ZE and ZF are vertical angles with mZE= 9x + 12 and mZF= 3x + 24.
What is the value of x?

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]

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].

24 ounce can / 8 ounces = 3 pizzas per can.

3 pizzas per can x 4 cans = 12 total  pizzas.

The answer is D.

Answer: D.) 12 pizza

Answer:

x = - 6, x = [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Assuming you require the solution to the equation

Given

2x² + 9x - 18 = 0

To factor the quadratic

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × - 18 = - 36 and sum = + 9

The factors are + 12 and - 3

Use these factors to split the x- term

2x² + 12x - 3x - 18 = 0 ( factor the first/second and third/fourth terms )

2x(x + 6) - 3(x + 6) = 0 ← factor out (x + 6) from each term

(x + 6)(2x - 3) = 0

Equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = [tex]\frac{3}{2}[/tex]

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]

Hello

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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:

sqrt(3)

Step-by-step explanation:

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

Solve for r

Answer:

D. WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.

Step-by-step explanation:

edge2021

The statement which best explains that the quadrilateral WXYZ can be a parallelogram is D. WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.

Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.

Opposite sides are parallel, and the opposite sides and opposite angles are equal.

In order to find this, we have to know the properties of the diagonals of a parallelogram.

Here given a parallelogram WXYZ.

The diagonals of a parallelogram bisect each other.

That is, if WXYZ is a parallelogram,

WC = CY and ZC = CX

But it is unknown that these are equal.

Hence the correct option is D.

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Answer:

-2

Step-by-step explanation:

f(x)= 5x-12

f(2)= 5(2)-12 = 10 - 12 = -2

Answer: -2

Step-by-step explanation: f(x)= 5x-12

f(2)= 5(2)-12 = 10 - 12 = -2

thats how i do it

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

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:

25747 is all you mentioned except irrational

Step-by-step explanation:

Whole numbers are counting numbers or also 0. If you can count to it and you can but no one wants to in this cases because that's a big number, then it is a whole number for sure. So 25747 is a whole number which means it is also an integer and also a rational number.  It is definitely not irrational.

25,747 is a positive whole number and thus is classified as an integer. It is also a rational number, but it is not an irrational number. Therefore, 25,747 is both a whole number and a rational number.

The number 25,747 is an example of a positive whole number and can also be classified as an integer. In mathematics, an integer is defined as any whole number without a fractional or decimal component, which can be positive, negative, or zero. Since 25,747 is a whole number greater than zero, it is specifically a positive integer.

A rational number is a number that can be expressed as the ratio of two integers, such as fractions or any number that has a finite or repeating decimal expansion. Clearly, 25,747 qualifies as a rational number since it can be written as 25,747/1.

An irrational number, on the other hand, cannot be expressed as a simple fraction - examples include π (pi) and √2 (the square root of 2), both of which have non-repeating, non-terminating decimal expansions. Therefore, 25,747 is not irrational.

In conclusion, 25,747 is a positive whole number, which means it is an integer and a rational number, but not an irrational number.

Answer:

Both a and b

Step-by-step explanation:

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:

The greatest number of the two is 5

Step-by-step explanation:

Ratios = 5 : 4

Total ratio = 5 + 4 = 9

Sum = 99

To determine the greatest number, solve

5/9 × 99

495/9 = 55

and the second no.

4/9 × 99

396/9 = 44

So the numbers are 55 : 44

The greatest number is 5. ( which is 55)

The greater of the two numbers is 55.

Given:

Ratio of the two numbers is 5:4.

Let, the common factor between two numbers be x.

∴ The two numbers are 5x and 4x.

According to the given condition:

⇒ 5x + 4x = 99

⇒ 9x = 99

⇒ x = 11

The two numbers are:

5x = 5 × 11

5x = 55

4x = 4 × 11

4x = 44

Therefore, 55 is the greater of the two numbers.

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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: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:

The standard form of the equation for this line can be:

l: 2x + 5y = -15.

Step-by-step explanation:

Start by finding the slope of this line.

For a line that goes through the two points [tex](x_0, y_0)[/tex] and [tex](x_1, y_1)[/tex],

[tex]\displaystyle \text{Slope} = \frac{y_{1} - y_{0}}{x_{1} - x_{0}}[/tex].

For this line,

[tex]\displaystyle \text{Slope} = \frac{(-1) - (-7)}{(-5) - 10} = -\frac{2}{5}[/tex].

Find the slope-point form of this line's equation using

The slope-point form of the equation of a line

should be [tex]l:\; y - y_{0} = m(x - x_0)[/tex].

For this line,

The equation in slope-point form will be

[tex]\displaystyle l:\; y - (-1) = -\frac{2}{5}(x - (-5))[/tex].

The standard form of the equation of a line in a cartesian plane is

[tex]l: \; ax + by = c[/tex]

where

[tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are integers. [tex]a \ge 0[/tex].

Multiply both sides of the slope-point form equation of this line by [tex]5[/tex]:

[tex]l:\; 5 y + 5 = -2x -10[/tex].

Add [tex](2x-5)[/tex] to both sides of the equation:

[tex]l: \; 2x + 5y = -15[/tex].

Therefore, the equation of this line in standard form is [tex]l: \; 2x + 5y = -15[/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:

they are the same line! hence there are infinite number of solutions

Step-by-step explanation:

y-10=3x (rearrange)

we get:  y = 3x + 10 ----------- eq. (1)

2y=6x+20 (divide both sides by 2)

we get:  y = 3x + 10 ----------- eq. (2)

We can see that (1) = (2).

i.e they are the same line! hence there are infinite number of solutions.

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

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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)

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:

{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:

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: 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:

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.

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:

The zeroes of the function are -3 , -1 , 1 ⇒ 3rd answer

Step-by-step explanation:

* Lets explain the meaning of the zeroes of the function

- The zeroes of the function are the values of x when f(x) = 0

- That means the coordinates of the intersection points between the

 curve and the x-axis

- Ex: If the graph of f(x) intersects the x-axis at points (p , 0) , (q , 0) ,

 (r , 0) then the zeroes of f(x) are p , q , r

* Lets solve the problem

- The graph starts at the bottom left

- It continues up through the x-axis at negative three

- That means it intersects the x-axis at point (-3 , 0)

∴ The first zero of the function is -3

- It goes to a maximum around y equals three

- It goes back down through the x-axis at negative one

- That means it intersects the x-axis again at point (-1 , 0)

∴ The second zero of the function is -1

- It goes to a minimum around y equals negative one

- It goes back up through the x-axis at one

- That means it intersects the x-axis again at point (1 , 0)

∴ The third zero of the function is 1

∴ The function has three zeroes -3 , -1 , 1

* The zeroes of the function are -3 , -1 , 1

Answer:

The correct option is 1, 4 and 6.

Step-by-step explanation:

The given two-way table is

                          WIN          LOSS          TOTAL

HOME GAMES     6               10               16

AWAY GAMES      3                8                11

TOTAL                   9              18               27

Total number of home games won by team is 6 and total number of away games won by team is 3. It means the team is twice as likely to win a home game as they are an away game.

The correct option is 1.

Total number of home games = 16.

Home game won by team is

[tex]\frac{6}{16}=\frac{3}{8}[/tex]

Option 2 is incorrect.

Total games = 27

Total games won by the team = 9

Total part of games won by team is

[tex]\frac{9}{27}=\frac{1}{3}[/tex]

Option 3 is incorrect.

The team played a total of 27 games.

Option 4 is correct.

The team won a total of 9 games.

Option 5 is incorrect.

Total home games loose by team = 10

Total away games loose by team = 8

The team lost more home games than away games.

Option 6 is correct.

Therefore the correct option is 1, 4 and 6.

Answer:

4 and 6

Step-by-step explanation:

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