IF MDE = 50, FIND D.

length of rectangle =9cm

width of rectangle = b

perimeter of rectangle =24cm

perimeter of rectangle =2(l+b)

24=2(9+b)

9+b=12

b=3cm

Using the perimeter formula for a rectangle, the width of the rectangle is calculated to be 3 centimeters.

To find the width of the rectangle when the perimeter is 24 centimeters and the length is 9 centimeters, we can use the formula for the perimeter of a rectangle: P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. From the given information:

P = 24 cm

l = 9 cm

We can set up the equation as follows:

24 = 2(9) + 2w

24 = 18 + 2w

2w = 24 - 18

2w = 6

We then divide both sides by 2 to solve for w:

w = 6 / 2

w = 3 cm

Thus, the width of the rectangle is 3 centimeters.

Answer:

[ -9(x^2 - 16)] / [4(x^2 + 5x + 6)]  = 0

Step-by-step explanation:

Ok this will be a rational function with denominator (x + 2)(x + 3)  - to give the vertical asymptotes.

The numerator  will be a(x + 4)(x - 4)  to give the x-intercepts . The a is some constant.

As the y intercept is  (0,6) we have:

6 =   a(0-4)(0+4) /  (0+2)(0+3)

6 =  -16a / 6

-16a = 36

a = - 36/16 = -9/4.

So our equation is -9(x^2 - 16)/ 4(x^2 + 5x + 6)  = 0.

Answer:

4 students are working on fractions

Step-by-step explanation:

Answer:

a) 110,880

b) 8.61x10^37

c) 7.18x10^19

Step-by-step explanation:

To find the amount of options, use the following combination equation.

n!/[r! * (n - r)]

In this equation, n represents the amount of possible options and r represents the amount being chosen at a time. We can now calculate out the answer for each possibility.

a) In this case, n would equal 12 and r would equal 6.

n!/[r! * (n - r)]

12!/[6! * (12 - 6)]

479001600/[720*6]

479001600/4320

110,880

b) In this case, n would equal 36 and r would equal 6

n!/[r! * (n - r)]

36!/[6! * (12 - 6)]

3.72x10^41/[720*6]

3.72x10^41/4320

8.61x10^37

c) For this one, n would equal 24 and r would equal 6. We would also then have to divide the answer at the end by 2.

n!/[r! * (n - r)]

12!/[6! * (12 - 6)]

6.20x10^23/[720*6]

6.20x10^23/4320

1.44x10^20 ÷ 2 = 7.18x10^19

This question deals with calculating combinations of croissants chosen under various conditions, which exemplifies the use of combinations with repetition in mathematics. Solutions depend heavily on the specifics of each part, many of which require customized approaches to account for constraints like minimum selections or caps on certain items.

This question involves calculating different combinations of items from a set, which in this context are types of croissants being chosen in various quantities and conditions. Solving these problems requires understanding permutations and combinations, specifically combinations with repetition, as the order in which the croissants are selected does not matter but repeats are allowed.

We utilize the formula for combinations with repetition: C(n+r-1, r), where n is the number of types of items (in this case, croissants) and r is the number of items to choose.

For example, in part a) choosing a dozen croissants from 6 types would involve finding the combination with repetition of these 6 types over 12 selections.

However, specific formulas need to be applied to cater to the unique conditions stated in parts c) through f). Each of these parts imposes different constraints (e.g., minimum numbers of specific items, caps on how many of certain items can be chosen) that complicate the calculation and often require a piecewise approach or the inclusion/exclusion principle to accurately count the number of valid combinations.

Due to the complex and varied nature of each part of this question, and without specific formulas for parts c) through f), a general overview is provided instead of detailed solutions.

Each condition requires a tailored approach that involves breaking down the problem into smaller, manageable parts, and sometimes subtracting the cases that do not meet the given criteria from the total possible combinations.

Answer:

30 degrees

Step-by-step explanation:

Answer:  Measure of ∠BAM is 30°.

Step-by-step explanation:

As given in the question, points A and B split the circle with center O into two arcs in the attached figure below. Major of the minor arc is 150°. And, the point M splits the major arc in the ratio 2 : 5.

We are to find the measure of ∠BAM.

Since the measure of minor arc AB is 150°, so the measure of major arc AB will be

360° - 150° = 210°.

Also, point M divides the major arc AB in the ratio 2 : 5, so we have

[tex]arc~BM:arc~MA=2:5.[/tex]

Therefore, the measure of ∠BOM is given by

[tex]m\angle BOM=\dfrac{2}{2+5}\times210^\circ=\dfrac{2}{7}\times 210^\circ=60^\circ.[/tex]

We know that

the measure of the angle subtended at the center by an arc is equal to twice the measure of the angle subtended at the circumference by the same arc.

That is, on arc BC, we get

[tex]m\angle BOM=2\times m\angleBAM\\\\\Rightarrow m\angle BAM=\dfrac{m\angle BOM}{2}\\\\\\\Rightarrow m\angle BAM=\dfrac{60^\circ}{2}\\\\\Rightarrow m\angle BAM=30^\circ.[/tex]

Thus, the measure of ∠BAM is 30°.

where are the options??

Answer:

380.13

Step-by-step explanation:

11^2 x pi = 380.13

Answer:

coordinates

Step-by-step explanation:

The coordinates are the pairs of number giving a location of a point on the coordinate grid (example (4, 12) or (-3, 4) explain where the location point should be)

The pair of numbers giving the location of a point are called its coordinates.

Two perpendicular number lines define a Cartesian plane, which is named after Rene Descartes, a mathematician who codified its use in mathematics: the horizontal x-axis and the vertical y-axis, respectively. Any point in the plane can be described by an ordered pair of numbers using these axes.

In every direction, the Cartesian plane has an infinite length.

Given

A pair of numbers that use the horizontal and vertical distances between the two reference axes to describe a point's position on a coordinate plane. typically represented by the x- and y-values in the form (x, y).

Coordinates are the numbers who gives the location of point.

Hence, the pairs are called coordinates.

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Answer:

D

Step-by-step explanation:

-1  0  1  2  3  4  5  6  7

9 units.  distance is always positive.  

ans. D

Answer:

A) p = 2x - 4  for the expression. B) Your team scored 44 points.

Step-by-step explanation:

Let P represent the points your team made.

Since the question says "Your basketball team scored 4 fewer than twice as many points as the other team." this is how I came up with the expression.

p = 2x - 4 ( our points = 2 times more then the other teams points minus 4.

Using this expression and the given information that the other team made 24 points, I solved B.

44 = 2(24) - 4.

The expression for given statement can be found by system equation. We can create the system equation as per the statement.

(a) The expression for the number points your team scored is [tex]P=2x-4[/tex].

(b) Your team score 44 points.

Given:

Other team score [tex]x[/tex].

Let the [tex]P[/tex] is points scored by your team.

As per the statement, your basketball team scored 4 fewer than twice as many points, [tex]x[/tex] as the other team.

Convert the above statement in form of expression.

[tex]P=2x-4[/tex]

Thus, the expression for the number points your team scored is [tex]P=2x-4[/tex].

Substitute 24 for [tex]x[/tex] in above expression.

[tex]P=2\times 24-4\\P=44[/tex]

Thus, your team score 44 points.

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Answer:

56.1 in^2

Step-by-step explanation:

When given sides "a" and "b" and the angle α between them, the applicable formula for the area of the triangle is ...

A = (1/2)ab·sin(α)

Substituting the given values, we find the area to be ...

A = (1/2)(14.2 in)(8 in)sin(99°) ≈ 56.1 in^2

Answer:

56.1

Step-by-step explanation:

Diagram

Let's look at the diagram for a moment.

The 8 in line has been extended.

The dashed line is the height associated with the 8 inch line

The dashed line and the 8 inch line's extension meets at right angles.

Discussion

Normally you would take the 8 inch line and the height and divide their product by 2. You don't have the height. So you have to somehow get an expression for it.

The 81o angle is the supplement of the 99o angle. If you take the sine of both of them the sines are equal.

h = sin(81) * 14.2 because

sin(81) = opposite / hypotenuse.

opposite = hypotenuse * sin(81)

opposite = height = hypotenuse* sin(81)

height = 14.2 * sin(81)

Now we can find the area

Area

Area = height * base

base = 8

height = 14.2 * sin(81)

Area = 1/2 * 8 * 14.2 * sin(81)

Area = 56.1

61/3 - 42/3 = 19/3 feet

Hey there!

He turned 180° degrees so he is going back to his house (to probably get his wallet)

Hope this helps you!

God bless ❤️

xXxGolferGirlxXx

Answer:

1 3/16

Step-by-step explanation:

5/16 + (7/8= 14/16)

14/16 + 5/16= 19/16

16/16 = 1

3 LEFT OVER

1 3/16

Answer:

He caught 1 3/16 pounds of fish.

Minimum weight = 13/16 pounds.

Step-by-step explanation:

So far he caught 5/16 + 7/8

= 5/16 + 14/16 = 19/16

= 1 3/16 pounds.

Minimum wight of the third fish = 2 - 1 3/16

=  32/16 - 19/16

= 13/16 pounds.

Answer:

No

Step-by-step explanation:

No because (1,2) falls on the line, and the line is a dotted line, which means that any point on the line is not a solution to the inequality.

Answer:

  6.3  (x, y) = (3, 1)

  6.4  (x, y) = (-4, 2)

Step-by-step explanation:

An augmented matrix in this context is an array of the coefficients in the equation. For example, the equation x -2y = 3 can be represented by the row of numbers 1 -2 3. When writing the matrix by hand, we usually just separate the elements in a row using blank space. Some calculators require a comma or other character between matrix elements. The entire array is enclosed in square brackets.

An augmented matrix may have a vertical line separating the square matrix of coefficients from the rightmost column of constants.

Many graphing calculators have functions available for entering and solving linear equations in this form.

__

6.3 The augmented matrix is ...

[tex]\left[\begin{array}{cc|c}2&3&9\\1&-4&-1\end{array}\right][/tex]

This array can be used to solve the system of equations using "row operations." The idea is that any row can be multiplied by any number, and any row can be added to any other row (multiplied by some number or not). So, the same techniques used to solve a system by elimination can be used here.

We can, for example, subtract twice the second row from the first. Then we have ...

[tex]\left[\begin{array}{cc|c}2-2(1)&3-2(-4)&9-2(-1)\\1&-4&-1\end{array}\right]\\\\\left[\begin{array}{cc|c}0&11&11\\1&-4&-1\end{array}\right] \quad\text{simplified}\\\\\left[\begin{array}{cc|c}0&1&1\\1&-4&-1\end{array}\right] \quad\text{first row divided by 11}\\\\\left[\begin{array}{cc|c}0&1&1\\1+4(0)&-4+4(1)&-1+4(1)\end{array}\right] \quad\text{4 times row 1 added to row 2}\\\\\left[\begin{array}{cc|c}0&1&1\\1&0&3\end{array}\right] \quad\text{simplified}[/tex]

When we turn this last matrix back into equations, we get ...

  0x +y = 1

  1x + 0y = 3

That is, the solution is (x, y) = (3, 1).

__

6.4 The augmented matrix is ...

[tex]\left[\begin{array}{cc|c}4&5&-6\\3&2&-8\end{array}\right][/tex]

Let's start the solution of this one by dividing the first row by 4.

[tex]\left[\begin{array}{ccc}1&\frac{5}{4}&-\frac{3}{2}\\3&2&-8\end{array}\right] \\\\\left[\begin{array}{ccc}1&\frac{5}{4}&-\frac{3}{2}\\3-3(1)&2-3(\frac{5}{4})&-8-3(-\frac{3}{2})\end{array}\right] \quad\text{row 2 minus 3 times row 1}\\\\\left[\begin{array}{ccc}1&\frac{5}{4}&-\frac{3}{2}\\0&-\frac{7}{4}&-\frac{7}{2}\end{array}\right] \quad\text{simplify}\\\\\left[\begin{array}{ccc}1&\frac{5}{4}&-\frac{3}{2}\\0&1&2\end{array}\right] \quad\text{multiply row 2 by -4/7}[/tex]

We can eliminate the y-term in the first row by subtracting 5/4 times the second row. This will put the matrix in the form that shows us the solution directly.

[tex]\left[\begin{array}{ccc}1-\frac{5}{4}(0)&\frac{5}{4}-\frac{5}{4}(1)&-\frac{3}{2}-\frac{5}{4}(2)\\0&1&2\end{array}\right] \quad\text{row 1 minus 5/4 times row 2}\\\\\left[\begin{array}{ccc}1&0&-4\\0&1&2\end{array}\right][/tex]

This tells us ...

  x = -4

  y = 2

So the solution is (x, y) = (-4, 2).

An augmented matrix organizes the coefficients of a system of linear equations. After setting up the matrix with the coefficients from the equations, methods like Gaussian elimination or Gauss-Jordan elimination can be used to solve the matrix and consequently, solve the system.

An augmented matrix is a compact way of keeping track of the coefficients in a system of linear equations. Here's how to form it and solve the system:

Gaussian elimination involves using elementary row operations to manipulate the matrix to a form where the solution is easier to find, often called reduced row echelon form. For the Gauss-Jordan method, the main idea is to get zeros below (and above when possible) a leading 1, and make sure that leading 1 is the only nonzero entry in its column.

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Answer:

126.

Step-by-step explanation:

This is the number of combinations of 4 cards  from 9 cards:

= 9C4

= 9! / 4! 5!.

A quick way of calculating this is  

9*8*7*6

----------- =   9*2*7   =    126 combinations.

4*3*2*1

There are 126 different 4-card combinations possible when selecting 4 cards from a shuffled stack of 9 different cards.

To find out how many different 4-card combinations are possible from a stack of 9 different cards when 4 cards are turned face up, we need to use combinatorial mathematics. The formula needed here is the combination formula, which for selecting r items from a set of n items is given by C(n, r) = n! / (r!(n-r)!), where '!' denotes factorial.

Substituting the given values, we get C(9, 4) = 9! / (4!(9-4)!) = 9! / (4!5!) = (9×8×7×6) / (4×3×2×1) = 3024 / 24 = 126. So, there are 126 different combinations of 4 cards that can be turned face up from a shuffled stack of 9 different cards.

Answer:

60%

Step-by-step explanation:

It went up 12 dollars, and you need to find how much 12 is of 20 as a percent. You do 12/20 times 5/5 and get 60/100, so 60% markup

Answer:

Step-by-step explanation:

The Answer Well -12$

20 - 32 = -12

okay so you multiply .15 by 120 which is 18. then you multiply .10 by 120 which is 12. so you do 120 subtracted by 12 and 18 which the answer is 90

Final answer:

The shoes will cost $91.80 after both discounts have been applied.

Explanation:

To find the cost of the shoes, we need to apply two discounts.

First, we calculate the discount amount of 15% off $120 by multiplying $120 by 0.15, which gives us $18.

Then, we subtract this discount from the original price:

$120 - $18 = $102.

Next, we calculate the additional discount of 10% off $102 by multiplying $102 by 0.10, which gives us $10.20.

We subtract this discount from the discounted price:

$102 - $10.20 = $91.80.

So, the shoes will cost $91.80 after both discounts have been applied.

well, 1/6 of 3/4 is simply their product, thus

[tex]\bf \cfrac{3}{4}\cdot \cfrac{1}{6}\implies \cfrac{3}{6}\cdot \cfrac{1}{4}\implies \cfrac{1}{2}\cdot \cfrac{1}{4}\implies \cfrac{1}{8}[/tex]

Answer:

The area of the circle is [tex]530.93\ units^{2}[/tex]

Step-by-step explanation:

we know that

The area of a circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=26/2=13\ units[/tex] ----> the radius is half the diameter

assume

[tex]\pi=3.1416[/tex]

substitute

[tex]A=(3.1416)(13)^{2}=530.93\ units^{2}[/tex]

Answer:

Dependant Variable

Step-by-step explanation:

Answer:

Step-by-step explanation:

The response variable is the dependent variable.

Answer:

Its the First choice.

Step-by-step explanation:

(3 m-2 n)^-3  / 6m n^-2

= (1/27) m^6 n^-3 / 6 m n^-2

= m^5 n ^-3 / 27*6  n^-2

= m^5 n^2 / 162 n^3

= m^4 / 162 n  (answer).

The correct answer is option (A) m5 /162n

Let us solve step by step

See the attached figure for solution

Answer:

Volume of sphere = 4/3×22/7×radius×radius

4/3×22/7×8×8=268.19

Therefore the answer is approximately 268 cubic inches.

Hope this answer helps you.

Here's the right way:

[tex]\dfrac{x}{\frac 3 5} = \dfrac{20}{12}[/tex]

[tex]x = \dfrac{20}{12} \cdot \dfrac{3}{5} = 1[/tex]

Here's the way they want you to do it:

[tex]\dfrac{x}{\frac 3 5} = \dfrac{20}{12}[/tex]

[tex]12 x = 20 \times \dfrac{3}{5} = 12 \textrm{ FIRST BOX}[/tex]

[tex]x = 12/12 = 1 \textrm{ SECOND BOX}[/tex]

Answer: 12×=12

×=1, this the correct answer :3

QUESTION 1

The given logarithm is

[tex]\log_7\sqrt{a^3b^9}[/tex]

We rewrite to obtain;

[tex]\log_7(a^3b^9)^{\frac{1}{2}}[/tex]

Use the power rule of logarithm ; [tex]\log_a(m^n)=n\log_a(m)[/tex]

[tex]\frac{1}{2}\log_7(a^3b^9)[/tex]

Use the product rule; [tex]\log_a(mn)=\log_a(m)+\log_a(n)[/tex]

[tex]\frac{1}{2}[\log_7(a^3)+\log_7(b^9)][/tex]

Use the power rule of logarithms again;

[tex]\frac{1}{2}[3\log_7(a)+9\log_7(b)][/tex]

Or

[tex]\frac{3}{2}\log_7(a)+\frac{9}{2}\log_7(b)][/tex]

QUESTION 2

Given;

[tex]\log_6(\frac{x^5}{y^9})[/tex]

Apply the quotient rule of logarithm; [tex]\log_a(m)-\log_a(n)=\log_a(\frac{m}{n} )[/tex]

[tex]\log_6(\frac{x^5}{y^9})=\log_6(x^5)-\log_6(y^9)[/tex]

Apply the power rule to get;

[tex]\log_6(\frac{x^5}{y^9})=5\log_6(x)-9\log_6(y)[/tex]

QUESTION 3

Given;

[tex]\log_8(x^3y^7)[/tex]

Use the product rule to get;

[tex]=\log_8(x^3)+\log_8(y^7)[/tex]

Use the power rule now;

[tex]=3\log_8(x)+7\log_8(y)[/tex]

1952 + 384 = 2336 years

The answer is 15 units

- Ap3x