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2 years ago

Find the area of the shaded region. Round your answer to one decimal place, if necessary figure is not drawn the scale

Mathematics

1 answer:

pav-90 [236]2 years ago

3 0

Step-by-step explanation:

area of equilateral ∆ =

$( \sqrt{3} \div 4) {a}^{2}$

here a = 3

area of ∆ = 3.9 in^2

area of circle

$\pi {r}^{2}$

= 19.63 in^2

area of shared region = 19.63-3.9= 15.73 in^2

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Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule

Sergeeva-Olga [200]

Answer:

First term: 5

Fourth term: 5 1/2

Tenth term: 6 1/2

Step-by-step explanation:

Let's find the first, fourth and tenth terms of the arithmetic sequence described by the given rule:

A(n) = 5 + (n-1) (1/6)

First term:

A(1) = 5 + (1-1) (1/6)

A(1) = 5 + (0) (1/6)

A(1) = 5

Fourth term:

A(4) = 5 + (4-1) (1/6)

A(4) = 5 + (3) (1/6)

A(4) = 5 + 3/6 = 5 3/6 = 5 1/2 (simplifying)

Tenth term:

A(10) = 5 + (10-1) (1/6)

A(10) = 5 + (9) (1/6)

A (10) = 5 + 9/6 = 6 3/6 = 6 1/2 (simplifying)

5 0

3 years ago

Select the correct answer from each drop-down menu.

serious [3.7K]

Answer:

Center: (4,8)

Radius: 2.5

Equation: $(x-4)^2+(y-8)^2=6.25$

Step-by-step explanation:

It was given that; the endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5).

Note that the longest chord is the diameter;

The midpoint of the ends of the diameter gives us the center;

Use the midpoint formula;

$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )$

The center is at; $(\frac{4+4)}{2} ,\frac{5.5+10.5}{2}=(4,8)$

To find the radius, use the distance formula to find the distance from the center to one of the endpoints.

The distance formula is;

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$r=\sqrt{(4-4)^2+(10.5-8)^2}$

$r=\sqrt{0^2+(2.5)^2}$

$r=\sqrt{0^2+(2.5)^2}=2.5$

The equation of the circle in standard form is given by;

$(x-h)^2+(y-k)^2=r^2$

We substitute the center and the radius into the formula to get;

$(x-4)^2+(y-8)^2=2.5^2$

$(x-4)^2+(y-8)^2=6.25$

6 0

2 years ago

The line passes through (9,8) and is perpendicular to x-2y=-16

pickupchik [31]

The equation of line perpendicular to x-2y=-16 passing through (9,8) is: y=-2x+26

Step-by-step explanation:

Given

$x-2y=-16\\Adding\ 2y\ on\ both\ sides\\x=2y-16\\Adding\ 16\ on\ both\ sides\\x+16=2y-16+16\\x+16=2y\\2y=x+16\\Dividing\ both\ sides\ by\ 2\\\frac{2y}{2}=\frac{x+16}{2}\\y=\frac{x}{2}+\frac{16}{2}\\y=\frac{1}{2}x+8\\$

The equation is in slope-intercept form, the coefficient of x will be the slope of given line. The slope is: 1/2

As the product of slopes of two perpendicular lines is -1.

$\frac{1}{2}*m=-1\\m=-1*\frac{2}{1}\\m=-2$

Slope intercept form is:

$y=mx+b$

Putting the value of slope

y=-2x+b

To find the value of b, putting (9,8) in the equation

$8=-2(9)+b\\8=-18+b\\b=8+18\\b=26$

Putting the values of b and m

$y=-2x+26$

Hence,

The equation of line perpendicular to x-2y=-16 passing through (9,8) is: y=-2x+26

Keywords: Equation of line, Slope-intercept form

Learn more about equation of line at:

#LearnwithBrainly

4 0

3 years ago

Factor 5v^2 - 23v - 10

AfilCa [17]

Answer:

$(5v + 2)(v - 5)$

Step-by-step explanation:

Hello!

The expression is written in the form of $ax^2 + bx + c$

Let's factor by grouping:

$ac = -50$

The sum of the factors of -50 should add up to -23.

-25 and 2 work for this.

Expand and factor:

$5v^2 - 23v - 10$
$5v^2 - 25v + 2v - 10$
$5v(v - 5) +2(v -5 )$
$(5v + 2)(v - 5)$

The factored expression is $(5v + 2)(v - 5)$

7 0

1 year ago

Please help with this one.

quester [9]

Answer:

x = 7

Step-by-step explanation:

$\frac{3}{7} x + 5 = 8$

$\frac{3}{7} x = 8-5$

$\frac{3}{7} x = 3$

$x = 3 / \frac{3}{7}$

$x = 3 * \frac{7}{3}$ cancel 3

Then

$x = 7$

4 0

3 years ago

Find the area of the shaded region. Round your answer to one decimal place, if necessary figure is not drawn the scale​

Find the area of the shaded region. Round your answer to one decimal place, if necessary figure is not drawn the scale