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3 years ago

Use property to find sum pr product 8×51

2 answers:

7 0

If you take 8 and multiply it by 51 then you get 408. (1 times 8 is 8 then 5 times 8 is 40 and put them next to each other it's 408)

aksik [14]3 years ago

3 0

8 × 51 = 408

Eight times fifty-one equals four hundred eight

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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

A person whose eye level is 15 feet above the ground is looking at a building. The angle of elevation to the top of the building

uysha [10]

Answer:

61.97 feets

Step-by-step explanation:

Using trigonometry :

Horizontal distance between the person and building,

Let distance = d

Tan 15 = 15 / d

0.2679491 * d = 15

d = 15 / 0.2679491

d = 55.980781

To obtain the height, h :

tan 40 = (h-15)/d

d = 55.98

h-15 = 55.98 (tan 40°)

h - 15 = 55.98 * 0.8390996

h - 15 = 46.972797

h = 46.972797 + 15

h = 61.972797

h = 61.97 feets

4 0

3 years ago

Describe in detail how you would construct a 95% confidence interval for a set of 30 data points whose mean is 20 and population

postnew [5]

Answer:

We have been given confidence interval 95%, mean 20 , data set 30 and standard deviation 3.

We will use the formula: $mean\pm \frac{\sigma}{\sqrt{n}}\cdot (z-score)$

Here, $mean=20,\sigma=3,n=30,z-score=1.96$

Z-score value at 95% confidence interval is 1.96

On substituting the values in the formula to plug the values:

$20\pm\frac{3}{\sqrt{30}}\cdot (1.96)$

Now, we have a formula for marginal error: $z\cdot \frac{\sigma}{\sqrt{n}}$

Marginal error means your answer will be within that percentage only.

Say you have 3% marginal means your value will be within 3% real population 95% of the time.

7 0

4 years ago

What is the area of a square with side a = 3m?

Murrr4er [49]

Answer:

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Nick and Adam work out together neck weighs 160 pounds is and is gaining 30 pounds per week Adam weighs 195 pounds and is losing

muminat

Answer:

(N+n)=(A+a)

Step-by-step explanation:

Let N represent Nick's current weight

Let A represent Adam's current weight

Let n represent weight Nick gains weekly

Let a represent weight Adam looses weekly

5 0

3 years ago