Write the phrase "the product of a number v and 15" as an expression.
An expression for the phrase is

The length of side KL is approximately 4.8 cm.

To solve this problem, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all sides of the triangle. In other words:

a/sin(A) = b/sin(B) = c/sin(C)

Where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the angles opposite those sides.

Using the Law of Sines, we can set up the following proportion:

l/sin(L) = m/sin(M)

Where l is the length of side KL, L is the measure of angle KLM (which is 72 degrees), m is the length of side LM, and M is the measure of angle KML (which we can find by subtracting L from 180 degrees).

M = 180 - L

= 180 - 72

= 108 degrees

Now we can substitute the given values into the proportion and solve for l:

l/sin(72) = 5.9/sin(108)

l = sin(72) * (5.9/sin(108))

≈ 4.8 cm (rounded to the nearest 10th of a centimeter)

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Answer:

8x +36

Step-by-step explanation:

Answer:

8x +36

Step-by-step explanation:

You got robbed

Given statement solution is :- Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

3.1 Activity: Procedural and Conceptual Understanding in Action

Content Area: Fractions

Problem: Comparing Fractions

Objective: Students will demonstrate both procedural and conceptual understanding of comparing fractions.

Activity Steps:

Begin by introducing the concept of fractions and reviewing the basic procedures for comparing fractions (e.g., finding a common denominator, cross-multiplying).

Provide students with a set of fraction comparison problems (e.g., 2/3 vs. 3/4, 5/8 vs. 7/12) and ask them to solve the problems using the traditional procedural approach.

After students have solved the problems procedurally, engage them in a group discussion to explore the underlying concepts and relationships between fractions. Ask questions such as:

What does it mean for one fraction to be greater than or less than another?

Can you explain why we need a common denominator when comparing fractions?

How can you visually represent and compare fractions to better understand their relative sizes?

Introduce visual aids, such as fraction bars or manipulatives, to help students visualize the fractions and compare them conceptually. Encourage students to reason and explain their thinking.

Have students revisit the fraction comparison problems and solve them again, this time using the conceptual understanding gained from the group discussion and visual aids.

Compare the students' procedural solutions with their conceptual solutions, and discuss the similarities and differences.

Conclude the activity by emphasizing the importance of both procedural and conceptual understanding in solving fraction comparison problems effectively.

By incorporating both procedural and conceptual approaches, this activity allows students to develop a deeper understanding of comparing fractions. The procedural approach provides them with the necessary steps to solve problems efficiently, while the conceptual approach helps them grasp the underlying principles and relationships involved in fraction comparison.

3.2 Example: Conceptual Knowledge vs. Procedural Knowledge

Conceptual knowledge refers to the understanding of underlying concepts, principles, and relationships within a domain, whereas procedural knowledge focuses on knowing the specific steps or procedures to perform a task without necessarily understanding the underlying concepts.

Example: Division of Fractions

Conceptual Knowledge: Understanding the concept of division as the inverse operation of multiplication, and recognizing that dividing fractions is equivalent to multiplying by the reciprocal of the divisor. This understanding allows for generalization and application of division concepts to various fractions.

Procedural Knowledge: Following the specific steps to divide fractions, such as "invert the divisor and multiply" or "keep-change-flip" method. This knowledge involves applying the procedure without necessarily grasping the underlying concept or reasoning behind it.

In this example, Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

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The values of the complex expressions are ✓(x - iy) = a - ib and x² + y² =  (a + ib)²(a - ib)²

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

✓(x + iy) = a + ib

Changing the signs, we have

✓(x - iy) = a - ib

Multiply both expressions

This gives

✓(x + iy) * ✓(x - iy) =  (a + ib)(a - ib)

Square both sides

So, we have

(x + iy) * (x - iy) =  (a + ib)²(a - ib)²

This gives

x² + y² =  (a + ib)²(a - ib)²

Hence, the values of ✓(x - iy) is a - ib and x² + y² is  (a + ib)²(a - ib)²

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Answer:

C.

First, you square the x because it is inside the parentheses. Then, you multiply the -6 by 2, to get your exponent of -12 for the y.

Answer:

\( \huge \boxed{ \boxed{ \mathbb{C)} {x}^{2} {y}^{ - 12} }}\)

Step-by-step explanation:

\( step - 1 : define\)

\( {(xy}^{ - 6} ) ^{2} \)

Evaluando la función dada, veremos que la dosis para el niño debe ser 640 mg.

La funcion que debemos utilizar es:

d = 0.08*A*D

Donde, A es la edad del niño, en este caso: A = 8

D es la dosis correspondiente para un adulto, D = 1,000 mg

Reemplazando eso obtenemos:

d = 0.08*8*1,000mg = 640mg

Así, podemos concluir que al niño se le debe recetar una dosis de 640 mg.

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Answer: So, the sales tax on the item is $49.

Step-by-step explanation:

The sales tax rate is already given as 14%. It is stated that the item costs $350 before tax, and the sales tax rate is 14%. Therefore, the sales tax amount can be calculated by multiplying the cost of the item by the tax rate:

Sales tax amount = $350 * 14% = $350 * 0.14 = $49

So, the sales tax on the item is $49.

Answer:

1. x1=15.75.

2. 24/48=0.5

3. 24/25=0.96

Step-by-step explanation:

1. 15.75/18=0.875

2. you multiply 48 times 0.5 to find 24.

3. multiply 0.96 with 25 to get 24.

On solving the providewd question we can say that, public static double solve(double a, double b, double c, boolean flag )

A quadratic equation is a quadratic polynomial in one variable that looks like this: x = ax2 + bx + c. a 0. This polynomial has at least one solution since it is a second-order polynomial, according to the Fundamental Theorem of Algebra. The answer can actually work or be difficult.

public static double solve(double a, double b, double c, boolean flag)

{     double d = Math.sqrt(b*b - 4*a*c);     if(flag)

{         return (-b + d) / (2*a);     }

else {         return (-b - d) / (2*a);     } }

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Answer: y + 7x = -6

Step-by-step explanation:

Standard form: Ax + By = c, where a, b, and c are constants.

Distribute

y - 8 = -7x - 14

Add 8 and 7x to both sides:

y + 7x = -6

Hope it helps :)

The standard form of the equation is y = -7x-14

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given an equation, y-8 = -7(x+2)

We know that standard form of an equation of a line is y = mx+c

Converting into standard form,

y-8 = -7(x+2)

y-8 = -7x-14

y = -7x-14+8

y = -7x-6

Hence, The standard form of the equation is y = -7x-14

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Answer:

it's A

after multiplying you get the same answer

The given expression is equivalent to 2(x-3)(x-4) which is the correct answer that would be an option (B).

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The quadratic function is defined as a function containing the highest power of a variable is two.

The given expression as

⇒ 2x²-14x+24

Factor out common term 2 in the expression

⇒ 2(x² - 7x + 12)

⇒ 2(x² - 4x -3x + 12)

⇒ 2[x(x - 4) -3(x - 4)]

Factor out the common terms in the expression

⇒ 2(x-3)(x-4)

Hence, the given expression is equivalent to 2(x-3)(x-4).

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Answer:

SHEESH this ez 12x20 = 240cm

Step-by-step explanation:

If the radius of Jasmine's swimming pool is 4.2 meter, then it's circumference is 26.4 meters.

The "Circumference" of a circle is known as the distance around the boundary of a circle.

The circumference of a circle is given by the formula : 2 × π × radius,

where π (pi) is a mathematical constant approximately equal to 3.14,

We are given that Jasmine's swimming pool has a radius of 4.2 meters.
So, we can calculate the circumference of the pool as :

⇒ Circumference = 2 × 3.14 × 4.2 meters,

⇒ Circumference ≈ 26.4 meters,

Therefore, the circumference of Jasmine's swimming pool is 26.4 meters.

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Answer:

(3.9, - 9.3 )

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

Z (- 3.9, - 9.3 ) → Z' (3.9, - 9.3 )

The coordinates of the point after reflection across y-axis is Z' ( 3.9 , -9.3 )

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given data ,

Let the coordinates of the point be represented as Z ( -3.9 , -9.3 )

Now , let the coordinates of the reflected point be Z'

where the axis of reflection is y-axis

So , when you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Therefore , Z' = Z' ( 3.9 , -9.3 )

Hence , the reflected point is Z' ( 3.9 , -9.3 )

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The net cost of $2008 less 10/5/20 is $1305.20.

The net cost of $8220 less 30/5/10 is $4521

From the question, the net cost of

$2008 less 10/5/20:

10% of $2008 = $200.80

5% of $2008 = $100.40

20% of  $2008 = $401.60

Net discount = $200.80 + $100.40 +  $401.60 = $702.80

Net cost = $2008 - $702.80 = $1305.20

Therefore, the net cost of $2008 less 10/5/20 is $1305.20

$8220 less 30/5/10:

30% of $8220 = $2466

5% of $8220 = $411

10% of $8220 = $822

Net discount = $2466 + $411 + $822 = $3699

Net cost = $8220 - $3699 = $4521

Therefore, the net cost of $8220 less 30/5/10 is $4521.

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Answer:

$2.20

Step-by-step explanation:

Original price (before discount and before tax): $5

Discount is 60%.

Amount of discount is: 60% of $5 = 0.6 × $5 = $3

Price after 60% discount: $5 - $3 = $2

Tax is 10%.

Amount of tax is: 10% of $2 = 0.1 × $2 = $0.20

Final price = price after discount + tax = $2.00 + $0.20 = $2.20

A percentage is a way to describe a part of a whole. The final price of the candy, including the discount and a 10% sales tax is $2.2.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given that the cost of the candy is $5 and a 60% discount is given on the candy. Therefore, the price of the candy after the discount will be,

Discounted price = Price - 60% of price

                             = $5 - 0.60($5)

                             = $5 - $3

                             = $2

Now, on the price of the candy 10% sales tax will be added. Therefore, the Price of the candy after adding Tax will be,

Taxed price = Discounted price + 10% of discounted price

                    = $2 + 0.10($2)

                    = $2 + $0.2

                    = $2.02

Hence, the final price of the candy, including the discount and a 10% sales tax is $2.2.

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Armed force and other for Henderson high school is greater than

Johnson High School.

The mode for each school is college.

Options F and G are the correct answer.

We have,

The number of students in Henderson High School.

Work = 96

College = 114

Armed forced = 48

Other = 42

The number of students in Johnson High School.

Work = 30

College = 40

Armed forced = 15

Other = 15

From the information,

The number of students in Work for Henderson High School is greater than Johnson High School.

Now,

Henderson High School:

Armed force and other = 48 + 42 = 90

Mode = college

Johnson High School.

Armed force and other = 15 + 15 = 30

Mode = college

Thus,

Armed force and other for Henderson high school is greater than

Johnson High School.

The mode for each school is college.

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Answer:

increases by 30

Step-by-step explanation: its right

The vertex form of the quadratic equations in standard form are, respectively:

Case 9: y = 2 · (x + 2)² - 12

Case 10: y = - (1 / 2) · (x + 3 / 4)² + 33 / 32

Case 11: y = 3 · (x - 4 / 3)² - 16 / 3

Case 12: y = - 3 · (x - 3)²

Case 13: y = (x - 4)² + 3

Case 14: y = (x - 1)² - 7

Case 15: y = (x + 3 / 2)² - 9 / 4

Case 16: 2 · (x + 1 / 4)² - 1 / 8

Case 17: y = 2 · (x - 3)² - 7

Case 18: y = - 2 · (x + 1)² + 10

In this problem we find ten cases of quadratic equation in standard form, whose vertex form can be found by a combination of algebra properties known as completing the square. Completing the square consists in simplifying a part of the quadratic equation into a power of a binomial.

The two forms are introduced below:

Standard form

y = a · x² + b · x + c

Where a, b, c are real coefficients.

Vertex form

y - k = C · (x - h)²

Where:

Now we proceed to determine the vertex form of each quadratic equation:

Case 9

y = 2 · x² + 4 · x - 4

y = 2 · (x² + 2 · x - 2)

y = 2 · (x² + 2 · x + 4) - 12

y = 2 · (x + 2)² - 12

Case 10

y = - (1 / 2) · x² - 3 · x + 3

y = - (1 / 2) · [x² + (3 / 2) · x - 3 / 2]

y = - (1 / 2) · [x² + (3 / 2) · x + 9 / 16] + (1 / 2) · (33 / 16)

y = - (1 / 2) · (x + 3 / 4)² + 33 / 32

Case 11

y = 3 · x² - 8 · x

y = 3 · [x² - (8 / 3) · x]

y = 3 · [x² - (8 / 3) · x + 16 / 9] - 3 · (16 / 9)

y = 3 · (x - 4 / 3)² - 16 / 3

Case 12

y = - 3 · x² + 18 · x - 27

y = - 3 · (x² - 6 · x + 9)

y = - 3 · (x - 3)²

Case 13

y = x² - 8 · x + 19

y = (x² - 8 · x + 16) + 3

y = (x - 4)² + 3

Case 14

y = x² - 2 · x - 6

y = (x² - 2 · x + 1) - 7

y = (x - 1)² - 7

Case 15

y = x² + 3 · x

y = (x² + 3 · x + 9 / 4) - 9 / 4

y = (x + 3 / 2)² - 9 / 4

Case 16

y = 2 · x² + x

y = 2 · [x² + (1 / 2) · x]

y = 2 · [x² + (1 / 2) · x + 1 / 16] - 2 · (1 / 16)

y = 2 · (x + 1 / 4)² - 1 / 8

Case 17

y = 2 · x² - 12 · x + 11

y = 2 · (x² - 6 · x + 9) - 2 · (7 / 2)

y = 2 · (x - 3)² - 7

Case 18

y = - 2 · x² - 4 · x + 8

y = - 2 · (x² + 2 · x - 4)

y = - 2 · (x² + 2 · x + 1) + 2 · 5

y = - 2 · (x + 1)² + 10

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Answer:

d = 5 is a solution to the equation 13 - d = 8

Step-by-step explanation:

We have to solve 13 - d = 8

Now,

13 - d = 8,

We add d on both sides,

13 - d + d = 8 + d

13 = 8 + d

we subtract 8 from both sides,

13 - 8 = 8 - 8 + d

5 = d

d = 5

Hence the answer is 5

To simplify the expression \(\displaystyle\sf 5x-3(-5y+6x)+4y\), we can follow the order of operations, which involves simplifying the expressions within parentheses, applying the distributive property, and combining like terms.

Using \(\displaystyle\sf \) tags for formatting, the expression becomes:

\(\displaystyle\sf 5x-3(-5y+6x)+4y\)

First, we simplify the expression within the parentheses:

\(\displaystyle\sf 5x-3(-5y+6x)+4y\)

\(\displaystyle\sf 5x+15y-18x+4y\)

Next, we can combine the like terms:

\(\displaystyle\sf 5x-18x+15y+4y\)

\(\displaystyle\sf -13x+19y\)

Therefore, the simplified expression is \(\displaystyle\sf -13x+19y\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

I, III and IV

Step-by-step explanation:

Required

Determine equivalent expressions to \(6x^2 - 13x - 28\)

To do this, we simplify each of the given options.

\(I.\ 6x2+8x-21x-28\)

Simplify like terms

\(6x2+8x-21x-28\)

\(= 6x2-13x-28\)

This is equivalent to the given expression

\(II.\ 2x(3x + 4) + 7x(3x - 4)\)

Open Bracket

\(2x(3x + 4) + 7x(3x - 4)\)

\(2x*3x + 2x*4 + 7x*3x - 7x*4\)

\(6x^2 + 8x - 21x^2 - 28x\)

Collect Like Terms

\(6x^2 - 21x^2 + 8x - 28x\)

\(-15x^2 - 20x\)

This is not equivalent to the given expression

\(III.\ 2x(3x+4)-7(3x+4)\)

Open Bracket

\(2x(3x+4)-7(3x+4)\)

\(2x*3x + 2x*4 - 7*3x - 7*4\)

\(6x^2 + 8x - 21x - 28\)

Simplify Like Terms

\(6x^2 -13x - 28\)

This is equivalent to the given expression

\(IV.\ (3x + 4)(2x-7)\)

Open Brackets

\(3x * 2x - 3x * 7 + 4*2x-4*7\)

\(6x^2 - 21x+ 8x-21\)

Simplify like terms

\(6x^2 -13x-21\)

This is equivalent to the given expression

Hence: I, III and IV are equivalent to the given expression

\(\qquad \qquad \stackrel{indirect~\hfill }{\textit{inverse proportional variation}} \\\\ \textit{\underline{y} varies inversely with \underline{x} and \underline{z}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{xz}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill\\\\\)

\(y = \cfrac{k}{xz}\qquad \textit{we also know} \begin{cases} x=3\\ y=24\\ z=15 \end{cases}\implies 24=\cfrac{k}{(3)(15)} \\\\\\ 24(3)(15)=k\implies 1080=k~\hspace{10em}\boxed{y=\cfrac{1080}{xz}}\)

Answer:

-25x-45y, because if we have got + and -, so we will write minus.

Answer:

1 and 4 has same pairs of solution.

Step-by-step explanation:

Solutions for the given equations are:

\begin{gathered}1. (x+6)(x - 6) = 0\\(x+6) = 0, (x-6) = 0\\x = -6, x = 6\\\\2. (x + 6)(x + 6) = 0\\(x+6) = 0, (x+6) = 0\\x = -6, x = -6\\\\3. (x - 6)(x - 6) = 0\\(x-6) = 0, (x-6) = 0\\x = 6, x = 6\\\\4. (2x + 12)(2x - 12) = 0\\(2x+12) = 0, (2x-12) = 0\\x = -6, x = 6\\\\5. (2x - 12)(x - 12) = 0\\(2x-12) = 0, (x-12) = 0\\x = 6, x = 12\\\\6. (x+12)(x - 12) = 0\\(x+12) = 0, (x-12) = 0\\x = -12, x = 12\\\\7. (x +12)(x-6) = 0\\(x+12) = 0, (x-6) = 0\\x = -12, x = 6\end{gathered}

1.(x+6)(x−6)=0

(x+6)=0,(x−6)=0

x=−6,x=6

2.(x+6)(x+6)=0

(x+6)=0,(x+6)=0

x=−6,x=−6

3.(x−6)(x−6)=0

(x−6)=0,(x−6)=0

x=6,x=6

4.(2x+12)(2x−12)=0

(2x+12)=0,(2x−12)=0

x=−6,x=6

5.(2x−12)(x−12)=0

(2x−12)=0,(x−12)=0

x=6,x=12

6.(x+12)(x−12)=0

(x+12)=0,(x−12)=0

x=−12,x=12

7.(x+12)(x−6)=0

(x+12)=0,(x−6)=0

x=−12,x=6

(x+6)(x - 6) = 0 and (2x + 12)(2x - 12) = 0 have same pair of solutions.

Step-by-step explanation:

there you go :)

Answer:

99% of all balls she hits with this club will lie between the values in the interval.

Step-by-step explanation:

Edge  2022

Answer:

x = 18

y = 6

Step-by-step explanation:

In triangle UTR, measures of all angles are equal (60°). (given)

Therefore, it is an equilateral triangle.

So, it's sides will also be equal.

In triangle TRS, m angle T = m angle S

So, RT = RS = 11 (sides opposite to the equal angles are equal)

In triangle URT,

UT = RT (sides of equilateral triangle)

x - 7 = 11

x = 11 + 7

x = 18

In triangle TRS,

m angle T = m angle S = 5y°

m angle R = 180° - 60° = 120° (Linear pair angles)

5y° + 5y° + 120° = 180°

10y° = 180° - 120°

10y° = 60°

y = 60/10

y = 6

By performing the division, the jogging track is 0.45 miles long.

Division is a mathematical operation that involves the splitting of a quantity into equal parts or groups.

The problem asks us to convert a length of 792 yards to miles. To do this, we need to use a conversion factor to relate yards to miles. We know that there are 1760 yards in a mile, so we can use this relationship to convert the length in yards to miles.

To convert yards to miles, we divide the length in yards by the number of yards in a mile. This is because we want to cancel out the units of yards and be left with the corresponding number of miles.

So, 792 yards / 1760 yards/mile gives us the length of the jogging track in miles. We can simplify this expression by performing the division to get the result of 0.45 miles. Therefore, the jogging track is 0.45 miles long.

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