Clara found the product of 3 – 6y2 and y2 + 2. Her work is shown below.

(3 – 6y2)(y2 + 2) = 3(y2) + (–6y2)(2)

= 3y2 – 12y2

= –9y2

Is the student’s work correct?

No, she did not multiply –6y2 by 2 correctly.
No, she did not add 3y2 and –12y2 correctly.
No, she did not use the distributive property correctly.
Yes, she multiplied the binomials correctly.

Answer:

Darius needs [tex]26\frac{2}{3}[/tex] cups of bread cubes to make four batches of stuffing for a family reunion.

Step-by-step explanation:

Given:

bread cubes to make a batch of stuffing  =   6 2/3 cup

To Find:

Number of cups of bread cubes needed to make four batches of stuffing for a family reunion = ?

Solution:

According to the question, to make one batch of stuffing Darius needs [tex]6\frac{2}{3}[/tex] cups of bread cubes

So if he wants to make four batched, then the number of cups of bread cubes  will be four times  as needed for making one batch

Then

Number of cups of bread cubes needed to make four batches = 4 x  bread cubes needed to make a batch of stuffing

Number of cups of bread cubes needed to make four batches

=  [tex]4 \times 6\frac{2}{3}[/tex]

=>[tex]4 \times \frac{18+2}{3}[/tex]

=> [tex]4 \times \frac{20}{3}[/tex]

=>[tex]\frac{80}{3}[/tex]

=>[tex]26\frac{2}{3}[/tex]

Darius will need 80/3 cups of bread cubes to make four batches of stuffing for a family reunion.

To find out how many cups of bread cubes Darius will need to make four batches of stuffing for a family reunion, we need to multiply the amount of bread cubes used in one batch by the number of batches he wants to make. Darius uses 6 2/3 cups of bread cubes in one batch. So, to find the total amount of bread cubes needed for four batches, we can multiply 6 2/3 cups by 4.

First, we convert the mixed number into an improper fraction: 6 2/3 = (6 * 3 + 2)/3 = 20/3.

Next, multiply the improper fraction by 4: (20/3) * 4 = 80/3 cups.

Therefore, Darius will need 80/3 cups of bread cubes to make four batches of stuffing for a family reunion.

==============================================

Work Shown:

125 = 5*5*5 = (5)^3

x^12 = (x^4)*(x^4)*(x^4) = (x^4)^3

125x^12 = (5x^4)^3

[tex]\large \sqrt[3]{125x^{12}} = \left(125x^{12}\right)^{1/3}[/tex]

[tex]\large \sqrt[3]{125x^{12}} = \left((5x^4)^3\right)^{1/3}[/tex]

[tex]\large \sqrt[3]{125x^{12}} = (5x^4)^{3*(1/3)}[/tex]

[tex]\large \sqrt[3]{125x^{12}} = (5x^4)^{1}[/tex]

[tex]\large \sqrt[3]{125x^{12}} = \textbf{5x}^{\textbf{4}}[/tex]

Answer:

Step-by-step explanation:

[tex]125=5*5*5=5^{3}\\\\\ \sqrt[3]{125x^{12}}=\sqrt[3]{125*x^{4*3}}\\\\=\sqrt[3]{5^{3}*(x^{4})^{3}}=5*x^{4}=5x^{4}[/tex]

(1)   x = 12,   (2)   [tex]x=3\frac{1 }{2}[/tex]

Solution:

(1)     If the two triangles are similar and the angles of two triangles are congruent then the corresponding sides are in proportion.

⇒ [tex]\frac{25}{10}=\frac{30}{x}[/tex]

Do cross multiply.

⇒ [tex]25 \times x=30 \times 10[/tex]

Divide both sides of the equation by 25 to equal the expression.

⇒ [tex]x=\frac{30 \times 10}{25}[/tex]

⇒ x = 12

(2)   Side of triangle = [tex]4\frac{1}{3} =\frac{13}{3}[/tex]

If the two triangles are similar and the angles of two triangles are congruent then the corresponding sides are in proportion.

⇒ [tex]\frac{26}{\frac{13}{3} }=\frac{21}{x}[/tex]

Do cross multiply.

⇒ [tex]26 \times x=21 \times \frac{13}{3}[/tex]

⇒ [tex]26 \times x=7 \times 13[/tex]

Divide both sides of the equation by 26 to equal the expression.

⇒ [tex]x=\frac{7 \times 13}{26}[/tex]

⇒ [tex]x=\frac{7 }{2}[/tex]

⇒ [tex]x=3\frac{1 }{2}[/tex]

Will drank [tex]8\frac{1}{3}[/tex] grams of sugar.

Step-by-step explanation:

Given,

Amount of sugar in one bottle = [tex]3\frac{3}{9}=\frac{30}{9}\ grams[/tex]

Amount of bottles drank by Will = [tex]2+\frac{1}{2}=\frac{4+1}{2}=\frac{5}{2}\ bottles[/tex]

Total sugar drank by Will = Amount of sugar in one bottle * Amount of bottles drank by Will

Total sugar drank by Will = [tex]\frac{30}{9}*\frac{5}{2}[/tex]

Total sugar drank by Will = [tex]\frac{150}{18}=\frac{25}{3}[/tex]

Total sugar drank by Will = [tex]8\frac{1}{3}[/tex]

Will drank [tex]8\frac{1}{3}[/tex] grams of sugar.

Keywords: fraction, multiplication

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Answer:

w=9

Step-by-step explanation:

I hope this image is helpful to you.

.

.

The student's algebra problem is solved by gathering like terms, simplifying the equation, and then isolating 'w'. The solution to the equation is 'w = 9'.

The subject of this question is mathematics, specifically, the topic is algebra. The equation given is -4+w+17-2/3w=16. We need to solve this equation for 'w'.

To start, we should gather like terms. Therefore, -4 + 17 becomes 13, making our equation 13 + w - 2/3w = 16. We can also rearrange this to w - 2/3w instead, which results in 1/3w = 16 - 13, therefore, 1/3w = 3. To solve for w, we can multiply the both sides of the equation by 3, which leads to w = 3 * 3 or w = 9.

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Answer:

The dimensions of the rectangle are;

Width = 3 inches

Length = 9 inches

Step-by-step explanation:

Given;

We want to determine the dimensions of the rectangle;

Forming an equation, we get;

2 ( x + x + 6) = 24

4x + 12 = 24

With the equation we can solve for x

4x = 24 - 12

4x = 12

  x = 3

and (x + 6) = 9

Therefore;

Width = 3 inches

Length = 9 inches

The width of the rectangle is 3 inches and the length is 9 inches.

Let's assume that the width of the Rectangle dimensions is represented by 'w' inches.

Since the length is 6 inches more than the width, we can represent it as 'w + 6' inches.

The perimeter of a rectangle is the sum of all its sides.

In this case, the formula for the perimeter is 2(w + l), where w represents the width and l represents the length.

So, for this problem, we have the equation 2(w + w + 6) = 24.

Simplifying this equation, we get 4w + 12 = 24.

Solving for 'w', we find that the width is 3 inches.

Plugging this value back into the equation for the length, we find that the length is 9 inches.

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Answer:

Answer:

The relationship between the number of months after the first year and the amount remaining on the card is discrete

The independent variable is the

number of months after the first year

The dependent variable is the

amount remaining on the card.

There are 162 base ball cards

Solution:

Let "a" be the number of baseball training cards

Let "b" be the number of basket ball training cards

Trent has a collection of 198 baseball and basketball training cards

Therefore,

a + b = 198 -------- eqn 1

He has 4.5 times as many baseball cards as basketball cards

Number of baseball cards = 4.5(number of basketball cards)

a = 4.5b --------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 2 in eqn 1

4.5b + b = 198

5.5b = 198

b = 36

Substitute b = 36 in eqn 2

a = 4.5(36)

a = 162

Thus there are 162 base ball cards

Trent have 162 baseball cards in his collection.

Trent has a collection of 198 baseball and basketball training cards, with baseball cards being 4.5 times as many as basketball cards. To find out how many baseball cards Trent has, we can set up a system of equations.

Let x be the number of basketball cards.

Since the number of baseball cards is 4.5 times the number of basketball cards, the number of baseball cards is 4.5x.

The total number of cards is 198, so x + 4.5x = 198.

Solving this equation, we find x = 36. Therefore, the number of baseball cards Trent has is 4.5*36 = 162 baseball cards.

Answer:

see attached picture please

Answer:

If each grid square represents one block, then the number of box he walked will be 30 blocks.

Step-by-step explanation:

Tommy walks from his home to the mall and then walks to a movie theater.

His home is at (0,0), the mall is at (0,8) and the movie theater is at (7,8).

Now, distance from (0,0) to (0,8) is 8 units and the distance from (0,8) to (7,8) is 7 units.

So, total distance covered is (8 + 7) = 15 units.

After leaving the theater Tommy walks to the store before returning home.

The store is at (7,0).

Now, the distance from (7,8) to (7,0) is 8 units and the distance from (7,0) to (0,0) is 7 units.

So, total distance covered is (8 + 7) = 15 units.

If each grid square represents one block, then the number of the box he walked will be (15 + 15) = 30 blocks. (Answer)

Answer:

Step-by-step explanation:it is the second option. :)

Answer:

Top right = second choose

Step-by-step explanation:

Answer:

The length of the shadow the telephone booth is 12 ft.

Step-by-step explanation:

Given:

An adult elephant that is 10 ft tall casts a shadow that is 15 ft long.

The length of the telephone booth is 8 ft.

Now, to find the length of the shadow the telephone booth casts.

Let the length of the shadow the telephone booth be [tex]x.[/tex]

As given, an adult elephant that is 10 ft tall casts a shadow that is 15 ft long.

So, 10 ft is equivalent to 15 ft.

Thus, 8 ft is equivalent to [tex]x.[/tex]

Now, to get the length of the shadow of the booth we get cross multiplication method:

[tex]\frac{10}{15} =\frac{8}{x}[/tex]

By cross multiplying we get:

[tex]10x=120[/tex]

Dividing both sides by 10 we get:

[tex]x=12.[/tex]

Therefore, the length of the shadow the telephone booth is 12 ft.

Answer:

Square

Got it correct on my test just now

Answer:

The correct answer is that Zack used 2 7/8 gallons to water his garden on the fifth week.

Step-by-step explanation:

Let's find out the pattern Zack is using to water his garden, this way:

First week =  1 3/8  gallons of water

Second week = 1 3/4 gallons of water = 1 3/8 + 3/8 = 1 6/8 = 1 3/4

Third week = 2 1/8 gallons of water = 1 3/4 + 3/8 = 1 6/8 + 3/8 = 2 1/8

The constant of adding every week is 3/8 gallons, therefore,

Fourth week = 2 1/8 + 3/8 = 2 4/8 = 2 1/2 gallons of water

Fifth week = 2 1/2 + 3/8 = 2 4/8 + 3/8 = 2 7/8 gallons of water

The correct answer is that Zack used 2 7/8 gallons to water his garden on the fifth week.

Following the pattern of increasing water usage by 3/8 gallons each week, Zack will use 2 7/8 gallons of water in the fifth week.

Zack watered his garden with increasing amounts of water over the first three weeks. Since there is a pattern, we can deduce the amount of water he will use in the fifth week by identifying the pattern and then continuing it.

Observing the pattern, we see that Zack is increasing the amount of water by 3/8 gallons each week. The progression in gallons is:

Continuing this pattern:

Therefore, Zack will use 2 7/8 gallons of water on the fifth week.

Answer:

1 1/6

Step-by-step explanation:

because it takes more to get to 12 than 6

11/6 is bigger because if you convert both into decimal form

11/6=1.83

14/12=1.16

Answer:

The special quadrilateral formed by connecting the midpoints of the sides of the original quadrilateral is :  a rhombus

Step-by-step explanation:

Look at the photo below for the figure

:)

Yolanda's was 25 years old when they were married.

Step-by-step explanation:

Let,

Age of Xavier = x

Age of Yolanda = x + 4

Combined age = 126

According to given statement;

Xavier's age + Yolanda's age = 126

[tex]x+(x+4)=126\\x+x+4=126\\2x=126-4\\2x=122\\[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{122}{2}\\x=61[/tex]

Yolanda's age = x+4 = 61+4 = 65

Age when married = 65 - 40 = 25

Yolanda's was 25 years old when they were married.

Keywords: word problems, addition

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Answer:3√(p/q)3

Step-by-step explanation: Find the cube root .

The law used to simplify the expression [tex]( (p/q)^3 \)[/tex] is the "Power of a Quotient" rule.

The correct option is (b).

The "Power of a Quotient" rule states that when a fraction is raised to a power, we can raise both the numerator and denominator to that power individually. Mathematically, it is represented as:

[tex]\[ \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} \][/tex]

Applied to the expression [tex]\( (p/q)^3 \)[/tex], we raise both[tex]\( p \) and \( q \)[/tex] to the power of 3:

[tex]\[ \left(\frac{p}{q}\right)^3 = \frac{p^3}{q^3} \][/tex]

This simplification allows us to express the original expression in terms of powers of the numerator and denominator separately. In other words, the exponent 3 is distributed to both [tex]\( p \) and \( q \), resulting in \( p^3 \)[/tex]in the numerator and [tex]\( q^3 \)[/tex] in the denominator.

Using this rule, we can handle expressions involving powers of fractions efficiently, breaking them down into simpler terms that are easier to work with or evaluate. It's particularly useful when dealing with algebraic expressions or equations where fractions with powers are involved, providing a systematic approach to simplification.

complete question given below:

Which law would you use to simplify the expression

[tex](p\q)^3[/tex]?

a.power of a power

b.power of a quotient

c.quotient of powers

d.power of a product

Answer:

- 2

Step-by-step explanation:

I think this right!! Hope it helps!!

The complete set of ordered pairs for the relation y = 2(x + 11), where x belongs to the set (-2, -1, 0, 1, 2), is {(-2, 18), (-1, 20), (0, 22), (1, 24), (2, 26)}.

The given equation is y = 2(x + 11), where x takes values from the set (-2, -1, 0, 1, 2). To find the corresponding y-values for each x-value, we substitute the given x-values into the equation and calculate the y-values.

For x = -2:

y = 2(-2 + 11) = 2 * 9 = 18

So, the ordered pair is (-2, 18).

For x = -1:

y = 2(-1 + 11) = 2 * 10 = 20

Ordered pair: (-1, 20).

For x = 0:

y = 2(0 + 11) = 2 * 11 = 22

Ordered pair: (0, 22).

For x = 1:

y = 2(1 + 11) = 2 * 12 = 24

Ordered pair: (1, 24).

For x = 2:

y = 2(2 + 11) = 2 * 13 = 26

Ordered pair: (2, 26).

Combining all these ordered pairs, we have the complete set of ordered pairs for the given relation:

{(-2, 18), (-1, 20), (0, 22), (1, 24), (2, 26)}.

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Answer:

6

Step-by-step explanation:

16/4=4 (to brother) 16-4=12 (whats remaining) 12/2=6 (to sister)

Ruby gives her sister 6 animals.

To find out how many animals Ruby gives her sister, we need to follow the instructions step by step. Ruby starts with 16 stuffed animals. She gives 1/4 of her collection to her brother, which is equal to 16 * 1/4 = 4. Now Ruby has 16 - 4 = 12 stuffed animals left. Then she gives half of the remaining animals to her sister, which is equal to 12 * 1/2 = 6. So Ruby gives her sister 6 animals.

Answer:16x-15

Step-by-step explanation:

3x-9+13x-6

Collect like terms

3x+13x-9-6

16x-15

Answer:

0.00019120128

Step-by-step explanation:

1.6x1.6x1.6 x .00004668

To read 43.106 correctly, say 'forty-three point one zero six'

To read the number 43.106 correctly, we start by reading the whole number part, which is 43. This is read as 'forty-three'.

Next, we read the decimal part. The first digit after the decimal point is read as 'one', the second digit as 'zero', and the third digit as 'six'. Finally, we put all the parts together and read the number as 'forty-three point one zero six'.

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Answer:

w=5

Step-by-step explanation:

First you have to write out the equation. Then you distribute negative 4 to 3w then you distribute -4 to -1 you get 4. Then you need to combine like terms and you get 3W. then you need to subtract four from each side you get 15 equals 3W then divide aside by three and you get W equals five

Answer:

[tex]\displaystyle \frac{d}{dx}[\tan x] = \sec^2 x[/tex]

General Formulas and Concepts:

Pre-Calculus

Calculus

Differentiation

Derivative Rule [Quotient Rule]:                                                                           [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]

Step-by-step explanation:

*Note:

This is a known trigonometric derivative.

Step 1: Define

Identify

[tex]\displaystyle y = \tan x[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

The derivative of tanx in calculus is sec^2x, which represents the slope of the curve at any point x for the function tanx.

The derivative of a function measures how the function changes as its input changes. In calculus, the derivative is a concept that describes the rate at which a quantity changes.

In the context of your question, the derivative of tanx or tangent x is sec^2x or secant squared x. This is a standard result that is usually memorized in calculus courses and can be derived using the limit definition of the derivative and trigonometric identities.

To put it in simpler terms, if tanx were the equation of a curve, the derivative (sec^2x) would represent the slope of that curve at any point x. This is key to understanding how the function behaves at different points and predicting its future behavior.

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Answer:

2

Step-by-step explanation:

There are 2 units of distance separating -5 and -3.

Answer:

60 degrees

Step-by-step explanation:

180-90=90

90-30=60

Answer:

1a : a branch of mathematics that deals usually with the nonnegative real numbers including sometimes the transfinite cardinals and with the application of the operations of addition, subtraction, multiplication, and division to them. b : a treatise on arithmetic. 2 : computation, calculation.

Step-by-step explanation:

Final answer:

Arithmetic is a branch of mathematics dealing with numbers, including operations like addition, subtraction, multiplication, and division; it is recognized for its universality and foundational importance in various fields of study.

Explanation:

Arithmetic is a fundamental branch of mathematics that involves the study and manipulation of numbers. It includes the basic operations of addition, subtraction, multiplication, and division. These operations are essential for understanding and working with numbers in both simple and complex mathematical contexts, such as the calculation of quantities, relationships, and patterns. Arithmetic is universally acknowledged for its constant and indubitable truths, such as two plus three always equalling five. This branch of mathematics is not only vital in academic settings but is also crucial in everyday decisions and processes regardless of the period or location. Arithmetic serves as the basis for more advanced mathematical studies and is woven intricately into various fields such as physics, astronomy, and engineering, highlighting its foundational importance in the sciences and beyond.

Answer

-8/3 (fraction)

or in decimal form it would be -2.6 (the six would be repeating)

Step-by-step explanation: