Mrs. Carroll’s garden has a total of 448 flowers arranged with 28 flowers in each row. How many rows are there in Mrs. Carroll’s garden?



19


12


16


10

The following area tagged expression or sentence as;

1. Expression

2. Expression

3. Sentence

4. Sentence

5. Expression

Algebraic expressions are described as expressions that are composed of variables, terms, coefficients, factors and constants.

These expressions are also identified with various mathematical or arithmetic operations, such as;

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Answer:

1) When r = 2, M = 20.

2) When M  = 540, r = 6.

Step-by-step explanation:

M is a directly proportional to r cubed

This means that the equation for M has the following format:

\(M = ar^3\)

In which a is a multiplier.

When r=4 M=160.

We use this to find a. So

\(M = ar^3\)

\(160 = a(4^3)\)

\(64a = 160\)

\(a = \frac{160}{64}\)

\(a = 2.5\)

So

\(M = 2.5r^3\)

1) work out the value of M when r=2

\(M = 2.5*2^3 = 2.5*8 = 20\)

When r = 2, M = 20.

2) work out the value of r when M=540

\(M = 2.5r^3\)

\(540 = 2.5r^3\)

\(r^3 = \frac{540}{2.5}\)

\(r^3 = 216\)

\(r = \sqrt[3]{216}\)

\(r = 6\)

When M  = 540, r = 6.

(a) Since u = cos(x) gives du = -sin(x) dx, we have

∫ sin(x) cos(x) dx = - ∫ (-sin(x)) cos(x) dx

= - ∫ cos(x) d(cos(x))

= - ∫ u du

= - 1/2 u² + C

= -1/2 cos²(x) + C

(b) Now u = sin(x) gives du = cos(x) dx, so

∫ sin(x) cos(x) dx = ∫ sin(x) d(sin(x))

= ∫ u du

= 1/2 u² + C

= 1/2 sin²(x) + C

(c) Since sin(2x) = 2 sin(x) cos(x), we have

∫ sin(x) cos(x) dx = 1/2 ∫ sin(2x) dx

Substitute u = 2x, so that du = 2 dx, and

∫ sin(x) cos(x) dx = 1/2 ∫ sin(2x) dx

= 1/4 ∫ 2 sin(2x) dx

= 1/4 ∫ sin(u) du

= -1/4 cos(u) + C

= -1/4 cos(2x) + C

(d) Integrate by parts, setting

u = sin(x)          ==>  du = cos(x) dx

dv = cos(x) dx  ==>  v = sin(x)

Then

∫ sin(x) cos(x) dx = sin²(x) - ∫ sin(x) cos(x) dx

2 ∫ sin(x) cos(x) dx = sin²(x) + C

∫ sin(x) cos(x) dx = 1/2 sin²(x) + C

The solutions in (b) and (d) are identical, but all 4 are equivalent, and this follows from the identities,

sin²(x) + cos²(x) = 1

cos(2x) = cos²(x) - sin²(x)

Given:

Soccer 8

Baseball/Softball 3

Volleyball 5

Track and field 4

Let's solve for the following:

• 1. What is the sample size:

The sample size can be said to be the total number of responses a survey receives.

Therefore, we have:

Sample size = 8 + 3 + 5 + 4 = 20

The sample size is 20

• 2. What is the probability that a student will prefer soccer?

To find the probability a student will prefer soccer, apply the formula:

Thus, we have:

Therefore, the probability a student will prefer soccer is 0.4

• 3. What is the probability that a student will prefer volleyball?

Apply the formula:

Hence, we have:

Therefore, the probability a student will prefer volleyball is 0.25

4. There are 550 students in the school. Predict how many students at the school prefer track and field.

To find the number of students who prefer track and fied, apply the formula:

Thus, we have:

Therefore, if there are 550 students, 110 students will prefer track and field.

ANSWER:

• 1.) 20

• 2.) 0.4

• 3.) 0.25

• 4.) 110

We can see that both the height and base ratios are 1/3, which means that Triangle D is 1/3 the size of Triangle C. Therefore, the scale factor applied to Triangle C to create Triangle D is 1/3.

It has three angles which always add up to 180 degrees.

3. We know that the ratio of the height to the base of a right triangle is constant for similar triangles. Therefore, we can find the scale factor by dividing the height of Triangle D by the height of Triangle C, and dividing the base of Triangle D by the base of Triangle C.

The height ratio is:  1.5 in / 4.5 in = 1/3

The base ratio is:  2 in / 6 in = 1/3

4. If the scale of 1:6 was applied to Figure B, it means that every linear dimension (length, width, height) of Figure L is 1/6th the corresponding dimension of Figure B.

Since area is a two-dimensional measure, we can use the scale factor squared to find the ratio of the areas. Therefore, the ratio of the areas of Figure L to Figure B is:   (1/6)² = 1/36

This means that Figure L has 1/36th the area of Figure B.

If Figure B has an area of 6 square inches, then the area of Figure L is:

Area of Figure L = (1/36) × Area of Figure B

Area of Figure L = (1/36) × 6 square inches

Area of Figure L = 0.1667 square inches (rounded to four decimal places)

Therefore, the area of Figure L is approximately 0.1667 square inches.

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Answer:

Step-by-step explanation:

Here is the completed table of function values for f(x) = -x² + 6:

x -2 -1 0 1 2

f(x) -2 5 6 5 2

To graph the function, you can plot the points from the table on a coordinate plane and connect them with a smooth curve. The graph of f(x) = -x² + 6 is a downward-facing parabola that opens up to the point (0, 6), as shown below:

          7

          |

          |

          |

          |

          |

          |

          |

          |

  -----0------

          |

          |

          |

          |

          |

          |

          |

          |

         -2

The vertex of the parabola is located at the point (0, 6), and the axis of symmetry is the vertical line x = 0.

Answer:

y = 0.5 - x/2

Step-by-step explanation:

The -1 power means the inverse function of f(x). This means that you will write the function in terms of x and y, replaces x's with y's and vice versa, and then write the new function in terms of x.

f(x) = 1 - 2x

y = 1 - 2x

Switch variable places.

x = 1 - 2y

Solve for y.

2y = 1 - x

y = 0.5 - x/2

The number of points to be removed from the graph is 2

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

The graph

From the graph, we can see that

2 points have the same y coordinates

Another 2 points have the same y coordinates

For it to be a function, one of the 2 points must be removed each

So, we have the number of points to be removed from the graph is 2

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Answer:

Step-by-step explanation:

4(4) = -7(-3) - 5

16 = 21 - 5

16 = 16

answer is D

Answer: (-3.4)

Step-by-step explanation: took test 6.02

Foundations wrap up Systems of Equations

Answer:

Step-by-step explanation:

Set each equation equal to y, then graph each equation.

y = -x² + x + 6      (parabola)

y = 2x + 8            (line)

Notice that the system has NO SOLUTION because the parabola and the line never intersect.

Answer:

B

Step-by-step explanation:

i just did the question on edge

The value of the required missing angle is;

m<JKM = 35°

We know from geometry that the sum of angles in a triangle sums up to 180 degrees.

Now, we are trying told that in the given Triangle that the angle m<J = 55 degrees.

We also see that the angle <KMJ is equal to 90 degrees becasue it is a right angle.

Thus to find the angle m<JKM, we can write the name expression as;

m<JKM = 180 - (90 + 55)

m<JKM = 35°

Thus that's the value of the required missing angle.

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Answer: 19!!

Step-by-step explanation:

Step-by-step explanation:

Given that

From the figure :

m angle 1 = 48°

Let m angle 2 = x°

And it is clearly m angle 1 and m angle 2 = 90°

90° = m angle 1 + m angle 2

Substitute the above values in equation then

⇛90° = 48°+x°

Shift the constant 50 from RHS to LHS, changing it's sign.

⇛ 90°-48° = x°

⇛42° = x°

⇛ x° = 42°

Therefore, m angle 2 = 42°

Answer: Hence, the value of m angle 2 is 42°

Additional comment:

The sum of the two angles is 90° then they are Complementary angles. The Complementary angle of x° is (90-x)°

Please let me know if you have any other questions.

Answer:

X = 22

Step-by-step explanation:

This is a right triangle which means the angles add up to 90° total. So if 1 side is 15 and another side is 53 then 15 + 53 = 68 and 90 - 68 = 22 so X = 22 which is the missing side.

Answer:

360 cm cubed

Step-by-step explanation:

Use the volume formula.

V=whl

V=12 x 6 x 5

V=360

By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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The values 8, 15 and 17 is a Pythagorean triple and therefore a right angle triangle.

A Pythagorean triple is a set of three positive integers, a, b, and c, such that a^2 + b^2 = c^2, which represents the sides of a right-angled triangle, where c is the hypotenuse.

In this problem, we can we can check if the values are for a right angle triangle.

Assuming this is a right angle triangle which obeys Pythagoras theorem, the longest side will be the hypothenuse.

c² = a² + b²

17² = 15² + 8²

289 = 225 + 64

289 = 289

From the calculation above, the values of is a Pythagorean triple.

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Answer:

\(n = \frac{53}{79}\)

Step-by-step explanation:

79 : 53

divide by 79 on both sides

\(1 : \frac{53}{79}\)

\(n = \frac{53}{79}\)

Answer: 1 : 1.49

Step-by-step explanation:

the starting Ratio was= 79 : 53

now its 1 : ?

The first number was divided by 79 so we divide the other number by 79.

1 : 53 is now

1 : 1.49 (This is rounded to the 2d.p since the question asked for it)

Step-by-step explanation:

Hello! In order to get the best explication for your question, here's the link to a useful website:

https://geometryhelp.net/area-parallelogram-diagonals/

I believe, it's better for you to understand how to use the Heron's formula in other contexts so as to understand deeper into details how to apply it

Hope it helped!

Answer:36.7

Step-by-step explanation:

(h,k) are the coordinates of the vertex.

Use the given point (x,y) and the vertex (h,k) in the equation above to find the value of a:

Point: (-3 ,1) x = -3 y=1

Vertex: (-4 , -2) h= -4 k=-2

Use the vertex and a to write the equation:

Answer:

False

Step-by-step explanation:

Answer:

0.5 km

Step-by-step explanation:

0.5 kilometers is by far the largest measurement here.

Complete question is;

In 1986, a family member invested $100 each month into a savings account with an interest rate of 0.25% (that didn't change). In 2016, you decided you needed to use that saved up money for a big purchase, so you cash the savings account out.

How much money should be in the account using the FV formula?

Answer:

FV = $107.78

Step-by-step explanation:

We are given;

Present value; PV = 100

Interest rate; r = 0.25% = 0.0025

We are told the PV was in 1986 and In 2016 you decided you needed to use that saved up money .

This is a period of 30 years.

Thus, the number of compounding periods is n = 30

Formula for FV is;

FV = PV(1 + r)ⁿ

FV = 100(1 + 0.0025)^(30)

FV = $107.78

Then it will take approximately 6.3 hours for the culture to grow to 80,000 bacteria

The given formula for the number of bacteria in a culture after t hours is:y = 5000(3)^tWe are required to find the number of hours it will take the culture to grow to 80,000.

This can be done by setting y equal to 80,000 and then solving for t.5000(3)^t = 80,000

Divide both sides by 5000:3^t = 16Now, we need to solve for t by taking the logarithm of both sides.

However, it is easier to use logarithmic properties to simplify the equation first.3^t = 2^4

Raise both sides to the power of (1/log3):log3(3^t) = log3(2^4)t = 4/log3(2)Using a calculator, log3(2) ≈ 0.631, so:t ≈ 4/0.631 ≈ 6.3.

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The water that should be added to 14mL of 9% alcohol solution to reduce the concentration to 7% is 4ml.

Here; In this problem we have a concentration problem, represented by the volume of the solvent divided by the volume of the entire solution. The initial and final concentrations of the solutions are presented in the following formulas;

Given;

14mL of 9% alcohol solution.

Initial concentration;

9/ 100 = x / 14

x = 63/50

Final concentration;

7 / 100 = x / (14 + y)

(14 + y)=x*100/7

y=18-14

y=4

Therefore, water must be added to reduce the concentration will be 4ml.

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For this case we have a quadratic equation of the form:

ax² + bx + c = 0

Rewriting the equation we have:

3k² -4k - 7 = 0

So we have to:

a = 3

b = -4

c = -7

The solutions will come from:

k = -b±√b²-4(a)(c)/2(a)

Thus, the value of "b" is -4

Answer:

b = -4

Answer: -4

Step-by-step explanation:

i took the quiz its -4