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Anarel [89]
3 years ago
8

What is the product of (3x-9) and 6x↑2-2x+5 Write your answer in standard form.

Mathematics
1 answer:
klio [65]3 years ago
3 0

Answer:

a. 18x^3 -60x^2 + 33x - 45

b. No

Step-by-step explanation:

Given:

(3x-9) and 6x^2-2x+5

=> the production of them is:

(3x-9)(6x^2-2x+5) , we will use distributive law to solve this To do that. we first multiply  6x^2-2x+5 by 3x then by -9. This is done as follows

= 3x (6x^2-2x+5) - 9(6x^2-2x+5)  = (3x * 6x^2-3x * 2x+3x *5) - (9* 6x^2-9* 2x+9* 5)\\\\= (18x^3 -6x^2+ 15x) - (54x^2 - 18x +45)

Then Open both brackets

= 18x^3 -6x^2+ 15x -54x^2 + 18x -45

After that, we group the same terms

= 18x^3 -(6x^2 +54x^2)+ (15x  + 18x) -45

= 18x^3 -60x^2 + 33x - 45

(b) Is the product of (3x-9) and  6x^2-2x+5  equal to the product of (9x-3) and 6x^2-2x+5

No, let find the product of (9x-3) and 6x^2-2x+5 , we will use distributive law to solve this as the above example.

= (9x-3)(6x^2-2x+5)

= 9x (6x^2-2x+5) - 3(6x^2-2x+5)

=(9x * 6x^2 - 9x * 2x + 9x *5) - (3* 6x^2 - 3 * 2x + 3* 5)

= (54x^3  - 18x^2+ 45x) - (18x^2 - 6x +15)

After that, we open the bracket to find the same terms

= 54x^3  - 18x^2+ 45x -18x^2 + 6x -15

= 54x^3  - 18x^2 -18x^2 + 45x  + 6x -15

= 54x^3  - 36x^2 + 51x  -15  

As you can see 54x^3  - 36x^2 + 51x  -15   ≠18x^3 -60x^2 + 33x - 45

Hope it will find you well.

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GrogVix [38]
4m+3+5m the combine like terms. 4m+5m=9m+3 divide 9 by 3 which give you 3, the property is distributive property, combing like term i forgot the last one name
5 0
3 years ago
Which expression is equivalent to 4x+20?
max2010maxim [7]

Answer:

4x+20=

6x-10

Step-by-step explanation:

Simplifying: 4x + 20 = 6x + -10

Reorder the terms: 20 + 4x = 6x + -10

Reorder the terms: 20 + 4x = -10 + 6x

Solving: 20 + 4x = -10 + 6x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-6x' to each side of the equation: 20 + 4x + -6x = -10 + 6x + -6x

Combine like terms: 4x + -6x = -2x: 20 + -2x = -10 + 6x + -6x

Combine like terms: 6x + -6x = 0: 20 + -2x = -10 + 0: 20 + -2x = -10

Add '-20' to each side of the equation: 20 + -20 + -2x = -10 + -20

Combine like terms: 20 + -20 = 0: 0 + -2x = -10 + -20: -2x = -10 + -20

Combine like terms: -10 + -20 = -30: -2x = -30

Divide each side by '-2': x = 15

Simplifying: x = 15

4 0
3 years ago
Write the number in two other forms 8.517
8090 [49]
8,517 8,000+500+10+7
7 0
3 years ago
WILL AWARD BRAINLIEST (Find the measure of the complement and supplement)
melisa1 [442]

Answer:

The complement is 53  and the supplement is 143

Step-by-step explanation:

Two complementary angles add to 90

PQR and x = 90

37+x = 90

Subtract 37 from each side

37-37 +x =90-37

x = 53

The complement is 53


Two supplementary angles add to 180 degrees

PQR and x = 180

37+x = 180

Subtract 37 from each side

37-37 +x= 180-37

x = 143

The supplement is 143

8 0
3 years ago
A roast turkey is taken from an oven when its temperature has reached 185 degrees F and is placed on a table in a room where the
Vedmedyk [2.9K]
(a) Using Newton's Law of Cooling, \dfrac{dT}{dt} = k(T - T_s), we have \dfrac{dT}{dt} = k(T - 75) where T is temperature after T minutes.
Separate by dividing both sides by T - 75 to get \dfrac{dT}{T - 75} = k dt. Integrate both sides to get \ln|T - 75| = kt + C.

Since T(0) = 185, we solve for C:
|185 - 75| = k(0) + C\ \Rightarrow\ C = \ln 110
So we get \ln|T - 75| = kt + \ln 110. Use T(30) = 150 to solve for k:
\ln| 150 - 75 | = 30k + \ln 110\ \Rightarrow\ \ln 75 - \ln 110= 30k \Rightarrow \\ k= \frac{1}{30}\ln (75/110) = \frac{1}{30}\ln(15/22)

So

\ln|T - 75| = kt + \ln 110 \Rightarrow |T - 75| = e^{kt + \ln110} \Rightarrow \\ \\
|T - 75| = 110e^{kt} \Rightarrow T - 75 = \pm110e^{(1/30)\ln(15/22)t}  \Rightarrow \\
T = 75 \pm110e^{(1/30)\ln(15/22)t}

But choose Positive because T > 75. Temp of turkey can't go under.

T(t) = 75 + 110e^{(1/30)\ln(15/22)t} \\
T(45) = 75 + 110e^{(1/30)\ln(15/22)(45)}  = 136.929 \approx 137{}^{\circ}F

(b)

T(t) = 75 + 110e^{(1/30)\ln(15/22)t} = 75 + 110(15/22)^{t/30}  \\
100 = 75 + 110(15/22)^{t/30}   \\
25 = 110(15/22)^{t/30}  
\frac{25}{110} = (15/22)^{t/30}   \\
\ln(25/110) / ln(15/22) = t/30 \\
t = 30\ln(25/110) / ln(15/22)  \approx 116\ \mathrm{min}

Dogs of the AMS.
4 0
3 years ago
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