how do I create equal groups that represent the fact 28÷4=7?

Answer:

7

Step-by-step explanation:

She found that 7 red m&ms were in the bag.

Domain of the function represented by the graph of a quadratic function y = \(x^2\) – 4 with a minimum value at the point (0,-4) is all real numbers.

The correct answer is option D.

To determine the domain of the quadratic function y = \(x^2\) - 4, we need to consider the x-values for which the function is defined. Since a quadratic function is defined for all real numbers, the domain of this function is "all real numbers."

Let's analyze the given function and its graph to understand why the domain is "all real numbers."

The function y =  \(x^2\) - 4 represents a parabola that opens upward, which means it extends infinitely in both positive and negative x-directions. The vertex of the parabola is at the point (0, -4), indicating that the minimum value of the function occurs at x = 0.

Since there are no restrictions or limitations on the x-values for which the function is defined, the domain is unrestricted and encompasses all real numbers. In other words, the function can be evaluated and calculated for any real value of x, whether it is a negative number, zero, or a positive number.

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Answer:

31.4

Step-by-step explanation:

10 x 3.14 ( pi) =31.4in2

Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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Answer:

what

Step-by-step explanation:

where is the question its not showing

Answer:

3) x = 14

4) x = 5

Step-by-step explanation:

First, let's separate the triangle into two separate triangles.

Let's start with number 3. Here, we have one triangle with the sides of 25, 15, and the parallel line. But, we also have another triangle that has sides of 25+(x+6), 27, and the other parallel line.

So, since the two lines in the triangle are parallel, we can say that the angles are equal of both triangles are equal

Since the angles are equal, that means that the triangles are similar.

The triangles being similar means that they don't exactly have the same size or area, but they're similar in proportion. One triangle just looks like the other but smaller.

Since they have the same proportions, that means that there must be some sort of scale to compare the triangles. That is known as the scale factor.

We can find the scale factor by comparing two corresponding sides of the two triangles we made. The side that is 15 long corresponds with the side that is 27 long.

If we want the scale factor, we see how much 15 needs to multiply by to be 27

let s be the scale factor

15s = 27

s = 9/5 or 1.8

That means that the larger triangle's sides are 9/5 times larger.

Knowing this, we can look at the other side. The side that is 25 long corresponds with the side that is 25+(x+6)

Since we know that larger is side is 9/5 times larger than the short side, we can write it like this

(9/5)(25) = 25+(x+6)

45 = x+31

14 = x

Now, let's move on to number 4, where we pretty much do the same thing.

The side that is 30 long corresponds with the side that is 50 long

30s = 50

s = 5/3

The side that is 9x-3 long corresponds with the side that is 9x-3+28 long

(5/3)(9x-3) = 9x-3+28

15x-5 = 9x+25

6x = 30

x = 5

Answer:

3m 95cm

Step-by-step explanation:

its... simple math? i added 2 and 1; and 30 and 65?

Answer:

8 cubic units

Step-by-step explanation:

Let he vertices of the parallelepiped be A = (4,2,4), B= (6,3,8), C = (6,1,10) and D =  (0,6,3)

The edges of the parallelepiped are

AB = (6,3,8)  - (4,2,4) = (2,1,4)

AC = (6,1,10) - (4,2,4) = (2,-1,6)

AD = (0,6,3) - (4,2,4) = (-4,4,-1)

Therefore the volume of the parallelopiped is = |[AB,AC,AD]|

=  \($ \begin{vmatrix}\ 2\ \ \ 1\ \ \ \ 4\ \\2\ -1\ \ \ 6 \\-4\ \ \ 4\ -1 \end{vmatrix}$\)

= |2(1-24)+1(-2+24)+4(8-4)|

= |2(-23) + 1(22) + 4(4)|

= |8|

=8 cubic units

So, in 1 minute Emma can read (1/2) page of the book.

The remaining book will be read in (13/30) days.

As Emma can read 4 pages of a book in 8 minutes.

So, from here, we can rewrite it as,

In 8 minutes, Emma can read 4 pages of a book.

So, in 1 minute she can read (4/8)= (1/2) page of the book.

Olivia reads (2/5) of her book on Monday on Tuesday she reads 1/6 of the book,

Let us assume that the total book is 1

So, the sum of books read on Monday and Tuesday will be \((\frac{2}{5}+\frac{1}{6}) = \frac{12+5}{30}=\frac{17}{30}\)

So, the remaining book will be read in \(1-\frac{17}{30}=\frac{30-17}{30}=\frac{13}{30}\)

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Answer:

1/3a

Step-by-step explanation:

\( \frac{(a - 3)}{15a} \times \frac{5}{(a - 3)} = \frac{5}{15a} = \frac{1}{3a} \)

The meaning of the point with an x-coordinate of 2 is in 2 seconds, the commuter travels 120 feet.

An equation is an expression that shows the relationship between two or more numbers and variables.

Independent variables represent function inputs that do not depend on other values, while dependent variables represent function outputs that depends on other values.

From the graph, the x coordinate 2, have a y coordinate of 120. Hence:

The meaning of the point with an x-coordinate of 2 is in 2 seconds, the commuter travels 120 feet.

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The table that represents a linear equation is the first one, and the line can be:

y = -4x - 1

A general linear function can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Now, notice that if we evaluate the line in x + 1, we will get:

y = a*(x + 1) + b

y = a*x + a + b

So, for an increase of one unit on the variable x, we have a constant increase in the y value.

Now, if you look at the first table, you can see that for each increase of 1 unit on the value of x, the value of y decreases by 4.

So that is the table that can represent a linear function.

And the line is:

y = -4x - 1

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Answer:

wwwwwwwwwwwww

Step-by-step explanation:

The approximate area of the shaded region of the circle is 191 metres squared.

The radius of the circle below is given as 9 metres. The approximate area of the shaded region of the circle can be found as follows:

area of the shaded region = area of the circle - area of the sector uncoloured

Therefore,

area of the circle = πr²

where

Therefore,

area of the circle = π × 9²

area of the circle = 81π m²

Hence,

area of the sector uncoloured = ∅ / 360 × πr²

where

Therefore,

area of the sector uncoloured = 90 / 360 × π × 9²

area of the sector uncoloured = 1 / 4 × π × 81

area of the sector uncoloured = 81 / 4 π

Hence,

area of the shaded region = 81π  - 20.25π

area of the shaded region = 60.75π

area of the shaded region = 190.755

area of the shaded region = 191 m²

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Answer: I think ts -1/2

Step-by-step explanation: x+3x=-3x-2+3x

4x=-2

4x/4=-2/4

x= -1/2

Answer:

Parent function:

f(x) = √x

Add a number to the value of the function, such as k:

f(x) = (√x) + k

If k is positive, the function moves up. If k is negative, the function moves down.

The perimeter of the figure described in the question is 42.84cm

The figure is defined by a half circle is joined to an equilateral triangle with side lengths of 12 units.

So the perimeter of the figure will be equal to half of the circumference of the triangle plus the length of the two exposed sides of the triangle.

The diameter of the circle will also be 12 units, remember that the circumference of a circle of diameter D is:

C = 3.14*D

In this case, the circumference of half circle is:

C = 3.14*D/2

Replacing the value of the diameter:

C = 3.14*12cm/2 = 18.84cm

Adding the two sides of the triangle we get the perimeter.

P = 18.84cm + 2*12cm = 42.84cm

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The calculated period of the function is 12

From the question, we have the following parameters that can be used in our computation:

The graph

By definition, the period of the function is calculated as

Period = Difference between cycles or the length of one complete cycle

Using the above as a guide, we have the following:

Period = 13 - 1

Evaluate

Period = 12

Hence, the period of the function is 12

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Answer:

Step-by-step explanation:

From the question, a water glass can hold 2/9 of a litre of water, to know the number of glasses of water that can be filled with a 3-litres bottle, the following steps are crucial;

1 water of glass = 2/9 litre of water

x = 3 litre of water

cross multiplying;

2/9 * x = 3*1

2x/9 = 3

2x = 27

Dividing both sides by 2;

2x/2 = 27/2

x = 13 1/2

This means 13 1/2 glasses of water can be filled with a 3-litre bottle.

Answer:

  3. L(15055) is the number of pages ...

  4. true

Step-by-step explanation:

3. The problem tells you that L( ) is a function of the number of words. (That means the number in parentheses in L( ) is a word count.) The first two answer choices describe the function as being of a number of pages, so are incorrect. The last answer choice matches the description of the function.

__

4. Compound interest represents a growth function. Account values in later years will be more than values in earlier years. So ...

  D(2) < D(7) is TRUE

While the integral is doable in the given order of variables (factorize the denominator and expand into partial fractions), swapping the order make things easier.

\(\displaystyle \int_0^4 \int_{\sqrt x}^2 \frac{dy\,dx}{4+y^3} = \int_0^2 \int_0^{y^2} \frac{dx\,dy}{4+y^3} \\\\ ~~~~~~~~ = \int_0^2 \frac{y^2}{4+y^3} \, dy \\\\ ~~~~~~~~ = \frac13 \int_4^{12} \frac{du}u \\\\ ~~~~~~~~ = \frac13 (\ln(12) - \ln(4)) = \boxed{\frac{\ln(3)}3}\)

Answer:

1/2

Step-by-step explanation:

Area= 3/8

Width=3/4

Length=?

3/8=0.375

3/4x1/2=3/8 (0.375)

Answer:

100xy

Step-by-step explanation:

The height of the cylinder is 4x³y² unit.

The correct option is A.

A cylinder is a 3D solid form made up of two bases that are parallel and identical and are connected by a curving surface. These bases resemble spherical disks. The axis of the cylinder form is a line drawn through the center or connecting the centers of two circular bases.

Given:

A cylinder has a volume of 20x⁶y⁴ units cubed.

The base of the cylinder has an area of 5x³y² units squared.

And the volume of the cylinder V = Base area x height.

So, 20x⁶y⁴ = 5x³y² (height).

The height of the cylinder = 20x⁶y⁴/ 5x³y²

The height of the cylinder = 4x³y²

Therefore,  4x³y² is the height of the cylinder.

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The complete question is given in the attached image.

The statements supported by the data in the table are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

To determine which statements are supported by the data in the table, let's analyze the given information:

The mean number of cars sold in a month is the same at both dealerships.

To calculate the mean, we need to find the average number of cars sold each month at each dealership.

For Admiral Autos:

(4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13

For Countywide Cars:

(9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13

Since both dealerships have an average of 13 cars sold per month, the statement is supported.

The median number of cars sold in a month is the same at both dealerships.

To find the median, we arrange the numbers in ascending order and select the middle value.

For Admiral Autos: 4, 10, 15, 17, 19

Median = 15

For Countywide Cars: 9, 10, 14, 15, 17

Median = 14

Since the medians are different (15 for Admiral Autos and 14 for Countywide Cars), the statement is not supported.

The total number of cars sold is the same at both dealerships.

To find the total number of cars sold, we sum up the values for each dealership.

For Admiral Autos: 4 + 19 + 15 + 10 + 17 = 65

For Countywide Cars: 9 + 17 + 14 + 10 + 15 = 65

Since both dealerships sold a total of 65 cars, the statement is supported.

The range of the number of cars sold is the same for both dealerships.

The range is determined by subtracting the lowest value from the highest value.

For Admiral Autos: 19 - 4 = 15

For Countywide Cars: 17 - 9 = 8

Since the ranges are different (15 for Admiral Autos and 8 for Countywide Cars), the statement is not supported.

The data for Admiral Autos shows greater variability.

To determine the variability, we can look at the range or consider the differences between each data point and the mean.

As we saw earlier, the range for Admiral Autos is 15, while for Countywide Cars, it is 8. Additionally, the data points for Admiral Autos are more spread out, with larger differences from the mean compared to Countywide Cars. Therefore, the statement is supported.

Based on the analysis, the statements supported by the data are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

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Answer:

22

Step-by-step explanation:

2x+4+x-10=60

3x-6=60

3x=66

x=22

Answer:

\(\boxed{\bold{\huge{\boxed{Option \ 4: \ x = 22}}}}\)

Step-by-step explanation:

If AD is a ray inside angle ABC

Then

∠ABD + ∠DBC = ∠ABC

2x + 4 + x - 10 = 60

3x - 6 = 60

Adding 6 to both sides

3x = 60 + 6

3x = 66

Dividing both sides by 3

x = 22

Answer:

5, 6

Step-by-step explanation:

Answer:

Los números son:

6 y 5

Step-by-step explanation:

Planteamiento:

a * b = 30

a + b = 11

Desarrollo:

De la segunda ecuación del planteamiento:

a = 11-b    

Sustituyendo esta última ecuación en la primer ecuación del planteamiento:

(11-b)*b = 30

11*b + b*-b = 30

11b - b² - 30 = 0

-b² + 11b - 30 = 0

b = {-11±√((11²)-(4*-1*-30))} / (2*-1)

b = {-11±√(121-120)} /-2

b = {-11±√1} / -2

b = {-11±1} / -2

b₁ = {-11-1} / -2 = -12/-2 = 6

b₂ = {-11+1} / -2 = -10/-2 = 5

Comprobación:

6*5 = 30

6+5 = 11

Answer:

26) Let the first number be x.

Sum of three consecutive even numbers:

\(x+(x+2)+(x+4)=-84\)

\(x+x+2+x+4=-84\\\)

\(3x+6=-84\)

Subtract 6 from both sides:

\(3x+6-6=-84-6\)

\(3x=-90\)

Divide both sides by 3:

\(\frac{3x}{3}=\frac{-90}{3}\)

\(x=-30\)

To find the other two numbers, add 2 and 4 respectively:

\((-30+2=-28)(-30+4=-26)\)

27) Let the first number be x.

Sum of three consecutive odd integers:

\(x+(x+2)+(x+4)=141\)

\(3x+6=141\)

Subtract 6 from both sides:

\(3x+6-6=141-6\\3x=135\)

Divide both sides by 3:

\(\frac{3x}{3}=\frac{135}{3}\\x=45\)

To find the other two numbers, add 2 and 4 respectively:

\((45+2=47)(45+4=49)\)

28) Let the first number be x.

Sum of four consecutive integers:

\(x+(x+1)+(x+2)+(x+3)=54\)

\(4x+6=54\)

Subtract 6 from both sides:

\(4x+6-6=54-6\\4x=48\)

Divide both sides by 4:

\(\frac{4x}{4}=\frac{48}{4}\\x=12\)

To find the other three numbers, add 1, 2 and 3 respectively:

\((12+1=13)(12+2=14)(12+3=15)\)

29) Let the first number be x.

Sum of four consecutive integers:

\(x+(x+1)+(x+2)+(x+3)=-142\)

\(4x+6=-142\\\)

Subtract 6 from both sides:

\(4x+6-6=-142-6\)

\(4x=-148\)

Divide both sides by 4:

\(\frac{4x}{4}=\frac{-148}{4}\\x=-37\)

To find the other three numbers, add 1, 2 and 3 respectively:

\((-37+1=-36)(-37+2=-35)(-37+3=-34)\)

The total value of the furniture sold by Joyce last week is A = $ 6,733.33

Given data ,

Let's call the value of the furniture Joyce sold "x".

She receives 10% commission on the first $1,200 of sales, which is $120:

Commission on first $1,200 = 0.1 * 1200 = 120

The remaining sales that she earns commission on is the difference between the total value of the furniture sold and the first $1,200:

Remaining sales = x - 1200

She earns 15% commission on the remaining sales, which is 0.15 times the remaining sales:

Commission on remaining sales = 0.15 * (x - 1200)

Her total earnings from commission last week was $950. So we can write an equation:

Commission on first $1,200 + Commission on remaining sales = $950

Substituting the expressions we found for the two commissions, we get:

120 + 0.15(x - 1200) = 950

120 + 0.15x - 180 = 950

On simplifying the equation , we get

0.15x - 60 = 950

0.15x = 1010

x = 6,733.33

Hence , the value of the furniture Joyce sold last week was $6,733.33

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Answer: No, they are not equal

1 kilogram = 1000 grams

6 kilograms = 6*1000 = 6000 grams

so we see that 6 kilograms is larger than 600 grams

Put another way,

600 grams = 600/1000 = 0.6 kilograms