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2 years ago

I’m going to need a serious answer through this one or I’m screwed.

Mathematics

2 answers:

Dvinal [7]2 years ago

7 0

Answer:

58.83 ft^2

Step-by-step explanation:

Finding the radius:

A = πr^2

90 = πr^2

90/π = r^2

28.6 = r^2

5.3 = r

Using the area of a sector of a circle formula:

θ/360 x πr^2

240/360 x π(5.3)^2

= 58.83 ft^2

Elina [12.6K]2 years ago

5 0

Answer:

A = 60 ft²

Step-by-step explanation:

the area (A) of the shaded sector is calculated as

A = area of circle × fraction of circle

= 90 × $\frac{240}{360}$

= 90 × $\frac{2}{3}$

= 30 × 2

= 60 ft²

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1/(2 2/3)=1/2x+(3 1/4x)

Anna71 [15]

Answer:

$x = \frac{32}{45}$

Step-by-step explanation:

Given

$1 * (2\frac{2}{3}) = \frac{1}{2}x + 3\frac{1}{4}x$

Required

Solve for x

Express all fractions as improper

$1 * \frac{8}{3} = \frac{1}{2}x + \frac{13}{4}x$

Take LCM

$1 * \frac{8}{3} = \frac{2 + 13}{4}x$

$\frac{8}{3} = \frac{15}{4}x$

Cross Multiply

$15x * 3 = 4 * 8$

$45x = 32$

Make x the subject

$x = \frac{32}{45}$

7 0

3 years ago

Let $A = (4,-1)$, $B = (6,2)$, and $C = (-1,2)$. There exists a point $X$ and a constant $k$ such that for any point $P$,

goldfiish [28.3K]

Answer:

k=32

Step-by-step explanation:

Given the points:

$A = (4,-1)$, $B = (6,2)$, and $C = (-1,2)$.$

The first step is to find the Centroid of the triangle.

Centroid, X

$=\left(\dfrac{x_1+x_2+x_3}{3} ,\dfrac{y_1+y_2+y_3}{3} \right)\\=\left(\dfrac{4+6+(-1)}{3} ,\dfrac{-1+2+2}{3} \right)\\=\left(\dfrac{9}{3} ,\dfrac{3}{3} \right)=(3,1)$

Next, let P be a point (x,y)

Using the distance formula, $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$PA^2=(x-4)^2+(y-(-1))^2\\PB^2=(x-6)^2+(y-2)^2\\PC^2=(x-(-1))^2+(y-2)^2\\PX^2=(x-3)^2+(y-1)^2\\$

On Substitution into: $PA^2 + PB^2 + PC^2 = 3PX^2 + k$

$(x-4)^2+(y-(-1))^2+(x-6)^2+(y-2)^2+(x-(-1))^2+(y-2)^2=3[(x-3)^2+(y-1)^2]+k$

Let us simplify the LHS first

$\\LHS: x^2-8x+16+y^2+2y+1+x^2-12x+36+y^2\\-4y+4+x^2+2x+1+y^2-4y+4\\=3x^2-18x+3y^2-6y+62$

Also, the Right Hand Side

$RHS:3[(x-3)^2+(y-1)^2]+k\\=3[x^2-6x+9+y^2-2y+1]+k\\=3x^2-18x+27+3y^2-6y+3+k\\=3x^2+3y^2-18x-6y+30+k$

Therefore:

$3x^2-18x+3y^2-6y+62=3x^2+3y^2-18x-6y+30+k\\k=3x^2-18x+3y^2-6y+62-3x^2-3y^2+18x+6y-30\\k=3x^2-3x^2+3y^2-3y^2-18x+18x+62-30\\k=32$

7 0

3 years ago

Brooke measures the height of her bean plant for a science project. The bean plant is 12.5 inches tall.

Fofino [41]

Answer:

4.92125984

Step-by-step explanation:

3 0

3 years ago

A business has $10,000 in its bank account. In order to build an addition onto its office, it takes out a loan for $30,000 and d

ser-zykov [4K]

Answer:

The new account balance is $40000

Step-by-step explanation:

The number line is not given. However, the question can be solved without it.

Given

$Balance = \$10000$

$Loan = \$30000$

Required

Determine the new balance

$New\ Balance = Initial\ Balance + Loan\ Amount$

$New\ Balance = \$10000 + \$30000$

$New\ Balance = \$40000$

Hence:

The new account balance is $40000

7 0

3 years ago

Determine The Period

kolezko [41]

Check the picture below.

notice, if we start checking its pattern from the 10th unit, backwards, it begins to repeat at the unit 4, namely, every 6 units.

5 0

2 years ago