What is 10 1/3 + 7/9 =

A dog trainer is trying to find a triangular area behind his house that encloses 1800 square feet for his dog to run. He has the

aliina [53]

Answer:

$C = (30,500)$

Step-by-step explanation:

Given

$Area = 1800ft^2$

$A = (6,0)$

$B = (0,25)$

$C(x,y) = (30,y)$

Required

Determine the coordinates of C

The area of triangle is calculated as thus:

$Area = \frac{|A_x(B_y - C_y) + B_x(C_y - A_y) + C_x(A_y - B_y)|}{2}$

This gives:

$1800= \frac{|6(25 - y) + 0(y - 0) + 30(0 - 25)|}{2}$

$1800= \frac{|6(25 - y) + 30(0- 25)|}{2}$

$1800= \frac{|6(25 - y) + 30(-25)|}{2}$

$1800= \frac{|150 - 6y -750 |}{2}$

$1800= \frac{|150 -750- 6y |}{2}$

$1800= \frac{|-600- 6y |}{2}$

Multiply through by 2

$2 * 1800= |-600- 6y|$

$3600= |-600- 6y|$

$3600= |-(600+ 6y)|$

$3600= 600+ 6y$

Solve for 6y

$6y = 3600 - 600$

$6y = 3000$

Solve for y

$y = 3000/6$

$y = 500$

Hence:

The point is:

$C = (30,500)$

7 0

3 years ago

Question 2 (5 points)

Anuta_ua [19.1K]

Answer:

The greatest common factor is 8xyz

Step-by-step explanation:

To find the greatest common factor of an expression involving numbers and variables, we find each greatest common factor separately.

Numbers:

48, 24 and 56.

We find the greatest common factor factoring them simultaneously while all can be factored by the same number. The GCF is the multiplication of the factors. So

48 - 24 - 56|2

24 - 12 - 28|2

12 - 6 - 14|2

6 - 3 - 7|

They cant be factored by the same factors anymore, so the numeric GCF is 8.

Variables:

For each variable, the GCF will be the lowest exponent.

Variable x: We have exponents 1, 2 and 2. So the GCF is $x^1 = x$

Variable y: We have exponents 3, 3 and 1. So the GCF is $y^1 = y$

Variable z: We have exponents 1, 1 and 1. So the GCF is $z^1 = z$

The greatest common factor is:

$8*x*y*z = 8xyz$

4 0

3 years ago

Is there a unit rate for these tables?

svlad2 [7]

Yes for the second the table each passing minute the distance increase by 1.5.
that equation is for rate of change

7 0

3 years ago

The probability of winning on an arcade game is 0. 659. if you play the arcade game 30 times, what is the probability of winning

mrs_skeptik [129]

The probability of winning exactly 21 times is:-0.32

Given,

The probability of winning on an arcade game, p = 0.659

Number of times you play arcade game, n = 30

By assuming this as a normal distribution, we get

Mean=μ=30×0.659 =19.77

Standard deviation, σ = $\sqrt{np(1-p)}$

= $\sqrt{30(0.659)(1-0.659)}$

≈ 2.60

Let X be a binomial variable

Then, the z score for x = 21 will be:

z = (x - μ) / σ = $\frac{21-19.77}{2.60}$

≈ 0.47

Now, the probability of winning exactly 21 times

P (x ≥ z) = P (21 ≥ 0.47) = 0.32

Hence the probability of winning exactly 21 times is 0.32

Learn more about probability here:-brainly.com/question/13067945

#SPJ4

5 0

2 years ago

A 10 foot tree create a shadow that is 15 feet long. Find the angle of elevation of the sun

Solnce55 [7]

Answer:

The angle of elevation of the sun is 33.7⁰

Step-by-step explanation:

let the height of the tree, T = 10 foot

length of the shadow created by the tree, B = 15 feet long

Height of the tree and the shadow of the tree forms a right angle triangle with the remaining side that joins the two which is known as hypotenuse.

Let the remaining side, hypotenuse, L = ?

Apply Pythagoras theorem;

L ² = T² + B²

L ² = 10² + 15²

L ² = 325

L = √325

L = 18.03 ft

The angle of elevation of the sun, is the angle facing the height of the tree with the length of the shadow of the tree as adjacent of the triangle.

Let the angle of elevation = θ

tan θ = opp / adj

tan θ = 10 / 15

tan θ = 0.66667

θ = tan ⁻¹ (0.66667)

θ = 33.7⁰

Therefore, the angle of elevation of the sun is 33.7⁰

5 0

4 years ago