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3 years ago

A rectangle is removed from the right hand corner of a square board. What is the area of the remaining board in square feet?

Mathematics

2 answers:

alukav5142 [94]3 years ago

7 0

Answer:

Step-by-step explanation:

<h3>METHOD 1:</h3>

<em>(picture #1)</em>

$A_1=(12)(8)=96\ ft^2\\\\A_2=(2)(4)=8\ ft^2\\\\A=A_1+A_2\Rightarrow A=96+8=104\ ft^2$

<h3>METHOD 2:</h3>

<em>(picture #2)</em>

$A_1=(12)(12)=144\ ft^2\\\\A_2=(10)(4)=40\ ft^2\\\\A=A_1-A_2\Rightarrow A=144-40=104\ ft^2$

irinina [24]3 years ago

5 0

Answer:

104 ft²

Step-by-step explanation:

12² - 4 x (12-2) = 144 - 40 = 104

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According to the Fundamental Theorem of Algebra, which polynomial function has exactly 8 roots?

HACTEHA [7]

Answer:

Option (1)

Step-by-step explanation:

Fundamental theorem of Algebra states degree of the polynomial defines the number of roots of the polynomial.

8 roots means degree of the polynomial = 8

Option (1)

f(x) = (3x² - 4x - 5)(2x⁶- 5)

When we multiply (3x²) and (2x⁶),

(3x²)(2x⁶) = 6x⁸

Therefore, degree of the polynomial = 8

And number of roots = 8

Option (2)

f(x) = (3x⁴ + 2x)⁴

By solving the expression,

Leading term of the polynomial = (3x⁴)⁴

= 81x¹⁶

Therefore, degree of the polynomial = 16

And number of roots = 16

Option (3)

f(x) = (4x² - 7)³

Leading term of the polynomial = (4x²)³

= 64x⁶

Degree of the polynomial = 6

Number of roots = 6

Option (4)

f(x) = (6x⁸ - 4x⁵ - 1)(3x² - 4)

By simplifying the expression,

Leading term of the polynomial = (6x⁸)(3x²)

= 18x¹⁰

Degree of the polynomial = 10

Therefore, number of roots = 10

3 0

3 years ago

Help plz !! I will give you points or anything !!

pashok25 [27]

Answer:

Answer C is correct

Step-by-step explanation:

-200(3/4) = -600/4 = -150 ft

3 0

2 years ago

A tennis player keeps track of the number of successful first serves he makes. During the first 8 service points of a game, only

Andru [333]

Answer:

He needs 7 more consecutive successful first serves to raise his first serve percentage to 60%.

Step-by-step explanation:

After n consecutive serves, his total number of serves is going to be n+8, since he has already served 8 times. In the best case, his number of successful first serves is n+2.

His percentage of succesful first serves is the division of the number of succesful first serves divided by the total number of serves. So

$P = \frac{n+2}{n+8}$

We want $P = 0.60$ . So

$0.6 = \frac{n+2}{n+8}$

$n+2 = 0.6*(n+8)$

$n + 2 = 0.6n + 4.8$

$n - 0.6n = 4.8 - 2$

$0.4n = 2.8$

$n = \frac{2.8}{0.4}$

$n = 7$

He needs 7 more consecutive successful first serves to raise his first serve percentage to 60%.

5 0

3 years ago

In Δ A B C, the measure of the largest angle is 32 less than 3 times the smallest angle. The measure of the middle angle is 8 mo

AlladinOne [14]

Answer:

52degrees

Step-by-step explanation:

Let the measure of the largest angle be x

middle angle be y

smallest angle be z

Since the sum of angle in a triangle is 180 degrees, hence;

x + y + z = 180 .... 1

If the measure of the largest angle is 32 less than 3 times the smallest angle, then;

x = 3z - 32

3z = x+ 32

z = x+32/3 ..... 2

If he measure of the middle angle is 8 more than half the measure of the largest angle, then;

y = x/2 + 8 .... 3

Substitute 2 and 3 into 1;

x + x/2 + 8 + (x+32)/3 = 180

multiply through by 6

6x + 3x + 48 + 2(x+32) = 1080

9x + 48 + 2x + 64 = 1080

11x + 112 = 1080

11x = 1080-112

11x = 968

x = 968/11

x = 88 degrees

Get the middle angle y;

Since y = x/2 + 8

y = 88/2 + 8

y = 44 + 8

y = 52 degrees

Hence the measure of the middle angle is 52degrees

5 0

3 years ago

15a2-6ab-8a2 - 5ab + 20+ a? - ab - 31 -

Crazy boy [7]

-12ab+7a power of 2 +a 11

6 0

3 years ago