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Gwar [14]
3 years ago
11

Serena simplify the expression 3 (2x - 6 - x + 1 )^2 - 2 + 4x in step 1 she simplified within the parentheses in step 2 she expa

nded the exponent witch is a possible next step
Mathematics
1 answer:
xz_007 [3.2K]3 years ago
4 0

Answer:

For step three she could multiply the two parenthesis against each other to get 3(x² - 10x + 25) - 2 + 4x

Step-by-step explanation:

step 1: 3(x - 5)² - 2 + 4x

step 2: 3(x - 5)(x - 5) - 2 + 4x

For step three she could multiply the two parenthesis against each other to get 3(x² - 10x + 25) - 2 + 4x

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The diagonal length of a rectangular playing field is 76 feet, and its width is 48 feet. How long is the playing field?
Sauron [17]

The length of playing field is 58.9 feet

<u>Solution:</u>

Given that, the diagonal length of a rectangular playing field is 76 feet,  

And its width is 48 feet.  

<em><u>To find: length of playing field</u></em>

Now, we know that, <em>diagonal, width and length of a rectangle will form an right angle triangle with diagonal as hypotenuse. </em>

So, now, in a right angled triangle  we can use pythagorean theorem to find the length

Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

By above definition, In a right angled triangle ABC we get

c^2 = a^2 + b^2

Where "c" is the length of hypotenuse

"a" is the length of one leg of right angled triangle

"b" is the length of other leg of right angled triangle

\begin{array}{l}{\text {Then, diagonal = width }^{2}+\text { length }^{2}} \\\\ {76^{2}=48^{2}+\text {length }^{2}} \\\\ {\text {Length }^{2}=76^{2}-48^{2}} \\\\ {\text {Length }^{2}=5776-2304}\end{array}

\begin{array}{l}{\text { Length }^{2}=3472} \\\\ {\text { Length }=\sqrt{3472}} \\\\ {\text { Length }=58.92}\end{array}

Hence, the length of the rectangular field is 58.9 feet

7 0
3 years ago
Type the missing number in this sequence:
Gelneren [198K]
The answer would be 62
3 0
2 years ago
Read 2 more answers
Reduce -10/-5 dont know how too reduce
Agata [3.3K]

Answer:

-10/-5= 2 simply divide

2 negatives multiplied and/ or divided by is a positive number

5 0
2 years ago
Find the equation of the tangent line and normal line to the curve y=(6+4x)2 at the point (6,900). Write the equations of the li
Ksenya-84 [330]

Answer:

Equation of the tangent to the curve

y = 240x - 215994

Equation of the normal

y = (-1/240)x + 9.75 = - 0.00417x + 9.75

Step-by-step explanation:

y = (6 + 4x)² = 36 + 48x + 16x² = 16x² + 48x + 36

dy/dx = 32x + 48

At the point (6,900),

dy/dx = 32(6) + 48 = 240

Equation of the tangent at point (a,b) is

(y - b) = m(x - a)

a = 6, b = 900, m = 240

y - 6 = 240(x - 900)

In the y = mx + b form,

y - 6 = 240x - 216000

y = 240x - 215994

The slope of the normal line = -(1/slope of the tangent line) (since they're both perpenducular to each other)

Slope of the normal line = -1/240

Equation of normal

y - 6 = (-1/240)(x - 900)

y - 6 = (-x/240) + 3.75

y = (-1/240)x + 9.75

y = - 0.00417x + 9.75

8 0
3 years ago
A sign on the pumps at a gas station encourages customers to have their oil checked, and claims that one out of 10 cars needs to
Archy [21]

Answer:

0.2916, 0.1488, 0.0319

Step-by-step explanation:

Given that a sign on the pumps at a gas station encourages customers to have their oil checked, and claims that one out of 10 cars needs to have oil added.

Since each trial is independent there is a constant probability for any random car to need oil is 0.10

Let X be the number of cars that need oil

A) Here X is BIN(4,0.1)

P(X=1) = 4C1(0.1)(0.9)^3 \\= 0.2916

B) Here X is Bin (8, 0.1)

P(x=2) = 8C2 (0.1)^2 (0.9)^6\\\\=0.1488

C) Here X is Bin (20,5)

P(x=5) = 20C5 (0.1)^5 (0.9)^{15} \\=0.0319

3 0
3 years ago
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