Factor completely 16x4 − 81.

(2x − 3)(2x − 3)(4x2 + 9)
(2x − 3)(2x + 3)(4x2 + 9)
(2x − 3)(2x + 3)(4x2 − 9)
(2x + 3)(2x + 3)(4x2 + 9)

Answer:

Distribution

Step-by-step explanation:

On the second step he distributed the 1/4 to x, but not to twelve.

Answer:

Andre made a mistake in the first part of the equation when he was distributing.

Step-by-step explanation:

He got the 1/4x but forgot to distribute to the 12 which would have gotten him 1/4x + 3

Answer:

6 cm

Step-by-step explanation:

Answer:

Here is the complete question:

The ratio of the number of dogs to the number of cats is 4:5. There are 270 animals on the rescue farm. for each of the following statements, explain whether statements is true or false and why:

a. The number of dogs is 4/5 the number of cats.

b. 4/5 of the pets at the farm are dogs.

c. There are exactly 30 more cats than dogs.

d. There are exactly 30 dogs at the farm.

e. 5/9 of the pets at the farm are cats.

a,c and e are true statements.

Step-by-step explanation:

Let the number of dogs be "d' and number of cats be "c".

According to the question:

⇒ [tex]c+d=270[/tex]   ...equation (i)

Arranging the ratio:

⇒ [tex]\frac{4}{5} = \frac{d}{c}[/tex]

⇒ [tex]4c=5d[/tex]

⇒ [tex]c=(\frac{5}{4})d[/tex]    ...equation (ii)

Plugging (ii) in equation (i).

⇒ [tex]c+d=270[/tex]

⇒ [tex]\frac{5}{4} d+d=270[/tex]

⇒ [tex]\frac{5d+4d}{4} =270[/tex]

⇒ [tex]9d=270\times 4[/tex]

⇒ [tex]d=\frac{270\times 4}{9}[/tex]

⇒ [tex]d=120[/tex]

Number of dogs "d" = 120

Number of cats "c" = (270-120) = 150

Lets check each statement:

a.

The number of dogs is 4/5 the number of cats.

⇒ [tex]\frac{4}{5} \times 150[/tex]

⇒ [tex]\frac{4\times 150}{5}[/tex]

⇒ [tex]120[/tex]

Statement is true.

b.

4/5 of the pets at the farm are dogs.

⇒ [tex]\frac{4}{5} \times 270[/tex]

⇒ [tex]216[/tex]

Number of dogs = 120

So the above statement is false.

c.

There are exactly 30 more cats than dogs.

⇒ [tex]c-d =30[/tex]

⇒ [tex]150-120=30[/tex]

Statement is true.

d.

There are exactly 30 dogs at the farm.

False, as there are 120 dogs

e.

5/9 of the pets at the farm are cats.

⇒ [tex]\frac{5}{9} \times 270[/tex]

⇒ [tex]150[/tex]

Statement is true.

So,

Statement  a,c and e are true as we could observe in the explanation.

To solve the equation I = v/r and show how R = v/l, we can rearrange the equation I = v/r to solve for r, which gives r = v/I. Then substitute v/l for I to get r = v/(v/l) = l. Therefore, R = l.

To solve for R = v/l, we can start by rearranging the equation I = v/r to solve for r. Multiply both sides of the equation by r to isolate it, which gives us I * r = v. Then divide both sides of the equation by I to solve for r, which gives us r = v/I. Now substitute v/l for I to get r = v/(v/l). Simplify the expression by multiplying the numerator and denominator by l, which gives us r = lv/v = l. Therefore, R = l.

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This shows how the original equation [tex]\( I = \frac{v}{r} \)[/tex]can be rearranged to solve for[tex]\( R \) (or \( r \))[/tex] in the form [tex]\( R = \frac{v}{I} \)[/tex]. It is important to note that in the context of physics, [tex]\( I \)[/tex] typically represents current, [tex]\( v \)[/tex]represents voltage, and [tex]\( R \)[/tex] represents resistance. The equation [tex]\( I = \frac{v}{r} \)[/tex] is Ohm's law, which relates the voltage, current, and resistance in an electrical circuit. The rearranged form [tex]\( R = \frac{v}{I} \)[/tex] is used to find the resistance when the voltage and current are known.

To solve the equation [tex]\( I = \frac{v}{r} \)[/tex] for [tex]\( R \)[/tex], we need to isolate [tex]\( R \)[/tex] on one side of the equation. Here are the steps to do so:

1. Start with the original equation:

[tex]\[ I = \frac{v}{r} \][/tex]

2. Multiply both sides of the equation by [tex]\( r \)[/tex] to eliminate the denominator:

[tex]\[ I \cdot r = v \][/tex]

3. Now, we want to solve for [tex]\( R \)[/tex], so we need to divide both sides of the equation by [tex]\( I \)[/tex] to isolate [tex]\( R \)[/tex] on one side:

[tex]\[ r = \frac{v}{I} \][/tex]

4. Notice that in the original equation, [tex]\( I \)[/tex] is used, but in the desired equation, [tex]\( R \)[/tex] is used. This seems to be a typo in the question, as [tex]\( I \)[/tex]and [tex]\( R \)[/tex] are likely meant to represent the same variable. Assuming [tex]\( I \)[/tex]and [tex]\( R \)[/tex] are the same, we can rewrite the equation as:

[tex]\[ R = \frac{v}{I} \][/tex]

5. Now, we have [tex]\( R \)[/tex] isolated on one side, which is the desired form of the equation.

Therefore, the final answer, assuming [tex]\( I \)[/tex] and [tex]\( R \)[/tex] represent the same variable, is:

[tex]\[ \boxed{R = \frac{v}{I}} \][/tex]

Answer:

7 to 5 or 7/5

Step-by-step explanation:

Step-by-step explanation:

The odds of seeing a black cat are 25% every day.

It also means that the possibility of seeing  a black cat is once in 4 days, since 25%

Given, we have not seen one black cat in 3 days.

The chance of seeing a black cat on the 4th day = ?

= 100 % since we have not seen it in the past three days.

Answer:

he has 11.4 dollars left

Step-by-step explanation:

54.26+34.34=88.6

100-88.6=11.4

Answer:

11.40

Step-by-step explanation:

I did the math.

54.26+34.34=88.6

100-88.6=11.40

Answer:

20 liters of water

he will need 20 liters of water

Step-by-step explanation:

if james has 40 bottles that hold 500 milliliter then he needs 20,000 milliliters of water or 20 liters. :)

Answer:

Step-by-step explanation:

The lengths of the sides corresponding to DE and DF in triangle ABC are 3.75cm and 5cm respectively as triangles DEF and ABC are similar and their sides are in proportion.

Since triangles DEF and ABC are similar, then their corresponding side lengths are proportional. This means the ratio of the lengths of corresponding sides in both triangles remains constant.

Therefore, the lengths of the corresponding sides in triangle ABC will be in the same ratio as that of the sides in triangle DEF. Since we know the lengths of sides DE and DF in triangle DEF are 6cm and 8cm respectively, we can conclude that the lengths of the sides corresponding to DE and DF in triangle ABC will be in the same ratio as 6 and 8.

The ratio of 6 and 8 can be simplified to 3:4. Therefore, given that the length of side EF in triangle ABC is 5cm, we can apply cross-multiplication to find the lengths of the other sides. For example, using the ratio 3:4 to find the length corresponding to DE in triangle ABC, we would get 5/4 * 3 = 3.75cm. Similarly, "for DF we would get 5/4 * 4 = 5cm".

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The lengths of sides DE and DF in triangle DEF are 6 cm and 8 cm, respectively.

Since triangle DEF is similar to triangle ABC, the corresponding sides of both triangles are proportional. This means that the ratio of any two corresponding sides in the two triangles will be the same. Let's denote the lengths of the corresponding sides in triangle ABC as follows: side AB corresponds to DE, side BC corresponds to EF, and side AC corresponds to DF.

Given that EF is 5 cm, we can set up the following proportion using the corresponding sides of the two triangles:

[tex]\[\frac{DE}{AB} = \frac{EF}{BC} = \frac{DF}{AC}\][/tex]

We know the lengths of DE and DF, so we can express the lengths of AB and AC in terms of the lengths of DE and DF, using the proportion:

[tex]\[\frac{6}{AB} = \frac{5}{BC} = \frac{8}{AC}\][/tex]

From the proportion, we can solve for AB and AC:

[tex]\[AB = \frac{6}{5} \times BC\][/tex]

[tex]\[AC = \frac{8}{5} \times BC\][/tex]

Since we do not have the actual length of BC, we cannot determine the exact lengths of AB and AC. However, we can express them in terms of BC, the corresponding side in triangle ABC. If BC is known, we can simply multiply it by the respective ratios to find AB and AC.

In conclusion, the lengths of sides DE and DF in triangle DEF are 6 cm and 8 cm, respectively, and the lengths of the corresponding sides AB and AC in triangle ABC can be calculated once the length of BC is known, using the ratios derived from the similarity of the triangles.

Probability that a student will play both is 7/30

Step-by-step explanation:

Total students = 30

No. of students who play basketball = 18

Probability that a student will play basketball = 18/30

= 3/5

No. of students who play baseball = 9

Probability that a student will play baseball = 9/30

= 3/10

No. of students who play neither sport = 10

Probability that a student will play neither sport = 10/30

= 1/3

To find :

Probability that a student will play both = p(student will play both)

No.of students who play sport = 30 - 10

= 20

Out of 20 students 18 play basketball and 9 play baseball.

So, some students play both the sports.

No. of students who play both sports = 18 + 9 - 20

= 7

p(student will play both) = 7/30

Probability that a student will play both is 7/30

Answer:

I also think it is A.

Step-by-step explanation:

This is because the mean will be pulled towards the skewed side. Causing,  the mean become greater than the median. Also, most of the Data points are to left side of the graph. Therefore, making the answer A.

Please mark me the brainliest.

The answer choice which describes the probability distribution below is:

This refers to the way in which probabilities are distributed over values of a random variable.

With this in mind, we can see that based on the fact that the mean will be pulled towards the skewed side. then there would be a disproportionate value between the mean and the median so that the majority of the data points are to the left of the mean

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Answer:

14x² - 21

Step-by-step explanation:

In order to expand the expression, you simply need to multiply 7 by 2x², then by -3.

2x² × 7 = 14x²

-3 × 7 = -21

Therefore, the area of the entire rectangle is 14x² - 21 (you will not need to solve for x, as there is no way to do that without knowing the area first).

Answer:

1/4

Step-by-step explanation:

There are 360 degrees in a circle and we have 90 degrees

90/360 = 1/4

Answer:

1/4

Step-by-step explanation:

There are 360 degrees in a circle.

The part she cut out was 90/360

That can be simplified to 1/4.

Therefore, Shani cut out 1/4 of the circle.

Answer:

Hey!

If a car is losing value at a constant rate, then a linear function would work better. For example, say that a car dealership is buying used cars. They will buy it for the asking price, but subtract 500 dollars for each year the car has been in existence. So, if you had a car from 2015 that cost you $2,000, and it's 2018, the dealership would buy it for 2000-(500 * the amount of years it has been since the car was made). Therefore, as 2018-2015=3, we have 2,000-500*3=2,000-1,500=500 as the value of the car after three years, and linear function (in the form of

, with y representing the end cost, b representing the starting cost, m representing the amount the car depreciates in value every year, and x being the amount of years) is 500=(-500*3+2000) in our situation here. Similarly, if the minivan depreciates 3,000 dollars in the first year, based on our knowledge and being forced to use linear function, we can assume that the minivan loses 3,000 dollars every year, making our equation y=(-3000*x)+29,248, with y representing the value of the car at the end, x representing the amount of years, and b representing the starting cost.

However, say that the car loses 50% of its value every year. This means that if you originally bought a car for 2,000 dollars in 2015, in 2016 it would be world 2,000/2=1,000 , 1,000/2=500 the year after that, and so on. We can try to put this into a linear function, but it's hard to put into one equation because we're not subtracting or adding to the cost of the car by a specific amount each year. If we had our equation as y=-0.5*x+2000, this wouldn't work because it's adding to the original amount, not multiplying. However, if we used an exponential equation such as y=b(m^a), with y representing the end cost, b representing the starting cost, m representing the amount multiplied per year, and a representing the amount of years. This works because we start with a value, and multiply it by an amount each year. Since 50%=0.5, we plug that into m to get y=2,000(0.5^a). Therefore, this works really well here. If the minivan were to depreciate by 3,000 every year, starting at $29,248, this means that we first have to find out what we multiply 29,248 by the first year to subtract 3,000. As, after one year, the value is 29,248-3,000=26,248, we have 26,248=29,248(m^1). Therefore, we can divide 29,248 by both sides to get around 0.9 as our answer for m. Thus, our equation is y=29,248(0.9^a). This type of equation would not work if we subtracted an amount every year because we're not multiplying by the same amount then. For example, if a toy was valued at 3$ and gained a value of one dollar every year, we could multiply the toy by 4/3 the first year to get 4, but the next year we wouldn't get 5.

Feel free to ask further questions! :)

Answer:

B.

Step-by-step explanation:

I'm assuming it's written like this when solving it:  [tex]9\frac{4}{5} x-\frac{4}{80} x[/tex]

first change the mixed number to an improper fraction and change to a common denominator

[tex]\frac{49}{5}x-\frac{4}{80}[/tex]  -----> [tex]\frac{784}{80} - \frac{4}{80}[/tex]

[tex]\frac{784}{80}x - \frac{4}{80}x = \frac{39}{4}x\\[/tex] ≈ [tex]9\frac{4}{5}x[/tex]

Answer:

( 7x + 11  )( 7x-  11 )

Step-by-step explanation:

( 7x + 11  )( 7x-  11 )

Because 7*7 is 49

-11*11= -121

7*11=77

-7*11= -77

77-77=0

so the answer is 49x^2-121

To factorize 49x^2-121, we can apply the difference of squares method. The factorization of 49x^2-121 is (7x + 11)(7x - 11).

To factorize the quadratic expression 49x^2 - 121, we first identify it as a difference of squares. This allows us to rewrite it as (7x)^2 - 11^2. Utilizing the difference of squares factoring pattern, we then break it down as (a + b)(a - b), where in this case, a = 7x and b = 11. Consequently, the factorization of 49x^2 - 121 simplifies to (7x + 11)(7x - 11). This method efficiently breaks down the quadratic expression into its constituent linear factors, providing a clearer representation for mathematical analysis and problem-solving purposes.

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Answer:

y=4(1/2)

Step-by-step explanation:

Answer:

y = 8 × (½)^x

Step-by-step explanation:

y = a(b^x)

8 = a(b⁰)

a = 8

y = 8(b^x)

½ = 8(b^4)

1/16 = b⁴

b = ½

y = 8 × (½)^x

Final answer:

Barbara Butler's pay for the week can be calculated by multiplying the total number of tables she assembled by the payment rate per table. The formula for total pay is Total Pay = Number of Tables × Pay Rate per Table.

Explanation:

Barbara Butler's pay for the week:

Number of tables she assembled = Total of tables assembled

Butler's total pay = Number of tables assembled x Payment per table

Calculation:

Assuming she assembled:

Table 1: 5 tables

Table 2: 7 tables

Table 3: 11 tables

Butler's pay for the week = (5 + 7 + 11) x $6.39

Butler's pay for the week = $108.66

The unit rate for 5 revaluations in 50 seconds is 1 revaluation per 10 seconds.

To find the unit rate, divide the number of revaluations by the number of seconds. In this case, the unit rate is 5 revaluations per 50 seconds. To simplify this, divide both numbers by 5 to get 1 revaluation per 10 seconds. So, the unit rate is 1 revaluation per 10 seconds.

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Answer: C.1.5

This is the correct answer so i hope it helps.

Answer:

C.1.5

just took on eg

Step-by-step explanation:

A Tyler made mistake in the third step

B Tyler didi not multiply 4 by 6

C 9 - 20x + 24

- 20x + 15

-5 (4x - 3)

Tyler is using the distributive property on the expression 9 - 4(5x – 6).

His work

9 - 4(5x - 6)

9+(-4)(5x +-6)

9 +-20x +-6

3 – 20x

The distributive property states that an expression that is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.

A . Tyler made mistake in the third step

B . Tyler did not multiply 4 by 6

C. Correct steps are,

9 - 4(5x - 6)

9+(-4)(5x +-6)

9 - 20x + 24

- 20x + 15

-5 (4x - 3)

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Answer: He should have used the mean to determine the average because the data sets are approximately symmetric.

Step-by-step explanation

Answer:

B

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

x = 10

Step-by-step explanation:

1/2 x - 2 = 3

1/2 x = 3 + 2

1/2 x = 5

x = 5 / (1/2)

x = 10

Answer:

0

Step-by-step explanation:

Answer:

The range of the data set listed above would be 0.

Step-by-step explanation:

Because there is no greatest or least number, then its just 0. Just to make sure you could enter your data set into www.calculator.net. When I entered it, it said 0 :)

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Answer:

The frequency table is shown below.

Step-by-step explanation:

(i) Half of the tuna sandwich were on white bread = 21

On brown bread, tuna = 42 - 21 = 21

(ii) 25% of the ham sandwiches sold were on brown bread.

= 25% (32) = 8

On white bread, 32 - 8 = 24

Frequency table:

                     Tuna             Cheese          Ham         Total

Brown             21                     11                    8                40

White              21                     15                  24               60

Total                42                     26                 32              100

Answer:

[tex]20 ft\times 60 ft[/tex] or [tex]30ft\times 40ft[/tex]

Step-by-step explanation:

We are given that

Total fencing used=100 ft

Area enclosed=1200 square ft

Let length of rectangular pig pen=x

Breadth of rectangular pig pen=y

Fencing used=2x+y

[tex]100=2x+y[/tex]

[tex]y=100-2x[/tex]

Area of rectangular pig pen=[tex]xy=x(100-2x)[/tex]

[tex]1200=100x-2x^2[/tex]

[tex]2x^2-100x+1200=0[/tex]

[tex]x^2-50x+600=0[/tex]

[tex]x^2-20x-30x+600=0[/tex]

[tex]x(x-20)-30(x-20)=0[/tex]

[tex](x-20)(x-30)=0[/tex]

[tex]x=20[/tex]

[tex]x-30=0\implies x=30[/tex]

When x=20ft

[tex]y=100-2(20)=60[/tex]ft

When x=30 ft

[tex]y=100-2(30)=40[/tex]ft

Dimension of fence is give  by

[tex]20 ft\times 60 ft[/tex] or [tex]30ft\times 40ft[/tex]