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2 years ago

A circular picture is 8 inches in diameter.

Mathematics

1 answer:

erma4kov [3.2K]2 years ago

8 0

Answer:

Part A :

Area = π*r² = π(d/2)² = π*(8/2)² =

π*4² = π*16 square inches

Part B:

d=8+4 = 12 and r = d/2 = 6 inches

We know :

Area = π*r²

Area = π*6²

=36π

Hope This Answer To Your Question!

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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

2 years ago

1. Which point on the axis satisfies the inequality y

grigory [225]

Answer:

1) Point $(1,0)$ -----> see the attached figure N $1$

2) The value of x is $4$

3) I quadrant

4) $(1,1)$

5) $y>-5x+3$

Step-by-step explanation:

Part 1)

we know that

If the point satisfy the inequality

then

the point must be included in the shaded area

The point $(1,0)$ is included in the shaded area

Part 2)

we have

$x-2y\geq 4$

see the attached figure N $2$

we know that

The value for x on the boundary line and the x axis is equal to the x-intercept of the line $x-2y= 4$

For $y=0$

Find the value of x

$x-2(0)= 4$

$x=4$

The solution is $x=4$

Part 3)

we have

$x\geq 0$ -----> inequality A

The solution of the inequality A is in the first and fourth quadrant

$y\geq 0$ -----> inequality B

The solution of the inequality B is in the first and second quadrant

the solution of the inequality A and the inequality B is the first quadrant

Part 4) Which ordered pair is a solution of the inequality?

we have

$y\geq 4x-5$

we know that

If a ordered pair is a solution of the inequality

then

the ordered pair must be satisfy the inequality

we're going to verify all the cases

case A) point $(3,4)$

Substitute the value of x and y in the inequality

$x=3,y=4$

$4\geq 4(3)-5$

$4\geq 7$ ------> is not true

therefore

the point $(3,4)$ is not a solution of the inequality

case B) point $(2,1)$

Substitute the value of x and y in the inequality

$x=2,y=1$

$1\geq 4(2)-5$

$1\geq 3$ ------> is not true

therefore

the point $(2,1)$ is not a solution of the inequality

case C) point $(3,0)$

Substitute the value of x and y in the inequality

$x=3,y=0$

$0\geq 4(3)-5$

$0\geq 7$ ------> is not true

therefore

the point $(3,0)$ is not a solution of the inequality

case D) point $(1,1)$

Substitute the value of x and y in the inequality

$x=1,y=1$

$1\geq 4(1)-5$

$1\geq -1$ ------> is true

therefore

the point $(1,1)$ is a solution of the inequality

Part 5) Write an inequality to match the graph

we know that

The equation of the line has a negative slope

The y-intercept is the point $(3,0)$

The x-intercept is a positive number

The solution is the shaded area above the dashed line

the equation of the line is $y=-5x+3$

The inequality is $y>-5x+3$

3 0

3 years ago

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Maria and Nate graphed lines on a coordinate plane. Maria's line is represented by the equation y = -5/6x +8. Nate's line is per

likoan [24]

Answer:

Option C: 6x-5y=15

Explanation:

y = -5/6x +8

8 is the y-intercept

-5/6x is the slope

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*: (=' :') this

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6 0

2 years ago

What does 7m- m equal

Norma-Jean [14]

$7m-m\rightarrow7m-1m=m(7-1)\rightarrow6m$

7m-m is equal to 6m.

4 0

7 months ago

Help Please!? Thank You!

swat32

A. left 2 units

the vertex form of a parabola is
y = a(x-h)^2 + k
(h,k) is the point of the vertex

since h is -2 in (x+2)^2
the function is shifted 2 units left

3 0

2 years ago