1. 10
2. 5√2 in
1. The ratio for a 30-60-90 triangle is x:x√3:2x
x is the shortest leg so 2*x =2*5 = 10
2. the ratio of a 45-45-90 triangle is x:x:x√2
x is one leg so x * √2 = 5*√2 = 5√2
we conclude that the dimensions and area of the scaled figure are:
- l₂ = 48 in
- w₂= 32in
- A₂ = 1,536 in^2
How to find the dimensions of the large rectangle?
First, we know that the large rectangle is the smaller rectangle rescaled, with a scale factor k = 4.
This means that each dimension of the smaller rectangle must be multiplied by 4 to get the correspondent dimension on the larger rectangle.
The dimensions of the smaller rectangle are:
l₁ = 12in
w₁ = 8in
Then the correspondent dimensions of the large rectangle are:
l₂ = 4*12in = 48 in
w₂= 4*8in = 32in
Now, the area of the large rectangle is given by the product between the two dimensions, we will get:
A₂ = 48in*32in = 1,536 in^2
Then, we conclude that the dimensions and area of the scaled figure are:
- l₂ = 48 in
- w₂= 32in
- A₂ = 1,536 in^2
If you want to learn more about rectangles:
brainly.com/question/17297081
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Answer:
7x + 2y = 1
Step-by-step explanation:
1. Find the slope of the line.
(y2-y1)/(x2-x1) ----> (11 - (-3))/((-3) -1) ----> (11+3)/ (-3 -1) ----> 14/-4
*lets simplify into (7/-2)*
2. Write into slope intercept form.
y=mx+b (m is the slope) (b is the y intercept)
y = (7/-2)x + b
We now need to find the value of b, this can be done by plugging in values of x and y, and using algebra to solve.
11 = (7/-2)(-3) + b
11 = 10.5 + b
b = 0.5 or 1/2
slope intercept form y = (7/-2)x + 1/2
Now we convert to standard form: ax+by=c
*In this form we our a term cannot be a fraction nor can it be negative*
1. Get x and y on the same side, and since our x term is negative right now, we can make it positive by adding it on both sides.
(7/2)x + y = 1/2
2. We now want to get rid of the fraction in term a, so we multiply the entire function by two, so the denominator cancels out.
2(7/2)x + 2y = 2(1/2)
Simplify and you get
7x + 2y = 1
Answer:
The Babylonians employed a number system based around values of 60, and they developed a specific sign—two small wedges—to differentiate between magnitudes in the same way that modern decimal-based systems use zeros to distinguish between tenths, hundreds and thousandths.
