A. Directions/Instructions:

Given

Solution (3 points)

Final Answer (1 point)

Ex. : 5ab( 4a3 + 2ab - 3b4)

=5ab( 4a3 + 2ab - 3b4)


=20a4b+10a2b2-15ab5

=20a4b+10a2b2-15ab5

1. (6k + 5)(5k + 5)









2. (a2+6a-4)(2a-4)









3. (4x2-5x-21)÷(x-3)










Perform the operation on the following algebraic expressions and apply the laws of exponents. (3 points)













B. Directions/Instructions:


Perform the operation on the following algebraic expressions and apply the laws of exponents. (3 points)


Given

Solution (2 points)

Final Answer

Example: 8c52d42

=8c52d42


=64c104d8

=16c10d8

1. (4x5y3)2









2. 18c8(-2c)2









3. 3a2bab24ab2c3c

Answer:

15/56

Step-by-step explanation:

multiply the top fractions by making the equation the following

3x5

-------

8x7

_________________________

3x5 =15

8x7= 56

hope this helps :)

The solution to the product of fractions is 13/56

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

3/8 * 5/7

Evaluate the product of 3 and 5

So, we have

3/8 * 5/7 = 13/8 * 1/7

Evaluate the product of 8 and 7

So, we have

3/8 * 5/7 = 13/56

Hence, the solution is 13/56

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Answer:

ABCDEFG = 3211000

Step-by-step explanation:

A counts the number of zeroes, and there are 3 zeroes (E, F, G), so A = 3.B counts the number of ones, and there are 2 ones (C, D), so B = 2.C counts the number of twos, and there is 1 two (B), so C = 1.D counts the number of threes, and there is 1 three (A), so D = 1.There is no four, five, six in, so E, F, G are all zeroes.

Answer:

The triangles are not similar

Step-by-step explanation:

We can say whether the triangle UVW is similar to triangle LMN or not by looking at the side lengths' ratio:

If they are similar then the side's must be proportional

VU/LM = VW/NM

35/25 = 22/16 cross multiply expressions

560 = 550 this is not an equation so we cannot say the triangles are similar.

Given,

Distance (d)= 2955 km

Time (t)= 13 hr

To Find,

Speed (s)=?

[tex]s = \frac{d}{t} \\ \\ s = \frac{2995}{13} \\ \\ s = 227.308 \: \: \text{km/hr}[/tex]

Rounding To Nearest Whole Number= 227 Km/hr

[tex] \therefore \text{speed} = 227 \text{km/hr}[/tex]

Answer:

As Per Provided Information

Distance travelled by the car is 2955 Km

and it takes 13 hours to cover that distance .

We have been asked to determine the speed of the car .

[tex] \boxed{\bf \: speed \: = \dfrac{Distance Travelled by Car}{Total Time Taken }}[/tex]

substituting the value we get

[tex] \longrightarrow\sf \: Speed = \dfrac{2955}{13} \\ \\ \\ \longrightarrow\sf \: Speed = \cancel\dfrac{2955}{13} \\ \\ \\ \longrightarrow\sf \: Speed =227.30 \\ \\ \\ \longrightarrow\sf \: Speed \approx227 \: km {hr}^{ - 1} [/tex]

Therefore,

Answer:

78.1428571429

Step-by-step explanation:

Answer:

Using the percentile concept, it is found that the maximum age of the youngest 25% of the passengers is of 30.

When a measure is in the xth percentile of a data-set, it is greater than x% of the measures and lesser than (100 - x)%.

Researching the problem on the internet, it is found that the distribution of the ages is described by a box and whisker plot, which states that:

Hence, the maximum age of the youngest 25% of the passengers is of 30.

More can be learned about the percentile concept at https://brainly.com/question/24495213

Answer:

z3 = 216      take the cube root of both sides

z = 6 cm  = the side length

Answer: B

Step-by-step explanation:

These are vertical angles, so x+97=2x+32, meaning x=65.

So, the measure of angle 1 = 65 + 97 = 162 degrees

The value of m∠1, given that m∠1 = x + 97 and m∠2 = 2x + 32 is 162° (2nd option)

First, we shall list out the given parameters from the question. This is given below:

Next, we shall obtain the value of x. Details below:

m∠1 = m∠2 (vertically opposite angle)

x + 97 = 2x + 32

Solving for x, we have:

97 - 32 = 2x - x

65 = x

Thus,

x = 65

Now, we shall obtain the value of m∠1 as follow:

m∠1 = x + 97

x = 65

Therefore,

m∠1 = 65 + 97

= 162°

Thus, the value of m∠1 is 162° (2nd option)

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Answer:

When you divide 4/16 by 4 it equals 1/4. which is known as 0.25 or 25% of a whole.  

Step-by-step explanation:

The central angle (127 degrees) is the angle at point K

The measures of JL and JML are 127 and 233 degrees, respectively

From the complete question, we have:

JL = 127 degrees.

The sum of angles at a point is 360 degrees

So, we have:

JML + 127 = 360

Subtract 127 from both sides

JML = 233

Hence, the measures of JL and JML are 127 and 233 degrees, respectively

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The fraction of the compact disks ordered  by the owner of the music store that are Soft Rock is 13/28.

A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator. The numerator is the number above while the denominator is the number below.

1 - (1/4 + 2/7)

1 -[ (7 + 8) /28]

1 - 15/28 = 13/28

Answer:

B

Step-by-step explanation:

4(-2)-8 = -16, so not C
4(-1)-8 = -12, so not A or D
4(0)-8 = -8, so not D
4(1)-8 = -4, so not A or D
4(2)-8 = 0, so not D

Answer:

d

Step-by-step explanation:

I mean the 1st and 2nd ones are unreasonable and 3 is jus unrealistic

Step-by-step explanation:

STEP

1

:

Pulling out like terms

1.1 Pull out like factors :

-6y - 30 = -6 • (y + 5)

Equation at the end of step

1

:

STEP

2

:

Equations which are never true:

2.1 Solve : -6 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

2.2 Solve : y+5 = 0

Subtract 5 from both sides of the equation :

y = -5

One solution was found :

y = -5

Answer: y=-5

Explanation:

3y-1-9y=29

3y-9y=-6y

-6y-1=29

+1 on both sides

-6y=30

÷-6

y=-5

Answer:

No, it isn't.

Step-by-step explanation:

In (-9, 8), -9 is the x coordinate. The y is 8. In order for -9 to have been a solution, the y would have had to been -9.

Here's what I mean:

(The graph I drew is in the image. I hope it makes sense! Sorry for my bad handwriting, I'm not used to writing on computers.)

I hope this helps!

-No one

Answer:

10 kg

Step-by-step explanation:

Let x be the mass of her cat.

1)

2x + 6 = 16

2x = 16 - 6

2x = 10

x = 10/2

x = 5

2)

2(5)

= 10

Answer:10kg

Step-by-step explanation:

Answer:

x = -1

Step-by-step explanation:

2x + 5x = -7

7x = -7

x = -1

Answer:   yes  

Step-by-step explanation:

Answer:

there is not enough information to solve

Step-by-step explanation:

You need two ordered pairs to calculate the average rate of change.

Let's say the value of the function at n = 1 is a, and the value of the function at n = 3 is b, then the average rate of change from n = 1 to n = 3 is

(b - a)/(3 - 1) = (b - a)/2

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\$25000\\ P=\textit{original amount deposited}\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &5 \end{cases}[/tex]

[tex]25000=P\left(1+\frac{0.08}{12}\right)^{12\cdot 5}\implies 25000=P\left( \frac{151}{150} \right)^{60} \\\\\\ \cfrac{25000}{\left( \frac{151}{150} \right)^{60}}=P\implies 16780.26 \approx P[/tex]

The best chance is an illustration of probability

The 21st position in line gives you the best chance of being the first duplicate birthday

Assume you are in the nth position, the probability of getting a free ticket is:

P(n) = P'(first n - 1 people share a birthday) * P(birthday with first n -1 people)

Mathematically, the above can be represented as:

P(n) = [365/365 * 364/365 * 363/365 * ... * (365 - (n -2))/365] * [(n -1)/365]

Such that: n [tex]\le[/tex] 365

When simplified, the equation becomes

p(n)/p(n+1) = 365/(366 - n) * (n - 1)/n

Where

p(n)/p(n+1) > 1

So, we have:

365/(366 - n) * (n - 1)/n > 1

Evaluate the product

(365n -365)/(366n - n²) > 1

Cross multiply

365n -365 > 366n - n²

Collect like terms

n² + 365n - 366n - 365 > 0

Evaluate the difference

n²  - n - 365 > 0

Solve for n using a graphing calculator;

n > - 18.6 or n >19.6

n cannot be negative.

So, we have:

n > 19.6

Approximate to nearest integer

n > 20

The least integer value of n is:

n = 21

Hence, the 21st position in line gives you the best chance of being the first duplicate birthday

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Answer:

4x8-12=m

Step-by-step explanation:

4 trays x each containing 8 muffins - 12 muffins(giving away)

[tex]\rightarrow[/tex] First side(a) of triangle = 17in.

[tex]\rightarrow[/tex] Second side(b) of triangle = 13in.

[tex]\rightarrow[/tex] Perimeter of triangle = 45in.

[tex]\rightarrow[/tex]Third side of the triangle.

[tex]\rightarrow[/tex] Perimeter of triangle = sum of all side(a+b+c).

[tex]\rightarrow[/tex] Perimeter of triangle = a + b + c.(putting the value of perimeter, side a and b from the above given)

[tex]\rightarrow[/tex] [tex]\sf{45\: = \: 17+13+c}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{45\: = \: 30+c}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{45-30\: = \:c}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{15in.\: = \: c}[/tex]

Therefore, third side = 15in.

[tex]\rightarrow[/tex]To convert this value into feet we need to divide it by 12, because there are 12 inches in a foot.

[tex]\rightarrow[/tex] [tex]\sf{\frac{15}{12}}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{1.25feet}[/tex]

________________________________

Hope it helps you:)

Answer:

Side 3 = 1.25 feet

Step-by-step explanation:

Given :

To Find :

Solving :

Answer: 20

Step-by-step explanation: a to d, just count how many squares. and you get 5, and there are 4 sides and it's a perfect square so 5 x 4 = 20, so it is 20, you didn't show what the unit will be so don't forget to write that down!