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patriot [66]
3 years ago
7

Rewrite each expression below using the distributive property then evaluate each expression for X equals two and Y equals five.

a.8x-4= b.6y2+24y c. 7X(y -2) d. 3(9+y)

Mathematics
1 answer:
Anit [1.1K]3 years ago
4 0
A)8*2-4            b)6*5+2+24*5                c)7*2(5-2)                  d)3(9+5)
  12                      30+2+120                     14*3                             3*14
                            152                                  42                              42
i hope it helps

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What is the sum or difference?
dlinn [17]
1. Ans: Option (B) -6x^4

Explanation:
Given: 2x^4 - 8x^4
Take the common out:
=> x^4(2 - 8)

Hence: => [tex]-6x^4[/tex] (Option B)

2. Ans: Option (D) -3y^5

Explanation:
Given: 6y^5 - 9y^5
Take the common term(s) out:
=> y^5(6-9)

Hence: => -3y^5 (Option D)

3. Ans: Option (B) 9x^2 - 12x + 6<span> quadratic trinomial 

Explanation:
</span>Given: 6 - 12x + 13x^2 - 4x^2

The standard form of polynomial function must have the highest powered value at the start, then the second highest and so on.

=> 
13x^2 - 4x^2 - 12x + 6
=> 9x^2 - 12x + 6 (Option B)

4. Ans: Option (C) 7.3x^2 + 0.8x + 1.3

Explanation:
In order to find the total number of C<span>ommon and Endler's guppies, you need to add both Common and Endler's guppies' polynomials, as follows:

</span>Common guppies: 3.1x^2 +6.0x + 0.3<span>
Endler's guppies:   </span>4.2x^2 - 5.2x + 1.0
(add both)
-----------------------------------------------------------------
Total number:          7.3x^2 +0.8x + 1.3
-----------------------------------------------------------------
Hence the ans is Option(C) 7.3x^2 + 0.8x + 1.3

5. Ans: Option (D) 2x^2(133 - 18 \pi )

Explanation:
First let's find the total area of the yard:
Total Area of the Yard = 14x * 19x = 266x^2

Now the area of the circular fountain:
Area of the Circular Fountain = \pi r^2
Since, r=6x
Therefore,
Area of the Circular Fountain = \pi (6x)^2 = 36 \pi x^2

Now the final Area of the yard would be:
Final area of the Yard = Total Area of the Yard - Area of the Circular Fountain
Final area of the Yard = 266x^2 - 36 \pi x^2
=> Final area of the Yard = 2x^2(133 - 18 \pi) (Option D)

6. Ans: Option (A) 56x^2

Explanation:
First let's find the total area of the lot:
Total Area of the lot= 6x * 10x = 60x^2

Now the area of the stadium:
Area of the stadium = 1x * 4x = 4x^2

Now the final Area of the lot would be:
Final area of the lot= Total Area of the lot - Area of the stadium
Final area of the lot= 60x^2 - 4x^2
=> Final area of the lot = 56x^2 (Option A)

-i
4 0
3 years ago
Read 2 more answers
Compare the light gathering power of an 8" primary mirror with a 6" primary mirror. The 8" mirror has how much light gathering p
tankabanditka [31]

Answer:

1.778 times more or 16/9 times more

Step-by-step explanation:

Given:

- Mirror 1: D_1 = 8''

- Mirror 2: D_2 = 6"

Find:

Compare the light gathering power of an 8" primary mirror with a 6" primary mirror. The 8" mirror has how much light gathering power?

Solution:

- The light gathering power of a mirror (LGP) is proportional to the Area of the objects:

                                           LGP ∝ A

- Whereas, Area is proportional to the squared of the diameter i.e an area of a circle:

                                           A ∝ D^2

- Hence,                              LGP ∝ D^2

- Now compare the two diameters given:

                                           LGP_1 ∝ (D_1)^2

                                           LGP ∝ (D_2)^2

- Take a ratio of both:

                           LGP_1/LGP_2 ∝ (D_1)^2 / (D_2)^2

- Plug in the values:

                               LGP_1/LGP_2 ∝ (8)^2 / (6)^2

- Compute:             LGP_1/LGP_2 ∝ 16/9 ≅ 1.778 times more

6 0
3 years ago
1) A family consisting of three persons—A, B, and C—goes to a medical clinic that always has a doctor at each of stations 1, 2,
crimeas [40]

Answer:

Step-by-step explanation:

Let us record the station number 1, 2 or 3 for each family member A, B or C.

I am attaching a table containing total outcomes. Outcomes are presented along rows while the assigned station to each member is written along columns. For ease of understanding, 1 3 2 in the table should be interpreted as family member A being assigned to station 1, member B to station 3 and member C to station number 2, respectively.

From table it is clear that the total outcomes possible are 27.

We know that, probability can be defined as,

PROBABITILY = \frac{NUMBER\;OF\;DESIRED\;OUTCOMES}{TOTAL\;NUMBER\;OF\;OUTCOMES}

a) All Members Assigned to the Same Station.

Cases for all members being assigned to same station are as follows:

[1 1 1], [2 2 2], [3 3 3] (outcome number 1, 14 and 27 in the table).

Therefore,

PROBABILITY\;(Case\;a) = \frac{3}{27}\\\\PROBABILITY\;(Case\;a) = 0.111

b) At Most Two Members Assigned to the Same Station.

It means that maximum of 2 members can have the same station. Cases for this situation are as follows:

[1 1 2], [1 1 3], [1 2 1], [1 2 2], [1 3 1], [1 3 3], [2 1 1], [2 1 2], [2 2 1], [2 2 3], [2 3 2],

[2 3 3], [3 1 1], [3 1 3], [3 2 2], [3 2 3], [3 3 1], [3 3 2]

(outcome number 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 17, 18, 19, 21, 23, 24, 25 and 26 in the table).

Therefore,

PROBABILITY\;(Case\;b) = \frac{18}{27}\\\\PROBABILITY\;(Case\;b) = 0.666

c) All Members Assigned to a Different Station.

For this scenario, we have the following results:

[1 2 3], [1 3 2], [2 1 3], [2 3 1], [3 1 2], [3 2 1] (outcome number 6, 8, 12, 16, 20 and 22 in the table).

Therefore,

PROBABILITY\;(Case\;c) = \frac{6}{27}\\\\PROBABILITY\;(Case\;c) = 0.222

3 0
3 years ago
In ABC, what is the value of x<br><br> 5.5<br> 6.5<br> 55<br> 65
vekshin1

<em>Answer:</em>

( B ) x = 6.5

<em>Step-by-step explanation:</em>

We know that all the angles of a triangle equal 180 when added together. So lets make an equation for this question.

(10x-10) + (10x+8) + 8x = 180

I just took all the angles and added them together to make 180. Now solve for x.

10x - 10 + 10x + 8 + 8x = 180 <em>(combined like terms)</em>

28x -2 = 180 <em>(added 2 to both sides)</em>

28x = 182 <em>(divided both sides by 28)</em>

x = 6.5

6 0
3 years ago
Read 2 more answers
Which sequence represents an arithmetic sequence?
MArishka [77]

Answer:

D

Step-by-step explanation:

We know that an arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is always constant.

−5, −7, −10, −14, −19, …

Here difference between -5 and -7 is -2

But difference between -10 and -7 is -3

⇒ Difference is not constant.

Therefore, this sequence does not represents an arithmetic sequence.

1.5, −1.5, 1.5, −1.5, …  

Here difference between 1.5 and -1.5 is 3

But difference between -1.5 and 1.5 is 3

⇒ Difference is not constant.

Therefore, this sequence does not represents an arithmetic sequence.

4.1, 5.1, 6.2, 7.2, …  

Here difference between 4.1 and 5.1 is 1

But difference between 6.2 and 5.1 is 1.1

⇒ Difference is not constant.

Therefore, this sequence does not represents an arithmetic sequence.

−1.5, −1, −0.5, 0, …

Here difference between -1.5 and -1 is 0.5

But difference between -1 and -0.5 is 0.5

⇒ Difference is constant.

Therefore, this sequence represents an arithmetic sequence.

plz mark brainliest

7 0
3 years ago
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