f(x) = x - 14 and g(x) = x² + 14. Then the function (fog)(x) will be x².

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The functions are given below.

If the function are f(x) = x - 14 and g(x) = x² + 14

Then the function (fog)(x) will be

(fog)(x) = g(x) - 14

(fog)(x) = x² + 14 - 14

(fog)(x) = x²

More about the function link is given below.

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Hello

Good Luck

Goodbye ♥

Answer:

x=5

Step-by-step explanation:

10x+5=6x+25

10x=6x+25-5

10x-6x=25-5

4x=20

x=5

GOOD LUCK ! ;)

Answer: Option B

A reflection about the x-axis, a vertical stretch by a factor of 2, a horizontal shift of 1 unit to the right, and a vertical shift downward of 6 units.

Step-by-step explanation:

If the graph of the function [tex]g(x)=cf(h-h) +b[/tex]  represents the transformations made to the graph of [tex]y= f(x)[/tex]  then, by definition:

If  [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor c.

If  [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor c

If [tex]c <0[/tex]  then the graph is reflected on the x axis.

If [tex]b> 0[/tex] the graph moves vertically  upwards b units.

If [tex]b <0[/tex] the graph moves vertically down  b units

If [tex]h> 0[/tex] then the graph of f(x) moves horizontally h units to the left

If [tex]h <0[/tex] then the graph of f(x) moves horizontally h units to the right

In this problem we have the function [tex]g(x) = -2((x - 1)^2 + 3)[/tex] and our parent function is [tex]f(x) = x^2[/tex]

therefore it is true that [tex]c =-2<0[/tex]  and [tex]b =-6 <0[/tex] and [tex]h=-1<0[/tex]

Therefore the graph is reflected on the x axis, stretched vertically by a factor 2. The graph of f(x) moves horizontally 1 units to the right and shift downward of 6 units.

The answer is (B) A reflection about the x-axis, a vertical stretch by a factor of 2, a horizontal shift of 1 unit to the right, and a vertical shift downward of 6 units.

Final answer:

The correct transformations from f(x) = x² to g(x) = −2[(x − 1)² + 3] are a reflection about the x-axis, a vertical stretch by 2, a horizontal shift 1 unit to the right, and a vertical shift 3 units upwards, which is option (B) in the list provided.

Explanation:

The function g(x) = −2[(x − 1)² + 3] has undergone several transformations from the base function f(x) = x^2. These transformations include a reflection about the x-axis due to the negative sign in front of the equation, indicating that a flip has happened vertically. A vertical stretch by a factor of 2 is also evident from the coefficient 2 before the parenthesis.

The term (x - 1) inside the parenthesis indicates a horizontal shift of 1 unit to the right since we subtract from x to move the graph to the right. Lastly, the +3 at the end of the equation signifies a vertical shift of 3 units upwards, which is a change in the y-value of every point on the graph.

Therefore, the correct sequence of transformations to obtain g(x) from f(x) is: a reflection about the x-axis, a vertical stretch by a factor of 2, a horizontal shift of 1 unit to the right, and a vertical shift of 3 units upwards, which corresponds to option (B) provided by the student.

Answer:

sqrt(3)

Step-by-step explanation:

Surface area of a sphere = 4pi(r)^2

Solve for r

The best way to describe a ratio is option c, which is 'A comparison of two numbers'.

A ratio shows us the number of times a number contains another number. therefore, it helps us to compare two numbers.

As we have already discussed the ratio is the comparison of two numbers for a particular.

Hence, the best way to describe a ratio is option c, which is 'A comparison of two numbers'.

Learn more about Ratio:

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Answer: First Option

[tex]x= -3.396[/tex]

Step-by-step explanation:

We have the following expression

[tex]log_{\frac{3}{4}}25 = 3x -1[/tex]

To solve the equation add 1 to both sides of the equality

[tex]log_{\frac{3}{4}}25 +1= 3x -1+1[/tex]

[tex]log_{\frac{3}{4}}25 +1= 3x[/tex]

Divide between 3 to both sides of the equation

[tex]\frac{log_{\frac{3}{4}}25 +1}{3}= x[/tex]

[tex]x= \frac{-11.19 +1}{3}[/tex]

[tex]x= -3.396[/tex]

The answer is the first option

Answer:

D. offer possible answers to historical questions.

Step-by-step explanation:

An argument is a statement which a historian proposes. In order to back up the statement the historian provides proof. The argument is then read by other historians and the proof is analyzed. After the analysis if other historians come to the same conclusion which the statement points to then the argument is accepted.

So, this is the way to offer possible answers to historical questions.

Step-by-step explanation:

0.76+0.64/0.76-0.64

1.40/0.12

11.66

is the answer

Answer:

11.4300523

Step-by-step explanation:

cos 40° = 0.7660444431

sin 40° = 0.6427876097

cos 40° + sin 40° = 1.408832053

cos 40° - sin 40° = 0.1232568334

1.408832053 ÷ 0.1232568334 = 11.4300523

Answer:

3/11 + 5 5/8 > 5 6/8

Step-by-step explanation:

find the LCD's for both sides of the comparison. After this, add fractions from the same side of the comparison. Then, you must compare the two and check your answer. Have a nice day!

Answer:

Last option: 7

Step-by-step explanation:

The Standard form of a quadratic equation is the following:

[tex]ax^{2}+bx+c=0[/tex]

Where "a" is the quadratic coefficient (This coefficient cannot be 0), "b" is the linear coefficient, "c" is the constant and "x" is the variable.

In this case you have the quadratic equation [tex]3x^2 + 5x + 7 = 0[/tex] which is written is Standarf form. Then, you can identify that:

[tex]a=3\\b=5\\c=7[/tex]

Therefore the value of "c" is 7.

For this case we have that the sum of 3 consecutive integers is 24, if we represent by means of an equation we have:

[tex]x + (x + 2) + (x + 4) = - 24\\x + x + 2 + x + 4 = -24\\3x + 6 = -24\\3x = -24-6\\x = \frac {-30} {3}\\x = -10[/tex]

Thus, the three consecutive numbers are:

[tex]x = -10\\x = -10 + 2= -8\\x = -10 + 4 = -6[/tex]

Answer:

-10,-8,-6

Answer: [tex]-10,-8,-6[/tex]

Step-by-step explanation:

Let be:

 [tex]x[/tex], [tex]x+2[/tex] and  [tex]x+4[/tex] the three consecutive even integers whose sum is -24

Then, we can write this expression:

 [tex]x+(x+2)+(x+4)=-24[/tex]

Now, we must solve for "x":

[tex]3x+6=-24\\\\3x=-24-6\\\\3x=-30\\\\x=\frac{-30}{3}\\\\x=-10[/tex]

Then you get that the others integers are:

[tex]x+2=-10+2=-8[/tex]

[tex]x+4=-10+4=-6[/tex]

Therefore, the  three consecutive even integers whose sum is -24 are:

[tex]-10,-8,-6[/tex]

Final answer:

The ordered pair of M after rotating 90 degrees clockwise is (-6,5).

Explanation:

When a point undergoes a 90-degree clockwise rotation around the origin, a distinct transformation occurs. Specifically, the x-coordinate of the original point becomes the negative value of its original y-coordinate, and the y-coordinate takes on the positive value of the original x-coordinate. This geometric operation is fundamental in transforming coordinates.

Taking point M(5,6) as an example, after the 90-degree clockwise rotation, the new coordinates manifest as (-6,5). This rotation plays a crucial role in various mathematical and geometric applications, contributing to the understanding of spatial transformations and coordinate systems.

Answer:

y=2/3 x+2

Step-by-step explanation:

The equation of a linear graph is given as

y=mx+c

m is the slope of the line while c is the y intercept

As shown from the graph, the y-intercept is 2

The slope can be calculated by diving the height by the length:

2/3

y=2/3 x+2

[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{4}{5}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{5}{4}}\qquad \stackrel{negative~reciprocal}{+\cfrac{5}{4}\implies \cfrac{5}{4}}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-0}{2-(-2)}\implies \cfrac{5}{2+2}\implies \cfrac{5}{4} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{9}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{9-(-1)}{10-2}\implies \cfrac{9+1}{8}\implies \cfrac{10}{8}\implies \cfrac{5}{4}[/tex]

Answer: Im pretty sure it answer options 1 and 5

Step-by-step explanation: 1) (-2,0) and (2,5)      5) (2,-1) and (10,9)

its on edg.

Answer:

$7.63

Step-by-step explanation:

We are given:

r=9 icnhes

We have to find the area of the circular ornament first. The formula for area of circle is:

Area= πr^2

Putting the value of r

Area=3.14*(9)^2

=3.14*81

=254.34 Square inches

As the company pays $0.03 for 1 square inch, for 254.34 square inch the company will have to pay:

=254.34*0.03

=$7.6302

Rounding off to the nearest cent

The cost for one ornament = $7.63

Answer:

$30.52

Step-by-step explanation:

4 x 9^2 x 3.14 x 0.03 = around 30.52

Answer:

b) (-6, 0)

Step-by-step explanation:

The quickest method to use is to put "0" in for y, then figure out which term for x would make the equation authentic, or genuine.

Answer:

Both a and b

Step-by-step explanation:

Answer:

From the looks of things, it seems to be 140 ft, the maximum height being 150 ft and the minimum height being 10 ft. Find the difference, and that should be your answer :)

Answer:C 140

Step-by-step explanation:

−x = 4 − 3x + 6

Move the -3x to the other side and simplify 4+6.

2x= 10

Divide both sides by 2

x=5.

Answer: First option.

Step-by-step explanation:

Given the equation [tex]-x = 4- 3x + 6[/tex], you need to solve for the variable "x" to find its value.

Add the like terms on the right side of the equation:

 [tex]-x = 10-3x [/tex]

Now you need to subtract 10 from both sides of the equation:

 [tex]-x-10 = 10- 3x -10[/tex]

 [tex]-x-10 =- 3x[/tex]

 The next step is to add "x" to both sides of the equation:

  [tex]-x-10+x = - 3x +x[/tex]

   [tex]-10 = - 2x[/tex]

And finally, divide both side by -2:

[tex]\frac{-10}{-2}=\frac{-2x}{-2}\\\\x=5[/tex]